{"notes":{"apply NNPP; intro":"Proof by contradiction: assume the statement is false and show that this assumption is impossible.","destruct (classic (exists y : Thing, Gives y x)) as [Hs|Hs]":"Two cases: either something gives existence to x, or nothing does.","firstorder":"Rocq's first-order automation closes or simplifies the goal.","assumption":"The goal is already one of the hypotheses."},"tasks":[{"key":"round5/imkan_b_necessary_exists","id":"imkan_b_necessary_exists","run":"round5","title":"Dalīl al-imkān, conclusion (shorter route)","english":"A Necessary Existent exists.","stmt":"MP008 -> OP001 -> SP001 -> exists n, Necessary n","proved":true,"script":"(firstorder). { (apply NNPP; intro). { (unfold Necessary, MP008, OP001 in *; sauto q: on). } }","seconds":73.6,"expansions":2,"calls":80,"root":0,"goals":["============================\nMP008 -> OP001 -> SP001 -> exists n, Necessary n","H : MP008\nH0 : OP001\nx : Thing\nH1 : Exists x\nX : Prop\nX0 : Prop\n============================\n@ex Thing (fun n : Thing => Necessary n)","H : forall (x : Thing) (_ : Exists x) (_ : not (ThroughAnother x)), Ess x\nH0 : forall (x y : Thing) (_ : Gives y x), OfItself y\nx : Thing\nH1 : Exists x\nX : Prop\nX0 : Prop\n============================\n@ex Thing (fun n : Thing => and (Exists n) (Ess n))","H : not (forall (_ : MP008) (_ : OP001) (_ : SP001), @ex Thing (fun n : Thing => Necessary n))\n============================\nFalse","H : MP008\nH0 : OP001\nx : Thing\nH1 : Exists x\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\n============================\n@ex Thing (fun n : Thing => Necessary n)","H : forall (x : Thing) (_ : Exists x) (_ : not (ThroughAnother x)), Ess x\nH0 : forall (x y : Thing) (_ : Gives y x), OfItself y\nx : Thing\nH1 : Exists x\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\n============================\n@ex Thing (fun n : Thing => and (Exists n) (Ess n))","H : MP008\nH0 : OP001\nx : Thing\nH1 : Exists x\nX : Prop\nX0 : Prop\n============================\nNecessary x","H : MP008\nH0 : OP001\nx : Thing\nH1 : Exists x\nX : Prop\nX0 : Prop\nH2 : Necessary x\n============================\n@ex Thing (fun n : Thing => Necessary n)","H : MP008\nH0 : OP001\nx : Thing\nH1 : Exists x\nX : Prop\nX0 : Prop\nHs : Necessary x\n============================\n@ex Thing (fun n : Thing => Necessary n)","H : MP008\nH0 : OP001\nx : Thing\nH1 : Exists x\nX : Prop\nX0 : Prop\nHs : not (Necessary x)\n============================\n@ex Thing (fun n : Thing => Necessary n)","H : MP008\nH0 : OP001\nx : Thing\nH1 : Exists x\nX : Prop\nX0 : Prop\nH2 : not (@ex Thing (fun n : Thing => Necessary n))\n============================\nFalse","H : MP008\nH0 : OP001\nx : Thing\nH1 : Exists x\nX : Prop\nX0 : Prop\n============================\nExists x","H : MP008\nH0 : OP001\nx : Thing\nH1 : Exists x\nX : Prop\nX0 : Prop\n============================\nEss x"],"events":[{"g":0,"t":"assumption","w":"auto","ok":false,"err":"Error: No such assumption."},{"g":0,"t":"tauto","w":"auto","ok":false,"err":"Error: Tactic failure: Classical tauto failed."},{"g":0,"t":"firstorder","w":"auto","ok":true,"c":[1]},{"g":0,"t":"congruence","w":"auto","ok":false,"err":"Error: Tactic failure: congruence failed."},{"g":0,"t":"unfold Necessary, MP008, OP001, SP001 in *; firstorder","w":"auto","ok":true,"c":[2]},{"g":0,"t":"unfold Necessary, MP008, OP001, SP001 in *; hammer","w":"hammer","ok":false,"err":"Error: Error running vampire."},{"g":0,"t":"apply NNPP; intro","w":"model","ok":true,"c":[3]},{"g":0,"t":"exists 1","w":"model","ok":false,"err":"rejected"},{"g":0,"t":"split","w":"model","ok":false,"err":"Error: Unable to find an instance for the variable x."},{"g":0,"t":"right","w":"model","ok":false,"err":"Error: Not an inductive goal with 2 constructors."},{"g":0,"t":"exists 2","w":"model","ok":false,"err":"rejected"},{"g":0,"t":"exists 3","w":"model","ok":false,"err":"rejected"},{"g":0,"t":"exists 1%nat","w":"model","ok":false,"err":"rejected"},{"g":0,"t":"exists 1; assumption","w":"model","ok":false,"err":"rejected"},{"g":1,"t":"assumption","w":"auto","ok":false,"err":"Error: No such assumption."},{"g":1,"t":"tauto","w":"auto","ok":false,"err":"Error: Tactic failure: Classical tauto failed."},{"g":1,"t":"firstorder","w":"auto","ok":true,"c":[4]},{"g":1,"t":"congruence","w":"auto","ok":false,"err":"Error: Tactic failure: congruence failed."},{"g":1,"t":"unfold Necessary, MP008, OP001 in *; firstorder","w":"auto","ok":true,"c":[5]},{"g":1,"t":"unfold Necessary, MP008, OP001 in *; hammer","w":"hammer","ok":false,"err":"Error: Hammer failed: ATPs failed to f"},{"g":1,"t":"exists x","w":"model","ok":true,"c":[6]},{"g":1,"t":"exists x; assumption","w":"model","ok":false,"err":"Error: No such assumption."},{"g":1,"t":"assert (Necessary x)","w":"model","ok":true,"c":[6,7]},{"g":7,"t":"firstorder","w":"auto","ok":true,"c":[],"eager":true},{"g":1,"t":"destruct (classic (Necessary x)) as [Hs|Hs]","w":"model","ok":true,"c":[8,9]},{"g":8,"t":"firstorder","w":"auto","ok":true,"c":[],"eager":true},{"g":1,"t":"exists x; trivial","w":"model","ok":true,"c":[6]},{"g":1,"t":"assert (Exists x : Thing, Necessary x)","w":"model","ok":false,"err":"rejected"},{"g":1,"t":"destruct (classic (Exists x : Thing, Necessary x)) as [Hs|Hs]","w":"model","ok":false,"err":"rejected"},{"g":1,"t":"assert (Exists y : Thing, Necessary y)","w":"model","ok":false,"err":"Error: The variable y was "},{"g":1,"t":"destruct (classic (Exists y : Thing, Necessary y)) as [Hs|Hs]","w":"model","ok":false,"err":"rejected"},{"g":1,"t":"apply NNPP; intro","w":"model","ok":true,"c":[10]},{"g":10,"t":"unfold Necessary, MP008, OP001 in *; sauto q: on","w":"hammer","ok":true,"c":[],"eager":true},{"g":1,"t":"exists x; constructor","w":"model","ok":true,"c":[11,12]},{"g":11,"t":"assumption","w":"auto","ok":true,"c":[],"eager":true}],"proof":[2,31,32],"proofFile":"files/proofs/round5/imkan_b_necessary_exists.v"},{"key":"round5/step3_possible_needs_cause","id":"step3_possible_needs_cause","run":"round5","title":"Dalīl al-imkān, step 3","english":"A possible existent needs a cause.","stmt":"MP008 -> forall x, Possible x -> ThroughAnother x","proved":true,"script":"(unfold ThroughAnother, Possible, MP008 in *; firstorder). { (apply NNPP; intro). { (firstorder). } }","seconds":73.7,"expansions":3,"calls":111,"root":0,"goals":["============================\nMP008 -> forall x, Possible x -> ThroughAnother x","H : MP008\nx : Thing\nH0 : Exists x\nH1 : not (Ess x)\nX : Prop\nX0 : Prop\n============================\nThroughAnother x","H : forall (x : Thing) (_ : Exists x) (_ : not (ThroughAnother x)), Ess x\nx : Thing\nH0 : Exists x\nH1 : not (Ess x)\nX : Prop\nX0 : Prop\n============================\n@ex Thing (fun y : Thing => Gives y x)","MP008 : Pilot.MP008\n============================\nforall (x : Thing) (_ : Possible x), ThroughAnother x","MP008 : Pilot.MP008\nH : Thing\n============================\nforall _ : Possible H, ThroughAnother H","MP008 : Pilot.MP008\nH' : Thing\n============================\nforall _ : Possible H', ThroughAnother H'","H : MP008\nx : Thing\nH0 : Exists x\nH1 : not (Ess x)\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\n============================\nThroughAnother x","H : forall (x : Thing) (_ : Exists x) (_ : not (ThroughAnother x)), Ess x\nx : Thing\nH0 : Exists x\nH1 : not (Ess x)\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\n============================\n@ex Thing (fun y : Thing => Gives y x)","H : MP008\nx : Thing\nH0 : Exists x\nH1 : not (Ess x)\nX : Prop\nX0 : Prop\n============================\nGives x x","H : MP008\nx : Thing\nH0 : Exists x\nH1 : not (Ess x)\nX : Prop\nX0 : Prop\n============================\n@eq Prop X X0","H : MP008\nx : Thing\nH0 : Exists x\nH1 : not (Ess x)\nX : Prop\nX0 : Prop\nH2 : @eq Prop X X0\n============================\nThroughAnother x","H : MP008\nx : Thing\nH0 : Exists x\nH1 : not (Ess x)\nX : Prop\nX0 : Prop\nHs : @eq Prop X X0\n============================\nThroughAnother x","H : MP008\nx : Thing\nH0 : Exists x\nH1 : not (Ess x)\nX : Prop\nX0 : Prop\nHs : not (@eq Prop X X0)\n============================\nThroughAnother x","H : MP008\nx : Thing\nH0 : Exists x\nH1 : not (Ess x)\nX : Prop\nX0 : Prop\n============================\nEss x","H : forall (x : Thing) (_ : Exists x) (_ : not (@ex Thing (fun y : Thing => Gives y x))), Ess x\nx : Thing\nH0 : Exists x\nH1 : not (Ess x)\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\n============================\n@ex Thing (fun y : Thing => Gives y x)","H : forall (x : Thing) (_ : Exists x) (_ : not (ThroughAnother x)), Ess x\nx : Thing\nH0 : Exists x\nH1 : not (Ess x)\nX : Prop\nX0 : Prop\n============================\nGives x x","H : forall (x : Thing) (_ : Exists x) (_ : not (ThroughAnother x)), Ess x\nx : Thing\nH0 : Exists x\nH1 : not (Ess x)\nX : Prop\nX0 : Prop\nH2 : not (@ex Thing (fun y : Thing => Gives y x))\n============================\nFalse"],"events":[{"g":0,"t":"assumption","w":"auto","ok":false,"err":"Error: No such assumption."},{"g":0,"t":"tauto","w":"auto","ok":false,"err":"Error: Tactic failure: Classical tauto failed."},{"g":0,"t":"firstorder","w":"auto","ok":true,"c":[1]},{"g":0,"t":"congruence","w":"auto","ok":false,"err":"Error: Tactic failure: congruence failed."},{"g":0,"t":"unfold ThroughAnother, Possible, MP008 in *; firstorder","w":"auto","ok":true,"c":[2]},{"g":0,"t":"unfold ThroughAnother, Possible, MP008 in *; hammer","w":"hammer","ok":false,"err":"rejected"},{"g":0,"t":"intros MP008","w":"model","ok":true,"c":[3]},{"g":0,"t":"right","w":"model","ok":false,"err":"Error: Not an inductive goal with 2 constructors."},{"g":0,"t":"apply MP008'","w":"model","ok":false,"err":"Error: The variable MP008' was not found in the current environment."},{"g":0,"t":"left","w":"model","ok":false,"err":"Error: Not an inductive goal with 2 constructors."},{"g":0,"t":"intros MP008 H","w":"model","ok":true,"c":[4]},{"g":0,"t":"split","w":"model","ok":false,"err":"Error: Unable to find an instance for the variable x."},{"g":0,"t":"intros MP008 H'","w":"model","ok":true,"c":[5]},{"g":0,"t":"apply MP008","w":"model","ok":false,"err":"Error: Applied theorem does not have enough premises."},{"g":1,"t":"assumption","w":"auto","ok":false,"err":"Error: No such assumption."},{"g":1,"t":"tauto","w":"auto","ok":false,"err":"Error: Tactic failure: Classical tauto failed."},{"g":1,"t":"firstorder","w":"auto","ok":true,"c":[6]},{"g":1,"t":"congruence","w":"auto","ok":false,"err":"Error: Tactic failure: congruence failed."},{"g":1,"t":"unfold ThroughAnother, MP008 in *; firstorder","w":"auto","ok":true,"c":[7]},{"g":1,"t":"unfold ThroughAnother, MP008 in *; hammer","w":"hammer","ok":false,"err":"Error: Hammer failed: ATPs failed to f"},{"g":1,"t":"exists x","w":"model","ok":true,"c":[8]},{"g":1,"t":"assert (X = X0)","w":"model","ok":true,"c":[9,10]},{"g":1,"t":"destruct (classic (X = X0)) as [Hs|Hs]","w":"model","ok":true,"c":[11,12]},{"g":1,"t":"exists x; assumption","w":"model","ok":false,"err":"Error: No such assumption."},{"g":1,"t":"elim H1","w":"model","ok":true,"c":[13]},{"g":1,"t":"apply ThroughAnotherIntro with X0","w":"model","ok":false,"err":"Error: The variable Through"},{"g":1,"t":"exists x; trivial","w":"model","ok":true,"c":[8]},{"g":2,"t":"assumption","w":"auto","ok":false,"err":"Error: No such assumption."},{"g":2,"t":"tauto","w":"auto","ok":false,"err":"Error: Tactic failure: Classical tauto failed."},{"g":2,"t":"firstorder","w":"auto","ok":true,"c":[7]},{"g":2,"t":"congruence","w":"auto","ok":false,"err":"Error: Tactic failure: congruence failed."},{"g":2,"t":"unfold ThroughAnother in *; firstorder","w":"auto","ok":true,"c":[14]},{"g":2,"t":"unfold ThroughAnother in *; hammer","w":"hammer","ok":false,"err":"Error: Hammer failed: ATPs failed to f"},{"g":2,"t":"exists x","w":"model","ok":true,"c":[15]},{"g":2,"t":"exists X","w":"model","ok":false,"err":"rejected"},{"g":2,"t":"apply NNPP; intro","w":"model","ok":true,"c":[16]},{"g":16,"t":"firstorder","w":"auto","ok":true,"c":[],"eager":true},{"g":2,"t":"assert (Gives x X)","w":"model","ok":false,"err":"rejected"},{"g":2,"t":"destruct (classic (Gives x X)) as [Hs|Hs]","w":"model","ok":false,"err":"rejected"},{"g":2,"t":"exists x; assumption","w":"model","ok":false,"err":"Error: No such assumption."},{"g":2,"t":"exists x; intros","w":"model","ok":true,"c":[15]}],"proof":[4,35,36],"proofFile":"files/proofs/round5/step3_possible_needs_cause.v"},{"key":"round5/pr011_something_caused","id":"pr011_something_caused","run":"round5","title":"The universe is caused","english":"Something in the universe has its existence through another.","stmt":"MP008 -> OP006 -> exists x, InUniverse x /\\ Possible x /\\ ThroughAnother x","proved":true,"script":"(apply NNPP; intro). { (unfold ThroughAnother, Possible, InUniverse, MP008, OP006 in *; sfirstorder). }","seconds":21.9,"expansions":1,"calls":20,"root":0,"goals":["============================\nMP008 -> OP006 -> exists x, InUniverse x /\\ Possible x /\\ ThroughAnother x","H : MP008\nx : Thing\nH1 : Exists x\nH2 : not (Ess x)\nH0 : @eq Thing x Universe\n============================\n@ex Thing (fun x0 : Thing => and (InUniverse x0) (and (Possible x0) (ThroughAnother x0)))","H : MP008\nx : Thing\nH1 : Exists x\nH2 : not (Ess x)\nH0 : PartOf x Universe\n============================\n@ex Thing (fun x0 : Thing => and (InUniverse x0) (and (Possible x0) (ThroughAnother x0)))","H : forall (x : Thing) (_ : Exists x) (_ : not (ThroughAnother x)), Ess x\nx : Thing\nH1 : Exists x\nH2 : not (Ess x)\nH0 : @eq Thing x Universe\n============================\n@ex Thing (fun x0 : Thing => and (or (@eq Thing x0 Universe) (PartOf x0 Universe)) (and (and (Exists x0) (not (Ess x0))) (@ex Thing (fun y : Thing => Gives y x0))))","H : forall (x : Thing) (_ : Exists x) (_ : not (ThroughAnother x)), Ess x\nx : Thing\nH1 : Exists x\nH2 : not (Ess x)\nH0 : PartOf x Universe\n============================\n@ex Thing (fun x0 : Thing => and (or (@eq Thing x0 Universe) (PartOf x0 Universe)) (and (and (Exists x0) (not (Ess x0))) (@ex Thing (fun y : Thing => Gives y x0))))","H : not (forall (_ : MP008) (_ : OP006), @ex Thing (fun x : Thing => and (InUniverse x) (and (Possible x) (ThroughAnother x))))\n============================\nFalse"],"events":[{"g":0,"t":"assumption","w":"auto","ok":false,"err":"Error: No such assumption."},{"g":0,"t":"tauto","w":"auto","ok":false,"err":"Error: Tactic failure: Classical tauto failed."},{"g":0,"t":"firstorder","w":"auto","ok":true,"c":[1,2]},{"g":0,"t":"congruence","w":"auto","ok":false,"err":"Error: Tactic failure: congruence failed."},{"g":0,"t":"unfold ThroughAnother, Possible, InUniverse, MP008, OP006 in *; firstorder","w":"auto","ok":true,"c":[3,4]},{"g":0,"t":"unfold ThroughAnother, Possible, InUniverse, MP008, OP006 in *; hammer","w":"hammer","ok":false,"err":"rejected"},{"g":0,"t":"apply NNPP; intro","w":"model","ok":true,"c":[5]},{"g":5,"t":"unfold ThroughAnother, Possible, InUniverse, MP008, OP006 in *; sfirstorder","w":"hammer","ok":true,"c":[],"eager":true},{"g":0,"t":"right","w":"model","ok":false,"err":"Error: Not an inductive goal with 2 constructors."},{"g":0,"t":"exists 1","w":"model","ok":false,"err":"Error: In environment"},{"g":0,"t":"split","w":"model","ok":false,"err":"Error: Unable to find an instance for the variable x."},{"g":0,"t":"exists 2","w":"model","ok":false,"err":"Error: In environment"},{"g":0,"t":"exists 1%nat","w":"model","ok":false,"err":"Error: In environment"},{"g":0,"t":"exists 6","w":"model","ok":false,"err":"rejected"},{"g":0,"t":"exists 3","w":"model","ok":false,"err":"Error: In environment"}],"proof":[6,7],"proofFile":"files/proofs/round5/pr011_something_caused.v"},{"key":"round5/kalima_first_cause","id":"kalima_first_cause","run":"round5","title":"Dalīl al-kalima, the first cause","english":"If the universe has its existence through another, it has a first cause that exists of itself.","stmt":"OP001 -> ThroughAnother Universe -> exists b, Gives b Universe /\\ OfItself b /\\ (forall y, ~ Gives y b)","proved":true,"script":"(unfold ThroughAnother, OfItself, OP001 in *; sfirstorder).","seconds":3.0,"expansions":1,"calls":6,"root":0,"goals":["============================\nOP001 -> ThroughAnother Universe -> exists b, Gives b Universe /\\ OfItself b /\\ (forall y, ~ Gives y b)","H : OP001\nx : Thing\nH0 : Gives x Universe\n============================\n@ex Thing (fun b : Thing => and (Gives b Universe) (and (OfItself b) (forall y : Thing, not (Gives y b))))","H : forall (x y : Thing) (_ : Gives y x), OfItself y\nx : Thing\nH0 : Gives x Universe\n============================\n@ex Thing (fun b : Thing => and (Gives b Universe) (and (and (Exists b) (not (ThroughAnother b))) (forall y : Thing, not (Gives y b))))"],"events":[{"g":0,"t":"assumption","w":"auto","ok":false,"err":"Error: No such assumption."},{"g":0,"t":"tauto","w":"auto","ok":false,"err":"Error: Tactic failure: Classical tauto failed."},{"g":0,"t":"firstorder","w":"auto","ok":true,"c":[1]},{"g":0,"t":"congruence","w":"auto","ok":false,"err":"Error: Tactic failure: congruence failed."},{"g":0,"t":"unfold ThroughAnother, OfItself, OP001 in *; firstorder","w":"auto","ok":true,"c":[2]},{"g":0,"t":"unfold ThroughAnother, OfItself, OP001 in *; sfirstorder","w":"hammer","ok":true,"c":[]}],"proof":[5],"proofFile":"files/proofs/round5/kalima_first_cause.v"},{"key":"round5/pr002_no_self_creation","id":"pr002_no_self_creation","run":"round5","title":"Dalīl al-kalima, premise 2","english":"Nothing gives existence to itself.","stmt":"MP001 -> MP002 -> forall x, ~ Gives x x","proved":true,"script":"(firstorder).","seconds":2.1,"expansions":1,"calls":3,"root":0,"goals":["============================\nMP001 -> MP002 -> forall x, ~ Gives x x"],"events":[{"g":0,"t":"assumption","w":"auto","ok":false,"err":"Error: No such assumption."},{"g":0,"t":"tauto","w":"auto","ok":false,"err":"Error: Tactic failure: Classical tauto failed."},{"g":0,"t":"firstorder","w":"auto","ok":true,"c":[]}],"proof":[2],"proofFile":"files/proofs/round5/pr002_no_self_creation.v"},{"key":"round5/pr004_no_two_step_giving","id":"pr004_no_two_step_giving","run":"round5","title":"Dalīl al-kalima, premise 4 (key step)","english":"What receives existence does not give existence to anything.","stmt":"OP001 -> forall x y z, Gives y x -> ~ Gives z y","proved":true,"script":"(firstorder).","seconds":2.2,"expansions":1,"calls":3,"root":0,"goals":["============================\nOP001 -> forall x y z, Gives y x -> ~ Gives z y"],"events":[{"g":0,"t":"assumption","w":"auto","ok":false,"err":"Error: No such assumption."},{"g":0,"t":"tauto","w":"auto","ok":false,"err":"Error: Tactic failure: Classical tauto failed."},{"g":0,"t":"firstorder","w":"auto","ok":true,"c":[]}],"proof":[2],"proofFile":"files/proofs/round5/pr004_no_two_step_giving.v"},{"key":"round6/imkan_s1_division","id":"imkan_s1_division","run":"round6","title":"Dalīl al-imkān, step 1","english":"Every existent is necessary or possible in itself, and not both.","stmt":"forall x, Exists x -> (Necessary x \\/ Possible x) /\\ ~ (Necessary x /\\ Possible x)","proved":true,"script":"(intros x; apply NNPP; trivial). { (firstorder). }","seconds":23.7,"expansions":1,"calls":38,"root":0,"goals":["============================\nforall x, Exists x -> (Necessary x \\/ Possible x) /\\ ~ (Necessary x /\\ Possible x)","x : Thing\nH : Exists x\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\n============================\nor (Necessary x) (Possible x)","x : Thing\nH : Exists x\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\n============================\nor (and (Exists x) (Ess x)) (and (Exists x) (not (Ess x)))","x : Thing\nH : Exists x\n============================\nand (or (Necessary x) (Possible x)) (not (and (Necessary x) (Possible x)))","x : Thing\n============================\nforall _ : Exists x, and (or (Necessary x) (Possible x)) (not (and (Necessary x) (Possible x)))","x : Thing\n============================\nnot (not (forall _ : Exists x, and (or (Necessary x) (Possible x)) (not (and (Necessary x) (Possible x)))))","x : Thing\nH : not (forall _ : Exists x, and (or (Necessary x) (Possible x)) (not (and (Necessary x) (Possible x))))\n============================\nFalse"],"events":[{"g":0,"t":"assumption","w":"auto","ok":false,"err":"Error: No such assumption."},{"g":0,"t":"tauto","w":"auto","ok":false,"err":"Error: Tactic failure: Classical tauto failed."},{"g":0,"t":"firstorder","w":"auto","ok":true,"c":[1]},{"g":0,"t":"congruence","w":"auto","ok":false,"err":"Error: Tactic failure: congruence failed."},{"g":0,"t":"unfold Necessary, Possible in *; firstorder","w":"auto","ok":true,"c":[2]},{"g":0,"t":"unfold Necessary, Possible in *; hammer","w":"hammer","ok":false,"err":"rejected"},{"g":0,"t":"destruct x; constructor","w":"model","ok":false,"err":"Error: Not an inductive definition."},{"g":0,"t":"intros","w":"model","ok":true,"c":[3]},{"g":0,"t":"intros x H","w":"model","ok":true,"c":[3]},{"g":0,"t":"intros x; apply NNPP; assumption","w":"model","ok":false,"err":"Error: No such assumpt"},{"g":0,"t":"intro","w":"model","ok":true,"c":[4]},{"g":0,"t":"intros x; apply NNPP; trivial","w":"model","ok":true,"c":[5]},{"g":5,"t":"firstorder","w":"auto","ok":true,"c":[],"eager":true},{"g":0,"t":"destruct x","w":"model","ok":false,"err":"Error: Not an inductive definition."},{"g":0,"t":"intros x; apply NNPP; intro","w":"model","ok":true,"c":[6]},{"g":6,"t":"firstorder","w":"auto","ok":true,"c":[],"eager":true}],"proof":[11,12],"proofFile":"files/proofs/round6/imkan_s1_division.v"},{"key":"round6/imkan_s2_necessary_cannot_fail","id":"imkan_s2_necessary_cannot_fail","run":"round6","title":"Dalīl al-imkān, step 2","english":"The non-existence of what is necessary in itself is not possible.","stmt":"MP007 -> forall x, Necessary x -> ~ NonExistencePossible x","proved":true,"script":"(firstorder).","seconds":0.8,"expansions":1,"calls":3,"root":0,"goals":["============================\nMP007 -> forall x, Necessary x -> ~ NonExistencePossible x"],"events":[{"g":0,"t":"assumption","w":"auto","ok":false,"err":"Error: No such assumption."},{"g":0,"t":"tauto","w":"auto","ok":false,"err":"Error: Tactic failure: Classical tauto failed."},{"g":0,"t":"firstorder","w":"auto","ok":true,"c":[]}],"proof":[2],"proofFile":"files/proofs/round6/imkan_s2_necessary_cannot_fail.v"},{"key":"round6/imkan_s4_no_self_causation","id":"imkan_s4_no_self_causation","run":"round6","title":"Dalīl al-imkān, step 4","english":"Nothing gives existence to itself.","stmt":"MP001 -> MP002 -> forall A, ~ Gives A A","proved":true,"script":"(firstorder).","seconds":0.7,"expansions":1,"calls":3,"root":0,"goals":["============================\nMP001 -> MP002 -> forall A, ~ Gives A A"],"events":[{"g":0,"t":"assumption","w":"auto","ok":false,"err":"Error: No such assumption."},{"g":0,"t":"tauto","w":"auto","ok":false,"err":"Error: Tactic failure: Classical tauto failed."},{"g":0,"t":"firstorder","w":"auto","ok":true,"c":[]}],"proof":[2],"proofFile":"files/proofs/round6/imkan_s4_no_self_causation.v"},{"key":"round6/imkan_s5_none_outside","id":"imkan_s5_none_outside","run":"round6","title":"Dalīl al-imkān, step 5","english":"No possible existent lies outside the aggregate of possibles.","stmt":"forall A, AggregateOfPossibles A -> forall p, p <> A -> Possible p -> MemberOf p A","proved":true,"script":"(firstorder).","seconds":0.5,"expansions":1,"calls":3,"root":0,"goals":["============================\nforall A, AggregateOfPossibles A -> forall p, p <> A -> Possible p -> MemberOf p A"],"events":[{"g":0,"t":"assumption","w":"auto","ok":false,"err":"Error: No such assumption."},{"g":0,"t":"tauto","w":"auto","ok":false,"err":"Error: Tactic failure: Classical tauto failed."},{"g":0,"t":"firstorder","w":"auto","ok":true,"c":[]}],"proof":[2],"proofFile":"files/proofs/round6/imkan_s5_none_outside.v"},{"key":"round5/pr003_no_circle","id":"pr003_no_circle","run":"round5","title":"Dalīl al-kalima, premise 3 (not yet proved)","english":"No chain of existence-giving returns to where it started.","stmt":"MP001 -> MP002 -> MP003 -> forall x, ~ clos_trans Thing DependsOn x x","proved":false,"script":"","seconds":906.1,"expansions":21,"calls":739,"root":0,"goals":["============================\nMP001 -> MP002 -> MP003 -> forall x, ~ clos_trans Thing DependsOn x x","H : MP001\nH0 : MP002\nH1 : MP003\nx : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\n============================\nnot (clos_trans Thing DependsOn x x)","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nx : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\n============================\nnot (clos_trans Thing (fun x0 y : Thing => Gives y x0) x x)","H : MP001\nH0 : MP002\nH1 : MP003\nx : Thing\n============================\nnot (clos_trans Thing DependsOn x x)","H : not (forall (_ : MP001) (_ : MP002) (_ : MP003) (x : Thing), not (clos_trans Thing DependsOn x x))\n============================\nFalse","D0 : MP001\nD1 : MP002\n============================\nforall (_ : MP003) (x : Thing), not (clos_trans Thing DependsOn x x)","D0 : MP001\n============================\nforall (_ : MP002) (_ : MP003) (x : Thing), not (clos_trans Thing DependsOn x x)","H : MP001\nH0 : MP002\nH1 : MP003\nx : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\n============================\nnot (clos_trans Thing DependsOn x x)","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nx : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\n============================\nnot (clos_trans Thing (fun x0 y : Thing => Gives y x0) x x)","H : MP001\nH0 : MP002\nH1 : MP003\nx : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nH2 : clos_trans Thing DependsOn x x\n============================\nFalse","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nx : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nH2 : clos_trans Thing (fun x0 y : Thing => Gives y x0) x x\n============================\nFalse","H : MP001\nH0 : MP002\nH1 : MP003\nx : Thing\nH2 : clos_trans Thing DependsOn x x\n============================\nFalse","H : MP001\nH0 : MP002\nH1 : MP003\nx : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\n============================\nnot (clos_trans Thing DependsOn x x)","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nx : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\n============================\nnot (clos_trans Thing (fun x0 y : Thing => Gives y x0) x x)","H : MP001\nH0 : MP002\nH1 : MP003\nx : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nH5 : clos_trans Thing DependsOn x x\n============================\nFalse","H : MP001\nH0 : MP002\nH1 : MP003\nx : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nH2 : clos_trans Thing DependsOn x x\n============================\nFalse","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nx : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nH2 : not (not (clos_trans Thing (fun x0 y : Thing => Gives y x0) x x))\n============================\nFalse","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nx : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nH2 : clos_trans Thing (fun x0 y : Thing => Gives y x0) x x\n============================\nFalse","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nx : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nH5 : clos_trans Thing (fun x0 y : Thing => Gives y x0) x x\n============================\nFalse","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nx : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\n============================\nnot (not (not (clos_trans Thing (fun x0 y : Thing => Gives y x0) x x)))","H : MP001\nH0 : MP002\nH1 : MP003\nx : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\nX8 : Prop\nX9 : Prop\nX10 : Prop\n============================\nnot (clos_trans Thing DependsOn x x)","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nx : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\nX8 : Prop\nX9 : Prop\nX10 : Prop\n============================\nnot (clos_trans Thing (fun x0 y : Thing => Gives y x0) x x)","H : MP001\nH0 : MP002\nH1 : MP003\nx : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\nH8 : clos_trans Thing DependsOn x x\n============================\nFalse","H : MP001\nH0 : MP002\nH1 : MP003\nx : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\nH2 : clos_trans Thing DependsOn x x\n============================\nFalse","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nx : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\nH2 : not (not (clos_trans Thing (fun x0 y : Thing => Gives y x0) x x))\n============================\nFalse","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nx : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\nH2 : clos_trans Thing (fun x0 y : Thing => Gives y x0) x x\n============================\nFalse","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nx : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\nH8 : clos_trans Thing (fun x0 y : Thing => Gives y x0) x x\n============================\nFalse","H : not (forall (_ : MP001) (_ : MP002) (_ : MP003) (x : Thing), not (clos_trans Thing DependsOn x x))\n============================\nforall (_ : MP001) (_ : MP002) (_ : MP003) (x : Thing), not (clos_trans Thing DependsOn x x)","H : not (forall (_ : MP001) (_ : MP002) (_ : MP003) (x : Thing), not (clos_trans Thing DependsOn x x))\n============================\nnot (not False)","H : not (forall (_ : MP001) (_ : MP002) (_ : MP003) (x : Thing), not (clos_trans Thing DependsOn x x))\n============================\nforall _ : MP001, MP002","H : not (forall (_ : MP001) (_ : MP002) (_ : MP003) (x : Thing), not (clos_trans Thing DependsOn x x))\nH0 : forall _ : MP001, MP002\n============================\nFalse","H : not (forall (_ : MP001) (_ : MP002) (_ : MP003) (x : Thing), not (clos_trans Thing DependsOn x x))\nHs : forall _ : MP001, MP002\n============================\nFalse","H : not (forall (_ : MP001) (_ : MP002) (_ : MP003) (x : Thing), not (clos_trans Thing DependsOn x x))\nHs : not (forall _ : MP001, MP002)\n============================\nFalse","H : not (forall (_ : MP001) (_ : MP002) (_ : MP003) (x : Thing), not (clos_trans Thing DependsOn x x))\nH0 : not False\n============================\nFalse","H : MP001\nH0 : MP002\nH1 : MP003\nx : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\nX8 : Prop\nX9 : Prop\nX10 : Prop\nX11 : Prop\nX12 : Prop\nX13 : Prop\n============================\nnot (clos_trans Thing DependsOn x x)","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nx : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\nX8 : Prop\nX9 : Prop\nX10 : Prop\nX11 : Prop\nX12 : Prop\nX13 : Prop\n============================\nnot (clos_trans Thing (fun x0 y : Thing => Gives y x0) x x)","H : MP001\nH0 : MP002\nH1 : MP003\nx : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\nX8 : Prop\nX9 : Prop\nX10 : Prop\nH10 : clos_trans Thing DependsOn x x\n============================\nFalse","H : MP001\nH0 : MP002\nH1 : MP003\nx : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\nX8 : Prop\nX9 : Prop\nX10 : Prop\nH2 : clos_trans Thing DependsOn x x\n============================\nFalse","H : MP001\nH0 : MP002\nH1 : MP003\nx : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\nX8 : Prop\nX9 : Prop\nX10 : Prop\nHX : clos_trans Thing DependsOn x x\n============================\nFalse","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nx : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\nX8 : Prop\nX9 : Prop\nX10 : Prop\nH2 : not (not (clos_trans Thing (fun x0 y : Thing => Gives y x0) x x))\n============================\nFalse","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nx : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\nX8 : Prop\nX9 : Prop\nX10 : Prop\nH2 : clos_trans Thing (fun x0 y : Thing => Gives y x0) x x\n============================\nFalse","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nx : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\nX8 : Prop\nX9 : Prop\nX10 : Prop\nH10 : clos_trans Thing (fun x0 y : Thing => Gives y x0) x x\n============================\nFalse","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nx : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nH2 : not (not (clos_trans Thing (fun x0 y : Thing => Gives y x0) x x))\nX5 : Prop\nX6 : Prop\nX7 : Prop\n============================\nFalse","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nx : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nH2 : not (not (clos_trans Thing (fun x0 y : Thing => Gives y x0) x x))\n============================\nnot (clos_trans Thing (fun x0 y : Thing => Gives y x0) x x)","H : MP001\nH0 : MP002\nH1 : MP003\nx : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nH2 : clos_trans Thing DependsOn x x\nX2 : Prop\nX3 : Prop\nX4 : Prop\n============================\nFalse","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nx : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nH2 : clos_trans Thing (fun x y : Thing => Gives y x) x x\nX2 : Prop\nX3 : Prop\nX4 : Prop\n============================\nFalse","H : MP001\nH0 : MP002\nH1 : MP003\nx : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nH2 : clos_trans Thing DependsOn x x\n============================\nnot (not False)","H : MP001\nH0 : MP002\nH1 : MP003\nx : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nH2 : clos_trans Thing DependsOn x x\nH3 : not False\n============================\nFalse","H : MP001\nH0 : MP002\nH1 : MP003\nx : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nH2 : clos_trans Thing DependsOn x x\n============================\nforall (x0 y : Thing) (_ : DependsOn x0 y), False","H : MP001\nH0 : MP002\nH1 : MP003\nx : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nH2 : clos_trans Thing DependsOn x x\n============================\nforall (x0 y z : Thing) (_ : clos_trans Thing DependsOn x0 y) (_ : False) (_ : clos_trans Thing DependsOn y z) (_ : False), False","H : MP001\nH0 : MP002\nH1 : MP003\nx : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\n============================\nforall _ : clos_trans Thing DependsOn x x, False","H : MP001\nH0 : MP002\nH1 : MP003\nx : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nH2 : clos_trans Thing DependsOn x x\n============================\nforall _ : clos_trans Thing DependsOn x x, False","H : MP001\nH0 : MP002\nH1 : MP003\nx : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nH2 : clos_trans Thing DependsOn x x\n============================\nclos_trans Thing DependsOn x x","D0 : MP001\nD1 : MP002\nH : MP003\nx : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\n============================\nnot (clos_trans Thing DependsOn x x)","D0 : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nD1 : forall (x y : Thing) (_ : Gives y x), Through x y\nH : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nx : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\n============================\nnot (clos_trans Thing (fun x0 y : Thing => Gives y x0) x x)","D0 : MP001\nD1 : MP002\nMP003 : Pilot.MP003\n============================\nforall x : Thing, not (clos_trans Thing DependsOn x x)","D0 : MP001\nD1 : MP002\nH : MP003\nx : Thing\n============================\nnot (clos_trans Thing DependsOn x x)","D0 : MP001\nD1 : MP002\nx : MP003\nH : Thing\n============================\nnot (clos_trans Thing DependsOn H H)","D0 : MP001\nD1 : MP002\n============================\nforall x : Thing, not (clos_trans Thing DependsOn x x)","D0 : MP001\nD1 : MP002\nM : MP003\nP : Thing\n============================\nnot (clos_trans Thing DependsOn P P)","H : MP001\nH0 : MP002\nH1 : MP003\nx : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\nX8 : Prop\nX9 : Prop\nX10 : Prop\nX11 : Prop\nX12 : Prop\nX13 : Prop\nX14 : Prop\nX15 : Prop\nX16 : Prop\n============================\nnot (clos_trans Thing DependsOn x x)","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nx : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\nX8 : Prop\nX9 : Prop\nX10 : Prop\nX11 : Prop\nX12 : Prop\nX13 : Prop\nX14 : Prop\nX15 : Prop\nX16 : Prop\n============================\nnot (clos_trans Thing (fun x0 y : Thing => Gives y x0) x x)","H : MP001\nH0 : MP002\nH1 : MP003\nx : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\nX8 : Prop\nX9 : Prop\nX10 : Prop\nX11 : Prop\nX12 : Prop\nX13 : Prop\nH2 : clos_trans Thing DependsOn x x\n============================\nFalse","H : MP001\nH0 : MP002\nH1 : MP003\nx : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\nX8 : Prop\nX9 : Prop\nX10 : Prop\nX11 : Prop\nX12 : Prop\nX13 : Prop\nH12 : clos_trans Thing DependsOn x x\n============================\nFalse","H : MP001\nH0 : MP002\nH1 : MP003\nx : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\nX8 : Prop\nX9 : Prop\nX10 : Prop\nX11 : Prop\nX12 : Prop\nX13 : Prop\nH10 : clos_trans Thing DependsOn x x\n============================\nFalse","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nx : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\nX8 : Prop\nX9 : Prop\nX10 : Prop\nX11 : Prop\nX12 : Prop\nX13 : Prop\nH2 : not (not (clos_trans Thing (fun x0 y : Thing => Gives y x0) x x))\n============================\nFalse","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nx : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\nX8 : Prop\nX9 : Prop\nX10 : Prop\nX11 : Prop\nX12 : Prop\nX13 : Prop\nH2 : clos_trans Thing (fun x0 y : Thing => Gives y x0) x x\n============================\nFalse","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nx : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\nX8 : Prop\nX9 : Prop\nX10 : Prop\nX11 : Prop\nX12 : Prop\nX13 : Prop\nH12 : clos_trans Thing (fun x0 y : Thing => Gives y x0) x x\n============================\nFalse","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nx : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\nX8 : Prop\nX9 : Prop\nX10 : Prop\nX11 : Prop\nX12 : Prop\nX13 : Prop\nH10 : clos_trans Thing (fun x0 y : Thing => Gives y x0) x x\n============================\nFalse","H : MP001\nH0 : MP002\nH1 : MP003\nx : Thing\nH2 : clos_trans Thing DependsOn x x\nX : Prop\nX0 : Prop\nX1 : Prop\n============================\nFalse","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nx : Thing\nH2 : clos_trans Thing (fun x y : Thing => Gives y x) x x\nX : Prop\nX0 : Prop\nX1 : Prop\n============================\nFalse","H : MP001\nH0 : MP002\nH1 : MP003\nx : Thing\nH2 : clos_trans Thing DependsOn x x\n============================\nforall (x0 y : Thing) (_ : DependsOn x0 y), False","H : MP001\nH0 : MP002\nH1 : MP003\nx : Thing\nH2 : clos_trans Thing DependsOn x x\n============================\nforall (x0 y z : Thing) (_ : clos_trans Thing DependsOn x0 y) (_ : False) (_ : clos_trans Thing DependsOn y z) (_ : False), False","H : MP001\nH0 : MP002\nH1 : MP003\nx : Thing\nH2 : clos_trans Thing DependsOn x x\nH3 : not False\n============================\nFalse","H : MP001\nH0 : MP002\nH1 : MP003\nx : Thing\n============================\nforall _ : clos_trans Thing DependsOn x x, False","H : MP001\nH0 : MP002\nH1 : MP003\nx : Thing\nH2 : clos_trans Thing DependsOn x x\n============================\nnot (not False)","H : MP001\nH0 : MP002\nH1 : MP003\nx : Thing\nH2 : clos_trans Thing DependsOn x x\n============================\nforall _ : DependsOn x x, False","H : MP001\nH0 : MP002\nH1 : MP003\nx : Thing\nH2 : clos_trans Thing DependsOn x x\n============================\nDependsOn x x","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nx : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nH2 : clos_trans Thing (fun x0 y : Thing => Gives y x0) x x\nX2 : Prop\nX3 : Prop\nX4 : Prop\n============================\nFalse","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nx : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nH2 : clos_trans Thing (fun x0 y : Thing => Gives y x0) x x\n============================\nGives x x","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nx : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nH2 : clos_trans Thing (fun x0 y : Thing => Gives y x0) x x\nH3 : Gives x x\n============================\nFalse","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nx : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nH2 : clos_trans Thing (fun x0 y : Thing => Gives y x0) x x\nHs : Gives x x\n============================\nFalse","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nx : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nH2 : clos_trans Thing (fun x0 y : Thing => Gives y x0) x x\nHs : not (Gives x x)\n============================\nFalse","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nx : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nH2 : clos_trans Thing (fun x0 y : Thing => Gives y x0) x x\n============================\nforall (x0 y : Thing) (_ : Gives y x0), False","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nx : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nH2 : clos_trans Thing (fun x0 y : Thing => Gives y x0) x x\n============================\nforall (x0 y z : Thing) (_ : clos_trans Thing (fun x1 y0 : Thing => Gives y0 x1) x0 y) (_ : False) (_ : clos_trans Thing (fun x1 y0 : Thing => Gives y0 x1) y z) (_ : False), False","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nx : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\n============================\nforall _ : clos_trans Thing (fun x0 y : Thing => Gives y x0) x x, False","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nx : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nH2 : clos_trans Thing (fun x0 y : Thing => Gives y x0) x x\n============================\nforall _ : clos_trans Thing (fun x0 y : Thing => Gives y x0) x x, False","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nx : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nH2 : clos_trans Thing (fun x0 y : Thing => Gives y x0) x x\n============================\nforall _ : forall _ : Gives x x, Through x x, False","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nx : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\nH2 : not (not (clos_trans Thing (fun x0 y : Thing => Gives y x0) x x))\nX8 : Prop\nX9 : Prop\nX10 : Prop\n============================\nFalse","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nx : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\nH2 : not (not (clos_trans Thing (fun x0 y : Thing => Gives y x0) x x))\n============================\nnot (clos_trans Thing (fun x0 y : Thing => Gives y x0) x x)","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nx : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\nH2 : not (not (clos_trans Thing (fun x0 y : Thing => Gives y x0) x x))\nH3 : clos_trans Thing (fun x0 y : Thing => Gives y x0) x x\n============================\nFalse","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nx : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nH2 : not (not (clos_trans Thing (fun x0 y : Thing => Gives y x0) x x))\nX5 : Prop\nX6 : Prop\nX7 : Prop\nX8 : Prop\nX9 : Prop\nX10 : Prop\n============================\nFalse","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nx : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nH2 : not (not (clos_trans Thing (fun x0 y : Thing => Gives y x0) x x))\nX5 : Prop\nX6 : Prop\nX7 : Prop\n============================\nnot (clos_trans Thing (fun x0 y : Thing => Gives y x0) x x)","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nx : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nH2 : not (not (clos_trans Thing (fun x0 y : Thing => Gives y x0) x x))\nX5 : Prop\nX6 : Prop\nX7 : Prop\n============================\nforall _ : Gives x x, False","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nx : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nH2 : not (not (clos_trans Thing (fun x0 y : Thing => Gives y x0) x x))\nX5 : Prop\nX6 : Prop\nX7 : Prop\n============================\nGives x x","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nx : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nH2 : clos_trans Thing (fun x0 y : Thing => Gives y x0) x x\nX5 : Prop\nX6 : Prop\nX7 : Prop\n============================\nFalse","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nx : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\n============================\nforall _ : clos_trans Thing (fun x0 y : Thing => Gives y x0) x x, False","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nx : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nH2 : clos_trans Thing (fun x0 y : Thing => Gives y x0) x x\n============================\nforall (x0 y : Thing) (_ : Gives y x0), False","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nx : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nH2 : clos_trans Thing (fun x0 y : Thing => Gives y x0) x x\n============================\nforall (x0 y z : Thing) (_ : clos_trans Thing (fun x1 y0 : Thing => Gives y0 x1) x0 y) (_ : False) (_ : clos_trans Thing (fun x1 y0 : Thing => Gives y0 x1) y z) (_ : False), False","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nx : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nH2 : clos_trans Thing (fun x0 y : Thing => Gives y x0) x x\n============================\nforall _ : clos_trans Thing (fun x0 y : Thing => Gives y x0) x x, False"],"events":[{"g":0,"t":"assumption","w":"auto","ok":false,"err":"Error: No such assumption."},{"g":0,"t":"tauto","w":"auto","ok":false,"err":"Error: Tactic failure: Classical tauto failed."},{"g":0,"t":"firstorder","w":"auto","ok":true,"c":[1]},{"g":0,"t":"congruence","w":"auto","ok":false,"err":"Error: Tactic failure: congruence failed."},{"g":0,"t":"unfold DependsOn, MP001, MP002, MP003 in *; firstorder","w":"auto","ok":true,"c":[2]},{"g":0,"t":"unfold DependsOn, MP001, MP002, MP003 in *; hammer","w":"hammer","ok":false,"err":"Error: Error running vampire."},{"g":0,"t":"intros","w":"model","ok":true,"c":[3]},{"g":0,"t":"apply NNPP; intro","w":"model","ok":true,"c":[4]},{"g":0,"t":"split","w":"model","ok":false,"err":"Error: Not an inductive goal with 1 constructor."},{"g":0,"t":"right","w":"model","ok":false,"err":"Error: Not an inductive goal with 2 constructors."},{"g":0,"t":"intros D0 D1","w":"model","ok":true,"c":[5]},{"g":0,"t":"intros D0","w":"model","ok":true,"c":[6]},{"g":0,"t":"induction 1","w":"model","ok":false,"err":"Error: Unable to find an instance for the variables x, y."},{"g":0,"t":"assert (~ clos_trans Thing DependsOn)","w":"model","ok":false,"err":"rejected"},{"g":0,"t":"destruct (classic (~ clos_trans Thing DependsOn)) as [Hs|Hs]","w":"model","ok":false,"err":"rejected"},{"g":1,"t":"assumption","w":"auto","ok":false,"err":"Error: No such assumption."},{"g":1,"t":"tauto","w":"auto","ok":false,"err":"Error: Tactic failure: Classical tauto failed."},{"g":1,"t":"firstorder","w":"auto","ok":true,"c":[7]},{"g":1,"t":"congruence","w":"auto","ok":false,"err":"Error: Tactic failure: congruence failed."},{"g":1,"t":"unfold DependsOn, MP001, MP002, MP003 in *; firstorder","w":"auto","ok":true,"c":[8]},{"g":1,"t":"unfold DependsOn, MP001, MP002, MP003 in *; hammer","w":"hammer","ok":false,"err":"Error: Hammer failed: ATPs failed to f"},{"g":1,"t":"intros H2 H3","w":"model","ok":false,"err":"Error: No product even after head-reduction."},{"g":1,"t":"intros H2","w":"model","ok":true,"c":[9]},{"g":1,"t":"apply not_clos_trans","w":"model","ok":false,"err":"Error: The variable not_clos_trans was not found in the cu"},{"g":1,"t":"intro H2","w":"model","ok":true,"c":[9]},{"g":1,"t":"apply clos_trans_not_dependsOn","w":"model","ok":false,"err":"Error: The variable clos_tra"},{"g":1,"t":"intro","w":"model","ok":true,"c":[9]},{"g":1,"t":"intros H' H''","w":"model","ok":false,"err":"Error: No product even after head-reduction."},{"g":1,"t":"intros H' H'0","w":"model","ok":false,"err":"Error: No product even after head-reduction."},{"g":2,"t":"assumption","w":"auto","ok":false,"err":"Error: No such assumption."},{"g":2,"t":"tauto","w":"auto","ok":false,"err":"Error: Tactic failure: Classical tauto failed."},{"g":2,"t":"firstorder","w":"auto","ok":true,"c":[8]},{"g":2,"t":"congruence","w":"auto","ok":false,"err":"Error: Tactic failure: congruence failed."},{"g":2,"t":"hammer","w":"hammer","ok":false,"err":"Error: Hammer failed: ATPs failed to f"},{"g":2,"t":"exists x","w":"model","ok":false,"err":"Error: Not an inductive goal with 1 constructor."},{"g":2,"t":"intros H2 H3","w":"model","ok":false,"err":"Error: No product even after head-reduction."},{"g":2,"t":"intro H2","w":"model","ok":true,"c":[10]},{"g":2,"t":"apply H","w":"model","ok":false,"err":"rejected"},{"g":2,"t":"apply not_clos_trans","w":"model","ok":false,"err":"Error: The variable not_clos_trans was not found in the cu"},{"g":2,"t":"intros H' H'0","w":"model","ok":false,"err":"Error: No product even after head-reduction."},{"g":2,"t":"apply Not_Clos_Trans","w":"model","ok":false,"err":"Error: The variable Not_Clos_Trans was not found in the cu"},{"g":2,"t":"intros H2","w":"model","ok":true,"c":[10]},{"g":3,"t":"assumption","w":"auto","ok":false,"err":"Error: No such assumption."},{"g":3,"t":"tauto","w":"auto","ok":false,"err":"Error: Tactic failure: Classical tauto failed."},{"g":3,"t":"firstorder","w":"auto","ok":true,"c":[1]},{"g":3,"t":"congruence","w":"auto","ok":false,"err":"Error: Tactic failure: congruence failed."},{"g":3,"t":"unfold DependsOn, MP001, MP002, MP003 in *; firstorder","w":"auto","ok":true,"c":[2]},{"g":3,"t":"unfold DependsOn, MP001, MP002, MP003 in *; hammer","w":"hammer","ok":false,"err":"Error: Hammer failed: ATPs failed to f"},{"g":3,"t":"apply not_clos_trans","w":"model","ok":false,"err":"Error: The variable not_clos_trans was not found in the cu"},{"g":3,"t":"intros H2 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x y /\\ forall z, ~ DependsOn y z)","proved":false,"script":"","seconds":902.7,"expansions":16,"calls":861,"root":0,"goals":["============================\nforall x, (exists y, (x = y \\/ clos_trans Thing DependsOn x y) /\\ DependsOn y y) \\/ (exists y, (x = y \\/ clos_trans Thing DependsOn x y) /\\ clos_trans Thing DependsOn y y /\\ ~ DependsOn y y) \\/ (exists S : Thing -> Prop, S x /\\ forall a, S a -> exists b, S b /\\ DependsOn a b) \\/ ((forall y, ~ DependsOn x y) \\/ exists y, clos_trans Thing DependsOn x y /\\ forall z, ~ DependsOn y z)","x : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\n============================\nor (@ex Thing (fun y : Thing => and (or (@eq Thing x y) (clos_trans Thing DependsOn x y)) (DependsOn y y))) (or (@ex Thing (fun y : Thing => and (or (@eq Thing x y) (clos_trans Thing DependsOn x y)) (and (clos_trans Thing DependsOn y y) (not (DependsOn y y))))) (or (@ex (forall _ : Thing, Prop) (fun S : forall _ : Thing, Prop => and (S x) (forall (a : Thing) (_ 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Thing\n============================\nor (@ex Thing (fun y : Thing => and (or (@eq Thing x y) (clos_trans Thing DependsOn x y)) (DependsOn y y))) (or (@ex Thing (fun y : Thing => and (or (@eq Thing x y) (clos_trans Thing DependsOn x y)) (and (clos_trans Thing DependsOn y y) (not (DependsOn y y))))) (or (@ex (forall _ : Thing, Prop) (fun S : forall _ : Thing, Prop => and (S x) (forall (a : Thing) (_ : S a), @ex Thing (fun b : Thing => and (S b) (DependsOn a b))))) (or (forall y : Thing, not (DependsOn x y)) (@ex Thing (fun y : Thing => and (clos_trans Thing DependsOn x y) (forall z : Thing, not (DependsOn y z)))))))","x0 : Thing\n============================\nor (@ex Thing (fun y : Thing => and (or (@eq Thing x0 y) (clos_trans Thing DependsOn x0 y)) (DependsOn y y))) (or (@ex Thing (fun y : Thing => and (or (@eq Thing x0 y) (clos_trans Thing DependsOn x0 y)) (and (clos_trans Thing DependsOn y y) (not (DependsOn y y))))) (or (@ex (forall _ : Thing, Prop) (fun S : forall _ : Thing, Prop => and (S x0) (forall (a : Thing) (_ : S a), @ex Thing (fun b : Thing => and (S b) (DependsOn a b))))) (or (forall y : Thing, not (DependsOn x0 y)) (@ex Thing (fun y : Thing => and (clos_trans Thing DependsOn x0 y) (forall z : Thing, not (DependsOn y z)))))))","x : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\n============================\nor (@ex Thing (fun y : Thing => and (or (@eq Thing x y) (clos_trans Thing DependsOn x y)) (DependsOn y y))) (or (@ex Thing (fun y : Thing => and (or (@eq Thing x y) (clos_trans Thing DependsOn x y)) (and (clos_trans Thing DependsOn y y) (not (DependsOn y y))))) (or (@ex (forall _ : Thing, Prop) (fun S : forall _ : Thing, Prop => and (S x) (forall (a : Thing) (_ : S a), @ex Thing (fun b : Thing => and (S b) (DependsOn a b))))) (or (forall y : Thing, not (DependsOn x y)) (@ex Thing (fun y : Thing => and (clos_trans Thing DependsOn x y) (forall z : Thing, not (DependsOn y z)))))))","x : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\n============================\nor (@ex Thing (fun y : Thing => and (or (@eq Thing x y) (clos_trans Thing (fun x0 y0 : Thing => Gives y0 x0) x y)) (Gives y y))) (or (@ex Thing (fun y : Thing => and (or (@eq Thing x y) (clos_trans Thing (fun x0 y0 : Thing => Gives y0 x0) x y)) (and (clos_trans Thing (fun x0 y0 : Thing => Gives y0 x0) y y) (not (Gives y y))))) (or (@ex (forall _ : Thing, Prop) (fun S : forall _ : Thing, Prop => and (S x) (forall (a : Thing) (_ : S a), @ex Thing (fun b : Thing => and (S b) (Gives b a))))) (or (forall y : Thing, not (Gives y x)) (@ex Thing (fun y : Thing => and (clos_trans Thing (fun x0 y0 : Thing => Gives y0 x0) x y) (forall z : Thing, not (Gives z y)))))))","x : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\n============================\n@ex Thing (fun y : Thing => and (or (@eq Thing x y) (clos_trans Thing DependsOn x y)) (DependsOn y y))","x : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\n============================\nor (@ex Thing (fun y : Thing => and (or (@eq Thing x y) (clos_trans Thing DependsOn x y)) (and (clos_trans Thing DependsOn y y) (not (DependsOn y y))))) (or (@ex (forall _ : Thing, Prop) (fun S : forall _ : Thing, Prop => and (S x) (forall (a : Thing) (_ : S a), @ex Thing (fun b : Thing => and (S b) (DependsOn a b))))) (or (forall y : Thing, not (DependsOn x y)) (@ex Thing (fun y : Thing => and (clos_trans Thing DependsOn x y) (forall z : Thing, not (DependsOn y z))))))","x : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nH : not (or (@ex Thing (fun y : Thing => and (or (@eq Thing x y) (clos_trans Thing DependsOn x y)) (DependsOn y y))) (or (@ex Thing (fun y : Thing => and (or (@eq Thing x y) (clos_trans Thing DependsOn x y)) (and (clos_trans Thing DependsOn y y) (not (DependsOn y y))))) (or (@ex (forall _ : Thing, Prop) (fun S : forall _ : Thing, Prop => and (S x) (forall (a : Thing) (_ : S a), @ex Thing (fun b : Thing => and (S b) (DependsOn a b))))) (or (forall y : Thing, not (DependsOn x y)) (@ex Thing (fun y : Thing => and (clos_trans Thing DependsOn x y) (forall z : Thing, not (DependsOn y z))))))))\n============================\nFalse","x : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\n============================\n@eq Thing x x","x : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nH : @eq Thing x x\n============================\nor (@ex Thing (fun y : Thing => and (or (@eq Thing x y) (clos_trans Thing DependsOn x y)) (DependsOn y y))) (or (@ex Thing (fun y : Thing => and (or (@eq Thing x y) (clos_trans Thing DependsOn x y)) (and (clos_trans Thing DependsOn y y) (not (DependsOn y y))))) (or (@ex (forall _ : Thing, Prop) (fun S : forall _ : Thing, Prop => and (S x) (forall (a : Thing) (_ : S a), @ex Thing (fun b : Thing => and (S b) (DependsOn a b))))) (or (forall y : Thing, not (DependsOn x y)) (@ex Thing (fun y : Thing => and (clos_trans Thing DependsOn x y) (forall z : Thing, not (DependsOn y z)))))))","x : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nHs : @eq Thing x x\n============================\nor (@ex Thing (fun y : Thing => and (or (@eq Thing x y) (clos_trans Thing DependsOn x y)) (DependsOn y y))) (or (@ex Thing (fun y : Thing => and (or (@eq Thing x y) (clos_trans Thing DependsOn x y)) (and (clos_trans Thing DependsOn y y) (not (DependsOn y y))))) (or (@ex (forall _ : Thing, Prop) (fun S : forall _ : Thing, Prop => and (S x) (forall (a : Thing) (_ : S a), @ex Thing (fun b : Thing => and (S b) (DependsOn a b))))) (or (forall y : Thing, not (DependsOn x y)) (@ex Thing (fun y : Thing => and (clos_trans Thing DependsOn x y) (forall z : Thing, not (DependsOn y z)))))))","x : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nHs : not (@eq Thing x x)\n============================\nor (@ex Thing (fun y : Thing => and (or (@eq Thing x y) (clos_trans Thing DependsOn x y)) (DependsOn y y))) (or (@ex Thing (fun y : Thing => and (or (@eq Thing x y) (clos_trans Thing DependsOn x y)) (and (clos_trans Thing DependsOn y y) (not (DependsOn y y))))) (or (@ex (forall _ : Thing, Prop) (fun S : forall _ : Thing, Prop => and (S x) (forall (a : Thing) (_ : S a), @ex Thing (fun b : Thing => and (S b) (DependsOn a b))))) (or (forall y : Thing, not (DependsOn x y)) (@ex Thing (fun y : Thing => and (clos_trans Thing DependsOn x y) (forall z : Thing, not (DependsOn y z)))))))","x : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\n============================\nor (@ex Thing (fun y : Thing => and (or (@eq Thing x y) (clos_trans Thing (fun x0 y0 : Thing => Gives y0 x0) x y)) (and (clos_trans Thing (fun x0 y0 : Thing => Gives y0 x0) y y) (not (Gives y y))))) (or (@ex (forall _ : Thing, Prop) (fun S : forall _ : Thing, Prop => and (S x) (forall (a : Thing) (_ : S a), @ex Thing (fun b : Thing => and (S b) (Gives b a))))) (or (forall y : Thing, not (Gives y x)) (@ex Thing (fun y : Thing => and (clos_trans Thing (fun x0 y0 : Thing => Gives y0 x0) x y) (forall z : Thing, not (Gives z y))))))","x : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\n============================\n@ex Thing (fun y : Thing => and (or (@eq Thing x y) (clos_trans Thing (fun x0 y0 : Thing => Gives y0 x0) x y)) (Gives y y))","x : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nH : not (or (@ex Thing (fun y : Thing => and (or (@eq Thing x y) (clos_trans Thing (fun x0 y0 : Thing => Gives y0 x0) x y)) (Gives y y))) (or (@ex Thing (fun y : Thing => and (or (@eq Thing x y) (clos_trans Thing (fun x0 y0 : Thing => Gives y0 x0) x y)) (and (clos_trans Thing (fun x0 y0 : Thing => Gives y0 x0) y y) (not (Gives y y))))) (or (@ex (forall _ : Thing, Prop) (fun S : forall _ : Thing, Prop => and (S x) (forall (a : Thing) (_ : S a), @ex Thing (fun b : Thing => and (S b) (Gives b a))))) (or (forall y : Thing, not (Gives y x)) (@ex Thing (fun y : Thing => and (clos_trans Thing (fun x0 y0 : Thing => Gives y0 x0) x y) (forall z : Thing, not (Gives z y))))))))\n============================\nFalse","x : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nH : @eq Thing x x\n============================\nor (@ex Thing (fun y : Thing => and (or (@eq Thing x y) (clos_trans Thing (fun x0 y0 : Thing => Gives y0 x0) x y)) (Gives y y))) (or (@ex Thing (fun y : Thing => and (or (@eq Thing x y) (clos_trans Thing (fun x0 y0 : Thing => Gives y0 x0) x y)) (and (clos_trans Thing (fun x0 y0 : Thing => Gives y0 x0) y y) (not (Gives y y))))) (or (@ex (forall _ : Thing, Prop) (fun S : forall _ : Thing, Prop => and (S x) (forall (a : Thing) (_ : S a), @ex Thing (fun b : Thing => and (S b) (Gives b a))))) (or (forall y : Thing, not (Gives y x)) (@ex Thing (fun y : Thing => and (clos_trans Thing (fun x0 y0 : Thing => Gives y0 x0) x y) (forall z : Thing, not (Gives z y)))))))","x : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nHs : @eq Thing x x\n============================\nor (@ex Thing (fun y : Thing => and (or (@eq Thing x y) (clos_trans Thing (fun x0 y0 : Thing => Gives y0 x0) x y)) (Gives y y))) (or (@ex Thing (fun y : Thing => and (or (@eq Thing x y) (clos_trans Thing (fun x0 y0 : Thing => Gives y0 x0) x y)) (and (clos_trans Thing (fun x0 y0 : Thing => Gives y0 x0) y y) (not (Gives y y))))) (or (@ex (forall _ : Thing, Prop) (fun S : forall _ : Thing, Prop => and (S x) (forall (a : Thing) (_ : S a), @ex Thing (fun b : Thing => and (S b) (Gives b a))))) (or (forall y : Thing, not (Gives y x)) (@ex Thing (fun y : Thing => and (clos_trans Thing (fun x0 y0 : Thing => Gives y0 x0) x y) (forall z : Thing, not (Gives z y)))))))","x : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nHs : not (@eq Thing x x)\n============================\nor (@ex Thing (fun y : Thing => and (or (@eq Thing x y) (clos_trans Thing (fun x0 y0 : Thing => Gives y0 x0) x y)) (Gives y y))) (or (@ex Thing (fun y : Thing => and (or (@eq Thing x y) (clos_trans Thing (fun x0 y0 : Thing => Gives y0 x0) x y)) (and (clos_trans Thing (fun x0 y0 : Thing => Gives y0 x0) y y) (not (Gives y y))))) (or (@ex (forall _ : Thing, Prop) (fun S : forall _ : Thing, Prop => and (S x) (forall (a : Thing) (_ : S a), @ex Thing (fun b : Thing => and (S b) (Gives b a))))) (or (forall y : Thing, not (Gives y x)) (@ex Thing (fun y : Thing => and (clos_trans Thing (fun x0 y0 : Thing => Gives y0 x0) x y) (forall z : Thing, not (Gives z y)))))))","x : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\n============================\n@ex Thing (fun y : Thing => and (or (@eq Thing x y) (clos_trans Thing (fun x0 y0 : Thing => Gives y0 x0) x y)) (and (clos_trans Thing (fun x0 y0 : Thing => Gives y0 x0) y y) (not (Gives y y))))","x : Thing\n============================\nor (@ex Thing (fun y : Thing => and (or (@eq Thing x y) (clos_trans Thing DependsOn x y)) (and (clos_trans Thing DependsOn y y) (not (DependsOn y y))))) (or (@ex (forall _ : Thing, Prop) (fun S : forall _ : Thing, Prop => and (S x) (forall (a : Thing) (_ : S a), @ex Thing (fun b : Thing => and (S b) (DependsOn a b))))) (or (forall y : Thing, not (DependsOn x y)) (@ex Thing (fun y : Thing => and (clos_trans Thing DependsOn x y) (forall z : Thing, not (DependsOn y z))))))","x : Thing\n============================\n@ex Thing (fun y : Thing => and (or (@eq Thing x y) (clos_trans Thing DependsOn x y)) (DependsOn y y))","x : Thing\nH : not (or (@ex Thing (fun y : Thing => and (or (@eq Thing x y) (clos_trans Thing DependsOn x y)) (DependsOn y y))) (or (@ex Thing (fun y : Thing => and (or (@eq Thing x y) (clos_trans Thing DependsOn x y)) (and (clos_trans Thing DependsOn y y) (not (DependsOn y y))))) (or (@ex (forall _ : Thing, Prop) (fun S : forall _ : Thing, Prop => and (S x) (forall (a : Thing) (_ : S a), @ex Thing (fun b : Thing => and (S b) (DependsOn a b))))) (or (forall y : Thing, not (DependsOn x y)) (@ex Thing (fun y : Thing => and (clos_trans Thing DependsOn x y) (forall z : Thing, not (DependsOn y z))))))))\n============================\nFalse","x : Thing\n============================\n@ex Thing (fun y : Thing => @eq Thing x y)","x : Thing\nH : @ex Thing (fun y : Thing => @eq Thing x y)\n============================\nor (@ex Thing (fun y : Thing => and (or (@eq Thing x y) (clos_trans Thing DependsOn x y)) (DependsOn y y))) (or (@ex Thing (fun y : Thing => and (or (@eq Thing x y) (clos_trans Thing DependsOn x y)) (and (clos_trans Thing DependsOn y y) (not (DependsOn y y))))) (or (@ex (forall _ : Thing, Prop) (fun S : forall _ : Thing, Prop => and (S x) (forall (a : Thing) (_ : S a), @ex Thing (fun b : Thing => and (S b) (DependsOn a b))))) (or (forall y : Thing, not (DependsOn x y)) (@ex Thing (fun y : Thing => and (clos_trans Thing DependsOn x y) (forall z : Thing, not (DependsOn y z)))))))","x : Thing\nHs : @ex Thing (fun y : Thing => @eq Thing x y)\n============================\nor (@ex Thing (fun y : Thing => and (or (@eq Thing x y) (clos_trans Thing DependsOn x y)) (DependsOn y y))) (or (@ex Thing (fun y : Thing => and (or (@eq Thing x y) (clos_trans Thing DependsOn x y)) (and (clos_trans Thing DependsOn y y) (not (DependsOn y y))))) (or (@ex (forall _ : Thing, Prop) (fun S : forall _ : Thing, Prop => and (S x) (forall (a : Thing) (_ : S a), @ex Thing (fun b : Thing => and (S b) (DependsOn a b))))) (or (forall y : Thing, not (DependsOn x y)) (@ex Thing (fun y : Thing => and (clos_trans Thing DependsOn x y) (forall z : Thing, not (DependsOn y z)))))))","x : Thing\nHs : not (@ex Thing (fun y : Thing => @eq Thing x y))\n============================\nor (@ex Thing (fun y : Thing => and (or (@eq Thing x y) (clos_trans Thing DependsOn x y)) (DependsOn y y))) (or (@ex Thing (fun y : Thing => and (or (@eq Thing x y) (clos_trans Thing DependsOn x y)) (and (clos_trans Thing DependsOn y y) (not (DependsOn y y))))) (or (@ex (forall _ : Thing, Prop) (fun S : forall _ : Thing, Prop => and (S x) (forall (a : Thing) (_ : S a), @ex Thing (fun b : Thing => and (S b) (DependsOn a b))))) (or (forall y : Thing, not (DependsOn x y)) (@ex Thing (fun y : Thing => and (clos_trans Thing DependsOn x y) (forall z : Thing, not (DependsOn y z)))))))","x : Thing\n============================\n@eq Thing x x","x : Thing\nH : @eq Thing x x\n============================\nor (@ex Thing (fun y : Thing => and (or (@eq Thing x y) (clos_trans Thing DependsOn x y)) (DependsOn y y))) (or (@ex Thing (fun y : Thing => and (or (@eq Thing x y) (clos_trans Thing DependsOn x y)) (and (clos_trans Thing DependsOn y y) (not (DependsOn y y))))) (or (@ex (forall _ : Thing, Prop) (fun S : forall _ : Thing, Prop => and (S x) (forall (a : Thing) (_ : S a), @ex Thing (fun b : Thing => and (S b) (DependsOn a b))))) (or (forall y : Thing, not (DependsOn x y)) (@ex Thing (fun y : Thing => and (clos_trans Thing DependsOn x y) (forall z : Thing, not (DependsOn y z)))))))","x : Thing\nHs : @eq Thing x x\n============================\nor (@ex Thing (fun y : Thing => and (or (@eq Thing x y) (clos_trans Thing DependsOn x y)) (DependsOn y y))) (or (@ex Thing (fun y : Thing => and (or (@eq Thing x y) (clos_trans Thing DependsOn x y)) (and (clos_trans Thing DependsOn y y) (not (DependsOn y y))))) (or (@ex (forall _ : Thing, Prop) (fun S : forall _ : Thing, Prop => and (S x) (forall (a : Thing) (_ : S a), @ex Thing (fun b : Thing => and (S b) (DependsOn a b))))) (or (forall y : Thing, not (DependsOn x y)) (@ex Thing (fun y : Thing => and (clos_trans Thing DependsOn x y) (forall z : Thing, not (DependsOn y z)))))))","x : Thing\nHs : not (@eq Thing x x)\n============================\nor (@ex Thing (fun y : Thing => and (or (@eq Thing x y) (clos_trans Thing DependsOn x y)) (DependsOn y y))) (or (@ex Thing (fun y : Thing => and (or (@eq Thing x y) (clos_trans Thing DependsOn x y)) (and (clos_trans Thing DependsOn y y) (not (DependsOn y y))))) (or (@ex (forall _ : Thing, Prop) (fun S : forall _ : Thing, Prop => and (S x) (forall (a : Thing) (_ : S a), @ex Thing (fun b : Thing => and (S b) (DependsOn a b))))) (or (forall y : Thing, not (DependsOn x y)) (@ex Thing (fun y : Thing => and (clos_trans Thing DependsOn x y) (forall z : Thing, not (DependsOn y z)))))))","x : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\nX8 : Prop\nX9 : Prop\nX10 : Prop\n============================\nor (@ex Thing (fun y : Thing => and (or (@eq Thing x y) (clos_trans Thing DependsOn x y)) (DependsOn y y))) (or (@ex Thing (fun y : Thing => and (or (@eq Thing x y) (clos_trans Thing DependsOn x y)) (and (clos_trans Thing DependsOn y y) (not (DependsOn y y))))) (or (@ex (forall _ : Thing, Prop) (fun S : forall _ : Thing, Prop => and (S x) (forall (a : Thing) (_ : S a), @ex Thing (fun b : Thing => and (S b) (DependsOn a b))))) (or (forall y : Thing, not (DependsOn x y)) (@ex Thing (fun y : Thing => and (clos_trans Thing DependsOn x y) (forall z : Thing, not (DependsOn y z)))))))","x : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\nX8 : Prop\nX9 : Prop\nX10 : Prop\n============================\nor (@ex Thing (fun y : Thing => and (or (@eq Thing x y) (clos_trans Thing (fun x0 y0 : Thing => Gives y0 x0) x y)) (Gives y y))) (or (@ex Thing (fun y : Thing => and (or (@eq Thing x y) (clos_trans Thing (fun x0 y0 : Thing => Gives y0 x0) x y)) (and (clos_trans Thing (fun x0 y0 : Thing => Gives y0 x0) y y) (not (Gives y y))))) (or (@ex (forall _ : Thing, Prop) (fun S : forall _ : Thing, Prop => and (S x) (forall (a : Thing) (_ : S a), @ex Thing (fun b : Thing => and (S b) (Gives b a))))) (or (forall y : Thing, not (Gives y x)) (@ex Thing (fun y : Thing => and (clos_trans Thing (fun x0 y0 : Thing => Gives y0 x0) x y) (forall z : Thing, not (Gives z y)))))))","x : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\n============================\n@ex Thing (fun y : Thing => and (or (@eq Thing x y) (clos_trans Thing DependsOn x y)) (DependsOn y y))","x : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\n============================\nor (@ex Thing (fun y : Thing => and (or (@eq Thing x y) (clos_trans Thing DependsOn x y)) (and (clos_trans Thing DependsOn y y) (not (DependsOn y y))))) (or (@ex (forall _ : Thing, Prop) (fun S : forall _ : Thing, Prop => and (S x) (forall (a : Thing) (_ : S a), @ex Thing (fun b : Thing => and (S b) (DependsOn a b))))) (or (forall y : Thing, not (DependsOn x y)) (@ex Thing (fun y : Thing => and (clos_trans Thing DependsOn x y) (forall z : Thing, not (DependsOn y z))))))","x : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nH : not (or (@ex Thing (fun y : Thing => and (or (@eq Thing x y) (clos_trans Thing DependsOn x y)) (DependsOn y y))) (or (@ex Thing (fun y : Thing => and (or (@eq Thing x y) (clos_trans Thing DependsOn x y)) (and (clos_trans Thing DependsOn y y) (not (DependsOn y y))))) (or (@ex (forall _ : Thing, Prop) (fun S : forall _ : Thing, Prop => and (S x) (forall (a : Thing) (_ : S a), @ex Thing (fun b : Thing => and (S b) (DependsOn a b))))) (or (forall y : Thing, not (DependsOn x y)) (@ex Thing (fun y : Thing => and (clos_trans Thing DependsOn x y) (forall z : Thing, not (DependsOn y z))))))))\n============================\nFalse","x : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\n============================\n@eq Thing x x","x : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nH : @eq Thing x x\n============================\nor (@ex Thing (fun y : Thing => and (or (@eq Thing x y) (clos_trans Thing DependsOn x y)) (DependsOn y y))) (or (@ex Thing (fun y : Thing => and (or (@eq Thing x y) (clos_trans Thing DependsOn x y)) (and (clos_trans Thing DependsOn y y) (not (DependsOn y y))))) (or (@ex (forall _ : Thing, Prop) (fun S : forall _ : Thing, Prop => and (S x) (forall (a : Thing) (_ : S a), @ex Thing (fun b : Thing => and (S b) (DependsOn a b))))) (or (forall y : Thing, not (DependsOn x y)) (@ex Thing (fun y : Thing => and (clos_trans Thing DependsOn x y) (forall z : Thing, not (DependsOn y z)))))))","x : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nHs : @eq Thing x x\n============================\nor (@ex Thing (fun y : Thing => and (or (@eq Thing x y) (clos_trans Thing DependsOn x y)) (DependsOn y y))) (or (@ex Thing (fun y : Thing => and (or (@eq Thing x y) (clos_trans Thing DependsOn x y)) (and (clos_trans Thing DependsOn y y) (not (DependsOn y y))))) (or (@ex (forall _ : Thing, Prop) (fun S : forall _ : Thing, Prop => and (S x) (forall (a : Thing) (_ : S a), @ex Thing (fun b : Thing => and (S b) (DependsOn a b))))) (or (forall y : Thing, not (DependsOn x y)) (@ex Thing (fun y : Thing => and (clos_trans Thing DependsOn x y) (forall z : Thing, not (DependsOn y z)))))))","x : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nHs : not (@eq Thing x x)\n============================\nor (@ex Thing (fun y : Thing => and (or (@eq Thing x y) (clos_trans Thing DependsOn x y)) (DependsOn y y))) (or (@ex Thing (fun y : Thing => and (or (@eq Thing x y) (clos_trans Thing DependsOn x y)) (and (clos_trans Thing DependsOn y y) (not (DependsOn y y))))) (or (@ex (forall _ : Thing, Prop) (fun S : forall _ : Thing, Prop => and (S x) (forall (a : Thing) (_ : S a), @ex Thing (fun b : Thing => and (S b) (DependsOn a b))))) (or (forall y : Thing, not (DependsOn x y)) (@ex Thing (fun y : Thing => and (clos_trans Thing DependsOn x y) (forall z : Thing, not (DependsOn y z)))))))","x : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\n============================\nor (@ex Thing (fun y : Thing => and (or (@eq Thing x y) (clos_trans Thing (fun x0 y0 : Thing => Gives y0 x0) x y)) (and (clos_trans Thing (fun x0 y0 : Thing => Gives y0 x0) y y) (not (Gives y y))))) (or (@ex (forall _ : Thing, Prop) (fun S : forall _ : Thing, Prop => and (S x) (forall (a : Thing) (_ : S a), @ex Thing (fun b : Thing => and (S b) (Gives b a))))) (or (forall y : Thing, not (Gives y x)) (@ex Thing (fun y : Thing => and (clos_trans Thing (fun x0 y0 : Thing => Gives y0 x0) x y) (forall z : Thing, not (Gives z y))))))","x : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\n============================\n@ex Thing (fun y : Thing => and (or (@eq Thing x y) (clos_trans Thing (fun x0 y0 : Thing => Gives y0 x0) x y)) (Gives y y))","x : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nH : not (or (@ex Thing (fun y : Thing => and (or (@eq Thing x y) (clos_trans Thing (fun x0 y0 : Thing => Gives y0 x0) x y)) (Gives y y))) (or (@ex Thing (fun y : Thing => and (or (@eq Thing x y) (clos_trans Thing (fun x0 y0 : Thing => Gives y0 x0) x y)) (and (clos_trans Thing (fun x0 y0 : Thing => Gives y0 x0) y y) (not (Gives y y))))) (or (@ex (forall _ : Thing, Prop) (fun S : forall _ : Thing, Prop => and (S x) (forall (a : Thing) (_ : S a), @ex Thing (fun b : Thing => and (S b) (Gives b a))))) (or (forall y : Thing, not (Gives y x)) (@ex Thing (fun y : Thing => and (clos_trans Thing (fun x0 y0 : Thing => Gives y0 x0) x y) (forall z : Thing, not (Gives z y))))))))\n============================\nFalse","x : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\n============================\n@ex Thing (fun y : Thing => and (or (@eq Thing x y) (clos_trans Thing (fun x0 y0 : Thing => Gives y0 x0) x y)) (and (clos_trans Thing (fun x0 y0 : Thing => Gives y0 x0) y y) (not (Gives y y))))","x : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\nX8 : Prop\nX9 : Prop\nX10 : Prop\nX11 : Prop\nX12 : Prop\nX13 : Prop\nX14 : Prop\n============================\nor (@ex Thing (fun y : Thing => and (or (@eq Thing x y) (clos_trans Thing DependsOn x y)) (DependsOn y y))) (or (@ex Thing (fun y : Thing => and (or (@eq Thing x y) (clos_trans Thing DependsOn x y)) (and (clos_trans Thing DependsOn y y) (not (DependsOn y y))))) (or (@ex (forall _ : Thing, Prop) (fun S : forall _ : Thing, Prop => and (S x) (forall (a : Thing) (_ : S a), @ex Thing (fun b : Thing => and (S b) (DependsOn a b))))) (or (forall y : Thing, not (DependsOn x y)) (@ex Thing (fun y : Thing => and (clos_trans Thing DependsOn x y) (forall z : Thing, not (DependsOn y z)))))))","x : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\nX8 : Prop\nX9 : Prop\nX10 : Prop\nX11 : Prop\nX12 : Prop\nX13 : Prop\nX14 : Prop\n============================\nor (@ex Thing (fun y : Thing => and (or (@eq Thing x y) (clos_trans Thing (fun x0 y0 : Thing => Gives y0 x0) x y)) (Gives y y))) (or (@ex Thing (fun y : Thing => and (or (@eq Thing x y) (clos_trans Thing (fun x0 y0 : Thing => Gives y0 x0) x y)) (and (clos_trans Thing (fun x0 y0 : Thing => Gives y0 x0) y y) (not (Gives y y))))) (or (@ex (forall _ : Thing, Prop) (fun S : forall _ : Thing, Prop => and (S x) (forall (a : Thing) (_ : S a), @ex Thing (fun b : Thing => and (S b) (Gives b a))))) (or (forall y : Thing, not (Gives y x)) (@ex Thing (fun y : Thing => and (clos_trans Thing (fun x0 y0 : Thing => Gives y0 x0) x y) (forall z : Thing, not (Gives z y)))))))","x : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\nX8 : Prop\nX9 : Prop\nX10 : Prop\n============================\n@ex Thing (fun y : Thing => and (or (@eq Thing x y) (clos_trans Thing DependsOn x y)) (DependsOn y y))","x : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\nX8 : Prop\nX9 : Prop\nX10 : Prop\n============================\nor (@ex Thing (fun y : Thing => and (or (@eq Thing x y) (clos_trans Thing DependsOn x y)) (and (clos_trans Thing DependsOn y y) (not (DependsOn y y))))) (or (@ex (forall _ : Thing, Prop) (fun S : forall _ : Thing, Prop => and (S x) (forall (a : Thing) (_ : S a), @ex Thing (fun b : Thing => and (S b) (DependsOn a b))))) (or (forall y : Thing, not (DependsOn x y)) (@ex Thing (fun y : Thing => and (clos_trans Thing DependsOn x y) (forall z : Thing, not (DependsOn y z))))))","x : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\nX8 : Prop\nX9 : Prop\nX10 : Prop\nH : not (or (@ex Thing (fun y : Thing => and (or (@eq Thing x y) (clos_trans Thing DependsOn x y)) (DependsOn y y))) (or (@ex Thing (fun y : Thing => and (or (@eq Thing x y) (clos_trans Thing DependsOn x y)) (and (clos_trans Thing DependsOn y y) (not (DependsOn y y))))) (or (@ex (forall _ : Thing, Prop) (fun S : forall _ : Thing, Prop => and (S x) (forall (a : Thing) (_ : S a), @ex Thing (fun b : Thing => and (S b) (DependsOn a b))))) (or (forall y : Thing, not (DependsOn x y)) (@ex Thing (fun y : Thing => and (clos_trans Thing DependsOn x y) (forall z : Thing, not (DependsOn y z))))))))\n============================\nFalse","x : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\nX8 : Prop\nX9 : Prop\nX10 : Prop\n============================\n@eq Thing x x","x : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\nX8 : Prop\nX9 : Prop\nX10 : Prop\nH : @eq Thing x x\n============================\nor (@ex Thing (fun y : Thing => and (or (@eq Thing x y) (clos_trans Thing DependsOn x y)) (DependsOn y y))) (or (@ex Thing (fun y : Thing => and (or (@eq Thing x y) (clos_trans Thing DependsOn x y)) (and (clos_trans Thing DependsOn y y) (not (DependsOn y y))))) (or (@ex (forall _ : Thing, Prop) (fun S : forall _ : Thing, Prop => and (S x) (forall (a : Thing) (_ : S a), @ex Thing (fun b : Thing => and (S b) (DependsOn a b))))) (or (forall y : Thing, not (DependsOn x y)) (@ex Thing (fun y : Thing => and (clos_trans Thing DependsOn x y) (forall z : Thing, not (DependsOn y z)))))))","x : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\nX8 : Prop\nX9 : Prop\nX10 : Prop\nHs : @eq Thing x x\n============================\nor (@ex Thing (fun y : Thing => and (or (@eq Thing x y) (clos_trans Thing DependsOn x y)) (DependsOn y y))) (or (@ex Thing (fun y : Thing => and (or (@eq Thing x y) (clos_trans Thing DependsOn x y)) (and (clos_trans Thing DependsOn y y) (not (DependsOn y y))))) (or (@ex (forall _ : Thing, Prop) (fun S : forall _ : Thing, Prop => and (S x) (forall (a : Thing) (_ : S a), @ex Thing (fun b : Thing => and (S b) (DependsOn a b))))) (or (forall y : Thing, not (DependsOn x y)) (@ex Thing (fun y : Thing => and (clos_trans Thing DependsOn x y) (forall z : Thing, not (DependsOn y z)))))))","x : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\nX8 : Prop\nX9 : Prop\nX10 : Prop\nHs : not (@eq Thing x x)\n============================\nor (@ex Thing (fun y : Thing => and (or (@eq Thing x y) (clos_trans Thing DependsOn x y)) (DependsOn y y))) (or (@ex Thing (fun y : Thing => and (or (@eq Thing x y) (clos_trans Thing DependsOn x y)) (and (clos_trans Thing DependsOn y y) (not (DependsOn y y))))) (or (@ex (forall _ : Thing, Prop) (fun S : forall _ : Thing, Prop => and (S x) (forall (a : Thing) (_ : S a), @ex Thing (fun b : Thing => and (S b) (DependsOn a b))))) (or (forall y : Thing, not (DependsOn x y)) (@ex Thing (fun y : Thing => and (clos_trans Thing DependsOn x y) (forall z : Thing, not (DependsOn y z)))))))","x : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\nX8 : Prop\nX9 : Prop\nX10 : Prop\n============================\nor (@ex Thing (fun y : Thing => and (or (@eq Thing x y) (clos_trans Thing (fun x0 y0 : Thing => Gives y0 x0) x y)) (and (clos_trans Thing (fun x0 y0 : Thing => Gives y0 x0) y y) (not (Gives y y))))) (or (@ex (forall _ : Thing, Prop) (fun S : forall _ : Thing, Prop => and (S x) (forall (a : Thing) (_ : S a), @ex Thing (fun b : Thing => and (S b) (Gives b a))))) (or (forall y : Thing, not (Gives y x)) (@ex Thing (fun y : Thing => and (clos_trans Thing (fun x0 y0 : Thing => Gives y0 x0) x y) (forall z : Thing, not (Gives z y))))))","x : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\nX8 : Prop\nX9 : Prop\nX10 : Prop\n============================\n@ex Thing (fun y : Thing => and (or (@eq Thing x y) (clos_trans Thing (fun x0 y0 : Thing => Gives y0 x0) x y)) (Gives y y))","x : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\nX8 : Prop\nX9 : Prop\nX10 : Prop\nH : not (or (@ex Thing (fun y : Thing => and (or (@eq Thing x y) (clos_trans Thing (fun x0 y0 : Thing => Gives y0 x0) x y)) (Gives y y))) (or (@ex Thing (fun y : Thing => and (or (@eq Thing x y) (clos_trans Thing (fun x0 y0 : Thing => Gives y0 x0) x y)) (and (clos_trans Thing (fun x0 y0 : Thing => Gives y0 x0) y y) (not (Gives y y))))) (or (@ex (forall _ : Thing, Prop) (fun S : forall _ : Thing, Prop => and (S x) (forall (a : Thing) (_ : S a), @ex Thing (fun b : Thing => and (S b) (Gives b a))))) (or (forall y : Thing, not (Gives y x)) (@ex Thing (fun y : Thing => and (clos_trans Thing (fun x0 y0 : Thing => Gives y0 x0) x y) (forall z : Thing, not (Gives z y))))))))\n============================\nFalse","x : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\nX8 : Prop\nX9 : Prop\nX10 : Prop\n============================\nGives x x","x : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\nX8 : Prop\nX9 : Prop\nX10 : Prop\nH : Gives x x\n============================\nor (@ex Thing (fun y : Thing => and (or (@eq Thing x y) (clos_trans Thing (fun x0 y0 : Thing => Gives y0 x0) x y)) (Gives y y))) (or (@ex Thing (fun y : Thing => and (or (@eq Thing x y) (clos_trans Thing (fun x0 y0 : Thing => Gives y0 x0) x y)) (and (clos_trans Thing (fun x0 y0 : Thing => Gives y0 x0) y y) (not (Gives y y))))) (or (@ex (forall _ : Thing, Prop) (fun S : forall _ : Thing, Prop => and (S x) (forall (a : Thing) (_ : S a), @ex Thing (fun b : Thing => and (S b) (Gives b a))))) (or (forall y : Thing, not (Gives y x)) (@ex Thing (fun y : Thing => and (clos_trans Thing (fun x0 y0 : Thing => Gives y0 x0) x y) (forall z : Thing, not (Gives z y)))))))","x : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\nX8 : Prop\nX9 : Prop\nX10 : Prop\nHs : Gives x x\n============================\nor (@ex Thing (fun y : Thing => and (or (@eq Thing x y) (clos_trans Thing (fun x0 y0 : Thing => Gives y0 x0) x y)) (Gives y y))) (or (@ex Thing (fun y : Thing => and (or (@eq Thing x y) (clos_trans Thing (fun x0 y0 : Thing => Gives y0 x0) x y)) (and (clos_trans Thing (fun x0 y0 : Thing => Gives y0 x0) y y) (not (Gives y y))))) (or (@ex (forall _ : Thing, Prop) (fun S : forall _ : Thing, Prop => and (S x) (forall (a : Thing) (_ : S a), @ex Thing (fun b : Thing => and (S b) (Gives b a))))) (or (forall y : Thing, not (Gives y x)) (@ex Thing (fun y : Thing => and (clos_trans Thing (fun x0 y0 : Thing => Gives y0 x0) x y) (forall z : Thing, not (Gives z y)))))))","x : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\nX8 : Prop\nX9 : Prop\nX10 : Prop\nHs : not (Gives x x)\n============================\nor (@ex Thing (fun y : Thing => and (or (@eq Thing x y) (clos_trans Thing (fun x0 y0 : Thing => Gives y0 x0) x y)) (Gives y y))) (or (@ex Thing (fun y : Thing => and (or (@eq Thing x y) (clos_trans Thing (fun x0 y0 : Thing => Gives y0 x0) x y)) (and (clos_trans Thing (fun x0 y0 : Thing => Gives y0 x0) y y) (not (Gives y y))))) (or (@ex (forall _ : Thing, Prop) (fun S : forall _ : Thing, Prop => and (S x) (forall (a : Thing) (_ : S a), @ex Thing (fun b : Thing => and (S b) (Gives b a))))) (or (forall y : Thing, not (Gives y x)) (@ex Thing (fun y : Thing => and (clos_trans Thing (fun x0 y0 : Thing => Gives y0 x0) x y) (forall z : Thing, not (Gives z y)))))))","x : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\nX8 : Prop\nX9 : Prop\nX10 : Prop\n============================\n@ex Thing (fun y : Thing => and (or (@eq Thing x y) (clos_trans Thing (fun x0 y0 : Thing => Gives y0 x0) x y)) (and (clos_trans Thing (fun x0 y0 : Thing => Gives y0 x0) y y) (not (Gives y y))))","x : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\n============================\nand (or (@eq Thing x x) (clos_trans Thing DependsOn x x)) (DependsOn x x)","x : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\n============================\nor (@eq Thing x x) (clos_trans Thing DependsOn x x)","x : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\n============================\nDependsOn x x","x : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\n============================\nor (@ex (forall _ : Thing, Prop) (fun S : forall _ : Thing, Prop => and (S x) (forall (a : Thing) (_ : S a), @ex Thing (fun b : Thing => and (S b) (Gives b a))))) (or (forall y : Thing, not (Gives y x)) (@ex Thing (fun y : Thing => and (clos_trans Thing (fun x0 y0 : Thing => Gives y0 x0) x y) (forall z : Thing, not (Gives z y)))))","x : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nH : not (or (@ex Thing (fun y : Thing => and (or (@eq Thing x y) (clos_trans Thing (fun x0 y0 : Thing => Gives y0 x0) x y)) (and (clos_trans Thing (fun x0 y0 : Thing => Gives y0 x0) y y) (not (Gives y y))))) (or (@ex (forall _ : Thing, Prop) (fun S : forall _ : Thing, Prop => and (S x) (forall (a : Thing) (_ : S a), @ex Thing (fun b : Thing => and (S b) (Gives b a))))) (or (forall y : Thing, not (Gives y x)) (@ex Thing (fun y : Thing => and (clos_trans Thing (fun x0 y0 : Thing => Gives y0 x0) x y) (forall z : Thing, not (Gives z y)))))))\n============================\nFalse","x : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\n============================\nGives x x","x : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nH : Gives x x\n============================\nor (@ex Thing (fun y : Thing => and (or (@eq Thing x y) (clos_trans Thing (fun x0 y0 : Thing => Gives y0 x0) x y)) (and (clos_trans Thing (fun x0 y0 : Thing => Gives y0 x0) y y) (not (Gives y y))))) (or (@ex (forall _ : Thing, Prop) (fun S : forall _ : Thing, Prop => and (S x) (forall (a : Thing) (_ : S a), @ex Thing (fun b : Thing => and (S b) (Gives b a))))) (or (forall y : Thing, not (Gives y x)) (@ex Thing (fun y : Thing => and (clos_trans Thing (fun x0 y0 : Thing => Gives y0 x0) x y) (forall z : Thing, not (Gives z y))))))","x : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nHs : Gives x x\n============================\nor (@ex Thing (fun y : Thing => and (or (@eq Thing x y) (clos_trans Thing (fun x0 y0 : Thing => Gives y0 x0) x y)) (and (clos_trans Thing (fun x0 y0 : Thing => Gives y0 x0) y y) (not (Gives y y))))) (or (@ex (forall _ : Thing, Prop) (fun S : forall _ : Thing, Prop => and (S x) (forall (a : Thing) (_ : S a), @ex Thing (fun b : Thing => and (S b) (Gives b a))))) (or (forall y : Thing, not (Gives y x)) (@ex Thing (fun y : Thing => and (clos_trans Thing (fun x0 y0 : Thing => Gives y0 x0) x y) (forall z : Thing, not (Gives z y))))))","x : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nHs : not (Gives x x)\n============================\nor (@ex Thing (fun y : Thing => and (or (@eq Thing x y) (clos_trans Thing (fun x0 y0 : Thing => Gives y0 x0) x y)) (and (clos_trans Thing (fun x0 y0 : Thing => Gives y0 x0) y y) (not (Gives y y))))) (or (@ex (forall _ : Thing, Prop) (fun S : forall _ : Thing, Prop => and (S x) (forall (a : Thing) (_ : S a), @ex Thing (fun b : Thing => and (S b) (Gives b a))))) (or (forall y : Thing, not (Gives y x)) (@ex Thing (fun y : Thing => and (clos_trans Thing (fun x0 y0 : Thing => Gives y0 x0) x y) (forall z : Thing, not (Gives z y))))))","x : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nH : @eq Thing x x\n============================\nor (@ex Thing (fun y : Thing => and (or (@eq Thing x y) (clos_trans Thing (fun x0 y0 : Thing => Gives y0 x0) x y)) (and (clos_trans Thing (fun x0 y0 : Thing => Gives y0 x0) y y) (not (Gives y y))))) (or (@ex (forall _ : Thing, Prop) (fun S : forall _ : Thing, Prop => and (S x) (forall (a : Thing) (_ : S a), @ex Thing (fun b : Thing => and (S b) (Gives b a))))) (or (forall y : Thing, not (Gives y x)) (@ex Thing (fun y : Thing => and (clos_trans Thing (fun x0 y0 : Thing => Gives y0 x0) x y) (forall z : Thing, not (Gives z y))))))","x : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nHs : @eq Thing x x\n============================\nor (@ex Thing (fun y : Thing => and (or (@eq Thing x y) (clos_trans Thing (fun x0 y0 : Thing => Gives y0 x0) x y)) (and (clos_trans Thing (fun x0 y0 : Thing => Gives y0 x0) y y) (not (Gives y y))))) (or (@ex (forall _ : Thing, Prop) (fun S : forall _ : Thing, Prop => and (S x) (forall (a : Thing) (_ : S a), @ex Thing (fun b : Thing => and (S b) (Gives b a))))) (or (forall y : Thing, not (Gives y x)) (@ex Thing (fun y : Thing => and (clos_trans Thing (fun x0 y0 : Thing => Gives y0 x0) x y) (forall z : Thing, not (Gives z y))))))","x : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nHs : not (@eq Thing x x)\n============================\nor (@ex Thing (fun y : Thing => and (or (@eq Thing x y) (clos_trans Thing (fun x0 y0 : Thing => Gives y0 x0) x y)) (and (clos_trans Thing (fun x0 y0 : Thing => Gives y0 x0) y y) (not (Gives y y))))) (or (@ex (forall _ : Thing, Prop) (fun S : forall _ : Thing, Prop => and (S x) (forall (a : Thing) (_ : S a), @ex Thing (fun b : Thing => and (S b) (Gives b a))))) (or (forall y : Thing, not (Gives y x)) (@ex Thing (fun y : Thing => and (clos_trans Thing (fun x0 y0 : Thing => Gives y0 x0) x y) (forall z : Thing, not (Gives z y))))))","x : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\n============================\nand (or (@eq Thing x x) (clos_trans Thing (fun x0 y0 : Thing => Gives y0 x0) x x)) (Gives x x)","x : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\n============================\nor (@eq Thing x x) (clos_trans Thing (fun x0 y0 : Thing => Gives y0 x0) x x)","x : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nH : or (@eq Thing x x) (clos_trans Thing (fun x0 y0 : Thing => Gives y0 x0) x x)\n============================\n@ex Thing (fun y : Thing => and (or (@eq Thing x y) (clos_trans Thing (fun x0 y0 : Thing => Gives y0 x0) x y)) (Gives y y))","x : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nHs : or (@eq Thing x x) (clos_trans Thing (fun x0 y0 : Thing => Gives y0 x0) x x)\n============================\n@ex Thing (fun y : Thing => and (or (@eq Thing x y) (clos_trans Thing (fun x0 y0 : Thing => Gives y0 x0) x y)) (Gives y y))","x : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nHs : not (or (@eq Thing x x) (clos_trans Thing (fun x0 y0 : Thing => Gives y0 x0) x x))\n============================\n@ex Thing (fun y : Thing => and (or (@eq Thing x y) (clos_trans Thing (fun x0 y0 : Thing => Gives y0 x0) x y)) (Gives y y))","x : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\n============================\n@ex Thing (fun y : Thing => and (or (@eq Thing x y) (clos_trans Thing DependsOn x y)) (and (clos_trans Thing DependsOn y y) (not (DependsOn y y))))","x : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\n============================\nor (@ex (forall _ : Thing, Prop) (fun S : forall _ : Thing, Prop => and (S x) (forall (a : Thing) (_ : S a), @ex Thing (fun b : Thing => and (S b) (DependsOn a b))))) (or (forall y : Thing, not (DependsOn x y)) (@ex Thing (fun y : Thing => and (clos_trans Thing DependsOn x y) (forall z : Thing, not (DependsOn y z)))))","x : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nH : not (or (@ex Thing (fun y : Thing => and (or (@eq Thing x y) (clos_trans Thing DependsOn x y)) (and (clos_trans Thing DependsOn y y) (not (DependsOn y y))))) (or (@ex (forall _ : Thing, Prop) (fun S : forall _ : Thing, Prop => and (S x) (forall (a : Thing) (_ : S a), @ex Thing (fun b : Thing => and (S b) (DependsOn a b))))) (or (forall y : Thing, not (DependsOn x y)) (@ex Thing (fun y : Thing => and (clos_trans Thing DependsOn x y) (forall z : Thing, not (DependsOn y z)))))))\n============================\nFalse","x : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nH : @eq Thing x x\n============================\nor (@ex Thing (fun y : Thing => and (or (@eq Thing x y) (clos_trans Thing DependsOn x y)) (and (clos_trans Thing DependsOn y y) (not (DependsOn y y))))) (or (@ex (forall _ : Thing, Prop) (fun S : forall _ : Thing, Prop => and (S x) (forall (a : Thing) (_ : S a), @ex Thing (fun b : Thing => and (S b) (DependsOn a b))))) (or (forall y : Thing, not (DependsOn x y)) (@ex Thing (fun y : Thing => and (clos_trans Thing DependsOn x y) (forall z : Thing, not (DependsOn y z))))))","x : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nHs : @eq Thing x x\n============================\nor (@ex Thing (fun y : Thing => and (or (@eq Thing x y) (clos_trans Thing DependsOn x y)) (and (clos_trans Thing DependsOn y y) (not (DependsOn y y))))) (or (@ex (forall _ : Thing, Prop) (fun S : forall _ : Thing, Prop => and (S x) (forall (a : Thing) (_ : S a), @ex Thing (fun b : Thing => and (S b) (DependsOn a b))))) (or (forall y : Thing, not (DependsOn x y)) (@ex Thing (fun y : Thing => and (clos_trans Thing DependsOn x y) (forall z : Thing, not (DependsOn y z))))))","x : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nHs : not (@eq Thing x x)\n============================\nor (@ex Thing (fun y : Thing => and (or (@eq Thing x y) (clos_trans Thing DependsOn x y)) (and (clos_trans Thing DependsOn y y) (not (DependsOn y y))))) (or (@ex (forall _ : Thing, Prop) (fun S : forall _ : 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(@ex (forall _ : Thing, Prop) (fun S : forall _ : Thing, Prop => and (S x) (forall (a : Thing) (_ : S a), @ex Thing (fun b : Thing => and (S b) (DependsOn a b))))) (or (forall y : Thing, not (DependsOn x y)) (@ex Thing (fun y : Thing => and (clos_trans Thing DependsOn x y) (forall z : Thing, not (DependsOn y z)))))))\n============================\nFalse","x : Thing\nH : @ex Thing (fun y : Thing => @eq Thing x y)\n============================\nor (@ex Thing (fun y : Thing => and (or (@eq Thing x y) (clos_trans Thing DependsOn x y)) (and (clos_trans Thing DependsOn y y) (not (DependsOn y y))))) (or (@ex (forall _ : Thing, Prop) (fun S : forall _ : Thing, Prop => and (S x) (forall (a : Thing) (_ : S a), @ex Thing (fun b : Thing => and (S b) (DependsOn a b))))) (or (forall y : Thing, not (DependsOn x y)) (@ex Thing (fun y : Thing => and (clos_trans Thing DependsOn x y) (forall z : Thing, not (DependsOn y z))))))","x : Thing\nHs : @ex Thing (fun y : Thing => @eq Thing x y)\n============================\nor (@ex Thing (fun y : Thing => and (or (@eq Thing x y) (clos_trans Thing DependsOn x y)) (and (clos_trans Thing DependsOn y y) (not (DependsOn y y))))) (or (@ex (forall _ : Thing, Prop) (fun S : forall _ : Thing, Prop => and (S x) (forall (a : Thing) (_ : S a), @ex Thing (fun b : Thing => and (S b) (DependsOn a b))))) (or (forall y : Thing, not (DependsOn x y)) (@ex Thing (fun y : Thing => and (clos_trans Thing DependsOn x y) (forall z : Thing, not (DependsOn y z))))))","x : Thing\nHs : not (@ex Thing (fun y : Thing => @eq Thing x y))\n============================\nor (@ex Thing (fun y : Thing => and (or (@eq Thing x y) (clos_trans Thing DependsOn x y)) (and (clos_trans Thing DependsOn y y) (not (DependsOn y y))))) (or (@ex (forall _ : Thing, Prop) (fun S : forall _ : Thing, Prop => and (S x) (forall (a : Thing) (_ : S a), @ex Thing (fun b : Thing => and (S b) (DependsOn a b))))) (or (forall y : Thing, not (DependsOn x y)) (@ex Thing (fun y : Thing => 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Thing (fun b : Thing => and (S b) (DependsOn a b))))) (or (forall y : Thing, not (DependsOn x y)) (@ex Thing (fun y : Thing => and (clos_trans Thing DependsOn x y) (forall z : Thing, not (DependsOn y z)))))))","x : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\nX8 : Prop\nX9 : Prop\nX10 : Prop\nX11 : Prop\nX12 : Prop\nX13 : Prop\nX14 : Prop\nX15 : Prop\nX16 : Prop\nX17 : Prop\nX18 : Prop\n============================\nor (@ex Thing (fun y : Thing => and (or (@eq Thing x y) (clos_trans Thing (fun x0 y0 : Thing => Gives y0 x0) x y)) (Gives y y))) (or (@ex Thing (fun y : Thing => and (or (@eq Thing x y) (clos_trans Thing (fun x0 y0 : Thing => Gives y0 x0) x y)) (and (clos_trans Thing (fun x0 y0 : Thing => Gives y0 x0) y y) (not (Gives y y))))) (or (@ex (forall _ : Thing, Prop) (fun S : forall _ : Thing, Prop => and (S x) (forall (a : Thing) (_ : S a), @ex Thing (fun b : Thing => and (S b) (Gives b a))))) (or (forall y : Thing, not (Gives y x)) (@ex Thing (fun y : Thing => and (clos_trans Thing (fun x0 y0 : Thing => Gives y0 x0) x y) (forall z : Thing, not (Gives z y)))))))","x : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\nX8 : Prop\nX9 : Prop\nX10 : Prop\nX11 : Prop\nX12 : Prop\nX13 : Prop\nX14 : Prop\n============================\nor (@ex Thing (fun y : Thing => and (or (@eq Thing x y) (clos_trans Thing DependsOn x y)) (and (clos_trans Thing DependsOn y y) (not (DependsOn y y))))) (or (@ex (forall _ : Thing, Prop) (fun S : forall _ : Thing, Prop => and (S x) (forall (a : Thing) (_ : S a), @ex Thing (fun b : Thing => and (S b) (DependsOn a b))))) (or (forall y : Thing, not (DependsOn x y)) (@ex Thing (fun y : Thing => and (clos_trans Thing DependsOn x y) (forall z : Thing, not (DependsOn y z))))))","x : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\nX8 : Prop\nX9 : Prop\nX10 : Prop\nX11 : Prop\nX12 : Prop\nX13 : Prop\nX14 : Prop\n============================\n@ex Thing (fun y : Thing => and (or (@eq Thing x y) (clos_trans Thing DependsOn x y)) (DependsOn y y))","x : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\nX8 : Prop\nX9 : Prop\nX10 : Prop\nX11 : Prop\nX12 : Prop\nX13 : Prop\nX14 : Prop\nH : not (or (@ex Thing (fun y : Thing => and (or (@eq Thing x y) (clos_trans Thing DependsOn x y)) (DependsOn y y))) (or (@ex Thing (fun y : Thing => and (or (@eq Thing x y) (clos_trans Thing DependsOn x y)) (and (clos_trans Thing DependsOn y y) (not (DependsOn y y))))) (or (@ex (forall _ : Thing, Prop) (fun S : forall _ : Thing, Prop => and (S x) (forall (a : Thing) (_ : S a), @ex Thing (fun b : Thing => and (S b) (DependsOn a b))))) (or (forall y : Thing, not (DependsOn x y)) (@ex Thing (fun y : Thing => and (clos_trans Thing DependsOn x y) (forall z : Thing, not (DependsOn y z))))))))\n============================\nFalse","x : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\nX8 : Prop\nX9 : Prop\nX10 : Prop\nX11 : Prop\nX12 : Prop\nX13 : Prop\nX14 : Prop\n============================\n@eq Thing x x","x : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\nX8 : Prop\nX9 : Prop\nX10 : Prop\nX11 : Prop\nX12 : Prop\nX13 : Prop\nX14 : Prop\nH : @eq Thing x x\n============================\nor (@ex Thing (fun y : Thing => and (or (@eq Thing x y) (clos_trans Thing DependsOn x y)) (DependsOn y y))) (or (@ex Thing (fun y : Thing => and (or (@eq Thing x y) (clos_trans Thing DependsOn x y)) (and (clos_trans Thing DependsOn y y) (not (DependsOn y y))))) (or (@ex (forall _ : Thing, Prop) (fun S : forall _ : Thing, Prop => and (S x) (forall (a : Thing) (_ : S a), @ex Thing (fun b : Thing => and (S b) (DependsOn a b))))) (or (forall y : Thing, not (DependsOn x y)) (@ex Thing (fun y : Thing => and (clos_trans Thing DependsOn x y) (forall z : Thing, not (DependsOn y z)))))))","x : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\nX8 : Prop\nX9 : Prop\nX10 : Prop\nX11 : Prop\nX12 : Prop\nX13 : Prop\nX14 : Prop\nHs : @eq Thing x x\n============================\nor (@ex Thing (fun y : Thing => and (or (@eq Thing x y) (clos_trans Thing DependsOn x y)) (DependsOn y y))) (or (@ex Thing (fun y : Thing => and (or (@eq Thing x y) (clos_trans Thing DependsOn x y)) (and (clos_trans Thing DependsOn y y) (not (DependsOn y y))))) (or (@ex (forall _ : Thing, Prop) (fun S : forall _ : Thing, Prop => and (S x) (forall (a : Thing) (_ : S a), @ex Thing (fun b : Thing => and (S b) (DependsOn a b))))) (or (forall y : Thing, not (DependsOn x y)) (@ex Thing (fun y : Thing => and (clos_trans Thing DependsOn x y) (forall z : Thing, not (DependsOn y z)))))))","x : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\nX8 : Prop\nX9 : Prop\nX10 : Prop\nX11 : Prop\nX12 : Prop\nX13 : Prop\nX14 : Prop\nHs : not (@eq Thing x x)\n============================\nor (@ex Thing (fun y : Thing => and (or (@eq Thing x y) (clos_trans Thing DependsOn x y)) (DependsOn y y))) (or (@ex Thing (fun y : Thing => and (or (@eq Thing x y) (clos_trans Thing DependsOn x y)) (and (clos_trans Thing DependsOn y y) (not (DependsOn y y))))) (or (@ex (forall _ : Thing, Prop) (fun S : forall _ : Thing, Prop => and (S x) (forall (a : Thing) (_ : S a), @ex Thing (fun b : Thing => and (S b) (DependsOn a b))))) (or (forall y : Thing, not (DependsOn x y)) (@ex Thing (fun y : Thing => and (clos_trans Thing DependsOn x y) (forall z : Thing, not (DependsOn y z)))))))","x : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\nX8 : Prop\nX9 : Prop\nX10 : Prop\nX11 : Prop\nX12 : Prop\nX13 : Prop\nX14 : Prop\n============================\nor (@ex Thing (fun y : Thing => and (or (@eq Thing x y) (clos_trans Thing (fun x0 y0 : Thing => Gives y0 x0) x y)) (and (clos_trans Thing (fun x0 y0 : Thing => Gives y0 x0) y y) (not (Gives y y))))) (or (@ex (forall _ : Thing, Prop) (fun S : forall _ : Thing, Prop => and (S x) (forall (a : Thing) (_ : S a), @ex Thing (fun b : Thing => and (S b) (Gives b a))))) (or (forall y : Thing, not (Gives y x)) (@ex Thing (fun y : Thing => and (clos_trans Thing (fun x0 y0 : Thing => Gives y0 x0) x y) (forall z : Thing, not (Gives z y))))))","x : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\nX8 : Prop\nX9 : Prop\nX10 : Prop\nX11 : Prop\nX12 : Prop\nX13 : Prop\nX14 : Prop\n============================\n@ex Thing (fun y : Thing => and (or (@eq Thing x y) (clos_trans Thing (fun x0 y0 : Thing => Gives y0 x0) x y)) (Gives y y))","x : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\nX8 : Prop\nX9 : Prop\nX10 : Prop\nX11 : Prop\nX12 : Prop\nX13 : Prop\nX14 : Prop\nH : not (or (@ex Thing (fun y : Thing => and (or (@eq Thing x y) (clos_trans Thing (fun x0 y0 : Thing => Gives y0 x0) x y)) (Gives y y))) (or (@ex Thing (fun y : Thing => and (or (@eq Thing x y) (clos_trans Thing (fun x0 y0 : Thing => Gives y0 x0) x y)) (and (clos_trans Thing (fun x0 y0 : Thing => Gives y0 x0) y y) (not (Gives y y))))) (or (@ex (forall _ : Thing, Prop) (fun S : forall _ : Thing, Prop => and (S x) (forall (a : Thing) (_ : S a), @ex Thing (fun b : Thing => and (S b) (Gives b a))))) (or (forall y : Thing, not (Gives y x)) (@ex Thing (fun y : Thing => and (clos_trans Thing (fun x0 y0 : Thing => Gives y0 x0) x y) (forall z : Thing, not (Gives z y))))))))\n============================\nFalse","x : Thing\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\nX8 : Prop\nX9 : Prop\nX10 : Prop\nX11 : Prop\nX12 : Prop\nX13 : Prop\nX14 : 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even after head-reduction."},{"g":45,"t":"generalize (clos_trans DependsOn x)","w":"model","ok":false,"err":"rejected"},{"g":46,"t":"assumption","w":"auto","ok":false,"err":"Error: No such assumption."},{"g":46,"t":"tauto","w":"auto","ok":false,"err":"Error: Tactic failure: Classical tauto failed."},{"g":46,"t":"firstorder","w":"auto","ok":true,"c":[95]},{"g":46,"t":"congruence","w":"auto","ok":false,"err":"Error: Tactic failure: congruence failed."},{"g":46,"t":"hammer","w":"hammer","ok":false,"err":"Error: Hammer failed: ATPs failed to f"},{"g":46,"t":"right","w":"model","ok":true,"c":[103]},{"g":46,"t":"left","w":"model","ok":true,"c":[104]},{"g":46,"t":"apply NNPP; intro","w":"model","ok":true,"c":[105]},{"g":46,"t":"right; intros","w":"model","ok":true,"c":[103]},{"g":46,"t":"left; intros","w":"model","ok":true,"c":[104]},{"g":46,"t":"assert (Gives x x)","w":"model","ok":true,"c":[106,107]},{"g":107,"t":"firstorder","w":"auto","ok":true,"c":[],"eager":true},{"g":46,"t":"destruct (classic (Gives x x)) as [Hs|Hs]","w":"model","ok":true,"c":[108,109]},{"g":108,"t":"firstorder","w":"auto","ok":true,"c":[],"eager":true}],"proof":[],"proofFile":null},{"key":"round6/kalima_unconditional","id":"kalima_unconditional","run":"round6","title":"Dalīl al-kalima, the conclusion without the “if”","english":"Something in the universe has a giver of existence that is necessary and depends on nothing.","stmt":"MP001 -> MP002 -> MP003 -> OP001 -> MP008 -> OP006 -> exists x b, InUniverse x /\\ Gives b x /\\ Exists b /\\ Necessary b /\\ Independent b","proved":false,"script":"","seconds":901.6,"expansions":13,"calls":690,"root":0,"goals":["============================\nMP001 -> MP002 -> MP003 -> OP001 -> MP008 -> OP006 -> exists x b, InUniverse x /\\ Gives b x /\\ Exists b /\\ Necessary b /\\ Independent b","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : OP001\nH3 : MP008\nx : Thing\nH5 : Exists x\nH6 : not (Ess x)\nH4 : @eq Thing x Universe\n============================\n@ex Thing (fun x0 : Thing => @ex Thing (fun b : Thing => and (InUniverse x0) (and (Gives b x0) (and (Exists b) (and (Necessary b) (Independent b))))))","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : OP001\nH3 : MP008\nx : Thing\nH5 : Exists x\nH6 : not (Ess x)\nH4 : PartOf x Universe\n============================\n@ex Thing (fun x0 : Thing => @ex Thing (fun b : Thing => and (InUniverse x0) (and (Gives b x0) (and (Exists b) (and (Necessary b) (Independent b))))))","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (x y : Thing) (_ : Gives y x), OfItself y\nH3 : forall (x : Thing) (_ : Exists x) (_ : not (ThroughAnother x)), Ess x\nx : Thing\nH5 : Exists x\nH6 : not (Ess x)\nH4 : @eq Thing x Universe\n============================\n@ex Thing (fun x0 : Thing => @ex Thing (fun b : Thing => and (or (@eq Thing x0 Universe) (PartOf x0 Universe)) (and (Gives b x0) (and (Exists b) (and (and (Exists b) (Ess b)) (forall y : Thing, not (DependsOn b y)))))))","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (x y : Thing) (_ : Gives y x), OfItself y\nH3 : forall (x : Thing) (_ : Exists x) (_ : not (ThroughAnother x)), Ess x\nx : Thing\nH5 : Exists x\nH6 : not (Ess x)\nH4 : PartOf x Universe\n============================\n@ex Thing (fun x0 : Thing => @ex Thing (fun b : Thing => and (or (@eq Thing x0 Universe) (PartOf x0 Universe)) (and (Gives b x0) (and (Exists b) (and (and (Exists b) (Ess b)) (forall y : Thing, not (DependsOn b y)))))))","H : not (forall (_ : MP001) (_ : MP002) (_ : MP003) (_ : OP001) (_ : MP008) (_ : OP006), @ex Thing (fun x : Thing => @ex Thing (fun b : Thing => and (InUniverse x) (and (Gives b x) (and (Exists b) (and (Necessary b) (Independent b)))))))\n============================\nFalse","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : OP001\nH3 : MP008\nx : Thing\nH5 : Exists x\nH6 : not (Ess x)\nH4 : @eq Thing x Universe\n============================\n@ex Thing (fun b : Thing => and (InUniverse x) (and (Gives b x) (and (Exists b) (and (Necessary b) (Independent b)))))","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : OP001\nH3 : MP008\nx : Thing\nH5 : Exists x\nH6 : not (Ess x)\nH4 : @eq Thing x Universe\n============================\n@ex Thing (fun b : Thing => and (InUniverse Universe) (and (Gives b Universe) (and (Exists b) (and (Necessary b) (Independent b)))))","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : OP001\nH3 : MP008\nx : Thing\nH5 : Exists x\nH6 : not (Ess x)\nH4 : @eq Thing x Universe\n============================\nInUniverse x","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : OP001\nH3 : MP008\nx : Thing\nH5 : Exists x\nH6 : not (Ess x)\nH4 : @eq Thing x Universe\n============================\nand (Gives Universe x) (and (Exists Universe) (and (Necessary Universe) (Independent Universe)))","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : OP001\nH3 : MP008\nx : Thing\nH5 : Exists x\nH6 : not (Ess x)\nH4 : @eq Thing x Universe\n============================\nGives Universe x","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : OP001\nH3 : MP008\nx : Thing\nH5 : Exists x\nH6 : not (Ess x)\nH4 : @eq Thing x Universe\n============================\nExists Universe","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : OP001\nH3 : MP008\nx : Thing\nH5 : Exists x\nH6 : not (Ess x)\nH4 : @eq Thing x Universe\n============================\nEss Universe","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : OP001\nH3 : MP008\nx : Thing\nH5 : Exists x\nH6 : not (Ess x)\nH4 : @eq Thing x Universe\n============================\nIndependent Universe","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : OP001\nH3 : MP008\nx : Thing\nH5 : Exists x\nH6 : not (Ess x)\nH4 : PartOf x Universe\n============================\n@ex Thing (fun b : Thing => and (InUniverse x) (and (Gives b x) (and (Exists b) (and (Necessary b) (Independent b)))))","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : OP001\nH3 : MP008\nx : Thing\nH5 : Exists x\nH6 : not (Ess x)\nH4 : PartOf x Universe\n============================\nInUniverse x","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : OP001\nH3 : MP008\nx : Thing\nH5 : Exists x\nH6 : not (Ess x)\nH4 : PartOf x Universe\n============================\nand (Gives Universe x) (and (Exists Universe) (and (Necessary Universe) (Independent Universe)))","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : OP001\nH3 : MP008\nx : Thing\nH5 : Exists x\nH6 : not (Ess x)\nH4 : PartOf x Universe\n============================\nGives Universe x","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : OP001\nH3 : MP008\nx : Thing\nH5 : Exists x\nH6 : not (Ess x)\nH4 : PartOf x Universe\n============================\nExists Universe","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : OP001\nH3 : MP008\nx : Thing\nH5 : Exists x\nH6 : not (Ess x)\nH4 : PartOf x Universe\n============================\nEss Universe","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : OP001\nH3 : MP008\nx : Thing\nH5 : Exists x\nH6 : not (Ess x)\nH4 : PartOf x Universe\n============================\nIndependent Universe","x : Thing\n============================\n@ex Thing (fun b : Thing => and (InUniverse x) (and (Gives b x) (and (Exists b) (and (Necessary b) (Independent b)))))","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (x y : Thing) (_ : Gives y x), and (Exists y) (not (ThroughAnother y))\nH3 : forall (x : Thing) (_ : Exists x) (_ : not (@ex Thing (fun y : Thing => Gives y x))), Ess x\nx : Thing\nH5 : Exists x\nH6 : not (Ess x)\nH4 : @eq Thing x Universe\n============================\n@ex Thing (fun x0 : Thing => @ex Thing (fun b : Thing => and (or (@eq Thing x0 Universe) (PartOf x0 Universe)) (and (Gives b x0) (and (Exists b) (and (and (Exists b) (Ess b)) (forall y : Thing, not (Gives y b)))))))","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (x y : Thing) (_ : Gives y x), OfItself y\nH3 : forall (x : Thing) (_ : Exists x) (_ : not (ThroughAnother x)), Ess x\nx : Thing\nH5 : Exists x\nH6 : not (Ess x)\nH4 : @eq Thing x Universe\n============================\n@ex Thing (fun b : Thing => and (or (@eq Thing x Universe) (PartOf x Universe)) (and (Gives b x) (and (Exists b) (and (and (Exists b) (Ess b)) (forall y : Thing, not (DependsOn b y))))))","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (x y : Thing) (_ : Gives y x), OfItself y\nH3 : forall (x : Thing) (_ : Exists x) (_ : not (ThroughAnother x)), Ess x\nx : Thing\nH5 : Exists x\nH6 : not (Ess x)\nH4 : @eq Thing x Universe\n============================\nor (@eq Thing x Universe) (PartOf x Universe)","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (x y : Thing) (_ : Gives y x), OfItself y\nH3 : forall (x : Thing) (_ : Exists x) (_ : not (ThroughAnother x)), Ess x\nx : Thing\nH5 : Exists x\nH6 : not (Ess x)\nH4 : @eq Thing x Universe\n============================\nand (Gives Universe x) (and (Exists Universe) (and (and (Exists Universe) (Ess Universe)) (forall y : Thing, not (DependsOn Universe y))))","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (x y : Thing) (_ : Gives y x), OfItself y\nH3 : forall (x : Thing) (_ : Exists x) (_ : not (ThroughAnother x)), Ess x\nx : Thing\nH5 : Exists x\nH6 : not (Ess x)\nH4 : @eq Thing x Universe\n============================\nGives x Universe","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (x y : Thing) (_ : Gives y x), OfItself y\nH3 : forall (x : Thing) (_ : Exists x) (_ : not (ThroughAnother x)), Ess x\nx : Thing\nH5 : Exists x\nH6 : not (Ess x)\nH4 : @eq Thing x Universe\nH7 : Gives x Universe\n============================\n@ex Thing (fun x0 : Thing => @ex Thing (fun b : Thing => and (or (@eq Thing x0 Universe) (PartOf x0 Universe)) (and (Gives b x0) (and (Exists b) (and (and (Exists b) (Ess b)) (forall y : Thing, not (DependsOn b y)))))))","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (x y : Thing) (_ : Gives y x), OfItself y\nH3 : forall (x : Thing) (_ : Exists x) (_ : not (ThroughAnother x)), Ess x\nx : Thing\nH5 : Exists x\nH6 : not (Ess x)\nH4 : @eq Thing x Universe\nHs : Gives x Universe\n============================\n@ex Thing (fun x0 : Thing => @ex Thing (fun b : Thing => and (or (@eq Thing x0 Universe) (PartOf x0 Universe)) (and (Gives b x0) (and (Exists b) (and (and (Exists b) (Ess b)) (forall y : Thing, not (DependsOn b y)))))))","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (x y : Thing) (_ : Gives y x), OfItself y\nH3 : forall (x : Thing) (_ : Exists x) (_ : not (ThroughAnother x)), Ess x\nx : Thing\nH5 : Exists x\nH6 : not (Ess x)\nH4 : @eq Thing x Universe\nHs : not (Gives x Universe)\n============================\n@ex Thing (fun x0 : Thing => @ex Thing (fun b : Thing => and (or (@eq Thing x0 Universe) (PartOf x0 Universe)) (and (Gives b x0) (and (Exists b) (and (and (Exists b) (Ess b)) (forall y : Thing, not (DependsOn b y)))))))","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (x y : Thing) (_ : Gives y x), OfItself y\nH3 : forall (x : Thing) (_ : Exists x) (_ : not (ThroughAnother x)), Ess x\nx : Thing\nH5 : Exists x\nH6 : not (Ess x)\nH4 : @eq Thing x Universe\n============================\nand (or (@eq Thing x Universe) (PartOf x Universe)) (and (Gives Universe x) (and (Exists Universe) (and (and (Exists Universe) (Ess Universe)) (forall y : Thing, not (DependsOn Universe y)))))","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (x y : Thing) (_ : Gives y x), and (Exists y) (not (ThroughAnother y))\nH3 : forall (x : Thing) (_ : Exists x) (_ : not (@ex Thing (fun y : Thing => Gives y x))), Ess x\nx : Thing\nH5 : Exists x\nH6 : not (Ess x)\nH4 : PartOf x Universe\n============================\n@ex Thing (fun x0 : Thing => @ex Thing (fun b : Thing => and (or (@eq Thing x0 Universe) (PartOf x0 Universe)) (and (Gives b x0) (and (Exists b) (and (and (Exists b) (Ess b)) (forall y : Thing, not (Gives y b)))))))","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (x y : Thing) (_ : Gives y x), OfItself y\nH3 : forall (x : Thing) (_ : Exists x) (_ : not (ThroughAnother x)), Ess x\nx : Thing\nH5 : Exists x\nH6 : not (Ess x)\nH4 : PartOf x Universe\n============================\n@ex Thing (fun b : Thing => and (or (@eq Thing x Universe) (PartOf x Universe)) (and (Gives b x) (and (Exists b) (and (and (Exists b) (Ess b)) (forall y : Thing, not (DependsOn b y))))))","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (x y : Thing) (_ : Gives y x), OfItself y\nH3 : forall (x : Thing) (_ : Exists x) (_ : not (ThroughAnother x)), Ess x\nx : Thing\nH5 : Exists x\nH6 : not (Ess x)\nH4 : PartOf x Universe\n============================\nor (@eq Thing x Universe) (PartOf x Universe)","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (x y : Thing) (_ : Gives y x), OfItself y\nH3 : forall (x : Thing) (_ : Exists x) (_ : not (ThroughAnother x)), Ess x\nx : Thing\nH5 : Exists x\nH6 : not (Ess x)\nH4 : PartOf x Universe\n============================\nand (Gives Universe x) (and (Exists Universe) (and (and (Exists Universe) (Ess Universe)) (forall y : Thing, not (DependsOn Universe y))))","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (x y : Thing) (_ : Gives y x), and (Exists y) (not (@ex Thing (fun y0 : Thing => Gives y0 y)))\nH3 : forall (x : Thing) (_ : Exists x) (_ : not (@ex Thing (fun y : Thing => Gives y x))), Ess x\nx : Thing\nH5 : Exists x\nH6 : not (Ess x)\nH4 : @eq Thing x Universe\n============================\n@ex Thing (fun x0 : Thing => @ex Thing (fun b : Thing => and (or (@eq Thing x0 Universe) (PartOf x0 Universe)) (and (Gives b x0) (and (Exists b) (and (and (Exists b) (Ess b)) (forall y : Thing, not (Gives y b)))))))","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (x y : Thing) (_ : Gives y x), and (Exists y) (not (ThroughAnother y))\nH3 : forall (x : Thing) (_ : Exists x) (_ : not (@ex Thing (fun y : Thing => Gives y x))), Ess x\nx : Thing\nH5 : Exists x\nH6 : not (Ess x)\nH4 : @eq Thing x Universe\n============================\n@ex Thing (fun b : Thing => and (or (@eq Thing x Universe) (PartOf x Universe)) (and (Gives b x) (and (Exists b) (and (and (Exists b) (Ess b)) (forall y : Thing, not (Gives y b))))))","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (x y : Thing) (_ : Gives y x), and (Exists y) (not (ThroughAnother y))\nH3 : forall (x : Thing) (_ : Exists x) (_ : not (@ex Thing (fun y : Thing => Gives y x))), Ess x\nx : Thing\nH5 : Exists x\nH6 : not (Ess x)\nH4 : @eq Thing x Universe\n============================\nor (@eq Thing x Universe) (PartOf x Universe)","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (x y : Thing) (_ : Gives y x), and (Exists y) (not (ThroughAnother y))\nH3 : forall (x : Thing) (_ : Exists x) (_ : not (@ex Thing (fun y : Thing => Gives y x))), Ess x\nx : Thing\nH5 : Exists x\nH6 : not (Ess x)\nH4 : @eq Thing x Universe\n============================\nand (Gives Universe x) (and (Exists Universe) (and (and (Exists Universe) (Ess Universe)) (forall y : Thing, not (Gives y Universe))))","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (x y : Thing) (_ : Gives y x), and (Exists y) (not (ThroughAnother y))\nH3 : forall (x : Thing) (_ : Exists x) (_ : not (@ex Thing (fun y : Thing => Gives y x))), Ess x\nx : Thing\nH5 : Exists x\nH6 : not (Ess x)\nH4 : @eq Thing x Universe\n============================\nGives x Universe","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (x y : Thing) (_ : Gives y x), and (Exists y) (not (ThroughAnother y))\nH3 : forall (x : Thing) (_ : Exists x) (_ : not (@ex Thing (fun y : Thing => Gives y x))), Ess x\nx : Thing\nH5 : Exists x\nH6 : not (Ess x)\nH4 : @eq Thing x Universe\nH7 : Gives x Universe\n============================\n@ex Thing (fun x0 : Thing => @ex Thing (fun b : Thing => and (or (@eq Thing x0 Universe) (PartOf x0 Universe)) (and (Gives b x0) (and (Exists b) (and (and (Exists b) (Ess b)) (forall y : Thing, not (Gives y b)))))))","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (x y : Thing) (_ : Gives y x), and (Exists y) (not (ThroughAnother y))\nH3 : forall (x : Thing) (_ : Exists x) (_ : not (@ex Thing (fun y : Thing => Gives y x))), Ess x\nx : Thing\nH5 : Exists x\nH6 : not (Ess x)\nH4 : @eq Thing x Universe\nHs : Gives x Universe\n============================\n@ex Thing (fun x0 : Thing => @ex Thing (fun b : Thing => and (or (@eq Thing x0 Universe) (PartOf x0 Universe)) (and (Gives b x0) (and (Exists b) (and (and (Exists b) (Ess b)) (forall y : Thing, not (Gives y b)))))))","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (x y : Thing) (_ : Gives y x), and (Exists y) (not (ThroughAnother y))\nH3 : forall (x : Thing) (_ : Exists x) (_ : not (@ex Thing (fun y : Thing => Gives y x))), Ess x\nx : Thing\nH5 : Exists x\nH6 : not (Ess x)\nH4 : @eq Thing x Universe\nHs : not (Gives x Universe)\n============================\n@ex Thing (fun x0 : Thing => @ex Thing (fun b : Thing => and (or (@eq Thing x0 Universe) (PartOf x0 Universe)) (and (Gives b x0) (and (Exists b) (and (and (Exists b) (Ess b)) (forall y : Thing, not (Gives y b)))))))","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (x y : Thing) (_ : Gives y x), and (Exists y) (not (ThroughAnother y))\nH3 : forall (x : Thing) (_ : Exists x) (_ : not (@ex Thing (fun y : Thing => Gives y x))), Ess x\nx : Thing\nH5 : Exists x\nH6 : not (Ess x)\nH4 : @eq Thing x Universe\n============================\nand (or (@eq Thing x Universe) (PartOf x Universe)) (and (Gives Universe x) (and (Exists Universe) (and (and (Exists Universe) (Ess Universe)) (forall y : Thing, not (Gives y Universe)))))","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (x y : Thing) (_ : Gives y x), and (Exists y) (not (@ex Thing (fun y0 : Thing => Gives y0 y)))\nH3 : forall (x : Thing) (_ : Exists x) (_ : not (@ex Thing (fun y : Thing => Gives y x))), Ess x\nx : Thing\nH5 : Exists x\nH6 : not (Ess x)\nH4 : PartOf x Universe\n============================\n@ex Thing (fun x0 : Thing => @ex Thing (fun b : Thing => and (or (@eq Thing x0 Universe) (PartOf x0 Universe)) (and (Gives b x0) (and (Exists b) (and (and (Exists b) (Ess b)) (forall y : Thing, not (Gives y b)))))))","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (x y : Thing) (_ : Gives y x), and (Exists y) (not (ThroughAnother y))\nH3 : forall (x : Thing) (_ : Exists x) (_ : not (@ex Thing (fun y : Thing => Gives y x))), Ess x\nx : Thing\nH5 : Exists x\nH6 : not (Ess x)\nH4 : PartOf x Universe\n============================\n@ex Thing (fun b : Thing => and (or (@eq Thing x Universe) (PartOf x Universe)) (and (Gives b x) (and (Exists b) (and (and (Exists b) (Ess b)) (forall y : Thing, not (Gives y b))))))","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (x y : Thing) (_ : Gives y x), and (Exists y) (not (ThroughAnother y))\nH3 : forall (x : Thing) (_ : Exists x) (_ : not (@ex Thing (fun y : Thing => Gives y x))), Ess x\nx : Thing\nH5 : Exists x\nH6 : not (Ess x)\nH4 : PartOf x Universe\n============================\nor (@eq Thing x Universe) (PartOf x Universe)","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (x y : Thing) (_ : Gives y x), and (Exists y) (not (ThroughAnother y))\nH3 : forall (x : Thing) (_ : Exists x) (_ : not (@ex Thing (fun y : Thing => Gives y x))), Ess x\nx : Thing\nH5 : Exists x\nH6 : not (Ess x)\nH4 : PartOf x Universe\n============================\nand (Gives Universe x) (and (Exists Universe) (and (and (Exists Universe) (Ess Universe)) (forall y : Thing, not (Gives y Universe))))","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (x y : Thing) (_ : Gives y x), and (Exists y) (not (ThroughAnother y))\nH3 : forall (x : Thing) (_ : Exists x) (_ : not (@ex Thing (fun y : Thing => Gives y x))), Ess x\nx : Thing\nH5 : Exists x\nH6 : not (Ess x)\nH4 : PartOf x Universe\n============================\nGives x x","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (x y : Thing) (_ : Gives y x), and (Exists y) (not (ThroughAnother y))\nH3 : forall (x : Thing) (_ : Exists x) (_ : not (@ex Thing (fun y : Thing => Gives y x))), Ess x\nx : Thing\nH5 : Exists x\nH6 : not (Ess x)\nH4 : PartOf x Universe\nH7 : Gives x x\n============================\n@ex Thing (fun x0 : Thing => @ex Thing (fun b : Thing => and (or (@eq Thing x0 Universe) (PartOf x0 Universe)) (and (Gives b x0) (and (Exists b) (and (and (Exists b) (Ess b)) (forall y : Thing, not (Gives y b)))))))","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (x y : Thing) (_ : Gives y x), and (Exists y) (not (ThroughAnother y))\nH3 : forall (x : Thing) (_ : Exists x) (_ : not (@ex Thing (fun y : Thing => Gives y x))), Ess x\nx : Thing\nH5 : Exists x\nH6 : not (Ess x)\nH4 : PartOf x Universe\nHs : Gives x x\n============================\n@ex Thing (fun x0 : Thing => @ex Thing (fun b : Thing => and (or (@eq Thing x0 Universe) (PartOf x0 Universe)) (and (Gives b x0) (and (Exists b) (and (and (Exists b) (Ess b)) (forall y : Thing, not (Gives y b)))))))","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (x y : Thing) (_ : Gives y x), and (Exists y) (not (ThroughAnother y))\nH3 : forall (x : Thing) (_ : Exists x) (_ : not (@ex Thing (fun y : Thing => Gives y x))), Ess x\nx : Thing\nH5 : Exists x\nH6 : not (Ess x)\nH4 : PartOf x Universe\nHs : not (Gives x x)\n============================\n@ex Thing (fun x0 : Thing => @ex Thing (fun b : Thing => and (or (@eq Thing x0 Universe) (PartOf x0 Universe)) (and (Gives b x0) (and (Exists b) (and (and (Exists b) (Ess b)) (forall y : Thing, not (Gives y b)))))))","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (x y : Thing) (_ : Gives y x), and (Exists y) (not (ThroughAnother y))\nH3 : forall (x : Thing) (_ : Exists x) (_ : not (@ex Thing (fun y : Thing => Gives y x))), Ess x\nx : Thing\nH5 : Exists x\nH6 : not (Ess x)\nH4 : PartOf x Universe\n============================\nGives Universe x","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (x y : Thing) (_ : Gives y x), and (Exists y) (not (ThroughAnother y))\nH3 : forall (x : Thing) (_ : Exists x) (_ : not (@ex Thing (fun y : Thing => Gives y x))), Ess x\nx : Thing\nH5 : Exists x\nH6 : not (Ess x)\nH4 : PartOf x Universe\n============================\nExists Universe","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (x y : Thing) (_ : Gives y x), and (Exists y) (not (ThroughAnother y))\nH3 : forall (x : Thing) (_ : Exists x) (_ : not (@ex Thing (fun y : Thing => Gives y x))), Ess x\nx : Thing\nH5 : Exists x\nH6 : not (Ess x)\nH4 : PartOf x Universe\n============================\nEss Universe","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (x y : Thing) (_ : Gives y x), and (Exists y) (not (ThroughAnother y))\nH3 : forall (x : Thing) (_ : Exists x) (_ : not (@ex Thing (fun y : Thing => Gives y x))), Ess x\nx : Thing\nH5 : Exists x\nH6 : not (Ess x)\nH4 : PartOf x Universe\n============================\nforall y : Thing, not (Gives y Universe)","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (x y : Thing) (_ : Gives y x), OfItself y\nH3 : forall (x : Thing) (_ : Exists x) (_ : not (ThroughAnother x)), Ess x\nx : Thing\nH5 : Exists x\nH6 : not (Ess x)\nH4 : @eq Thing x Universe\n============================\nand (or (@eq Thing x Universe) (PartOf x Universe)) (and (Gives x x) (and (Exists x) (and (and (Exists x) (Ess x)) (forall y : Thing, not (DependsOn x y)))))","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (x y : Thing) (_ : Gives y x), OfItself y\nH3 : forall (x : Thing) (_ : Exists x) (_ : not (ThroughAnother x)), Ess x\nx : Thing\nH5 : Exists x\nH6 : not (Ess x)\nH4 : @eq Thing x Universe\nH7 : Gives x Universe\n============================\n@ex Thing (fun b : Thing => and (or (@eq Thing x Universe) (PartOf x Universe)) (and (Gives b x) (and (Exists b) (and (and (Exists b) (Ess b)) (forall y : Thing, not (DependsOn b y))))))","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (x y : Thing) (_ : Gives y x), OfItself y\nH3 : forall (x : Thing) (_ : Exists x) (_ : not (ThroughAnother x)), Ess x\nx : Thing\nH5 : Exists x\nH6 : not (Ess x)\nH4 : @eq Thing x Universe\nHs : Gives x Universe\n============================\n@ex Thing (fun b : Thing => and (or (@eq Thing x Universe) (PartOf x Universe)) (and (Gives b x) (and (Exists b) (and (and (Exists b) (Ess b)) (forall y : Thing, not (DependsOn b y))))))","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (x y : Thing) (_ : Gives y x), OfItself y\nH3 : forall (x : Thing) (_ : Exists x) (_ : not (ThroughAnother x)), Ess x\nx : Thing\nH5 : Exists x\nH6 : not (Ess x)\nH4 : @eq Thing x Universe\nHs : not (Gives x Universe)\n============================\n@ex Thing (fun b : Thing => and (or (@eq Thing x Universe) (PartOf x Universe)) (and (Gives b x) (and (Exists b) (and (and (Exists b) (Ess b)) (forall y : Thing, not (DependsOn b y))))))","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (x y : Thing) (_ : Gives y x), OfItself y\nH3 : forall (x : Thing) (_ : Exists x) (_ : not (ThroughAnother x)), Ess x\nx : Thing\nH5 : Exists x\nH6 : not (Ess x)\nH4 : @eq Thing x Universe\n============================\nand (Gives x x) (and (Exists x) (and (and (Exists x) (Ess x)) (forall y : Thing, not (DependsOn x y))))","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (x y : Thing) (_ : Gives y x), OfItself y\nH3 : forall (x : Thing) (_ : Exists x) (_ : not (ThroughAnother x)), Ess x\nx : Thing\nH5 : Exists x\nH6 : not (Ess x)\nH4 : PartOf x Universe\n============================\nand (or (@eq Thing x Universe) (PartOf x Universe)) (and (Gives x x) (and (Exists x) (and (and (Exists x) (Ess x)) (forall y : Thing, not (DependsOn x y)))))","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (x y : Thing) (_ : Gives y x), OfItself y\nH3 : forall (x : Thing) (_ : Exists x) (_ : not (ThroughAnother x)), Ess x\nx : Thing\nH5 : Exists x\nH6 : not (Ess x)\nH4 : PartOf x Universe\n============================\nand (Gives x x) (and (Exists x) (and (and (Exists x) (Ess x)) (forall y : Thing, not (DependsOn x y))))","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (x y : Thing) (_ : Gives y x), OfItself y\nH3 : forall (x : Thing) (_ : Exists x) (_ : not (ThroughAnother x)), Ess x\nx : Thing\nH5 : Exists x\nH6 : not (Ess x)\nH4 : PartOf x Universe\n============================\nGives x Universe","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (x y : Thing) (_ : Gives y x), OfItself y\nH3 : forall (x : Thing) (_ : Exists x) (_ : not (ThroughAnother x)), Ess x\nx : Thing\nH5 : Exists x\nH6 : not (Ess x)\nH4 : PartOf x Universe\nH7 : Gives x Universe\n============================\n@ex Thing (fun b : Thing => and (or (@eq Thing x Universe) (PartOf x Universe)) (and (Gives b x) (and (Exists b) (and (and (Exists b) (Ess b)) (forall y : Thing, not (DependsOn b y))))))","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (x y : Thing) (_ : Gives y x), OfItself y\nH3 : forall (x : Thing) (_ : Exists x) (_ : not (ThroughAnother x)), Ess x\nx : Thing\nH5 : Exists x\nH6 : not (Ess x)\nH4 : PartOf x Universe\nHs : Gives x Universe\n============================\n@ex Thing (fun b : Thing => and (or (@eq Thing x Universe) (PartOf x Universe)) (and (Gives b x) (and (Exists b) (and (and (Exists b) (Ess b)) (forall y : Thing, not (DependsOn b y))))))","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (x y : Thing) (_ : Gives y x), OfItself y\nH3 : forall (x : Thing) (_ : Exists x) (_ : not (ThroughAnother x)), Ess x\nx : Thing\nH5 : Exists x\nH6 : not (Ess x)\nH4 : PartOf x Universe\nHs : not (Gives x Universe)\n============================\n@ex Thing (fun b : Thing => and (or (@eq Thing x Universe) (PartOf x Universe)) (and (Gives b x) (and (Exists b) (and (and (Exists b) (Ess b)) (forall y : Thing, not (DependsOn b y))))))","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (x y : Thing) (_ : Gives y x), OfItself y\nH3 : forall (x : Thing) (_ : Exists x) (_ : not (ThroughAnother x)), Ess x\nx : Thing\nH5 : Exists x\nH6 : not (Ess x)\nH4 : PartOf x Universe\n============================\nGives x x","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (x y : Thing) (_ : Gives y x), OfItself y\nH3 : forall (x : Thing) (_ : Exists x) (_ : not (ThroughAnother x)), Ess x\nx : Thing\nH5 : Exists x\nH6 : not (Ess x)\nH4 : PartOf x Universe\nH7 : Gives x x\n============================\n@ex Thing (fun b : Thing => and (or (@eq Thing x Universe) (PartOf x Universe)) (and (Gives b x) (and (Exists b) (and (and (Exists b) (Ess b)) (forall y : Thing, not (DependsOn b y))))))","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (x y : Thing) (_ : Gives y x), OfItself y\nH3 : forall (x : Thing) (_ : Exists x) (_ : not (ThroughAnother x)), Ess x\nx : Thing\nH5 : Exists x\nH6 : not (Ess x)\nH4 : PartOf x Universe\nHs : Gives x x\n============================\n@ex Thing (fun b : Thing => and (or (@eq Thing x Universe) (PartOf x Universe)) (and (Gives b x) (and (Exists b) (and (and (Exists b) (Ess b)) (forall y : Thing, not (DependsOn b y))))))","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (x y : Thing) (_ : Gives y x), OfItself y\nH3 : forall (x : Thing) (_ : Exists x) (_ : not (ThroughAnother x)), Ess x\nx : Thing\nH5 : Exists x\nH6 : not (Ess x)\nH4 : PartOf x Universe\nHs : not (Gives x x)\n============================\n@ex Thing (fun b : Thing => and (or (@eq Thing x Universe) (PartOf x Universe)) (and (Gives b x) (and (Exists b) (and (and (Exists b) (Ess b)) (forall y : Thing, not (DependsOn b y))))))","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : OP001\nH3 : MP008\nx : Thing\nH5 : Exists x\nH6 : not (Ess x)\nH4 : @eq Thing x Universe\n============================\nand (InUniverse x) (and (Gives Universe x) (and (Exists Universe) (and (Necessary Universe) (Independent Universe))))","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : OP001\nH3 : MP008\nx : Thing\nH5 : Exists x\nH6 : not (Ess x)\nH4 : @eq Thing x Universe\n============================\nand (InUniverse x) (and (Gives x x) (and (Exists x) (and (Necessary x) (Independent x))))","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (x y : Thing) (_ : Gives y x), and (Exists y) (not (@ex Thing (fun y0 : Thing => Gives y0 y)))\nH3 : forall (x : Thing) (_ : Exists x) (_ : not (@ex Thing (fun y : Thing => Gives y x))), Ess x\nx : Thing\nH5 : Exists x\nH6 : not (Ess x)\nH4 : @eq Thing x Universe\n============================\n@ex Thing (fun b : Thing => and (or (@eq Thing x Universe) (PartOf x Universe)) (and (Gives b x) (and (Exists b) (and (and (Exists b) (Ess b)) (forall y : Thing, not (Gives y b))))))","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (x y : Thing) (_ : Gives y x), and (Exists y) (not (@ex Thing (fun y0 : Thing => Gives y0 y)))\nH3 : forall (x : Thing) (_ : Exists x) (_ : not (@ex Thing (fun y : Thing => Gives y x))), Ess x\nx : Thing\nH5 : Exists x\nH6 : not (Ess x)\nH4 : @eq Thing x Universe\n============================\nor (@eq Thing x Universe) (PartOf x Universe)","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (x y : Thing) (_ : Gives y x), and (Exists y) (not (@ex Thing (fun y0 : Thing => Gives y0 y)))\nH3 : forall (x : Thing) (_ : Exists x) (_ : not (@ex Thing (fun y : Thing => Gives y x))), Ess x\nx : Thing\nH5 : Exists x\nH6 : not (Ess x)\nH4 : @eq Thing x Universe\n============================\nand (Gives Universe x) (and (Exists Universe) (and (and (Exists Universe) (Ess Universe)) (forall y : Thing, not (Gives y Universe))))","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (x y : Thing) (_ : Gives y x), and (Exists y) (not (@ex Thing (fun y0 : Thing => Gives y0 y)))\nH3 : forall (x : Thing) (_ : Exists x) (_ : not (@ex Thing (fun y : Thing => Gives y x))), Ess x\nx : Thing\nH5 : Exists x\nH6 : not (Ess x)\nH4 : @eq Thing x Universe\n============================\nGives x Universe","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (x y : Thing) (_ : Gives y x), and (Exists y) (not (@ex Thing (fun y0 : Thing => Gives y0 y)))\nH3 : forall (x : Thing) (_ : Exists x) (_ : not (@ex Thing (fun y : Thing => Gives y x))), Ess x\nx : Thing\nH5 : Exists x\nH6 : not (Ess x)\nH4 : @eq Thing x Universe\nH7 : Gives x Universe\n============================\n@ex Thing (fun x0 : Thing => @ex Thing (fun b : Thing => and (or (@eq Thing x0 Universe) (PartOf x0 Universe)) (and (Gives b x0) (and (Exists b) (and (and (Exists b) (Ess b)) (forall y : Thing, not (Gives y b)))))))","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (x y : Thing) (_ : Gives y x), and (Exists y) (not (@ex Thing (fun y0 : Thing => Gives y0 y)))\nH3 : forall (x : Thing) (_ : Exists x) (_ : not (@ex Thing (fun y : Thing => Gives y x))), Ess x\nx : Thing\nH5 : Exists x\nH6 : not (Ess x)\nH4 : @eq Thing x Universe\nHs : Gives x Universe\n============================\n@ex Thing (fun x0 : Thing => @ex Thing (fun b : Thing => and (or (@eq Thing x0 Universe) (PartOf x0 Universe)) (and (Gives b x0) (and (Exists b) (and (and (Exists b) (Ess b)) (forall y : Thing, not (Gives y b)))))))","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (x y : Thing) (_ : Gives y x), and (Exists y) (not (@ex Thing (fun y0 : Thing => Gives y0 y)))\nH3 : forall (x : Thing) (_ : Exists x) (_ : not (@ex Thing (fun y : Thing => Gives y x))), Ess x\nx : Thing\nH5 : Exists x\nH6 : not (Ess x)\nH4 : @eq Thing x Universe\nHs : not (Gives x Universe)\n============================\n@ex Thing (fun x0 : Thing => @ex Thing (fun b : Thing => and (or (@eq Thing x0 Universe) (PartOf x0 Universe)) (and (Gives b x0) (and (Exists b) (and (and (Exists b) (Ess b)) (forall y : Thing, not (Gives y b)))))))","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (x y : Thing) (_ : Gives y x), and (Exists y) (not (@ex Thing (fun y0 : Thing => Gives y0 y)))\nH3 : forall (x : Thing) (_ : Exists x) (_ : not (@ex Thing (fun y : Thing => Gives y x))), Ess x\nx : Thing\nH5 : Exists x\nH6 : not (Ess x)\nH4 : @eq Thing x Universe\n============================\nand (or (@eq Thing x Universe) (PartOf x Universe)) (and (Gives Universe x) (and (Exists Universe) (and (and (Exists Universe) (Ess Universe)) (forall y : Thing, not (Gives y Universe)))))","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (x y : Thing) (_ : Gives y x), and (Exists y) (not (@ex Thing (fun y0 : Thing => Gives y0 y)))\nH3 : forall (x : Thing) (_ : Exists x) (_ : not (@ex Thing (fun y : Thing => Gives y x))), Ess x\nx : Thing\nH5 : Exists x\nH6 : not (Ess x)\nH4 : @eq Thing x Universe\n============================\nGives x x","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (x y : Thing) (_ : Gives y x), and (Exists y) (not (@ex Thing (fun y0 : Thing => Gives y0 y)))\nH3 : forall (x : Thing) (_ : Exists x) (_ : not (@ex Thing (fun y : Thing => Gives y x))), Ess x\nx : Thing\nH5 : Exists x\nH6 : not (Ess x)\nH4 : @eq Thing x Universe\nH7 : Gives x x\n============================\n@ex Thing (fun x0 : Thing => @ex Thing (fun b : Thing => and (or (@eq Thing x0 Universe) (PartOf x0 Universe)) (and (Gives b x0) (and (Exists b) (and (and (Exists b) (Ess b)) (forall y : Thing, not (Gives y b)))))))","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (x y : Thing) (_ : Gives y x), and (Exists y) (not (@ex Thing (fun y0 : Thing => Gives y0 y)))\nH3 : forall (x : Thing) (_ : Exists x) (_ : not (@ex Thing (fun y : Thing => Gives y x))), Ess x\nx : Thing\nH5 : Exists x\nH6 : not (Ess x)\nH4 : @eq Thing x Universe\nHs : Gives x x\n============================\n@ex Thing (fun x0 : Thing => @ex Thing (fun b : Thing => and (or (@eq Thing x0 Universe) (PartOf x0 Universe)) (and (Gives b x0) (and (Exists b) (and (and (Exists b) (Ess b)) (forall y : Thing, not (Gives y b)))))))","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (x y : Thing) (_ : Gives y x), and (Exists y) (not (@ex Thing (fun y0 : Thing => Gives y0 y)))\nH3 : forall (x : Thing) (_ : Exists x) (_ : not (@ex Thing (fun y : Thing => Gives y x))), Ess x\nx : Thing\nH5 : Exists x\nH6 : not (Ess x)\nH4 : @eq Thing x Universe\nHs : not (Gives x x)\n============================\n@ex Thing (fun x0 : Thing => @ex Thing (fun b : Thing => and (or (@eq Thing x0 Universe) (PartOf x0 Universe)) (and (Gives b x0) (and (Exists b) (and (and (Exists b) (Ess b)) (forall y : Thing, not (Gives y b)))))))","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (x y : Thing) (_ : Gives y x), and (Exists y) (not (@ex Thing (fun y0 : Thing => Gives y0 y)))\nH3 : forall (x : Thing) (_ : Exists x) (_ : not (@ex Thing (fun y : Thing => Gives y x))), Ess x\nx : Thing\nH5 : Exists x\nH6 : not (Ess x)\nH4 : PartOf x Universe\n============================\n@ex Thing (fun b : Thing => and (or (@eq Thing x Universe) (PartOf x Universe)) (and (Gives b x) (and (Exists b) (and (and (Exists b) (Ess b)) (forall y : Thing, not (Gives y b))))))","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (x y : Thing) (_ : Gives y x), and (Exists y) (not (@ex Thing (fun y0 : Thing => Gives y0 y)))\nH3 : forall (x : Thing) (_ : Exists x) (_ : not (@ex Thing (fun y : Thing => Gives y x))), Ess x\nx : Thing\nH5 : Exists x\nH6 : not (Ess x)\nH4 : PartOf x Universe\n============================\nor (@eq Thing x Universe) (PartOf x Universe)","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (x y : Thing) (_ : Gives y x), and (Exists y) (not (@ex Thing (fun y0 : Thing => Gives y0 y)))\nH3 : forall (x : Thing) (_ : Exists x) (_ : not (@ex Thing (fun y : Thing => Gives y x))), Ess x\nx : Thing\nH5 : Exists x\nH6 : not (Ess x)\nH4 : PartOf x Universe\n============================\nand (Gives Universe x) (and (Exists Universe) (and (and (Exists Universe) (Ess Universe)) (forall y : Thing, not (Gives y Universe))))","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (x y : Thing) (_ : Gives y x), and (Exists y) (not (@ex Thing (fun y0 : Thing => Gives y0 y)))\nH3 : forall (x : Thing) (_ : Exists x) (_ : not (@ex Thing (fun y : Thing => Gives y x))), Ess x\nx : Thing\nH5 : Exists x\nH6 : not (Ess x)\nH4 : PartOf x Universe\n============================\nGives x x","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (x y : Thing) (_ : Gives y x), and (Exists y) (not (@ex Thing (fun y0 : Thing => Gives y0 y)))\nH3 : forall (x : Thing) (_ : Exists x) (_ : not (@ex Thing (fun y : Thing => Gives y x))), Ess x\nx : Thing\nH5 : Exists x\nH6 : not (Ess x)\nH4 : PartOf x Universe\nH7 : Gives x x\n============================\n@ex Thing (fun x0 : Thing => @ex Thing (fun b : Thing => and (or (@eq Thing x0 Universe) (PartOf x0 Universe)) (and (Gives b x0) (and (Exists b) (and (and (Exists b) (Ess b)) (forall y : Thing, not (Gives y b)))))))","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (x y : Thing) (_ : Gives y x), and (Exists y) (not (@ex Thing (fun y0 : Thing => Gives y0 y)))\nH3 : forall (x : Thing) (_ : Exists x) (_ : not (@ex Thing (fun y : Thing => Gives y x))), Ess x\nx : Thing\nH5 : Exists x\nH6 : not (Ess x)\nH4 : PartOf x Universe\nHs : Gives x x\n============================\n@ex Thing (fun x0 : Thing => @ex Thing (fun b : Thing => and (or (@eq Thing x0 Universe) (PartOf x0 Universe)) (and (Gives b x0) (and (Exists b) (and (and (Exists b) (Ess b)) (forall y : Thing, not (Gives y b)))))))","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (x y : Thing) (_ : Gives y x), and (Exists y) (not (@ex Thing (fun y0 : Thing => Gives y0 y)))\nH3 : forall (x : Thing) (_ : Exists x) (_ : not (@ex Thing (fun y : Thing => Gives y x))), Ess x\nx : Thing\nH5 : Exists x\nH6 : not (Ess x)\nH4 : PartOf x Universe\nHs : not (Gives x x)\n============================\n@ex Thing (fun x0 : Thing => @ex Thing (fun b : Thing => and (or (@eq Thing x0 Universe) (PartOf x0 Universe)) (and (Gives b x0) (and (Exists b) (and (and (Exists b) (Ess b)) (forall y : Thing, not (Gives y b)))))))","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (x y : Thing) (_ : Gives y x), and (Exists y) (not (@ex Thing (fun y0 : Thing => Gives y0 y)))\nH3 : forall (x : Thing) (_ : Exists x) (_ : not (@ex Thing (fun y : Thing => Gives y x))), Ess x\nx : Thing\nH5 : Exists x\nH6 : not (Ess x)\nH4 : PartOf x Universe\n============================\nGives Universe x","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (x y : Thing) (_ : Gives y x), and (Exists y) (not (@ex Thing (fun y0 : Thing => Gives y0 y)))\nH3 : forall (x : Thing) (_ : Exists x) (_ : not (@ex Thing (fun y : Thing => Gives y x))), Ess x\nx : Thing\nH5 : Exists x\nH6 : not (Ess x)\nH4 : PartOf x Universe\n============================\nExists Universe","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (x y : Thing) (_ : Gives y x), and (Exists y) (not (@ex Thing (fun y0 : Thing => Gives y0 y)))\nH3 : forall (x : Thing) (_ : Exists x) (_ : not (@ex Thing (fun y : Thing => Gives y x))), Ess x\nx : Thing\nH5 : Exists x\nH6 : not (Ess x)\nH4 : PartOf x Universe\n============================\nEss Universe","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (x y : Thing) (_ : Gives y x), and (Exists y) (not (@ex Thing (fun y0 : Thing => Gives y0 y)))\nH3 : forall (x : Thing) (_ : Exists x) (_ : not (@ex Thing (fun y : Thing => Gives y x))), Ess x\nx : Thing\nH5 : Exists x\nH6 : not (Ess x)\nH4 : PartOf x Universe\n============================\nforall y : Thing, not (Gives y Universe)"],"events":[{"g":0,"t":"assumption","w":"auto","ok":false,"err":"Error: No such assumption."},{"g":0,"t":"tauto","w":"auto","ok":false,"err":"Error: Tactic failure: Classical tauto failed."},{"g":0,"t":"firstorder","w":"auto","ok":true,"c":[1,2]},{"g":0,"t":"congruence","w":"auto","ok":false,"err":"Error: Tactic failure: congruence failed."},{"g":0,"t":"unfold Necessary, InUniverse, MP001, MP002, MP003, MP008, OP001, OP006, Independent in *; firstorder","w":"auto","ok":true,"c":[3,4]},{"g":0,"t":"unfold Necessary, InUniverse, MP001, MP002, MP003, MP008, OP001, OP006, Independent in *; hammer","w":"hammer","ok":false,"err":"rejected"},{"g":0,"t":"apply NNPP; intro","w":"model","ok":true,"c":[5]},{"g":0,"t":"right","w":"model","ok":false,"err":"Error: Not an inductive goal with 2 constructors."},{"g":0,"t":"exists OP006","w":"model","ok":false,"err":"rejected"},{"g":0,"t":"split","w":"model","ok":false,"err":"Error: Unable to find an instance for the variable x."},{"g":0,"t":"apply MP003; intro","w":"model","ok":false,"err":"Error: Applied theorem does not have enough premises."},{"g":0,"t":"exists x","w":"model","ok":false,"err":"Error: The variable x was not found in the current environment."},{"g":0,"t":"exists OP001","w":"model","ok":false,"err":"rejected"},{"g":0,"t":"exists MP008","w":"model","ok":false,"err":"rejected"},{"g":1,"t":"assumption","w":"auto","ok":false,"err":"Error: No such assumption."},{"g":1,"t":"tauto","w":"auto","ok":false,"err":"Error: Tactic failure: Classical tauto failed."},{"g":1,"t":"firstorder","w":"auto","ok":true,"c":[1]},{"g":1,"t":"congruence","w":"auto","ok":false,"err":"Error: Tactic failure: congruence failed."},{"g":1,"t":"unfold Necessary, InUniverse, MP001, MP002, MP003, MP008, OP001, Independent in *; firstorder","w":"auto","ok":true,"c":[3]},{"g":1,"t":"unfold Necessary, InUniverse, MP001, MP002, MP003, MP008, OP001, Independent in *; hammer","w":"hammer","ok":false,"err":"Error: Hammer failed: ATPs failed to f"},{"g":1,"t":"exists x","w":"model","ok":true,"c":[6]},{"g":1,"t":"exists Universe","w":"model","ok":true,"c":[7]},{"g":1,"t":"exists x; exists Universe; split","w":"model","ok":true,"c":[8,9]},{"g":8,"t":"firstorder","w":"auto","ok":true,"c":[],"eager":true},{"g":1,"t":"exists H3","w":"model","ok":false,"err":"rejected"},{"g":1,"t":"exists x; exists Universe; split; trivial","w":"model","ok":true,"c":[8,9]},{"g":1,"t":"exists x; exists Universe; repeat split","w":"model","ok":true,"c":[8,10,11,11,12,13]},{"g":11,"t":"congruence","w":"auto","ok":true,"c":[],"eager":true},{"g":11,"t":"congruence","w":"auto","ok":true,"c":[],"eager":true},{"g":2,"t":"assumption","w":"auto","ok":false,"err":"Error: No such assumption."},{"g":2,"t":"tauto","w":"auto","ok":false,"err":"Error: Tactic failure: Classical tauto failed."},{"g":2,"t":"firstorder","w":"auto","ok":true,"c":[2]},{"g":2,"t":"congruence","w":"auto","ok":false,"err":"Error: Tactic failure: congruence failed."},{"g":2,"t":"unfold Necessary, InUniverse, MP001, MP002, MP003, MP008, OP001, Independent in *; firstorder","w":"auto","ok":true,"c":[4]},{"g":2,"t":"unfold Necessary, InUniverse, MP001, MP002, MP003, MP008, OP001, Independent in *; hammer","w":"hammer","ok":false,"err":"Error: Hammer failed: ATPs failed to f"},{"g":2,"t":"exists x","w":"model","ok":true,"c":[14]},{"g":2,"t":"exists x; exists Universe; split","w":"model","ok":true,"c":[15,16]},{"g":15,"t":"firstorder","w":"auto","ok":true,"c":[],"eager":true},{"g":2,"t":"exists x; try assumption","w":"model","ok":true,"c":[14]},{"g":2,"t":"exists x; exists Universe; split; trivial","w":"model","ok":true,"c":[15,16]},{"g":2,"t":"exists x; exists Universe; repeat split","w":"model","ok":true,"c":[15,17,18,18,19,20]},{"g":2,"t":"exists x; split","w":"model","ok":false,"err":"Error: Unable to find an instance for the variable x."},{"g":2,"t":"exists x; try easy; clear","w":"model","ok":true,"c":[21]},{"g":3,"t":"assumption","w":"auto","ok":false,"err":"Error: No such assumption."},{"g":3,"t":"tauto","w":"auto","ok":false,"err":"Error: Tactic failure: Classical tauto failed."},{"g":3,"t":"firstorder","w":"auto","ok":true,"c":[3]},{"g":3,"t":"congruence","w":"auto","ok":false,"err":"Error: Tactic failure: congruence failed."},{"g":3,"t":"unfold DependsOn, ThroughAnother, OfItself in *; firstorder","w":"auto","ok":true,"c":[22]},{"g":3,"t":"unfold DependsOn, ThroughAnother, OfItself in *; hammer","w":"hammer","ok":false,"err":"Error: Hammer failed: ATPs failed to f"},{"g":3,"t":"exists x","w":"model","ok":true,"c":[23]},{"g":3,"t":"exists x; exists Universe; split","w":"model","ok":true,"c":[24,25]},{"g":24,"t":"tauto","w":"auto","ok":true,"c":[],"eager":true},{"g":3,"t":"assert (Gives x Universe)","w":"model","ok":true,"c":[26,27]},{"g":3,"t":"destruct (classic (Gives x Universe)) as [Hs|Hs]","w":"model","ok":true,"c":[28,29]},{"g":3,"t":"exists x, Universe","w":"model","ok":true,"c":[30]},{"g":3,"t":"exists y","w":"model","ok":false,"err":"Error: The variable y was not found in the current environment."},{"g":4,"t":"assumption","w":"auto","ok":false,"err":"Error: No such assumption."},{"g":4,"t":"tauto","w":"auto","ok":false,"err":"Error: Tactic failure: Classical tauto failed."},{"g":4,"t":"firstorder","w":"auto","ok":true,"c":[4]},{"g":4,"t":"congruence","w":"auto","ok":false,"err":"Error: Tactic failure: congruence failed."},{"g":4,"t":"unfold DependsOn, ThroughAnother, OfItself in *; firstorder","w":"auto","ok":true,"c":[31]},{"g":4,"t":"unfold DependsOn, ThroughAnother, OfItself in *; hammer","w":"hammer","ok":false,"err":"rejected"},{"g":4,"t":"exists x","w":"model","ok":true,"c":[32]},{"g":4,"t":"exists x; exists Universe; split","w":"model","ok":true,"c":[33,34]},{"g":33,"t":"tauto","w":"auto","ok":true,"c":[],"eager":true},{"g":4,"t":"exists x; try assumption","w":"model","ok":true,"c":[32]},{"g":4,"t":"assert (Gives y x)","w":"model","ok":false,"err":"Error: The variable y was not found in the current environment."},{"g":4,"t":"destruct (classic (Gives y x)) as [Hs|Hs]","w":"model","ok":false,"err":"Error: The"},{"g":4,"t":"exists x; exists Universe; assumption","w":"model","ok":false,"err":"Error: "},{"g":4,"t":"exists y","w":"model","ok":false,"err":"Error: The variable y was not found in the current environment."},{"g":4,"t":"exists x; intros","w":"model","ok":true,"c":[32]},{"g":22,"t":"assumption","w":"auto","ok":false,"err":"Error: No such assumption."},{"g":22,"t":"tauto","w":"auto","ok":false,"err":"Error: Tactic failure: Classical tauto failed."},{"g":22,"t":"firstorder","w":"auto","ok":true,"c":[22]},{"g":22,"t":"congruence","w":"auto","ok":false,"err":"Error: Tactic failure: congruence failed."},{"g":22,"t":"unfold ThroughAnother in *; firstorder","w":"auto","ok":true,"c":[35]},{"g":22,"t":"unfold ThroughAnother in *; hammer","w":"hammer","ok":false,"err":"Error: Hammer failed: ATPs failed to f"},{"g":22,"t":"exists x","w":"model","ok":true,"c":[36]},{"g":22,"t":"exists x; exists Universe; split","w":"model","ok":true,"c":[37,38]},{"g":37,"t":"tauto","w":"auto","ok":true,"c":[],"eager":true},{"g":22,"t":"assert (Gives x Universe)","w":"model","ok":true,"c":[39,40]},{"g":22,"t":"destruct (classic (Gives x Universe)) as [Hs|Hs]","w":"model","ok":true,"c":[41,42]},{"g":22,"t":"exists x, Universe","w":"model","ok":true,"c":[43]},{"g":22,"t":"assert (Gives b x)","w":"model","ok":false,"err":"Error: The variable b was not found in the current environment."},{"g":22,"t":"destruct (classic (Gives b x)) as [Hs|Hs]","w":"model","ok":false,"err":"Error: The"},{"g":22,"t":"exists y","w":"model","ok":false,"err":"Error: The variable y was not found in the current environment."},{"g":31,"t":"assumption","w":"auto","ok":false,"err":"Error: No such assumption."},{"g":31,"t":"tauto","w":"auto","ok":false,"err":"Error: Tactic failure: Classical tauto failed."},{"g":31,"t":"firstorder","w":"auto","ok":true,"c":[31]},{"g":31,"t":"congruence","w":"auto","ok":false,"err":"Error: Tactic failure: congruence failed."},{"g":31,"t":"unfold ThroughAnother in *; firstorder","w":"auto","ok":true,"c":[44]},{"g":31,"t":"unfold ThroughAnother in *; hammer","w":"hammer","ok":false,"err":"rejected"},{"g":31,"t":"exists x","w":"model","ok":true,"c":[45]},{"g":31,"t":"exists x; exists Universe; split","w":"model","ok":true,"c":[46,47]},{"g":46,"t":"tauto","w":"auto","ok":true,"c":[],"eager":true},{"g":31,"t":"assert (Gives x x)","w":"model","ok":true,"c":[48,49]},{"g":49,"t":"firstorder","w":"auto","ok":true,"c":[],"eager":true},{"g":31,"t":"destruct (classic (Gives x x)) as [Hs|Hs]","w":"model","ok":true,"c":[50,51]},{"g":50,"t":"firstorder","w":"auto","ok":true,"c":[],"eager":true},{"g":31,"t":"assert (Gives y x)","w":"model","ok":false,"err":"Error: The variable y was not found in the current environment."},{"g":31,"t":"destruct (classic (Gives y x)) as [Hs|Hs]","w":"model","ok":false,"err":"Error: The"},{"g":31,"t":"assert (In x Universe)","w":"model","ok":false,"err":"Error: The variable In was not found in the current environment."},{"g":31,"t":"destruct (classic (In x Universe)) as [Hs|Hs]","w":"model","ok":false,"err":"Error: "},{"g":31,"t":"exists x; exists Universe; repeat split","w":"model","ok":true,"c":[46,52,53,53,54,55]},{"g":31,"t":"exists x; try assumption","w":"model","ok":true,"c":[45]},{"g":23,"t":"assumption","w":"auto","ok":false,"err":"Error: No such assumption."},{"g":23,"t":"tauto","w":"auto","ok":false,"err":"Error: Tactic failure: Classical tauto failed."},{"g":23,"t":"firstorder","w":"auto","ok":false,"err":"Error: Timeout!"},{"g":23,"t":"congruence","w":"auto","ok":false,"err":"Error: Tactic failure: congruence failed."},{"g":23,"t":"unfold DependsOn, ThroughAnother, OfItself in *; firstorder","w":"auto","ok":false,"err":"rejected"},{"g":23,"t":"unfold DependsOn, ThroughAnother, OfItself in *; hammer","w":"hammer","ok":false,"err":"rejected"},{"g":23,"t":"exists x","w":"model","ok":true,"c":[56]},{"g":23,"t":"exists y","w":"model","ok":false,"err":"Error: The variable y was not found in the current environment."},{"g":23,"t":"exists Universe","w":"model","ok":true,"c":[30]},{"g":23,"t":"exists y; split","w":"model","ok":false,"err":"Error: The variable y was not found in the current environment."},{"g":23,"t":"assert (Gives x Universe)","w":"model","ok":true,"c":[26,57]},{"g":23,"t":"destruct (classic (Gives x Universe)) as [Hs|Hs]","w":"model","ok":true,"c":[58,59]},{"g":23,"t":"exists x; split","w":"model","ok":true,"c":[24,60]},{"g":23,"t":"exists Universe; split","w":"model","ok":true,"c":[24,25]},{"g":23,"t":"exists y; intros","w":"model","ok":false,"err":"Error: The variable y was not found in the current environment."},{"g":32,"t":"assumption","w":"auto","ok":false,"err":"Error: No such assumption."},{"g":32,"t":"tauto","w":"auto","ok":false,"err":"Error: Tactic failure: Classical tauto failed."},{"g":32,"t":"firstorder","w":"auto","ok":true,"c":[32]},{"g":32,"t":"congruence","w":"auto","ok":false,"err":"Error: Tactic failure: congruence failed."},{"g":32,"t":"unfold DependsOn, ThroughAnother, OfItself in *; firstorder","w":"auto","ok":true,"c":[45]},{"g":32,"t":"unfold DependsOn, ThroughAnother, OfItself in *; hammer","w":"hammer","ok":false,"err":"rejected"},{"g":32,"t":"exists y","w":"model","ok":false,"err":"Error: The variable y was not found in the current environment."},{"g":32,"t":"exists x","w":"model","ok":true,"c":[61]},{"g":32,"t":"exists y; split","w":"model","ok":false,"err":"Error: The variable y was not found in the current environment."},{"g":32,"t":"exists x; split","w":"model","ok":true,"c":[33,62]},{"g":32,"t":"exists yada","w":"model","ok":false,"err":"Error: The variable yada was not found in the current environment."},{"g":32,"t":"assert (Gives x Universe)","w":"model","ok":true,"c":[63,64]},{"g":32,"t":"destruct (classic (Gives x Universe)) as [Hs|Hs]","w":"model","ok":true,"c":[65,66]},{"g":32,"t":"exists y; intros","w":"model","ok":false,"err":"Error: The variable y was not found in the current environment."},{"g":32,"t":"assert (Gives x x)","w":"model","ok":true,"c":[67,68]},{"g":68,"t":"firstorder","w":"auto","ok":true,"c":[],"eager":true},{"g":32,"t":"destruct (classic (Gives x x)) as [Hs|Hs]","w":"model","ok":true,"c":[69,70]},{"g":69,"t":"firstorder","w":"auto","ok":true,"c":[],"eager":true},{"g":6,"t":"assumption","w":"auto","ok":false,"err":"Error: No such assumption."},{"g":6,"t":"tauto","w":"auto","ok":false,"err":"Error: Tactic failure: Classical tauto failed."},{"g":6,"t":"firstorder","w":"auto","ok":false,"err":"Error: Timeout!"},{"g":6,"t":"congruence","w":"auto","ok":false,"err":"Error: Tactic failure: congruence failed."},{"g":6,"t":"unfold Necessary, InUniverse, MP001, MP002, MP003, MP008, OP001, Independent in *; firstorder","w":"auto","ok":false,"err":"rejected"},{"g":6,"t":"unfold Necessary, InUniverse, MP001, MP002, MP003, MP008, OP001, Independent in *; hammer","w":"hammer","ok":false,"err":"Error: Hammer failed: ATPs failed to f"},{"g":6,"t":"exists Universe","w":"model","ok":true,"c":[71]},{"g":6,"t":"exists H3","w":"model","ok":false,"err":"rejected"},{"g":6,"t":"exists Universe; split; trivial","w":"model","ok":true,"c":[8,9]},{"g":6,"t":"exists H4","w":"model","ok":false,"err":"rejected"},{"g":6,"t":"exists x","w":"model","ok":true,"c":[72]},{"g":6,"t":"exists Universe; split","w":"model","ok":true,"c":[8,9]},{"g":6,"t":"exists Universe; split; [ trivial | idtac ]","w":"model","ok":true,"c":[8,9]},{"g":6,"t":"exists Universe; split; [ assumption | idtac ]","w":"model","ok":false,"err":"rejected"},{"g":35,"t":"assumption","w":"auto","ok":false,"err":"Error: No such assumption."},{"g":35,"t":"tauto","w":"auto","ok":false,"err":"Error: Tactic failure: Classical tauto failed."},{"g":35,"t":"firstorder","w":"auto","ok":true,"c":[35]},{"g":35,"t":"congruence","w":"auto","ok":false,"err":"Error: Tactic failure: congruence failed."},{"g":35,"t":"hammer","w":"hammer","ok":false,"err":"Error: Hammer failed: ATPs failed to f"},{"g":35,"t":"exists x","w":"model","ok":true,"c":[73]},{"g":35,"t":"exists x; exists Universe; split","w":"model","ok":true,"c":[74,75]},{"g":74,"t":"tauto","w":"auto","ok":true,"c":[],"eager":true},{"g":35,"t":"assert (Gives b x)","w":"model","ok":false,"err":"Error: The variable b was not found in the current environment."},{"g":35,"t":"destruct (classic (Gives b x)) as [Hs|Hs]","w":"model","ok":false,"err":"Error: The"},{"g":35,"t":"assert (Gives x Universe)","w":"model","ok":true,"c":[76,77]},{"g":35,"t":"destruct (classic (Gives x Universe)) as [Hs|Hs]","w":"model","ok":true,"c":[78,79]},{"g":35,"t":"exists x, Universe","w":"model","ok":true,"c":[80]},{"g":35,"t":"exists y","w":"model","ok":false,"err":"Error: The variable y was not found in the current environment."},{"g":35,"t":"exists x; exists Universe","w":"model","ok":true,"c":[80]},{"g":35,"t":"assert (Gives x x)","w":"model","ok":true,"c":[81,82]},{"g":82,"t":"firstorder","w":"auto","ok":true,"c":[],"eager":true},{"g":35,"t":"destruct (classic (Gives x x)) as [Hs|Hs]","w":"model","ok":true,"c":[83,84]},{"g":83,"t":"firstorder","w":"auto","ok":true,"c":[],"eager":true},{"g":44,"t":"assumption","w":"auto","ok":false,"err":"Error: No such assumption."},{"g":44,"t":"tauto","w":"auto","ok":false,"err":"Error: Tactic failure: Classical tauto failed."},{"g":44,"t":"firstorder","w":"auto","ok":true,"c":[44]},{"g":44,"t":"congruence","w":"auto","ok":false,"err":"Error: Tactic failure: congruence failed."},{"g":44,"t":"hammer","w":"hammer","ok":false,"err":"rejected"},{"g":44,"t":"exists x","w":"model","ok":true,"c":[85]},{"g":44,"t":"exists x; exists Universe; split","w":"model","ok":true,"c":[86,87]},{"g":86,"t":"tauto","w":"auto","ok":true,"c":[],"eager":true},{"g":44,"t":"assert (Gives x x)","w":"model","ok":true,"c":[88,89]},{"g":89,"t":"firstorder","w":"auto","ok":true,"c":[],"eager":true},{"g":44,"t":"destruct (classic (Gives x x)) as [Hs|Hs]","w":"model","ok":true,"c":[90,91]},{"g":90,"t":"firstorder","w":"auto","ok":true,"c":[],"eager":true},{"g":44,"t":"exists x; exists Universe; repeat split","w":"model","ok":true,"c":[86,92,93,93,94,95]},{"g":44,"t":"assert (Gives y x)","w":"model","ok":false,"err":"Error: The variable y was not found in the current environment."},{"g":44,"t":"destruct (classic (Gives y x)) as [Hs|Hs]","w":"model","ok":false,"err":"Error: The"},{"g":44,"t":"assert (In x Universe)","w":"model","ok":false,"err":"Error: The variable In was not found in the current environment."},{"g":44,"t":"destruct (classic (In x Universe)) as [Hs|Hs]","w":"model","ok":false,"err":"Error: "},{"g":44,"t":"exists x; try assumption","w":"model","ok":true,"c":[85]},{"g":14,"t":"assumption","w":"auto","ok":false,"err":"Error: No such assumption."},{"g":14,"t":"tauto","w":"auto","ok":false,"err":"Error: Tactic failure: Classical tauto failed."},{"g":14,"t":"firstorder","w":"auto","ok":false,"err":"Error: Timeout!"},{"g":14,"t":"congruence","w":"auto","ok":false,"err":"Error: Tactic failure: congruence failed."},{"g":14,"t":"unfold Necessary, InUniverse, MP001, MP002, MP003, MP008, OP001, Independent in *; firstorder","w":"auto","ok":false,"err":"rejected"}],"proof":[],"proofFile":null},{"key":"round6/imkan_s6_aggregate_possible_caused","id":"imkan_s6_aggregate_possible_caused","run":"round6","title":"Dalīl al-imkān, step 6","english":"The aggregate is itself possible, and so has its existence through another.","stmt":"MP008 -> MP010 -> forall A, AggregateOfPossibles A -> Exists A -> (exists p, p <> A /\\ Possible p) -> Possible A /\\ ThroughAnother A","proved":false,"script":"","seconds":901.5,"expansions":13,"calls":540,"root":0,"goals":["============================\nMP008 -> MP010 -> forall A, AggregateOfPossibles A -> Exists A -> (exists p, p <> A /\\ Possible p) -> Possible A /\\ ThroughAnother A","H : MP008\nH0 : MP010\nA : Thing\nH1 : AggregateOfPossibles A\nH2 : Exists A\nH3 : @ex Thing (fun p : Thing => and (not (@eq Thing p A)) (Possible p))\n============================\nPossible A","H : MP008\nH0 : MP010\nA : Thing\nH1 : AggregateOfPossibles A\nH2 : Exists A\nH3 : @ex Thing (fun p : Thing => and (not (@eq Thing p A)) (Possible p))\n============================\nThroughAnother A","H : MP008\nH0 : MP010\nA : Thing\nH1 : AggregateOfPossibles A\nH2 : Exists A\nH3 : @ex Thing (fun p : Thing => and (not (@eq Thing p A)) (Possible p))\n============================\nforall (x : Thing) (_ : and (not (@eq Thing x A)) (Possible x)), Possible A","H : MP008\nH0 : MP010\nA : Thing\nH1 : AggregateOfPossibles A\nH2 : Exists A\nH3 : @ex Thing (fun p : Thing => and (not (@eq Thing p A)) (Possible p))\nx : Thing\nH4 : and (not (@eq Thing x A)) (Possible x)\n============================\nPossible A","H : MP008\nH0 : MP010\nA : Thing\nH1 : AggregateOfPossibles A\nH2 : Exists A\nx : Thing\nH4 : not (@eq Thing x A)\nH5 : Possible x\n============================\nPossible A","H : MP008\nH0 : MP010\nA : Thing\nH1 : AggregateOfPossibles A\nH2 : Exists A\nH3 : @ex Thing (fun p : Thing => and (not (@eq Thing p A)) (Possible p))\n============================\n@ex Thing (fun p : Thing => Possible p)","H : MP008\nH0 : MP010\nA : Thing\nH1 : AggregateOfPossibles A\nH2 : Exists A\nH3 : @ex Thing (fun p : Thing => and (not (@eq Thing p A)) (Possible p))\nH4 : @ex Thing (fun p : Thing => Possible p)\n============================\nPossible A","H : MP008\nH0 : MP010\nA : Thing\nH1 : AggregateOfPossibles A\nH2 : Exists A\nH3 : @ex Thing (fun p : Thing => and (not (@eq Thing p A)) (Possible p))\nHs : @ex Thing (fun p : Thing => Possible p)\n============================\nPossible A","H : MP008\nH0 : MP010\nA : Thing\nH1 : AggregateOfPossibles A\nH2 : Exists A\nH3 : @ex Thing (fun p : Thing => and (not (@eq Thing p A)) (Possible p))\nHs : not (@ex Thing (fun p : Thing => Possible p))\n============================\nPossible A","H : MP008\nH0 : MP010\nA : Thing\nH1 : AggregateOfPossibles A\nH2 : Exists A\np : Thing\nH4 : not (@eq Thing p A)\nH5 : Possible p\n============================\nPossible A","H : MP008\nH0 : MP010\nA : Thing\nH1 : AggregateOfPossibles A\nH2 : Exists A\nH3 : @ex Thing (fun p : Thing => and (not (@eq Thing p A)) (Possible p))\nH4 : @ex Thing (fun p : Thing => Possible p)\n============================\nThroughAnother A","H : MP008\nH0 : MP010\nA : Thing\nH1 : AggregateOfPossibles A\nH2 : Exists A\nH3 : @ex Thing (fun p : Thing => and (not (@eq Thing p A)) (Possible p))\nHs : @ex Thing (fun p : Thing => Possible p)\n============================\nThroughAnother A","H : MP008\nH0 : MP010\nA : Thing\nH1 : AggregateOfPossibles A\nH2 : Exists A\nH3 : @ex Thing (fun p : Thing => and (not (@eq Thing p A)) (Possible p))\nHs : not (@ex Thing (fun p : Thing => Possible p))\n============================\nThroughAnother A","H : MP008\nH0 : MP010\nA : Thing\nH1 : AggregateOfPossibles A\nH2 : Exists A\nH3 : @ex Thing (fun p : Thing => and (not (@eq Thing p A)) (Possible p))\nB : Thing\nH4 : and (not (@eq Thing B A)) (Possible B)\n============================\nThroughAnother A","H : MP008\nH0 : MP010\nA : Thing\nH1 : AggregateOfPossibles A\nH2 : Exists A\nH3 : @ex Thing (fun p : Thing => and (not (@eq Thing p A)) (Possible p))\nx : Thing\nH4 : and (not (@eq Thing x A)) (Possible x)\nx0 : Thing\nH5 : and (not (@eq Thing x0 A)) (Possible x0)\n============================\nPossible A","H : MP008\nH0 : MP010\nA : Thing\nH1 : AggregateOfPossibles A\nH2 : Exists A\nH3 : @ex Thing (fun p : Thing => and (not (@eq Thing p A)) (Possible p))\nx : Thing\nH3' : and (not (@eq Thing x A)) (Possible x)\n============================\nPossible A","H : MP008\nH0 : MP010\nA : Thing\nH1 : AggregateOfPossibles A\nH2 : Exists A\nH3 : @ex Thing (fun p : Thing => and (not (@eq Thing p A)) (Possible p))\nx : Thing\nP : and (not (@eq Thing x A)) (Possible x)\n============================\nPossible A","H : MP008\nH0 : MP010\nA : Thing\nH1 : AggregateOfPossibles A\nH2 : Exists A\nH3 : @ex Thing (fun p : Thing => and (not (@eq Thing p A)) (Possible p))\nX : Thing\nH4 : and (not (@eq Thing X A)) (Possible X)\n============================\nPossible A","H : MP008\nH0 : MP010\nA : Thing\nH1 : AggregateOfPossibles A\nH2 : Exists A\nH3 : @ex Thing (fun p : Thing => and (not (@eq Thing p A)) (Possible p))\nx : Thing\nH4 : and (not (@eq Thing x A)) (Possible x)\n============================\nforall (_ : not (@eq Thing x A)) (_ : Possible x), Possible A","H : MP008\nH0 : MP010\nA : Thing\nH1 : AggregateOfPossibles A\nH2 : Exists A\nH3 : @ex Thing (fun p : Thing => and (not (@eq Thing p A)) (Possible p))\nx : Thing\nH4 : and (not (@eq Thing x A)) (Possible x)\n============================\nforall (x0 : Thing) (_ : and (not (@eq Thing x0 A)) (Possible x0)), Possible A","H : MP008\nH0 : MP010\nA : Thing\nH1 : AggregateOfPossibles A\nH2 : Exists A\nH3 : @ex Thing (fun p : Thing => and (not (@eq Thing p A)) (Possible p))\nx : Thing\nH4 : and (not (@eq Thing x A)) (Possible x)\nH5 : not (@eq Thing x A)\nH6 : Possible x\n============================\nPossible A","H : MP008\nH0 : MP010\nA : Thing\nH1 : AggregateOfPossibles A\nH2 : Exists A\nH3 : @ex Thing (fun p : Thing => and (not (@eq Thing p A)) (Possible p))\nx : Thing\nH4 : and (not (@eq Thing x A)) (Possible x)\n============================\nExists A","H : MP008\nH0 : MP010\nA : Thing\nH1 : AggregateOfPossibles A\nH2 : Exists A\nH3 : @ex Thing (fun p : Thing => and (not (@eq Thing p A)) (Possible p))\nx : Thing\nH4 : and (not (@eq Thing x A)) (Possible x)\n============================\nnot (Ess A)","H : MP008\nH0 : MP010\nA : Thing\nH1 : AggregateOfPossibles A\nH2 : Exists A\nH3 : @ex Thing (fun p : Thing => and (not (@eq Thing p A)) (Possible p))\nx : Thing\nH4 : and (not (@eq Thing x A)) (Possible x)\n============================\n@eq Thing x A","H : MP008\nH0 : MP010\nA : Thing\nH1 : AggregateOfPossibles A\nH2 : Exists A\nH3 : @ex Thing (fun p : Thing => and (not (@eq Thing p A)) (Possible p))\nx : Thing\nH4 : and (not (@eq Thing x A)) (Possible x)\nH5 : @eq Thing x A\n============================\nPossible A","H : MP008\nH0 : MP010\nA : Thing\nH1 : AggregateOfPossibles A\nH2 : Exists A\nH3 : @ex Thing (fun p : Thing => and (not (@eq Thing p A)) (Possible p))\nx : Thing\nH4 : and (not (@eq Thing x A)) (Possible x)\nHs : @eq Thing x A\n============================\nPossible A","H : MP008\nH0 : MP010\nA : Thing\nH1 : AggregateOfPossibles A\nH2 : Exists A\nH3 : @ex Thing (fun p : Thing => and (not (@eq Thing p A)) (Possible p))\nx : Thing\nH4 : and (not (@eq Thing x A)) (Possible x)\nHs : not (@eq Thing x A)\n============================\nPossible A","H : MP008\nH0 : MP010\nA : Thing\nH1 : AggregateOfPossibles A\nH2 : Exists A\nH3 : @ex Thing (fun p : Thing => and (not (@eq Thing p A)) (Possible p))\nx : Thing\nH4 : and (not (@eq Thing x A)) (Possible x)\n============================\n@eq Thing A x","H : MP008\nH0 : MP010\nA : Thing\nH1 : AggregateOfPossibles A\nH2 : Exists A\nH3 : @ex Thing (fun p : Thing => and (not (@eq Thing p A)) (Possible p))\nx : Thing\nH4 : and (not (@eq Thing x A)) (Possible x)\nH5 : @eq Thing A x\n============================\nPossible A","H : MP008\nH0 : MP010\nA : Thing\nH1 : AggregateOfPossibles A\nH2 : Exists A\nH3 : @ex Thing (fun p : Thing => and (not (@eq Thing p A)) (Possible p))\nx : Thing\nH4 : and (not (@eq Thing x A)) (Possible x)\nHs : @eq Thing A x\n============================\nPossible A","H : MP008\nH0 : MP010\nA : Thing\nH1 : AggregateOfPossibles A\nH2 : Exists A\nH3 : @ex Thing (fun p : Thing => and (not (@eq Thing p A)) (Possible p))\nx : Thing\nH4 : and (not (@eq Thing x A)) (Possible x)\nHs : not (@eq Thing A x)\n============================\nPossible A","H : MP008\nH0 : MP010\nA : Thing\nH1 : AggregateOfPossibles A\nH2 : Exists A\nH3 : @ex Thing (fun p : Thing => and (not (@eq Thing p A)) (Possible p))\nH4 : @ex Thing (fun p : Thing => Possible p)\n============================\nforall (x : Thing) (_ : Possible x), Possible A","H : MP008\nH0 : MP010\nA : Thing\nH1 : AggregateOfPossibles A\nH2 : Exists A\nH3 : @ex Thing (fun p : Thing => and (not (@eq Thing p A)) (Possible p))\nH4 : @ex Thing (fun p : Thing => Possible p)\n============================\n@ex Thing (fun p : Thing => Possible p)","H : MP008\nH0 : MP010\nA : Thing\nH1 : AggregateOfPossibles A\nH2 : Exists A\nH3 : @ex Thing (fun p : Thing => and (not (@eq Thing p A)) (Possible p))\nH4 : @ex Thing (fun p : Thing => Possible p)\nH5 : @ex Thing (fun p : Thing => Possible p)\n============================\nPossible A","H : MP008\nH0 : MP010\nA : Thing\nH1 : AggregateOfPossibles A\nH2 : Exists A\nH3 : @ex Thing (fun p : Thing => and (not (@eq Thing p A)) (Possible p))\nH4 : @ex Thing (fun p : Thing => Possible p)\nHs : @ex Thing (fun p : Thing => Possible p)\n============================\nPossible A","H : MP008\nH0 : MP010\nA : Thing\nH1 : AggregateOfPossibles A\nH2 : Exists A\nH3 : @ex Thing (fun p : Thing => and (not (@eq Thing p A)) (Possible p))\nH4 : @ex Thing (fun p : Thing => Possible p)\nHs : not (@ex Thing (fun p : Thing => Possible p))\n============================\nPossible A","H : MP008\nH0 : MP010\nA : Thing\nH1 : AggregateOfPossibles A\nH2 : Exists A\nH3 : @ex Thing (fun p : Thing => and (not (@eq Thing p A)) (Possible p))\nx : Thing\nH4 : Possible x\n============================\nPossible A","H : MP008\nH0 : MP010\nA : Thing\nH1 : AggregateOfPossibles A\nH2 : Exists A\nH3 : @ex Thing (fun p : Thing => and (not (@eq Thing p A)) (Possible p))\nHs : @ex Thing (fun p : Thing => Possible p)\n============================\nforall (x : Thing) (_ : Possible x), Possible A","H : MP008\nH0 : MP010\nA : Thing\nH1 : AggregateOfPossibles A\nH2 : Exists A\nH3 : @ex Thing (fun p : Thing => and (not (@eq Thing p A)) (Possible p))\nHs : @ex Thing (fun p : Thing => Possible p)\n============================\nforall _ : @ex Thing (fun p : Thing => Possible p), Possible A","H : MP008\nH0 : MP010\nA : Thing\nH1 : AggregateOfPossibles A\nH2 : Exists A\nH3 : @ex Thing (fun p : Thing => and (not (@eq Thing p A)) (Possible p))\nHs : @ex Thing (fun p : Thing => Possible p)\nx : Thing\nH4 : Possible x\n============================\nPossible A","H : MP008\nH0 : MP010\nA : Thing\nH1 : AggregateOfPossibles A\nH2 : Exists A\nH3 : @ex Thing (fun p : Thing => and (not (@eq Thing p A)) (Possible p))\nH4 : @ex Thing (fun p : Thing => Possible p)\nH5 : @ex Thing (fun p : Thing => Possible p)\n============================\nThroughAnother A","H : MP008\nH0 : MP010\nA : Thing\nH1 : AggregateOfPossibles A\nH2 : Exists A\nH3 : @ex Thing (fun p : Thing => and (not (@eq Thing p A)) (Possible p))\nH4 : @ex Thing (fun p : Thing => Possible p)\nHs : @ex Thing (fun p : Thing => Possible p)\n============================\nThroughAnother A","H : MP008\nH0 : MP010\nA : Thing\nH1 : AggregateOfPossibles A\nH2 : Exists A\nH3 : @ex Thing (fun p : Thing => and (not (@eq Thing p A)) (Possible p))\nH4 : @ex Thing (fun p : Thing => Possible p)\nHs : not (@ex Thing (fun p : Thing => Possible p))\n============================\nThroughAnother A","H : MP008\nH0 : MP010\nA : Thing\nH1 : AggregateOfPossibles A\nH2 : Exists A\nH3 : @ex Thing (fun p : Thing => and (not (@eq Thing p A)) (Possible p))\nH4 : @ex Thing (fun p : Thing => Possible p)\nH5 : @ex Thing (fun p : Thing => and (not (@eq Thing p A)) (Possible p))\n============================\nThroughAnother A","H : MP008\nH0 : MP010\nA : Thing\nH1 : AggregateOfPossibles A\nH2 : Exists A\nH3 : @ex Thing (fun p : Thing => and (not (@eq Thing p A)) (Possible p))\np : Thing\nH5 : Exists p\nH6 : not (Ess p)\n============================\nThroughAnother A","H : MP008\nH0 : MP010\nA : Thing\nH1 : AggregateOfPossibles A\nH2 : Exists A\np : Thing\nH5 : not (@eq Thing p A)\nH6 : Possible p\nH4 : @ex Thing (fun p : Thing => Possible p)\n============================\nThroughAnother A","H : MP008\nH0 : MP010\nA : Thing\nH1 : AggregateOfPossibles A\nH2 : Exists A\nH3 : @ex Thing (fun p : Thing => and (not (@eq Thing p A)) (Possible p))\nH4 : @ex Thing (fun p : Thing => Possible p)\n============================\nforall (x : Thing) (_ : Possible x), ThroughAnother A","H : MP008\nH0 : MP010\nA : Thing\nH1 : AggregateOfPossibles A\nH2 : Exists A\nH3 : @ex Thing (fun p : Thing => and (not (@eq Thing p A)) (Possible p))\nHs : @ex Thing (fun p : Thing => Possible p)\n============================\n@ex Thing (fun p : Thing => Possible p)","H : MP008\nH0 : MP010\nA : Thing\nH1 : AggregateOfPossibles A\nH2 : Exists A\nH3 : @ex Thing (fun p : Thing => and (not (@eq Thing p A)) (Possible p))\nHs : @ex Thing (fun p : Thing => Possible p)\nH4 : @ex Thing (fun p : Thing => Possible p)\n============================\nThroughAnother A","H : MP008\nH0 : MP010\nA : Thing\nH1 : AggregateOfPossibles A\nH2 : Exists A\nH3 : @ex Thing (fun p : Thing => and (not (@eq Thing p A)) (Possible p))\nHs : @ex Thing (fun p : Thing => Possible p)\n============================\nforall (x : Thing) (_ : Possible x), ThroughAnother A","H : MP008\nH0 : MP010\nA : Thing\nH1 : AggregateOfPossibles A\nH2 : Exists A\nH3 : @ex Thing (fun p : Thing => and (not (@eq Thing p A)) (Possible p))\nHs : @ex Thing (fun p : Thing => Possible p)\nH4 : @ex Thing (fun p : Thing => and (not (@eq Thing p A)) (Possible p))\n============================\nThroughAnother A","H : MP008\nH0 : MP010\nA : Thing\nH1 : AggregateOfPossibles A\nH2 : Exists A\nH3 : @ex Thing (fun p : Thing => and (not (@eq Thing p A)) (Possible p))\np : Thing\nH4 : Exists p\nH5 : not (Ess p)\n============================\nThroughAnother A","H : MP008\nH0 : MP010\nA : Thing\nH1 : AggregateOfPossibles A\nH2 : Exists A\nH3 : @ex Thing (fun p : Thing => and (not (@eq Thing p A)) (Possible p))\np : Thing\nHs : Possible p\n============================\nThroughAnother A","H : MP008\nH0 : MP010\nA : Thing\nH1 : AggregateOfPossibles A\nH2 : Exists A\nH3 : @ex Thing (fun p : Thing => and (not (@eq Thing p A)) (Possible p))\np : Thing\nHt : Exists p\nHx : not (Ess p)\n============================\nThroughAnother A","H : MP008\nH0 : MP010\nA : Thing\nH1 : AggregateOfPossibles A\nH2 : Exists A\nH3 : @ex Thing (fun p : Thing => and (not (@eq Thing p A)) (Possible p))\nx : Thing\nH4 : and (not (@eq Thing x A)) (Possible x)\nH5 : not (@eq Thing x A)\nH6 : Possible x\n============================\nExists A","H : MP008\nH0 : MP010\nA : Thing\nH1 : AggregateOfPossibles A\nH2 : Exists A\nH3 : @ex Thing (fun p : Thing => and (not (@eq Thing p A)) (Possible p))\nx : Thing\nH4 : and (not (@eq Thing x A)) (Possible x)\nH5 : not (@eq Thing x A)\nH6 : Possible x\n============================\nnot (Ess A)","H : MP008\nH0 : MP010\nA : Thing\nH1 : AggregateOfPossibles A\nH2 : Exists A\nH3 : @ex Thing (fun p : Thing => and (not (@eq Thing p A)) (Possible p))\nx : Thing\nH4 : and (not (@eq Thing x A)) (Possible x)\nH5 : not (@eq Thing x A)\n============================\nforall _ : Possible x, Possible A","H : MP008\nH0 : MP010\nA : Thing\nH1 : AggregateOfPossibles A\nH2 : Exists A\nH3 : @ex Thing (fun p : Thing => and (not (@eq Thing p A)) (Possible p))\nx : Thing\nH4 : and (not (@eq Thing x A)) (Possible x)\nx1 : not (@eq Thing x A)\nH5 : Possible x\n============================\nPossible A","H : MP008\nH0 : MP010\nA : Thing\nH1 : AggregateOfPossibles A\nH2 : Exists A\nH3 : @ex Thing (fun p : Thing => and (not (@eq Thing p A)) (Possible p))\nx : Thing\nH4 : and (not (@eq Thing x A)) (Possible x)\nx0 : not (@eq Thing x A)\nH5 : Possible x\n============================\nPossible A","H : MP008\nH0 : MP010\nA : Thing\nH1 : AggregateOfPossibles A\nH2 : Exists A\nH3 : @ex Thing (fun p : Thing => and (not (@eq Thing p A)) (Possible p))\nx : Thing\nH4 : and (not (@eq Thing x A)) (Possible x)\n============================\nforall (_ : @ex Thing (fun p : Thing => and (not (@eq Thing p A)) (Possible p))) (_ : not (@eq Thing x A)) (_ : Possible x), Possible A","H : MP008\nH0 : MP010\nA : Thing\nH1 : AggregateOfPossibles A\nH2 : Exists A\nH3 : @ex Thing (fun p : Thing => and (not (@eq Thing p A)) (Possible p))\nB : Thing\nH4 : and (not (@eq Thing B A)) (Possible B)\n============================\nPossible B","H : MP008\nH0 : MP010\nA : Thing\nH1 : AggregateOfPossibles A\nH2 : Exists A\nH3 : @ex Thing (fun p : Thing => and (not (@eq Thing p A)) (Possible p))\nB : Thing\nH4 : and (not (@eq Thing B A)) (Possible B)\nH5 : Possible B\n============================\nThroughAnother A","H : MP008\nH0 : MP010\nA : Thing\nH1 : AggregateOfPossibles A\nH2 : Exists A\nH3 : @ex Thing (fun p : Thing => and (not (@eq Thing p A)) (Possible p))\nB : Thing\nH4 : and (not (@eq Thing B A)) (Possible B)\nHs : Possible B\n============================\nThroughAnother A","H : MP008\nH0 : MP010\nA : Thing\nH1 : AggregateOfPossibles A\nH2 : Exists A\nH3 : @ex Thing (fun p : Thing => and (not (@eq Thing p A)) (Possible p))\nB : Thing\nH4 : and (not (@eq Thing B A)) (Possible B)\nHs : not (Possible B)\n============================\nThroughAnother A","H : MP008\nH0 : MP010\nA : Thing\nH1 : AggregateOfPossibles A\nH2 : Exists A\nH3 : @ex Thing (fun p : Thing => and (not (@eq Thing p A)) (Possible p))\nB : Thing\nH4 : and (not (@eq Thing B A)) (Possible B)\n============================\nforall (x : Thing) (_ : and (not (@eq Thing x A)) (Possible x)), ThroughAnother A","H : MP008\nH0 : MP010\nA : Thing\nH1 : AggregateOfPossibles A\nH2 : Exists A\nH3 : @ex Thing (fun p : Thing => and (not (@eq Thing p A)) (Possible p))\nB : Thing\nH4 : and (not (@eq Thing B A)) (Possible B)\n============================\n@eq Thing A B","H : MP008\nH0 : MP010\nA : Thing\nH1 : AggregateOfPossibles A\nH2 : Exists A\nH3 : @ex Thing (fun p : Thing => and (not (@eq Thing p A)) (Possible p))\nB : Thing\nH4 : and (not (@eq Thing B A)) (Possible B)\nH5 : @eq Thing A B\n============================\nThroughAnother A"],"events":[{"g":0,"t":"assumption","w":"auto","ok":false,"err":"Error: No such assumption."},{"g":0,"t":"tauto","w":"auto","ok":false,"err":"Error: Tactic failure: Classical tauto failed."},{"g":0,"t":"firstorder","w":"auto","ok":false,"err":"Error: Timeout!"},{"g":0,"t":"congruence","w":"auto","ok":false,"err":"Error: Tactic failure: congruence failed."},{"g":0,"t":"unfold ThroughAnother, Possible, MP008, AggregateOfPossibles, MP010 in *; firstorder","w":"auto","ok":false,"err":"rejected"},{"g":0,"t":"unfold ThroughAnother, Possible, MP008, AggregateOfPossibles, MP010 in *; hammer","w":"hammer","ok":false,"err":"rejected"},{"g":0,"t":"split","w":"model","ok":true,"c":[1,2]},{"g":0,"t":"right","w":"model","ok":false,"err":"Error: Not an inductive goal with 2 constructors."},{"g":0,"t":"apply AggregateOfPossibles_intro","w":"model","ok":false,"err":"Error: The variable Ag"},{"g":0,"t":"apply DefineAggregateOfPossibles","w":"model","ok":false,"err":"Error: The variable De"},{"g":0,"t":"apply AggregateOfPossibles_intro; Auto","w":"model","ok":false,"err":"rejected"},{"g":1,"t":"assumption","w":"auto","ok":false,"err":"Error: No such assumption."},{"g":1,"t":"tauto","w":"auto","ok":false,"err":"Error: Tactic failure: Classical tauto failed."},{"g":1,"t":"firstorder","w":"auto","ok":false,"err":"Error: Timeout!"},{"g":1,"t":"congruence","w":"auto","ok":false,"err":"Error: Tactic failure: congruence failed."},{"g":1,"t":"unfold Possible, MP008, AggregateOfPossibles, MP010 in *; firstorder","w":"auto","ok":false,"err":"rejected"},{"g":1,"t":"unfold Possible, MP008, AggregateOfPossibles, MP010 in *; hammer","w":"hammer","ok":false,"err":"Error: Hammer failed: ATPs failed to f"},{"g":1,"t":"elim H3","w":"model","ok":true,"c":[3]},{"g":1,"t":"elim H3; intros","w":"model","ok":true,"c":[4]},{"g":1,"t":"destruct H3 as [? [H4 H5]]","w":"model","ok":true,"c":[5]},{"g":1,"t":"assert (exists p : Thing, Possible p)","w":"model","ok":true,"c":[6,7]},{"g":6,"t":"firstorder","w":"auto","ok":true,"c":[],"eager":true},{"g":1,"t":"destruct (classic (exists p : Thing, Possible p)) as [Hs|Hs]","w":"model","ok":true,"c":[8,9]},{"g":9,"t":"firstorder","w":"auto","ok":true,"c":[],"eager":true},{"g":1,"t":"destruct H3 as [p [H4 H5]]","w":"model","ok":true,"c":[10]},{"g":2,"t":"assumption","w":"auto","ok":false,"err":"Error: No such assumption."},{"g":2,"t":"tauto","w":"auto","ok":false,"err":"Error: Tactic failure: Classical tauto failed."},{"g":2,"t":"firstorder","w":"auto","ok":false,"err":"Error: Timeout!"},{"g":2,"t":"congruence","w":"auto","ok":false,"err":"Error: Tactic failure: congruence failed."},{"g":2,"t":"unfold ThroughAnother, Possible, MP008, AggregateOfPossibles, MP010 in *; firstorder","w":"auto","ok":false,"err":"rejected"},{"g":2,"t":"unfold ThroughAnother, Possible, MP008, AggregateOfPossibles, MP010 in *; hammer","w":"hammer","ok":false,"err":"Error: Hammer failed: ATPs failed to f"},{"g":2,"t":"assert (exists p : Thing, Possible p)","w":"model","ok":true,"c":[6,11]},{"g":2,"t":"destruct (classic (exists p : Thing, Possible p)) as [Hs|Hs]","w":"model","ok":true,"c":[12,13]},{"g":13,"t":"firstorder","w":"auto","ok":true,"c":[],"eager":true},{"g":2,"t":"case (H3); intros B H4","w":"model","ok":true,"c":[14]},{"g":3,"t":"assumption","w":"auto","ok":false,"err":"Error: No such assumption."},{"g":3,"t":"tauto","w":"auto","ok":false,"err":"Error: Tactic failure: Classical tauto failed."},{"g":3,"t":"firstorder","w":"auto","ok":false,"err":"Error: Timeout!"},{"g":3,"t":"congruence","w":"auto","ok":false,"err":"Error: Tactic failure: congruence failed."},{"g":3,"t":"unfold Possible, MP008, AggregateOfPossibles, MP010 in *; firstorder","w":"auto","ok":false,"err":"rejected"},{"g":3,"t":"unfold Possible, MP008, AggregateOfPossibles, MP010 in *; hammer","w":"hammer","ok":false,"err":"rejected"},{"g":3,"t":"intros x H4","w":"model","ok":true,"c":[4]},{"g":3,"t":"intros","w":"model","ok":true,"c":[4]},{"g":3,"t":"elim H3; intros","w":"model","ok":true,"c":[15]},{"g":3,"t":"intros x H4; possible","w":"model","ok":false,"err":"Error: The reference possible was not found in the curr"},{"g":3,"t":"intros x H3'","w":"model","ok":true,"c":[16]},{"g":3,"t":"intros x P","w":"model","ok":true,"c":[17]},{"g":3,"t":"intros X H4","w":"model","ok":true,"c":[18]},{"g":3,"t":"intros x H4; try assumption","w":"model","ok":true,"c":[4]},{"g":4,"t":"assumption","w":"auto","ok":false,"err":"Error: No such assumption."},{"g":4,"t":"tauto","w":"auto","ok":false,"err":"Error: Tactic failure: Classical tauto failed."},{"g":4,"t":"firstorder","w":"auto","ok":false,"err":"Error: Timeout!"},{"g":4,"t":"congruence","w":"auto","ok":false,"err":"Error: Tactic failure: congruence failed."},{"g":4,"t":"unfold Possible, MP008, AggregateOfPossibles, MP010 in *; firstorder","w":"auto","ok":false,"err":"rejected"},{"g":4,"t":"unfold Possible, MP008, AggregateOfPossibles, MP010 in *; hammer","w":"hammer","ok":false,"err":"Error: Hammer failed: ATPs failed to f"},{"g":4,"t":"elim H4","w":"model","ok":true,"c":[19]},{"g":4,"t":"elim H3","w":"model","ok":true,"c":[20]},{"g":4,"t":"elim H3; intros","w":"model","ok":true,"c":[15]},{"g":4,"t":"elim H4; intros","w":"model","ok":true,"c":[21]},{"g":4,"t":"split","w":"model","ok":true,"c":[22,23]},{"g":22,"t":"assumption","w":"auto","ok":true,"c":[],"eager":true},{"g":4,"t":"assert (x = A)","w":"model","ok":true,"c":[24,25]},{"g":25,"t":"tauto","w":"auto","ok":true,"c":[],"eager":true},{"g":4,"t":"destruct (classic (x = A)) as [Hs|Hs]","w":"model","ok":true,"c":[26,27]},{"g":26,"t":"tauto","w":"auto","ok":true,"c":[],"eager":true},{"g":4,"t":"assert (A = x)","w":"model","ok":true,"c":[28,29]},{"g":29,"t":"firstorder","w":"auto","ok":true,"c":[],"eager":true},{"g":4,"t":"destruct (classic (A = x)) as [Hs|Hs]","w":"model","ok":true,"c":[30,31]},{"g":30,"t":"firstorder","w":"auto","ok":true,"c":[],"eager":true},{"g":5,"t":"assumption","w":"auto","ok":false,"err":"Error: No such assumption."},{"g":5,"t":"tauto","w":"auto","ok":false,"err":"Error: Tactic failure: Classical tauto failed."},{"g":5,"t":"firstorder","w":"auto","ok":false,"err":"Error: Timeout!"},{"g":5,"t":"congruence","w":"auto","ok":false,"err":"Error: Tactic failure: congruence failed."},{"g":5,"t":"unfold Possible, MP008, AggregateOfPossibles, MP010 in *; firstorder","w":"auto","ok":false,"err":"rejected"},{"g":5,"t":"unfold Possible, MP008, AggregateOfPossibles, MP010 in *; hammer","w":"hammer","ok":false,"err":"Error: Hammer failed: ATPs failed to f"},{"g":5,"t":"apply possible_commutative","w":"model","ok":false,"err":"Error: The variable possible_commutative"},{"g":5,"t":"apply Possible_Commutative with x; assumption","w":"model","ok":false,"err":"rejected"},{"g":7,"t":"assumption","w":"auto","ok":false,"err":"Error: No such assumption."},{"g":7,"t":"tauto","w":"auto","ok":false,"err":"Error: Tactic failure: Classical tauto failed."},{"g":7,"t":"firstorder","w":"auto","ok":false,"err":"Error: Timeout!"},{"g":7,"t":"congruence","w":"auto","ok":false,"err":"Error: Tactic failure: congruence failed."},{"g":7,"t":"unfold Possible, MP008, AggregateOfPossibles, MP010 in *; firstorder","w":"auto","ok":false,"err":"rejected"},{"g":7,"t":"unfold Possible, MP008, AggregateOfPossibles, MP010 in *; hammer","w":"hammer","ok":false,"err":"Error: Hammer failed: ATPs failed to f"},{"g":7,"t":"elim H4","w":"model","ok":true,"c":[32]},{"g":7,"t":"assert (exists p : Thing, Possible p)","w":"model","ok":true,"c":[33,34]},{"g":33,"t":"assumption","w":"auto","ok":true,"c":[],"eager":true},{"g":7,"t":"destruct (classic (exists p : Thing, Possible p)) as [Hs|Hs]","w":"model","ok":true,"c":[35,36]},{"g":36,"t":"tauto","w":"auto","ok":true,"c":[],"eager":true},{"g":7,"t":"apply Possible_Commutative","w":"model","ok":false,"err":"Error: The variable Possible_Commutative"},{"g":7,"t":"destruct H4 as [? ?? ?]","w":"model","ok":true,"c":[37]},{"g":8,"t":"assumption","w":"auto","ok":false,"err":"Error: No such assumption."},{"g":8,"t":"tauto","w":"auto","ok":false,"err":"Error: Tactic failure: Classical tauto failed."},{"g":8,"t":"firstorder","w":"auto","ok":false,"err":"Error: Timeout!"},{"g":8,"t":"congruence","w":"auto","ok":false,"err":"Error: Tactic failure: congruence failed."},{"g":8,"t":"unfold Possible, MP008, AggregateOfPossibles, MP010 in *; firstorder","w":"auto","ok":false,"err":"rejected"},{"g":8,"t":"unfold Possible, MP008, AggregateOfPossibles, MP010 in *; hammer","w":"hammer","ok":false,"err":"Error: Hammer failed: ATPs failed to f"},{"g":8,"t":"apply Possible_Commutative","w":"model","ok":false,"err":"Error: The variable Possible_Commutative"},{"g":8,"t":"apply Possible_A","w":"model","ok":false,"err":"Error: The variable Possible_A was not found in the current environmen"},{"g":8,"t":"elim Hs","w":"model","ok":true,"c":[38]},{"g":8,"t":"generalize Hs","w":"model","ok":true,"c":[39]},{"g":8,"t":"elim Hs; intros","w":"model","ok":true,"c":[40]},{"g":10,"t":"assumption","w":"auto","ok":false,"err":"Error: No such assumption."},{"g":10,"t":"tauto","w":"auto","ok":false,"err":"Error: Tactic failure: Classical tauto failed."},{"g":10,"t":"firstorder","w":"auto","ok":false,"err":"Error: Timeout!"},{"g":10,"t":"congruence","w":"auto","ok":false,"err":"Error: Tactic failure: congruence failed."},{"g":10,"t":"unfold Possible, MP008, AggregateOfPossibles, MP010 in *; firstorder","w":"auto","ok":false,"err":"rejected"},{"g":10,"t":"unfold Possible, MP008, AggregateOfPossibles, MP010 in *; hammer","w":"hammer","ok":false,"err":"Error: Hammer failed: ATPs failed to f"},{"g":10,"t":"apply possible_commutative","w":"model","ok":false,"err":"Error: The variable possible_commutative"},{"g":10,"t":"apply Possible_Commutative with p; assumption","w":"model","ok":false,"err":"rejected"},{"g":11,"t":"assumption","w":"auto","ok":false,"err":"Error: No such assumption."},{"g":11,"t":"tauto","w":"auto","ok":false,"err":"Error: Tactic failure: Classical tauto failed."},{"g":11,"t":"firstorder","w":"auto","ok":false,"err":"Error: Timeout!"},{"g":11,"t":"congruence","w":"auto","ok":false,"err":"Error: Tactic failure: congruence failed."},{"g":11,"t":"unfold ThroughAnother, Possible, MP008, AggregateOfPossibles, MP010 in *; firstorder","w":"auto","ok":false,"err":"rejected"},{"g":11,"t":"unfold ThroughAnother, Possible, MP008, AggregateOfPossibles, MP010 in *; hammer","w":"hammer","ok":false,"err":"Error: Hammer failed: ATPs failed to f"},{"g":11,"t":"assert (exists p : Thing, Possible p)","w":"model","ok":true,"c":[33,41]},{"g":11,"t":"destruct (classic (exists p : Thing, Possible p)) as [Hs|Hs]","w":"model","ok":true,"c":[42,43]},{"g":43,"t":"tauto","w":"auto","ok":true,"c":[],"eager":true},{"g":11,"t":"assert (H5 := H3)","w":"model","ok":true,"c":[44]},{"g":11,"t":"destruct (classic (= H3)) as [Hs|Hs]","w":"model","ok":false,"err":"Error: Syntax error: [term"},{"g":11,"t":"assert (Exists p : Thing, Possible p)","w":"model","ok":false,"err":"Error: The variable p was no"},{"g":11,"t":"destruct (classic (Exists p : Thing, Possible p)) as [Hs|Hs]","w":"model","ok":false,"err":"rejected"},{"g":11,"t":"destruct H4 as [p [H5 H6] ]","w":"model","ok":true,"c":[45]},{"g":11,"t":"destruct H3 as [p [H5 H6] ]","w":"model","ok":true,"c":[46]},{"g":11,"t":"elim H4","w":"model","ok":true,"c":[47]},{"g":11,"t":"destruct H4 as [p [H5 H6]]","w":"model","ok":true,"c":[45]},{"g":12,"t":"assumption","w":"auto","ok":false,"err":"Error: No such assumption."},{"g":12,"t":"tauto","w":"auto","ok":false,"err":"Error: Tactic failure: Classical tauto failed."},{"g":12,"t":"firstorder","w":"auto","ok":false,"err":"Error: Timeout!"},{"g":12,"t":"congruence","w":"auto","ok":false,"err":"Error: Tactic failure: congruence failed."},{"g":12,"t":"unfold ThroughAnother, Possible, MP008, AggregateOfPossibles, MP010 in *; firstorder","w":"auto","ok":false,"err":"rejected"},{"g":12,"t":"unfold ThroughAnother, Possible, MP008, AggregateOfPossibles, MP010 in *; hammer","w":"hammer","ok":false,"err":"Error: Hammer failed: ATPs failed to f"},{"g":12,"t":"assert (exists p : Thing, Possible p)","w":"model","ok":true,"c":[48,49]},{"g":48,"t":"assumption","w":"auto","ok":true,"c":[],"eager":true},{"g":12,"t":"destruct (classic (exists p : Thing, Possible p)) as [Hs|Hs]","w":"model","ok":false,"err":"rejected"},{"g":12,"t":"case Hs","w":"model","ok":true,"c":[50]},{"g":12,"t":"assert (H4 := H3)","w":"model","ok":true,"c":[51]},{"g":12,"t":"destruct (classic (= H3)) as [Hs|Hs]","w":"model","ok":false,"err":"Error: Syntax error: [term"},{"g":12,"t":"destruct Hs as [p [H4 H5] ]","w":"model","ok":true,"c":[52]},{"g":12,"t":"destruct Hs as [p Hs]","w":"model","ok":true,"c":[53]},{"g":12,"t":"destruct Hs as [p [H4 H5]]","w":"model","ok":true,"c":[52]},{"g":12,"t":"destruct Hs as [p [Ht Hx] ]","w":"model","ok":true,"c":[54]},{"g":19,"t":"assumption","w":"auto","ok":false,"err":"Error: No such assumption."},{"g":19,"t":"tauto","w":"auto","ok":false,"err":"Error: Tactic failure: Classical tauto failed."},{"g":19,"t":"firstorder","w":"auto","ok":false,"err":"Error: Timeout!"},{"g":19,"t":"congruence","w":"auto","ok":false,"err":"Error: Tactic failure: congruence failed."},{"g":19,"t":"unfold Possible, MP008, AggregateOfPossibles, MP010 in *; firstorder","w":"auto","ok":false,"err":"rejected"},{"g":19,"t":"unfold Possible, MP008, AggregateOfPossibles, MP010 in *; hammer","w":"hammer","ok":false,"err":"rejected"},{"g":19,"t":"intros H5 H6","w":"model","ok":true,"c":[21]},{"g":19,"t":"intros","w":"model","ok":true,"c":[21]},{"g":19,"t":"split","w":"model","ok":true,"c":[55,56]},{"g":55,"t":"assumption","w":"auto","ok":true,"c":[],"eager":true},{"g":19,"t":"intro","w":"model","ok":true,"c":[57]},{"g":19,"t":"intros x1 H5","w":"model","ok":true,"c":[58]},{"g":19,"t":"intros x0 H5","w":"model","ok":true,"c":[59]},{"g":19,"t":"generalize H3","w":"model","ok":true,"c":[60]},{"g":14,"t":"assumption","w":"auto","ok":false,"err":"Error: No such assumption."},{"g":14,"t":"tauto","w":"auto","ok":false,"err":"Error: Tactic failure: Classical tauto failed."},{"g":14,"t":"firstorder","w":"auto","ok":false,"err":"Error: Timeout!"},{"g":14,"t":"congruence","w":"auto","ok":false,"err":"Error: Tactic failure: congruence failed."},{"g":14,"t":"unfold ThroughAnother, Possible, MP008, AggregateOfPossibles, MP010 in *; firstorder","w":"auto","ok":false,"err":"rejected"},{"g":14,"t":"unfold ThroughAnother, Possible, MP008, AggregateOfPossibles, MP010 in *; hammer","w":"hammer","ok":false,"err":"Error: Hammer failed: ATPs failed to f"},{"g":14,"t":"assert (Possible B)","w":"model","ok":true,"c":[61,62]},{"g":61,"t":"tauto","w":"auto","ok":true,"c":[],"eager":true},{"g":14,"t":"destruct (classic (Possible B)) as [Hs|Hs]","w":"model","ok":true,"c":[63,64]},{"g":64,"t":"tauto","w":"auto","ok":true,"c":[],"eager":true},{"g":14,"t":"split","w":"model","ok":false,"err":"Error: Unable to find an instance for the variable x."},{"g":14,"t":"elim H3","w":"model","ok":true,"c":[65]},{"g":14,"t":"assert (A = B)","w":"model","ok":true,"c":[66,67]},{"g":67,"t":"firstorder","w":"auto","ok":true,"c":[],"eager":true}],"proof":[],"proofFile":null},{"key":"round6/imkan_s7_cause_not_member","id":"imkan_s7_cause_not_member","run":"round6","title":"Dalīl al-imkān, step 7","english":"What gives existence to the aggregate is not one of its members.","stmt":"MP001 -> MP002 -> MP003 -> MP011 -> forall c A, Gives c A -> ~ MemberOf c A","proved":false,"script":"","seconds":900.3,"expansions":34,"calls":820,"root":0,"goals":["============================\nMP001 -> MP002 -> MP003 -> MP011 -> forall c A, Gives c A -> ~ MemberOf c A","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP011\nc : Thing\nA : Thing\nH3 : Gives c A\nX : Prop\nX0 : Prop\nX1 : Prop\n============================\nnot (MemberOf c A)","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nc : Thing\nA : Thing\nH3 : Gives c A\nX : Prop\nX0 : Prop\nX1 : Prop\n============================\nnot (MemberOf c A)","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP011\nc : Thing\nA : Thing\nH3 : Gives c A\n============================\nnot (MemberOf c A)","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP011\nc : Thing\nA : Thing\nH3 : Gives c A\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\n============================\nnot (MemberOf c A)","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nc : Thing\nA : Thing\nH3 : Gives c A\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\n============================\nnot (MemberOf c A)","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nc : Thing\nA : Thing\nH3 : Gives c A\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\n============================\nnot (MemberOf c A)","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nc : Thing\nA : Thing\nH3 : Gives c A\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\n============================\nGives c A","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nc : Thing\nA : Thing\nH3 : Gives c A\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nH4 : Gives c A\n============================\nnot (MemberOf c A)","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nc : Thing\nA : Thing\nH3 : Gives c A\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nHs : Gives c A\n============================\nnot (MemberOf c A)","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nc : Thing\nA : Thing\nH3 : Gives c A\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nHs : not (Gives c A)\n============================\nnot (MemberOf c A)","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP011\nc : Thing\nA : Thing\nH3 : Gives c A\nH4 : MemberOf c A\n============================\nFalse","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nc : Thing\nA : Thing\nH3 : Gives c A\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\nX8 : Prop\nX9 : Prop\nX10 : Prop\n============================\nnot (MemberOf c A)","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nc : Thing\nA : Thing\nH3 : Gives c A\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\n============================\nGives c A","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nc : Thing\nA : Thing\nH3 : Gives c A\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\nH4 : Gives c A\n============================\nnot (MemberOf c A)","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nc : Thing\nA : Thing\nH3 : Gives c A\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\nHs : Gives c A\n============================\nnot (MemberOf c A)","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nc : Thing\nA : Thing\nH3 : Gives c A\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\nHs : not (Gives c A)\n============================\nnot (MemberOf c A)","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nc : Thing\nA : Thing\nH3 : Gives c A\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\nX8 : Prop\nX9 : Prop\nX10 : Prop\nX11 : Prop\nX12 : Prop\nX13 : Prop\n============================\nnot (MemberOf c A)","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nc : Thing\nA : Thing\nH3 : Gives c A\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\nX8 : Prop\nX9 : Prop\nX10 : Prop\n============================\nGives c A","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nc : Thing\nA : Thing\nH3 : Gives c A\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\nX8 : Prop\nX9 : Prop\nX10 : Prop\nH4 : Gives c A\n============================\nnot (MemberOf c A)","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nc : Thing\nA : Thing\nH3 : Gives c A\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\nX8 : Prop\nX9 : Prop\nX10 : Prop\nHs : Gives c A\n============================\nnot (MemberOf c A)","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nc : Thing\nA : Thing\nH3 : Gives c A\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\nX8 : Prop\nX9 : Prop\nX10 : Prop\nHs : not (Gives c A)\n============================\nnot (MemberOf c A)","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nc : Thing\nA : Thing\nH3 : Gives c A\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\nX8 : Prop\nX9 : Prop\nX10 : Prop\nX11 : Prop\nX12 : Prop\nX13 : Prop\n============================\nGives c A","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nc : Thing\nA : Thing\nH3 : Gives c A\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\nX8 : Prop\nX9 : Prop\nX10 : Prop\nX11 : Prop\nX12 : Prop\nX13 : Prop\nH4 : Gives c A\n============================\nnot (MemberOf c A)","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nc : Thing\nA : Thing\nH3 : Gives c A\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\nX8 : Prop\nX9 : Prop\nX10 : Prop\nX11 : Prop\nX12 : Prop\nX13 : Prop\nHs : Gives c A\n============================\nnot (MemberOf c A)","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nc : Thing\nA : Thing\nH3 : Gives c A\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\nX8 : Prop\nX9 : Prop\nX10 : Prop\nX11 : Prop\nX12 : Prop\nX13 : Prop\nHs : not (Gives c A)\n============================\nnot (MemberOf c A)","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nc : Thing\nA : Thing\nH3 : Gives c A\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nH4 : Gives c A\nX5 : Prop\nX6 : Prop\nX7 : Prop\n============================\nnot (MemberOf c A)","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nc : Thing\nA : Thing\nH3 : Gives c A\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nH4 : Gives c A\nH5 : Gives c A\n============================\nnot (MemberOf c A)","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nc : Thing\nA : Thing\nH3 : Gives c A\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nH4 : Gives c A\n============================\nGives c A","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nc : Thing\nA : Thing\nH3 : Gives c A\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nH4 : Gives c A\nHs : Gives c A\n============================\nnot (MemberOf c A)","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nc : Thing\nA : Thing\nH3 : Gives c A\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nH4 : Gives c A\nHs : not (Gives c A)\n============================\nnot (MemberOf c A)","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP011\nc : Thing\nA : Thing\nH3 : Gives c A\nH4 : MemberOf c A\nX : Prop\nX0 : Prop\nX1 : Prop\n============================\nFalse","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nc : Thing\nA : Thing\nH3 : Gives c A\nH4 : MemberOf c A\nX : Prop\nX0 : Prop\nX1 : Prop\n============================\nFalse","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP011\nc : Thing\nA : Thing\nH3 : Gives c A\nH4 : MemberOf c A\n============================\nGives c A","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP011\nc : Thing\nA : Thing\nH3 : Gives c A\nH4 : MemberOf c A\nH5 : Gives c A\n============================\nFalse","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP011\nc : Thing\nA : Thing\nH3 : Gives c A\nH4 : MemberOf c A\nHs : Gives c A\n============================\nFalse","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP011\nc : Thing\nA : Thing\nH3 : Gives c A\nH4 : MemberOf c A\nHs : not (Gives c A)\n============================\nFalse","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nc : Thing\nA : Thing\nH3 : Gives c A\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\nH4 : Gives c A\nX8 : Prop\nX9 : Prop\nX10 : Prop\n============================\nnot (MemberOf c A)","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nc : Thing\nA : Thing\nH3 : Gives c A\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\nH4 : Gives c A\n============================\nGives c A","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nc : Thing\nA : Thing\nH3 : Gives c A\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\nH4 : Gives c A\nH5 : Gives c A\n============================\nnot (MemberOf c A)","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nc : Thing\nA : Thing\nH3 : Gives c A\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\nH4 : Gives c A\nHs : Gives c A\n============================\nnot (MemberOf c A)","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nc : Thing\nA : Thing\nH3 : Gives c A\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\nH4 : Gives c A\nHs : not (Gives c A)\n============================\nnot (MemberOf c A)","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nc : Thing\nA : Thing\nH3 : Gives c A\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nH4 : Gives c A\nX5 : Prop\nX6 : Prop\nX7 : Prop\nX8 : Prop\nX9 : Prop\nX10 : Prop\n============================\nnot (MemberOf c A)","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nc : Thing\nA : Thing\nH3 : Gives c A\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nH4 : Gives c A\nX5 : Prop\nX6 : Prop\nX7 : Prop\n============================\nGives c A","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nc : Thing\nA : Thing\nH3 : Gives c A\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nH4 : Gives c A\nX5 : Prop\nX6 : Prop\nX7 : Prop\nH5 : Gives c A\n============================\nnot (MemberOf c A)","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nc : Thing\nA : Thing\nH3 : Gives c A\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nH4 : Gives c A\nX5 : Prop\nX6 : Prop\nX7 : Prop\nHs : Gives c A\n============================\nnot (MemberOf c A)","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nc : Thing\nA : Thing\nH3 : Gives c A\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nH4 : Gives c A\nX5 : Prop\nX6 : Prop\nX7 : Prop\nHs : not (Gives c A)\n============================\nnot (MemberOf c A)","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP011\nc : Thing\nA : Thing\nH3 : Gives c A\nH4 : MemberOf c A\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\n============================\nFalse","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nc : Thing\nA : Thing\nH3 : Gives c A\nH4 : MemberOf c A\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\n============================\nFalse","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP011\nc : Thing\nA : Thing\nH4 : MemberOf c A\nX : Prop\nX0 : Prop\nX1 : Prop\n============================\nforall _ : Gives c A, False","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nc : Thing\nA : Thing\nH3 : Gives c A\nH4 : MemberOf c A\nX : Prop\nX0 : Prop\nX1 : Prop\n============================\n@eq Thing c A","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nc : Thing\nA : Thing\nH3 : Gives c A\nH4 : MemberOf c A\nX : Prop\nX0 : Prop\nX1 : Prop\nH5 : @eq Thing c A\n============================\nFalse","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nc : Thing\nA : Thing\nH3 : Gives c A\nH4 : MemberOf c A\nX : Prop\nX0 : Prop\nX1 : Prop\nHs : @eq Thing c A\n============================\nFalse","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nc : Thing\nA : Thing\nH3 : Gives c A\nH4 : MemberOf c A\nX : Prop\nX0 : Prop\nX1 : Prop\nHs : not (@eq Thing c A)\n============================\nFalse","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nc : Thing\nA : Thing\nH3 : Gives c A\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\nH4 : Gives c A\nX8 : Prop\nX9 : Prop\nX10 : Prop\nX11 : Prop\nX12 : Prop\nX13 : Prop\n============================\nnot (MemberOf c A)","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nc : Thing\nA : Thing\nH3 : Gives c A\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\nH4 : Gives c A\nX8 : Prop\nX9 : Prop\nX10 : Prop\n============================\nGives c c","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nc : Thing\nA : Thing\nH3 : Gives c A\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\nH4 : Gives c A\nX8 : Prop\nX9 : Prop\nX10 : Prop\nH5 : Gives c c\n============================\nnot (MemberOf c A)","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nc : Thing\nA : Thing\nH3 : Gives c A\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\nH4 : Gives c A\nX8 : Prop\nX9 : Prop\nX10 : Prop\nHs : Gives c c\n============================\nnot (MemberOf c A)","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nc : Thing\nA : Thing\nH3 : Gives c A\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\nH4 : Gives c A\nX8 : Prop\nX9 : Prop\nX10 : Prop\nHs : not (Gives c c)\n============================\nnot (MemberOf c A)","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nc : Thing\nA : Thing\nH3 : Gives c A\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\nH4 : Gives c A\nX8 : Prop\nX9 : Prop\nX10 : Prop\n============================\nGives c A","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nc : Thing\nA : Thing\nH3 : Gives c A\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\nH4 : Gives c A\nX8 : Prop\nX9 : Prop\nX10 : Prop\nH5 : Gives c A\n============================\nnot (MemberOf c A)","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nc : Thing\nA : Thing\nH3 : Gives c A\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\nH4 : Gives c A\nX8 : Prop\nX9 : Prop\nX10 : Prop\nHs : Gives c A\n============================\nnot (MemberOf c A)","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nc : Thing\nA : Thing\nH3 : Gives c A\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\nH4 : Gives c A\nX8 : Prop\nX9 : Prop\nX10 : Prop\nHs : not (Gives c A)\n============================\nnot (MemberOf c A)","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nc : Thing\nA : Thing\nH3 : Gives c A\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nH4 : Gives c A\nX5 : Prop\nX6 : Prop\nX7 : Prop\nX8 : Prop\nX9 : Prop\nX10 : Prop\nX11 : Prop\nX12 : Prop\nX13 : Prop\n============================\nnot (MemberOf c A)","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nc : Thing\nA : Thing\nH3 : Gives c A\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nH4 : Gives c A\nX5 : Prop\nX6 : Prop\nX7 : Prop\nX8 : Prop\nX9 : Prop\nX10 : Prop\n============================\nGives c c","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nc : Thing\nA : Thing\nH3 : Gives c A\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nH4 : Gives c A\nX5 : Prop\nX6 : Prop\nX7 : Prop\nX8 : Prop\nX9 : Prop\nX10 : Prop\nH5 : Gives c c\n============================\nnot (MemberOf c A)","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nc : Thing\nA : Thing\nH3 : Gives c A\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nH4 : Gives c A\nX5 : Prop\nX6 : Prop\nX7 : Prop\nX8 : Prop\nX9 : Prop\nX10 : Prop\nHs : Gives c c\n============================\nnot (MemberOf c A)","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nc : Thing\nA : Thing\nH3 : Gives c A\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nH4 : Gives c A\nX5 : Prop\nX6 : Prop\nX7 : Prop\nX8 : Prop\nX9 : Prop\nX10 : Prop\nHs : not (Gives c c)\n============================\nnot (MemberOf c A)","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nc : Thing\nA : Thing\nH3 : Gives c A\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nH4 : Gives c A\nX5 : Prop\nX6 : Prop\nX7 : Prop\nX8 : Prop\nX9 : Prop\nX10 : Prop\n============================\nGives c A","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nc : Thing\nA : Thing\nH3 : Gives c A\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nH4 : Gives c A\nX5 : Prop\nX6 : Prop\nX7 : Prop\nX8 : Prop\nX9 : Prop\nX10 : Prop\nH5 : Gives c A\n============================\nnot (MemberOf c A)","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nc : Thing\nA : Thing\nH3 : Gives c A\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nH4 : Gives c A\nX5 : Prop\nX6 : Prop\nX7 : Prop\nX8 : Prop\nX9 : Prop\nX10 : Prop\nHs : Gives c A\n============================\nnot (MemberOf c A)","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nc : Thing\nA : Thing\nH3 : Gives c A\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nH4 : Gives c A\nX5 : Prop\nX6 : Prop\nX7 : Prop\nX8 : Prop\nX9 : Prop\nX10 : Prop\nHs : not (Gives c A)\n============================\nnot (MemberOf c A)","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nc : Thing\nA : Thing\nH3 : Gives c A\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\nX8 : Prop\nX9 : Prop\nX10 : Prop\nH4 : Gives c A\nX11 : Prop\nX12 : Prop\nX13 : Prop\n============================\nnot (MemberOf c A)","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nc : Thing\nA : Thing\nH3 : Gives c A\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\nX8 : Prop\nX9 : Prop\nX10 : Prop\nH4 : Gives c A\n============================\nGives c A","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nc : Thing\nA : Thing\nH3 : Gives c A\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\nX8 : Prop\nX9 : Prop\nX10 : Prop\nH4 : Gives c A\nH5 : Gives c A\n============================\nnot (MemberOf c A)","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nc : Thing\nA : Thing\nH3 : Gives c A\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\nX8 : Prop\nX9 : Prop\nX10 : Prop\nH4 : Gives c A\nHs : Gives c A\n============================\nnot (MemberOf c A)","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nc : Thing\nA : Thing\nH3 : Gives c A\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\nX8 : Prop\nX9 : Prop\nX10 : Prop\nH4 : Gives c A\nHs : not (Gives c A)\n============================\nnot (MemberOf c A)","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nc : Thing\nA : Thing\nH3 : Gives c A\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\nX8 : Prop\nX9 : Prop\nX10 : Prop\nHs : Gives c A\nX11 : Prop\nX12 : Prop\nX13 : Prop\n============================\nnot (MemberOf c A)","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP011\nc : Thing\nA : Thing\nH3 : Gives c A\nH4 : MemberOf c A\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\n============================\nFalse","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nc : Thing\nA : Thing\nH3 : Gives c A\nH4 : MemberOf c A\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\n============================\nFalse","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nc : Thing\nA : Thing\nH3 : Gives c A\nH4 : MemberOf c A\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\n============================\n@eq Thing c A","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nc : Thing\nA : Thing\nH3 : Gives c A\nH4 : MemberOf c A\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nH5 : @eq Thing c A\n============================\nFalse","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nc : Thing\nA : Thing\nH3 : Gives c A\nH4 : MemberOf c A\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nHs : @eq Thing c A\n============================\nFalse","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nc : Thing\nA : Thing\nH3 : Gives c A\nH4 : MemberOf c A\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nHs : not (@eq Thing c A)\n============================\nFalse","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nc : Thing\nA : Thing\nH3 : Gives c A\nH4 : MemberOf c A\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nHs : Gives c A\n============================\nFalse","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nc : Thing\nA : Thing\nH3 : Gives c A\nH4 : MemberOf c A\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nHs : not (Gives c A)\n============================\nFalse","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nc : Thing\nA : Thing\nH3 : Gives c A\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\nH4 : Gives c A\nX8 : Prop\nX9 : Prop\nX10 : Prop\nX11 : Prop\nX12 : Prop\nX13 : Prop\nX14 : Prop\nX15 : Prop\nX16 : Prop\n============================\nnot (MemberOf c A)","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nc : Thing\nA : Thing\nH3 : Gives c A\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\nH4 : Gives c A\nX8 : Prop\nX9 : Prop\nX10 : Prop\nX11 : Prop\nX12 : Prop\nX13 : Prop\n============================\nGives c A","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nc : Thing\nA : Thing\nH3 : Gives c A\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\nH4 : Gives c A\nX8 : Prop\nX9 : Prop\nX10 : Prop\nX11 : Prop\nX12 : Prop\nX13 : Prop\nH5 : Gives c A\n============================\nnot (MemberOf c A)","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nc : Thing\nA : Thing\nH3 : Gives c A\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\nH4 : Gives c A\nX8 : Prop\nX9 : Prop\nX10 : Prop\nX11 : Prop\nX12 : Prop\nX13 : Prop\nHs : Gives c A\n============================\nnot (MemberOf c A)","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nc : Thing\nA : Thing\nH3 : Gives c A\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\nH4 : Gives c A\nX8 : Prop\nX9 : Prop\nX10 : Prop\nX11 : Prop\nX12 : Prop\nX13 : Prop\nHs : not (Gives c A)\n============================\nnot (MemberOf c A)","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nc : Thing\nA : Thing\nH3 : Gives c A\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\nX8 : Prop\nX9 : Prop\nX10 : Prop\nX11 : Prop\nX12 : Prop\nX13 : Prop\nH4 : Gives c A\nX14 : Prop\nX15 : Prop\nX16 : Prop\n============================\nnot (MemberOf c A)","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nc : Thing\nA : Thing\nH3 : Gives c A\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\nX8 : Prop\nX9 : Prop\nX10 : Prop\nX11 : Prop\nX12 : Prop\nX13 : Prop\nH4 : Gives c A\n============================\nGives c A","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nc : Thing\nA : Thing\nH3 : Gives c A\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\nX8 : Prop\nX9 : Prop\nX10 : Prop\nX11 : Prop\nX12 : Prop\nX13 : Prop\nH4 : Gives c A\nH5 : Gives c A\n============================\nnot (MemberOf c A)","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nc : Thing\nA : Thing\nH3 : Gives c A\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\nX8 : Prop\nX9 : Prop\nX10 : Prop\nX11 : Prop\nX12 : Prop\nX13 : Prop\nH4 : Gives c A\nHs : Gives c A\n============================\nnot (MemberOf c A)","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nc : Thing\nA : Thing\nH3 : Gives c A\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\nX8 : Prop\nX9 : Prop\nX10 : Prop\nX11 : Prop\nX12 : Prop\nX13 : Prop\nH4 : Gives c A\nHs : not (Gives c A)\n============================\nnot (MemberOf c A)","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nc : Thing\nA : Thing\nH3 : Gives c A\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\nX8 : Prop\nX9 : Prop\nX10 : Prop\nX11 : Prop\nX12 : Prop\nX13 : Prop\nHs : Gives c A\nX14 : Prop\nX15 : Prop\nX16 : Prop\n============================\nnot (MemberOf c A)","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nc : Thing\nA : Thing\nH3 : Gives c A\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nH4 : Gives c A\nX5 : Prop\nX6 : Prop\nX7 : Prop\nX8 : Prop\nX9 : Prop\nX10 : Prop\nX11 : Prop\nX12 : Prop\nX13 : Prop\nX14 : Prop\nX15 : Prop\nX16 : Prop\n============================\nnot (MemberOf c A)","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nc : Thing\nA : Thing\nH3 : Gives c A\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nH4 : Gives c A\nX5 : Prop\nX6 : Prop\nX7 : Prop\nX8 : Prop\nX9 : Prop\nX10 : Prop\nX11 : Prop\nX12 : Prop\nX13 : Prop\n============================\nGives c A","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nc : Thing\nA : Thing\nH3 : Gives c A\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nH4 : Gives c A\nX5 : Prop\nX6 : Prop\nX7 : Prop\nX8 : Prop\nX9 : Prop\nX10 : Prop\nX11 : Prop\nX12 : Prop\nX13 : Prop\nH5 : Gives c A\n============================\nnot (MemberOf c A)","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nc : Thing\nA : Thing\nH3 : Gives c A\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nH4 : Gives c A\nX5 : Prop\nX6 : Prop\nX7 : Prop\nX8 : Prop\nX9 : Prop\nX10 : Prop\nX11 : Prop\nX12 : Prop\nX13 : Prop\nHs : Gives c A\n============================\nnot (MemberOf c A)","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nc : Thing\nA : Thing\nH3 : Gives c A\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nH4 : Gives c A\nX5 : Prop\nX6 : Prop\nX7 : Prop\nX8 : Prop\nX9 : Prop\nX10 : Prop\nX11 : Prop\nX12 : Prop\nX13 : Prop\nHs : not (Gives c A)\n============================\nnot (MemberOf c A)","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nc : Thing\nA : Thing\nH3 : Gives c A\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\nX8 : Prop\nX9 : Prop\nX10 : Prop\nH4 : Gives c A\nX11 : Prop\nX12 : Prop\nX13 : Prop\nX14 : Prop\nX15 : Prop\nX16 : Prop\n============================\nnot (MemberOf c A)","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nc : Thing\nA : Thing\nH3 : Gives c A\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\nX8 : Prop\nX9 : Prop\nX10 : Prop\nH4 : Gives c A\nX11 : Prop\nX12 : Prop\nX13 : Prop\n============================\nGives c A","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nc : Thing\nA : Thing\nH3 : Gives c A\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\nX8 : Prop\nX9 : Prop\nX10 : Prop\nH4 : Gives c A\nX11 : Prop\nX12 : Prop\nX13 : Prop\nH5 : Gives c A\n============================\nnot (MemberOf c A)","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nc : Thing\nA : Thing\nH3 : Gives c A\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\nX8 : Prop\nX9 : Prop\nX10 : Prop\nH4 : Gives c A\nX11 : Prop\nX12 : Prop\nX13 : Prop\nHs : Gives c A\n============================\nnot (MemberOf c A)","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nc : Thing\nA : Thing\nH3 : Gives c A\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\nX8 : Prop\nX9 : Prop\nX10 : Prop\nH4 : Gives c A\nX11 : Prop\nX12 : Prop\nX13 : Prop\nHs : not (Gives c A)\n============================\nnot (MemberOf c A)","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nc : Thing\nA : Thing\nH3 : Gives c A\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\nX8 : Prop\nX9 : Prop\nX10 : Prop\nHs : Gives c A\nX11 : Prop\nX12 : Prop\nX13 : Prop\nX14 : Prop\nX15 : Prop\nX16 : Prop\n============================\nnot (MemberOf c A)","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP011\nc : Thing\nA : Thing\nH3 : Gives c A\nH4 : MemberOf c A\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\nX8 : Prop\nX9 : Prop\nX10 : Prop\n============================\nFalse","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nc : Thing\nA : Thing\nH3 : Gives c A\nH4 : MemberOf c A\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\nX8 : Prop\nX9 : Prop\nX10 : Prop\n============================\nFalse","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP011\nc : Thing\nA : Thing\nH3 : Gives c A\nH4 : MemberOf c A\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\n============================\nforall _ : Gives c A, False","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP011\nc : Thing\nA : Thing\nH3 : Gives c A\nH4 : MemberOf c A\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\n============================\nGives c A","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP011\nc : Thing\nA : Thing\nH3 : Gives c A\nH4 : MemberOf c A\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\nH5 : Gives c A\n============================\nFalse","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP011\nc : Thing\nA : Thing\nH3 : Gives c A\nH4 : MemberOf c A\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\nHs : Gives c A\n============================\nFalse","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP011\nc : Thing\nA : Thing\nH3 : Gives c A\nH4 : MemberOf c A\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\nHs : not (Gives c A)\n============================\nFalse","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nc : Thing\nA : Thing\nH3 : Gives c A\nH4 : MemberOf c A\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\n============================\n@eq Thing c A","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nc : Thing\nA : Thing\nH3 : Gives c A\nH4 : MemberOf c A\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\nH5 : @eq Thing c A\n============================\nFalse","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nc : Thing\nA : Thing\nH3 : Gives c A\nH4 : MemberOf c A\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\nHs : @eq Thing c A\n============================\nFalse","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nc : Thing\nA : Thing\nH3 : Gives c A\nH4 : MemberOf c A\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\nHs : not (@eq Thing c A)\n============================\nFalse","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nc : Thing\nA : Thing\nH3 : Gives c A\nH4 : MemberOf c A\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\nHs : Gives c A\n============================\nFalse","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nc : Thing\nA : Thing\nH3 : Gives c A\nH4 : MemberOf c A\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\nHs : not (Gives c A)\n============================\nFalse","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nc : Thing\nA : Thing\nH3 : Gives c A\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\nH4 : Gives c A\nX8 : Prop\nX9 : Prop\nX10 : Prop\nX11 : Prop\nX12 : Prop\nX13 : Prop\nX14 : Prop\nX15 : Prop\nX16 : Prop\n============================\nGives c A","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nc : Thing\nA : Thing\nH3 : Gives c A\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\nH4 : Gives c A\nX8 : Prop\nX9 : Prop\nX10 : Prop\nX11 : Prop\nX12 : Prop\nX13 : Prop\nX14 : Prop\nX15 : Prop\nX16 : Prop\nH5 : Gives c A\n============================\nnot (MemberOf c A)","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nc : Thing\nA : Thing\nH3 : Gives c A\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\nH4 : Gives c A\nX8 : Prop\nX9 : Prop\nX10 : Prop\nX11 : Prop\nX12 : Prop\nX13 : Prop\nX14 : Prop\nX15 : Prop\nX16 : Prop\nHs : Gives c A\n============================\nnot (MemberOf c A)","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nc : Thing\nA : Thing\nH3 : Gives c A\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\nH4 : Gives c A\nX8 : Prop\nX9 : Prop\nX10 : Prop\nX11 : Prop\nX12 : Prop\nX13 : Prop\nX14 : Prop\nX15 : Prop\nX16 : Prop\nHs : not (Gives c A)\n============================\nnot (MemberOf c A)","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nc : Thing\nA : Thing\nH3 : Gives c A\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\nX8 : Prop\nX9 : Prop\nX10 : Prop\nX11 : Prop\nX12 : Prop\nX13 : Prop\nH4 : Gives c A\nX14 : Prop\nX15 : Prop\nX16 : Prop\nX17 : Prop\nX18 : Prop\nX19 : Prop\n============================\nnot (MemberOf c A)","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nc : Thing\nA : Thing\nH3 : Gives c A\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\nX8 : Prop\nX9 : Prop\nX10 : Prop\nX11 : Prop\nX12 : Prop\nX13 : Prop\nH4 : Gives c A\nX14 : Prop\nX15 : Prop\nX16 : Prop\n============================\nGives c A","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nc : Thing\nA : Thing\nH3 : Gives c A\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\nX8 : Prop\nX9 : Prop\nX10 : Prop\nX11 : Prop\nX12 : Prop\nX13 : Prop\nH4 : Gives c A\nX14 : Prop\nX15 : Prop\nX16 : Prop\nH5 : Gives c A\n============================\nnot (MemberOf c A)","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nc : Thing\nA : Thing\nH3 : Gives c A\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\nX8 : Prop\nX9 : Prop\nX10 : Prop\nX11 : Prop\nX12 : Prop\nX13 : Prop\nH4 : Gives c A\nX14 : Prop\nX15 : Prop\nX16 : Prop\nHs : Gives c A\n============================\nnot (MemberOf c A)","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nc : Thing\nA : Thing\nH3 : Gives c A\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\nX8 : Prop\nX9 : Prop\nX10 : Prop\nX11 : Prop\nX12 : Prop\nX13 : Prop\nH4 : Gives c A\nX14 : Prop\nX15 : Prop\nX16 : Prop\nHs : not (Gives c A)\n============================\nnot (MemberOf c A)","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nc : Thing\nA : Thing\nH3 : Gives c A\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\nX8 : Prop\nX9 : Prop\nX10 : Prop\nX11 : Prop\nX12 : Prop\nX13 : Prop\nH4 : Gives c A\nX14 : Prop\nX15 : Prop\nX16 : Prop\n============================\nGives c c","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nc : Thing\nA : Thing\nH3 : Gives c A\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\nX8 : Prop\nX9 : Prop\nX10 : Prop\nX11 : Prop\nX12 : Prop\nX13 : Prop\nH4 : Gives c A\nX14 : Prop\nX15 : Prop\nX16 : Prop\nH5 : Gives c c\n============================\nnot (MemberOf c A)","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nc : Thing\nA : Thing\nH3 : Gives c A\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\nX8 : Prop\nX9 : Prop\nX10 : Prop\nX11 : Prop\nX12 : Prop\nX13 : Prop\nH4 : Gives c A\nX14 : Prop\nX15 : Prop\nX16 : Prop\nHs : Gives c c\n============================\nnot (MemberOf c A)","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nc : Thing\nA : Thing\nH3 : Gives c A\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\nX8 : Prop\nX9 : Prop\nX10 : Prop\nX11 : Prop\nX12 : Prop\nX13 : Prop\nH4 : Gives c A\nX14 : Prop\nX15 : Prop\nX16 : Prop\nHs : not (Gives c c)\n============================\nnot (MemberOf c A)","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nc : Thing\nA : Thing\nH3 : Gives c A\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\nX8 : Prop\nX9 : Prop\nX10 : Prop\nX11 : Prop\nX12 : Prop\nX13 : Prop\nHs : Gives c A\nX14 : Prop\nX15 : Prop\nX16 : Prop\nX17 : Prop\nX18 : Prop\nX19 : Prop\n============================\nnot (MemberOf c A)"],"events":[{"g":0,"t":"assumption","w":"auto","ok":false,"err":"Error: No such assumption."},{"g":0,"t":"tauto","w":"auto","ok":false,"err":"Error: Tactic failure: Classical tauto failed."},{"g":0,"t":"firstorder","w":"auto","ok":true,"c":[1]},{"g":0,"t":"congruence","w":"auto","ok":false,"err":"Error: Tactic failure: congruence failed."},{"g":0,"t":"unfold MP001, MP002, MP003, MP011 in *; firstorder","w":"auto","ok":true,"c":[2]},{"g":0,"t":"unfold MP001, MP002, MP003, MP011 in *; hammer","w":"hammer","ok":false,"err":"Error: Hammer failed: ATPs failed to f"},{"g":0,"t":"split","w":"model","ok":false,"err":"Error: Not an inductive goal with 1 constructor."},{"g":0,"t":"intros","w":"model","ok":true,"c":[3]},{"g":0,"t":"right","w":"model","ok":false,"err":"Error: Not an inductive goal with 2 constructors."},{"g":0,"t":"split; intros","w":"model","ok":false,"err":"Error: Not an inductive goal with 1 constructor."},{"g":1,"t":"assumption","w":"auto","ok":false,"err":"Error: No such assumption."},{"g":1,"t":"tauto","w":"auto","ok":false,"err":"Error: Tactic failure: Classical tauto failed."},{"g":1,"t":"firstorder","w":"auto","ok":true,"c":[4]},{"g":1,"t":"congruence","w":"auto","ok":false,"err":"Error: Tactic failure: congruence failed."},{"g":1,"t":"unfold MP001, MP002, MP003, MP011 in *; firstorder","w":"auto","ok":true,"c":[5]},{"g":1,"t":"unfold MP001, MP002, MP003, MP011 in *; hammer","w":"hammer","ok":false,"err":"Error: Hammer failed: ATPs failed to f"},{"g":1,"t":"apply not_Gives","w":"model","ok":false,"err":"Error: The variable not_Gives was not found in the current environment."},{"g":1,"t":"apply GivesNoC of c A","w":"model","ok":false,"err":"Error: Syntax error: ')' expected after [ltac_expr] (in [lt"},{"g":2,"t":"assumption","w":"auto","ok":false,"err":"Error: No such assumption."},{"g":2,"t":"tauto","w":"auto","ok":false,"err":"Error: Tactic failure: Classical tauto failed."},{"g":2,"t":"firstorder","w":"auto","ok":false,"err":"Error: Timeout!"},{"g":2,"t":"congruence","w":"auto","ok":false,"err":"Error: Tactic failure: congruence failed."},{"g":2,"t":"hammer","w":"hammer","ok":false,"err":"Error: Hammer failed: ATPs failed to f"},{"g":2,"t":"apply H0","w":"model","ok":false,"err":"rejected"},{"g":2,"t":"apply H1","w":"model","ok":false,"err":"rejected"},{"g":2,"t":"apply H1; intros","w":"model","ok":false,"err":"rejected"},{"g":2,"t":"assert (Gives c 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firstorder","w":"auto","ok":true,"c":[6]},{"g":4,"t":"unfold MP001, MP002, MP003, MP011 in *; hammer","w":"hammer","ok":false,"err":"Error: Hammer failed: ATPs failed to f"},{"g":4,"t":"apply not_Gives_c","w":"model","ok":false,"err":"Error: The variable not_Gives_c was not found in the current enviro"},{"g":4,"t":"apply not_Gives","w":"model","ok":false,"err":"Error: The variable not_Gives was not found in the current environment."},{"g":4,"t":"intros","w":"model","ok":true,"c":[4]},{"g":5,"t":"assumption","w":"auto","ok":false,"err":"Error: No such assumption."},{"g":5,"t":"tauto","w":"auto","ok":false,"err":"Error: Tactic failure: Classical tauto failed."},{"g":5,"t":"firstorder","w":"auto","ok":true,"c":[6]},{"g":5,"t":"congruence","w":"auto","ok":false,"err":"Error: Tactic failure: congruence failed."},{"g":5,"t":"hammer","w":"hammer","ok":false,"err":"Error: Hammer failed: ATPs failed to f"},{"g":5,"t":"apply H0","w":"model","ok":false,"err":"rejected"},{"g":5,"t":"apply 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Tactic failure: Classical tauto failed."},{"g":3,"t":"firstorder","w":"auto","ok":true,"c":[1]},{"g":3,"t":"congruence","w":"auto","ok":false,"err":"Error: Tactic failure: congruence failed."},{"g":3,"t":"unfold MP001, MP002, MP003, MP011 in *; firstorder","w":"auto","ok":true,"c":[2]},{"g":3,"t":"unfold MP001, MP002, MP003, MP011 in *; hammer","w":"hammer","ok":false,"err":"Error: Hammer failed: ATPs failed to f"},{"g":3,"t":"intro","w":"model","ok":true,"c":[11]},{"g":3,"t":"apply not_Gives_c","w":"model","ok":false,"err":"Error: The variable not_Gives_c was not found in the current enviro"},{"g":3,"t":"apply GivesNoMemOf; trivial","w":"model","ok":false,"err":"Error: The variable GivesNoMemOf was not found"},{"g":6,"t":"assumption","w":"auto","ok":false,"err":"Error: No such assumption."},{"g":6,"t":"tauto","w":"auto","ok":false,"err":"Error: Tactic failure: Classical tauto failed."},{"g":6,"t":"firstorder","w":"auto","ok":true,"c":[12]},{"g":6,"t":"congruence","w":"auto","ok":false,"err":"Error: Tactic failure: congruence failed."},{"g":6,"t":"hammer","w":"hammer","ok":false,"err":"Error: Hammer failed: ATPs failed to f"},{"g":6,"t":"apply H0","w":"model","ok":false,"err":"rejected"},{"g":6,"t":"apply H1","w":"model","ok":false,"err":"rejected"},{"g":6,"t":"apply H1; intros","w":"model","ok":false,"err":"rejected"},{"g":6,"t":"assert (Gives c A)","w":"model","ok":true,"c":[13,14]},{"g":13,"t":"assumption","w":"auto","ok":true,"c":[],"eager":true},{"g":6,"t":"destruct (classic (Gives c A)) as [Hs|Hs]","w":"model","ok":true,"c":[15,16]},{"g":16,"t":"tauto","w":"auto","ok":true,"c":[],"eager":true},{"g":6,"t":"apply H1; ApplyH","w":"model","ok":false,"err":"Error: The reference ApplyH was not found in the current environment."},{"g":6,"t":"apply H1; apply H2","w":"model","ok":false,"err":"rejected"},{"g":6,"t":"assert (G : Gives c 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Timeout!"},{"g":17,"t":"congruence","w":"auto","ok":false,"err":"Error: Tactic failure: congruence failed."},{"g":17,"t":"hammer","w":"hammer","ok":false,"err":"Error: Hammer failed: ATPs failed to f"},{"g":17,"t":"apply H0","w":"model","ok":false,"err":"rejected"},{"g":17,"t":"apply H1","w":"model","ok":false,"err":"rejected"},{"g":17,"t":"apply H1; intros","w":"model","ok":false,"err":"rejected"},{"g":17,"t":"assert (Gives c A)","w":"model","ok":true,"c":[22,23]},{"g":22,"t":"assumption","w":"auto","ok":true,"c":[],"eager":true},{"g":17,"t":"destruct (classic (Gives c A)) as [Hs|Hs]","w":"model","ok":true,"c":[24,25]},{"g":25,"t":"tauto","w":"auto","ok":true,"c":[],"eager":true},{"g":17,"t":"assert (Gives y A)","w":"model","ok":false,"err":"Error: The variable y was not found in the current environment."},{"g":17,"t":"destruct (classic (Gives y A)) as [Hs|Hs]","w":"model","ok":false,"err":"Error: The"},{"g":17,"t":"intros","w":"model","ok":true,"c":[17]},{"g":17,"t":"apply H1; 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MP011 in *; hammer","w":"hammer","ok":false,"err":"Error: Hammer failed: ATPs failed to f"},{"g":78,"t":"elim X7","w":"model","ok":false,"err":"Error: Not an inductive product."},{"g":78,"t":"cut (Gives c A)","w":"model","ok":true,"c":[110,111]},{"g":111,"t":"assumption","w":"auto","ok":true,"c":[],"eager":true},{"g":78,"t":"assert (Gives c A)","w":"model","ok":true,"c":[111,112]},{"g":78,"t":"destruct (classic (Gives c A)) as [Hs|Hs]","w":"model","ok":true,"c":[113,114]},{"g":114,"t":"tauto","w":"auto","ok":true,"c":[],"eager":true},{"g":78,"t":"apply (G1 c A H3)","w":"model","ok":false,"err":"Error: The variable G1 was not found in the current environment."},{"g":78,"t":"generalize (gives_empty c A H3)","w":"model","ok":false,"err":"Error: The variable gives_empty w"},{"g":78,"t":"apply (G1 c A H H3)","w":"model","ok":false,"err":"Error: The variable G1 was not found in the current environment."},{"g":78,"t":"apply (G1 c A H3 X)","w":"model","ok":false,"err":"Error: The variable G1 was not found in the current environment."},{"g":78,"t":"generalize (gives_copies c A H3)","w":"model","ok":false,"err":"Error: The variable gives_copi"},{"g":79,"t":"assumption","w":"auto","ok":false,"err":"Error: No such assumption."},{"g":79,"t":"tauto","w":"auto","ok":false,"err":"Error: Tactic failure: Classical tauto failed."},{"g":79,"t":"firstorder","w":"auto","ok":true,"c":[109]},{"g":79,"t":"congruence","w":"auto","ok":false,"err":"Error: Tactic failure: congruence failed."},{"g":79,"t":"hammer","w":"hammer","ok":false,"err":"Error: Hammer failed: ATPs failed to f"},{"g":79,"t":"apply H","w":"model","ok":false,"err":"rejected"},{"g":79,"t":"assert (Gives c X)","w":"model","ok":false,"err":"rejected"},{"g":79,"t":"destruct (classic (Gives c X)) as [Hs|Hs]","w":"model","ok":false,"err":"rejected"},{"g":79,"t":"cut (Gives c X)","w":"model","ok":false,"err":"rejected"},{"g":79,"t":"assert (c = A)","w":"model","ok":true,"c":[115,116]},{"g":79,"t":"destruct (classic (c = A)) as [Hs|Hs]","w":"model","ok":true,"c":[117,118]},{"g":79,"t":"generalize (H c A H3)","w":"model","ok":false,"err":"rejected"},{"g":79,"t":"destruct (classic (Gives c A)) as [Hs|Hs]","w":"model","ok":true,"c":[119,120]},{"g":120,"t":"tauto","w":"auto","ok":true,"c":[],"eager":true},{"g":79,"t":"destruct (classic (Gives y x)) as [Hs|Hs]","w":"model","ok":false,"err":"Error: The"},{"g":79,"t":"generalize (H0 c X1)","w":"model","ok":false,"err":"rejected"},{"g":86,"t":"assumption","w":"auto","ok":false,"err":"Error: No such assumption."},{"g":86,"t":"tauto","w":"auto","ok":false,"err":"Error: Tactic failure: Classical tauto failed."},{"g":86,"t":"firstorder","w":"auto","ok":false,"err":"Error: Timeout!"},{"g":86,"t":"congruence","w":"auto","ok":false,"err":"Error: Tactic failure: congruence failed."},{"g":86,"t":"hammer","w":"hammer","ok":false,"err":"Error: Hammer failed: ATPs failed to f"},{"g":86,"t":"apply H0","w":"model","ok":false,"err":"rejected"},{"g":86,"t":"apply H1","w":"model","ok":false,"err":"rejected"},{"g":86,"t":"apply H1; intros","w":"model","ok":false,"err":"rejected"},{"g":86,"t":"apply H1; ApplyH","w":"model","ok":false,"err":"Error: The reference ApplyH was not found in the current environment."},{"g":86,"t":"intros","w":"model","ok":true,"c":[86]},{"g":86,"t":"assert (Gives c A)","w":"model","ok":true,"c":[121,122]},{"g":121,"t":"assumption","w":"auto","ok":true,"c":[],"eager":true},{"g":86,"t":"destruct (classic (Gives c A)) as [Hs|Hs]","w":"model","ok":true,"c":[123,124]},{"g":124,"t":"tauto","w":"auto","ok":true,"c":[],"eager":true},{"g":86,"t":"apply H1; apply H2","w":"model","ok":false,"err":"rejected"},{"g":91,"t":"assumption","w":"auto","ok":false,"err":"Error: No such assumption."},{"g":91,"t":"tauto","w":"auto","ok":false,"err":"Error: Tactic failure: Classical tauto failed."},{"g":91,"t":"firstorder","w":"auto","ok":true,"c":[125]},{"g":91,"t":"congruence","w":"auto","ok":false,"err":"Error: Tactic failure: congruence failed."},{"g":91,"t":"hammer","w":"hammer","ok":false,"err":"Error: Hammer failed: ATPs failed to f"},{"g":91,"t":"apply H0","w":"model","ok":false,"err":"rejected"},{"g":91,"t":"apply H1","w":"model","ok":false,"err":"rejected"},{"g":91,"t":"apply H1; ApplyH","w":"model","ok":false,"err":"Error: The reference ApplyH was not found in the current environment."},{"g":91,"t":"assert (Gives c A)","w":"model","ok":true,"c":[126,127]},{"g":126,"t":"assumption","w":"auto","ok":true,"c":[],"eager":true},{"g":91,"t":"destruct (classic (Gives c A)) as [Hs|Hs]","w":"model","ok":true,"c":[128,129]},{"g":129,"t":"tauto","w":"auto","ok":true,"c":[],"eager":true},{"g":91,"t":"intros","w":"model","ok":true,"c":[91]},{"g":91,"t":"apply H0; ApplyH","w":"model","ok":false,"err":"Error: The reference ApplyH was not found in the current environment."},{"g":91,"t":"assert (Gives c c)","w":"model","ok":true,"c":[130,131]},{"g":131,"t":"firstorder","w":"auto","ok":true,"c":[],"eager":true},{"g":91,"t":"destruct (classic (Gives c c)) as [Hs|Hs]","w":"model","ok":true,"c":[132,133]},{"g":132,"t":"firstorder","w":"auto","ok":true,"c":[],"eager":true},{"g":96,"t":"assumption","w":"auto","ok":false,"err":"Error: No such assumption."},{"g":96,"t":"tauto","w":"auto","ok":false,"err":"Error: Tactic failure: Classical tauto failed."},{"g":96,"t":"firstorder","w":"auto","ok":true,"c":[134]},{"g":96,"t":"congruence","w":"auto","ok":false,"err":"Error: Tactic failure: congruence failed."},{"g":96,"t":"hammer","w":"hammer","ok":false,"err":"Error: Hammer failed: ATPs failed to f"}],"proof":[],"proofFile":null},{"key":"round6/imkan_s8_no_internal_cause","id":"imkan_s8_no_internal_cause","run":"round6","title":"Dalīl al-imkān, step 8","english":"Neither a member, nor a group of members, nor the aggregate gives the aggregate existence.","stmt":"MP001 -> MP002 -> MP003 -> MP010 -> MP011 -> forall A, AggregateOfPossibles A -> (forall x, ~ Gives x x) /\\ ~ Gives A A /\\ (forall c, MemberOf c A -> ~ Gives c A) /\\ (forall B, B <> A -> Exists B -> (exists p, MemberOf p B) -> (forall p, MemberOf p B -> MemberOf p A) -> ~ Gives B A)","proved":false,"script":"","seconds":902.7,"expansions":10,"calls":562,"root":0,"goals":["============================\nMP001 -> MP002 -> MP003 -> MP010 -> MP011 -> forall A, AggregateOfPossibles A -> (forall x, ~ Gives x x) /\\ ~ Gives A A /\\ (forall c, MemberOf c A -> ~ Gives c A) /\\ (forall B, B <> A -> Exists B -> (exists p, MemberOf p B) -> (forall p, MemberOf p B -> MemberOf p A) -> ~ Gives B A)","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP010\nH3 : MP011\nA : Thing\nH4 : AggregateOfPossibles A\n============================\nand (forall x : Thing, not (Gives x x)) (and (not (Gives A A)) (and (forall (c : Thing) (_ : MemberOf c A), not (Gives c A)) (forall (B : Thing) (_ : not (@eq Thing B A)) (_ : Exists B) (_ : @ex Thing (fun p : Thing => MemberOf p B)) (_ : forall (p : Thing) (_ : MemberOf p B), MemberOf p A), not (Gives B A))))","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP010\nH3 : MP011\nA : Thing\nH4 : AggregateOfPossibles A\n============================\nforall x : Thing, not (Gives x x)","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP010\nH3 : MP011\nA : Thing\nH4 : AggregateOfPossibles A\n============================\nand (not (Gives A A)) (and (forall (c : Thing) (_ : MemberOf c A), not (Gives c A)) (forall (B : Thing) (_ : not (@eq Thing B A)) (_ : Exists B) (_ : @ex Thing (fun p : Thing => MemberOf p B)) (_ : forall (p : Thing) (_ : MemberOf p B), MemberOf p A), not (Gives B A)))","A0 : MP001\n============================\nforall (_ : MP002) (_ : MP003) (_ : MP010) (_ : MP011) (A : Thing) (_ : AggregateOfPossibles A), and (forall x : Thing, not (Gives x x)) (and (not (Gives A A)) (and (forall (c : Thing) (_ : MemberOf c A), not (Gives c A)) (forall (B : Thing) (_ : not (@eq Thing B A)) (_ : Exists B) (_ : @ex Thing (fun p : Thing => MemberOf p B)) (_ : forall (p : Thing) (_ : MemberOf p B), MemberOf p A), not (Gives B A))))","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP010\nH3 : MP011\nA : Thing\nH4 : AggregateOfPossibles A\nx : Thing\n============================\nnot (Gives x x)","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP010\nH3 : MP011\nA : Thing\nH4 : AggregateOfPossibles A\n============================\nnot (Gives A A)","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP010\nH3 : MP011\nA : Thing\nH4 : AggregateOfPossibles A\nH5 : not (Gives A A)\n============================\nand (forall x : Thing, not (Gives x x)) (and (not (Gives A A)) (and (forall (c : Thing) (_ : MemberOf c A), not (Gives c A)) (forall (B : Thing) (_ : not (@eq Thing B A)) (_ : Exists B) (_ : @ex Thing (fun p : Thing => MemberOf p B)) (_ : forall (p : Thing) (_ : MemberOf p B), MemberOf p A), not (Gives B A))))","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP010\nH3 : MP011\nA : Thing\nH4 : AggregateOfPossibles A\nHs : not (Gives A A)\n============================\nand (forall x : Thing, not (Gives x x)) (and (not (Gives A A)) (and (forall (c : Thing) (_ : MemberOf c A), not (Gives c A)) (forall (B : Thing) (_ : not (@eq Thing B A)) (_ : Exists B) (_ : @ex Thing (fun p : Thing => MemberOf p B)) (_ : forall (p : Thing) (_ : MemberOf p B), MemberOf p A), not (Gives B A))))","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP010\nH3 : MP011\nA : Thing\nH4 : AggregateOfPossibles A\nHs : not (not (Gives A A))\n============================\nand (forall x : Thing, not (Gives x x)) (and (not (Gives A A)) (and (forall (c : Thing) (_ : MemberOf c A), not (Gives c A)) (forall (B : Thing) (_ : not (@eq Thing B A)) (_ : Exists B) (_ : @ex Thing (fun p : Thing => MemberOf p B)) (_ : forall (p : Thing) (_ : MemberOf p B), MemberOf p A), not (Gives B A))))","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP010\nH3 : MP011\nA : Thing\nH4 : AggregateOfPossibles A\n============================\nGives A A","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP010\nH3 : MP011\nA : Thing\nH4 : AggregateOfPossibles A\nH5 : Gives A A\n============================\nand (forall x : Thing, not (Gives x x)) (and (not (Gives A A)) (and (forall (c : Thing) (_ : MemberOf c A), not (Gives c A)) (forall (B : Thing) (_ : not (@eq Thing B A)) (_ : Exists B) (_ : @ex Thing (fun p : Thing => MemberOf p B)) (_ : forall (p : Thing) (_ : MemberOf p B), MemberOf p A), not (Gives B A))))","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP010\nH3 : MP011\nA : Thing\nH4 : AggregateOfPossibles A\nHs : Gives A A\n============================\nand (forall x : Thing, not (Gives x x)) (and (not (Gives A A)) (and (forall (c : Thing) (_ : MemberOf c A), not (Gives c A)) (forall (B : Thing) (_ : not (@eq Thing B A)) (_ : Exists B) (_ : @ex Thing (fun p : Thing => MemberOf p B)) (_ : forall (p : Thing) (_ : MemberOf p B), MemberOf p A), not (Gives B A))))","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP010\nH3 : MP011\nA : Thing\nH4 : AggregateOfPossibles A\n============================\nThing","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP010\nH3 : MP011\nA : Thing\nH4 : AggregateOfPossibles A\nB : Thing\n============================\nand (forall x : Thing, not (Gives x x)) (and (not (Gives A A)) (and (forall (c : Thing) (_ : MemberOf c A), not (Gives c A)) (forall (B0 : Thing) (_ : not (@eq Thing B0 A)) (_ : Exists B0) (_ : @ex Thing (fun p : Thing => MemberOf p B0)) (_ : forall (p : Thing) (_ : MemberOf p B0), MemberOf p A), not (Gives B0 A))))","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP010\nH3 : MP011\nA : Thing\nH4 : AggregateOfPossibles A\n============================\nand (forall (c : Thing) (_ : MemberOf c A), not (Gives c A)) (forall (B : Thing) (_ : not (@eq Thing B A)) (_ : Exists B) (_ : @ex Thing (fun p : Thing => MemberOf p B)) (_ : forall (p : Thing) (_ : MemberOf p B), MemberOf p A), not (Gives B A))","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP010\nH3 : MP011\nA : Thing\nH4 : AggregateOfPossibles A\nH5 : Gives A A\n============================\nand (not (Gives A A)) (and (forall (c : Thing) (_ : MemberOf c A), not (Gives c A)) (forall (B : Thing) (_ : not (@eq Thing B A)) (_ : Exists B) (_ : @ex Thing (fun p : Thing => MemberOf p B)) (_ : forall (p : Thing) (_ : MemberOf p B), MemberOf p A), not (Gives B A)))","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP010\nH3 : MP011\nA : Thing\nH4 : AggregateOfPossibles A\nHs : Gives A A\n============================\nand (not (Gives A A)) (and (forall (c : Thing) (_ : MemberOf c A), not (Gives c A)) (forall (B : Thing) (_ : not (@eq Thing B A)) (_ : Exists B) (_ : @ex Thing (fun p : Thing => MemberOf p B)) (_ : forall (p : Thing) (_ : MemberOf p B), MemberOf p A), not (Gives B A)))","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP010\nH3 : MP011\nA : Thing\nH4 : AggregateOfPossibles A\nHs : not (Gives A A)\n============================\nand (not (Gives A A)) (and (forall (c : Thing) (_ : MemberOf c A), not (Gives c A)) (forall (B : Thing) (_ : not (@eq Thing B A)) (_ : Exists B) (_ : @ex Thing (fun p : Thing => MemberOf p B)) (_ : forall (p : Thing) (_ : MemberOf p B), MemberOf p A), not (Gives B A)))","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP010\nH3 : MP011\nA : Thing\nH4 : AggregateOfPossibles A\nB : Thing\n============================\nand (not (Gives A A)) (and (forall (c : Thing) (_ : MemberOf c A), not (Gives c A)) (forall (B0 : Thing) (_ : not (@eq Thing B0 A)) (_ : Exists B0) (_ : @ex Thing (fun p : Thing => MemberOf p B0)) (_ : forall (p : Thing) (_ : MemberOf p B0), MemberOf p A), not (Gives B0 A)))","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP010\nH3 : MP011\nA : Thing\nH4 : AggregateOfPossibles A\nH5 : not (Gives A A)\n============================\nand (not (Gives A A)) (and (forall (c : Thing) (_ : MemberOf c A), not (Gives c A)) (forall (B : Thing) (_ : not (@eq Thing B A)) (_ : Exists B) (_ : @ex Thing (fun p : Thing => MemberOf p B)) (_ : forall (p : Thing) (_ : MemberOf p B), MemberOf p A), not (Gives B A)))","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP010\nH3 : MP011\nA : Thing\nH4 : AggregateOfPossibles A\nHs : not (not (Gives A A))\n============================\nand (not (Gives A A)) (and (forall (c : Thing) (_ : MemberOf c A), not (Gives c A)) (forall (B : Thing) (_ : not (@eq Thing B A)) (_ : Exists B) (_ : @ex Thing (fun p : Thing => MemberOf p B)) (_ : forall (p : Thing) (_ : MemberOf p B), MemberOf p A), not (Gives B A)))","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP010\nH3 : MP011\nA : Thing\nH4 : AggregateOfPossibles A\n============================\nforall (c : Thing) (_ : MemberOf c A), not (Gives c A)","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP010\nH3 : MP011\nA : Thing\nH4 : AggregateOfPossibles A\n============================\nforall (B : Thing) (_ : not (@eq Thing B A)) (_ : Exists B) (_ : @ex Thing (fun p : Thing => MemberOf p B)) (_ : forall (p : Thing) (_ : MemberOf p B), MemberOf p A), not (Gives B A)","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP010\nH3 : MP011\nA : Thing\nH4 : AggregateOfPossibles A\nc : Thing\nH5 : MemberOf c A\n============================\nnot (Gives c A)","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP010\nH3 : MP011\nA : Thing\nH4 : AggregateOfPossibles A\nB : Thing\nH5 : not (@eq Thing B A)\nH6 : Exists B\nH7 : @ex Thing (fun p : Thing => MemberOf p B)\nH8 : forall (p : Thing) (_ : MemberOf p B), MemberOf p A\n============================\nnot (Gives B A)","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP010\nH3 : MP011\nA : Thing\nH4 : AggregateOfPossibles A\nH5 : Gives A A\n============================\nand (forall (c : Thing) (_ : MemberOf c A), not (Gives c A)) (forall (B : Thing) (_ : not (@eq Thing B A)) (_ : Exists B) (_ : @ex Thing (fun p : Thing => MemberOf p B)) (_ : forall (p : Thing) (_ : MemberOf p B), MemberOf p A), not (Gives B A))","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP010\nH3 : MP011\nA : Thing\nH4 : AggregateOfPossibles A\nHs : Gives A A\n============================\nand (forall (c : Thing) (_ : MemberOf c A), not (Gives c A)) (forall (B : Thing) (_ : not (@eq Thing B A)) (_ : Exists B) (_ : @ex Thing (fun p : Thing => MemberOf p B)) (_ : forall (p : Thing) (_ : MemberOf p B), MemberOf p A), not (Gives B A))","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP010\nH3 : MP011\nA : Thing\nH4 : AggregateOfPossibles A\nHs : not (Gives A A)\n============================\nand (forall (c : Thing) (_ : MemberOf c A), not (Gives c A)) (forall (B : Thing) (_ : not (@eq Thing B A)) (_ : Exists B) (_ : @ex Thing (fun p : Thing => MemberOf p B)) (_ : forall (p : Thing) (_ : MemberOf p B), MemberOf p A), not (Gives B A))","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP010\nH3 : MP011\nA : Thing\nH4 : AggregateOfPossibles A\nB : Thing\n============================\nand (forall (c : Thing) (_ : MemberOf c A), not (Gives c A)) (forall (B0 : Thing) (_ : not (@eq Thing B0 A)) (_ : Exists B0) (_ : @ex Thing (fun p : Thing => MemberOf p B0)) (_ : forall (p : Thing) (_ : MemberOf p B0), MemberOf p A), not (Gives B0 A))","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP010\nH3 : MP011\nA : Thing\nH4 : and (forall (p : Thing) (_ : not (@eq Thing p A)), iff (MemberOf p A) (Possible p)) (not (MemberOf A A))\n============================\nand (forall (c : Thing) (_ : MemberOf c A), not (Gives c A)) (forall (B : Thing) (_ : not (@eq Thing B A)) (_ : Exists B) (_ : @ex Thing (fun p : Thing => MemberOf p B)) (_ : forall (p : Thing) (_ : MemberOf p B), MemberOf p A), not (Gives B A))","A0 : MP001\nMP002 : Pilot.MP002\nMP003 : Pilot.MP003\n============================\nforall (_ : MP010) (_ : MP011) (A : Thing) (_ : AggregateOfPossibles A), and (forall x : Thing, not (Gives x x)) (and (not (Gives A A)) (and (forall (c : Thing) (_ : MemberOf c A), not (Gives c A)) (forall (B : Thing) (_ : not (@eq Thing B A)) (_ : Exists B) (_ : @ex Thing (fun p : Thing => MemberOf p B)) (_ : forall (p : Thing) (_ : MemberOf p B), MemberOf p A), not (Gives B A))))","A0 : MP001\nH : MP002\nH0 : MP003\nH1 : MP010\nH2 : MP011\nA : Thing\nH3 : AggregateOfPossibles A\n============================\nand (forall x : Thing, not (Gives x x)) (and (not (Gives A A)) (and (forall (c : Thing) (_ : MemberOf c A), not (Gives c A)) (forall (B : Thing) (_ : not (@eq Thing B A)) (_ : Exists B) (_ : @ex Thing (fun p : Thing => MemberOf p B)) (_ : forall (p : Thing) (_ : MemberOf p B), MemberOf p A), not (Gives B A))))","A0 : MP001\nMP02 : MP002\nMP03 : MP003\n============================\nforall (_ : MP010) (_ : MP011) (A : Thing) (_ : AggregateOfPossibles A), and (forall x : Thing, not (Gives x x)) (and (not (Gives A A)) (and (forall (c : Thing) (_ : MemberOf c A), not (Gives c A)) (forall (B : Thing) (_ : not (@eq Thing B A)) (_ : Exists B) (_ : @ex Thing (fun p : Thing => MemberOf p B)) (_ : forall (p : Thing) (_ : MemberOf p B), MemberOf p A), not (Gives B A))))","A0 : MP001\nH : MP002\nH0 : MP003\nH1 : MP010\nH2 : MP011\nA : Thing\nH3 : AggregateOfPossibles A\n============================\nforall x : Thing, not (Gives x x)","A0 : MP001\nH : MP002\nH0 : MP003\nH1 : MP010\nH2 : MP011\nA : Thing\nH3 : AggregateOfPossibles A\n============================\nand (not (Gives A A)) (and (forall (c : Thing) (_ : MemberOf c A), not (Gives c A)) (forall (B : Thing) (_ : not (@eq Thing B A)) (_ : Exists B) (_ : @ex Thing (fun p : Thing => MemberOf p B)) (_ : forall (p : Thing) (_ : MemberOf p B), MemberOf p A), not (Gives B A)))","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP010\nH3 : MP011\nA : Thing\nH4 : AggregateOfPossibles A\nC : Thing\nH5 : MemberOf C A\n============================\nnot (Gives C A)","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP010\nH3 : MP011\nA : Thing\nH4 : AggregateOfPossibles A\nB : Thing\nH5 : MemberOf B A\n============================\nnot (Gives B A)","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP010\nH3 : MP011\nA : Thing\nH4 : AggregateOfPossibles A\nC : Thing\nM : MemberOf C A\n============================\nnot (Gives C A)","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP010\nH3 : MP011\nA : Thing\nH4 : AggregateOfPossibles A\nD : Thing\nH5 : MemberOf D A\n============================\nnot (Gives D A)","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP010\nH3 : MP011\nA : Thing\nH4 : AggregateOfPossibles A\nC : Thing\nH'0 : MemberOf C A\n============================\nnot (Gives C A)","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP010\nH3 : MP011\nA : Thing\nH4 : AggregateOfPossibles A\nB : Thing\nH5 : not (@eq Thing B A)\nH6 : Exists B\nH7 : @ex Thing (fun p : Thing => MemberOf p B)\n============================\nforall _ : forall (p : Thing) (_ : MemberOf p B), MemberOf p A, not (Gives B A)","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP010\nH3 : MP011\nA : Thing\nH4 : AggregateOfPossibles A\nB : Thing\nH5 : not (@eq Thing B A)\nH6 : Exists B\n============================\nforall (_ : @ex Thing (fun p : Thing => MemberOf p B)) (_ : forall (p : Thing) (_ : MemberOf p B), MemberOf p A), not (Gives B A)","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP010\nH3 : MP011\nA : Thing\nH4 : AggregateOfPossibles A\nB : Thing\nH5 : not (@eq Thing B A)\n============================\nforall (_ : Exists B) (_ : @ex Thing (fun p : Thing => MemberOf p B)) (_ : forall (p : Thing) (_ : MemberOf p B), MemberOf p A), not (Gives B A)","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP010\nH3 : MP011\nA : Thing\nH4 : AggregateOfPossibles A\nB : Thing\nH5 : not (@eq Thing B A)\nH6 : Exists B\nA0 : @ex Thing (fun p : Thing => MemberOf p B)\nH7 : forall (p : Thing) (_ : MemberOf p B), MemberOf p A\n============================\nnot (Gives B A)","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP010\nH3 : MP011\nA : Thing\nH4 : AggregateOfPossibles A\nB : Thing\nH5 : not (@eq Thing B A)\nH6 : Exists B\nH7 : @ex Thing (fun p : Thing => MemberOf p B)\nG : forall (p : Thing) (_ : MemberOf p B), MemberOf p A\n============================\nnot (Gives B A)","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP010\nH3 : MP011\nA : Thing\nH4 : AggregateOfPossibles A\nC : Thing\nH5 : not (@eq Thing C A)\nH6 : Exists C\nH7 : @ex Thing (fun p : Thing => MemberOf p C)\n============================\nforall _ : forall (p : Thing) (_ : MemberOf p C), MemberOf p A, not (Gives C A)","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP010\nH3 : MP011\nA : Thing\nH4 : AggregateOfPossibles A\nHs : not (Gives A A)\n============================\nnot (Gives A A)","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP010\nH3 : MP011\nA : Thing\nH4 : AggregateOfPossibles A\nHs : not (Gives A A)\n============================\nforall _ : not (Gives A A), and (not (Gives A A)) (and (forall (c : Thing) (_ : MemberOf c A), not (Gives c A)) (forall (B : Thing) (_ : not (@eq Thing B A)) (_ : Exists B) (_ : @ex Thing (fun p : Thing => MemberOf p B)) (_ : forall (p : Thing) (_ : MemberOf p B), MemberOf p A), not (Gives B A)))","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP010\nH3 : MP011\nA : Thing\nH4 : AggregateOfPossibles A\nHs : not (Gives A A)\nHs0 : not (Gives A A)\n============================\nand (not (Gives A A)) (and (forall (c : Thing) (_ : MemberOf c A), not (Gives c A)) (forall (B : Thing) (_ : not (@eq Thing B A)) (_ : Exists B) (_ : @ex Thing (fun p : Thing => MemberOf p B)) (_ : forall (p : Thing) (_ : MemberOf p B), MemberOf p A), not (Gives B A)))","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP010\nH3 : MP011\nA : Thing\nH4 : AggregateOfPossibles A\nH5 : not (Gives A A)\n============================\nforall x : Thing, not (Gives x x)","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP010\nH3 : MP011\nA : Thing\nH4 : AggregateOfPossibles A\nH5 : not (Gives A A)\nx : Thing\n============================\nnot (Gives x x)","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP010\nH3 : MP011\nA : Thing\nH4 : AggregateOfPossibles A\nH5 : not (Gives A A)\n============================\nGives A A","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP010\nH3 : MP011\nA : Thing\nH4 : AggregateOfPossibles A\nH5 : not (Gives A A)\nH6 : Gives A A\n============================\nand (forall x : Thing, not (Gives x x)) (and (not (Gives A A)) (and (forall (c : Thing) (_ : MemberOf c A), not (Gives c A)) (forall (B : Thing) (_ : not (@eq Thing B A)) (_ : Exists B) (_ : @ex Thing (fun p : Thing => MemberOf p B)) (_ : forall (p : Thing) (_ : MemberOf p B), MemberOf p A), not (Gives B A))))","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP010\nH3 : MP011\nA : Thing\nH4 : AggregateOfPossibles A\nH5 : not (Gives A A)\nHs : Gives A A\n============================\nand (forall x : Thing, not (Gives x x)) (and (not (Gives A A)) (and (forall (c : Thing) (_ : MemberOf c A), not (Gives c A)) (forall (B : Thing) (_ : not (@eq Thing B A)) (_ : Exists B) (_ : @ex Thing (fun p : Thing => MemberOf p B)) (_ : forall (p : Thing) (_ : MemberOf p B), MemberOf p A), not (Gives B A))))","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP010\nH3 : MP011\nA : Thing\nH4 : AggregateOfPossibles A\nH5 : not (Gives A A)\nHs : not (Gives A A)\n============================\nand (forall x : Thing, not (Gives x x)) (and (not (Gives A A)) (and (forall (c : Thing) (_ : MemberOf c A), not (Gives c A)) (forall (B : Thing) (_ : not (@eq Thing B A)) (_ : Exists B) (_ : @ex Thing (fun p : Thing => MemberOf p B)) (_ : forall (p : Thing) (_ : MemberOf p B), MemberOf p A), not (Gives B A))))","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP010\nH3 : MP011\nA : Thing\nH4 : AggregateOfPossibles A\nH5 : not (Gives A A)\n============================\nnot (Gives A A)","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP010\nH3 : MP011\nA : Thing\nH4 : AggregateOfPossibles A\nH5 : not (Gives A A)\nH6 : not (Gives A A)\n============================\nand (forall x : Thing, not (Gives x x)) (and (not (Gives A A)) (and (forall (c : Thing) (_ : MemberOf c A), not (Gives c A)) (forall (B : Thing) (_ : not (@eq Thing B A)) (_ : Exists B) (_ : @ex Thing (fun p : Thing => MemberOf p B)) (_ : forall (p : Thing) (_ : MemberOf p B), MemberOf p A), not (Gives B A))))","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP010\nH3 : MP011\nA : Thing\nH4 : AggregateOfPossibles A\nH5 : not (Gives A A)\nHs : not (not (Gives A A))\n============================\nand (forall x : Thing, not (Gives x x)) (and (not (Gives A A)) (and (forall (c : Thing) (_ : MemberOf c A), not (Gives c A)) (forall (B : Thing) (_ : not (@eq Thing B A)) (_ : Exists B) (_ : @ex Thing (fun p : Thing => MemberOf p B)) (_ : forall (p : Thing) (_ : MemberOf p B), MemberOf p A), not (Gives B A))))","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP010\nH3 : MP011\nA : Thing\nH4 : AggregateOfPossibles A\nHs : not (Gives A A)\n============================\nforall x : Thing, not (Gives x x)","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP010\nH3 : MP011\nA : Thing\nH4 : AggregateOfPossibles A\nHs : not (Gives A A)\nx : Thing\n============================\nnot (Gives x x)","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP010\nH3 : MP011\nA : Thing\nH4 : AggregateOfPossibles A\nHs : not (Gives A A)\n============================\nGives A A","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP010\nH3 : MP011\nA : Thing\nH4 : AggregateOfPossibles A\nHs : not (Gives A A)\nH5 : Gives A A\n============================\nand (forall x : Thing, not (Gives x x)) (and (not (Gives A A)) (and (forall (c : Thing) (_ : MemberOf c A), not (Gives c A)) (forall (B : Thing) (_ : not (@eq Thing B A)) (_ : Exists B) (_ : @ex Thing (fun p : Thing => MemberOf p B)) (_ : forall (p : Thing) (_ : MemberOf p B), MemberOf p A), not (Gives B A))))","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP010\nH3 : MP011\nA : Thing\nH4 : AggregateOfPossibles A\nHs : not (Gives A A)\n============================\nforall _ : not (Gives A A), and (forall x : Thing, not (Gives x x)) (and (not (Gives A A)) (and (forall (c : Thing) (_ : MemberOf c A), not (Gives c A)) (forall (B : Thing) (_ : not (@eq Thing B A)) (_ : Exists B) (_ : @ex Thing (fun p : Thing => MemberOf p B)) (_ : forall (p : Thing) (_ : MemberOf p B), MemberOf p A), not (Gives B A))))","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP010\nH3 : MP011\nA : Thing\nH4 : AggregateOfPossibles A\nHs : not (Gives A A)\nH5 : not (Gives A A)\n============================\nand (forall x : Thing, not (Gives x x)) (and (not (Gives A A)) (and (forall (c : Thing) (_ : MemberOf c A), not (Gives c A)) (forall (B : Thing) (_ : not (@eq Thing B A)) (_ : Exists B) (_ : @ex Thing (fun p : Thing => MemberOf p B)) (_ : forall (p : Thing) (_ : MemberOf p B), MemberOf p A), not (Gives B A))))","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP010\nH3 : MP011\nA : Thing\nH4 : AggregateOfPossibles A\nHs : not (Gives A A)\n============================\nThing","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP010\nH3 : MP011\nA : Thing\nH4 : AggregateOfPossibles A\nHs : not (Gives A A)\nB : Thing\n============================\nand (forall x : Thing, not (Gives x x)) (and (not (Gives A A)) (and (forall (c : Thing) (_ : MemberOf c A), not (Gives c A)) (forall (B0 : Thing) (_ : not (@eq Thing B0 A)) (_ : Exists B0) (_ : @ex Thing (fun p : Thing => MemberOf p B0)) (_ : forall (p : Thing) (_ : MemberOf p B0), MemberOf p A), not (Gives B0 A))))"],"events":[{"g":0,"t":"assumption","w":"auto","ok":false,"err":"Error: No such assumption."},{"g":0,"t":"tauto","w":"auto","ok":false,"err":"Error: Timeout!"},{"g":0,"t":"firstorder","w":"auto","ok":false,"err":"Error: Timeout!"},{"g":0,"t":"congruence","w":"auto","ok":false,"err":"Error: Tactic failure: congruence failed."},{"g":0,"t":"unfold MP001, MP002, MP003, AggregateOfPossibles, MP010, MP011 in *; firstorder","w":"auto","ok":false,"err":"rejected"},{"g":0,"t":"unfold MP001, MP002, MP003, AggregateOfPossibles, MP010, MP011 in *; hammer","w":"hammer","ok":false,"err":"rejected"},{"g":0,"t":"right","w":"model","ok":false,"err":"Error: Not an inductive goal with 2 constructors."},{"g":0,"t":"intros","w":"model","ok":true,"c":[1]},{"g":0,"t":"split","w":"model","ok":true,"c":[2,3]},{"g":2,"t":"firstorder","w":"auto","ok":true,"c":[],"eager":true},{"g":0,"t":"exists A","w":"model","ok":false,"err":"Error: The variable A was not found in the current environment."},{"g":0,"t":"apply MP003; intro","w":"model","ok":false,"err":"Error: Applied theorem does not have enough premises."},{"g":0,"t":"apply MP003","w":"model","ok":false,"err":"Error: Applied theorem does not have enough premises."},{"g":0,"t":"intros A0","w":"model","ok":true,"c":[4]},{"g":0,"t":"apply AggregateOfPossibles_intro","w":"model","ok":false,"err":"Error: The variable Ag"},{"g":1,"t":"assumption","w":"auto","ok":false,"err":"Error: No such assumption."},{"g":1,"t":"tauto","w":"auto","ok":false,"err":"Error: Tactic failure: Classical tauto failed."},{"g":1,"t":"firstorder","w":"auto","ok":false,"err":"Error: Timeout!"},{"g":1,"t":"congruence","w":"auto","ok":false,"err":"Error: Tactic failure: congruence failed."},{"g":1,"t":"unfold MP001, MP002, MP003, AggregateOfPossibles, MP010, MP011 in *; firstorder","w":"auto","ok":false,"err":"rejected"},{"g":1,"t":"unfold MP001, MP002, MP003, AggregateOfPossibles, MP010, MP011 in *; hammer","w":"hammer","ok":false,"err":"Error: Hammer failed: ATPs failed to f"},{"g":1,"t":"split","w":"model","ok":true,"c":[2,3]},{"g":1,"t":"split; intros","w":"model","ok":true,"c":[5,3]},{"g":5,"t":"firstorder","w":"auto","ok":true,"c":[],"eager":true},{"g":1,"t":"assert (~ Gives A A)","w":"model","ok":true,"c":[6,7]},{"g":6,"t":"firstorder","w":"auto","ok":true,"c":[],"eager":true},{"g":1,"t":"destruct (classic (~ Gives A A)) as [Hs|Hs]","w":"model","ok":true,"c":[8,9]},{"g":9,"t":"firstorder","w":"auto","ok":true,"c":[],"eager":true},{"g":1,"t":"assert (Gives A A)","w":"model","ok":true,"c":[10,11]},{"g":11,"t":"firstorder","w":"auto","ok":true,"c":[],"eager":true},{"g":1,"t":"destruct (classic (Gives A A)) as [Hs|Hs]","w":"model","ok":true,"c":[12,8]},{"g":12,"t":"firstorder","w":"auto","ok":true,"c":[],"eager":true},{"g":1,"t":"intros","w":"model","ok":true,"c":[1]},{"g":1,"t":"assert (B : Thing)","w":"model","ok":true,"c":[13,14]},{"g":13,"t":"assumption","w":"auto","ok":true,"c":[],"eager":true},{"g":1,"t":"destruct (classic (Thing)) as [Hs|Hs]","w":"model","ok":false,"err":"rejected"},{"g":1,"t":"generalize (GivesA A)","w":"model","ok":false,"err":"Error: The variable GivesA was not found in the current en"},{"g":3,"t":"assumption","w":"auto","ok":false,"err":"Error: No such assumption."},{"g":3,"t":"tauto","w":"auto","ok":false,"err":"Error: Tactic failure: Classical tauto failed."},{"g":3,"t":"firstorder","w":"auto","ok":false,"err":"Error: Timeout!"},{"g":3,"t":"congruence","w":"auto","ok":false,"err":"Error: Tactic failure: congruence failed."},{"g":3,"t":"unfold MP001, MP002, MP003, AggregateOfPossibles, MP010, MP011 in *; firstorder","w":"auto","ok":false,"err":"rejected"},{"g":3,"t":"unfold MP001, MP002, MP003, AggregateOfPossibles, MP010, MP011 in *; hammer","w":"hammer","ok":false,"err":"Error: Hammer failed: ATPs failed to f"},{"g":3,"t":"split","w":"model","ok":true,"c":[6,15]},{"g":3,"t":"assert (Gives A A)","w":"model","ok":true,"c":[10,16]},{"g":16,"t":"firstorder","w":"auto","ok":true,"c":[],"eager":true},{"g":3,"t":"destruct (classic (Gives A A)) as [Hs|Hs]","w":"model","ok":true,"c":[17,18]},{"g":17,"t":"firstorder","w":"auto","ok":true,"c":[],"eager":true},{"g":3,"t":"split; intros","w":"model","ok":true,"c":[6,15]},{"g":3,"t":"assert (B : Thing)","w":"model","ok":true,"c":[13,19]},{"g":3,"t":"destruct (classic (Thing)) as [Hs|Hs]","w":"model","ok":false,"err":"rejected"},{"g":3,"t":"assert (~ Gives A A)","w":"model","ok":true,"c":[6,20]},{"g":3,"t":"destruct (classic (~ Gives A A)) as [Hs|Hs]","w":"model","ok":true,"c":[18,21]},{"g":21,"t":"firstorder","w":"auto","ok":true,"c":[],"eager":true},{"g":3,"t":"destruct (classic (Gives B A)) as [Hs|Hs]","w":"model","ok":false,"err":"Error: The"},{"g":3,"t":"apply PossibleOfNoGives","w":"model","ok":false,"err":"Error: The variable PossibleOfNoGives was not fou"},{"g":15,"t":"assumption","w":"auto","ok":false,"err":"Error: No such assumption."},{"g":15,"t":"tauto","w":"auto","ok":false,"err":"Error: Tactic failure: Classical tauto failed."},{"g":15,"t":"firstorder","w":"auto","ok":false,"err":"Error: Timeout!"},{"g":15,"t":"congruence","w":"auto","ok":false,"err":"Error: Tactic failure: congruence failed."},{"g":15,"t":"unfold MP001, MP002, MP003, AggregateOfPossibles, MP010, MP011 in *; firstorder","w":"auto","ok":false,"err":"rejected"},{"g":15,"t":"unfold MP001, MP002, MP003, AggregateOfPossibles, MP010, MP011 in *; hammer","w":"hammer","ok":false,"err":"Error: Hammer failed: ATPs failed to f"},{"g":15,"t":"split","w":"model","ok":true,"c":[22,23]},{"g":15,"t":"split; intros","w":"model","ok":true,"c":[24,25]},{"g":15,"t":"intros","w":"model","ok":true,"c":[15]},{"g":15,"t":"assert (Gives A A)","w":"model","ok":true,"c":[10,26]},{"g":26,"t":"firstorder","w":"auto","ok":true,"c":[],"eager":true},{"g":15,"t":"destruct (classic (Gives A A)) as [Hs|Hs]","w":"model","ok":true,"c":[27,28]},{"g":27,"t":"firstorder","w":"auto","ok":true,"c":[],"eager":true},{"g":15,"t":"assert (B : Thing)","w":"model","ok":true,"c":[13,29]},{"g":15,"t":"destruct (classic (Thing)) as [Hs|Hs]","w":"model","ok":false,"err":"rejected"},{"g":15,"t":"unfold AggregateOfPossibles in H4","w":"model","ok":true,"c":[30]},{"g":15,"t":"assert (Gives A A = true)","w":"model","ok":false,"err":"rejected"},{"g":15,"t":"destruct (classic (Gives A A = true)) as [Hs|Hs]","w":"model","ok":false,"err":"rejected"},{"g":15,"t":"destruct (classic (AggregateOfPossibles A A)) as [Hs|Hs]","w":"model","ok":false,"err":"Error: Illegal application (Non-functional construction): "},{"g":4,"t":"assumption","w":"auto","ok":false,"err":"Error: No such assumption."},{"g":4,"t":"tauto","w":"auto","ok":false,"err":"Error: Tactic failure: Classical tauto failed."},{"g":4,"t":"firstorder","w":"auto","ok":false,"err":"Error: Timeout!"},{"g":4,"t":"congruence","w":"auto","ok":false,"err":"Error: Tactic failure: congruence failed."},{"g":4,"t":"unfold MP001, MP002, MP003, AggregateOfPossibles, MP010, MP011 in *; firstorder","w":"auto","ok":false,"err":"rejected"},{"g":4,"t":"unfold MP001, MP002, MP003, AggregateOfPossibles, MP010, MP011 in *; hammer","w":"hammer","ok":false,"err":"Error: Hammer failed: ATPs failed to f"},{"g":4,"t":"intros MP002 MP003","w":"model","ok":true,"c":[31]},{"g":4,"t":"intros","w":"model","ok":true,"c":[32]},{"g":4,"t":"intros MP002 MP003 A0","w":"model","ok":false,"err":"Error: A0 is already used."},{"g":4,"t":"intros MP02 MP03","w":"model","ok":true,"c":[33]},{"g":4,"t":"split","w":"model","ok":true,"c":[34,35]},{"g":34,"t":"firstorder","w":"auto","ok":true,"c":[],"eager":true},{"g":4,"t":"intros MP02 MP03 A0","w":"model","ok":false,"err":"Error: A0 is already used."},{"g":4,"t":"intros; split","w":"model","ok":true,"c":[34,35]},{"g":4,"t":"intros MP02 MP03 A0 HB0","w":"model","ok":false,"err":"Error: A0 is already used."},{"g":22,"t":"assumption","w":"auto","ok":false,"err":"Error: No such assumption."},{"g":22,"t":"tauto","w":"auto","ok":false,"err":"Error: Tactic failure: Classical tauto failed."},{"g":22,"t":"firstorder","w":"auto","ok":false,"err":"Error: Timeout!"},{"g":22,"t":"congruence","w":"auto","ok":false,"err":"Error: Tactic failure: congruence failed."},{"g":22,"t":"unfold MP001, MP002, MP003, AggregateOfPossibles, MP010, MP011 in *; firstorder","w":"auto","ok":false,"err":"rejected"},{"g":22,"t":"unfold MP001, MP002, MP003, AggregateOfPossibles, MP010, MP011 in *; hammer","w":"hammer","ok":false,"err":"Error: Hammer failed: ATPs failed to f"},{"g":22,"t":"intros C H5","w":"model","ok":true,"c":[36]},{"g":22,"t":"intros c H5","w":"model","ok":true,"c":[24]},{"g":22,"t":"intros B H5","w":"model","ok":true,"c":[37]},{"g":22,"t":"intros C M","w":"model","ok":true,"c":[38]},{"g":22,"t":"intros D H5","w":"model","ok":true,"c":[39]},{"g":22,"t":"intros C H'0","w":"model","ok":true,"c":[40]},{"g":23,"t":"assumption","w":"auto","ok":false,"err":"Error: No such assumption."},{"g":23,"t":"tauto","w":"auto","ok":false,"err":"Error: Tactic failure: Classical tauto failed."},{"g":23,"t":"firstorder","w":"auto","ok":false,"err":"Error: Timeout!"},{"g":23,"t":"congruence","w":"auto","ok":false,"err":"Error: Tactic failure: congruence failed."},{"g":23,"t":"unfold MP001, MP002, MP003, AggregateOfPossibles, MP010, MP011 in *; firstorder","w":"auto","ok":false,"err":"rejected"},{"g":23,"t":"unfold MP001, MP002, MP003, AggregateOfPossibles, MP010, MP011 in *; hammer","w":"hammer","ok":false,"err":"Error: Hammer failed: ATPs failed to f"},{"g":23,"t":"intros B H5 H6 H7","w":"model","ok":true,"c":[41]},{"g":23,"t":"intros","w":"model","ok":true,"c":[25]},{"g":23,"t":"intros B H5 H6","w":"model","ok":true,"c":[42]},{"g":23,"t":"intros B H5 H6 H7 H8","w":"model","ok":true,"c":[25]},{"g":23,"t":"intros B H5","w":"model","ok":true,"c":[43]},{"g":23,"t":"intros B H5 H6 A0 H7","w":"model","ok":true,"c":[44]},{"g":23,"t":"intros B H5 H6 H7 G","w":"model","ok":true,"c":[45]},{"g":23,"t":"intros C H5 H6 H7","w":"model","ok":true,"c":[46]},{"g":18,"t":"assumption","w":"auto","ok":false,"err":"Error: No such assumption."},{"g":18,"t":"tauto","w":"auto","ok":false,"err":"Error: Tactic failure: Classical tauto failed."},{"g":18,"t":"firstorder","w":"auto","ok":false,"err":"Error: Timeout!"},{"g":18,"t":"congruence","w":"auto","ok":false,"err":"Error: Tactic failure: congruence failed."},{"g":18,"t":"unfold MP001, MP002, MP003, AggregateOfPossibles, MP010, MP011 in *; firstorder","w":"auto","ok":false,"err":"rejected"},{"g":18,"t":"unfold MP001, MP002, MP003, AggregateOfPossibles, MP010, MP011 in *; hammer","w":"hammer","ok":false,"err":"Error: Hammer failed: ATPs failed to f"},{"g":18,"t":"split","w":"model","ok":true,"c":[47,28]},{"g":47,"t":"assumption","w":"auto","ok":true,"c":[],"eager":true},{"g":18,"t":"split; intros","w":"model","ok":true,"c":[47,28]},{"g":18,"t":"generalize Hs","w":"model","ok":true,"c":[48]},{"g":18,"t":"split; trivial","w":"model","ok":true,"c":[28]},{"g":18,"t":"intros","w":"model","ok":true,"c":[18]},{"g":18,"t":"split; try assumption","w":"model","ok":true,"c":[28]},{"g":18,"t":"generalize Hs; intro","w":"model","ok":true,"c":[49]},{"g":7,"t":"assumption","w":"auto","ok":false,"err":"Error: No such assumption."},{"g":7,"t":"tauto","w":"auto","ok":false,"err":"Error: Tactic failure: Classical tauto failed."},{"g":7,"t":"firstorder","w":"auto","ok":false,"err":"Error: Timeout!"},{"g":7,"t":"congruence","w":"auto","ok":false,"err":"Error: Tactic failure: congruence failed."},{"g":7,"t":"unfold MP001, MP002, MP003, AggregateOfPossibles, MP010, MP011 in *; firstorder","w":"auto","ok":false,"err":"rejected"},{"g":7,"t":"unfold MP001, MP002, MP003, AggregateOfPossibles, MP010, MP011 in *; hammer","w":"hammer","ok":false,"err":"Error: Hammer failed: ATPs failed to f"},{"g":7,"t":"split","w":"model","ok":true,"c":[50,20]},{"g":50,"t":"firstorder","w":"auto","ok":true,"c":[],"eager":true},{"g":7,"t":"split; intros","w":"model","ok":true,"c":[51,20]},{"g":51,"t":"firstorder","w":"auto","ok":true,"c":[],"eager":true},{"g":7,"t":"assert (Gives A A)","w":"model","ok":true,"c":[52,53]},{"g":53,"t":"tauto","w":"auto","ok":true,"c":[],"eager":true},{"g":7,"t":"destruct (classic (Gives A A)) as [Hs|Hs]","w":"model","ok":true,"c":[54,55]},{"g":54,"t":"tauto","w":"auto","ok":true,"c":[],"eager":true},{"g":7,"t":"assert (~ Gives A A)","w":"model","ok":true,"c":[56,57]},{"g":56,"t":"assumption","w":"auto","ok":true,"c":[],"eager":true},{"g":7,"t":"destruct (classic (~ Gives A A)) as [Hs|Hs]","w":"model","ok":true,"c":[55,58]},{"g":58,"t":"tauto","w":"auto","ok":true,"c":[],"eager":true},{"g":7,"t":"assert (not Gives A A)","w":"model","ok":false,"err":"rejected"},{"g":7,"t":"destruct (classic (not Gives A A)) as [Hs|Hs]","w":"model","ok":false,"err":"rejected"},{"g":7,"t":"generalize (GivesA A A)","w":"model","ok":false,"err":"Error: The variable GivesA was not found in the curren"},{"g":7,"t":"split; intros; apply H7","w":"model","ok":false,"err":"Error: The variable H7 was not found in the curre"},{"g":8,"t":"assumption","w":"auto","ok":false,"err":"Error: No such assumption."},{"g":8,"t":"tauto","w":"auto","ok":false,"err":"Error: Tactic failure: Classical tauto failed."},{"g":8,"t":"firstorder","w":"auto","ok":false,"err":"Error: Timeout!"},{"g":8,"t":"congruence","w":"auto","ok":false,"err":"Error: Tactic failure: congruence failed."},{"g":8,"t":"unfold MP001, MP002, MP003, AggregateOfPossibles, MP010, MP011 in *; firstorder","w":"auto","ok":false,"err":"rejected"},{"g":8,"t":"unfold MP001, MP002, MP003, AggregateOfPossibles, MP010, MP011 in *; hammer","w":"hammer","ok":false,"err":"Error: Hammer failed: ATPs failed to f"},{"g":8,"t":"split","w":"model","ok":true,"c":[59,18]},{"g":59,"t":"firstorder","w":"auto","ok":true,"c":[],"eager":true},{"g":8,"t":"split; intros","w":"model","ok":true,"c":[60,18]},{"g":60,"t":"firstorder","w":"auto","ok":true,"c":[],"eager":true},{"g":8,"t":"assert (Gives A A)","w":"model","ok":true,"c":[61,62]},{"g":62,"t":"tauto","w":"auto","ok":true,"c":[],"eager":true},{"g":8,"t":"destruct (classic (Gives A A)) as [Hs|Hs]","w":"model","ok":false,"err":"rejected"},{"g":8,"t":"generalize Hs","w":"model","ok":true,"c":[63]},{"g":8,"t":"assert (~ Gives A A)","w":"model","ok":true,"c":[47,64]},{"g":8,"t":"destruct (classic (~ Gives A A)) as [Hs|Hs]","w":"model","ok":false,"err":"rejected"},{"g":8,"t":"assert (B : Thing)","w":"model","ok":true,"c":[65,66]},{"g":65,"t":"assumption","w":"auto","ok":true,"c":[],"eager":true}],"proof":[],"proofFile":null},{"key":"round6/imkan_s9_cause_outside","id":"imkan_s9_cause_outside","run":"round6","title":"Dalīl al-imkān, step 9","english":"The cause of the aggregate lies outside it and is not possible.","stmt":"MP001 -> MP002 -> MP003 -> MP011 -> forall A c, AggregateOfPossibles A -> Gives c A -> ~ MemberOf c A /\\ c <> A /\\ ~ Possible c","proved":false,"script":"","seconds":903.1,"expansions":14,"calls":560,"root":0,"goals":["============================\nMP001 -> MP002 -> MP003 -> MP011 -> forall A c, AggregateOfPossibles A -> Gives c A -> ~ MemberOf c A /\\ c <> A /\\ ~ Possible c","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP011\nA : Thing\nc : Thing\nH3 : AggregateOfPossibles A\nH4 : Gives c A\n============================\nnot (MemberOf c A)","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP011\nA : Thing\nc : Thing\nH3 : AggregateOfPossibles A\nH4 : Gives c A\n============================\nand (not (@eq Thing c A)) (not (Possible c))","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP011\nA : Thing\nc : Thing\nH3 : AggregateOfPossibles A\nH4 : Gives c A\n============================\nand (not (MemberOf c A)) (and (not (@eq Thing c A)) (not (Possible c)))","A : MP001\nc : MP002\n============================\nforall (_ : MP003) (_ : MP011) (A0 c0 : Thing) (_ : AggregateOfPossibles A0) (_ : Gives c0 A0), and (not (MemberOf c0 A0)) (and (not (@eq Thing c0 A0)) (not (Possible c0)))","A0 : MP001\nc0 : MP002\n============================\nforall (_ : MP003) (_ : MP011) (A c : Thing) (_ : AggregateOfPossibles A) (_ : Gives c A), and (not (MemberOf c A)) (and (not (@eq Thing c A)) (not (Possible c)))","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP011\nA : Thing\nc : Thing\nH3 : AggregateOfPossibles A\nH4 : Gives c A\n============================\n@eq Thing c A","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP011\nA : Thing\nc : Thing\nH3 : AggregateOfPossibles A\nH4 : Gives c A\nH5 : @eq Thing c A\n============================\nand (not (MemberOf c A)) (and (not (@eq Thing c A)) (not (Possible c)))","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP011\nA : Thing\nc : Thing\nH3 : AggregateOfPossibles A\nH4 : Gives c A\nHs : @eq Thing c A\n============================\nand (not (MemberOf c A)) (and (not (@eq Thing c A)) (not (Possible c)))","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP011\nA : Thing\nc : Thing\nH3 : AggregateOfPossibles A\nH4 : Gives c A\nHs : not (@eq Thing c A)\n============================\nand (not (MemberOf c A)) (and (not (@eq Thing c A)) (not (Possible c)))","A : MP001\nc : MP002\nH : MP003\nH0 : MP011\nA0 : Thing\nc0 : Thing\nH1 : AggregateOfPossibles A0\nH2 : Gives c0 A0\n============================\nand (not (MemberOf c0 A0)) (and (not (@eq Thing c0 A0)) (not (Possible c0)))","A : MP001\nc : MP002\nx : MP003\nx0 : MP011\nA1 : Thing\nc0 : Thing\n============================\nforall (_ : AggregateOfPossibles A1) (_ : Gives c0 A1), and (not (MemberOf c0 A1)) (and (not (@eq Thing c0 A1)) (not (Possible c0)))","A : MP001\nc : MP002\nH : not (forall (_ : MP003) (_ : MP011) (A0 c0 : Thing) (_ : AggregateOfPossibles A0) (_ : Gives c0 A0), and (not (MemberOf c0 A0)) (and (not (@eq Thing c0 A0)) (not (Possible c0))))\n============================\nFalse","A : MP001\nc : MP002\nA0 : MP003\nc0 : MP011\n============================\nforall (A1 c1 : Thing) (_ : AggregateOfPossibles A1) (_ : Gives c1 A1), and (not (MemberOf c1 A1)) (and (not (@eq Thing c1 A1)) (not (Possible c1)))","A : MP001\nc : MP002\nx : MP003\nx0 : MP011\nA0 : Thing\nc0 : Thing\n============================\nforall (_ : AggregateOfPossibles A0) (_ : Gives c0 A0), and (not (MemberOf c0 A0)) (and (not (@eq Thing c0 A0)) (not (Possible c0)))","A : MP001\nc : MP002\nX : MP003\nH1 : MP011\nX0 : Thing\nH2 : Thing\n============================\nforall (_ : AggregateOfPossibles X0) (_ : Gives H2 X0), and (not (MemberOf H2 X0)) (and (not (@eq Thing H2 X0)) (not (Possible H2)))","A : MP001\nc : MP002\nx : MP003\ny : MP011\nz : Thing\nA1 : Thing\nc1 : AggregateOfPossibles z\n============================\nforall _ : Gives A1 z, and (not (MemberOf A1 z)) (and (not (@eq Thing A1 z)) (not (Possible A1)))","A : MP001\nc : MP002\nx : MP003\ny : MP011\nz : Thing\nA1 : Thing\n============================\nforall (_ : AggregateOfPossibles z) (_ : Gives A1 z), and (not (MemberOf A1 z)) (and (not (@eq Thing A1 z)) (not (Possible A1)))","A0 : MP001\nc0 : MP002\nH : MP003\nH0 : MP011\nA : Thing\nc : Thing\nH1 : AggregateOfPossibles A\nH2 : Gives c A\n============================\nand (not (MemberOf c A)) (and (not (@eq Thing c A)) (not (Possible c)))","A0 : MP001\nc0 : MP002\nx : MP003\ny : MP011\n============================\nforall (A c : Thing) (_ : AggregateOfPossibles A) (_ : Gives c A), and (not (MemberOf c A)) (and (not (@eq Thing c A)) (not (Possible c)))","A0 : MP001\nc0 : MP002\nx : MP003\ny : MP011\nz : Thing\nHx : Thing\nHy : AggregateOfPossibles z\nHz : Gives Hx z\n============================\nand (not (MemberOf Hx z)) (and (not (@eq Thing Hx z)) (not (Possible Hx)))","A0 : MP001\nc0 : MP002\nx : MP003\nx0 : MP011\nA : Thing\nc : Thing\nH : AggregateOfPossibles A\nH0 : Gives c A\n============================\nand (not (MemberOf c A)) (and (not (@eq Thing c A)) (not (Possible c)))","A : MP001\nc : MP002\nH : MP003\nH0 : MP011\nA0 : Thing\nc0 : Thing\nH1 : AggregateOfPossibles A0\nH2 : Gives c0 A0\n============================\nnot (MemberOf c0 A0)","A : MP001\nc : MP002\nH : MP003\nH0 : MP011\nA0 : Thing\nc0 : Thing\nH1 : AggregateOfPossibles A0\nH2 : Gives c0 A0\n============================\nand (not (@eq Thing c0 A0)) (not (Possible c0))","A : MP001\nc : MP002\nH : MP003\nH0 : MP011\nA0 : Thing\nc0 : Thing\nH1 : forall (p : Thing) (_ : not (@eq Thing p A0)), iff (MemberOf p A0) (Possible p)\nH3 : not (MemberOf A0 A0)\nH2 : Gives c0 A0\n============================\nand (not (MemberOf c0 A0)) (and (not (@eq Thing c0 A0)) (not (Possible c0)))","A : MP001\nc : MP002\nH : MP003\nH0 : MP011\nA0 : Thing\nc0 : Thing\nd : forall (p : Thing) (_ : not (@eq Thing p A0)), iff (MemberOf p A0) (Possible p)\nH3 : not (MemberOf A0 A0)\nH2 : Gives c0 A0\n============================\nand (not (MemberOf c0 A0)) (and (not (@eq Thing c0 A0)) (not (Possible c0)))","A : MP001\nc : MP002\nH : MP003\nH0 : MP011\nA0 : Thing\nc0 : Thing\nn : forall (p : Thing) (_ : not (@eq Thing p A0)), iff (MemberOf p A0) (Possible p)\nH3 : not (MemberOf A0 A0)\nH2 : Gives c0 A0\n============================\nand (not (MemberOf c0 A0)) (and (not (@eq Thing c0 A0)) (not (Possible c0)))","A : MP001\nc : MP002\nx : MP003\nx0 : MP011\nA1 : Thing\nc0 : Thing\nH : AggregateOfPossibles A1\nH0 : Gives c0 A1\n============================\nnot (MemberOf c0 A1)","A : MP001\nc : MP002\nx : MP003\nx0 : MP011\nA1 : Thing\nc0 : Thing\nH : AggregateOfPossibles A1\nH0 : Gives c0 A1\n============================\nand (not (@eq Thing c0 A1)) (not (Possible c0))","A : MP001\nc : MP002\nx : MP003\nx0 : MP011\nA1 : Thing\nc0 : Thing\nA2 : AggregateOfPossibles A1\nG1 : Gives c0 A1\n============================\nand (not (MemberOf c0 A1)) (and (not (@eq Thing c0 A1)) (not (Possible c0)))","A : MP001\nc : MP002\nx : MP003\nx0 : MP011\nA1 : Thing\nc0 : Thing\nA2 : AggregateOfPossibles A1\nG : Gives c0 A1\n============================\nand (not (MemberOf c0 A1)) (and (not (@eq Thing c0 A1)) (not (Possible c0)))","A : MP001\nc : MP002\nx : MP003\nx0 : MP011\nA1 : Thing\n============================\nforall (c0 : Thing) (_ : AggregateOfPossibles A1) (_ : Gives c0 A1), and (not (MemberOf c0 A1)) (and (not (@eq Thing c0 A1)) (not (Possible c0)))","A : MP001\nc : MP002\nx : MP003\nx0 : MP011\nA1 : Thing\nc0 : Thing\nA2 : AggregateOfPossibles A1\nG0 : Gives c0 A1\n============================\nand (not (MemberOf c0 A1)) (and (not (@eq Thing c0 A1)) (not (Possible c0)))","A : MP001\nc : MP002\nH : not (forall (_ : MP003) (_ : MP011) (A0 c0 : Thing) (_ : AggregateOfPossibles A0) (_ : Gives c0 A0), and (not (MemberOf c0 A0)) (and (not (@eq Thing c0 A0)) (not (Possible c0))))\n============================\nforall (_ : MP003) (_ : MP011) (A0 c0 : Thing) (_ : AggregateOfPossibles A0) (_ : Gives c0 A0), and (not (MemberOf c0 A0)) (and (not (@eq Thing c0 A0)) (not (Possible c0)))","A : MP001\nc : MP002\nH : not (forall (_ : MP003) (_ : MP011) (A0 c0 : Thing) (_ : AggregateOfPossibles A0) (_ : Gives c0 A0), and (not (MemberOf c0 A0)) (and (not (@eq Thing c0 A0)) (not (Possible c0))))\nH0 : MP003\nH1 : MP011\nA0 : Thing\nc0 : Thing\nH2 : AggregateOfPossibles A0\nH3 : Gives c0 A0\n============================\nand (not (MemberOf c0 A0)) (and (not (@eq Thing c0 A0)) (not (Possible c0)))","A0 : MP001\nc0 : MP002\nH : MP003\nH0 : MP011\nA : Thing\nc : Thing\nH1 : AggregateOfPossibles A\nH2 : Gives c A\n============================\nnot (MemberOf c A)","A0 : MP001\nc0 : MP002\nH : MP003\nH0 : MP011\nA : Thing\nc : Thing\nH1 : AggregateOfPossibles A\nH2 : Gives c A\n============================\nand (not (@eq Thing c A)) (not (Possible c))","A0 : MP001\nc0 : MP002\nH : MP003\nH0 : MP011\nA : Thing\nc : Thing\nH1 : AggregateOfPossibles A\nH2 : Gives c A\n============================\nGives c A","A0 : MP001\nc0 : MP002\nH : MP003\nH0 : MP011\nA : Thing\nc : Thing\nH1 : AggregateOfPossibles A\nH2 : Gives c A\nH3 : Gives c A\n============================\nand (not (MemberOf c A)) (and (not (@eq Thing c A)) (not (Possible c)))","A0 : MP001\nc0 : MP002\nH : MP003\nH0 : MP011\nA : Thing\nc : Thing\nH1 : AggregateOfPossibles A\nH2 : Gives c A\nHs : Gives c A\n============================\nand (not (MemberOf c A)) (and (not (@eq Thing c A)) (not (Possible c)))","A0 : MP001\nc0 : MP002\nH : MP003\nH0 : MP011\nA : Thing\nc : Thing\nH1 : AggregateOfPossibles A\nH2 : Gives c A\nHs : not (Gives c A)\n============================\nand (not (MemberOf c A)) (and (not (@eq Thing c A)) (not (Possible c)))","A : MP001\nc : MP002\nA0 : MP003\nc0 : MP011\nA1 : Thing\nc1 : Thing\nH : AggregateOfPossibles A1\nH0 : Gives c1 A1\n============================\nand (not (MemberOf c1 A1)) (and (not (@eq Thing c1 A1)) (not (Possible c1)))","A : MP001\nc : MP002\nA0 : MP003\nc0 : MP011\nA1 : Thing\nc1 : Thing\nH0 : AggregateOfPossibles A1\nH1 : Gives c1 A1\n============================\nand (not (MemberOf c1 A1)) (and (not (@eq Thing c1 A1)) (not (Possible c1)))","A : MP001\nc : MP002\nA0 : MP003\nc0 : MP011\nA1 : Thing\nc1 : Thing\nH : AggregateOfPossibles A1\nAggregate1 : Gives c1 A1\n============================\nand (not (MemberOf c1 A1)) (and (not (@eq Thing c1 A1)) (not (Possible c1)))","A : MP001\nc : MP002\nA0 : MP003\nc0 : MP011\nA1 : Thing\nc1 : Thing\nH0 : AggregateOfPossibles A1\n============================\nforall _ : Gives c1 A1, and (not (MemberOf c1 A1)) (and (not (@eq Thing c1 A1)) (not (Possible c1)))","A : MP001\nc : MP002\nA0 : MP003\nc0 : MP011\nA1 : Thing\nc1 : Thing\nH : AggregateOfPossibles A1\nA2 : Gives c1 A1\n============================\nand (not (MemberOf c1 A1)) (and (not (@eq Thing c1 A1)) (not (Possible c1)))","A : MP001\nc : MP002\nA0 : MP003\nc0 : MP011\nA1 : Thing\nc1 : Thing\nH' : AggregateOfPossibles A1\nH1 : Gives c1 A1\n============================\nand (not (MemberOf c1 A1)) (and (not (@eq Thing c1 A1)) (not (Possible c1)))","A : MP001\nc : MP002\nA0 : MP003\nc0 : MP011\nA1 : Thing\nc1 : Thing\nH : AggregateOfPossibles A1\nH0 : Gives c1 A1\n============================\nnot (MemberOf c1 A1)","A : MP001\nc : MP002\nA0 : MP003\nc0 : MP011\nA1 : Thing\nc1 : Thing\nH : AggregateOfPossibles A1\nH0 : Gives c1 A1\n============================\nand (not (@eq Thing c1 A1)) (not (Possible c1))","A : MP001\nc : MP002\nx : MP003\nx0 : MP011\nA0 : Thing\nc0 : Thing\nH : AggregateOfPossibles A0\nH0 : Gives c0 A0\n============================\nnot (MemberOf c0 A0)","A : MP001\nc : MP002\nx : MP003\nx0 : MP011\nA0 : Thing\nc0 : Thing\nH : AggregateOfPossibles A0\nH0 : Gives c0 A0\n============================\nand (not (@eq Thing c0 A0)) (not (Possible c0))","A : MP001\nc : MP002\nx : MP003\nx0 : MP011\nA0 : Thing\nc0 : Thing\nA1 : AggregateOfPossibles A0\nG1 : Gives c0 A0\n============================\nand (not (MemberOf c0 A0)) (and (not (@eq Thing c0 A0)) (not (Possible c0)))","A : MP001\nc : MP002\nx : MP003\nx0 : MP011\nA0 : Thing\nc0 : Thing\nA1 : AggregateOfPossibles A0\nG : Gives c0 A0\n============================\nand (not (MemberOf c0 A0)) (and (not (@eq Thing c0 A0)) (not (Possible c0)))","A : MP001\nc : MP002\nx : MP003\nx0 : MP011\nA0 : Thing\nc0 : Thing\nHc0 : AggregateOfPossibles A0\n============================\nforall _ : Gives c0 A0, and (not (MemberOf c0 A0)) (and (not (@eq Thing c0 A0)) (not (Possible c0)))","A : MP001\nc : MP002\nx : MP003\nx0 : MP011\nA0 : Thing\nc0 : Thing\nHc0 : AggregateOfPossibles A0\nH : Gives c0 A0\n============================\nand (not (MemberOf c0 A0)) (and (not (@eq Thing c0 A0)) (not (Possible c0)))","A : MP001\nc : MP002\nx : MP003\nx0 : MP011\nA0 : Thing\nc0 : Thing\nHc0 : AggregateOfPossibles A0\nH1 : Gives c0 A0\n============================\nand (not (MemberOf c0 A0)) (and (not (@eq Thing c0 A0)) (not (Possible c0)))","A : MP001\nc : MP002\nX : MP003\nH1 : MP011\nX0 : Thing\nH2 : Thing\nA0 : AggregateOfPossibles X0\nG0 : Gives H2 X0\n============================\nand (not (MemberOf H2 X0)) (and (not (@eq Thing H2 X0)) (not (Possible H2)))","A : MP001\nc : MP002\nX : MP003\nH1 : MP011\nX0 : Thing\nH2 : Thing\nA0 : AggregateOfPossibles X0\nG : Gives H2 X0\n============================\nand (not (MemberOf H2 X0)) (and (not (@eq Thing H2 X0)) (not (Possible H2)))","A : MP001\nc : MP002\nx : MP003\ny : MP011\nz : Thing\nA1 : Thing\nc1 : AggregateOfPossibles z\nGivesA1 : Gives A1 z\n============================\nand (not (MemberOf A1 z)) (and (not (@eq Thing A1 z)) (not (Possible A1)))","A : MP001\nc : MP002\nx : MP003\ny : MP011\nz : Thing\nA1 : Thing\nc1 : AggregateOfPossibles z\nG1 : Gives A1 z\n============================\nand (not (MemberOf A1 z)) (and (not (@eq Thing A1 z)) (not (Possible A1)))","A : MP001\nc : MP002\nx : MP003\ny : MP011\nz : Thing\nA1 : Thing\nc1 : AggregateOfPossibles z\nG : Gives A1 z\n============================\nand (not (MemberOf A1 z)) (and (not (@eq Thing A1 z)) (not (Possible A1)))","A : MP001\nc : MP002\nx : MP003\ny : MP011\nz : Thing\nA1 : Thing\nc1 : AggregateOfPossibles z\ng : Gives A1 z\n============================\nand (not (MemberOf A1 z)) (and (not (@eq Thing A1 z)) (not (Possible A1)))"],"events":[{"g":0,"t":"assumption","w":"auto","ok":false,"err":"Error: No such assumption."},{"g":0,"t":"tauto","w":"auto","ok":false,"err":"Error: Tactic failure: Classical tauto failed."},{"g":0,"t":"firstorder","w":"auto","ok":false,"err":"Error: Timeout!"},{"g":0,"t":"congruence","w":"auto","ok":false,"err":"Error: Tactic failure: congruence failed."},{"g":0,"t":"unfold Possible, MP001, MP002, MP003, AggregateOfPossibles, MP011 in *; firstorder","w":"auto","ok":false,"err":"rejected"},{"g":0,"t":"unfold Possible, MP001, MP002, MP003, AggregateOfPossibles, MP011 in *; hammer","w":"hammer","ok":false,"err":"Error: Hammer failed: ATPs failed to f"},{"g":0,"t":"right","w":"model","ok":false,"err":"Error: Not an inductive goal with 2 constructors."},{"g":0,"t":"split","w":"model","ok":true,"c":[1,2]},{"g":0,"t":"intros","w":"model","ok":true,"c":[3]},{"g":0,"t":"intros A c","w":"model","ok":true,"c":[4]},{"g":0,"t":"intros A0 c0","w":"model","ok":true,"c":[5]},{"g":1,"t":"assumption","w":"auto","ok":false,"err":"Error: No such assumption."},{"g":1,"t":"tauto","w":"auto","ok":false,"err":"Error: Tactic failure: Classical tauto failed."},{"g":1,"t":"firstorder","w":"auto","ok":false,"err":"Error: Timeout!"},{"g":1,"t":"congruence","w":"auto","ok":false,"err":"Error: Tactic failure: congruence failed."},{"g":1,"t":"unfold MP001, MP002, MP003, AggregateOfPossibles, MP011 in *; firstorder","w":"auto","ok":false,"err":"rejected"},{"g":1,"t":"unfold MP001, MP002, MP003, AggregateOfPossibles, MP011 in *; hammer","w":"hammer","ok":false,"err":"Error: Hammer failed: ATPs failed to f"},{"g":3,"t":"assumption","w":"auto","ok":false,"err":"Error: No such assumption."},{"g":3,"t":"tauto","w":"auto","ok":false,"err":"Error: Tactic failure: Classical tauto failed."},{"g":3,"t":"firstorder","w":"auto","ok":false,"err":"Error: Timeout!"},{"g":3,"t":"congruence","w":"auto","ok":false,"err":"Error: Tactic failure: congruence failed."},{"g":3,"t":"unfold Possible, MP001, MP002, MP003, AggregateOfPossibles, MP011 in *; firstorder","w":"auto","ok":false,"err":"rejected"},{"g":3,"t":"unfold Possible, MP001, MP002, MP003, AggregateOfPossibles, MP011 in *; hammer","w":"hammer","ok":false,"err":"Error: Hammer failed: ATPs failed to f"},{"g":3,"t":"split","w":"model","ok":true,"c":[1,2]},{"g":3,"t":"unfold Gives in H4","w":"model","ok":false,"err":"Error: Cannot coerce Gives to an evaluable reference."},{"g":3,"t":"split; intros","w":"model","ok":true,"c":[1,2]},{"g":3,"t":"assert (c = A)","w":"model","ok":true,"c":[6,7]},{"g":3,"t":"destruct (classic (c = A)) as [Hs|Hs]","w":"model","ok":true,"c":[8,9]},{"g":3,"t":"apply AggregateOfPossiblesGivesNotPossible in H3","w":"model","ok":false,"err":"rejected"},{"g":3,"t":"apply AggregateOfPossiblesNotMemberOfGives in H3","w":"model","ok":false,"err":"rejected"},{"g":4,"t":"assumption","w":"auto","ok":false,"err":"Error: No such assumption."},{"g":4,"t":"tauto","w":"auto","ok":false,"err":"Error: Tactic failure: Classical tauto failed."},{"g":4,"t":"firstorder","w":"auto","ok":false,"err":"Error: Timeout!"},{"g":4,"t":"congruence","w":"auto","ok":false,"err":"Error: Tactic failure: congruence failed."},{"g":4,"t":"unfold Possible, MP001, MP002, MP003, AggregateOfPossibles, MP011 in *; firstorder","w":"auto","ok":false,"err":"rejected"},{"g":4,"t":"unfold Possible, MP001, MP002, MP003, AggregateOfPossibles, MP011 in *; hammer","w":"hammer","ok":false,"err":"Error: Hammer failed: ATPs failed to f"},{"g":4,"t":"intros","w":"model","ok":true,"c":[10]},{"g":4,"t":"intros x x0 A1 c0","w":"model","ok":true,"c":[11]},{"g":4,"t":"apply NNPP; intro","w":"model","ok":true,"c":[12]},{"g":4,"t":"intros A0 c0","w":"model","ok":true,"c":[13]},{"g":4,"t":"intros x x0 A0 c0","w":"model","ok":true,"c":[14]},{"g":4,"t":"intros X H1 X0 H2","w":"model","ok":true,"c":[15]},{"g":4,"t":"intros x y z A1 c1","w":"model","ok":true,"c":[16]},{"g":4,"t":"intros x y z A1","w":"model","ok":true,"c":[17]},{"g":5,"t":"assumption","w":"auto","ok":false,"err":"Error: No such assumption."},{"g":5,"t":"tauto","w":"auto","ok":false,"err":"Error: Tactic failure: Classical tauto failed."},{"g":5,"t":"firstorder","w":"auto","ok":false,"err":"Error: Timeout!"},{"g":5,"t":"congruence","w":"auto","ok":false,"err":"Error: Tactic failure: congruence failed."},{"g":5,"t":"unfold Possible, MP001, MP002, MP003, AggregateOfPossibles, MP011 in *; firstorder","w":"auto","ok":false,"err":"rejected"},{"g":5,"t":"unfold Possible, MP001, MP002, MP003, AggregateOfPossibles, MP011 in *; hammer","w":"hammer","ok":false,"err":"Error: Hammer failed: ATPs failed to f"},{"g":5,"t":"intros","w":"model","ok":true,"c":[18]},{"g":5,"t":"intros x y","w":"model","ok":true,"c":[19]},{"g":5,"t":"intros。","w":"model","ok":false,"err":"Error: Syntax Error: Lexer: Undefined token"},{"g":5,"t":"intros A0 C0 D0","w":"model","ok":false,"err":"Error: A0 is already used."},{"g":5,"t":"intros x y z A0 C0","w":"model","ok":false,"err":"Error: A0 is already used."},{"g":5,"t":"intros x y z Hx Hy Hz","w":"model","ok":true,"c":[20]},{"g":5,"t":"intros x x0 A c H H0","w":"model","ok":true,"c":[21]},{"g":5,"t":"intros A0 C0 D0 E0","w":"model","ok":false,"err":"Error: A0 is already used."},{"g":10,"t":"assumption","w":"auto","ok":false,"err":"Error: No such assumption."},{"g":10,"t":"tauto","w":"auto","ok":false,"err":"Error: Tactic failure: Classical tauto failed."},{"g":10,"t":"firstorder","w":"auto","ok":false,"err":"Error: Timeout!"},{"g":10,"t":"congruence","w":"auto","ok":false,"err":"Error: Tactic failure: congruence failed."},{"g":10,"t":"unfold Possible, MP001, MP002, MP003, AggregateOfPossibles, MP011 in *; firstorder","w":"auto","ok":false,"err":"rejected"},{"g":10,"t":"unfold Possible, MP001, MP002, MP003, AggregateOfPossibles, MP011 in *; hammer","w":"hammer","ok":false,"err":"Error: Hammer failed: ATPs failed to f"},{"g":10,"t":"split","w":"model","ok":true,"c":[22,23]},{"g":10,"t":"split; intros","w":"model","ok":true,"c":[22,23]},{"g":10,"t":"unfold Gives in H2","w":"model","ok":false,"err":"Error: Cannot coerce Gives to an evaluable reference."},{"g":10,"t":"destruct H1","w":"model","ok":true,"c":[24]},{"g":10,"t":"destruct H1 as (d,H3)","w":"model","ok":true,"c":[25]},{"g":10,"t":"assert (H3 := H2 c0)","w":"model","ok":false,"err":"Error: Illegal application (Non-functional construction): "},{"g":10,"t":"destruct (classic (= H2 c0)) as [Hs|Hs]","w":"model","ok":false,"err":"Error: Syntax error:"},{"g":10,"t":"destruct H1 as (n,H3)","w":"model","ok":true,"c":[26]},{"g":10,"t":"assert (H3 := H1 H2)","w":"model","ok":false,"err":"Error: Illegal application (Non-functional construction): "},{"g":10,"t":"destruct (classic (= H1 H2)) as [Hs|Hs]","w":"model","ok":false,"err":"Error: Syntax error:"},{"g":11,"t":"assumption","w":"auto","ok":false,"err":"Error: No such assumption."},{"g":11,"t":"tauto","w":"auto","ok":false,"err":"Error: Tactic failure: Classical tauto failed."},{"g":11,"t":"firstorder","w":"auto","ok":false,"err":"Error: Timeout!"},{"g":11,"t":"congruence","w":"auto","ok":false,"err":"Error: Tactic failure: congruence failed."},{"g":11,"t":"unfold Possible, MP001, MP002, MP003, AggregateOfPossibles, MP011 in *; firstorder","w":"auto","ok":false,"err":"rejected"},{"g":11,"t":"unfold Possible, MP001, MP002, MP003, AggregateOfPossibles, MP011 in *; hammer","w":"hammer","ok":false,"err":"Error: Hammer failed: ATPs failed to f"},{"g":11,"t":"split","w":"model","ok":true,"c":[27,28]},{"g":11,"t":"unfold Gives in |- *","w":"model","ok":false,"err":"Error: Cannot coerce Gives to an evaluable reference."},{"g":11,"t":"intros A2 G1","w":"model","ok":true,"c":[29]},{"g":11,"t":"intros A2 G","w":"model","ok":true,"c":[30]},{"g":11,"t":"intros A2 G C0","w":"model","ok":false,"err":"Error: No product even after head-reduction."},{"g":11,"t":"generalize c0; clear c0","w":"model","ok":true,"c":[31]},{"g":11,"t":"intros A2 G0","w":"model","ok":true,"c":[32]},{"g":11,"t":"intros A2 G0 H1","w":"model","ok":false,"err":"Error: No product even after head-reduction."},{"g":12,"t":"assumption","w":"auto","ok":false,"err":"Error: No such assumption."},{"g":12,"t":"tauto","w":"auto","ok":false,"err":"Error: Tactic failure: Classical tauto failed."},{"g":12,"t":"firstorder","w":"auto","ok":false,"err":"Error: Timeout!"},{"g":12,"t":"congruence","w":"auto","ok":false,"err":"Error: Tactic failure: congruence failed."},{"g":12,"t":"unfold Possible, MP001, MP002, MP003, AggregateOfPossibles, MP011 in *; firstorder","w":"auto","ok":false,"err":"rejected"},{"g":12,"t":"unfold Possible, MP001, MP002, MP003, AggregateOfPossibles, MP011 in *; hammer","w":"hammer","ok":false,"err":"Error: Hammer failed: ATPs failed to f"},{"g":12,"t":"apply H","w":"model","ok":true,"c":[33]},{"g":12,"t":"elim H","w":"model","ok":true,"c":[33]},{"g":12,"t":"elim H; intros","w":"model","ok":true,"c":[34]},{"g":12,"t":"elim H; clear H","w":"model","ok":true,"c":[4]},{"g":12,"t":"apply H; clear H","w":"model","ok":true,"c":[4]},{"g":18,"t":"assumption","w":"auto","ok":false,"err":"Error: No such assumption."},{"g":18,"t":"tauto","w":"auto","ok":false,"err":"Error: Tactic failure: Classical tauto failed."},{"g":18,"t":"firstorder","w":"auto","ok":false,"err":"Error: Timeout!"},{"g":18,"t":"congruence","w":"auto","ok":false,"err":"Error: Tactic failure: congruence failed."},{"g":18,"t":"unfold Possible, MP001, MP002, MP003, AggregateOfPossibles, MP011 in *; firstorder","w":"auto","ok":false,"err":"rejected"},{"g":18,"t":"unfold Possible, MP001, MP002, MP003, AggregateOfPossibles, MP011 in *; hammer","w":"hammer","ok":false,"err":"Error: Hammer failed: ATPs failed to f"},{"g":18,"t":"split","w":"model","ok":true,"c":[35,36]},{"g":18,"t":"split; intros","w":"model","ok":true,"c":[35,36]},{"g":18,"t":"unfold Gives in H2","w":"model","ok":false,"err":"Error: Cannot coerce Gives to an evaluable reference."},{"g":18,"t":"assert (Gives c A)","w":"model","ok":true,"c":[37,38]},{"g":37,"t":"assumption","w":"auto","ok":true,"c":[],"eager":true},{"g":18,"t":"destruct (classic (Gives c A)) as [Hs|Hs]","w":"model","ok":true,"c":[39,40]},{"g":40,"t":"tauto","w":"auto","ok":true,"c":[],"eager":true},{"g":18,"t":"destruct (AggregateOfPossiblesDistinctAR _ _ _ H1)","w":"model","ok":false,"err":"rejected"},{"g":18,"t":"assert (H3 := AggregateOfPossiblesGives c A H1)","w":"model","ok":false,"err":"rejected"},{"g":18,"t":"destruct (classic (= AggregateOfPossiblesGives c A H1)) as [Hs|Hs]","w":"model","ok":false,"err":"rejected"},{"g":18,"t":"assert (H3 := AggregateOfPossiblesGives c H1)","w":"model","ok":false,"err":"rejected"},{"g":18,"t":"destruct (classic (= AggregateOfPossiblesGives c H1)) as [Hs|Hs]","w":"model","ok":false,"err":"rejected"},{"g":13,"t":"assumption","w":"auto","ok":false,"err":"Error: No such assumption."},{"g":13,"t":"tauto","w":"auto","ok":false,"err":"Error: Tactic failure: Classical tauto failed."},{"g":13,"t":"firstorder","w":"auto","ok":false,"err":"Error: Timeout!"},{"g":13,"t":"congruence","w":"auto","ok":false,"err":"Error: Tactic failure: congruence failed."},{"g":13,"t":"unfold Possible, MP001, MP002, MP003, AggregateOfPossibles, MP011 in *; firstorder","w":"auto","ok":false,"err":"rejected"},{"g":13,"t":"unfold Possible, MP001, MP002, MP003, AggregateOfPossibles, MP011 in *; hammer","w":"hammer","ok":false,"err":"Error: Hammer failed: ATPs failed to f"},{"g":13,"t":"intros A1 c1 H H0","w":"model","ok":true,"c":[41]},{"g":13,"t":"intros A1 c1 H0 H1","w":"model","ok":true,"c":[42]},{"g":13,"t":"intros A1 c1 H Aggregate1","w":"model","ok":true,"c":[43]},{"g":13,"t":"intros A1 c1 H0","w":"model","ok":true,"c":[44]},{"g":13,"t":"intros A1 c1 H A2","w":"model","ok":true,"c":[45]},{"g":13,"t":"intros A1 c1 H' H1","w":"model","ok":true,"c":[46]},{"g":13,"t":"intros","w":"model","ok":true,"c":[41]},{"g":13,"t":"split","w":"model","ok":true,"c":[47,48]},{"g":22,"t":"assumption","w":"auto","ok":false,"err":"Error: No such assumption."},{"g":22,"t":"tauto","w":"auto","ok":false,"err":"Error: Tactic failure: Classical tauto failed."},{"g":22,"t":"firstorder","w":"auto","ok":false,"err":"Error: Timeout!"},{"g":22,"t":"congruence","w":"auto","ok":false,"err":"Error: Tactic failure: congruence failed."},{"g":22,"t":"unfold MP001, MP002, MP003, AggregateOfPossibles, MP011 in *; firstorder","w":"auto","ok":false,"err":"rejected"},{"g":22,"t":"unfold MP001, MP002, MP003, AggregateOfPossibles, MP011 in *; hammer","w":"hammer","ok":false,"err":"Error: Hammer failed: ATPs failed to f"},{"g":14,"t":"assumption","w":"auto","ok":false,"err":"Error: No such assumption."},{"g":14,"t":"tauto","w":"auto","ok":false,"err":"Error: Tactic failure: Classical tauto failed."},{"g":14,"t":"firstorder","w":"auto","ok":false,"err":"Error: Timeout!"},{"g":14,"t":"congruence","w":"auto","ok":false,"err":"Error: Tactic failure: congruence failed."},{"g":14,"t":"unfold Possible, MP001, MP002, MP003, AggregateOfPossibles, MP011 in *; firstorder","w":"auto","ok":false,"err":"rejected"},{"g":14,"t":"unfold Possible, MP001, MP002, MP003, AggregateOfPossibles, MP011 in *; hammer","w":"hammer","ok":false,"err":"Error: Hammer failed: ATPs failed to f"},{"g":14,"t":"split","w":"model","ok":true,"c":[49,50]},{"g":14,"t":"unfold Gives in |- *","w":"model","ok":false,"err":"Error: Cannot coerce Gives to an evaluable reference."},{"g":14,"t":"intros A1 G1","w":"model","ok":true,"c":[51]},{"g":14,"t":"intros A1 G","w":"model","ok":true,"c":[52]},{"g":14,"t":"intros Hc0","w":"model","ok":true,"c":[53]},{"g":14,"t":"intros Hc0 H","w":"model","ok":true,"c":[54]},{"g":14,"t":"generalize A0 Gives_c0","w":"model","ok":false,"err":"Error: The variable Gives_c0 was not found in the cu"},{"g":14,"t":"intros Hc0 H1","w":"model","ok":true,"c":[55]},{"g":15,"t":"assumption","w":"auto","ok":false,"err":"Error: No such assumption."},{"g":15,"t":"tauto","w":"auto","ok":false,"err":"Error: Tactic failure: Classical tauto failed."},{"g":15,"t":"firstorder","w":"auto","ok":false,"err":"Error: Timeout!"},{"g":15,"t":"congruence","w":"auto","ok":false,"err":"Error: Tactic failure: congruence failed."},{"g":15,"t":"unfold Possible, MP001, MP002, MP003, AggregateOfPossibles, MP011 in *; firstorder","w":"auto","ok":false,"err":"rejected"},{"g":15,"t":"unfold Possible, MP001, MP002, MP003, AggregateOfPossibles, MP011 in *; hammer","w":"hammer","ok":false,"err":"Error: Hammer failed: ATPs failed to f"},{"g":15,"t":"intros A0 G0","w":"model","ok":true,"c":[56]},{"g":15,"t":"intros A0 G","w":"model","ok":true,"c":[57]},{"g":15,"t":"intros A0 G H3","w":"model","ok":false,"err":"Error: No product even after head-reduction."},{"g":15,"t":"unfold Gives in H2; intros","w":"model","ok":false,"err":"Error: Cannot coerce Gives to an evaluable refer"},{"g":15,"t":"intros A0 B0 C0 D0","w":"model","ok":false,"err":"Error: No product even after head-reduction."},{"g":15,"t":"intros A0 B0 C0","w":"model","ok":false,"err":"Error: No product even after head-reduction."},{"g":15,"t":"intros A0 B0 C0 D0 E0","w":"model","ok":false,"err":"Error: No product even after head-reduction."},{"g":15,"t":"apply AggregatesGivesNoMemH2; assumption","w":"model","ok":false,"err":"Error: The"},{"g":16,"t":"assumption","w":"auto","ok":false,"err":"Error: No such assumption."},{"g":16,"t":"tauto","w":"auto","ok":false,"err":"Error: Tactic failure: Classical tauto failed."},{"g":16,"t":"firstorder","w":"auto","ok":false,"err":"Error: Timeout!"},{"g":16,"t":"congruence","w":"auto","ok":false,"err":"Error: Tactic failure: congruence failed."},{"g":16,"t":"unfold Possible, MP001, MP002, MP003, AggregateOfPossibles, MP011 in *; firstorder","w":"auto","ok":false,"err":"rejected"},{"g":16,"t":"unfold Possible, MP001, MP002, MP003, AggregateOfPossibles, MP011 in *; hammer","w":"hammer","ok":false,"err":"Error: Hammer failed: ATPs failed to f"},{"g":16,"t":"intros GivesA1","w":"model","ok":true,"c":[58]},{"g":16,"t":"intros G1","w":"model","ok":true,"c":[59]},{"g":16,"t":"intros G","w":"model","ok":true,"c":[60]},{"g":16,"t":"intros G1; Contradiction","w":"model","ok":false,"err":"Error: The reference Contradiction was not fou"},{"g":16,"t":"intros GivesA1; basic_simpl","w":"model","ok":false,"err":"Error: The reference basic_simpl was "},{"g":16,"t":"intros g","w":"model","ok":true,"c":[61]}],"proof":[],"proofFile":null},{"key":"round6/imkan_s10_cause_necessary","id":"imkan_s10_cause_necessary","run":"round6","title":"Dalīl al-imkān, step 10","english":"That cause is necessary in itself.","stmt":"MP001 -> MP002 -> MP003 -> MP011 -> MP012 -> forall A c, AggregateOfPossibles A -> Gives c A -> Necessary c","proved":false,"script":"","seconds":900.6,"expansions":17,"calls":688,"root":0,"goals":["============================\nMP001 -> MP002 -> MP003 -> MP011 -> MP012 -> forall A c, AggregateOfPossibles A -> Gives c A -> Necessary c","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP011\nH3 : MP012\nA : Thing\nc : Thing\nH5 : Gives c A\nH4 : forall (p : Thing) (_ : not (@eq Thing p A)), iff (MemberOf p A) (Possible p)\nH6 : not (MemberOf A A)\nX : Prop\n============================\nEss c","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nH3 : forall (y x : Thing) (_ : Gives y x), Exists y\nA : Thing\nc : Thing\nH5 : Gives c A\nH4 : forall (p : Thing) (_ : not (@eq Thing p A)), iff (MemberOf p A) (Possible p)\nH6 : not (MemberOf A A)\nX : Prop\n============================\nEss c","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP011\nH3 : MP012\nA : Thing\nc : Thing\nH4 : AggregateOfPossibles A\nH5 : Gives c A\n============================\nExists c","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP011\nH3 : MP012\nA : Thing\nc : Thing\nH4 : AggregateOfPossibles A\nH5 : Gives c A\n============================\nEss c","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP011\nH3 : MP012\nA : Thing\nc : Thing\nH4 : AggregateOfPossibles A\nH5 : Gives c A\n============================\nNecessary c","A : MP001\nc : MP002\n============================\nforall (_ : MP003) (_ : MP011) (_ : MP012) (A0 c0 : Thing) (_ : AggregateOfPossibles A0) (_ : Gives c0 A0), Necessary c0","A0 : MP001\nc0 : MP002\n============================\nforall (_ : MP003) (_ : MP011) (_ : MP012) (A c : Thing) (_ : AggregateOfPossibles A) (_ : Gives c A), Necessary c","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP011\nH3 : MP012\nA : Thing\nc : Thing\nH5 : Gives c A\nH4 : forall (p : Thing) (_ : not (@eq Thing p A)), iff (MemberOf p A) (Possible p)\nH6 : not (MemberOf A A)\nX : Prop\nX0 : Prop\n============================\nEss c","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP011\nH3 : MP012\nA : Thing\nc : Thing\nH5 : Gives c A\nH4 : forall (p : Thing) (_ : not (@eq Thing p A)), iff (MemberOf p A) (Possible p)\nH6 : not (MemberOf A A)\nX : Prop\n============================\nGives c A","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP011\nH3 : MP012\nA : Thing\nc : Thing\nH5 : Gives c A\nH4 : forall (p : Thing) (_ : not (@eq Thing p A)), iff (MemberOf p A) (Possible p)\nH6 : not (MemberOf A A)\nX : Prop\nH7 : Gives c A\n============================\nEss c","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP011\nH3 : MP012\nA : Thing\nc : Thing\nH5 : Gives c A\nH4 : forall (p : Thing) (_ : not (@eq Thing p A)), iff (MemberOf p A) (Possible p)\nH6 : not (MemberOf A A)\nX : Prop\nHs : Gives c A\n============================\nEss c","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP011\nH3 : MP012\nA : Thing\nc : Thing\nH5 : Gives c A\nH4 : forall (p : Thing) (_ : not (@eq Thing p A)), iff (MemberOf p A) (Possible p)\nH6 : not (MemberOf A A)\nX : Prop\nHs : not (Gives c A)\n============================\nEss c","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP011\nH3 : MP012\nA : Thing\nc : Thing\nH5 : Gives c A\nH4 : forall (p : Thing) (_ : not (@eq Thing p A)), iff (MemberOf p A) (Possible p)\nH6 : not (MemberOf A A)\nX : Prop\nG : Gives c A\n============================\nEss c","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nH3 : forall (y x : Thing) (_ : Gives y x), Exists y\nA : Thing\nc : Thing\nH5 : Gives c A\nH4 : forall (p : Thing) (_ : not (@eq Thing p A)), iff (MemberOf p A) (Possible p)\nH6 : not (MemberOf A A)\nX : Prop\nX0 : Prop\n============================\nEss c","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nH3 : forall (y x : Thing) (_ : Gives y x), Exists y\nA : Thing\nc : Thing\nH5 : Gives c A\nH4 : forall (p : Thing) (_ : not (@eq Thing p A)), iff (MemberOf p A) (and (Exists p) (not (Ess p)))\nH6 : not (MemberOf A A)\nX : Prop\nX0 : Prop\nX1 : Prop\n============================\nEss c","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP011\nH3 : MP012\nA : Thing\nc : Thing\nH5 : Gives c A\nH4 : forall (p : Thing) (_ : not (@eq Thing p A)), iff (MemberOf p A) (Possible p)\nH6 : not (MemberOf A A)\nX : Prop\nX0 : Prop\n============================\n@eq Prop X X0","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP011\nH3 : MP012\nA : Thing\nc : Thing\nH5 : Gives c A\nH4 : forall (p : Thing) (_ : not (@eq Thing p A)), iff (MemberOf p A) (Possible p)\nH6 : not (MemberOf A A)\nX : Prop\nX0 : Prop\nH7 : @eq Prop X X0\n============================\nEss c","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP011\nH3 : MP012\nA : Thing\nc : Thing\nH5 : Gives c A\nH4 : forall (p : Thing) (_ : not (@eq Thing p A)), iff (MemberOf p A) (Possible p)\nH6 : not (MemberOf A A)\nX : Prop\nX0 : Prop\nHs : @eq Prop X X0\n============================\nEss c","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP011\nH3 : MP012\nA : Thing\nc : Thing\nH5 : Gives c A\nH4 : forall (p : Thing) (_ : not (@eq Thing p A)), iff (MemberOf p A) (Possible p)\nH6 : not (MemberOf A A)\nX : Prop\nX0 : Prop\nHs : not (@eq Prop X X0)\n============================\nEss c","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP011\nH3 : MP012\nA : Thing\nc : Thing\nH5 : Gives c A\nH4 : forall (p : Thing) (_ : not (@eq Thing p A)), iff (MemberOf p A) (Possible p)\nH6 : not (MemberOf A A)\nX : Prop\nX0 : Prop\n============================\nGives c A","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP011\nH3 : MP012\nA : Thing\nc : Thing\nH5 : Gives c A\nH4 : forall (p : Thing) (_ : not (@eq Thing p A)), iff (MemberOf p A) (Possible p)\nH6 : not (MemberOf A A)\nX : Prop\nX0 : Prop\nH7 : Gives c A\n============================\nEss c","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP011\nH3 : MP012\nA : Thing\nc : Thing\nH5 : Gives c A\nH4 : forall (p : Thing) (_ : not (@eq Thing p A)), iff (MemberOf p A) (Possible p)\nH6 : not (MemberOf A A)\nX : Prop\nX0 : Prop\nHs : Gives c A\n============================\nEss c","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP011\nH3 : MP012\nA : Thing\nc : Thing\nH5 : Gives c A\nH4 : forall (p : Thing) (_ : not (@eq Thing p A)), iff (MemberOf p A) (Possible p)\nH6 : not (MemberOf A A)\nX : Prop\nX0 : Prop\nHs : not (Gives c A)\n============================\nEss c","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nH3 : forall (y x : Thing) (_ : Gives y x), Exists y\nA : Thing\nc : Thing\nH5 : Gives c A\nH4 : forall (p : Thing) (_ : not (@eq Thing p A)), iff (MemberOf p A) (Possible p)\nH6 : not (MemberOf A A)\nX : Prop\nX0 : Prop\nX1 : Prop\n============================\nEss c","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nH3 : forall (y x : Thing) (_ : Gives y x), Exists y\nA : Thing\nc : Thing\nH5 : Gives c A\nH4 : forall (p : Thing) (_ : not (@eq Thing p A)), iff (MemberOf p A) (Possible p)\nH6 : not (MemberOf A A)\nX : Prop\nX0 : Prop\n============================\nGives c A","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nH3 : forall (y x : Thing) (_ : Gives y x), Exists y\nA : Thing\nc : Thing\nH5 : Gives c A\nH4 : forall (p : Thing) (_ : not (@eq Thing p A)), iff (MemberOf p A) (Possible p)\nH6 : not (MemberOf A A)\nX : Prop\nX0 : Prop\nH7 : Gives c A\n============================\nEss c","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nH3 : forall (y x : Thing) (_ : Gives y x), Exists y\nA : Thing\nc : Thing\nH5 : Gives c A\nH4 : forall (p : Thing) (_ : not (@eq Thing p A)), iff (MemberOf p A) (Possible p)\nH6 : not (MemberOf A A)\nX : Prop\nX0 : Prop\nHs : Gives c A\n============================\nEss c","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nH3 : forall (y x : Thing) (_ : Gives y x), Exists y\nA : Thing\nc : Thing\nH5 : Gives c A\nH4 : forall (p : Thing) (_ : not (@eq Thing p A)), iff (MemberOf p A) (Possible p)\nH6 : not (MemberOf A A)\nX : Prop\nX0 : Prop\nHs : not (Gives c A)\n============================\nEss c","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP011\nH3 : MP012\nA : Thing\nc : Thing\nH4 : AggregateOfPossibles A\nH5 : Gives c A\n============================\nGives c A","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP011\nH3 : MP012\nA : Thing\nc : Thing\nH4 : AggregateOfPossibles A\nH5 : Gives c A\nH6 : Gives c A\n============================\nEss c","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP011\nH3 : MP012\nA : Thing\nc : Thing\nH4 : AggregateOfPossibles A\nH5 : Gives c A\nHs : Gives c A\n============================\nEss c","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP011\nH3 : MP012\nA : Thing\nc : Thing\nH4 : AggregateOfPossibles A\nH5 : Gives c A\nHs : not (Gives c A)\n============================\nEss c","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP011\nH3 : MP012\nA : Thing\nc : Thing\nH4 : AggregateOfPossibles A\nH5 : Gives c A\n============================\nGives c c","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP011\nH3 : MP012\nA : Thing\nc : Thing\nH4 : AggregateOfPossibles A\nH5 : Gives c A\nH6 : Gives c c\n============================\nEss c","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP011\nH3 : MP012\nA : Thing\nc : Thing\nH4 : AggregateOfPossibles A\nH5 : Gives c A\nHs : Gives c c\n============================\nEss c","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP011\nH3 : MP012\nA : Thing\nc : Thing\nH4 : AggregateOfPossibles A\nH5 : Gives c A\nHs : not (Gives c c)\n============================\nEss c","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP011\nH3 : MP012\nA : Thing\nc : Thing\nH4 : AggregateOfPossibles A\nH5 : Gives c A\n============================\nAggregateOfPossibles A","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP011\nH3 : MP012\nA : Thing\nc : Thing\nH4 : AggregateOfPossibles A\nH5 : Gives c A\nH6 : AggregateOfPossibles A\n============================\nEss c","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP011\nH3 : MP012\nA : Thing\nc : Thing\nH4 : AggregateOfPossibles A\nH5 : Gives c A\nHs : AggregateOfPossibles A\n============================\nEss c","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP011\nH3 : MP012\nA : Thing\nc : Thing\nH4 : AggregateOfPossibles A\nH5 : Gives c A\nHs : not (AggregateOfPossibles A)\n============================\nEss c","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nH3 : forall (y x : Thing) (_ : Gives y x), Exists y\nA : Thing\nc : Thing\nH5 : Gives c A\nH4 : forall (p : Thing) (_ : not (@eq Thing p A)), iff (MemberOf p A) (and (Exists p) (not (Ess p)))\nH6 : not (MemberOf A A)\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\n============================\nEss c","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nH3 : forall (y x : Thing) (_ : Gives y x), Exists y\nA : Thing\nc : Thing\nH5 : Gives c A\nH4 : forall (p : Thing) (_ : not (@eq Thing p A)), iff (MemberOf p A) (and (Exists p) (not (Ess p)))\nH6 : not (MemberOf A A)\nX : Prop\nX0 : Prop\nX1 : Prop\n============================\nGives c A","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nH3 : forall (y x : Thing) (_ : Gives y x), Exists y\nA : Thing\nc : Thing\nH5 : Gives c A\nH4 : forall (p : Thing) (_ : not (@eq Thing p A)), iff (MemberOf p A) (and (Exists p) (not (Ess p)))\nH6 : not (MemberOf A A)\nX : Prop\nX0 : Prop\nX1 : Prop\nH7 : Gives c A\n============================\nEss c","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nH3 : forall (y x : Thing) (_ : Gives y x), Exists y\nA : Thing\nc : Thing\nH5 : Gives c A\nH4 : forall (p : Thing) (_ : not (@eq Thing p A)), iff (MemberOf p A) (and (Exists p) (not (Ess p)))\nH6 : not (MemberOf A A)\nX : Prop\nX0 : Prop\nX1 : Prop\nHs : Gives c A\n============================\nEss c","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nH3 : forall (y x : Thing) (_ : Gives y x), Exists y\nA : Thing\nc : Thing\nH5 : Gives c A\nH4 : forall (p : Thing) (_ : not (@eq Thing p A)), iff (MemberOf p A) (and (Exists p) (not (Ess p)))\nH6 : not (MemberOf A A)\nX : Prop\nX0 : Prop\nX1 : Prop\nHs : not (Gives c A)\n============================\nEss c","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nH3 : forall (y x : Thing) (_ : Gives y x), Exists y\nA : Thing\nc : Thing\nH5 : Gives c A\nH4 : forall (p : Thing) (_ : not (@eq Thing p A)), iff (MemberOf p A) (and (Exists p) (not (Ess p)))\nH6 : not (MemberOf A A)\nX : Prop\nX0 : Prop\nX1 : Prop\n============================\n@eq Thing c A","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nH3 : forall (y x : Thing) (_ : Gives y x), Exists y\nA : Thing\nc : Thing\nH5 : Gives c A\nH4 : forall (p : Thing) (_ : not (@eq Thing p A)), iff (MemberOf p A) (and (Exists p) (not (Ess p)))\nH6 : not (MemberOf A A)\nX : Prop\nX0 : Prop\nX1 : Prop\nH7 : @eq Thing c A\n============================\nEss c","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nH3 : forall (y x : Thing) (_ : Gives y x), Exists y\nA : Thing\nc : Thing\nH5 : Gives c A\nH4 : forall (p : Thing) (_ : not (@eq Thing p A)), iff (MemberOf p A) (and (Exists p) (not (Ess p)))\nH6 : not (MemberOf A A)\nX : Prop\nX0 : Prop\nX1 : Prop\nHs : @eq Thing c A\n============================\nEss c","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nH3 : forall (y x : Thing) (_ : Gives y x), Exists y\nA : Thing\nc : Thing\nH5 : Gives c A\nH4 : forall (p : Thing) (_ : not (@eq Thing p A)), iff (MemberOf p A) (and (Exists p) (not (Ess p)))\nH6 : not (MemberOf A A)\nX : Prop\nX0 : Prop\nX1 : Prop\nHs : not (@eq Thing c A)\n============================\nEss c","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nH3 : forall (y x : Thing) (_ : Gives y x), Exists y\nA : Thing\nc : Thing\nH5 : Gives c A\nH4 : forall (p : Thing) (_ : not (@eq Thing p A)), iff (MemberOf p A) (and (Exists p) (not (Ess p)))\nH6 : not (MemberOf A A)\nX : Prop\nX0 : Prop\nX1 : Prop\n============================\nforall _ : forall (p : Thing) (_ : not (@eq Thing p A)), iff (MemberOf p A) (and (Exists p) (not (Ess p))), Ess c","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nH3 : forall (y x : Thing) (_ : Gives y x), Exists y\nA : Thing\nc : Thing\nH5 : Gives c A\nH4 : forall (p : Thing) (_ : not (@eq Thing p A)), iff (MemberOf p A) (and (Exists p) (not (Ess p)))\nH6 : not (MemberOf A A)\nX : Prop\nX0 : Prop\nX1 : Prop\nHs : Gives A c\n============================\nEss c","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nH3 : forall (y x : Thing) (_ : Gives y x), Exists y\nA : Thing\nc : Thing\nH5 : Gives c A\nH4 : forall (p : Thing) (_ : not (@eq Thing p A)), iff (MemberOf p A) (and (Exists p) (not (Ess p)))\nH6 : not (MemberOf A A)\nX : Prop\nX0 : Prop\nX1 : Prop\nHs : not (Gives A c)\n============================\nEss c","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nH3 : forall (y x : Thing) (_ : Gives y x), Exists y\nA : Thing\nc : Thing\nH5 : Gives c A\nH4 : forall (p : Thing) (_ : not (@eq Thing p A)), iff (MemberOf p A) (Possible p)\nH6 : not (MemberOf A A)\nX : Prop\nX0 : Prop\nX1 : Prop\n============================\nGives A c","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nH3 : forall (y x : Thing) (_ : Gives y x), Exists y\nA : Thing\nc : Thing\nH5 : Gives c A\nH4 : forall (p : Thing) (_ : not (@eq Thing p A)), iff (MemberOf p A) (Possible p)\nH6 : not (MemberOf A A)\nX : Prop\nX0 : Prop\nX1 : Prop\nH7 : Gives A c\n============================\nEss c","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nH3 : forall (y x : Thing) (_ : Gives y x), Exists y\nA : Thing\nc : Thing\nH5 : Gives c A\nH4 : forall (p : Thing) (_ : not (@eq Thing p A)), iff (MemberOf p A) (Possible p)\nH6 : not (MemberOf A A)\nX : Prop\nX0 : Prop\nX1 : Prop\nHs : Gives A c\n============================\nEss c","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nH3 : forall (y x : Thing) (_ : Gives y x), Exists y\nA : Thing\nc : Thing\nH5 : Gives c A\nH4 : forall (p : Thing) (_ : not (@eq Thing p A)), iff (MemberOf p A) (Possible p)\nH6 : not (MemberOf A A)\nX : Prop\nX0 : Prop\nX1 : Prop\nHs : not (Gives A c)\n============================\nEss c","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nH3 : forall (y x : Thing) (_ : Gives y x), Exists y\nA : Thing\nc : Thing\nH5 : Gives c A\nH4 : forall (p : Thing) (_ : not (@eq Thing p A)), iff (MemberOf p A) (Possible p)\nH6 : not (MemberOf A A)\nX : Prop\nX0 : Prop\nX1 : Prop\n============================\nGives c A","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nH3 : forall (y x : Thing) (_ : Gives y x), Exists y\nA : Thing\nc : Thing\nH5 : Gives c A\nH4 : forall (p : Thing) (_ : not (@eq Thing p A)), iff (MemberOf p A) (Possible p)\nH6 : not (MemberOf A A)\nX : Prop\nX0 : Prop\nX1 : Prop\nH7 : Gives c A\n============================\nEss c","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nH3 : forall (y x : Thing) (_ : Gives y x), Exists y\nA : Thing\nc : Thing\nH5 : Gives c A\nH4 : forall (p : Thing) (_ : not (@eq Thing p A)), iff (MemberOf p A) (Possible p)\nH6 : not (MemberOf A A)\nX : Prop\nX0 : Prop\nX1 : Prop\nHs : Gives c A\n============================\nEss c","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nH3 : forall (y x : Thing) (_ : Gives y x), Exists y\nA : Thing\nc : Thing\nH5 : Gives c A\nH4 : forall (p : Thing) (_ : not (@eq Thing p A)), iff (MemberOf p A) (Possible p)\nH6 : not (MemberOf A A)\nX : Prop\nX0 : Prop\nX1 : Prop\nHs : not (Gives c A)\n============================\nEss c","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nH3 : forall (y x : Thing) (_ : Gives y x), Exists y\nA : Thing\nc : Thing\nH5 : Gives c A\nH4 : forall (p : Thing) (_ : not (@eq Thing p A)), iff (MemberOf p A) (Possible p)\nH6 : not (MemberOf A A)\nX : Prop\nX0 : Prop\nX1 : Prop\nHs : @eq Thing c A\n============================\nEss c","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nH3 : forall (y x : Thing) (_ : Gives y x), Exists y\nA : Thing\nc : Thing\nH5 : Gives c A\nH4 : forall (p : Thing) (_ : not (@eq Thing p A)), iff (MemberOf p A) (Possible p)\nH6 : not (MemberOf A A)\nX : Prop\nX0 : Prop\nX1 : Prop\nHs : not (@eq Thing c A)\n============================\nEss c","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nH3 : forall (y x : Thing) (_ : Gives y x), Exists y\nA : Thing\nc : Thing\nH5 : Gives c A\nH4 : forall (p : Thing) (_ : not (@eq Thing p A)), iff (MemberOf p A) (and (Exists p) (not (Ess p)))\nH6 : not (MemberOf A A)\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\n============================\nGives c A","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nH3 : forall (y x : Thing) (_ : Gives y x), Exists y\nA : Thing\nc : Thing\nH5 : Gives c A\nH4 : forall (p : Thing) (_ : not (@eq Thing p A)), iff (MemberOf p A) (and (Exists p) (not (Ess p)))\nH6 : not (MemberOf A A)\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nH7 : Gives c A\n============================\nEss c","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nH3 : forall (y x : Thing) (_ : Gives y x), Exists y\nA : Thing\nc : Thing\nH5 : Gives c A\nH4 : forall (p : Thing) (_ : not (@eq Thing p A)), iff (MemberOf p A) (and (Exists p) (not (Ess p)))\nH6 : not (MemberOf A A)\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nHs : Gives c A\n============================\nEss c","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nH3 : forall (y x : Thing) (_ : Gives y x), Exists y\nA : Thing\nc : Thing\nH5 : Gives c A\nH4 : forall (p : Thing) (_ : not (@eq Thing p A)), iff (MemberOf p A) (and (Exists p) (not (Ess p)))\nH6 : not (MemberOf A A)\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nHs : not (Gives c A)\n============================\nEss c","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nH3 : forall (y x : Thing) (_ : Gives y x), Exists y\nA : Thing\nc : Thing\nH5 : Gives c A\nH4 : forall (p : Thing) (_ : not (@eq Thing p A)), iff (MemberOf p A) (and (Exists p) (not (Ess p)))\nH6 : not (MemberOf A A)\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\n============================\n@eq Thing c A","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nH3 : forall (y x : Thing) (_ : Gives y x), Exists y\nA : Thing\nc : Thing\nH5 : Gives c A\nH4 : forall (p : Thing) (_ : not (@eq Thing p A)), iff (MemberOf p A) (and (Exists p) (not (Ess p)))\nH6 : not (MemberOf A A)\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nH7 : @eq Thing c A\n============================\nEss c","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nH3 : forall (y x : Thing) (_ : Gives y x), Exists y\nA : Thing\nc : Thing\nH5 : Gives c A\nH4 : forall (p : Thing) (_ : not (@eq Thing p A)), iff (MemberOf p A) (and (Exists p) (not (Ess p)))\nH6 : not (MemberOf A A)\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nHs : @eq Thing c A\n============================\nEss c","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nH3 : forall (y x : Thing) (_ : Gives y x), Exists y\nA : Thing\nc : Thing\nH5 : Gives c A\nH4 : forall (p : Thing) (_ : not (@eq Thing p A)), iff (MemberOf p A) (and (Exists p) (not (Ess p)))\nH6 : not (MemberOf A A)\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nHs : not (@eq Thing c A)\n============================\nEss c","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nH3 : forall (y x : Thing) (_ : Gives y x), Exists y\nA : Thing\nc : Thing\nH5 : Gives c A\nH4 : forall (p : Thing) (_ : not (@eq Thing p A)), iff (MemberOf p A) (and (Exists p) (not (Ess p)))\nH6 : not (MemberOf A A)\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\n============================\nforall _ : forall (p : Thing) (_ : not (@eq Thing p A)), iff (MemberOf p A) (and (Exists p) (not (Ess p))), Ess c","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP011\nH3 : MP012\nA : Thing\nc : Thing\nH4 : AggregateOfPossibles A\nH5 : Gives c A\nH6 : Gives c A\n============================\nNecessary c","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP011\nH3 : MP012\nA : Thing\nc : Thing\nH4 : AggregateOfPossibles A\nH5 : Gives c A\nHs : Gives c A\n============================\nNecessary c","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP011\nH3 : MP012\nA : Thing\nc : Thing\nH4 : AggregateOfPossibles A\nH5 : Gives c A\nHs : not (Gives c A)\n============================\nNecessary c","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP011\nH3 : MP012\nA : Thing\nc : Thing\nH4 : AggregateOfPossibles A\nH5 : Gives c A\nH6 : Necessary c\n============================\nNecessary c","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP011\nH3 : MP012\nA : Thing\nc : Thing\nH4 : AggregateOfPossibles A\nH5 : Gives c A\nHs : Necessary c\n============================\nNecessary c","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP011\nH3 : MP012\nA : Thing\nc : Thing\nH4 : AggregateOfPossibles A\nH5 : Gives c A\nHs : not (Necessary c)\n============================\nNecessary c","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nH3 : forall (y x : Thing) (_ : Gives y x), Exists y\nA : Thing\nc : Thing\nH5 : Gives c A\nH4 : forall (p : Thing) (_ : not (@eq Thing p A)), iff (MemberOf p A) (and (Exists p) (not (Ess p)))\nH6 : not (MemberOf A A)\nX : Prop\nX0 : Prop\nX1 : Prop\n============================\n@eq Prop X X0","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP011\nH3 : MP012\nA : Thing\nc : Thing\nH5 : Gives c A\nH4 : forall (p : Thing) (_ : not (@eq Thing p A)), iff (MemberOf p A) (Possible p)\nH6 : not (MemberOf A A)\nX : Prop\nX0 : Prop\n============================\nFalse","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP011\nH3 : MP012\nA : Thing\nc : Thing\nH5 : Gives c A\nH4 : forall (p : Thing) (_ : not (@eq Thing p A)), iff (MemberOf p A) (Possible p)\nH6 : not (MemberOf A A)\nX : Prop\nX0 : Prop\n============================\nMemberOf A A","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP011\nH3 : MP012\nA : Thing\nc : Thing\nH5 : Gives c A\nH4 : forall (p : Thing) (_ : not (@eq Thing p A)), iff (MemberOf p A) (Possible p)\nH6 : not (MemberOf A A)\nX : Prop\nX0 : Prop\nH7 : @eq Prop X X0\n============================\nforall _ : Gives c A, Ess c","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP011\nH3 : MP012\nA : Thing\nc : Thing\nH5 : Gives c A\nH4 : forall (p : Thing) (_ : not (@eq Thing p A)), iff (MemberOf p A) (Possible p)\nH6 : not (MemberOf A A)\nX : Prop\nX0 : Prop\nH7 : @eq Prop X X0\n============================\nGives c A","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP011\nH3 : MP012\nA : Thing\nc : Thing\nH5 : Gives c A\nH4 : forall (p : Thing) (_ : not (@eq Thing p A)), iff (MemberOf p A) (Possible p)\nH6 : not (MemberOf A A)\nX : Prop\nX0 : Prop\nH7 : @eq Prop X X0\n============================\n@eq Prop X X0","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP011\nH3 : MP012\nA : Thing\nc : Thing\nH5 : Gives c A\nH4 : forall (p : Thing) (_ : not (@eq Thing p A)), iff (MemberOf p A) (Possible p)\nH6 : not (MemberOf A A)\nX : Prop\nX0 : Prop\nH7 : @eq Prop X X0\nH8 : @eq Prop X X0\n============================\nEss c","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP011\nH3 : MP012\nA : Thing\nc : Thing\nH5 : Gives c A\nH4 : forall (p : Thing) (_ : not (@eq Thing p A)), iff (MemberOf p A) (Possible p)\nH6 : not (MemberOf A A)\nX : Prop\nX0 : Prop\nH7 : @eq Prop X X0\nHs : @eq Prop X X0\n============================\nEss c","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP011\nH3 : MP012\nA : Thing\nc : Thing\nH5 : Gives c A\nH4 : forall (p : Thing) (_ : not (@eq Thing p A)), iff (MemberOf p A) (Possible p)\nH6 : not (MemberOf A A)\nX : Prop\nX0 : Prop\nH7 : @eq Prop X X0\nHs : not (@eq Prop X X0)\n============================\nEss c","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP011\nH3 : MP012\nA : Thing\nc : Thing\nH5 : Gives c A\nH4 : forall (p : Thing) (_ : not (@eq Thing p A)), iff (MemberOf p A) (Possible p)\nH6 : not (MemberOf A A)\nX : Prop\nX0 : Prop\nH7 : @eq Prop X X0\nH8 : Gives c A\n============================\nEss c","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP011\nH3 : MP012\nA : Thing\nc : Thing\nH5 : Gives c A\nH4 : forall (p : Thing) (_ : not (@eq Thing p A)), iff (MemberOf p A) (Possible p)\nH6 : not (MemberOf A A)\nX : Prop\nX0 : Prop\nH7 : @eq Prop X X0\nHs : Gives c A\n============================\nEss c","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP011\nH3 : MP012\nA : Thing\nc : Thing\nH5 : Gives c A\nH4 : forall (p : Thing) (_ : not (@eq Thing p A)), iff (MemberOf p A) (Possible p)\nH6 : not (MemberOf A A)\nX : Prop\nX0 : Prop\nH7 : @eq Prop X X0\nHs : not (Gives c A)\n============================\nEss c","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP011\nH3 : MP012\nA : Thing\nc : Thing\nH5 : Gives c A\nH4 : forall (p : Thing) (_ : not (@eq Thing p A)), iff (MemberOf p A) (Possible p)\nH6 : not (MemberOf A A)\nX : Prop\nX0 : Prop\nH7 : @eq Prop X X0\nHs : @eq Thing A c\n============================\nEss c","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP011\nH3 : MP012\nA : Thing\nc : Thing\nH5 : Gives c A\nH4 : forall (p : Thing) (_ : not (@eq Thing p A)), iff (MemberOf p A) (Possible p)\nH6 : not (MemberOf A A)\nX : Prop\nX0 : Prop\nH7 : @eq Prop X X0\nHs : not (@eq Thing A c)\n============================\nEss c","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nH3 : forall (y x : Thing) (_ : Gives y x), Exists y\nA : Thing\nc : Thing\nH5 : Gives c A\nH4 : forall (p : Thing) (_ : not (@eq Thing p A)), iff (MemberOf p A) (and (Exists p) (not (Ess p)))\nH6 : not (MemberOf A A)\nX : Prop\nX0 : Prop\nHs : @eq Prop X X0\nX1 : Prop\n============================\nEss c","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP011\nH3 : MP012\nA : Thing\nc : Thing\nH5 : Gives c A\nH4 : forall (p : Thing) (_ : not (@eq Thing p A)), iff (MemberOf p A) (Possible p)\nH6 : not (MemberOf A A)\nX : Prop\nX0 : Prop\nHs : @eq Prop X X0\n============================\nforall _ : Gives c A, Ess c","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP011\nH3 : MP012\nA : Thing\nc : Thing\nH5 : Gives c A\nH4 : forall (p : Thing) (_ : not (@eq Thing p A)), iff (MemberOf p A) (Possible p)\nH6 : not (MemberOf A A)\nX : Prop\nX0 : Prop\nHs : @eq Prop X X0\n============================\nGives c A","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP011\nH3 : MP012\nA : Thing\nc : Thing\nH5 : Gives c A\nH4 : forall (p : Thing) (_ : not (@eq Thing p A)), iff (MemberOf p A) (Possible p)\nH6 : not (MemberOf A A)\nX : Prop\nX0 : Prop\nHs : @eq Prop X X0\nH7 : Gives c A\n============================\nEss c","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP011\nH3 : MP012\nA : Thing\nc : Thing\nH5 : Gives c A\nH4 : forall (p : Thing) (_ : not (@eq Thing p A)), iff (MemberOf p A) (Possible p)\nH6 : not (MemberOf A A)\nX : Prop\nX0 : Prop\nHs : @eq Prop X X0\n============================\n@eq Prop X X0","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP011\nH3 : MP012\nA : Thing\nc : Thing\nH5 : Gives c A\nH4 : forall (p : Thing) (_ : not (@eq Thing p A)), iff (MemberOf p A) (Possible p)\nH6 : not (MemberOf A A)\nX : Prop\nX0 : Prop\nHs : @eq Prop X X0\nH7 : @eq Prop X X0\n============================\nEss c","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP011\nH3 : MP012\nA : Thing\nc : Thing\nH5 : Gives c A\nH4 : forall (p : Thing) (_ : not (@eq Thing p A)), iff (MemberOf p A) (Possible p)\nH6 : not (MemberOf A A)\nX : Prop\nX0 : Prop\nHs : not (@eq Prop X X0)\n============================\n@eq Prop X X0","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP011\nH3 : MP012\nA : Thing\nc : Thing\nH5 : Gives c A\nH4 : forall (p : Thing) (_ : not (@eq Thing p A)), iff (MemberOf p A) (Possible p)\nH6 : not (MemberOf A A)\nX : Prop\nX0 : Prop\nHs : not (@eq Prop X X0)\nH7 : @eq Prop X X0\n============================\nEss c","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP011\nH3 : MP012\nA : Thing\nc : Thing\nH5 : Gives c A\nH4 : forall (p : Thing) (_ : not (@eq Thing p A)), iff (MemberOf p A) (Possible p)\nH6 : not (MemberOf A A)\nX : Prop\nX0 : Prop\nHs : not (@eq Prop X X0)\n============================\n@eq Thing A A","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP011\nH3 : MP012\nA : Thing\nc : Thing\nH5 : Gives c A\nH4 : forall (p : Thing) (_ : not (@eq Thing p A)), iff (MemberOf p A) (Possible p)\nH6 : not (MemberOf A A)\nX : Prop\nX0 : Prop\nHs : not (@eq Prop X X0)\nH7 : @eq Thing A A\n============================\nEss c","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP011\nH3 : MP012\nA : Thing\nc : Thing\nH5 : Gives c A\nH4 : forall (p : Thing) (_ : not (@eq Thing p A)), iff (MemberOf p A) (Possible p)\nH6 : not (MemberOf A A)\nX : Prop\nX0 : Prop\nHs : not (@eq Prop X X0)\n============================\nforall _ : Gives c A, Ess c","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP011\nH3 : MP012\nA : Thing\nc : Thing\nH5 : Gives c A\nH4 : forall (p : Thing) (_ : not (@eq Thing p A)), iff (MemberOf p A) (Possible p)\nH6 : not (MemberOf A A)\nX : Prop\nX0 : Prop\nHs : not (@eq Prop X X0)\n============================\nGives c A","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP011\nH3 : MP012\nA : Thing\nc : Thing\nH5 : Gives c A\nH4 : forall (p : Thing) (_ : not (@eq Thing p A)), iff (MemberOf p A) (Possible p)\nH6 : not (MemberOf A A)\nX : Prop\nHs : Gives c A\nX0 : Prop\n============================\nEss c","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nH3 : forall (y x : Thing) (_ : Gives y x), Exists y\nA : Thing\nc : Thing\nH5 : Gives c A\nH4 : forall (p : Thing) (_ : not (@eq Thing p A)), iff (MemberOf p A) (and (Exists p) (not (Ess p)))\nH6 : not (MemberOf A A)\nX : Prop\nHs : Gives c A\nX0 : Prop\n============================\nEss c","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP011\nH3 : MP012\nA : Thing\nc : Thing\nH5 : Gives c A\nH4 : forall (p : Thing) (_ : not (@eq Thing p A)), iff (MemberOf p A) (Possible p)\nH6 : not (MemberOf A A)\nX : Prop\nHs : Gives c A\n============================\nGives c A","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP011\nH3 : MP012\nA : Thing\nc : Thing\nH5 : Gives c A\nH4 : forall (p : Thing) (_ : not (@eq Thing p A)), iff (MemberOf p A) (Possible p)\nH6 : not (MemberOf A A)\nX : Prop\nHs : Gives c A\nH7 : Gives c A\n============================\nEss c","A : MP001\nc : MP002\nx : MP003\ny : MP011\nz : MP012\nA1 : Thing\nc1 : Thing\n============================\nforall (_ : AggregateOfPossibles A1) (_ : Gives c1 A1), Necessary c1","A : MP001\nc : MP002\nH : MP003\nH0 : MP011\nH1 : MP012\nA0 : Thing\nc0 : Thing\nH2 : AggregateOfPossibles A0\nH3 : Gives c0 A0\n============================\nNecessary c0","A : MP001\nc : MP002\nx : MP003\ny : MP011\nz : MP012\nH : Thing\nA1 : Thing\nc1 : AggregateOfPossibles H\n============================\nforall _ : Gives A1 H, Necessary A1","A : MP001\nc : MP002\nx : MP003\nx0 : MP011\ny : MP012\nz : Thing\nA1 : Thing\nc1 : AggregateOfPossibles z\n============================\nforall _ : Gives A1 z, Necessary A1","A : MP001\nc : MP002\ni0 : MP003\ni1 : MP011\ni2 : MP012\nA1 : Thing\nc1 : Thing\n============================\nforall (_ : AggregateOfPossibles A1) (_ : Gives c1 A1), Necessary c1","A : MP001\nc : MP002\nX : MP003\nH1 : MP011\nH2 : MP012\nA0 : Thing\nc0 : Thing\n============================\nforall (_ : AggregateOfPossibles A0) (_ : Gives c0 A0), Necessary c0","A : MP001\nc : MP002\nA0 : MP003\nc0 : MP011\nA12 : MP012\nB0 : Thing\nC0 : Thing\n============================\nforall (_ : AggregateOfPossibles B0) (_ : Gives C0 B0), Necessary C0"],"events":[{"g":0,"t":"assumption","w":"auto","ok":false,"err":"Error: No such assumption."},{"g":0,"t":"tauto","w":"auto","ok":false,"err":"Error: Tactic failure: Classical tauto failed."},{"g":0,"t":"firstorder","w":"auto","ok":true,"c":[1]},{"g":0,"t":"congruence","w":"auto","ok":false,"err":"Error: Tactic failure: congruence failed."},{"g":0,"t":"unfold Necessary, MP001, MP002, MP003, AggregateOfPossibles, MP011, MP012 in *; firstorder","w":"auto","ok":true,"c":[2]},{"g":0,"t":"unfold Necessary, MP001, MP002, MP003, AggregateOfPossibles, MP011, MP012 in *; hammer","w":"hammer","ok":false,"err":"Error: Hammer failed: ATPs failed to f"},{"g":0,"t":"right","w":"model","ok":false,"err":"Error: Not an inductive goal with 2 constructors."},{"g":0,"t":"split","w":"model","ok":true,"c":[3,4]},{"g":3,"t":"firstorder","w":"auto","ok":true,"c":[],"eager":true},{"g":0,"t":"left","w":"model","ok":false,"err":"Error: Not an inductive goal with 2 constructors."},{"g":0,"t":"intros","w":"model","ok":true,"c":[5]},{"g":0,"t":"intros A c","w":"model","ok":true,"c":[6]},{"g":0,"t":"intros A0 c0","w":"model","ok":true,"c":[7]},{"g":0,"t":"apply AggregateOfPossiblesR","w":"model","ok":false,"err":"Error: The variable AggregateOfPossib"},{"g":1,"t":"assumption","w":"auto","ok":false,"err":"Error: No such assumption."},{"g":1,"t":"tauto","w":"auto","ok":false,"err":"Error: Tactic failure: Classical tauto failed."},{"g":1,"t":"firstorder","w":"auto","ok":true,"c":[8]},{"g":1,"t":"congruence","w":"auto","ok":false,"err":"Error: Tactic failure: congruence failed."},{"g":1,"t":"unfold Possible, MP001, MP002, MP003, MP011, MP012 in *; firstorder","w":"auto","ok":false,"err":"rejected"},{"g":1,"t":"unfold Possible, MP001, MP002, MP003, MP011, MP012 in *; hammer","w":"hammer","ok":false,"err":"Error: Hammer failed: ATPs failed to f"},{"g":1,"t":"exists A","w":"model","ok":false,"err":"Error: Not an inductive definition."},{"g":1,"t":"assert (Gives c A)","w":"model","ok":true,"c":[9,10]},{"g":9,"t":"assumption","w":"auto","ok":true,"c":[],"eager":true},{"g":1,"t":"destruct (classic (Gives c A)) as [Hs|Hs]","w":"model","ok":true,"c":[11,12]},{"g":12,"t":"tauto","w":"auto","ok":true,"c":[],"eager":true},{"g":1,"t":"exists A; simplest","w":"model","ok":false,"err":"Error: The reference simplest was not found in the current envir"},{"g":1,"t":"exists A; trivial","w":"model","ok":false,"err":"Error: Not an inductive definition."},{"g":1,"t":"split","w":"model","ok":false,"err":"Error: Not an inductive definition."},{"g":1,"t":"assert (G : Gives c X)","w":"model","ok":false,"err":"rejected"},{"g":1,"t":"destruct (classic (Gives c X)) as [Hs|Hs]","w":"model","ok":false,"err":"rejected"},{"g":1,"t":"assert (G : Gives c A)","w":"model","ok":true,"c":[9,13]},{"g":2,"t":"assumption","w":"auto","ok":false,"err":"Error: No such assumption."},{"g":2,"t":"tauto","w":"auto","ok":false,"err":"Error: Tactic failure: Classical tauto failed."},{"g":2,"t":"firstorder","w":"auto","ok":true,"c":[14]},{"g":2,"t":"congruence","w":"auto","ok":false,"err":"Error: Tactic failure: congruence failed."},{"g":2,"t":"unfold Possible in *; firstorder","w":"auto","ok":false,"err":"Error: Timeout!"},{"g":2,"t":"unfold Possible in *; hammer","w":"hammer","ok":false,"err":"Error: Hammer failed: ATPs failed to f"},{"g":2,"t":"exists A","w":"model","ok":false,"err":"Error: Not an inductive definition."},{"g":2,"t":"exists a","w":"model","ok":false,"err":"Error: The variable a was not found in the current environment."},{"g":2,"t":"exists c","w":"model","ok":false,"err":"Error: Not an inductive definition."},{"g":2,"t":"exists A; assumption","w":"model","ok":false,"err":"Error: Not an inductive definition."},{"g":2,"t":"apply H2","w":"model","ok":false,"err":"rejected"},{"g":2,"t":"apply H2; intros","w":"model","ok":false,"err":"rejected"},{"g":8,"t":"assumption","w":"auto","ok":false,"err":"Error: No such assumption."},{"g":8,"t":"tauto","w":"auto","ok":false,"err":"Error: Tactic failure: Classical tauto failed."},{"g":8,"t":"firstorder","w":"auto","ok":false,"err":"Error: Timeout!"},{"g":8,"t":"congruence","w":"auto","ok":false,"err":"Error: Tactic failure: congruence failed."},{"g":8,"t":"unfold Possible, MP001, MP002, MP003, MP011, MP012 in *; firstorder","w":"auto","ok":true,"c":[15]},{"g":8,"t":"unfold Possible, MP001, MP002, MP003, MP011, MP012 in *; hammer","w":"hammer","ok":false,"err":"Error: Hammer failed: ATPs failed to f"},{"g":8,"t":"exists A","w":"model","ok":false,"err":"Error: Not an inductive definition."},{"g":8,"t":"assert (X = X0)","w":"model","ok":true,"c":[16,17]},{"g":8,"t":"destruct (classic (X = X0)) as [Hs|Hs]","w":"model","ok":true,"c":[18,19]},{"g":8,"t":"assert (Gives c A)","w":"model","ok":true,"c":[20,21]},{"g":20,"t":"assumption","w":"auto","ok":true,"c":[],"eager":true},{"g":8,"t":"destruct (classic (Gives c A)) as [Hs|Hs]","w":"model","ok":true,"c":[22,23]},{"g":23,"t":"tauto","w":"auto","ok":true,"c":[],"eager":true},{"g":8,"t":"exists A; simplest","w":"model","ok":false,"err":"Error: The reference simplest was not found in the current envir"},{"g":8,"t":"apply X","w":"model","ok":false,"err":"rejected"},{"g":8,"t":"assert (G : Gives c X)","w":"model","ok":false,"err":"rejected"},{"g":8,"t":"destruct (classic (Gives c X)) as [Hs|Hs]","w":"model","ok":false,"err":"rejected"},{"g":14,"t":"assumption","w":"auto","ok":false,"err":"Error: No such assumption."},{"g":14,"t":"tauto","w":"auto","ok":false,"err":"Error: Tactic failure: Classical tauto failed."},{"g":14,"t":"firstorder","w":"auto","ok":true,"c":[24]},{"g":14,"t":"congruence","w":"auto","ok":false,"err":"Error: Tactic failure: congruence failed."},{"g":14,"t":"unfold Possible in *; firstorder","w":"auto","ok":true,"c":[15]},{"g":14,"t":"unfold Possible in *; hammer","w":"hammer","ok":false,"err":"Error: Hammer failed: ATPs failed to f"},{"g":14,"t":"exists A","w":"model","ok":false,"err":"Error: Not an inductive definition."},{"g":14,"t":"assert (Gives y A)","w":"model","ok":false,"err":"Error: The variable y was not found in the current environment."},{"g":14,"t":"destruct (classic (Gives y A)) as [Hs|Hs]","w":"model","ok":false,"err":"Error: The"},{"g":14,"t":"exists a","w":"model","ok":false,"err":"Error: The variable a was not found in the current environment."},{"g":14,"t":"exists c","w":"model","ok":false,"err":"Error: Not an inductive definition."},{"g":14,"t":"assert (Gives A X)","w":"model","ok":false,"err":"rejected"},{"g":14,"t":"destruct (classic (Gives A X)) as [Hs|Hs]","w":"model","ok":false,"err":"rejected"},{"g":14,"t":"assert (Gives c A)","w":"model","ok":true,"c":[25,26]},{"g":25,"t":"assumption","w":"auto","ok":true,"c":[],"eager":true},{"g":14,"t":"destruct (classic (Gives c A)) as [Hs|Hs]","w":"model","ok":true,"c":[27,28]},{"g":28,"t":"tauto","w":"auto","ok":true,"c":[],"eager":true},{"g":4,"t":"assumption","w":"auto","ok":false,"err":"Error: No such assumption."},{"g":4,"t":"tauto","w":"auto","ok":false,"err":"Error: Tactic failure: Classical tauto failed."},{"g":4,"t":"firstorder","w":"auto","ok":false,"err":"Error: Timeout!"},{"g":4,"t":"congruence","w":"auto","ok":false,"err":"Error: Tactic failure: congruence failed."},{"g":4,"t":"unfold MP001, MP002, MP003, AggregateOfPossibles, MP011, MP012 in *; firstorder","w":"auto","ok":true,"c":[2]},{"g":4,"t":"unfold MP001, MP002, MP003, AggregateOfPossibles, MP011, MP012 in *; hammer","w":"hammer","ok":false,"err":"Error: Hammer failed: ATPs failed to f"},{"g":4,"t":"exists A","w":"model","ok":false,"err":"Error: Not an inductive definition."},{"g":4,"t":"assert (Gives c A)","w":"model","ok":true,"c":[29,30]},{"g":29,"t":"assumption","w":"auto","ok":true,"c":[],"eager":true},{"g":4,"t":"destruct (classic (Gives c A)) as [Hs|Hs]","w":"model","ok":true,"c":[31,32]},{"g":32,"t":"tauto","w":"auto","ok":true,"c":[],"eager":true},{"g":4,"t":"assert (Gives c c)","w":"model","ok":true,"c":[33,34]},{"g":4,"t":"destruct (classic (Gives c c)) as [Hs|Hs]","w":"model","ok":true,"c":[35,36]},{"g":4,"t":"assert (AggregateOfPossibles A)","w":"model","ok":true,"c":[37,38]},{"g":37,"t":"assumption","w":"auto","ok":true,"c":[],"eager":true},{"g":4,"t":"destruct (classic (AggregateOfPossibles A)) as [Hs|Hs]","w":"model","ok":true,"c":[39,40]},{"g":40,"t":"tauto","w":"auto","ok":true,"c":[],"eager":true},{"g":4,"t":"destruct (classic (AggregateOfPossibles A H4)) as [Hs|Hs]","w":"model","ok":false,"err":"Error: Illegal application (Non-functional construction): "},{"g":4,"t":"destruct (classic (AggregateOfPossibles c A)) as [Hs|Hs]","w":"model","ok":false,"err":"Error: Illegal application (Non-functional construction): "},{"g":4,"t":"destruct (classic (AggregateOfPossibles A GII)) as [Hs|Hs]","w":"model","ok":false,"err":"rejected"},{"g":15,"t":"assumption","w":"auto","ok":false,"err":"Error: No such assumption."},{"g":15,"t":"tauto","w":"auto","ok":false,"err":"Error: Tactic failure: Classical tauto failed."},{"g":15,"t":"firstorder","w":"auto","ok":true,"c":[41]},{"g":15,"t":"congruence","w":"auto","ok":false,"err":"Error: Tactic failure: congruence failed."},{"g":15,"t":"hammer","w":"hammer","ok":false,"err":"Error: Hammer failed: ATPs failed to f"},{"g":15,"t":"assert (Gives c A)","w":"model","ok":true,"c":[42,43]},{"g":42,"t":"assumption","w":"auto","ok":true,"c":[],"eager":true},{"g":15,"t":"destruct (classic (Gives c A)) as [Hs|Hs]","w":"model","ok":true,"c":[44,45]},{"g":45,"t":"tauto","w":"auto","ok":true,"c":[],"eager":true},{"g":15,"t":"exists c","w":"model","ok":false,"err":"Error: Not an inductive definition."},{"g":15,"t":"apply H4; assumption","w":"model","ok":false,"err":"rejected"},{"g":15,"t":"assert (c = A)","w":"model","ok":true,"c":[46,47]},{"g":15,"t":"destruct (classic (c = A)) as [Hs|Hs]","w":"model","ok":true,"c":[48,49]},{"g":15,"t":"generalize H4","w":"model","ok":true,"c":[50]},{"g":15,"t":"assert (Gives y c)","w":"model","ok":false,"err":"Error: The variable y was not found in the current environment."},{"g":15,"t":"destruct (classic (Gives y c)) as [Hs|Hs]","w":"model","ok":false,"err":"Error: The"},{"g":15,"t":"apply H4","w":"model","ok":false,"err":"rejected"},{"g":15,"t":"destruct (classic (Gives A c)) as [Hs|Hs]","w":"model","ok":true,"c":[51,52]},{"g":24,"t":"assumption","w":"auto","ok":false,"err":"Error: No such assumption."},{"g":24,"t":"tauto","w":"auto","ok":false,"err":"Error: Tactic failure: Classical tauto failed."},{"g":24,"t":"firstorder","w":"auto","ok":false,"err":"Error: Timeout!"},{"g":24,"t":"congruence","w":"auto","ok":false,"err":"Error: Tactic failure: congruence failed."},{"g":24,"t":"unfold Possible in *; firstorder","w":"auto","ok":true,"c":[41]},{"g":24,"t":"unfold Possible in *; hammer","w":"hammer","ok":false,"err":"Error: Hammer failed: ATPs failed to f"},{"g":24,"t":"exists c","w":"model","ok":false,"err":"Error: Not an inductive definition."},{"g":24,"t":"exists A","w":"model","ok":false,"err":"Error: Not an inductive definition."},{"g":24,"t":"assert (Gives y A)","w":"model","ok":false,"err":"Error: The variable y was not found in the current environment."},{"g":24,"t":"destruct (classic (Gives y A)) as [Hs|Hs]","w":"model","ok":false,"err":"Error: The"},{"g":24,"t":"assert (Gives A c)","w":"model","ok":true,"c":[53,54]},{"g":24,"t":"destruct (classic (Gives A c)) as [Hs|Hs]","w":"model","ok":true,"c":[55,56]},{"g":24,"t":"assert (Gives c A)","w":"model","ok":true,"c":[57,58]},{"g":57,"t":"assumption","w":"auto","ok":true,"c":[],"eager":true},{"g":24,"t":"destruct (classic (Gives c A)) as [Hs|Hs]","w":"model","ok":true,"c":[59,60]},{"g":60,"t":"tauto","w":"auto","ok":true,"c":[],"eager":true},{"g":24,"t":"destruct (classic (c = A)) as [Hs|Hs]","w":"model","ok":true,"c":[61,62]},{"g":24,"t":"destruct (classic (Gives A X)) as [Hs|Hs]","w":"model","ok":false,"err":"rejected"},{"g":24,"t":"destruct (classic (Gives y x)) as [Hs|Hs]","w":"model","ok":false,"err":"Error: The"},{"g":41,"t":"assumption","w":"auto","ok":false,"err":"Error: No such assumption."},{"g":41,"t":"tauto","w":"auto","ok":false,"err":"Error: Tactic failure: Classical tauto failed."},{"g":41,"t":"firstorder","w":"auto","ok":false,"err":"Error: Timeout!"},{"g":41,"t":"congruence","w":"auto","ok":false,"err":"Error: Tactic failure: congruence failed."},{"g":41,"t":"hammer","w":"hammer","ok":false,"err":"Error: Hammer failed: ATPs failed to f"},{"g":41,"t":"assert (Gives c A)","w":"model","ok":true,"c":[63,64]},{"g":63,"t":"assumption","w":"auto","ok":true,"c":[],"eager":true},{"g":41,"t":"destruct (classic (Gives c A)) as [Hs|Hs]","w":"model","ok":true,"c":[65,66]},{"g":66,"t":"tauto","w":"auto","ok":true,"c":[],"eager":true},{"g":41,"t":"exists c","w":"model","ok":false,"err":"Error: Not an inductive definition."},{"g":41,"t":"apply H2","w":"model","ok":false,"err":"rejected"},{"g":41,"t":"assert (c = A)","w":"model","ok":true,"c":[67,68]},{"g":41,"t":"destruct (classic (c = A)) as [Hs|Hs]","w":"model","ok":true,"c":[69,70]},{"g":41,"t":"apply H4; assumption","w":"model","ok":false,"err":"rejected"},{"g":41,"t":"assert (Gives c X)","w":"model","ok":false,"err":"rejected"},{"g":41,"t":"destruct (classic (Gives c X)) as [Hs|Hs]","w":"model","ok":false,"err":"rejected"},{"g":41,"t":"generalize H4","w":"model","ok":true,"c":[71]},{"g":41,"t":"apply H1","w":"model","ok":false,"err":"rejected"},{"g":5,"t":"assumption","w":"auto","ok":false,"err":"Error: No such assumption."},{"g":5,"t":"tauto","w":"auto","ok":false,"err":"Error: Tactic failure: Classical tauto failed."},{"g":5,"t":"firstorder","w":"auto","ok":true,"c":[1]},{"g":5,"t":"congruence","w":"auto","ok":false,"err":"Error: Tactic failure: congruence failed."},{"g":5,"t":"unfold Necessary, MP001, MP002, MP003, AggregateOfPossibles, MP011, MP012 in *; firstorder","w":"auto","ok":true,"c":[2]},{"g":5,"t":"unfold Necessary, MP001, MP002, MP003, AggregateOfPossibles, MP011, MP012 in *; hammer","w":"hammer","ok":false,"err":"Error: Hammer failed: ATPs failed to f"},{"g":5,"t":"exists A","w":"model","ok":false,"err":"Error: Not the right number of missing arguments (expected 0)."},{"g":5,"t":"assert (Gives c A)","w":"model","ok":true,"c":[29,72]},{"g":5,"t":"destruct (classic (Gives c A)) as [Hs|Hs]","w":"model","ok":true,"c":[73,74]},{"g":74,"t":"tauto","w":"auto","ok":true,"c":[],"eager":true},{"g":5,"t":"apply AggregateOfPossiblesNecessary with A","w":"model","ok":false,"err":"rejected"},{"g":5,"t":"assert (Necessary c)","w":"model","ok":true,"c":[5,75]},{"g":5,"t":"destruct (classic (Necessary c)) as [Hs|Hs]","w":"model","ok":true,"c":[76,77]},{"g":76,"t":"assumption","w":"auto","ok":true,"c":[],"eager":true},{"g":5,"t":"apply GivesNecessary with A; assumption","w":"model","ok":false,"err":"Error: The variable "},{"g":16,"t":"assumption","w":"auto","ok":false,"err":"Error: No such assumption."},{"g":16,"t":"tauto","w":"auto","ok":false,"err":"Error: Tactic failure: Classical tauto failed."},{"g":16,"t":"firstorder","w":"auto","ok":false,"err":"Error: Timeout!"},{"g":16,"t":"congruence","w":"auto","ok":false,"err":"Error: Tactic failure: congruence failed."},{"g":16,"t":"unfold Possible, MP001, MP002, MP003, MP011, MP012 in *; firstorder","w":"auto","ok":true,"c":[78]},{"g":16,"t":"unfold Possible, MP001, MP002, MP003, MP011, MP012 in *; hammer","w":"hammer","ok":false,"err":"Error: Hammer failed: ATPs failed to f"},{"g":16,"t":"apply Prop_equiv","w":"model","ok":false,"err":"Error: The variable Prop_equiv was not found in the current environmen"},{"g":16,"t":"apply False_ind","w":"model","ok":true,"c":[79]},{"g":16,"t":"elim X","w":"model","ok":false,"err":"Error: Not an inductive product."},{"g":16,"t":"elim H6","w":"model","ok":true,"c":[80]},{"g":16,"t":"apply false_ind","w":"model","ok":false,"err":"Error: The variable false_ind was not found in the current environment."},{"g":16,"t":"apply Prop_eq; trivial","w":"model","ok":false,"err":"Error: The variable Prop_eq was not found in the current envi"},{"g":16,"t":"elim H6; intros","w":"model","ok":true,"c":[80]},{"g":17,"t":"assumption","w":"auto","ok":false,"err":"Error: No such assumption."},{"g":17,"t":"tauto","w":"auto","ok":false,"err":"Error: Tactic failure: Classical tauto failed."},{"g":17,"t":"firstorder","w":"auto","ok":false,"err":"Error: Timeout!"},{"g":17,"t":"congruence","w":"auto","ok":false,"err":"Error: Tactic failure: congruence failed."},{"g":17,"t":"unfold Possible, MP001, MP002, MP003, MP011, MP012 in *; firstorder","w":"auto","ok":false,"err":"rejected"},{"g":17,"t":"unfold Possible, MP001, MP002, MP003, MP011, MP012 in *; hammer","w":"hammer","ok":false,"err":"Error: Hammer failed: ATPs failed to f"},{"g":17,"t":"exists A","w":"model","ok":false,"err":"Error: Not an inductive definition."},{"g":17,"t":"cut (Gives c A)","w":"model","ok":true,"c":[81,82]},{"g":82,"t":"assumption","w":"auto","ok":true,"c":[],"eager":true},{"g":17,"t":"assert (X = X0)","w":"model","ok":true,"c":[83,84]},{"g":83,"t":"assumption","w":"auto","ok":true,"c":[],"eager":true},{"g":17,"t":"destruct (classic (X = X0)) as [Hs|Hs]","w":"model","ok":true,"c":[85,86]},{"g":86,"t":"tauto","w":"auto","ok":true,"c":[],"eager":true},{"g":17,"t":"assert (Gives c A)","w":"model","ok":true,"c":[82,87]},{"g":17,"t":"destruct (classic (Gives c A)) as [Hs|Hs]","w":"model","ok":true,"c":[88,89]},{"g":89,"t":"tauto","w":"auto","ok":true,"c":[],"eager":true},{"g":17,"t":"destruct (classic (A = c)) as [Hs|Hs]","w":"model","ok":true,"c":[90,91]},{"g":17,"t":"apply H4","w":"model","ok":false,"err":"rejected"},{"g":17,"t":"apply H4; assumption","w":"model","ok":false,"err":"rejected"},{"g":18,"t":"assumption","w":"auto","ok":false,"err":"Error: No such assumption."},{"g":18,"t":"tauto","w":"auto","ok":false,"err":"Error: Tactic failure: Classical tauto failed."},{"g":18,"t":"firstorder","w":"auto","ok":false,"err":"Error: Timeout!"},{"g":18,"t":"congruence","w":"auto","ok":false,"err":"Error: Tactic failure: congruence failed."},{"g":18,"t":"unfold Possible, MP001, MP002, MP003, MP011, MP012 in *; firstorder","w":"auto","ok":true,"c":[92]},{"g":18,"t":"unfold Possible, MP001, MP002, MP003, MP011, MP012 in *; hammer","w":"hammer","ok":false,"err":"Error: Hammer failed: ATPs failed to f"},{"g":18,"t":"exists A","w":"model","ok":false,"err":"Error: Not an inductive definition."},{"g":18,"t":"cut (Gives c A)","w":"model","ok":true,"c":[93,94]},{"g":94,"t":"assumption","w":"auto","ok":true,"c":[],"eager":true},{"g":18,"t":"assert (Gives c A)","w":"model","ok":true,"c":[94,95]},{"g":18,"t":"destruct (classic (Gives c A)) as [Hs|Hs]","w":"model","ok":false,"err":"rejected"},{"g":18,"t":"assert (X = X0)","w":"model","ok":true,"c":[96,97]},{"g":96,"t":"assumption","w":"auto","ok":true,"c":[],"eager":true},{"g":18,"t":"destruct (classic (X = X0)) as [Hs|Hs]","w":"model","ok":false,"err":"Error: H"},{"g":18,"t":"destruct (classic (A = c)) as [Hs|Hs]","w":"model","ok":false,"err":"Error: Hs i"},{"g":18,"t":"apply H4","w":"model","ok":false,"err":"rejected"},{"g":18,"t":"apply H4; assumption","w":"model","ok":false,"err":"rejected"},{"g":19,"t":"assumption","w":"auto","ok":false,"err":"Error: No such assumption."},{"g":19,"t":"tauto","w":"auto","ok":false,"err":"Error: Tactic failure: Classical tauto failed."},{"g":19,"t":"firstorder","w":"auto","ok":false,"err":"Error: Timeout!"},{"g":19,"t":"congruence","w":"auto","ok":false,"err":"Error: Tactic failure: congruence failed."},{"g":19,"t":"unfold Possible, MP001, MP002, MP003, MP011, MP012 in *; firstorder","w":"auto","ok":false,"err":"rejected"},{"g":19,"t":"unfold Possible, MP001, MP002, MP003, MP011, MP012 in *; hammer","w":"hammer","ok":false,"err":"Error: Hammer failed: ATPs failed to f"},{"g":19,"t":"exists A","w":"model","ok":false,"err":"Error: Not an inductive definition."},{"g":19,"t":"assert (X = X0)","w":"model","ok":true,"c":[98,99]},{"g":99,"t":"tauto","w":"auto","ok":true,"c":[],"eager":true},{"g":19,"t":"destruct (classic (X = X0)) as [Hs|Hs]","w":"model","ok":false,"err":"Error: H"},{"g":19,"t":"assert (A = A)","w":"model","ok":true,"c":[100,101]},{"g":100,"t":"tauto","w":"auto","ok":true,"c":[],"eager":true},{"g":19,"t":"destruct (classic (A = A)) as [Hs|Hs]","w":"model","ok":false,"err":"Error: Hs i"},{"g":19,"t":"apply H4","w":"model","ok":false,"err":"rejected"},{"g":19,"t":"apply H4; assumption","w":"model","ok":false,"err":"rejected"},{"g":19,"t":"cut (Gives c A)","w":"model","ok":true,"c":[102,103]},{"g":103,"t":"assumption","w":"auto","ok":true,"c":[],"eager":true},{"g":10,"t":"assumption","w":"auto","ok":false,"err":"Error: No such assumption."},{"g":10,"t":"tauto","w":"auto","ok":false,"err":"Error: Tactic failure: Classical tauto failed."},{"g":10,"t":"firstorder","w":"auto","ok":false,"err":"Error: Timeout!"},{"g":10,"t":"congruence","w":"auto","ok":false,"err":"Error: Tactic failure: congruence failed."},{"g":10,"t":"unfold Possible, MP001, MP002, MP003, MP011, MP012 in *; firstorder","w":"auto","ok":false,"err":"rejected"},{"g":10,"t":"unfold Possible, MP001, MP002, MP003, MP011, MP012 in *; hammer","w":"hammer","ok":false,"err":"Error: Hammer failed: ATPs failed to f"},{"g":10,"t":"exists A","w":"model","ok":false,"err":"Error: Not an inductive definition."},{"g":10,"t":"exists A; simplest","w":"model","ok":false,"err":"Error: The reference simplest was not found in the current envir"},{"g":10,"t":"split","w":"model","ok":false,"err":"Error: Not an inductive definition."},{"g":10,"t":"assert (X = A)","w":"model","ok":false,"err":"rejected"},{"g":10,"t":"destruct (classic (X = A)) as [Hs|Hs]","w":"model","ok":false,"err":"rejected"},{"g":10,"t":"exists A; easy","w":"model","ok":false,"err":"Error: Not an inductive definition."},{"g":11,"t":"assumption","w":"auto","ok":false,"err":"Error: No such assumption."},{"g":11,"t":"tauto","w":"auto","ok":false,"err":"Error: Tactic failure: Classical tauto failed."},{"g":11,"t":"firstorder","w":"auto","ok":true,"c":[104]},{"g":11,"t":"congruence","w":"auto","ok":false,"err":"Error: Tactic failure: congruence failed."},{"g":11,"t":"unfold Possible, MP001, MP002, MP003, MP011, MP012 in *; firstorder","w":"auto","ok":true,"c":[105]},{"g":11,"t":"unfold Possible, MP001, MP002, MP003, MP011, MP012 in *; hammer","w":"hammer","ok":false,"err":"Error: Hammer failed: ATPs failed to f"},{"g":11,"t":"exists A","w":"model","ok":false,"err":"Error: Not an inductive definition."},{"g":11,"t":"assert (Gives c A)","w":"model","ok":true,"c":[106,107]},{"g":106,"t":"assumption","w":"auto","ok":true,"c":[],"eager":true},{"g":11,"t":"destruct (classic (Gives c A)) as [Hs|Hs]","w":"model","ok":false,"err":"rejected"},{"g":11,"t":"split","w":"model","ok":false,"err":"Error: Not an inductive definition."},{"g":11,"t":"apply H4","w":"model","ok":false,"err":"rejected"},{"g":11,"t":"apply H4; assumption","w":"model","ok":false,"err":"rejected"},{"g":6,"t":"assumption","w":"auto","ok":false,"err":"Error: No such assumption."},{"g":6,"t":"tauto","w":"auto","ok":false,"err":"Error: Tactic failure: Classical tauto failed."},{"g":6,"t":"firstorder","w":"auto","ok":false,"err":"Error: Timeout!"},{"g":6,"t":"congruence","w":"auto","ok":false,"err":"Error: Tactic failure: congruence failed."},{"g":6,"t":"unfold Necessary, MP001, MP002, MP003, AggregateOfPossibles, MP011, MP012 in *; firstorder","w":"auto","ok":false,"err":"rejected"},{"g":6,"t":"unfold Necessary, MP001, MP002, MP003, AggregateOfPossibles, MP011, MP012 in *; hammer","w":"hammer","ok":false,"err":"Error: Hammer failed: ATPs failed to f"},{"g":6,"t":"intros x y z A1 c1","w":"model","ok":true,"c":[108]},{"g":6,"t":"intros","w":"model","ok":true,"c":[109]},{"g":6,"t":"intros x y z H A1 c1","w":"model","ok":true,"c":[110]},{"g":6,"t":"intros x x0 y z A1 c1","w":"model","ok":true,"c":[111]},{"g":6,"t":"intros i0 i1 i2 A1 c1","w":"model","ok":true,"c":[112]},{"g":6,"t":"intros X H1 H2 A0 c0","w":"model","ok":true,"c":[113]},{"g":6,"t":"intros A0 c0 A12 B0 C0","w":"model","ok":true,"c":[114]}],"proof":[],"proofFile":null},{"key":"round6/imkan_s11_necessary_cause","id":"imkan_s11_necessary_cause","run":"round6","title":"Dalīl al-imkān, step 11","english":"The aggregate has a cause that is necessary in itself.","stmt":"MP001 -> MP002 -> MP003 -> MP008 -> MP010 -> MP011 -> MP012 -> forall A, AggregateOfPossibles A -> Exists A -> (exists p, p <> A /\\ Possible p) -> exists c, Gives c A /\\ Necessary c /\\ ~ MemberOf c A /\\ c <> A","proved":false,"script":"","seconds":901.7,"expansions":9,"calls":586,"root":0,"goals":["============================\nMP001 -> MP002 -> MP003 -> MP008 -> MP010 -> MP011 -> MP012 -> forall A, AggregateOfPossibles A -> Exists A -> (exists p, p <> A /\\ Possible p) -> exists c, Gives c A /\\ Necessary c /\\ ~ MemberOf c A /\\ c <> A","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP008\nH3 : MP010\nH4 : MP011\nH5 : MP012\nA : Thing\nH6 : AggregateOfPossibles A\nH7 : Exists A\nH8 : @ex Thing (fun p : Thing => and (not (@eq Thing p A)) (Possible p))\n============================\n@ex Thing (fun c : Thing => and (Gives c A) (and (Necessary c) (and (not (MemberOf c A)) (not (@eq Thing c A)))))","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP008\nH3 : MP010\nH4 : MP011\nH5 : MP012\nA : Thing\nH6 : AggregateOfPossibles A\nH7 : Exists A\nH8 : @ex Thing (fun p : Thing => and (not (@eq Thing p A)) (Possible p))\n============================\nforall (x : Thing) (_ : and (not (@eq Thing x A)) (Possible x)), @ex Thing (fun c : Thing => and (Gives c A) (and (Necessary c) (and (not (MemberOf c A)) (not (@eq Thing c A)))))","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP008\nH3 : MP010\nH4 : MP011\nH5 : MP012\nA : Thing\nH6 : AggregateOfPossibles A\nH7 : Exists A\nH8 : @ex Thing (fun p : Thing => and (not (@eq Thing p A)) (Possible p))\nC : Thing\nH9 : and (not (@eq Thing C A)) (Possible C)\n============================\n@ex Thing (fun c : Thing => and (Gives c A) (and (Necessary c) (and (not (MemberOf c A)) (not (@eq Thing c A)))))","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP008\nH3 : MP010\nH4 : MP011\nH5 : MP012\nA : Thing\nH6 : AggregateOfPossibles A\nH7 : Exists A\nH8 : @ex Thing (fun p : Thing => and (not (@eq Thing p A)) (Possible p))\nx : Thing\nH9 : and (not (@eq Thing x A)) (Possible x)\n============================\n@ex Thing (fun c : Thing => and (Gives c A) (and (Necessary c) (and (not (MemberOf c A)) (not (@eq Thing c A)))))","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP008\nH3 : MP010\nH4 : MP011\nH5 : MP012\nA : Thing\nH6 : AggregateOfPossibles A\nH7 : Exists A\nH8 : @ex Thing (fun p : Thing => and (not (@eq Thing p A)) (Possible p))\n============================\nand (Gives A A) (and (Necessary A) (and (not (MemberOf A A)) (not (@eq Thing A A))))","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP008\nH3 : MP010\nH4 : MP011\nH5 : MP012\nA : Thing\nH6 : AggregateOfPossibles A\nH7 : Exists A\nH8 : @ex Thing (fun p : Thing => and (not (@eq Thing p A)) (Possible p))\nB : Thing\nH9 : and (not (@eq Thing B A)) (Possible B)\n============================\n@ex Thing (fun c : Thing => and (Gives c A) (and (Necessary c) (and (not (MemberOf c A)) (not (@eq Thing c A)))))","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP008\nH3 : MP010\nH4 : MP011\nH5 : MP012\nA : Thing\nH6 : AggregateOfPossibles A\nH7 : Exists A\n============================\nforall (x : Thing) (_ : and (not (@eq Thing x A)) (Possible x)), @ex Thing (fun c : Thing => and (Gives c A) (and (Necessary c) (and (not (MemberOf c A)) (not (@eq Thing c A)))))","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP008\nH3 : MP010\nH4 : MP011\nH5 : MP012\nA : Thing\nH6 : AggregateOfPossibles A\nH7 : Exists A\nH8 : @ex Thing (fun p : Thing => and (not (@eq Thing p A)) (Possible p))\nx : Thing\nH10 : and (not (@eq Thing x A)) (Possible x)\n============================\n@ex Thing (fun c : Thing => and (Gives c A) (and (Necessary c) (and (not (MemberOf c A)) (not (@eq Thing c A)))))","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP008\nH3 : MP010\nH4 : MP011\nH5 : MP012\nA : Thing\nH6 : AggregateOfPossibles A\nH7 : Exists A\nH8 : @ex Thing (fun p : Thing => and (not (@eq Thing p A)) (Possible p))\nX : Thing\nPoss : and (not (@eq Thing X A)) (Possible X)\n============================\n@ex Thing (fun c : Thing => and (Gives c A) (and (Necessary c) (and (not (MemberOf c A)) (not (@eq Thing c A)))))","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP008\nH3 : MP010\nH4 : MP011\nH5 : MP012\nA : Thing\nH6 : AggregateOfPossibles A\nH7 : Exists A\nH8 : @ex Thing (fun p : Thing => and (not (@eq Thing p A)) (Possible p))\nx : Thing\nEX : and (not (@eq Thing x A)) (Possible x)\n============================\n@ex Thing (fun c : Thing => and (Gives c A) (and (Necessary c) (and (not (MemberOf c A)) (not (@eq Thing c A)))))","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP008\nH3 : MP010\nH4 : MP011\nH5 : MP012\nA : Thing\nH6 : AggregateOfPossibles A\nH7 : Exists A\nH8 : @ex Thing (fun p : Thing => and (not (@eq Thing p A)) (Possible p))\nx : Thing\nH8' : and (not (@eq Thing x A)) (Possible x)\n============================\n@ex Thing (fun c : Thing => and (Gives c A) (and (Necessary c) (and (not (MemberOf c A)) (not (@eq Thing c A)))))","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP008\nH3 : MP010\nH4 : MP011\nH5 : MP012\nA : Thing\nH6 : AggregateOfPossibles A\nH7 : Exists A\nH8 : @ex Thing (fun p : Thing => and (not (@eq Thing p A)) (Possible p))\nx : Thing\nH9 : and (not (@eq Thing x A)) (Possible x)\nx0 : Thing\nH10 : and (not (@eq Thing x0 A)) (Possible x0)\n============================\n@ex Thing (fun c : Thing => and (Gives c A) (and (Necessary c) (and (not (MemberOf c A)) (not (@eq Thing c A)))))","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP008\nH3 : MP010\nH4 : MP011\nH5 : MP012\nA : Thing\nH6 : AggregateOfPossibles A\nH7 : Exists A\n============================\nforall (x : Thing) (_ : and (not (@eq Thing x A)) (Possible x)) (x0 : Thing) (_ : and (not (@eq Thing x0 A)) (Possible x0)), @ex Thing (fun c : Thing => and (Gives c A) (and (Necessary c) (and (not (MemberOf c A)) (not (@eq Thing c A)))))","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP008\nH3 : MP010\nH4 : MP011\nH5 : MP012\nA : Thing\nH6 : AggregateOfPossibles A\nH7 : Exists A\nH8 : @ex Thing (fun p : Thing => and (not (@eq Thing p A)) (Possible p))\nC : Thing\nH9 : and (not (@eq Thing C A)) (Possible C)\n============================\nand (Gives C A) (and (Necessary C) (and (not (MemberOf C A)) (not (@eq Thing C A))))","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP008\nH3 : MP010\nH4 : MP011\nH5 : MP012\nA : Thing\nH6 : AggregateOfPossibles A\nH7 : Exists A\nH8 : @ex Thing (fun p : Thing => and (not (@eq Thing p A)) (Possible p))\nC : Thing\nH9 : and (not (@eq Thing C A)) (Possible C)\n============================\nGives C A","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP008\nH3 : MP010\nH4 : MP011\nH5 : MP012\nA : Thing\nH6 : AggregateOfPossibles A\nH7 : Exists A\nH8 : @ex Thing (fun p : Thing => and (not (@eq Thing p A)) (Possible p))\nC : Thing\nH9 : and (not (@eq Thing C A)) (Possible C)\n============================\nand (Necessary C) (and (not (MemberOf C A)) (not (@eq Thing C A)))","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP008\nH3 : MP010\nH4 : MP011\nH5 : MP012\nA : Thing\nH6 : AggregateOfPossibles A\nH7 : Exists A\nH8 : @ex Thing (fun p : Thing => and (not (@eq Thing p A)) (Possible p))\nC : Thing\nH9 : and (not (@eq Thing C A)) (Possible C)\n============================\nforall (_ : not (@eq Thing C A)) (_ : Possible C), @ex Thing (fun c : Thing => and (Gives c A) (and (Necessary c) (and (not (MemberOf c A)) (not (@eq Thing c A)))))","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP008\nH3 : MP010\nH4 : MP011\nH5 : MP012\nA : Thing\nH6 : AggregateOfPossibles A\nH7 : Exists A\nH8 : @ex Thing (fun p : Thing => and (not (@eq Thing p A)) (Possible p))\nC : Thing\nH9 : and (not (@eq Thing C A)) (Possible C)\nH10 : not (@eq Thing C A)\nH11 : Possible C\n============================\n@ex Thing (fun c : Thing => and (Gives c A) (and (Necessary c) (and (not (MemberOf c A)) (not (@eq Thing c A)))))","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP008\nH3 : MP010\nH4 : MP011\nH5 : MP012\nA : Thing\nH6 : AggregateOfPossibles A\nH7 : Exists A\nH8 : @ex Thing (fun p : Thing => and (not (@eq Thing p A)) (Possible p))\nC : Thing\nH9 : and (not (@eq Thing C A)) (Possible C)\nx : Thing\nH10 : and (not (@eq Thing x A)) (Possible x)\n============================\n@ex Thing (fun c : Thing => and (Gives c A) (and (Necessary c) (and (not (MemberOf c A)) (not (@eq Thing c A)))))","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP008\nH3 : MP010\nH4 : MP011\nH5 : MP012\nA : Thing\nH6 : AggregateOfPossibles A\nH7 : Exists A\nH8 : @ex Thing (fun p : Thing => and (not (@eq Thing p A)) (Possible p))\nx : Thing\nH9 : and (not (@eq Thing x A)) (Possible x)\n============================\nand (Gives x A) (and (Necessary x) (and (not (MemberOf x A)) (not (@eq Thing x A))))","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP008\nH3 : MP010\nH4 : MP011\nH5 : MP012\nA : Thing\nH6 : AggregateOfPossibles A\nH7 : Exists A\nH8 : @ex Thing (fun p : Thing => and (not (@eq Thing p A)) (Possible p))\nx : Thing\nH9 : and (not (@eq Thing x A)) (Possible x)\n============================\nGives x A","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP008\nH3 : MP010\nH4 : MP011\nH5 : MP012\nA : Thing\nH6 : AggregateOfPossibles A\nH7 : Exists A\nH8 : @ex Thing (fun p : Thing => and (not (@eq Thing p A)) (Possible p))\nx : Thing\nH9 : and (not (@eq Thing x A)) (Possible x)\n============================\nand (Necessary x) (and (not (MemberOf x A)) (not (@eq Thing x A)))","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP008\nH3 : MP010\nH4 : MP011\nH5 : MP012\nA : Thing\nH6 : AggregateOfPossibles A\nH7 : Exists A\nH8 : @ex Thing (fun p : Thing => and (not (@eq Thing p A)) (Possible p))\nx : Thing\nH9 : and (not (@eq Thing x A)) (Possible x)\n============================\nforall (_ : not (@eq Thing x A)) (_ : Possible x), @ex Thing (fun c : Thing => and (Gives c A) (and (Necessary c) (and (not (MemberOf c A)) (not (@eq Thing c A)))))","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP008\nH3 : MP010\nH4 : MP011\nH5 : MP012\nA : Thing\nH6 : AggregateOfPossibles A\nH7 : Exists A\nH8 : @ex Thing (fun p : Thing => and (not (@eq Thing p A)) (Possible p))\nx : Thing\nH9 : and (not (@eq Thing x A)) (Possible x)\nH10 : not (@eq Thing x A)\nH11 : Possible x\n============================\n@ex Thing (fun c : Thing => and (Gives c A) (and (Necessary c) (and (not (MemberOf c A)) (not (@eq Thing c A)))))","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP008\nH3 : MP010\nH4 : MP011\nH5 : MP012\nA : Thing\nH6 : AggregateOfPossibles A\nH7 : Exists A\nH8 : @ex Thing (fun p : Thing => and (not (@eq Thing p A)) (Possible p))\nx : Thing\nH9 : and (not (@eq Thing x A)) (Possible x)\n============================\nand (Gives A A) (and (Necessary A) (and (not (MemberOf A A)) (not (@eq Thing A A))))","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP008\nH3 : MP010\nH4 : MP011\nH5 : MP012\nA : Thing\nH6 : AggregateOfPossibles A\nH7 : Exists A\nH8 : @ex Thing (fun p : Thing => and (not (@eq Thing p A)) (Possible p))\nx : Thing\nH9 : and (not (@eq Thing x A)) (Possible x)\n============================\n@eq Thing A x","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP008\nH3 : MP010\nH4 : MP011\nH5 : MP012\nA : Thing\nH6 : AggregateOfPossibles A\nH7 : Exists A\nH8 : @ex Thing (fun p : Thing => and (not (@eq Thing p A)) (Possible p))\nx : Thing\nH9 : and (not (@eq Thing x A)) (Possible x)\nH10 : @eq Thing A x\n============================\n@ex Thing (fun c : Thing => and (Gives c A) (and (Necessary c) (and (not (MemberOf c A)) (not (@eq Thing c A)))))","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP008\nH3 : MP010\nH4 : MP011\nH5 : MP012\nA : Thing\nH6 : AggregateOfPossibles A\nH7 : Exists A\nH8 : @ex Thing (fun p : Thing => and (not (@eq Thing p A)) (Possible p))\nx : Thing\nH9 : and (not (@eq Thing x A)) (Possible x)\nHs : @eq Thing A x\n============================\n@ex Thing (fun c : Thing => and (Gives c A) (and (Necessary c) (and (not (MemberOf c A)) (not (@eq Thing c A)))))","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP008\nH3 : MP010\nH4 : MP011\nH5 : MP012\nA : Thing\nH6 : AggregateOfPossibles A\nH7 : Exists A\nH8 : @ex Thing (fun p : Thing => and (not (@eq Thing p A)) (Possible p))\nx : Thing\nH9 : and (not (@eq Thing x A)) (Possible x)\nHs : not (@eq Thing A x)\n============================\n@ex Thing (fun c : Thing => and (Gives c A) (and (Necessary c) (and (not (MemberOf c A)) (not (@eq Thing c A)))))","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP008\nH3 : MP010\nH4 : MP011\nH5 : MP012\nA : Thing\nH6 : AggregateOfPossibles A\nH7 : Exists A\nH8 : @ex Thing (fun p : Thing => and (not (@eq Thing p A)) (Possible p))\n============================\nGives A A","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP008\nH3 : MP010\nH4 : MP011\nH5 : MP012\nA : Thing\nH6 : AggregateOfPossibles A\nH7 : Exists A\nH8 : @ex Thing (fun p : Thing => and (not (@eq Thing p A)) (Possible p))\n============================\nand (Necessary A) (and (not (MemberOf A A)) (not (@eq Thing A A)))","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP008\nH3 : MP010\nH4 : MP011\nH5 : MP012\nA : Thing\nH6 : AggregateOfPossibles A\nH7 : Exists A\nH8 : @ex Thing (fun p : Thing => and (not (@eq Thing p A)) (Possible p))\n============================\nforall (x : Thing) (_ : and (not (@eq Thing x A)) (Possible x)), and (Gives A A) (and (Necessary A) (and (not (MemberOf A A)) (not (@eq Thing A A))))","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP008\nH3 : MP010\nH4 : MP011\nH5 : MP012\nA : Thing\nH6 : AggregateOfPossibles A\nH7 : Exists A\nH8 : @ex Thing (fun p : Thing => and (not (@eq Thing p A)) (Possible p))\nH9 : Gives A A\n============================\nand (Gives A A) (and (Necessary A) (and (not (MemberOf A A)) (not (@eq Thing A A))))","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP008\nH3 : MP010\nH4 : MP011\nH5 : MP012\nA : Thing\nH6 : AggregateOfPossibles A\nH7 : Exists A\nH8 : @ex Thing (fun p : Thing => and (not (@eq Thing p A)) (Possible p))\nHs : Gives A A\n============================\nand (Gives A A) (and (Necessary A) (and (not (MemberOf A A)) (not (@eq Thing A A))))","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP008\nH3 : MP010\nH4 : MP011\nH5 : MP012\nA : Thing\nH6 : AggregateOfPossibles A\nH7 : Exists A\nH8 : @ex Thing (fun p : Thing => and (not (@eq Thing p A)) (Possible p))\nHs : not (Gives A A)\n============================\nand (Gives A A) (and (Necessary A) (and (not (MemberOf A A)) (not (@eq Thing A A))))","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP008\nH3 : MP010\nH4 : MP011\nH5 : MP012\nA : Thing\nH6 : AggregateOfPossibles A\nH7 : Exists A\nH8 : @ex Thing (fun p : Thing => and (not (@eq Thing p A)) (Possible p))\n============================\nnot (@eq Thing A A)","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP008\nH3 : MP010\nH4 : MP011\nH5 : MP012\nA : Thing\nH6 : AggregateOfPossibles A\nH7 : Exists A\nH8 : @ex Thing (fun p : Thing => and (not (@eq Thing p A)) (Possible p))\nH9 : not (@eq Thing A A)\n============================\nand (Gives A A) (and (Necessary A) (and (not (MemberOf A A)) (not (@eq Thing A A))))","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP008\nH3 : MP010\nH4 : MP011\nH5 : MP012\nA : Thing\nH6 : AggregateOfPossibles A\nH7 : Exists A\nH8 : @ex Thing (fun p : Thing => and (not (@eq Thing p A)) (Possible p))\nHs : not (@eq Thing A A)\n============================\nand (Gives A A) (and (Necessary A) (and (not (MemberOf A A)) (not (@eq Thing A A))))","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP008\nH3 : MP010\nH4 : MP011\nH5 : MP012\nA : Thing\nH6 : AggregateOfPossibles A\nH7 : Exists A\nH8 : @ex Thing (fun p : Thing => and (not (@eq Thing p A)) (Possible p))\nHs : not (not (@eq Thing A A))\n============================\nand (Gives A A) (and (Necessary A) (and (not (MemberOf A A)) (not (@eq Thing A A))))","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP008\nH3 : MP010\nH4 : MP011\nH5 : MP012\nA : Thing\nH6 : AggregateOfPossibles A\nH7 : Exists A\nGivesNS : Thing\nH8 : and (not (@eq Thing GivesNS A)) (Possible GivesNS)\n============================\nand (Gives A A) (and (Necessary A) (and (not (MemberOf A A)) (not (@eq Thing A A))))","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP008\nH3 : MP010\nH4 : MP011\nH5 : MP012\nA : Thing\nH6 : AggregateOfPossibles A\nH7 : Exists A\nH8 : @ex Thing (fun p : Thing => and (not (@eq Thing p A)) (Possible p))\n============================\nnot (MemberOf A A)","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP008\nH3 : MP010\nH4 : MP011\nH5 : MP012\nA : Thing\nH6 : AggregateOfPossibles A\nH7 : Exists A\nH8 : @ex Thing (fun p : Thing => and (not (@eq Thing p A)) (Possible p))\nH9 : not (MemberOf A A)\n============================\nand (Gives A A) (and (Necessary A) (and (not (MemberOf A A)) (not (@eq Thing A A))))","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP008\nH3 : MP010\nH4 : MP011\nH5 : MP012\nA : Thing\nH6 : AggregateOfPossibles A\nH7 : Exists A\nH8 : @ex Thing (fun p : Thing => and (not (@eq Thing p A)) (Possible p))\nHs : not (MemberOf A A)\n============================\nand (Gives A A) (and (Necessary A) (and (not (MemberOf A A)) (not (@eq Thing A A))))","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP008\nH3 : MP010\nH4 : MP011\nH5 : MP012\nA : Thing\nH6 : AggregateOfPossibles A\nH7 : Exists A\nH8 : @ex Thing (fun p : Thing => and (not (@eq Thing p A)) (Possible p))\nHs : not (not (MemberOf A A))\n============================\nand (Gives A A) (and (Necessary A) (and (not (MemberOf A A)) (not (@eq Thing A A))))","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP008\nH3 : MP010\nH4 : MP011\nH5 : MP012\nA : Thing\nH6 : AggregateOfPossibles A\nH7 : Exists A\nGivesNE : Thing\nH8 : and (not (@eq Thing GivesNE A)) (Possible GivesNE)\n============================\nand (Gives A A) (and (Necessary A) (and (not (MemberOf A A)) (not (@eq Thing A A))))","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP008\nH3 : MP010\nH4 : MP011\nH5 : MP012\nA : Thing\nH6 : AggregateOfPossibles A\nH7 : Exists A\nH8 : @ex Thing (fun p : Thing => and (not (@eq Thing p A)) (Possible p))\nB : Thing\nH9 : and (not (@eq Thing B A)) (Possible B)\n============================\nand (Gives B A) (and (Necessary B) (and (not (MemberOf B A)) (not (@eq Thing B A))))","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP008\nH3 : MP010\nH4 : MP011\nH5 : MP012\nA : Thing\nH6 : AggregateOfPossibles A\nH7 : Exists A\nH8 : @ex Thing (fun p : Thing => and (not (@eq Thing p A)) (Possible p))\nB : Thing\nH9 : and (not (@eq Thing B A)) (Possible B)\n============================\nand (Gives A A) (and (Necessary A) (and (not (MemberOf A A)) (not (@eq Thing A A))))","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP008\nH3 : MP010\nH4 : MP011\nH5 : MP012\nA : Thing\nH6 : AggregateOfPossibles A\nH7 : Exists A\nH8 : @ex Thing (fun p : Thing => and (not (@eq Thing p A)) (Possible p))\nB : Thing\nH9 : and (not (@eq Thing B A)) (Possible B)\n============================\nGives B A","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP008\nH3 : MP010\nH4 : MP011\nH5 : MP012\nA : Thing\nH6 : AggregateOfPossibles A\nH7 : Exists A\nH8 : @ex Thing (fun p : Thing => and (not (@eq Thing p A)) (Possible p))\nB : Thing\nH9 : and (not (@eq Thing B A)) (Possible B)\n============================\nand (Necessary B) (and (not (MemberOf B A)) (not (@eq Thing B A)))","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP008\nH3 : MP010\nH4 : MP011\nH5 : MP012\nA : Thing\nH6 : AggregateOfPossibles A\nH7 : Exists A\nH8 : @ex Thing (fun p : Thing => and (not (@eq Thing p A)) (Possible p))\nB : Thing\nH9 : and (not (@eq Thing B A)) (Possible B)\n============================\nPossible B","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP008\nH3 : MP010\nH4 : MP011\nH5 : MP012\nA : Thing\nH6 : AggregateOfPossibles A\nH7 : Exists A\nH8 : @ex Thing (fun p : Thing => and (not (@eq Thing p A)) (Possible p))\nB : Thing\nH9 : and (not (@eq Thing B A)) (Possible B)\nH10 : Possible B\n============================\n@ex Thing (fun c : Thing => and (Gives c A) (and (Necessary c) (and (not (MemberOf c A)) (not (@eq Thing c A)))))","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP008\nH3 : MP010\nH4 : MP011\nH5 : MP012\nA : Thing\nH6 : AggregateOfPossibles A\nH7 : Exists A\nH8 : @ex Thing (fun p : Thing => and (not (@eq Thing p A)) (Possible p))\nB : Thing\nH9 : and (not (@eq Thing B A)) (Possible B)\nHs : Possible B\n============================\n@ex Thing (fun c : Thing => and (Gives c A) (and (Necessary c) (and (not (MemberOf c A)) (not (@eq Thing c A)))))","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP008\nH3 : MP010\nH4 : MP011\nH5 : MP012\nA : Thing\nH6 : AggregateOfPossibles A\nH7 : Exists A\nH8 : @ex Thing (fun p : Thing => and (not (@eq Thing p A)) (Possible p))\nB : Thing\nH9 : and (not (@eq Thing B A)) (Possible B)\nHs : not (Possible B)\n============================\n@ex Thing (fun c : Thing => and (Gives c A) (and (Necessary c) (and (not (MemberOf c A)) (not (@eq Thing c A)))))","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP008\nH3 : MP010\nH4 : MP011\nH5 : MP012\nA : Thing\nH6 : AggregateOfPossibles A\nH7 : Exists A\nH8 : @ex Thing (fun p : Thing => and (not (@eq Thing p A)) (Possible p))\nB : Thing\nH9 : and (not (@eq Thing B A)) (Possible B)\n============================\nforall (x : Thing) (_ : and (not (@eq Thing x A)) (Possible x)), @ex Thing (fun c : Thing => and (Gives c A) (and (Necessary c) (and (not (MemberOf c A)) (not (@eq Thing c A)))))","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP008\nH3 : MP010\nH4 : MP011\nH5 : MP012\nA : Thing\nH6 : AggregateOfPossibles A\nH7 : Exists A\nx : Thing\nH8 : and (not (@eq Thing x A)) (Possible x)\n============================\n@ex Thing (fun c : Thing => and (Gives c A) (and (Necessary c) (and (not (MemberOf c A)) (not (@eq Thing c A)))))","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP008\nH3 : MP010\nH4 : MP011\nH5 : MP012\nA : Thing\nH6 : AggregateOfPossibles A\nH7 : Exists A\nB : Thing\nPoss : and (not (@eq Thing B A)) (Possible B)\n============================\n@ex Thing (fun c : Thing => and (Gives c A) (and (Necessary c) (and (not (MemberOf c A)) (not (@eq Thing c A)))))","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP008\nH3 : MP010\nH4 : MP011\nH5 : MP012\nA : Thing\nH6 : AggregateOfPossibles A\nH7 : Exists A\nB : Thing\n============================\nforall _ : and (not (@eq Thing B A)) (Possible B), @ex Thing (fun c : Thing => and (Gives c A) (and (Necessary c) (and (not (MemberOf c A)) (not (@eq Thing c A)))))","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP008\nH3 : MP010\nH4 : MP011\nH5 : MP012\nA : Thing\nH6 : AggregateOfPossibles A\nH7 : Exists A\nx : Thing\nEX : and (not (@eq Thing x A)) (Possible x)\n============================\n@ex Thing (fun c : Thing => and (Gives c A) (and (Necessary c) (and (not (MemberOf c A)) (not (@eq Thing c A)))))","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP008\nH3 : MP010\nH4 : MP011\nH5 : MP012\nA : Thing\nH6 : AggregateOfPossibles A\nH7 : Exists A\nx : Thing\nIN : and (not (@eq Thing x A)) (Possible x)\n============================\n@ex Thing (fun c : Thing => and (Gives c A) (and (Necessary c) (and (not (MemberOf c A)) (not (@eq Thing c A)))))","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP008\nH3 : MP010\nH4 : MP011\nH5 : MP012\nA : Thing\nH6 : AggregateOfPossibles A\nH7 : Exists A\nB : Thing\nD : and (not (@eq Thing B A)) (Possible B)\n============================\n@ex Thing (fun c : Thing => and (Gives c A) (and (Necessary c) (and (not (MemberOf c A)) (not (@eq Thing c A)))))","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP008\nH3 : MP010\nH4 : MP011\nH5 : MP012\nA : Thing\nH6 : AggregateOfPossibles A\nH7 : Exists A\nB : Thing\nC : not (@eq Thing B A)\nD : Possible B\n============================\n@ex Thing (fun c : Thing => and (Gives c A) (and (Necessary c) (and (not (MemberOf c A)) (not (@eq Thing c A)))))","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP008\nH3 : MP010\nH4 : MP011\nH5 : MP012\nA : Thing\nH6 : AggregateOfPossibles A\nH7 : Exists A\nH8 : @ex Thing (fun p : Thing => and (not (@eq Thing p A)) (Possible p))\nC : Thing\nH9 : and (not (@eq Thing C A)) (Possible C)\n============================\nnot (@eq Thing C A)","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP008\nH3 : MP010\nH4 : MP011\nH5 : MP012\nA : Thing\nH6 : AggregateOfPossibles A\nH7 : Exists A\nH8 : @ex Thing (fun p : Thing => and (not (@eq Thing p A)) (Possible p))\nC : Thing\nH9 : and (not (@eq Thing C A)) (Possible C)\nH10 : not (@eq Thing C A)\n============================\nand (Gives C A) (and (Necessary C) (and (not (MemberOf C A)) (not (@eq Thing C A))))","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP008\nH3 : MP010\nH4 : MP011\nH5 : MP012\nA : Thing\nH6 : AggregateOfPossibles A\nH7 : Exists A\nH8 : @ex Thing (fun p : Thing => and (not (@eq Thing p A)) (Possible p))\nC : Thing\nH9 : and (not (@eq Thing C A)) (Possible C)\nHs : not (@eq Thing C A)\n============================\nand (Gives C A) (and (Necessary C) (and (not (MemberOf C A)) (not (@eq Thing C A))))","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP008\nH3 : MP010\nH4 : MP011\nH5 : MP012\nA : Thing\nH6 : AggregateOfPossibles A\nH7 : Exists A\nH8 : @ex Thing (fun p : Thing => and (not (@eq Thing p A)) (Possible p))\nC : Thing\nH9 : and (not (@eq Thing C A)) (Possible C)\nHs : not (not (@eq Thing C A))\n============================\nand (Gives C A) (and (Necessary C) (and (not (MemberOf C A)) (not (@eq Thing C A))))","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP008\nH3 : MP010\nH4 : MP011\nH5 : MP012\nA : Thing\nH6 : AggregateOfPossibles A\nH7 : Exists A\nH8 : @ex Thing (fun p : Thing => and (not (@eq Thing p A)) (Possible p))\nC : Thing\nH9 : and (not (@eq Thing C A)) (Possible C)\nH10 : Gives C A\n============================\nand (Gives C A) (and (Necessary C) (and (not (MemberOf C A)) (not (@eq Thing C A))))","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP008\nH3 : MP010\nH4 : MP011\nH5 : MP012\nA : Thing\nH6 : AggregateOfPossibles A\nH7 : Exists A\nH8 : @ex Thing (fun p : Thing => and (not (@eq Thing p A)) (Possible p))\nC : Thing\nH9 : and (not (@eq Thing C A)) (Possible C)\nHs : Gives C A\n============================\nand (Gives C A) (and (Necessary C) (and (not (MemberOf C A)) (not (@eq Thing C A))))","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP008\nH3 : MP010\nH4 : MP011\nH5 : MP012\nA : Thing\nH6 : AggregateOfPossibles A\nH7 : Exists A\nH8 : @ex Thing (fun p : Thing => and (not (@eq Thing p A)) (Possible p))\nC : Thing\nH9 : and (not (@eq Thing C A)) (Possible C)\nHs : not (Gives C A)\n============================\nand (Gives C A) (and (Necessary C) (and (not (MemberOf C A)) (not (@eq Thing C A))))","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP008\nH3 : MP010\nH4 : MP011\nH5 : MP012\nA : Thing\nH6 : AggregateOfPossibles A\nH7 : Exists A\nH8 : @ex Thing (fun p : Thing => and (not (@eq Thing p A)) (Possible p))\nC : Thing\nH9 : and (not (@eq Thing C A)) (Possible C)\n============================\nforall _ : and (not (@eq Thing C A)) (Possible C), and (Gives C A) (and (Necessary C) (and (not (MemberOf C A)) (not (@eq Thing C A))))","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP008\nH3 : MP010\nH4 : MP011\nH5 : MP012\nA : Thing\nH6 : AggregateOfPossibles A\nH7 : Exists A\nH8 : @ex Thing (fun p : Thing => and (not (@eq Thing p A)) (Possible p))\nC : Thing\nH9 : and (not (@eq Thing C A)) (Possible C)\n============================\nforall _ : @ex Thing (fun p : Thing => and (not (@eq Thing p A)) (Possible p)), and (Gives C A) (and (Necessary C) (and (not (MemberOf C A)) (not (@eq Thing C A))))","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP008\nH3 : MP010\nH4 : MP011\nH5 : MP012\nA : Thing\nH6 : AggregateOfPossibles A\nH7 : Exists A\nH8 : @ex Thing (fun p : Thing => and (not (@eq Thing p A)) (Possible p))\nC : Thing\nH9 : and (not (@eq Thing C A)) (Possible C)\n============================\nPossible C","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP008\nH3 : MP010\nH4 : MP011\nH5 : MP012\nA : Thing\nH6 : AggregateOfPossibles A\nH7 : Exists A\nH8 : @ex Thing (fun p : Thing => and (not (@eq Thing p A)) (Possible p))\nC : Thing\nH9 : and (not (@eq Thing C A)) (Possible C)\nH10 : Possible C\n============================\nand (Gives C A) (and (Necessary C) (and (not (MemberOf C A)) (not (@eq Thing C A))))","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP008\nH3 : MP010\nH4 : MP011\nH5 : MP012\nA : Thing\nH6 : AggregateOfPossibles A\nH7 : Exists A\nH8 : @ex Thing (fun p : Thing => and (not (@eq Thing p A)) (Possible p))\nC : Thing\nH9 : and (not (@eq Thing C A)) (Possible C)\nHs : Possible C\n============================\nand (Gives C A) (and (Necessary C) (and (not (MemberOf C A)) (not (@eq Thing C A))))","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP008\nH3 : MP010\nH4 : MP011\nH5 : MP012\nA : Thing\nH6 : AggregateOfPossibles A\nH7 : Exists A\nH8 : @ex Thing (fun p : Thing => and (not (@eq Thing p A)) (Possible p))\nC : Thing\nH9 : and (not (@eq Thing C A)) (Possible C)\nHs : not (Possible C)\n============================\nand (Gives C A) (and (Necessary C) (and (not (MemberOf C A)) (not (@eq Thing C A))))"],"events":[{"g":0,"t":"assumption","w":"auto","ok":false,"err":"Error: No such assumption."},{"g":0,"t":"tauto","w":"auto","ok":false,"err":"Error: Tactic failure: Classical tauto failed."},{"g":0,"t":"firstorder","w":"auto","ok":false,"err":"Error: Timeout!"},{"g":0,"t":"congruence","w":"auto","ok":false,"err":"Error: Tactic failure: congruence failed."},{"g":0,"t":"unfold Necessary, Possible, MP001, MP002, MP003, MP008, AggregateOfPossibles, MP010, MP011, MP012 in *; firstorder","w":"auto","ok":false,"err":"rejected"},{"g":0,"t":"unfold Necessary, Possible, MP001, MP002, MP003, MP008, AggregateOfPossibles, MP010, MP011, MP012 in *; hammer","w":"hammer","ok":false,"err":"Error: Hammer failed: ATPs failed to f"},{"g":0,"t":"split","w":"model","ok":false,"err":"Error: Unable to find an instance for the variable x."},{"g":0,"t":"intros","w":"model","ok":true,"c":[1]},{"g":0,"t":"right","w":"model","ok":false,"err":"Error: Not an inductive goal with 2 constructors."},{"g":0,"t":"apply MP012","w":"model","ok":false,"err":"Error: Applied theorem does not have enough premises."},{"g":0,"t":"exists 1","w":"model","ok":false,"err":"rejected"},{"g":0,"t":"exists MP008","w":"model","ok":false,"err":"rejected"},{"g":0,"t":"exists MP012","w":"model","ok":false,"err":"rejected"},{"g":0,"t":"exists GivesA","w":"model","ok":false,"err":"Error: The variable GivesA was not found in the current environment."},{"g":1,"t":"assumption","w":"auto","ok":false,"err":"Error: No such assumption."},{"g":1,"t":"tauto","w":"auto","ok":false,"err":"Error: Tactic failure: Classical tauto failed."},{"g":1,"t":"firstorder","w":"auto","ok":false,"err":"Error: Timeout!"},{"g":1,"t":"congruence","w":"auto","ok":false,"err":"Error: Tactic failure: congruence failed."},{"g":1,"t":"unfold Necessary, Possible, MP001, MP002, MP003, MP008, AggregateOfPossibles, MP010, MP011, MP012 in *; firstorder","w":"auto","ok":false,"err":"rejected"},{"g":1,"t":"unfold Necessary, Possible, MP001, MP002, MP003, MP008, AggregateOfPossibles, MP010, MP011, MP012 in *; hammer","w":"hammer","ok":false,"err":"Error: Hammer failed: ATPs failed to f"},{"g":1,"t":"elim H8","w":"model","ok":true,"c":[2]},{"g":1,"t":"elim H8; intros C H9","w":"model","ok":true,"c":[3]},{"g":1,"t":"elim H8; intros","w":"model","ok":true,"c":[4]},{"g":1,"t":"exists A","w":"model","ok":true,"c":[5]},{"g":1,"t":"elim H8; intros B H9","w":"model","ok":true,"c":[6]},{"g":1,"t":"elim H8; clear H8","w":"model","ok":true,"c":[7]},{"g":1,"t":"elim H8; intros C H8","w":"model","ok":false,"err":"Error: H8 is already used."},{"g":2,"t":"assumption","w":"auto","ok":false,"err":"Error: No such assumption."},{"g":2,"t":"tauto","w":"auto","ok":false,"err":"Error: Tactic failure: Classical tauto failed."},{"g":2,"t":"firstorder","w":"auto","ok":false,"err":"Error: Timeout!"},{"g":2,"t":"congruence","w":"auto","ok":false,"err":"Error: Tactic failure: congruence failed."},{"g":2,"t":"unfold Necessary, Possible, MP001, MP002, MP003, MP008, AggregateOfPossibles, MP010, MP011, MP012 in *; firstorder","w":"auto","ok":false,"err":"rejected"},{"g":2,"t":"unfold Necessary, Possible, MP001, MP002, MP003, MP008, AggregateOfPossibles, MP010, MP011, MP012 in *; hammer","w":"hammer","ok":false,"err":"Error: Hammer failed: ATPs failed to f"},{"g":2,"t":"intros x H10","w":"model","ok":true,"c":[8]},{"g":2,"t":"intros x H9","w":"model","ok":true,"c":[4]},{"g":2,"t":"intros","w":"model","ok":true,"c":[4]},{"g":2,"t":"intros X Poss","w":"model","ok":true,"c":[9]},{"g":2,"t":"intros x EX","w":"model","ok":true,"c":[10]},{"g":2,"t":"intros x H8'","w":"model","ok":true,"c":[11]},{"g":2,"t":"elim H8; intros","w":"model","ok":true,"c":[12]},{"g":2,"t":"elim H8; clear H8","w":"model","ok":true,"c":[13]},{"g":3,"t":"assumption","w":"auto","ok":false,"err":"Error: No such assumption."},{"g":3,"t":"tauto","w":"auto","ok":false,"err":"Error: Tactic failure: Classical tauto failed."},{"g":3,"t":"firstorder","w":"auto","ok":false,"err":"Error: Timeout!"},{"g":3,"t":"congruence","w":"auto","ok":false,"err":"Error: Tactic failure: congruence failed."},{"g":3,"t":"unfold Necessary, Possible, MP001, MP002, MP003, MP008, AggregateOfPossibles, MP010, MP011, MP012 in *; firstorder","w":"auto","ok":false,"err":"rejected"},{"g":3,"t":"unfold Necessary, Possible, MP001, MP002, MP003, MP008, AggregateOfPossibles, MP010, MP011, MP012 in *; hammer","w":"hammer","ok":false,"err":"Error: Hammer failed: ATPs failed to f"},{"g":3,"t":"exists C","w":"model","ok":true,"c":[14]},{"g":3,"t":"exists C; split","w":"model","ok":true,"c":[15,16]},{"g":3,"t":"split","w":"model","ok":false,"err":"Error: Unable to find an instance for the variable x."},{"g":3,"t":"exists C; split; trivial","w":"model","ok":true,"c":[15,16]},{"g":3,"t":"elim H9","w":"model","ok":true,"c":[17]},{"g":3,"t":"exists C; split; intros","w":"model","ok":true,"c":[15,16]},{"g":3,"t":"elim H9; intros","w":"model","ok":true,"c":[18]},{"g":3,"t":"elim H8; intros","w":"model","ok":true,"c":[19]},{"g":4,"t":"assumption","w":"auto","ok":false,"err":"Error: No such assumption."},{"g":4,"t":"tauto","w":"auto","ok":false,"err":"Error: Tactic failure: Classical tauto failed."},{"g":4,"t":"firstorder","w":"auto","ok":false,"err":"Error: Timeout!"},{"g":4,"t":"congruence","w":"auto","ok":false,"err":"Error: Tactic failure: congruence failed."},{"g":4,"t":"unfold Necessary, Possible, MP001, MP002, MP003, MP008, AggregateOfPossibles, MP010, MP011, MP012 in *; firstorder","w":"auto","ok":false,"err":"rejected"},{"g":4,"t":"unfold Necessary, Possible, MP001, MP002, MP003, MP008, AggregateOfPossibles, MP010, MP011, MP012 in *; hammer","w":"hammer","ok":false,"err":"Error: Hammer failed: ATPs failed to f"},{"g":4,"t":"exists x","w":"model","ok":true,"c":[20]},{"g":4,"t":"exists x; split","w":"model","ok":true,"c":[21,22]},{"g":4,"t":"split","w":"model","ok":false,"err":"Error: Unable to find an instance for the variable x."},{"g":4,"t":"elim H9","w":"model","ok":true,"c":[23]},{"g":4,"t":"elim H9; intros","w":"model","ok":true,"c":[24]},{"g":4,"t":"exists A","w":"model","ok":true,"c":[25]},{"g":4,"t":"exists H3","w":"model","ok":false,"err":"rejected"},{"g":4,"t":"assert (A = x)","w":"model","ok":true,"c":[26,27]},{"g":27,"t":"firstorder","w":"auto","ok":true,"c":[],"eager":true},{"g":4,"t":"destruct (classic (A = x)) as [Hs|Hs]","w":"model","ok":true,"c":[28,29]},{"g":28,"t":"firstorder","w":"auto","ok":true,"c":[],"eager":true},{"g":5,"t":"assumption","w":"auto","ok":false,"err":"Error: No such assumption."},{"g":5,"t":"tauto","w":"auto","ok":false,"err":"Error: Tactic failure: Classical tauto failed."},{"g":5,"t":"firstorder","w":"auto","ok":false,"err":"Error: Timeout!"},{"g":5,"t":"congruence","w":"auto","ok":false,"err":"Error: Tactic failure: congruence failed."},{"g":5,"t":"unfold Necessary, Possible, MP001, MP002, MP003, MP008, AggregateOfPossibles, MP010, MP011, MP012 in *; firstorder","w":"auto","ok":false,"err":"rejected"},{"g":5,"t":"unfold Necessary, Possible, MP001, MP002, MP003, MP008, AggregateOfPossibles, MP010, MP011, MP012 in *; hammer","w":"hammer","ok":false,"err":"Error: Hammer failed: ATPs failed to f"},{"g":5,"t":"split","w":"model","ok":true,"c":[30,31]},{"g":5,"t":"elim H8","w":"model","ok":true,"c":[32]},{"g":5,"t":"assert (Gives A A)","w":"model","ok":true,"c":[30,33]},{"g":33,"t":"firstorder","w":"auto","ok":true,"c":[],"eager":true},{"g":5,"t":"destruct (classic (Gives A A)) as [Hs|Hs]","w":"model","ok":true,"c":[34,35]},{"g":34,"t":"firstorder","w":"auto","ok":true,"c":[],"eager":true},{"g":5,"t":"assert (~ (A = A))","w":"model","ok":true,"c":[36,37]},{"g":37,"t":"tauto","w":"auto","ok":true,"c":[],"eager":true},{"g":5,"t":"destruct (classic (~ (A = A))) as [Hs|Hs]","w":"model","ok":true,"c":[38,39]},{"g":38,"t":"tauto","w":"auto","ok":true,"c":[],"eager":true},{"g":5,"t":"destruct H8 as [GivesNS]","w":"model","ok":true,"c":[40]},{"g":5,"t":"elim H8; intros","w":"model","ok":true,"c":[25]},{"g":5,"t":"assert (~ (MemberOf A A))","w":"model","ok":true,"c":[41,42]},{"g":41,"t":"firstorder","w":"auto","ok":true,"c":[],"eager":true},{"g":5,"t":"destruct (classic (~ (MemberOf A A))) as [Hs|Hs]","w":"model","ok":true,"c":[43,44]},{"g":44,"t":"firstorder","w":"auto","ok":true,"c":[],"eager":true},{"g":5,"t":"destruct H8 as [GivesNE]","w":"model","ok":true,"c":[45]},{"g":6,"t":"assumption","w":"auto","ok":false,"err":"Error: No such assumption."},{"g":6,"t":"tauto","w":"auto","ok":false,"err":"Error: Tactic failure: Classical tauto failed."},{"g":6,"t":"firstorder","w":"auto","ok":false,"err":"Error: Timeout!"},{"g":6,"t":"congruence","w":"auto","ok":false,"err":"Error: Tactic failure: congruence failed."},{"g":6,"t":"unfold Necessary, Possible, MP001, MP002, MP003, MP008, AggregateOfPossibles, MP010, MP011, MP012 in *; firstorder","w":"auto","ok":false,"err":"rejected"},{"g":6,"t":"unfold Necessary, Possible, MP001, MP002, MP003, MP008, AggregateOfPossibles, MP010, MP011, MP012 in *; hammer","w":"hammer","ok":false,"err":"Error: Hammer failed: ATPs failed to f"},{"g":6,"t":"exists B","w":"model","ok":true,"c":[46]},{"g":6,"t":"exists A","w":"model","ok":true,"c":[47]},{"g":6,"t":"exists B; split","w":"model","ok":true,"c":[48,49]},{"g":6,"t":"split","w":"model","ok":false,"err":"Error: Unable to find an instance for the variable x."},{"g":6,"t":"exists C","w":"model","ok":false,"err":"Error: The variable C was not found in the current environment."},{"g":6,"t":"assert (Possible B)","w":"model","ok":true,"c":[50,51]},{"g":50,"t":"tauto","w":"auto","ok":true,"c":[],"eager":true},{"g":6,"t":"destruct (classic (Possible B)) as [Hs|Hs]","w":"model","ok":true,"c":[52,53]},{"g":53,"t":"tauto","w":"auto","ok":true,"c":[],"eager":true},{"g":6,"t":"exists B; split; trivial","w":"model","ok":true,"c":[48,49]},{"g":6,"t":"elim H8","w":"model","ok":true,"c":[54]},{"g":7,"t":"assumption","w":"auto","ok":false,"err":"Error: No such assumption."},{"g":7,"t":"tauto","w":"auto","ok":false,"err":"Error: Tactic failure: Classical tauto failed."},{"g":7,"t":"firstorder","w":"auto","ok":false,"err":"Error: Timeout!"},{"g":7,"t":"congruence","w":"auto","ok":false,"err":"Error: Tactic failure: congruence failed."},{"g":7,"t":"unfold Necessary, Possible, MP001, MP002, MP003, MP008, AggregateOfPossibles, MP010, MP011, MP012 in *; firstorder","w":"auto","ok":false,"err":"rejected"},{"g":7,"t":"unfold Necessary, Possible, MP001, MP002, MP003, MP008, AggregateOfPossibles, MP010, MP011, MP012 in *; hammer","w":"hammer","ok":false,"err":"Error: Hammer failed: ATPs failed to f"},{"g":7,"t":"intros x H8","w":"model","ok":true,"c":[55]},{"g":7,"t":"intros","w":"model","ok":true,"c":[55]},{"g":7,"t":"intros B Poss","w":"model","ok":true,"c":[56]},{"g":7,"t":"intros B","w":"model","ok":true,"c":[57]},{"g":7,"t":"intros x EX","w":"model","ok":true,"c":[58]},{"g":7,"t":"intros x IN","w":"model","ok":true,"c":[59]},{"g":7,"t":"intros B D","w":"model","ok":true,"c":[60]},{"g":7,"t":"intros B [C D]","w":"model","ok":true,"c":[61]},{"g":14,"t":"assumption","w":"auto","ok":false,"err":"Error: No such assumption."},{"g":14,"t":"tauto","w":"auto","ok":false,"err":"Error: Tactic failure: Classical tauto failed."},{"g":14,"t":"firstorder","w":"auto","ok":false,"err":"Error: Timeout!"},{"g":14,"t":"congruence","w":"auto","ok":false,"err":"Error: Tactic failure: congruence failed."},{"g":14,"t":"unfold Necessary, Possible, MP001, MP002, MP003, MP008, AggregateOfPossibles, MP010, MP011, MP012 in *; firstorder","w":"auto","ok":false,"err":"rejected"},{"g":14,"t":"unfold Necessary, Possible, MP001, MP002, MP003, MP008, AggregateOfPossibles, MP010, MP011, MP012 in *; hammer","w":"hammer","ok":false,"err":"Error: Hammer failed: ATPs failed to f"},{"g":14,"t":"split","w":"model","ok":true,"c":[15,16]},{"g":14,"t":"assert (~ (C = A))","w":"model","ok":true,"c":[62,63]},{"g":62,"t":"tauto","w":"auto","ok":true,"c":[],"eager":true},{"g":14,"t":"destruct (classic (~ (C = A))) as [Hs|Hs]","w":"model","ok":true,"c":[64,65]},{"g":65,"t":"tauto","w":"auto","ok":true,"c":[],"eager":true},{"g":14,"t":"assert (Gives C A)","w":"model","ok":true,"c":[15,66]},{"g":14,"t":"destruct (classic (Gives C A)) as [Hs|Hs]","w":"model","ok":true,"c":[67,68]},{"g":14,"t":"generalize H9","w":"model","ok":true,"c":[69]},{"g":14,"t":"generalize H8","w":"model","ok":true,"c":[70]},{"g":14,"t":"assert (Possible C)","w":"model","ok":true,"c":[71,72]},{"g":71,"t":"tauto","w":"auto","ok":true,"c":[],"eager":true},{"g":14,"t":"destruct (classic (Possible C)) as [Hs|Hs]","w":"model","ok":true,"c":[73,74]}],"proof":[],"proofFile":null},{"key":"round6/imkan_s12_necessary_exists","id":"imkan_s12_necessary_exists","run":"round6","title":"Dalīl al-imkān, step 12 (aggregate route)","english":"A Necessary Existent exists.","stmt":"MP001 -> MP002 -> MP003 -> MP008 -> MP009 -> MP010 -> MP011 -> MP012 -> SP001 -> exists n, Necessary n","proved":false,"script":"","seconds":918.5,"expansions":29,"calls":944,"root":0,"goals":["============================\nMP001 -> MP002 -> MP003 -> MP008 -> MP009 -> MP010 -> MP011 -> MP012 -> SP001 -> exists n, Necessary n","============================\nforall (_ : MP001) (_ : MP002) (_ : MP003) (_ : MP008) (_ : MP009) (_ : MP010) (_ : MP011) (_ : MP012) (_ : @ex Thing (fun x : Thing => Exists x)), @ex Thing (fun n : Thing => Necessary n)","============================\nforall _ : MP003, MP008","H : forall _ : MP003, MP008\n============================\nforall (_ : MP001) (_ : MP002) (_ : MP003) (_ : MP008) (_ : MP009) (_ : MP010) (_ : MP011) (_ : MP012) (_ : SP001), @ex Thing (fun n : Thing => Necessary n)","Hs : forall _ : MP003, MP008\n============================\nforall (_ : MP001) (_ : MP002) (_ : MP003) (_ : MP008) (_ : MP009) (_ : MP010) (_ : MP011) (_ : MP012) (_ : SP001), @ex Thing (fun n : Thing => Necessary n)","Hs : not (forall _ : MP003, MP008)\n============================\nforall (_ : MP001) (_ : MP002) (_ : MP003) (_ : MP008) (_ : MP009) (_ : MP010) (_ : MP011) (_ : MP012) (_ : SP001), @ex Thing (fun n : Thing => Necessary n)","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP008\nH3 : MP009\nH4 : MP010\nH5 : MP011\nH6 : MP012\nH7 : @ex Thing (fun x : Thing => Exists x)\n============================\n@ex Thing (fun n : Thing => Necessary n)","x : MP001\ny : MP002\nz : MP003\nHx : MP008\nHx' : MP009\n============================\nforall (_ : MP010) (_ : MP011) (_ : MP012) (_ : @ex Thing (fun x0 : Thing => Exists x0)), @ex Thing (fun n : Thing => Necessary n)","x : MP001\ny : MP002\nz : MP003\nHx : MP008\nHn : MP009\n============================\nforall (_ : MP010) (_ : MP011) (_ : MP012) (_ : @ex Thing (fun x0 : Thing => Exists x0)), @ex Thing (fun n : Thing => Necessary n)","x : MP001\ny : MP002\nz : MP003\nHx : MP008\nHy : MP009\nHn : MP010\nH : MP011\n============================\nforall (_ : MP012) (_ : @ex Thing (fun x0 : Thing => Exists x0)), @ex Thing (fun n : Thing => Necessary n)","x : MP001\ny : MP002\nz : MP003\nHx : MP008\nHy : MP009\nHn : MP010\n============================\nforall (_ : MP011) (_ : MP012) (_ : @ex Thing (fun x0 : Thing => Exists x0)), @ex Thing (fun n : Thing => Necessary n)","H : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nx : Thing\nH0 : Exists x\nH1 : forall (x0 : Thing) (_ : (fun y : Thing => Gives y x) x0), False\nX : Prop\nX0 : Prop\n============================\nEss x","H : MP003\n============================\nMP008","H : forall _ : Pilot.MP003, MP008\nMP001 : Pilot.MP001\nMP002 : Pilot.MP002\nMP003 : Pilot.MP003\nSP001 : MP008\n============================\nforall (_ : MP009) (_ : MP010) (_ : MP011) (_ : MP012) (_ : Pilot.SP001), @ex Thing (fun n : Thing => Necessary n)","H : forall _ : MP003, MP008\nH0 : MP001\nH1 : MP002\nH2 : MP003\nH3 : MP008\nH4 : MP009\nH5 : MP010\nH6 : MP011\nH7 : MP012\nH8 : SP001\n============================\n@ex Thing (fun n : Thing => Necessary n)","H : forall _ : Pilot.MP003, MP008\nMP003 : Pilot.MP001\nMP002 : Pilot.MP002\nMP001 : Pilot.MP003\nSP001 : MP008\n============================\nforall (_ : MP009) (_ : MP010) (_ : MP011) (_ : MP012) (_ : Pilot.SP001), @ex Thing (fun n : Thing => Necessary n)","H : forall _ : Pilot.MP003, Pilot.MP008\nMP002 : MP001\nMP003 : Pilot.MP002\nMP008 : Pilot.MP003\nMP012 : Pilot.MP008\nSP001 : MP009\n============================\nforall (_ : MP010) (_ : MP011) (_ : Pilot.MP012) (_ : Pilot.SP001), @ex Thing (fun n : Thing => Necessary n)","H : forall _ : Pilot.MP003, Pilot.MP008\nMP001 : Pilot.MP001\nMP002 : Pilot.MP002\nMP003 : Pilot.MP003\nMP008 : Pilot.MP008\nSP001 : MP009\n============================\nforall (_ : MP010) (_ : MP011) (_ : MP012) (_ : Pilot.SP001), @ex Thing (fun n : Thing => Necessary n)","H : forall _ : Pilot.MP003, Pilot.MP008\nMP001 : Pilot.MP001\nMP002 : Pilot.MP002\nMP003 : Pilot.MP003\nMP008 : Pilot.MP008\nMP010 : MP009\n============================\nforall (_ : Pilot.MP010) (_ : MP011) (_ : MP012) (_ : SP001), @ex Thing (fun n : Thing => Necessary n)","Hs : forall _ : MP003, MP008\nH : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP008\nH3 : MP009\nH4 : MP010\nH5 : MP011\nH6 : MP012\nH7 : SP001\n============================\n@ex Thing (fun n : Thing => Necessary n)","Hs : forall _ : Pilot.MP003, MP008\nMP001 : Pilot.MP001\nMP002 : Pilot.MP002\nMP003 : Pilot.MP003\nSP001 : MP008\n============================\nforall (_ : MP009) (_ : MP010) (_ : MP011) (_ : MP012) (_ : Pilot.SP001), @ex Thing (fun n : Thing => Necessary n)","Hs : forall _ : Pilot.MP003, Pilot.MP008\nMP001 : Pilot.MP001\nMP002 : Pilot.MP002\nMP003 : Pilot.MP003\nMP008 : Pilot.MP008\nSP001 : MP009\n============================\nforall (_ : MP010) (_ : MP011) (_ : MP012) (_ : Pilot.SP001), @ex Thing (fun n : Thing => Necessary n)","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP008\nH3 : MP009\nH4 : MP010\nH5 : MP011\nH6 : MP012\nH7 : @ex Thing (fun x : Thing => Exists x)\n============================\n@ex Thing (fun x : Thing => Necessary x)","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP008\nH3 : MP009\nH4 : MP010\nH5 : MP011\nH6 : MP012\nH7 : @ex Thing (fun x : Thing => Exists x)\nH8 : @ex Thing (fun x : Thing => Necessary x)\n============================\n@ex Thing (fun n : Thing => Necessary n)","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP008\nH3 : MP009\nH4 : MP010\nH5 : MP011\nH6 : MP012\nH7 : @ex Thing (fun x : Thing => Exists x)\nHs : @ex Thing (fun x : Thing => Necessary x)\n============================\n@ex Thing (fun n : Thing => Necessary n)","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP008\nH3 : MP009\nH4 : MP010\nH5 : MP011\nH6 : MP012\nH7 : @ex Thing (fun x : Thing => Exists x)\nHs : not (@ex Thing (fun x : Thing => Necessary x))\n============================\n@ex Thing (fun n : Thing => Necessary n)","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP008\nH3 : MP009\nH4 : MP010\nH5 : MP011\nH6 : MP012\nH7 : @ex Thing (fun x : Thing => Exists x)\nH8 : @ex Thing (fun x : Thing => Exists x)\n============================\n@ex Thing (fun n : Thing => Necessary n)","H : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nx : Thing\nH0 : Exists x\nH1 : forall (x0 : Thing) (_ : (fun y : Thing => Gives y x) x0), False\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\n============================\nEss x","H : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nx : Thing\nH0 : Exists x\nH1 : forall (x0 : Thing) (_ : (fun y : Thing => Gives y x) x0), False\nX : Prop\nX0 : Prop\nH2 : forall _ : (fun y : Thing => Gives y x) x, False\n============================\nEss x","H : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nx : Thing\nH0 : Exists x\nH1 : forall (x0 : Thing) (_ : (fun y : Thing => Gives y x) x0), False\nX : Prop\nX0 : Prop\n============================\nGives x x","H : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nx : Thing\nH0 : Exists x\nH1 : forall (x0 : Thing) (_ : (fun y : Thing => Gives y x) x0), False\nX : Prop\nX0 : Prop\nH2 : Gives x x\n============================\nEss x","H : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nx : Thing\nH0 : Exists x\nH1 : forall (x0 : Thing) (_ : (fun y : Thing => Gives y x) x0), False\nX : Prop\nX0 : Prop\nHs : Gives x x\n============================\nEss x","H : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nx : Thing\nH0 : Exists x\nH1 : forall (x0 : Thing) (_ : (fun y : Thing => Gives y x) x0), False\nX : Prop\nX0 : Prop\nHs : not (Gives x x)\n============================\nEss x","H : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nx : Thing\nH0 : Exists x\nH1 : forall (x0 : Thing) (_ : (fun y : Thing => Gives y x) x0), False\nX : Prop\nX0 : Prop\nHs : forall x y : Thing, Gives y x\n============================\nEss x","H : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nx : Thing\nH0 : Exists x\nH1 : forall (x0 : Thing) (_ : (fun y : Thing => Gives y x) x0), False\nX : Prop\nX0 : Prop\nHs : not (forall x y : Thing, Gives y x)\n============================\nEss x","H : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nx : Thing\nH0 : Exists x\nH1 : forall (x0 : Thing) (_ : (fun y : Thing => Gives y x) x0), False\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\n============================\nEss x","H : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nx : Thing\nH0 : Exists x\nH1 : forall (x0 : Thing) (_ : (fun y : Thing => Gives y x) x0), False\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nH3 : forall _ : (fun y : Thing => Gives y x) x, False\n============================\nEss x","H : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nx : Thing\nH0 : Exists x\nH1 : forall (x0 : Thing) (_ : (fun y : Thing => Gives y x) x0), False\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nH2 : Ess x\n============================\nEss x","H : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nx : Thing\nH0 : Exists x\nH1 : forall (x0 : Thing) (_ : (fun y : Thing => Gives y x) x0), False\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nHs : Ess x\n============================\nEss x","H : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nx : Thing\nH0 : Exists x\nH1 : forall (x0 : Thing) (_ : (fun y : Thing => Gives y x) x0), False\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nHs : not (Ess x)\n============================\nEss x","H : MP003\nH0 : MP003\n============================\nMP008","H : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nx : Thing\nH0 : Exists x\nH1 : forall (x0 : Thing) (_ : (fun y : Thing => Gives y x) x0), False\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\n============================\nEss x","H : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nx : Thing\nH0 : Exists x\nH1 : forall (x0 : Thing) (_ : (fun y : Thing => Gives y x) x0), False\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nH5 : forall _ : (fun y : Thing => Gives y x) x, False\n============================\nEss x","H : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nx : Thing\nH0 : Exists x\nH1 : forall (x0 : Thing) (_ : (fun y : Thing => Gives y x) x0), False\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nH2 : Ess x\n============================\nEss x","H : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nx : Thing\nH0 : Exists x\nH1 : forall (x0 : Thing) (_ : (fun y : Thing => Gives y x) x0), False\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nHs : Ess x\n============================\nEss x","H : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nx : Thing\nH0 : Exists x\nH1 : forall (x0 : Thing) (_ : (fun y : Thing => Gives y x) x0), False\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nHs : not (Ess x)\n============================\nEss x","H : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nx : Thing\nH0 : Exists x\nH1 : forall (x0 : Thing) (_ : (fun y : Thing => Gives y x) x0), False\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nHs : forall x y : Thing, Gives y x\n============================\nEss x","H : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nx : Thing\nH0 : Exists x\nH1 : forall (x0 : Thing) (_ : (fun y : Thing => Gives y x) x0), False\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nHs : not (forall x y : Thing, Gives y x)\n============================\nEss x","H : forall _ : Pilot.MP003, MP008\nMP001 : Pilot.MP001\nMP002 : Pilot.MP002\nMP003 : Pilot.MP003\nSP001 : MP008\nMP009 : Pilot.MP009\nSP002 : MP010\n============================\nforall (_ : MP011) (_ : MP012) (_ : Pilot.SP001), @ex Thing (fun n : Thing => Necessary n)","H : forall _ : Pilot.MP003, MP008\nMP001 : Pilot.MP001\nMP002 : Pilot.MP002\nMP003 : Pilot.MP003\nSP001 : MP008\nMP003' : MP009\nSP003' : MP010\n============================\nforall (_ : MP011) (_ : MP012) (_ : Pilot.SP001), @ex Thing (fun n : Thing => Necessary n)","H : forall _ : Pilot.MP003, MP008\nMP001 : Pilot.MP001\nMP002 : Pilot.MP002\nMP003 : Pilot.MP003\nSP001 : MP008\nx : Thing\nH0 : and (AggregateOfPossibles x) (Exists x)\n============================\nforall (_ : MP010) (_ : MP011) (_ : MP012) (_ : Pilot.SP001), @ex Thing (fun n : Thing => Necessary n)","H : forall _ : Pilot.MP003, MP008\nMP001 : Pilot.MP001\nMP002 : Pilot.MP002\nMP003 : Pilot.MP003\nSP001 : MP008\n============================\n@ex Thing (fun p : Thing => Possible p)","H : forall _ : Pilot.MP003, MP008\nMP001 : Pilot.MP001\nMP002 : Pilot.MP002\nMP003 : Pilot.MP003\n============================\nforall (_ : MP008) (_ : MP009) (_ : MP010) (_ : MP011) (_ : MP012) (_ : SP001), @ex Thing (fun n : Thing => Necessary n)","H : forall _ : Pilot.MP003, MP008\nMP001 : Pilot.MP001\nMP002 : Pilot.MP002\nMP003 : Pilot.MP003\nSP001 : MP008\nMP009 : Pilot.MP009\nMP010 : Pilot.MP010\nSP002 : MP011\n============================\nforall (_ : MP012) (_ : Pilot.SP001), @ex Thing (fun n : Thing => Necessary n)","H : forall _ : Pilot.MP003, MP008\nMP001 : Pilot.MP001\nMP002 : Pilot.MP002\nMP003 : Pilot.MP003\nSP001 : MP008\nMP003' : MP009\nSP002' : MP010\n============================\nforall (_ : MP011) (_ : MP012) (_ : Pilot.SP001), @ex Thing (fun n : Thing => Necessary n)","H : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nx : Thing\nH0 : Exists x\nH1 : forall (x0 : Thing) (_ : (fun y : Thing => Gives y x) x0), False\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\nX8 : Prop\n============================\nEss x","H : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nx : Thing\nH0 : Exists x\nH1 : forall (x0 : Thing) (_ : (fun y : Thing => Gives y x) x0), False\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nH2 : Ess x\n============================\nEss x","H : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nx : Thing\nH0 : Exists x\nH1 : forall (x0 : Thing) (_ : (fun y : Thing => Gives y x) x0), False\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nHs : Ess x\n============================\nEss x","H : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nx : Thing\nH0 : Exists x\nH1 : forall (x0 : Thing) (_ : (fun y : Thing => Gives y x) x0), False\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nHs : not (Ess x)\n============================\nEss x","H : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nx : Thing\nH0 : Exists x\nH1 : forall (x0 : Thing) (_ : (fun y : Thing => Gives y x) x0), False\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nH7 : forall _ : (fun y : Thing => Gives y x) x, False\n============================\nEss x","Hs : forall _ : Pilot.MP003, MP008\nMP001 : Pilot.MP001\nMP002 : Pilot.MP002\nMP003 : Pilot.MP003\nSP001 : MP008\nMP009 : Pilot.MP009\nSP002 : MP010\n============================\nforall (_ : MP011) (_ : MP012) (_ : Pilot.SP001), @ex Thing (fun n : Thing => Necessary n)","Hs : forall _ : Pilot.MP003, MP008\nMP001 : Pilot.MP001\nMP002 : Pilot.MP002\nMP003 : Pilot.MP003\nSP001 : MP008\nMP003' : MP009\nSP003' : MP010\n============================\nforall (_ : MP011) (_ : MP012) (_ : Pilot.SP001), @ex Thing (fun n : Thing => Necessary n)","Hs : forall _ : Pilot.MP003, MP008\nMP001 : Pilot.MP001\nMP002 : Pilot.MP002\nMP003 : Pilot.MP003\n============================\nforall (_ : MP008) (_ : MP009) (_ : MP010) (_ : MP011) (_ : MP012) (_ : SP001), @ex Thing (fun n : Thing => Necessary n)","Hs : forall _ : Pilot.MP003, MP008\nMP001 : Pilot.MP001\nMP002 : Pilot.MP002\nMP003 : Pilot.MP003\nSP001 : MP008\nMP003' : MP009\nSP002' : MP010\n============================\nforall (_ : MP011) (_ : MP012) (_ : Pilot.SP001), @ex Thing (fun n : Thing => Necessary n)","Hs : forall _ : Pilot.MP003, MP008\nMP001 : Pilot.MP001\nMP002 : Pilot.MP002\nMP003 : Pilot.MP003\nSP001 : MP008\nx : Thing\nH : and (AggregateOfPossibles x) (Exists x)\n============================\nforall (_ : MP010) (_ : MP011) (_ : MP012) (_ : Pilot.SP001), @ex Thing (fun n : Thing => Necessary n)","Hs : forall _ : Pilot.MP003, MP008\nMP001 : Pilot.MP001\nMP002 : Pilot.MP002\nMP003 : Pilot.MP003\nSP001 : MP008\n============================\n@ex Thing (fun p : Thing => Possible p)","Hs : forall _ : Pilot.MP003, MP008\nMP001 : Pilot.MP001\nMP002 : Pilot.MP002\nMP003 : Pilot.MP003\nSP001 : MP008\nMP004 : MP009\nSP002 : MP010\n============================\nforall (_ : MP011) (_ : MP012) (_ : Pilot.SP001), @ex Thing (fun n : Thing => Necessary n)","Hs : forall _ : Pilot.MP003, MP008\nMP001 : Pilot.MP001\nMP002 : Pilot.MP002\nMP003 : Pilot.MP003\nSP001 : MP008\nH : MP009\nH0 : MP010\nH1 : MP011\nH2 : MP012\nH3 : Pilot.SP001\n============================\n@ex Thing (fun n : Thing => Necessary n)","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP008\nH3 : MP009\nH4 : MP010\nH5 : MP011\nH6 : MP012\nH7 : @ex Thing (fun x : Thing => Exists x)\nH8 : @ex Thing (fun x : Thing => Necessary x)\n============================\n@ex Thing (fun x : Thing => Necessary x)","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP008\nH3 : MP009\nH4 : MP010\nH5 : MP011\nH6 : MP012\nH7 : @ex Thing (fun x : Thing => Exists x)\nHs : @ex Thing (fun x : Thing => Necessary x)\n============================\n@ex Thing (fun x : Thing => Necessary x)","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP008\nH3 : MP009\nH4 : MP010\nH5 : MP011\nH6 : MP012\nH7 : @ex Thing (fun x : Thing => Exists x)\nHs : not (@ex Thing (fun x : Thing => Necessary x))\n============================\n@ex Thing (fun x : Thing => Necessary x)","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP008\nH3 : MP009\nH4 : MP010\nH5 : MP011\nH6 : MP012\nH7 : @ex Thing (fun x : Thing => Exists x)\nH8 : @ex Thing (fun x : Thing => Exists x)\n============================\n@ex Thing (fun x : Thing => Necessary x)","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP008\nH4 : MP010\nH5 : MP011\nH6 : MP012\nx : Thing\nH7 : Exists x\nH3 : forall (x : Thing) (_ : (fun p : Thing => Possible p) x), @ex Thing (fun A : Thing => and (AggregateOfPossibles A) (Exists A))\nH8 : forall (x : Thing) (_ : (fun x0 : Thing => Necessary x0) x), False\nX : Prop\n============================\n@ex Thing (fun n : Thing => Necessary n)","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (x : Thing) (_ : Exists x) (_ : not (ThroughAnother x)), Ess x\nH4 : forall (A : Thing) (_ : @ex Thing (fun p : Thing => MemberOf p A)) (_ : forall (p : Thing) (_ : MemberOf p A), not (Ess p)), not (Ess A)\nH5 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nH6 : forall (y x : Thing) (_ : Gives y x), Exists y\nx : Thing\nH7 : Exists x\nH3 : forall (x : Thing) (_ : (fun p : Thing => Possible p) x), @ex Thing (fun A : Thing => and (AggregateOfPossibles A) (Exists A))\nH8 : forall (x : Thing) (_ : (fun x0 : Thing => and (Exists x0) (Ess x0)) x), False\nX : Prop\n============================\n@ex Thing (fun n : Thing => and (Exists n) (Ess n))","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP008\nH3 : MP009\nH4 : MP010\nH5 : MP011\nH6 : MP012\nH7 : @ex Thing (fun x : Thing => Exists x)\nHs : not (@ex Thing (fun x : Thing => Necessary x))\nHn : @ex Thing (fun n : Thing => Necessary n)\n============================\n@ex Thing (fun n : Thing => Necessary n)","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP008\nH3 : MP009\nH4 : MP010\nH5 : MP011\nH6 : MP012\nH7 : @ex Thing (fun x : Thing => Exists x)\nHs : not (@ex Thing (fun x : Thing => Necessary x))\nH8 : @ex Thing (fun x : Thing => Necessary x)\n============================\n@ex Thing (fun n : Thing => Necessary n)","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP008\nH3 : MP009\nH4 : MP010\nH5 : MP011\nH6 : MP012\nH7 : @ex Thing (fun x : Thing => Exists x)\nHs : not (@ex Thing (fun x : Thing => Necessary x))\nH8 : @ex Thing (fun n : Thing => Necessary n)\n============================\n@ex Thing (fun n : Thing => Necessary n)","H : forall _ : Pilot.MP003, MP008\nMP003 : Pilot.MP001\nMP002 : Pilot.MP002\nMP001 : Pilot.MP003\nSP001 : MP008\nMP003' : MP009\nSP003' : MP010\n============================\nforall (_ : MP011) (_ : MP012) (_ : Pilot.SP001), @ex Thing (fun n : Thing => Necessary n)","H : forall _ : Pilot.MP003, MP008\nMP003 : Pilot.MP001\nMP002 : Pilot.MP002\nMP001 : Pilot.MP003\nSP001 : MP008\nx : Thing\nH0 : and (AggregateOfPossibles x) (Exists x)\n============================\nforall (_ : MP010) (_ : MP011) (_ : MP012) (_ : Pilot.SP001), @ex Thing (fun n : Thing => Necessary n)","H : forall _ : Pilot.MP003, MP008\nMP003 : Pilot.MP001\nMP002 : Pilot.MP002\nMP001 : Pilot.MP003\nSP001 : MP008\n============================\n@ex Thing (fun p : Thing => Possible p)","H : forall _ : Pilot.MP003, MP008\nMP003 : Pilot.MP001\nMP002 : Pilot.MP002\nMP001 : Pilot.MP003\nSP001 : MP008\nMP009 : Pilot.MP009\nSP002 : MP010\n============================\nforall (_ : MP011) (_ : MP012) (_ : Pilot.SP001), @ex Thing (fun n : Thing => Necessary n)","H : forall _ : Pilot.MP003, MP008\nMP003 : Pilot.MP001\nMP002 : Pilot.MP002\nMP001 : Pilot.MP003\n============================\nforall (_ : MP008) (_ : MP009) (_ : MP010) (_ : MP011) (_ : MP012) (_ : SP001), @ex Thing (fun n : Thing => Necessary n)","H : forall _ : Pilot.MP003, MP008\nMP003 : Pilot.MP001\nMP002 : Pilot.MP002\nMP001 : Pilot.MP003\nSP001 : MP008\nH0 : MP009\nH1 : MP010\nH2 : MP011\nH3 : MP012\nH4 : Pilot.SP001\n============================\n@ex Thing (fun n : Thing => Necessary n)","H : forall _ : Pilot.MP003, MP008\nMP003 : Pilot.MP001\nMP002 : Pilot.MP002\nMP001 : Pilot.MP003\nSP001 : MP008\nMP009 : Pilot.MP009\nSP009 : MP010\n============================\nforall (_ : MP011) (_ : MP012) (_ : Pilot.SP001), @ex Thing (fun n : Thing => Necessary n)","H : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nx : Thing\nH0 : Exists x\nH1 : forall (x0 : Thing) (_ : (fun y : Thing => Gives y x) x0), False\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\nX8 : Prop\nX9 : Prop\nX10 : Prop\n============================\nEss x","H : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nx : Thing\nH0 : Exists x\nH1 : forall (x0 : Thing) (_ : (fun y : Thing => Gives y x) x0), False\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\nX8 : Prop\nH2 : Ess x\n============================\nEss x","H : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nx : Thing\nH0 : Exists x\nH1 : forall (x0 : Thing) (_ : (fun y : Thing => Gives y x) x0), False\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\nX8 : Prop\nHs : Ess x\n============================\nEss x","H : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nx : Thing\nH0 : Exists x\nH1 : forall (x0 : Thing) (_ : (fun y : Thing => Gives y x) x0), False\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\nX8 : Prop\nHs : not (Ess x)\n============================\nEss x","H : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nx : Thing\nH0 : Exists x\nH1 : forall (x0 : Thing) (_ : (fun y : Thing => Gives y x) x0), False\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\nX8 : Prop\nX9 : Prop\n============================\nEss x","H : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nx : Thing\nH0 : Exists x\nH1 : forall (x0 : Thing) (_ : (fun y : Thing => Gives y x) x0), False\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\nX8 : Prop\nHs : forall x y : Thing, Gives y x\n============================\nEss x","H : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nx : Thing\nH0 : Exists x\nH1 : forall (x0 : Thing) (_ : (fun y : Thing => Gives y x) x0), False\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\nX5 : Prop\nX6 : Prop\nX7 : Prop\nX8 : Prop\nHs : not (forall x y : Thing, Gives y x)\n============================\nEss x","x : MP001\ny : MP002\nz : MP003\nHx : MP008\nHx' : MP009\nH : MP010\nH0 : MP011\nH1 : MP012\nH2 : @ex Thing (fun x0 : Thing => Exists x0)\n============================\n@ex Thing (fun n : Thing => Necessary n)","x : MP001\ny : MP002\nz : MP003\nHx : MP008\n============================\nforall (_ : MP009) (_ : MP010) (_ : MP011) (_ : MP012) (_ : @ex Thing (fun x0 : Thing => Exists x0)), @ex Thing (fun n : Thing => Necessary n)","y : MP002\nz : MP003\nHx : MP008\nHx' : MP009\n============================\nforall (_ : MP001) (_ : MP010) (_ : MP011) (_ : MP012) (_ : @ex Thing (fun x0 : Thing => Exists x0)), @ex Thing (fun n : Thing => Necessary n)","x : MP001\ny : MP002\nz : MP003\nHx : MP008\nHn : MP009\nH : MP010\nH0 : MP011\nH1 : MP012\nH2 : @ex Thing (fun x0 : Thing => Exists x0)\n============================\n@ex Thing (fun n : Thing => Necessary n)","x : MP001\ny : MP002\nz : MP003\nHx : MP008\nHn : MP009\n============================\nforall (_ : MP008) (_ : MP010) (_ : MP011) (_ : MP012) (_ : @ex Thing (fun x0 : Thing => Exists x0)), @ex Thing (fun n : Thing => Necessary n)","H : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nx : Thing\nH0 : Exists x\nH1 : forall (x0 : Thing) (_ : (fun y : Thing => Gives y x) x0), False\nX : Prop\nX0 : Prop\nH2 : forall _ : (fun y : Thing => Gives y x) x, False\nX1 : Prop\nX2 : Prop\n============================\nEss x","H : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nx : Thing\nH0 : Exists x\nH1 : forall (x0 : Thing) (_ : (fun y : Thing => Gives y x) x0), False\nX : Prop\nX0 : Prop\nH2 : forall _ : (fun y : Thing => Gives y x) x, False\n============================\nGives x x","H : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nx : Thing\nH0 : Exists x\nH1 : forall (x0 : Thing) (_ : (fun y : Thing => Gives y x) x0), False\nX : Prop\nX0 : Prop\nH2 : forall _ : (fun y : Thing => Gives y x) x, False\nH3 : Gives x x\n============================\nEss x","H : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nx : Thing\nH0 : Exists x\nH1 : forall (x0 : Thing) (_ : (fun y : Thing => Gives y x) x0), False\nX : Prop\nX0 : Prop\nH2 : forall _ : (fun y : Thing => Gives y x) x, False\nHs : Gives x x\n============================\nEss x","H : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nx : Thing\nH0 : Exists x\nH1 : forall (x0 : Thing) (_ : (fun y : Thing => Gives y x) x0), False\nX : Prop\nX0 : Prop\nH2 : forall _ : (fun y : Thing => Gives y x) x, False\nHs : not (Gives x x)\n============================\nEss x","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP008\nH3 : MP009\nH4 : MP010\nH5 : MP011\nH6 : MP012\nH7 : @ex Thing (fun x : Thing => Exists x)\nH8 : @ex Thing (fun x : Thing => Exists x)\nH9 : @ex Thing (fun x : Thing => Necessary x)\n============================\n@ex Thing (fun n : Thing => Necessary n)","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP008\nH3 : MP009\nH4 : MP010\nH5 : MP011\nH6 : MP012\nH7 : @ex Thing (fun x : Thing => Exists x)\nH8 : @ex Thing (fun x : Thing => Exists x)\nHs : @ex Thing (fun x : Thing => Necessary x)\n============================\n@ex Thing (fun n : Thing => Necessary n)","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP008\nH3 : MP009\nH4 : MP010\nH5 : MP011\nH6 : MP012\nH7 : @ex Thing (fun x : Thing => Exists x)\nH8 : @ex Thing (fun x : Thing => Exists x)\nHs : not (@ex Thing (fun x : Thing => Necessary x))\n============================\n@ex Thing (fun n : Thing => Necessary n)","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP008\nH3 : MP009\nH4 : MP010\nH5 : MP011\nH6 : MP012\nH7 : @ex Thing (fun x : Thing => Exists x)\nH8 : @ex Thing (fun x : Thing => Exists x)\nH9 : @ex Thing (fun x : Thing => Exists x)\n============================\n@ex Thing (fun n : Thing => Necessary n)","H : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nx : Thing\nH0 : Exists x\nH1 : forall (x0 : Thing) (_ : (fun y : Thing => Gives y x) x0), False\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\n============================\nGives x x","H : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nx : Thing\nH0 : Exists x\nH1 : forall (x0 : Thing) (_ : (fun y : Thing => Gives y x) x0), False\nX : Prop\nX0 : Prop\n============================\nforall _ : Prop, Gives x x","H : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nx : Thing\nH0 : Exists x\nH1 : forall (x0 : Thing) (_ : (fun y : Thing => Gives y x) x0), False\nX : Prop\nX0 : Prop\nHs : not (Gives x x)\nX1 : Prop\nX2 : Prop\n============================\nEss x","H : forall _ : Pilot.MP003, Pilot.MP008\nMP002 : MP001\nMP003 : Pilot.MP002\nMP008 : Pilot.MP003\nMP012 : Pilot.MP008\n============================\nforall (_ : MP009) (_ : MP010) (_ : MP011) (_ : Pilot.MP012) (_ : SP001), @ex Thing (fun n : Thing => Necessary n)","H : forall _ : Pilot.MP003, Pilot.MP008\nMP002 : MP001\nMP003 : Pilot.MP002\nMP008 : Pilot.MP003\nMP012 : Pilot.MP008\nSP001 : MP009\n============================\nforall (_ : MP009) (_ : MP010) (_ : MP011) (_ : Pilot.MP012) (_ : Pilot.SP001), @ex Thing (fun n : Thing => Necessary n)","H : forall _ : Pilot.MP003, Pilot.MP008\nMP002 : MP001\nMP003 : Pilot.MP002\nMP008 : Pilot.MP003\nMP012 : Pilot.MP008\nSP001 : MP009\nSP002 : MP010\nSP003 : MP011\n============================\nforall (_ : Pilot.MP012) (_ : Pilot.SP001), @ex Thing (fun n : Thing => Necessary n)","H : forall _ : Pilot.MP003, Pilot.MP008\nMP002 : MP001\nMP003 : Pilot.MP002\nMP008 : Pilot.MP003\nMP012 : Pilot.MP008\nSP001 : MP009\nMP010 : Pilot.MP010\nMP011 : Pilot.MP011\nHP : Pilot.MP012\nSH : Pilot.SP001\n============================\n@ex Thing (fun n : Thing => Necessary n)","H : forall _ : Pilot.MP003, Pilot.MP008\nMP001 : Pilot.MP001\nMP002 : Pilot.MP002\nMP003 : Pilot.MP003\nMP008 : Pilot.MP008\nSP001 : MP009\nSP002 : MP010\nSP003 : MP011\n============================\nforall (_ : MP012) (_ : Pilot.SP001), @ex Thing (fun n : Thing => Necessary n)","H : forall _ : Pilot.MP003, Pilot.MP008\nMP001 : Pilot.MP001\nMP002 : Pilot.MP002\nMP003 : Pilot.MP003\nMP008 : Pilot.MP008\n============================\nforall (_ : MP009) (_ : MP010) (_ : MP011) (_ : MP012) (_ : SP001), @ex Thing (fun n : Thing => Necessary n)","H : forall _ : Pilot.MP003, Pilot.MP008\nMP001 : Pilot.MP001\nMP002 : Pilot.MP002\nMP003 : Pilot.MP003\nMP008 : Pilot.MP008\nSP001 : MP009\n============================\nforall (_ : MP009) (_ : MP010) (_ : MP011) (_ : MP012) (_ : Pilot.SP001), @ex Thing (fun n : Thing => Necessary n)","H : forall _ : Pilot.MP003, Pilot.MP008\nMP002 : Pilot.MP002\nMP003 : Pilot.MP003\nMP008 : Pilot.MP008\nSP001 : MP009\n============================\nforall (_ : MP001) (_ : MP010) (_ : MP011) (_ : MP012) (_ : Pilot.SP001), @ex Thing (fun n : Thing => Necessary n)","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP008\nH4 : MP010\nH5 : MP011\nH6 : MP012\nx : Thing\nH7 : Exists x\nH3 : forall (x : Thing) (_ : (fun p : Thing => Possible p) x), @ex Thing (fun A : Thing => and (AggregateOfPossibles A) (Exists A))\nH8 : forall (x : Thing) (_ : (fun x0 : Thing => Necessary x0) x), False\nX : Prop\nX0 : Prop\n============================\n@ex Thing (fun n : Thing => Necessary n)","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (x : Thing) (_ : Exists x) (_ : not (ThroughAnother x)), Ess x\nH4 : forall (A : Thing) (_ : @ex Thing (fun p : Thing => MemberOf p A)) (_ : forall (p : Thing) (_ : MemberOf p A), not (Ess p)), not (Ess A)\nH5 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nH6 : forall (y x : Thing) (_ : Gives y x), Exists y\nx : Thing\nH7 : Exists x\nH3 : forall (x : Thing) (_ : and (Exists x) (not (Ess x))), @ex Thing (fun A : Thing => and (and (forall (p : Thing) (_ : not (@eq Thing p A)), iff (MemberOf p A) (Possible p)) (not (MemberOf A A))) (Exists A))\nH8 : forall (x : Thing) (_ : and (Exists x) (Ess x)), False\nX : Prop\nX0 : Prop\n============================\n@ex Thing (fun n : Thing => and (Exists n) (Ess n))","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP008\nH4 : MP010\nH5 : MP011\nH6 : MP012\nx : Thing\nH7 : Exists x\nH3 : forall (x : Thing) (_ : (fun p : Thing => Possible p) x), @ex Thing (fun A : Thing => and (AggregateOfPossibles A) (Exists A))\nH8 : forall (x : Thing) (_ : (fun x0 : Thing => Necessary x0) x), False\nX : Prop\n============================\nNecessary x","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP008\nH4 : MP010\nH5 : MP011\nH6 : MP012\nx : Thing\nH7 : Exists x\nH3 : forall (x : Thing) (_ : (fun p : Thing => Possible p) x), @ex Thing (fun A : Thing => and (AggregateOfPossibles A) (Exists A))\nH8 : forall (x : Thing) (_ : (fun x0 : Thing => Necessary x0) x), False\nX : Prop\n============================\nExists x","H : MP001\nH0 : MP002\nH1 : MP003\nH2 : MP008\nH4 : MP010\nH5 : MP011\nH6 : MP012\nx : Thing\nH7 : Exists x\nH3 : forall (x : Thing) (_ : (fun p : Thing => Possible p) x), @ex Thing (fun A : Thing => and (AggregateOfPossibles A) (Exists A))\nH8 : forall (x : Thing) (_ : (fun x0 : Thing => Necessary x0) x), False\nX : Prop\n============================\nEss x","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (x : Thing) (_ : Exists x) (_ : not (ThroughAnother x)), Ess x\nH4 : forall (A : Thing) (_ : @ex Thing (fun p : Thing => MemberOf p A)) (_ : forall (p : Thing) (_ : MemberOf p A), not (Ess p)), not (Ess A)\nH5 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nH6 : forall (y x : Thing) (_ : Gives y x), Exists y\nx : Thing\nH7 : Exists x\nH3 : forall (x : Thing) (_ : (fun p : Thing => Possible p) x), @ex Thing (fun A : Thing => and (AggregateOfPossibles A) (Exists A))\nH8 : forall (x : Thing) (_ : (fun x0 : Thing => and (Exists x0) (Ess x0)) x), False\nX : Prop\nX0 : Prop\n============================\n@ex Thing (fun n : Thing => and (Exists n) (Ess n))","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (x : Thing) (_ : Exists x) (_ : not (@ex Thing (fun y : Thing => Gives y x))), Ess x\nH4 : forall (A : Thing) (_ : @ex Thing (fun p : Thing => MemberOf p A)) (_ : forall (p : Thing) (_ : MemberOf p A), not (Ess p)), not (Ess A)\nH5 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nH6 : forall (y x : Thing) (_ : Gives y x), Exists y\nx : Thing\nH7 : Exists x\nH3 : forall (x : Thing) (_ : and (Exists x) (not (Ess x))), @ex Thing (fun A : Thing => and (and (forall (p : Thing) (_ : not (@eq Thing p A)), iff (MemberOf p A) (Possible p)) (not (MemberOf A A))) (Exists A))\nH8 : forall (x : Thing) (_ : and (Exists x) (Ess x)), False\nX : Prop\nX0 : Prop\n============================\n@ex Thing (fun n : Thing => and (Exists n) (Ess n))","H : forall (x y : Thing) (_ : Gives y x), not (Through y x)\nH0 : forall (x y : Thing) (_ : Gives y x), Through x y\nH1 : forall (x y z : Thing) (_ : Through x y) (_ : Through y z), Through x z\nH2 : forall (x : Thing) (_ : Exists x) (_ : not (ThroughAnother x)), Ess x\nH4 : forall (A : Thing) (_ : @ex Thing (fun p : Thing => MemberOf p A)) (_ : forall (p : Thing) (_ : MemberOf p A), not (Ess p)), not (Ess A)\nH5 : forall (c A p : Thing) (_ : Gives c A) (_ : MemberOf p A), clos_trans Thing Gives c p\nH6 : forall (y x : Thing) (_ : Gives y x), Exists y\nx : Thing\nH7 : Exists x\nH3 : forall (x : Thing) (_ : (fun p : Thing => Possible p) x), @ex Thing (fun A : Thing => and (AggregateOfPossibles A) (Exists A))\nH8 : forall (x : Thing) (_ : (fun x0 : Thing => and (Exists x0) 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[Hs|Hs]","w":"model","ok":false,"err":"Error: The variable "},{"g":17,"t":"generalize MP001; clear MP001","w":"model","ok":true,"c":[115]},{"g":72,"t":"assumption","w":"auto","ok":false,"err":"Error: No such assumption."},{"g":72,"t":"tauto","w":"auto","ok":false,"err":"Error: Tactic failure: Classical tauto failed."},{"g":72,"t":"firstorder","w":"auto","ok":true,"c":[116]},{"g":72,"t":"congruence","w":"auto","ok":false,"err":"Error: Tactic failure: congruence failed."},{"g":72,"t":"unfold Necessary, Possible, MP001, MP002, MP003, MP008, AggregateOfPossibles, MP010, MP011, MP012 in *; firstorder","w":"auto","ok":true,"c":[117]},{"g":72,"t":"unfold Necessary, Possible, MP001, MP002, MP003, MP008, AggregateOfPossibles, MP010, MP011, MP012 in *; hammer","w":"hammer","ok":false,"err":"Error: Hammer failed: ATPs failed to f"},{"g":72,"t":"exists x","w":"model","ok":true,"c":[118]},{"g":72,"t":"exists x; assumption","w":"model","ok":false,"err":"Error: No such assumption."},{"g":72,"t":"exists H5","w":"model","ok":false,"err":"rejected"},{"g":72,"t":"exists H6","w":"model","ok":false,"err":"rejected"},{"g":72,"t":"exists H","w":"model","ok":false,"err":"rejected"},{"g":72,"t":"apply H8","w":"model","ok":false,"err":"rejected"},{"g":72,"t":"exists x; split","w":"model","ok":true,"c":[119,120]},{"g":119,"t":"assumption","w":"auto","ok":true,"c":[],"eager":true},{"g":72,"t":"apply H8; assumption","w":"model","ok":false,"err":"rejected"},{"g":73,"t":"assumption","w":"auto","ok":false,"err":"Error: No such assumption."},{"g":73,"t":"tauto","w":"auto","ok":false,"err":"Error: Tactic failure: Classical tauto failed."},{"g":73,"t":"firstorder","w":"auto","ok":true,"c":[121]},{"g":73,"t":"congruence","w":"auto","ok":false,"err":"Error: Tactic failure: congruence failed."},{"g":73,"t":"unfold ThroughAnother, Possible, AggregateOfPossibles in *; firstorder","w":"auto","ok":true,"c":[122]},{"g":73,"t":"unfold ThroughAnother, Possible, AggregateOfPossibles in *; hammer","w":"hammer","ok":false,"err":"Error: Hammer failed: ATPs failed to f"},{"g":73,"t":"exists x","w":"model","ok":true,"c":[123]},{"g":73,"t":"exists x; split","w":"model","ok":true,"c":[124,125]},{"g":124,"t":"assumption","w":"auto","ok":true,"c":[],"eager":true},{"g":73,"t":"apply H8","w":"model","ok":false,"err":"rejected"},{"g":73,"t":"generalize H8","w":"model","ok":true,"c":[126]}],"proof":[],"proofFile":null},{"key":"round4/imkan_b_necessary_exists","id":"imkan_b_necessary_exists","run":"round4","title":"Dalīl al-imkān, conclusion (shorter route)","english":"A Necessary Existent exists.","stmt":"MP008 -> OP001 -> SP001 -> exists n, Necessary n","proved":true,"script":"(unfold Necessary, MP008, OP001, SP001 in *; firstorder). { (unfold ThroughAnother, OfItself in *; firstorder). { (destruct (classic (exists y : Thing, Gives y x)) as [Hs|Hs]). { (unfold ThroughAnother in *; fcrush). } { (firstorder). } } }","seconds":303.5,"expansions":6,"calls":296,"root":0,"goals":["============================\nMP008 -> OP001 -> SP001 -> exists n, Necessary n","H : MP008\nH0 : OP001\nx : Thing\nH1 : Exists x\nX : Prop\nX0 : Prop\n============================\n@ex Thing (fun n : Thing => Necessary n)","H : forall (x : Thing) (_ : Exists x) (_ : not (ThroughAnother x)), Ess x\nH0 : forall (x y : Thing) (_ : Gives y x), OfItself y\nx : Thing\nH1 : Exists x\nX : Prop\nX0 : Prop\n============================\n@ex Thing (fun n : Thing => and (Exists n) (Ess n))","H : not (forall (_ : MP008) (_ : OP001) (_ : SP001), @ex Thing (fun n : Thing => Necessary n))\n============================\nFalse","H : MP008\nH0 : OP001\nx : Thing\nH1 : Exists x\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\n============================\n@ex Thing (fun n : Thing => Necessary n)","H : forall (x : Thing) (_ : Exists x) (_ : not (ThroughAnother x)), Ess x\nH0 : forall (x y : Thing) (_ : Gives y x), OfItself y\nx : Thing\nH1 : Exists x\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\n============================\n@ex Thing (fun n : Thing => and (Exists n) (Ess n))","H : MP008\nH0 : OP001\nx : Thing\nH1 : Exists x\nX : Prop\nX0 : Prop\n============================\nNecessary x","H : MP008\nH0 : OP001\nx : Thing\nH1 : Exists x\nX : Prop\nX0 : Prop\n============================\nExists x","H : MP008\nH0 : OP001\nx : Thing\nH1 : Exists x\nX : Prop\nX0 : Prop\n============================\nEss x","H : forall (x : Thing) (_ : Exists x) (_ : not (@ex Thing (fun y : Thing => Gives y x))), Ess x\nH0 : forall (x y : Thing) (_ : Gives y x), and (Exists y) (not (ThroughAnother y))\nx : Thing\nH1 : Exists x\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\n============================\n@ex Thing (fun n : Thing => and (Exists n) (Ess n))","H : forall (x : Thing) (_ : Exists x) (_ : not (ThroughAnother x)), Ess x\nH0 : forall (x y : Thing) (_ : Gives y x), OfItself y\nx : Thing\nH1 : Exists x\nX : Prop\nX0 : Prop\n============================\nand (Exists x) (Ess x)","H : forall (x : Thing) (_ : Exists x) (_ : not (ThroughAnother x)), Ess x\nH0 : forall (x y : Thing) (_ : Gives y x), OfItself y\nx : Thing\nH1 : Exists x\nX : Prop\nX0 : Prop\n============================\nExists x","H : forall (x : Thing) (_ : Exists x) (_ : not (ThroughAnother x)), Ess x\nH0 : forall (x y : Thing) (_ : Gives y x), OfItself y\nx : Thing\nH1 : Exists x\nX : Prop\nX0 : Prop\n============================\nEss x","H : forall (x : Thing) (_ : Exists x) (_ : not (ThroughAnother x)), Ess x\nH0 : forall (x y : Thing) (_ : Gives y x), OfItself y\nx : Thing\nH1 : Exists x\nX : Prop\nX0 : Prop\nH2 : not (@ex Thing (fun n : Thing => and (Exists n) (Ess n)))\n============================\nFalse","H : forall (x : Thing) (_ : Exists x) (_ : not (ThroughAnother x)), Ess x\nH0 : forall (x y : Thing) (_ : Gives y x), OfItself y\nx : Thing\nH1 : Exists x\nX : Prop\nX0 : Prop\nH2 : Exists x\n============================\n@ex Thing (fun n : Thing => and (Exists n) (Ess n))","H : forall (x : Thing) (_ : Exists x) (_ : not (ThroughAnother x)), Ess x\nH0 : forall (x y : Thing) (_ : Gives y x), OfItself y\nx : Thing\nH1 : Exists x\nX : Prop\nX0 : Prop\nHs : Exists x\n============================\n@ex Thing (fun n : Thing => and (Exists n) (Ess n))","H : forall (x : Thing) (_ : Exists x) (_ : not (ThroughAnother x)), Ess x\nH0 : forall (x y : Thing) (_ : Gives y x), OfItself y\nx : Thing\nH1 : Exists x\nX : Prop\nX0 : Prop\nHs : not (Exists x)\n============================\n@ex Thing (fun n : Thing => and (Exists n) (Ess n))","H : MP008\nH0 : OP001\nx : Thing\nH1 : Exists x\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\n============================\n@ex Thing (fun n : Thing => Necessary n)","H : forall (x : Thing) (_ : Exists x) (_ : not (ThroughAnother x)), Ess x\nH0 : forall (x y : Thing) (_ : Gives y x), OfItself y\nx : Thing\nH1 : Exists x\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\n============================\n@ex Thing (fun n : Thing => and (Exists n) (Ess n))","H : MP008\nH0 : OP001\nx : Thing\nH1 : Exists x\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\n============================\nNecessary x","H : MP008\nH0 : OP001\nx : Thing\nH1 : Exists x\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\n============================\nExists x","H : MP008\nH0 : OP001\nx : Thing\nH1 : Exists x\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\n============================\nEss x","H : forall (x : Thing) (_ : Exists x) (_ : not (@ex Thing (fun y : Thing => Gives y x))), Ess x\nH0 : forall (x y : Thing) (_ : Gives y x), and (Exists y) (not (ThroughAnother y))\nx : Thing\nH1 : Exists x\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\n============================\n@ex Thing (fun n : Thing => and (Exists n) (Ess n))","H : forall (x : Thing) (_ : Exists x) (_ : not (ThroughAnother x)), Ess x\nH0 : forall (x y : Thing) (_ : Gives y x), OfItself y\nx : Thing\nH1 : Exists x\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\n============================\nand (Exists x) (Ess x)","H : forall (x : Thing) (_ : Exists x) (_ : not (ThroughAnother x)), Ess x\nH0 : forall (x y : Thing) (_ : Gives y x), OfItself y\nx : Thing\nH1 : Exists x\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\n============================\nExists x","H : forall (x : Thing) (_ : Exists x) (_ : not (ThroughAnother x)), Ess x\nH0 : forall (x y : Thing) (_ : Gives y x), OfItself y\nx : Thing\nH1 : Exists x\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\n============================\nEss x","H : forall (x : Thing) (_ : Exists x) (_ : not (ThroughAnother x)), Ess x\nH0 : forall (x y : Thing) (_ : Gives y x), OfItself y\nx : Thing\nH1 : Exists x\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nH2 : Exists x\n============================\n@ex Thing (fun n : Thing => and (Exists n) (Ess n))","H : forall (x : Thing) (_ : Exists x) (_ : not (ThroughAnother x)), Ess x\nH0 : forall (x y : Thing) (_ : Gives y x), OfItself y\nx : Thing\nH1 : Exists x\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nHs : Exists x\n============================\n@ex Thing (fun n : Thing => and (Exists n) (Ess n))","H : forall (x : Thing) (_ : Exists x) (_ : not (ThroughAnother x)), Ess x\nH0 : forall (x y : Thing) (_ : Gives y x), OfItself y\nx : Thing\nH1 : Exists x\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nHs : not (Exists x)\n============================\n@ex Thing (fun n : Thing => and (Exists n) (Ess n))","H : forall (x : Thing) (_ : Exists x) (_ : not (ThroughAnother x)), Ess x\nH0 : forall (x y : Thing) (_ : Gives y x), OfItself y\nx : Thing\nH1 : Exists x\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nH2 : not (@ex Thing (fun n : Thing => and (Exists n) (Ess n)))\n============================\nFalse","H : forall (x : Thing) (_ : Exists x) (_ : not (@ex Thing (fun y : Thing => Gives y x))), Ess x\nH0 : forall (x y : Thing) (_ : Gives y x), and (Exists y) (not (@ex Thing (fun y0 : Thing => Gives y0 y)))\nx : Thing\nH1 : Exists x\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nX3 : Prop\nX4 : Prop\n============================\n@ex Thing (fun n : Thing => and (Exists n) (Ess n))","H : forall (x : Thing) (_ : Exists x) (_ : not (@ex Thing (fun y : Thing => Gives y x))), Ess x\nH0 : forall (x y : Thing) (_ : Gives y x), and (Exists y) (not (ThroughAnother y))\nx : Thing\nH1 : Exists x\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\n============================\nand (Exists x) (Ess x)","H : forall (x : Thing) (_ : Exists x) (_ : not (@ex Thing (fun y : Thing => Gives y x))), Ess x\nH0 : forall (x y : Thing) (_ : Gives y x), and (Exists y) (not (ThroughAnother y))\nx : Thing\nH1 : Exists x\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\n============================\nExists x","H : forall (x : Thing) (_ : Exists x) (_ : not (@ex Thing (fun y : Thing => Gives y x))), Ess x\nH0 : forall (x y : Thing) (_ : Gives y x), and (Exists y) (not (ThroughAnother y))\nx : Thing\nH1 : Exists x\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\n============================\nEss x","H : forall (x : Thing) (_ : Exists x) (_ : not (@ex Thing (fun y : Thing => Gives y x))), Ess x\nH0 : forall (x y : Thing) (_ : Gives y x), and (Exists y) (not (ThroughAnother y))\nx : Thing\nH1 : Exists x\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nH2 : Exists x\n============================\n@ex Thing (fun n : Thing => and (Exists n) (Ess n))","H : forall (x : Thing) (_ : Exists x) (_ : not (@ex Thing (fun y : Thing => Gives y x))), Ess x\nH0 : forall (x y : Thing) (_ : Gives y x), and (Exists y) (not (ThroughAnother y))\nx : Thing\nH1 : Exists x\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nHs : Exists x\n============================\n@ex Thing (fun n : Thing => and (Exists n) (Ess n))","H : forall (x : Thing) (_ : Exists x) (_ : not (@ex Thing (fun y : Thing => Gives y x))), Ess x\nH0 : forall (x y : Thing) (_ : Gives y x), and (Exists y) (not (ThroughAnother y))\nx : Thing\nH1 : Exists x\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nHs : not (Exists x)\n============================\n@ex Thing (fun n : Thing => and (Exists n) (Ess n))","H : forall (x : Thing) (_ : Exists x) (_ : not (@ex Thing (fun y : Thing => Gives y x))), Ess x\nH0 : forall (x y : Thing) (_ : Gives y x), and (Exists y) (not (ThroughAnother y))\nx : Thing\nH1 : Exists x\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\n============================\n@ex Thing (fun y : Thing => Gives y x)","H : forall (x : Thing) (_ : Exists x) (_ : not (@ex Thing (fun y : Thing => Gives y x))), Ess x\nH0 : forall (x y : Thing) (_ : Gives y x), and (Exists y) (not (ThroughAnother y))\nx : Thing\nH1 : Exists x\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nH2 : @ex Thing (fun y : Thing => Gives y x)\n============================\n@ex Thing (fun n : Thing => and (Exists n) (Ess n))","H : forall (x : Thing) (_ : Exists x) (_ : not (@ex Thing (fun y : Thing => Gives y x))), Ess x\nH0 : forall (x y : Thing) (_ : Gives y x), and (Exists y) (not (ThroughAnother y))\nx : Thing\nH1 : Exists x\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nHs : @ex Thing (fun y : Thing => Gives y x)\n============================\n@ex Thing (fun n : Thing => and (Exists n) (Ess n))","H : forall (x : Thing) (_ : Exists x) (_ : not (@ex Thing (fun y : Thing => Gives y x))), Ess x\nH0 : forall (x y : Thing) (_ : Gives y x), and (Exists y) (not (ThroughAnother y))\nx : Thing\nH1 : Exists x\nX : Prop\nX0 : Prop\nX1 : Prop\nX2 : Prop\nHs : not (@ex Thing (fun y : Thing => Gives y x))\n============================\n@ex Thing (fun n : Thing => and (Exists n) (Ess n))"],"events":[{"g":0,"t":"assumption","w":"auto","ok":false,"err":"Error: No such assumption."},{"g":0,"t":"tauto","w":"auto","ok":false,"err":"Error: Tactic failure: Classical tauto failed."},{"g":0,"t":"firstorder","w":"auto","ok":true,"c":[1]},{"g":0,"t":"congruence","w":"auto","ok":false,"err":"Error: Tactic failure: congruence failed."},{"g":0,"t":"unfold Necessary, MP008, OP001, SP001 in *; firstorder","w":"auto","ok":true,"c":[2]},{"g":0,"t":"unfold Necessary, MP008, OP001, SP001 in *; hammer","w":"hammer","ok":false,"err":"rejected"},{"g":0,"t":"apply NNPP; intro","w":"model","ok":true,"c":[3]},{"g":0,"t":"right","w":"model","ok":false,"err":"Error: Not an inductive goal with 2 constructors."},{"g":0,"t":"split","w":"model","ok":false,"err":"Error: Unable to find an instance for the variable x."},{"g":0,"t":"exists 1","w":"model","ok":false,"err":"rejected"},{"g":0,"t":"left","w":"model","ok":false,"err":"Error: Not an inductive goal with 2 constructors."},{"g":0,"t":"exists 2","w":"model","ok":false,"err":"rejected"},{"g":0,"t":"exists 1; trivial","w":"model","ok":false,"err":"rejected"},{"g":0,"t":"exists 1; assumption","w":"model","ok":false,"err":"rejected"},{"g":1,"t":"assumption","w":"auto","ok":false,"err":"Error: No such assumption."},{"g":1,"t":"tauto","w":"auto","ok":false,"err":"Error: Tactic failure: Classical tauto failed."},{"g":1,"t":"firstorder","w":"auto","ok":true,"c":[4]},{"g":1,"t":"congruence","w":"auto","ok":false,"err":"Error: Tactic failure: congruence failed."},{"g":1,"t":"unfold Necessary, MP008, OP001 in *; firstorder","w":"auto","ok":true,"c":[5]},{"g":1,"t":"unfold Necessary, MP008, OP001 in *; hammer","w":"hammer","ok":false,"err":"rejected"},{"g":1,"t":"exists x","w":"model","ok":true,"c":[6]},{"g":1,"t":"exists x; assumption","w":"model","ok":false,"err":"Error: No such assumption."},{"g":1,"t":"exists x; trivial","w":"model","ok":true,"c":[6]},{"g":1,"t":"exists x; constructor","w":"model","ok":true,"c":[7,8]},{"g":7,"t":"assumption","w":"auto","ok":true,"c":[],"eager":true},{"g":1,"t":"exists x; split; trivial","w":"model","ok":true,"c":[8]},{"g":1,"t":"exists x; constructor; trivial","w":"model","ok":true,"c":[8]},{"g":2,"t":"assumption","w":"auto","ok":false,"err":"Error: No such assumption."},{"g":2,"t":"tauto","w":"auto","ok":false,"err":"Error: Tactic failure: Classical tauto failed."},{"g":2,"t":"firstorder","w":"auto","ok":true,"c":[5]},{"g":2,"t":"congruence","w":"auto","ok":false,"err":"Error: Tactic failure: congruence failed."},{"g":2,"t":"unfold ThroughAnother, OfItself in *; firstorder","w":"auto","ok":true,"c":[9]},{"g":2,"t":"unfold ThroughAnother, OfItself in *; hammer","w":"hammer","ok":false,"err":"rejected"},{"g":2,"t":"exists x","w":"model","ok":true,"c":[10]},{"g":2,"t":"exists x; split","w":"model","ok":true,"c":[11,12]},{"g":11,"t":"assumption","w":"auto","ok":true,"c":[],"eager":true},{"g":2,"t":"exists x; split; trivial","w":"model","ok":true,"c":[12]},{"g":2,"t":"apply NNPP; intro","w":"model","ok":true,"c":[13]},{"g":2,"t":"assert (Exists x)","w":"model","ok":true,"c":[11,14]},{"g":2,"t":"destruct (classic (Exists x)) as [Hs|Hs]","w":"model","ok":true,"c":[15,16]},{"g":16,"t":"tauto","w":"auto","ok":true,"c":[],"eager":true},{"g":2,"t":"exists x; split; assumption","w":"model","ok":false,"err":"Error: No such assumption."},{"g":2,"t":"exists x; split; [ assumption | idtac ]","w":"model","ok":true,"c":[12]},{"g":2,"t":"exists x; split; [ exists x | idtac ]","w":"model","ok":false,"err":"Error: Not an ind"},{"g":4,"t":"assumption","w":"auto","ok":false,"err":"Error: No such assumption."},{"g":4,"t":"tauto","w":"auto","ok":false,"err":"Error: Tactic failure: Classical tauto failed."},{"g":4,"t":"firstorder","w":"auto","ok":true,"c":[17]},{"g":4,"t":"congruence","w":"auto","ok":false,"err":"Error: Tactic failure: congruence failed."},{"g":4,"t":"unfold Necessary, MP008, OP001 in *; firstorder","w":"auto","ok":true,"c":[18]},{"g":4,"t":"unfold Necessary, MP008, OP001 in *; hammer","w":"hammer","ok":false,"err":"rejected"},{"g":4,"t":"exists x","w":"model","ok":true,"c":[19]},{"g":4,"t":"exists x; assumption","w":"model","ok":false,"err":"Error: No such assumption."},{"g":4,"t":"exists x; trivial","w":"model","ok":true,"c":[19]},{"g":4,"t":"exists x; 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