% Leo-III cross-check.
% PR-011, broader definition: MP-008 and OP-006 give something caused in the universe.
% Vocabulary.  Nothing is assumed about these symbols.
thf(ex_type, type, ex: $i > $o).                     % (ex @ X): X exists
thf(ess_type, type, ess: $i > $o).                   % (ess @ X): X's existence is from its nature
thf(gives_type, type, gives: $i > $i > $o).          % (gives @ Y @ X): Y gives existence to X
thf(nec_type, type, nec: $i > $o).
thf(poss_type, type, poss: $i > $o).
thf(ta_type, type, through_another: $i > $o).
thf(nec_def, definition, nec = (^[X:$i]: ((ex @ X) & (ess @ X)))).            % necessary in itself
thf(poss_def, definition, poss = (^[X:$i]: ((ex @ X) & ~ (ess @ X)))).        % possible in itself
thf(ta_def, definition, through_another = (^[X:$i]: ?[Y:$i]: (gives @ Y @ X))). % something gives X existence
thf(part_type, type, part: $i > $i > $o).            % (part @ P @ U): P is a part of U
thf(u_type, type, u: $i).                            % the universe
thf(mp008, axiom, ![X:$i]: (((ex @ X) & ~ (through_another @ X)) => (ess @ X))).   % MP-008
thf(op006, axiom, ?[X:$i]: (((X = u) | (part @ X @ u)) & (poss @ X))).                  % OP-006
thf(conclusion, conjecture, ?[X:$i]: (((X = u) | (part @ X @ u)) & (poss @ X) & (through_another @ X))).