%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET093+1 : TPTP v9.0.0. Bugfixed v7.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:25:11 AM UTC 2025
% Result : Theorem 0.21s 0.39s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SET093+1 : TPTP v9.0.0. Bugfixed v7.3.0.
% 0.04/0.12 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n001.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Jun 20 04:20:04 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.21/0.39 % SZS status Theorem
% 0.21/0.39 % SZS output start Proof
% 0.21/0.39 tff(member_type, type, (
% 0.21/0.39 member: ( $i * $i ) > $o)).
% 0.21/0.39 tff(universal_class_type, type, (
% 0.21/0.39 universal_class: $i)).
% 0.21/0.39 tff(unordered_pair_type, type, (
% 0.21/0.39 unordered_pair: ( $i * $i ) > $i)).
% 0.21/0.39 tff(member_of_type, type, (
% 0.21/0.39 member_of: $i > $i)).
% 0.21/0.39 tff(tptp_fun_X_7_type, type, (
% 0.21/0.39 tptp_fun_X_7: $i)).
% 0.21/0.39 tff(singleton_type, type, (
% 0.21/0.39 singleton: $i > $i)).
% 0.21/0.39 tff(1,plain,
% 0.21/0.39 ((~![X: $i] : ((~(singleton(member_of(X)) = X)) | member(X, universal_class))) <=> (~![X: $i] : ((~(singleton(member_of(X)) = X)) | member(X, universal_class)))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(2,plain,
% 0.21/0.39 ((~![X: $i] : ((singleton(member_of(X)) = X) => member(X, universal_class))) <=> (~![X: $i] : ((~(singleton(member_of(X)) = X)) | member(X, universal_class)))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(3,axiom,(~![X: $i] : ((singleton(member_of(X)) = X) => member(X, universal_class))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','corollary_2_to_singletons_are_sets')).
% 0.21/0.39 tff(4,plain,
% 0.21/0.39 (~![X: $i] : ((~(singleton(member_of(X)) = X)) | member(X, universal_class))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.21/0.39 tff(5,plain,
% 0.21/0.39 (~![X: $i] : ((~(singleton(member_of(X)) = X)) | member(X, universal_class))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.21/0.39 tff(6,plain,
% 0.21/0.39 (~![X: $i] : ((~(singleton(member_of(X)) = X)) | member(X, universal_class))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.21/0.39 tff(7,plain,
% 0.21/0.39 (~![X: $i] : ((~(singleton(member_of(X)) = X)) | member(X, universal_class))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.21/0.39 tff(8,plain,(
% 0.21/0.39 ~((~(singleton(member_of(X!7)) = X!7)) | member(X!7, universal_class))),
% 0.21/0.39 inference(skolemize,[status(sab)],[7])).
% 0.21/0.39 tff(9,plain,
% 0.21/0.39 (singleton(member_of(X!7)) = X!7),
% 0.21/0.39 inference(or_elim,[status(thm)],[8])).
% 0.21/0.39 tff(10,plain,
% 0.21/0.39 (^[X: $i] : refl((singleton(X) = unordered_pair(X, X)) <=> (singleton(X) = unordered_pair(X, X)))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(11,plain,
% 0.21/0.39 (![X: $i] : (singleton(X) = unordered_pair(X, X)) <=> ![X: $i] : (singleton(X) = unordered_pair(X, X))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[10])).
% 0.21/0.39 tff(12,plain,
% 0.21/0.39 (![X: $i] : (singleton(X) = unordered_pair(X, X)) <=> ![X: $i] : (singleton(X) = unordered_pair(X, X))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(13,axiom,(![X: $i] : (singleton(X) = unordered_pair(X, X))), file('/export/starexec/sandbox2/benchmark/Axioms/SET005+0.ax','singleton_set_defn')).
% 0.21/0.39 tff(14,plain,
% 0.21/0.39 (![X: $i] : (singleton(X) = unordered_pair(X, X))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.21/0.39 tff(15,plain,(
% 0.21/0.39 ![X: $i] : (singleton(X) = unordered_pair(X, X))),
% 0.21/0.39 inference(skolemize,[status(sab)],[14])).
% 0.21/0.39 tff(16,plain,
% 0.21/0.39 (![X: $i] : (singleton(X) = unordered_pair(X, X))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[15, 11])).
% 0.21/0.39 tff(17,plain,
% 0.21/0.39 ((~![X: $i] : (singleton(X) = unordered_pair(X, X))) | (singleton(member_of(X!7)) = unordered_pair(member_of(X!7), member_of(X!7)))),
% 0.21/0.39 inference(quant_inst,[status(thm)],[])).
% 0.21/0.39 tff(18,plain,
% 0.21/0.39 (singleton(member_of(X!7)) = unordered_pair(member_of(X!7), member_of(X!7))),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.21/0.39 tff(19,plain,
% 0.21/0.39 (unordered_pair(member_of(X!7), member_of(X!7)) = singleton(member_of(X!7))),
% 0.21/0.39 inference(symmetry,[status(thm)],[18])).
% 0.21/0.39 tff(20,plain,
% 0.21/0.39 (unordered_pair(member_of(X!7), member_of(X!7)) = X!7),
% 0.21/0.39 inference(transitivity,[status(thm)],[19, 9])).
% 0.21/0.39 tff(21,plain,
% 0.21/0.39 (member(unordered_pair(member_of(X!7), member_of(X!7)), universal_class) <=> member(X!7, universal_class)),
% 0.21/0.39 inference(monotonicity,[status(thm)],[20])).
% 0.21/0.39 tff(22,plain,
% 0.21/0.39 (member(X!7, universal_class) <=> member(unordered_pair(member_of(X!7), member_of(X!7)), universal_class)),
% 0.21/0.39 inference(symmetry,[status(thm)],[21])).
% 0.21/0.39 tff(23,plain,
% 0.21/0.39 ((~member(X!7, universal_class)) <=> (~member(unordered_pair(member_of(X!7), member_of(X!7)), universal_class))),
% 0.21/0.39 inference(monotonicity,[status(thm)],[22])).
% 0.21/0.39 tff(24,plain,
% 0.21/0.39 (~member(X!7, universal_class)),
% 0.21/0.39 inference(or_elim,[status(thm)],[8])).
% 0.21/0.39 tff(25,plain,
% 0.21/0.39 (~member(unordered_pair(member_of(X!7), member_of(X!7)), universal_class)),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.21/0.39 tff(26,plain,
% 0.21/0.39 (^[X: $i, Y: $i] : refl(member(unordered_pair(X, Y), universal_class) <=> member(unordered_pair(X, Y), universal_class))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(27,plain,
% 0.21/0.39 (![X: $i, Y: $i] : member(unordered_pair(X, Y), universal_class) <=> ![X: $i, Y: $i] : member(unordered_pair(X, Y), universal_class)),
% 0.21/0.39 inference(quant_intro,[status(thm)],[26])).
% 0.21/0.39 tff(28,plain,
% 0.21/0.39 (![X: $i, Y: $i] : member(unordered_pair(X, Y), universal_class) <=> ![X: $i, Y: $i] : member(unordered_pair(X, Y), universal_class)),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(29,axiom,(![X: $i, Y: $i] : member(unordered_pair(X, Y), universal_class)), file('/export/starexec/sandbox2/benchmark/Axioms/SET005+0.ax','unordered_pair')).
% 0.21/0.39 tff(30,plain,
% 0.21/0.39 (![X: $i, Y: $i] : member(unordered_pair(X, Y), universal_class)),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.21/0.39 tff(31,plain,(
% 0.21/0.39 ![X: $i, Y: $i] : member(unordered_pair(X, Y), universal_class)),
% 0.21/0.39 inference(skolemize,[status(sab)],[30])).
% 0.21/0.39 tff(32,plain,
% 0.21/0.39 (![X: $i, Y: $i] : member(unordered_pair(X, Y), universal_class)),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[31, 27])).
% 0.21/0.39 tff(33,plain,
% 0.21/0.39 ((~![X: $i, Y: $i] : member(unordered_pair(X, Y), universal_class)) | member(unordered_pair(member_of(X!7), member_of(X!7)), universal_class)),
% 0.21/0.39 inference(quant_inst,[status(thm)],[])).
% 0.21/0.39 tff(34,plain,
% 0.21/0.39 (member(unordered_pair(member_of(X!7), member_of(X!7)), universal_class)),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[33, 32])).
% 0.21/0.39 tff(35,plain,
% 0.21/0.39 ($false),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[34, 25])).
% 0.21/0.39 % SZS output end Proof
% 0.21/0.40 % E exiting
%------------------------------------------------------------------------------