%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET091+1 : TPTP v9.0.0. Bugfixed v7.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n005.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 0.16s 0.36s
% Output : Proof 0.16s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SET091+1 : TPTP v9.0.0. Bugfixed v7.3.0.
% 0.06/0.11 % Command : run_E %s %d THM
% 0.11/0.30 % Computer : n005.cluster.edu
% 0.11/0.30 % Model : x86_64 x86_64
% 0.11/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.30 % Memory : 8042.1875MB
% 0.11/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.30 % CPULimit : 300
% 0.11/0.30 % WCLimit : 300
% 0.11/0.30 % DateTime : Fri Jun 20 04:14:50 EDT 2025
% 0.11/0.30 % CPUTime :
% 0.16/0.36 % SZS status Theorem
% 0.16/0.36 % SZS output start Proof
% 0.16/0.36 tff(singleton_type, type, (
% 0.16/0.36 singleton: $i > $i)).
% 0.16/0.36 tff(member_of_type, type, (
% 0.16/0.36 member_of: $i > $i)).
% 0.16/0.36 tff(tptp_fun_U_7_type, type, (
% 0.16/0.36 tptp_fun_U_7: $i)).
% 0.16/0.36 tff(member_type, type, (
% 0.16/0.36 member: ( $i * $i ) > $o)).
% 0.16/0.36 tff(universal_class_type, type, (
% 0.16/0.36 universal_class: $i)).
% 0.16/0.36 tff(1,plain,
% 0.16/0.36 (((~(member_of(U!7) = U!7)) & ![Y: $i] : (~(member(Y, universal_class) & (U!7 = singleton(Y))))) <=> ((~(member_of(U!7) = U!7)) & ![Y: $i] : (~(member(Y, universal_class) & (U!7 = singleton(Y)))))),
% 0.16/0.36 inference(rewrite,[status(thm)],[])).
% 0.16/0.36 tff(2,plain,
% 0.16/0.36 ((~![U: $i] : ((member_of(U) = U) | ?[Y: $i] : (member(Y, universal_class) & (U = singleton(Y))))) <=> (~![U: $i] : ((member_of(U) = U) | ?[Y: $i] : (member(Y, universal_class) & (U = singleton(Y)))))),
% 0.16/0.36 inference(rewrite,[status(thm)],[])).
% 0.16/0.36 tff(3,plain,
% 0.16/0.36 ((~![X: $i, U: $i] : (((~?[Y: $i] : (member(Y, universal_class) & (X = singleton(Y)))) & (X = U)) => (member_of(X) = U))) <=> (~![U: $i] : ((member_of(U) = U) | ?[Y: $i] : (member(Y, universal_class) & (U = singleton(Y)))))),
% 0.16/0.36 inference(rewrite,[status(thm)],[])).
% 0.16/0.36 tff(4,axiom,(~![X: $i, U: $i] : (((~?[Y: $i] : (member(Y, universal_class) & (X = singleton(Y)))) & (X = U)) => (member_of(X) = U))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','member_when_not_a_singleton')).
% 0.16/0.36 tff(5,plain,
% 0.16/0.36 (~![U: $i] : ((member_of(U) = U) | ?[Y: $i] : (member(Y, universal_class) & (U = singleton(Y))))),
% 0.16/0.36 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.16/0.36 tff(6,plain,
% 0.16/0.36 (~![U: $i] : ((member_of(U) = U) | ?[Y: $i] : (member(Y, universal_class) & (U = singleton(Y))))),
% 0.16/0.36 inference(modus_ponens,[status(thm)],[5, 2])).
% 0.16/0.36 tff(7,plain,
% 0.16/0.36 (~![U: $i] : ((member_of(U) = U) | ?[Y: $i] : (member(Y, universal_class) & (U = singleton(Y))))),
% 0.16/0.36 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.16/0.36 tff(8,plain,
% 0.16/0.36 (~![U: $i] : ((member_of(U) = U) | ?[Y: $i] : (member(Y, universal_class) & (U = singleton(Y))))),
% 0.16/0.36 inference(modus_ponens,[status(thm)],[7, 2])).
% 0.16/0.36 tff(9,plain,
% 0.16/0.36 ((~(member_of(U!7) = U!7)) & ![Y: $i] : (~(member(Y, universal_class) & (U!7 = singleton(Y))))),
% 0.16/0.36 inference(modus_ponens,[status(thm)],[8, 1])).
% 0.16/0.36 tff(10,plain,
% 0.16/0.36 (~(member_of(U!7) = U!7)),
% 0.16/0.36 inference(and_elim,[status(thm)],[9])).
% 0.16/0.36 tff(11,plain,
% 0.16/0.36 (^[X: $i] : refl(((member_of(X) = X) | (singleton(member_of(X)) = X)) <=> ((member_of(X) = X) | (singleton(member_of(X)) = X)))),
% 0.16/0.36 inference(bind,[status(th)],[])).
% 0.16/0.36 tff(12,plain,
% 0.16/0.36 (![X: $i] : ((member_of(X) = X) | (singleton(member_of(X)) = X)) <=> ![X: $i] : ((member_of(X) = X) | (singleton(member_of(X)) = X))),
% 0.16/0.36 inference(quant_intro,[status(thm)],[11])).
% 0.16/0.36 tff(13,plain,
% 0.16/0.36 (![X: $i] : ((member_of(X) = X) | (singleton(member_of(X)) = X)) <=> ![X: $i] : ((member_of(X) = X) | (singleton(member_of(X)) = X))),
% 0.16/0.36 inference(rewrite,[status(thm)],[])).
% 0.16/0.36 tff(14,plain,
% 0.16/0.36 (^[X: $i] : rewrite(((singleton(member_of(X)) = X) | (member_of(X) = X)) <=> ((member_of(X) = X) | (singleton(member_of(X)) = X)))),
% 0.16/0.36 inference(bind,[status(th)],[])).
% 0.16/0.36 tff(15,plain,
% 0.16/0.36 (![X: $i] : ((singleton(member_of(X)) = X) | (member_of(X) = X)) <=> ![X: $i] : ((member_of(X) = X) | (singleton(member_of(X)) = X))),
% 0.16/0.36 inference(quant_intro,[status(thm)],[14])).
% 0.16/0.36 tff(16,axiom,(![X: $i] : ((singleton(member_of(X)) = X) | (member_of(X) = X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','singleton_self')).
% 0.16/0.36 tff(17,plain,
% 0.16/0.36 (![X: $i] : ((member_of(X) = X) | (singleton(member_of(X)) = X))),
% 0.16/0.36 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.16/0.36 tff(18,plain,
% 0.16/0.36 (![X: $i] : ((member_of(X) = X) | (singleton(member_of(X)) = X))),
% 0.16/0.36 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.16/0.36 tff(19,plain,(
% 0.16/0.36 ![X: $i] : ((member_of(X) = X) | (singleton(member_of(X)) = X))),
% 0.16/0.36 inference(skolemize,[status(sab)],[18])).
% 0.16/0.36 tff(20,plain,
% 0.16/0.36 (![X: $i] : ((member_of(X) = X) | (singleton(member_of(X)) = X))),
% 0.16/0.36 inference(modus_ponens,[status(thm)],[19, 12])).
% 0.16/0.36 tff(21,plain,
% 0.16/0.36 (((~![X: $i] : ((member_of(X) = X) | (singleton(member_of(X)) = X))) | ((member_of(U!7) = U!7) | (singleton(member_of(U!7)) = U!7))) <=> ((~![X: $i] : ((member_of(X) = X) | (singleton(member_of(X)) = X))) | (member_of(U!7) = U!7) | (singleton(member_of(U!7)) = U!7))),
% 0.16/0.36 inference(rewrite,[status(thm)],[])).
% 0.16/0.36 tff(22,plain,
% 0.16/0.36 ((~![X: $i] : ((member_of(X) = X) | (singleton(member_of(X)) = X))) | ((member_of(U!7) = U!7) | (singleton(member_of(U!7)) = U!7))),
% 0.16/0.36 inference(quant_inst,[status(thm)],[])).
% 0.16/0.36 tff(23,plain,
% 0.16/0.36 ((~![X: $i] : ((member_of(X) = X) | (singleton(member_of(X)) = X))) | (member_of(U!7) = U!7) | (singleton(member_of(U!7)) = U!7)),
% 0.16/0.36 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.16/0.36 tff(24,plain,
% 0.16/0.36 (singleton(member_of(U!7)) = U!7),
% 0.16/0.36 inference(unit_resolution,[status(thm)],[23, 20, 10])).
% 0.16/0.36 tff(25,plain,
% 0.16/0.36 (U!7 = singleton(member_of(U!7))),
% 0.16/0.36 inference(symmetry,[status(thm)],[24])).
% 0.16/0.36 tff(26,plain,
% 0.16/0.36 (^[X: $i] : refl(((member_of(X) = X) | member(member_of(X), universal_class)) <=> ((member_of(X) = X) | member(member_of(X), universal_class)))),
% 0.16/0.36 inference(bind,[status(th)],[])).
% 0.16/0.36 tff(27,plain,
% 0.16/0.36 (![X: $i] : ((member_of(X) = X) | member(member_of(X), universal_class)) <=> ![X: $i] : ((member_of(X) = X) | member(member_of(X), universal_class))),
% 0.16/0.36 inference(quant_intro,[status(thm)],[26])).
% 0.16/0.36 tff(28,plain,
% 0.16/0.36 (![X: $i] : ((member_of(X) = X) | member(member_of(X), universal_class)) <=> ![X: $i] : ((member_of(X) = X) | member(member_of(X), universal_class))),
% 0.16/0.36 inference(rewrite,[status(thm)],[])).
% 0.16/0.36 tff(29,plain,
% 0.16/0.36 (^[X: $i] : rewrite((member(member_of(X), universal_class) | (member_of(X) = X)) <=> ((member_of(X) = X) | member(member_of(X), universal_class)))),
% 0.16/0.36 inference(bind,[status(th)],[])).
% 0.16/0.36 tff(30,plain,
% 0.16/0.36 (![X: $i] : (member(member_of(X), universal_class) | (member_of(X) = X)) <=> ![X: $i] : ((member_of(X) = X) | member(member_of(X), universal_class))),
% 0.16/0.36 inference(quant_intro,[status(thm)],[29])).
% 0.16/0.36 tff(31,axiom,(![X: $i] : (member(member_of(X), universal_class) | (member_of(X) = X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','member_universal_self')).
% 0.16/0.36 tff(32,plain,
% 0.16/0.36 (![X: $i] : ((member_of(X) = X) | member(member_of(X), universal_class))),
% 0.16/0.36 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.16/0.36 tff(33,plain,
% 0.16/0.36 (![X: $i] : ((member_of(X) = X) | member(member_of(X), universal_class))),
% 0.16/0.36 inference(modus_ponens,[status(thm)],[32, 28])).
% 0.16/0.36 tff(34,plain,(
% 0.16/0.36 ![X: $i] : ((member_of(X) = X) | member(member_of(X), universal_class))),
% 0.16/0.36 inference(skolemize,[status(sab)],[33])).
% 0.16/0.36 tff(35,plain,
% 0.16/0.36 (![X: $i] : ((member_of(X) = X) | member(member_of(X), universal_class))),
% 0.16/0.36 inference(modus_ponens,[status(thm)],[34, 27])).
% 0.16/0.36 tff(36,plain,
% 0.16/0.36 (((~![X: $i] : ((member_of(X) = X) | member(member_of(X), universal_class))) | ((member_of(U!7) = U!7) | member(member_of(U!7), universal_class))) <=> ((~![X: $i] : ((member_of(X) = X) | member(member_of(X), universal_class))) | (member_of(U!7) = U!7) | member(member_of(U!7), universal_class))),
% 0.16/0.36 inference(rewrite,[status(thm)],[])).
% 0.16/0.36 tff(37,plain,
% 0.16/0.36 ((~![X: $i] : ((member_of(X) = X) | member(member_of(X), universal_class))) | ((member_of(U!7) = U!7) | member(member_of(U!7), universal_class))),
% 0.16/0.36 inference(quant_inst,[status(thm)],[])).
% 0.16/0.36 tff(38,plain,
% 0.16/0.36 ((~![X: $i] : ((member_of(X) = X) | member(member_of(X), universal_class))) | (member_of(U!7) = U!7) | member(member_of(U!7), universal_class)),
% 0.16/0.36 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.16/0.36 tff(39,plain,
% 0.16/0.36 (member(member_of(U!7), universal_class)),
% 0.16/0.36 inference(unit_resolution,[status(thm)],[38, 35, 10])).
% 0.16/0.36 tff(40,plain,
% 0.16/0.36 (^[Y: $i] : refl(((~member(Y, universal_class)) | (~(U!7 = singleton(Y)))) <=> ((~member(Y, universal_class)) | (~(U!7 = singleton(Y)))))),
% 0.16/0.36 inference(bind,[status(th)],[])).
% 0.16/0.36 tff(41,plain,
% 0.16/0.36 (![Y: $i] : ((~member(Y, universal_class)) | (~(U!7 = singleton(Y)))) <=> ![Y: $i] : ((~member(Y, universal_class)) | (~(U!7 = singleton(Y))))),
% 0.16/0.36 inference(quant_intro,[status(thm)],[40])).
% 0.16/0.36 tff(42,plain,
% 0.16/0.36 (^[Y: $i] : trans(monotonicity(rewrite((member(Y, universal_class) & (U!7 = singleton(Y))) <=> (~((~member(Y, universal_class)) | (~(U!7 = singleton(Y)))))), ((~(member(Y, universal_class) & (U!7 = singleton(Y)))) <=> (~(~((~member(Y, universal_class)) | (~(U!7 = singleton(Y)))))))), rewrite((~(~((~member(Y, universal_class)) | (~(U!7 = singleton(Y)))))) <=> ((~member(Y, universal_class)) | (~(U!7 = singleton(Y))))), ((~(member(Y, universal_class) & (U!7 = singleton(Y)))) <=> ((~member(Y, universal_class)) | (~(U!7 = singleton(Y))))))),
% 0.16/0.36 inference(bind,[status(th)],[])).
% 0.16/0.36 tff(43,plain,
% 0.16/0.36 (![Y: $i] : (~(member(Y, universal_class) & (U!7 = singleton(Y)))) <=> ![Y: $i] : ((~member(Y, universal_class)) | (~(U!7 = singleton(Y))))),
% 0.16/0.36 inference(quant_intro,[status(thm)],[42])).
% 0.16/0.36 tff(44,plain,
% 0.16/0.36 (![Y: $i] : (~(member(Y, universal_class) & (U!7 = singleton(Y))))),
% 0.16/0.36 inference(and_elim,[status(thm)],[9])).
% 0.16/0.36 tff(45,plain,
% 0.16/0.36 (![Y: $i] : ((~member(Y, universal_class)) | (~(U!7 = singleton(Y))))),
% 0.16/0.36 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.16/0.36 tff(46,plain,
% 0.16/0.36 (![Y: $i] : ((~member(Y, universal_class)) | (~(U!7 = singleton(Y))))),
% 0.16/0.36 inference(modus_ponens,[status(thm)],[45, 41])).
% 0.16/0.36 tff(47,plain,
% 0.16/0.36 (((~![Y: $i] : ((~member(Y, universal_class)) | (~(U!7 = singleton(Y))))) | ((~member(member_of(U!7), universal_class)) | (~(U!7 = singleton(member_of(U!7)))))) <=> ((~![Y: $i] : ((~member(Y, universal_class)) | (~(U!7 = singleton(Y))))) | (~member(member_of(U!7), universal_class)) | (~(U!7 = singleton(member_of(U!7)))))),
% 0.16/0.36 inference(rewrite,[status(thm)],[])).
% 0.16/0.36 tff(48,plain,
% 0.16/0.36 ((~![Y: $i] : ((~member(Y, universal_class)) | (~(U!7 = singleton(Y))))) | ((~member(member_of(U!7), universal_class)) | (~(U!7 = singleton(member_of(U!7)))))),
% 0.16/0.36 inference(quant_inst,[status(thm)],[])).
% 0.16/0.36 tff(49,plain,
% 0.16/0.36 ((~![Y: $i] : ((~member(Y, universal_class)) | (~(U!7 = singleton(Y))))) | (~member(member_of(U!7), universal_class)) | (~(U!7 = singleton(member_of(U!7))))),
% 0.16/0.36 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.16/0.36 tff(50,plain,
% 0.16/0.36 ($false),
% 0.16/0.36 inference(unit_resolution,[status(thm)],[49, 46, 39, 25])).
% 0.16/0.36 % SZS output end Proof
% 0.16/0.36 % E exiting
%------------------------------------------------------------------------------