TSTP Solution File: SET095+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET095+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n014.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 : Tue Sep 20 05:05:36 EDT 2022
% Result : Theorem 0.17s 0.39s
% Output : Proof 0.17s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SET095+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% 0.03/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.10/0.33 % Computer : n014.cluster.edu
% 0.10/0.33 % Model : x86_64 x86_64
% 0.10/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.33 % Memory : 8042.1875MB
% 0.10/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.33 % CPULimit : 300
% 0.10/0.33 % WCLimit : 300
% 0.10/0.33 % DateTime : Sat Sep 3 02:19:00 EDT 2022
% 0.10/0.33 % CPUTime :
% 0.10/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.10/0.33 Usage: tptp [options] [-file:]file
% 0.10/0.33 -h, -? prints this message.
% 0.10/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.10/0.33 -m, -model generate model.
% 0.10/0.33 -p, -proof generate proof.
% 0.10/0.33 -c, -core generate unsat core of named formulas.
% 0.10/0.33 -st, -statistics display statistics.
% 0.10/0.33 -t:timeout set timeout (in second).
% 0.10/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.10/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.10/0.33 -<param>:<value> configuration parameter and value.
% 0.10/0.33 -o:<output-file> file to place output in.
% 0.17/0.39 % SZS status Theorem
% 0.17/0.39 % SZS output start Proof
% 0.17/0.39 tff(member_type, type, (
% 0.17/0.39 member: ( $i * $i ) > $o)).
% 0.17/0.39 tff(tptp_fun_Y_7_type, type, (
% 0.17/0.39 tptp_fun_Y_7: $i)).
% 0.17/0.39 tff(tptp_fun_U_0_type, type, (
% 0.17/0.39 tptp_fun_U_0: ( $i * $i ) > $i)).
% 0.17/0.39 tff(singleton_type, type, (
% 0.17/0.39 singleton: $i > $i)).
% 0.17/0.39 tff(tptp_fun_X_8_type, type, (
% 0.17/0.39 tptp_fun_X_8: $i)).
% 0.17/0.39 tff(universal_class_type, type, (
% 0.17/0.39 universal_class: $i)).
% 0.17/0.39 tff(unordered_pair_type, type, (
% 0.17/0.39 unordered_pair: ( $i * $i ) > $i)).
% 0.17/0.39 tff(subclass_type, type, (
% 0.17/0.39 subclass: ( $i * $i ) > $o)).
% 0.17/0.39 tff(1,plain,
% 0.17/0.39 (^[U: $i, X: $i, Y: $i] : refl((member(U, unordered_pair(X, Y)) <=> (~((~member(U, universal_class)) | (~((U = Y) | (U = X)))))) <=> (member(U, unordered_pair(X, Y)) <=> (~((~member(U, universal_class)) | (~((U = Y) | (U = X)))))))),
% 0.17/0.39 inference(bind,[status(th)],[])).
% 0.17/0.39 tff(2,plain,
% 0.17/0.39 (![U: $i, X: $i, Y: $i] : (member(U, unordered_pair(X, Y)) <=> (~((~member(U, universal_class)) | (~((U = Y) | (U = X)))))) <=> ![U: $i, X: $i, Y: $i] : (member(U, unordered_pair(X, Y)) <=> (~((~member(U, universal_class)) | (~((U = Y) | (U = X))))))),
% 0.17/0.39 inference(quant_intro,[status(thm)],[1])).
% 0.17/0.39 tff(3,plain,
% 0.17/0.39 (^[U: $i, X: $i, Y: $i] : rewrite((member(U, unordered_pair(X, Y)) <=> (member(U, universal_class) & ((U = Y) | (U = X)))) <=> (member(U, unordered_pair(X, Y)) <=> (~((~member(U, universal_class)) | (~((U = Y) | (U = X)))))))),
% 0.17/0.39 inference(bind,[status(th)],[])).
% 0.17/0.39 tff(4,plain,
% 0.17/0.39 (![U: $i, X: $i, Y: $i] : (member(U, unordered_pair(X, Y)) <=> (member(U, universal_class) & ((U = Y) | (U = X)))) <=> ![U: $i, X: $i, Y: $i] : (member(U, unordered_pair(X, Y)) <=> (~((~member(U, universal_class)) | (~((U = Y) | (U = X))))))),
% 0.17/0.39 inference(quant_intro,[status(thm)],[3])).
% 0.17/0.39 tff(5,plain,
% 0.17/0.39 (![U: $i, X: $i, Y: $i] : (member(U, unordered_pair(X, Y)) <=> (member(U, universal_class) & ((U = Y) | (U = X)))) <=> ![U: $i, X: $i, Y: $i] : (member(U, unordered_pair(X, Y)) <=> (member(U, universal_class) & ((U = Y) | (U = X))))),
% 0.17/0.39 inference(rewrite,[status(thm)],[])).
% 0.17/0.39 tff(6,plain,
% 0.17/0.39 (^[U: $i, X: $i, Y: $i] : rewrite((member(U, unordered_pair(X, Y)) <=> (member(U, universal_class) & ((U = X) | (U = Y)))) <=> (member(U, unordered_pair(X, Y)) <=> (member(U, universal_class) & ((U = Y) | (U = X)))))),
% 0.17/0.39 inference(bind,[status(th)],[])).
% 0.17/0.39 tff(7,plain,
% 0.17/0.39 (![U: $i, X: $i, Y: $i] : (member(U, unordered_pair(X, Y)) <=> (member(U, universal_class) & ((U = X) | (U = Y)))) <=> ![U: $i, X: $i, Y: $i] : (member(U, unordered_pair(X, Y)) <=> (member(U, universal_class) & ((U = Y) | (U = X))))),
% 0.17/0.39 inference(quant_intro,[status(thm)],[6])).
% 0.17/0.39 tff(8,axiom,(![U: $i, X: $i, Y: $i] : (member(U, unordered_pair(X, Y)) <=> (member(U, universal_class) & ((U = X) | (U = Y))))), file('/export/starexec/sandbox/benchmark/Axioms/SET005+0.ax','unordered_pair_defn')).
% 0.17/0.39 tff(9,plain,
% 0.17/0.39 (![U: $i, X: $i, Y: $i] : (member(U, unordered_pair(X, Y)) <=> (member(U, universal_class) & ((U = Y) | (U = X))))),
% 0.17/0.39 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.17/0.39 tff(10,plain,
% 0.17/0.39 (![U: $i, X: $i, Y: $i] : (member(U, unordered_pair(X, Y)) <=> (member(U, universal_class) & ((U = Y) | (U = X))))),
% 0.17/0.39 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.17/0.39 tff(11,plain,(
% 0.17/0.39 ![U: $i, X: $i, Y: $i] : (member(U, unordered_pair(X, Y)) <=> (member(U, universal_class) & ((U = Y) | (U = X))))),
% 0.17/0.39 inference(skolemize,[status(sab)],[10])).
% 0.17/0.39 tff(12,plain,
% 0.17/0.39 (![U: $i, X: $i, Y: $i] : (member(U, unordered_pair(X, Y)) <=> (~((~member(U, universal_class)) | (~((U = Y) | (U = X))))))),
% 0.17/0.39 inference(modus_ponens,[status(thm)],[11, 4])).
% 0.17/0.39 tff(13,plain,
% 0.17/0.39 (![U: $i, X: $i, Y: $i] : (member(U, unordered_pair(X, Y)) <=> (~((~member(U, universal_class)) | (~((U = Y) | (U = X))))))),
% 0.17/0.39 inference(modus_ponens,[status(thm)],[12, 2])).
% 0.17/0.39 tff(14,plain,
% 0.17/0.39 (((~![U: $i, X: $i, Y: $i] : (member(U, unordered_pair(X, Y)) <=> (~((~member(U, universal_class)) | (~((U = Y) | (U = X))))))) | (member(tptp_fun_U_0(Y!7, singleton(X!8)), unordered_pair(X!8, X!8)) <=> (~((~member(tptp_fun_U_0(Y!7, singleton(X!8)), universal_class)) | (~(tptp_fun_U_0(Y!7, singleton(X!8)) = X!8)))))) <=> ((~![U: $i, X: $i, Y: $i] : (member(U, unordered_pair(X, Y)) <=> (~((~member(U, universal_class)) | (~((U = Y) | (U = X))))))) | (member(tptp_fun_U_0(Y!7, singleton(X!8)), unordered_pair(X!8, X!8)) <=> (~((~member(tptp_fun_U_0(Y!7, singleton(X!8)), universal_class)) | (~(tptp_fun_U_0(Y!7, singleton(X!8)) = X!8))))))),
% 0.17/0.39 inference(rewrite,[status(thm)],[])).
% 0.17/0.39 tff(15,plain,
% 0.17/0.39 ((member(tptp_fun_U_0(Y!7, singleton(X!8)), unordered_pair(X!8, X!8)) <=> (~((~member(tptp_fun_U_0(Y!7, singleton(X!8)), universal_class)) | (~((tptp_fun_U_0(Y!7, singleton(X!8)) = X!8) | (tptp_fun_U_0(Y!7, singleton(X!8)) = X!8)))))) <=> (member(tptp_fun_U_0(Y!7, singleton(X!8)), unordered_pair(X!8, X!8)) <=> (~((~member(tptp_fun_U_0(Y!7, singleton(X!8)), universal_class)) | (~(tptp_fun_U_0(Y!7, singleton(X!8)) = X!8)))))),
% 0.17/0.39 inference(rewrite,[status(thm)],[])).
% 0.17/0.39 tff(16,plain,
% 0.17/0.39 (((~![U: $i, X: $i, Y: $i] : (member(U, unordered_pair(X, Y)) <=> (~((~member(U, universal_class)) | (~((U = Y) | (U = X))))))) | (member(tptp_fun_U_0(Y!7, singleton(X!8)), unordered_pair(X!8, X!8)) <=> (~((~member(tptp_fun_U_0(Y!7, singleton(X!8)), universal_class)) | (~((tptp_fun_U_0(Y!7, singleton(X!8)) = X!8) | (tptp_fun_U_0(Y!7, singleton(X!8)) = X!8))))))) <=> ((~![U: $i, X: $i, Y: $i] : (member(U, unordered_pair(X, Y)) <=> (~((~member(U, universal_class)) | (~((U = Y) | (U = X))))))) | (member(tptp_fun_U_0(Y!7, singleton(X!8)), unordered_pair(X!8, X!8)) <=> (~((~member(tptp_fun_U_0(Y!7, singleton(X!8)), universal_class)) | (~(tptp_fun_U_0(Y!7, singleton(X!8)) = X!8))))))),
% 0.17/0.39 inference(monotonicity,[status(thm)],[15])).
% 0.17/0.39 tff(17,plain,
% 0.17/0.39 (((~![U: $i, X: $i, Y: $i] : (member(U, unordered_pair(X, Y)) <=> (~((~member(U, universal_class)) | (~((U = Y) | (U = X))))))) | (member(tptp_fun_U_0(Y!7, singleton(X!8)), unordered_pair(X!8, X!8)) <=> (~((~member(tptp_fun_U_0(Y!7, singleton(X!8)), universal_class)) | (~((tptp_fun_U_0(Y!7, singleton(X!8)) = X!8) | (tptp_fun_U_0(Y!7, singleton(X!8)) = X!8))))))) <=> ((~![U: $i, X: $i, Y: $i] : (member(U, unordered_pair(X, Y)) <=> (~((~member(U, universal_class)) | (~((U = Y) | (U = X))))))) | (member(tptp_fun_U_0(Y!7, singleton(X!8)), unordered_pair(X!8, X!8)) <=> (~((~member(tptp_fun_U_0(Y!7, singleton(X!8)), universal_class)) | (~(tptp_fun_U_0(Y!7, singleton(X!8)) = X!8))))))),
% 0.17/0.39 inference(transitivity,[status(thm)],[16, 14])).
% 0.17/0.39 tff(18,plain,
% 0.17/0.39 ((~![U: $i, X: $i, Y: $i] : (member(U, unordered_pair(X, Y)) <=> (~((~member(U, universal_class)) | (~((U = Y) | (U = X))))))) | (member(tptp_fun_U_0(Y!7, singleton(X!8)), unordered_pair(X!8, X!8)) <=> (~((~member(tptp_fun_U_0(Y!7, singleton(X!8)), universal_class)) | (~((tptp_fun_U_0(Y!7, singleton(X!8)) = X!8) | (tptp_fun_U_0(Y!7, singleton(X!8)) = X!8))))))),
% 0.17/0.39 inference(quant_inst,[status(thm)],[])).
% 0.17/0.39 tff(19,plain,
% 0.17/0.39 ((~![U: $i, X: $i, Y: $i] : (member(U, unordered_pair(X, Y)) <=> (~((~member(U, universal_class)) | (~((U = Y) | (U = X))))))) | (member(tptp_fun_U_0(Y!7, singleton(X!8)), unordered_pair(X!8, X!8)) <=> (~((~member(tptp_fun_U_0(Y!7, singleton(X!8)), universal_class)) | (~(tptp_fun_U_0(Y!7, singleton(X!8)) = X!8)))))),
% 0.17/0.39 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.17/0.39 tff(20,plain,
% 0.17/0.39 (member(tptp_fun_U_0(Y!7, singleton(X!8)), unordered_pair(X!8, X!8)) <=> (~((~member(tptp_fun_U_0(Y!7, singleton(X!8)), universal_class)) | (~(tptp_fun_U_0(Y!7, singleton(X!8)) = X!8))))),
% 0.17/0.39 inference(unit_resolution,[status(thm)],[19, 13])).
% 0.17/0.39 tff(21,plain,
% 0.17/0.39 (^[X: $i] : refl((singleton(X) = unordered_pair(X, X)) <=> (singleton(X) = unordered_pair(X, X)))),
% 0.17/0.39 inference(bind,[status(th)],[])).
% 0.17/0.39 tff(22,plain,
% 0.17/0.39 (![X: $i] : (singleton(X) = unordered_pair(X, X)) <=> ![X: $i] : (singleton(X) = unordered_pair(X, X))),
% 0.17/0.39 inference(quant_intro,[status(thm)],[21])).
% 0.17/0.39 tff(23,plain,
% 0.17/0.39 (![X: $i] : (singleton(X) = unordered_pair(X, X)) <=> ![X: $i] : (singleton(X) = unordered_pair(X, X))),
% 0.17/0.39 inference(rewrite,[status(thm)],[])).
% 0.17/0.39 tff(24,axiom,(![X: $i] : (singleton(X) = unordered_pair(X, X))), file('/export/starexec/sandbox/benchmark/Axioms/SET005+0.ax','singleton_set_defn')).
% 0.17/0.39 tff(25,plain,
% 0.17/0.39 (![X: $i] : (singleton(X) = unordered_pair(X, X))),
% 0.17/0.39 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.17/0.39 tff(26,plain,(
% 0.17/0.39 ![X: $i] : (singleton(X) = unordered_pair(X, X))),
% 0.17/0.39 inference(skolemize,[status(sab)],[25])).
% 0.17/0.39 tff(27,plain,
% 0.17/0.39 (![X: $i] : (singleton(X) = unordered_pair(X, X))),
% 0.17/0.39 inference(modus_ponens,[status(thm)],[26, 22])).
% 0.17/0.39 tff(28,plain,
% 0.17/0.39 ((~![X: $i] : (singleton(X) = unordered_pair(X, X))) | (singleton(X!8) = unordered_pair(X!8, X!8))),
% 0.17/0.39 inference(quant_inst,[status(thm)],[])).
% 0.17/0.39 tff(29,plain,
% 0.17/0.39 (singleton(X!8) = unordered_pair(X!8, X!8)),
% 0.17/0.39 inference(unit_resolution,[status(thm)],[28, 27])).
% 0.17/0.39 tff(30,plain,
% 0.17/0.39 (unordered_pair(X!8, X!8) = singleton(X!8)),
% 0.17/0.39 inference(symmetry,[status(thm)],[29])).
% 0.17/0.39 tff(31,plain,
% 0.17/0.39 (member(tptp_fun_U_0(Y!7, singleton(X!8)), unordered_pair(X!8, X!8)) <=> member(tptp_fun_U_0(Y!7, singleton(X!8)), singleton(X!8))),
% 0.17/0.39 inference(monotonicity,[status(thm)],[30])).
% 0.17/0.39 tff(32,plain,
% 0.17/0.39 (member(tptp_fun_U_0(Y!7, singleton(X!8)), singleton(X!8)) <=> member(tptp_fun_U_0(Y!7, singleton(X!8)), unordered_pair(X!8, X!8))),
% 0.17/0.39 inference(symmetry,[status(thm)],[31])).
% 0.17/0.39 tff(33,plain,
% 0.17/0.39 (^[X: $i, Y: $i] : refl((~((~((~subclass(X, Y)) | ![U: $i] : ((~member(U, X)) | member(U, Y)))) | (~(subclass(X, Y) | (~((~member(tptp_fun_U_0(Y, X), X)) | member(tptp_fun_U_0(Y, X), Y))))))) <=> (~((~((~subclass(X, Y)) | ![U: $i] : ((~member(U, X)) | member(U, Y)))) | (~(subclass(X, Y) | (~((~member(tptp_fun_U_0(Y, X), X)) | member(tptp_fun_U_0(Y, X), Y))))))))),
% 0.17/0.39 inference(bind,[status(th)],[])).
% 0.17/0.39 tff(34,plain,
% 0.17/0.39 (![X: $i, Y: $i] : (~((~((~subclass(X, Y)) | ![U: $i] : ((~member(U, X)) | member(U, Y)))) | (~(subclass(X, Y) | (~((~member(tptp_fun_U_0(Y, X), X)) | member(tptp_fun_U_0(Y, X), Y))))))) <=> ![X: $i, Y: $i] : (~((~((~subclass(X, Y)) | ![U: $i] : ((~member(U, X)) | member(U, Y)))) | (~(subclass(X, Y) | (~((~member(tptp_fun_U_0(Y, X), X)) | member(tptp_fun_U_0(Y, X), Y)))))))),
% 0.17/0.39 inference(quant_intro,[status(thm)],[33])).
% 0.17/0.39 tff(35,plain,
% 0.17/0.39 (^[X: $i, Y: $i] : rewrite((~((~((~subclass(X, Y)) | ![U: $i] : ((~member(U, X)) | member(U, Y)))) | (~(subclass(X, Y) | (~((~member(tptp_fun_U_0(Y, X), X)) | member(tptp_fun_U_0(Y, X), Y))))))) <=> (~((~((~subclass(X, Y)) | ![U: $i] : ((~member(U, X)) | member(U, Y)))) | (~(subclass(X, Y) | (~((~member(tptp_fun_U_0(Y, X), X)) | member(tptp_fun_U_0(Y, X), Y))))))))),
% 0.17/0.39 inference(bind,[status(th)],[])).
% 0.17/0.39 tff(36,plain,
% 0.17/0.39 (![X: $i, Y: $i] : (~((~((~subclass(X, Y)) | ![U: $i] : ((~member(U, X)) | member(U, Y)))) | (~(subclass(X, Y) | (~((~member(tptp_fun_U_0(Y, X), X)) | member(tptp_fun_U_0(Y, X), Y))))))) <=> ![X: $i, Y: $i] : (~((~((~subclass(X, Y)) | ![U: $i] : ((~member(U, X)) | member(U, Y)))) | (~(subclass(X, Y) | (~((~member(tptp_fun_U_0(Y, X), X)) | member(tptp_fun_U_0(Y, X), Y)))))))),
% 0.17/0.39 inference(quant_intro,[status(thm)],[35])).
% 0.17/0.39 tff(37,plain,
% 0.17/0.39 (![X: $i, Y: $i] : (~((~((~subclass(X, Y)) | ![U: $i] : ((~member(U, X)) | member(U, Y)))) | (~(subclass(X, Y) | (~((~member(tptp_fun_U_0(Y, X), X)) | member(tptp_fun_U_0(Y, X), Y))))))) <=> ![X: $i, Y: $i] : (~((~((~subclass(X, Y)) | ![U: $i] : ((~member(U, X)) | member(U, Y)))) | (~(subclass(X, Y) | (~((~member(tptp_fun_U_0(Y, X), X)) | member(tptp_fun_U_0(Y, X), Y)))))))),
% 0.17/0.39 inference(transitivity,[status(thm)],[36, 34])).
% 0.17/0.39 tff(38,plain,
% 0.17/0.39 (^[X: $i, Y: $i] : trans(monotonicity(rewrite(((~subclass(X, Y)) | ![U: $i] : ((~member(U, X)) | member(U, Y))) <=> ((~subclass(X, Y)) | ![U: $i] : ((~member(U, X)) | member(U, Y)))), rewrite((subclass(X, Y) | (~((~member(tptp_fun_U_0(Y, X), X)) | member(tptp_fun_U_0(Y, X), Y)))) <=> (subclass(X, Y) | (~((~member(tptp_fun_U_0(Y, X), X)) | member(tptp_fun_U_0(Y, X), Y))))), ((((~subclass(X, Y)) | ![U: $i] : ((~member(U, X)) | member(U, Y))) & (subclass(X, Y) | (~((~member(tptp_fun_U_0(Y, X), X)) | member(tptp_fun_U_0(Y, X), Y))))) <=> (((~subclass(X, Y)) | ![U: $i] : ((~member(U, X)) | member(U, Y))) & (subclass(X, Y) | (~((~member(tptp_fun_U_0(Y, X), X)) | member(tptp_fun_U_0(Y, X), Y))))))), rewrite((((~subclass(X, Y)) | ![U: $i] : ((~member(U, X)) | member(U, Y))) & (subclass(X, Y) | (~((~member(tptp_fun_U_0(Y, X), X)) | member(tptp_fun_U_0(Y, X), Y))))) <=> (~((~((~subclass(X, Y)) | ![U: $i] : ((~member(U, X)) | member(U, Y)))) | (~(subclass(X, Y) | (~((~member(tptp_fun_U_0(Y, X), X)) | member(tptp_fun_U_0(Y, X), Y)))))))), ((((~subclass(X, Y)) | ![U: $i] : ((~member(U, X)) | member(U, Y))) & (subclass(X, Y) | (~((~member(tptp_fun_U_0(Y, X), X)) | member(tptp_fun_U_0(Y, X), Y))))) <=> (~((~((~subclass(X, Y)) | ![U: $i] : ((~member(U, X)) | member(U, Y)))) | (~(subclass(X, Y) | (~((~member(tptp_fun_U_0(Y, X), X)) | member(tptp_fun_U_0(Y, X), Y)))))))))),
% 0.17/0.40 inference(bind,[status(th)],[])).
% 0.17/0.40 tff(39,plain,
% 0.17/0.40 (![X: $i, Y: $i] : (((~subclass(X, Y)) | ![U: $i] : ((~member(U, X)) | member(U, Y))) & (subclass(X, Y) | (~((~member(tptp_fun_U_0(Y, X), X)) | member(tptp_fun_U_0(Y, X), Y))))) <=> ![X: $i, Y: $i] : (~((~((~subclass(X, Y)) | ![U: $i] : ((~member(U, X)) | member(U, Y)))) | (~(subclass(X, Y) | (~((~member(tptp_fun_U_0(Y, X), X)) | member(tptp_fun_U_0(Y, X), Y)))))))),
% 0.17/0.40 inference(quant_intro,[status(thm)],[38])).
% 0.17/0.40 tff(40,plain,
% 0.17/0.40 (![X: $i, Y: $i] : (subclass(X, Y) <=> ![U: $i] : ((~member(U, X)) | member(U, Y))) <=> ![X: $i, Y: $i] : (subclass(X, Y) <=> ![U: $i] : ((~member(U, X)) | member(U, Y)))),
% 0.17/0.40 inference(rewrite,[status(thm)],[])).
% 0.17/0.40 tff(41,plain,
% 0.17/0.40 (^[X: $i, Y: $i] : rewrite((subclass(X, Y) <=> ![U: $i] : (member(U, X) => member(U, Y))) <=> (subclass(X, Y) <=> ![U: $i] : ((~member(U, X)) | member(U, Y))))),
% 0.17/0.40 inference(bind,[status(th)],[])).
% 0.17/0.40 tff(42,plain,
% 0.17/0.40 (![X: $i, Y: $i] : (subclass(X, Y) <=> ![U: $i] : (member(U, X) => member(U, Y))) <=> ![X: $i, Y: $i] : (subclass(X, Y) <=> ![U: $i] : ((~member(U, X)) | member(U, Y)))),
% 0.17/0.40 inference(quant_intro,[status(thm)],[41])).
% 0.17/0.40 tff(43,axiom,(![X: $i, Y: $i] : (subclass(X, Y) <=> ![U: $i] : (member(U, X) => member(U, Y)))), file('/export/starexec/sandbox/benchmark/Axioms/SET005+0.ax','subclass_defn')).
% 0.17/0.40 tff(44,plain,
% 0.17/0.40 (![X: $i, Y: $i] : (subclass(X, Y) <=> ![U: $i] : ((~member(U, X)) | member(U, Y)))),
% 0.17/0.40 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.17/0.40 tff(45,plain,
% 0.17/0.40 (![X: $i, Y: $i] : (subclass(X, Y) <=> ![U: $i] : ((~member(U, X)) | member(U, Y)))),
% 0.17/0.40 inference(modus_ponens,[status(thm)],[44, 40])).
% 0.17/0.40 tff(46,plain,(
% 0.17/0.40 ![X: $i, Y: $i] : (((~subclass(X, Y)) | ![U: $i] : ((~member(U, X)) | member(U, Y))) & (subclass(X, Y) | (~((~member(tptp_fun_U_0(Y, X), X)) | member(tptp_fun_U_0(Y, X), Y)))))),
% 0.17/0.40 inference(skolemize,[status(sab)],[45])).
% 0.17/0.40 tff(47,plain,
% 0.17/0.40 (![X: $i, Y: $i] : (~((~((~subclass(X, Y)) | ![U: $i] : ((~member(U, X)) | member(U, Y)))) | (~(subclass(X, Y) | (~((~member(tptp_fun_U_0(Y, X), X)) | member(tptp_fun_U_0(Y, X), Y)))))))),
% 0.17/0.40 inference(modus_ponens,[status(thm)],[46, 39])).
% 0.17/0.40 tff(48,plain,
% 0.17/0.40 (![X: $i, Y: $i] : (~((~((~subclass(X, Y)) | ![U: $i] : ((~member(U, X)) | member(U, Y)))) | (~(subclass(X, Y) | (~((~member(tptp_fun_U_0(Y, X), X)) | member(tptp_fun_U_0(Y, X), Y)))))))),
% 0.17/0.40 inference(modus_ponens,[status(thm)],[47, 37])).
% 0.17/0.40 tff(49,plain,
% 0.17/0.40 ((~![X: $i, Y: $i] : (~((~((~subclass(X, Y)) | ![U: $i] : ((~member(U, X)) | member(U, Y)))) | (~(subclass(X, Y) | (~((~member(tptp_fun_U_0(Y, X), X)) | member(tptp_fun_U_0(Y, X), Y)))))))) | (~((~((~subclass(singleton(X!8), Y!7)) | ![U: $i] : ((~member(U, singleton(X!8))) | member(U, Y!7)))) | (~(subclass(singleton(X!8), Y!7) | (~((~member(tptp_fun_U_0(Y!7, singleton(X!8)), singleton(X!8))) | member(tptp_fun_U_0(Y!7, singleton(X!8)), Y!7)))))))),
% 0.17/0.40 inference(quant_inst,[status(thm)],[])).
% 0.17/0.40 tff(50,plain,
% 0.17/0.40 (~((~((~subclass(singleton(X!8), Y!7)) | ![U: $i] : ((~member(U, singleton(X!8))) | member(U, Y!7)))) | (~(subclass(singleton(X!8), Y!7) | (~((~member(tptp_fun_U_0(Y!7, singleton(X!8)), singleton(X!8))) | member(tptp_fun_U_0(Y!7, singleton(X!8)), Y!7))))))),
% 0.17/0.40 inference(unit_resolution,[status(thm)],[49, 48])).
% 0.17/0.40 tff(51,plain,
% 0.17/0.40 (((~((~subclass(singleton(X!8), Y!7)) | ![U: $i] : ((~member(U, singleton(X!8))) | member(U, Y!7)))) | (~(subclass(singleton(X!8), Y!7) | (~((~member(tptp_fun_U_0(Y!7, singleton(X!8)), singleton(X!8))) | member(tptp_fun_U_0(Y!7, singleton(X!8)), Y!7)))))) | (subclass(singleton(X!8), Y!7) | (~((~member(tptp_fun_U_0(Y!7, singleton(X!8)), singleton(X!8))) | member(tptp_fun_U_0(Y!7, singleton(X!8)), Y!7))))),
% 0.17/0.40 inference(tautology,[status(thm)],[])).
% 0.17/0.40 tff(52,plain,
% 0.17/0.40 (subclass(singleton(X!8), Y!7) | (~((~member(tptp_fun_U_0(Y!7, singleton(X!8)), singleton(X!8))) | member(tptp_fun_U_0(Y!7, singleton(X!8)), Y!7)))),
% 0.17/0.40 inference(unit_resolution,[status(thm)],[51, 50])).
% 0.17/0.40 tff(53,plain,
% 0.17/0.40 ((~![X: $i, Y: $i] : ((~member(X, Y)) | subclass(singleton(X), Y))) <=> (~![X: $i, Y: $i] : ((~member(X, Y)) | subclass(singleton(X), Y)))),
% 0.17/0.40 inference(rewrite,[status(thm)],[])).
% 0.17/0.40 tff(54,plain,
% 0.17/0.40 ((~![X: $i, Y: $i] : (member(X, Y) => subclass(singleton(X), Y))) <=> (~![X: $i, Y: $i] : ((~member(X, Y)) | subclass(singleton(X), Y)))),
% 0.17/0.40 inference(rewrite,[status(thm)],[])).
% 0.17/0.40 tff(55,axiom,(~![X: $i, Y: $i] : (member(X, Y) => subclass(singleton(X), Y))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','property_of_singletons2')).
% 0.17/0.40 tff(56,plain,
% 0.17/0.40 (~![X: $i, Y: $i] : ((~member(X, Y)) | subclass(singleton(X), Y))),
% 0.17/0.40 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.17/0.40 tff(57,plain,
% 0.17/0.40 (~![X: $i, Y: $i] : ((~member(X, Y)) | subclass(singleton(X), Y))),
% 0.17/0.40 inference(modus_ponens,[status(thm)],[56, 53])).
% 0.17/0.40 tff(58,plain,
% 0.17/0.40 (~![X: $i, Y: $i] : ((~member(X, Y)) | subclass(singleton(X), Y))),
% 0.17/0.40 inference(modus_ponens,[status(thm)],[57, 53])).
% 0.17/0.40 tff(59,plain,
% 0.17/0.40 (~![X: $i, Y: $i] : ((~member(X, Y)) | subclass(singleton(X), Y))),
% 0.17/0.40 inference(modus_ponens,[status(thm)],[58, 53])).
% 0.17/0.40 tff(60,plain,
% 0.17/0.40 (~![X: $i, Y: $i] : ((~member(X, Y)) | subclass(singleton(X), Y))),
% 0.17/0.40 inference(modus_ponens,[status(thm)],[59, 53])).
% 0.17/0.40 tff(61,plain,
% 0.17/0.40 (~![X: $i, Y: $i] : ((~member(X, Y)) | subclass(singleton(X), Y))),
% 0.17/0.40 inference(modus_ponens,[status(thm)],[60, 53])).
% 0.17/0.40 tff(62,plain,
% 0.17/0.40 (~![X: $i, Y: $i] : ((~member(X, Y)) | subclass(singleton(X), Y))),
% 0.17/0.40 inference(modus_ponens,[status(thm)],[61, 53])).
% 0.17/0.40 tff(63,plain,(
% 0.17/0.40 ~((~member(X!8, Y!7)) | subclass(singleton(X!8), Y!7))),
% 0.17/0.40 inference(skolemize,[status(sab)],[62])).
% 0.17/0.40 tff(64,plain,
% 0.17/0.40 (~subclass(singleton(X!8), Y!7)),
% 0.17/0.40 inference(or_elim,[status(thm)],[63])).
% 0.17/0.40 tff(65,plain,
% 0.17/0.40 ((~(subclass(singleton(X!8), Y!7) | (~((~member(tptp_fun_U_0(Y!7, singleton(X!8)), singleton(X!8))) | member(tptp_fun_U_0(Y!7, singleton(X!8)), Y!7))))) | subclass(singleton(X!8), Y!7) | (~((~member(tptp_fun_U_0(Y!7, singleton(X!8)), singleton(X!8))) | member(tptp_fun_U_0(Y!7, singleton(X!8)), Y!7)))),
% 0.17/0.40 inference(tautology,[status(thm)],[])).
% 0.17/0.40 tff(66,plain,
% 0.17/0.40 ((~(subclass(singleton(X!8), Y!7) | (~((~member(tptp_fun_U_0(Y!7, singleton(X!8)), singleton(X!8))) | member(tptp_fun_U_0(Y!7, singleton(X!8)), Y!7))))) | (~((~member(tptp_fun_U_0(Y!7, singleton(X!8)), singleton(X!8))) | member(tptp_fun_U_0(Y!7, singleton(X!8)), Y!7)))),
% 0.17/0.40 inference(unit_resolution,[status(thm)],[65, 64])).
% 0.17/0.40 tff(67,plain,
% 0.17/0.40 (~((~member(tptp_fun_U_0(Y!7, singleton(X!8)), singleton(X!8))) | member(tptp_fun_U_0(Y!7, singleton(X!8)), Y!7))),
% 0.17/0.40 inference(unit_resolution,[status(thm)],[66, 52])).
% 0.17/0.40 tff(68,plain,
% 0.17/0.40 (((~member(tptp_fun_U_0(Y!7, singleton(X!8)), singleton(X!8))) | member(tptp_fun_U_0(Y!7, singleton(X!8)), Y!7)) | member(tptp_fun_U_0(Y!7, singleton(X!8)), singleton(X!8))),
% 0.17/0.40 inference(tautology,[status(thm)],[])).
% 0.17/0.40 tff(69,plain,
% 0.17/0.40 (member(tptp_fun_U_0(Y!7, singleton(X!8)), singleton(X!8))),
% 0.17/0.40 inference(unit_resolution,[status(thm)],[68, 67])).
% 0.17/0.40 tff(70,plain,
% 0.17/0.40 (member(tptp_fun_U_0(Y!7, singleton(X!8)), unordered_pair(X!8, X!8))),
% 0.17/0.40 inference(modus_ponens,[status(thm)],[69, 32])).
% 0.17/0.40 tff(71,plain,
% 0.17/0.40 ((~(member(tptp_fun_U_0(Y!7, singleton(X!8)), unordered_pair(X!8, X!8)) <=> (~((~member(tptp_fun_U_0(Y!7, singleton(X!8)), universal_class)) | (~(tptp_fun_U_0(Y!7, singleton(X!8)) = X!8)))))) | (~member(tptp_fun_U_0(Y!7, singleton(X!8)), unordered_pair(X!8, X!8))) | (~((~member(tptp_fun_U_0(Y!7, singleton(X!8)), universal_class)) | (~(tptp_fun_U_0(Y!7, singleton(X!8)) = X!8))))),
% 0.17/0.40 inference(tautology,[status(thm)],[])).
% 0.17/0.40 tff(72,plain,
% 0.17/0.40 (~((~member(tptp_fun_U_0(Y!7, singleton(X!8)), universal_class)) | (~(tptp_fun_U_0(Y!7, singleton(X!8)) = X!8)))),
% 0.17/0.40 inference(unit_resolution,[status(thm)],[71, 70, 20])).
% 0.17/0.40 tff(73,plain,
% 0.17/0.40 (((~member(tptp_fun_U_0(Y!7, singleton(X!8)), universal_class)) | (~(tptp_fun_U_0(Y!7, singleton(X!8)) = X!8))) | (tptp_fun_U_0(Y!7, singleton(X!8)) = X!8)),
% 0.17/0.40 inference(tautology,[status(thm)],[])).
% 0.17/0.40 tff(74,plain,
% 0.17/0.40 (tptp_fun_U_0(Y!7, singleton(X!8)) = X!8),
% 0.17/0.40 inference(unit_resolution,[status(thm)],[73, 72])).
% 0.17/0.40 tff(75,plain,
% 0.17/0.40 (member(tptp_fun_U_0(Y!7, singleton(X!8)), Y!7) <=> member(X!8, Y!7)),
% 0.17/0.40 inference(monotonicity,[status(thm)],[74])).
% 0.17/0.40 tff(76,plain,
% 0.17/0.40 (member(X!8, Y!7) <=> member(tptp_fun_U_0(Y!7, singleton(X!8)), Y!7)),
% 0.17/0.40 inference(symmetry,[status(thm)],[75])).
% 0.17/0.40 tff(77,plain,
% 0.17/0.40 (member(X!8, Y!7)),
% 0.17/0.40 inference(or_elim,[status(thm)],[63])).
% 0.17/0.40 tff(78,plain,
% 0.17/0.40 (member(tptp_fun_U_0(Y!7, singleton(X!8)), Y!7)),
% 0.17/0.40 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.17/0.40 tff(79,plain,
% 0.17/0.40 (((~member(tptp_fun_U_0(Y!7, singleton(X!8)), singleton(X!8))) | member(tptp_fun_U_0(Y!7, singleton(X!8)), Y!7)) | (~member(tptp_fun_U_0(Y!7, singleton(X!8)), Y!7))),
% 0.17/0.40 inference(tautology,[status(thm)],[])).
% 0.17/0.40 tff(80,plain,
% 0.17/0.40 (~member(tptp_fun_U_0(Y!7, singleton(X!8)), Y!7)),
% 0.17/0.40 inference(unit_resolution,[status(thm)],[79, 67])).
% 0.17/0.40 tff(81,plain,
% 0.17/0.40 ($false),
% 0.17/0.40 inference(unit_resolution,[status(thm)],[80, 78])).
% 0.17/0.40 % SZS output end Proof
%------------------------------------------------------------------------------