%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET691+4 : TPTP v9.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% 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 : Sat Jun 21 05:26:09 AM UTC 2025
% Result : Theorem 0.12s 0.36s
% Output : Proof 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET691+4 : TPTP v9.0.0. Released v2.2.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n014.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 05:38:09 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.36 % SZS status Theorem
% 0.12/0.36 % SZS output start Proof
% 0.12/0.36 tff(subset_type, type, (
% 0.12/0.36 subset: ( $i * $i ) > $o)).
% 0.12/0.36 tff(empty_set_type, type, (
% 0.12/0.36 empty_set: $i)).
% 0.12/0.36 tff(tptp_fun_A_3_type, type, (
% 0.12/0.36 tptp_fun_A_3: $i)).
% 0.12/0.36 tff(equal_set_type, type, (
% 0.12/0.36 equal_set: ( $i * $i ) > $o)).
% 0.12/0.36 tff(member_type, type, (
% 0.12/0.36 member: ( $i * $i ) > $o)).
% 0.12/0.36 tff(tptp_fun_X_0_type, type, (
% 0.12/0.36 tptp_fun_X_0: ( $i * $i ) > $i)).
% 0.12/0.36 tff(1,assumption,((~((~subset(empty_set, A!3)) | ![X: $i] : ((~member(X, empty_set)) | member(X, A!3)))) | (~(subset(empty_set, A!3) | (~((~member(tptp_fun_X_0(A!3, empty_set), empty_set)) | member(tptp_fun_X_0(A!3, empty_set), A!3)))))), introduced(assumption)).
% 0.12/0.36 tff(2,plain,
% 0.12/0.36 (^[A: $i, B: $i] : refl((~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))))),
% 0.12/0.36 inference(bind,[status(th)],[])).
% 0.12/0.36 tff(3,plain,
% 0.12/0.36 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.12/0.36 inference(quant_intro,[status(thm)],[2])).
% 0.12/0.36 tff(4,plain,
% 0.12/0.36 (^[A: $i, B: $i] : rewrite((~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))))),
% 0.12/0.36 inference(bind,[status(th)],[])).
% 0.12/0.36 tff(5,plain,
% 0.12/0.36 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.12/0.36 inference(quant_intro,[status(thm)],[4])).
% 0.12/0.36 tff(6,plain,
% 0.12/0.36 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.12/0.36 inference(transitivity,[status(thm)],[5, 3])).
% 0.12/0.36 tff(7,plain,
% 0.12/0.36 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) <=> ((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))), rewrite((subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))) <=> (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))), ((((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> (((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))), rewrite((((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))), ((((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(8,plain,
% 0.12/0.37 (![A: $i, B: $i] : (((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[7])).
% 0.12/0.37 tff(9,plain,
% 0.12/0.37 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(10,plain,
% 0.12/0.37 (^[A: $i, B: $i] : rewrite((subset(A, B) <=> ![X: $i] : (member(X, A) => member(X, B))) <=> (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(11,plain,
% 0.12/0.37 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : (member(X, A) => member(X, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[10])).
% 0.12/0.37 tff(12,axiom,(![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : (member(X, A) => member(X, B)))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax','subset')).
% 0.12/0.37 tff(13,plain,
% 0.12/0.37 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[12, 11])).
% 0.12/0.37 tff(14,plain,
% 0.12/0.37 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[13, 9])).
% 0.12/0.37 tff(15,plain,(
% 0.12/0.37 ![A: $i, B: $i] : (((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))),
% 0.12/0.37 inference(skolemize,[status(sab)],[14])).
% 0.12/0.37 tff(16,plain,
% 0.12/0.37 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[15, 8])).
% 0.12/0.37 tff(17,plain,
% 0.12/0.37 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[16, 6])).
% 0.12/0.37 tff(18,plain,
% 0.12/0.37 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))) | (~((~((~subset(empty_set, A!3)) | ![X: $i] : ((~member(X, empty_set)) | member(X, A!3)))) | (~(subset(empty_set, A!3) | (~((~member(tptp_fun_X_0(A!3, empty_set), empty_set)) | member(tptp_fun_X_0(A!3, empty_set), A!3)))))))),
% 0.12/0.37 inference(quant_inst,[status(thm)],[])).
% 0.12/0.37 tff(19,plain,
% 0.12/0.37 ($false),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[18, 17, 1])).
% 0.12/0.37 tff(20,plain,(~((~((~subset(empty_set, A!3)) | ![X: $i] : ((~member(X, empty_set)) | member(X, A!3)))) | (~(subset(empty_set, A!3) | (~((~member(tptp_fun_X_0(A!3, empty_set), empty_set)) | member(tptp_fun_X_0(A!3, empty_set), A!3))))))), inference(lemma,lemma(discharge,[]))).
% 0.12/0.37 tff(21,plain,
% 0.12/0.37 (((~((~subset(empty_set, A!3)) | ![X: $i] : ((~member(X, empty_set)) | member(X, A!3)))) | (~(subset(empty_set, A!3) | (~((~member(tptp_fun_X_0(A!3, empty_set), empty_set)) | member(tptp_fun_X_0(A!3, empty_set), A!3)))))) | (subset(empty_set, A!3) | (~((~member(tptp_fun_X_0(A!3, empty_set), empty_set)) | member(tptp_fun_X_0(A!3, empty_set), A!3))))),
% 0.12/0.37 inference(tautology,[status(thm)],[])).
% 0.12/0.37 tff(22,plain,
% 0.12/0.37 (subset(empty_set, A!3) | (~((~member(tptp_fun_X_0(A!3, empty_set), empty_set)) | member(tptp_fun_X_0(A!3, empty_set), A!3)))),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[21, 20])).
% 0.12/0.37 tff(23,assumption,(member(tptp_fun_X_0(A!3, empty_set), empty_set)), introduced(assumption)).
% 0.12/0.37 tff(24,plain,
% 0.12/0.37 (^[X: $i] : refl((~member(X, empty_set)) <=> (~member(X, empty_set)))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(25,plain,
% 0.12/0.37 (![X: $i] : (~member(X, empty_set)) <=> ![X: $i] : (~member(X, empty_set))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[24])).
% 0.12/0.37 tff(26,plain,
% 0.12/0.37 (![X: $i] : (~member(X, empty_set)) <=> ![X: $i] : (~member(X, empty_set))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(27,axiom,(![X: $i] : (~member(X, empty_set))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax','empty_set')).
% 0.12/0.37 tff(28,plain,
% 0.12/0.37 (![X: $i] : (~member(X, empty_set))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.12/0.37 tff(29,plain,(
% 0.12/0.37 ![X: $i] : (~member(X, empty_set))),
% 0.12/0.37 inference(skolemize,[status(sab)],[28])).
% 0.12/0.37 tff(30,plain,
% 0.12/0.37 (![X: $i] : (~member(X, empty_set))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.12/0.37 tff(31,plain,
% 0.12/0.37 ((~![X: $i] : (~member(X, empty_set))) | (~member(tptp_fun_X_0(A!3, empty_set), empty_set))),
% 0.12/0.37 inference(quant_inst,[status(thm)],[])).
% 0.12/0.37 tff(32,plain,
% 0.12/0.37 ($false),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[31, 30, 23])).
% 0.12/0.37 tff(33,plain,(~member(tptp_fun_X_0(A!3, empty_set), empty_set)), inference(lemma,lemma(discharge,[]))).
% 0.12/0.37 tff(34,plain,
% 0.12/0.37 (((~member(tptp_fun_X_0(A!3, empty_set), empty_set)) | member(tptp_fun_X_0(A!3, empty_set), A!3)) | member(tptp_fun_X_0(A!3, empty_set), empty_set)),
% 0.12/0.37 inference(tautology,[status(thm)],[])).
% 0.12/0.37 tff(35,plain,
% 0.12/0.37 ((~member(tptp_fun_X_0(A!3, empty_set), empty_set)) | member(tptp_fun_X_0(A!3, empty_set), A!3)),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[34, 33])).
% 0.12/0.37 tff(36,plain,
% 0.12/0.37 ((~(subset(empty_set, A!3) | (~((~member(tptp_fun_X_0(A!3, empty_set), empty_set)) | member(tptp_fun_X_0(A!3, empty_set), A!3))))) | subset(empty_set, A!3) | (~((~member(tptp_fun_X_0(A!3, empty_set), empty_set)) | member(tptp_fun_X_0(A!3, empty_set), A!3)))),
% 0.12/0.37 inference(tautology,[status(thm)],[])).
% 0.12/0.37 tff(37,plain,
% 0.12/0.37 ((~(subset(empty_set, A!3) | (~((~member(tptp_fun_X_0(A!3, empty_set), empty_set)) | member(tptp_fun_X_0(A!3, empty_set), A!3))))) | subset(empty_set, A!3)),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[36, 35])).
% 0.12/0.37 tff(38,plain,
% 0.12/0.37 (subset(empty_set, A!3)),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[37, 22])).
% 0.12/0.37 tff(39,assumption,(~equal_set(A!3, empty_set)), introduced(assumption)).
% 0.12/0.37 tff(40,plain,
% 0.12/0.37 ((~(subset(A!3, empty_set) <=> equal_set(A!3, empty_set))) <=> (~(subset(A!3, empty_set) <=> equal_set(A!3, empty_set)))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(41,plain,
% 0.12/0.37 ((~![A: $i] : (subset(A, empty_set) <=> equal_set(A, empty_set))) <=> (~![A: $i] : (subset(A, empty_set) <=> equal_set(A, empty_set)))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(42,axiom,(~![A: $i] : (subset(A, empty_set) <=> equal_set(A, empty_set))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thI16')).
% 0.12/0.37 tff(43,plain,
% 0.12/0.37 (~![A: $i] : (subset(A, empty_set) <=> equal_set(A, empty_set))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.12/0.37 tff(44,plain,
% 0.12/0.37 (~![A: $i] : (subset(A, empty_set) <=> equal_set(A, empty_set))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[43, 41])).
% 0.12/0.37 tff(45,plain,
% 0.12/0.37 (~![A: $i] : (subset(A, empty_set) <=> equal_set(A, empty_set))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[44, 41])).
% 0.12/0.37 tff(46,plain,
% 0.12/0.37 (~![A: $i] : (subset(A, empty_set) <=> equal_set(A, empty_set))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[45, 41])).
% 0.12/0.37 tff(47,plain,(
% 0.12/0.37 ~(subset(A!3, empty_set) <=> equal_set(A!3, empty_set))),
% 0.12/0.37 inference(skolemize,[status(sab)],[46])).
% 0.12/0.37 tff(48,plain,
% 0.12/0.37 (~(subset(A!3, empty_set) <=> equal_set(A!3, empty_set))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[47, 40])).
% 0.12/0.37 tff(49,plain,
% 0.12/0.37 ((subset(A!3, empty_set) <=> equal_set(A!3, empty_set)) | subset(A!3, empty_set) | equal_set(A!3, empty_set)),
% 0.12/0.37 inference(tautology,[status(thm)],[])).
% 0.12/0.37 tff(50,plain,
% 0.12/0.37 (subset(A!3, empty_set) | equal_set(A!3, empty_set)),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[49, 48])).
% 0.12/0.37 tff(51,plain,
% 0.12/0.37 (subset(A!3, empty_set)),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[50, 39])).
% 0.12/0.37 tff(52,plain,
% 0.12/0.37 (^[A: $i, B: $i] : refl((~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B))) <=> (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(53,plain,
% 0.12/0.37 (![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B))) <=> ![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[52])).
% 0.12/0.37 tff(54,plain,
% 0.12/0.37 (^[A: $i, B: $i] : trans(trans(monotonicity(rewrite((subset(A, B) & subset(B, A)) <=> (~((~subset(A, B)) | (~subset(B, A))))), ((equal_set(A, B) <=> (subset(A, B) & subset(B, A))) <=> (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A))))))), rewrite((equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A))))) <=> (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))), ((equal_set(A, B) <=> (subset(A, B) & subset(B, A))) <=> (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B))))), rewrite((~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B))) <=> (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))), ((equal_set(A, B) <=> (subset(A, B) & subset(B, A))) <=> (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(55,plain,
% 0.12/0.37 (![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A))) <=> ![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[54])).
% 0.12/0.37 tff(56,plain,
% 0.12/0.37 (![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A))) <=> ![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(57,axiom,(![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax','equal_set')).
% 0.12/0.37 tff(58,plain,
% 0.12/0.37 (![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.12/0.37 tff(59,plain,(
% 0.12/0.37 ![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 0.12/0.37 inference(skolemize,[status(sab)],[58])).
% 0.12/0.37 tff(60,plain,
% 0.12/0.37 (![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[59, 55])).
% 0.12/0.37 tff(61,plain,
% 0.12/0.37 (![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[60, 53])).
% 0.12/0.37 tff(62,plain,
% 0.12/0.37 ((~![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))) | (~(((~subset(A!3, empty_set)) | (~subset(empty_set, A!3))) <=> equal_set(A!3, empty_set)))),
% 0.12/0.37 inference(quant_inst,[status(thm)],[])).
% 0.12/0.37 tff(63,plain,
% 0.12/0.37 (~(((~subset(A!3, empty_set)) | (~subset(empty_set, A!3))) <=> equal_set(A!3, empty_set))),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[62, 61])).
% 0.12/0.37 tff(64,plain,
% 0.12/0.37 ((((~subset(A!3, empty_set)) | (~subset(empty_set, A!3))) <=> equal_set(A!3, empty_set)) | ((~subset(A!3, empty_set)) | (~subset(empty_set, A!3))) | equal_set(A!3, empty_set)),
% 0.12/0.37 inference(tautology,[status(thm)],[])).
% 0.12/0.37 tff(65,plain,
% 0.12/0.37 (((~subset(A!3, empty_set)) | (~subset(empty_set, A!3))) | equal_set(A!3, empty_set)),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[64, 63])).
% 0.12/0.37 tff(66,plain,
% 0.12/0.37 ((~subset(A!3, empty_set)) | (~subset(empty_set, A!3))),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[65, 39])).
% 0.12/0.37 tff(67,plain,
% 0.12/0.37 ((~((~subset(A!3, empty_set)) | (~subset(empty_set, A!3)))) | (~subset(A!3, empty_set)) | (~subset(empty_set, A!3))),
% 0.12/0.37 inference(tautology,[status(thm)],[])).
% 0.12/0.37 tff(68,plain,
% 0.12/0.37 ($false),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[67, 66, 51, 38])).
% 0.12/0.37 tff(69,plain,(equal_set(A!3, empty_set)), inference(lemma,lemma(discharge,[]))).
% 0.12/0.37 tff(70,plain,
% 0.12/0.37 ((subset(A!3, empty_set) <=> equal_set(A!3, empty_set)) | (~subset(A!3, empty_set)) | (~equal_set(A!3, empty_set))),
% 0.12/0.37 inference(tautology,[status(thm)],[])).
% 0.12/0.37 tff(71,plain,
% 0.12/0.37 ((~subset(A!3, empty_set)) | (~equal_set(A!3, empty_set))),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[70, 48])).
% 0.12/0.37 tff(72,plain,
% 0.12/0.37 (~subset(A!3, empty_set)),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[71, 69])).
% 0.12/0.37 tff(73,plain,
% 0.12/0.37 ((((~subset(A!3, empty_set)) | (~subset(empty_set, A!3))) <=> equal_set(A!3, empty_set)) | (~((~subset(A!3, empty_set)) | (~subset(empty_set, A!3)))) | (~equal_set(A!3, empty_set))),
% 0.12/0.37 inference(tautology,[status(thm)],[])).
% 0.12/0.37 tff(74,plain,
% 0.12/0.37 ((~((~subset(A!3, empty_set)) | (~subset(empty_set, A!3)))) | (~equal_set(A!3, empty_set))),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[73, 63])).
% 0.12/0.37 tff(75,plain,
% 0.12/0.37 (~((~subset(A!3, empty_set)) | (~subset(empty_set, A!3)))),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[74, 69])).
% 0.12/0.37 tff(76,plain,
% 0.12/0.37 (((~subset(A!3, empty_set)) | (~subset(empty_set, A!3))) | subset(A!3, empty_set)),
% 0.12/0.37 inference(tautology,[status(thm)],[])).
% 0.12/0.37 tff(77,plain,
% 0.12/0.37 ($false),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[76, 75, 72])).
% 0.12/0.37 % SZS output end Proof
% 0.12/0.37 % E exiting
%------------------------------------------------------------------------------