%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET688+4 : TPTP v9.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n003.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 0.13s 0.39s
% Output : Proof 0.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.14 % Problem : SET688+4 : TPTP v9.0.0. Released v2.2.0.
% 0.09/0.14 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n003.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Jun 20 05:38:24 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.13/0.39 % SZS status Theorem
% 0.13/0.39 % SZS output start Proof
% 0.13/0.39 tff(member_type, type, (
% 0.13/0.39 member: ( $i * $i ) > $o)).
% 0.13/0.39 tff(tptp_fun_C_3_type, type, (
% 0.13/0.39 tptp_fun_C_3: $i)).
% 0.13/0.39 tff(tptp_fun_X_0_type, type, (
% 0.13/0.39 tptp_fun_X_0: ( $i * $i ) > $i)).
% 0.13/0.39 tff(tptp_fun_B_4_type, type, (
% 0.13/0.39 tptp_fun_B_4: $i)).
% 0.13/0.39 tff(tptp_fun_A_5_type, type, (
% 0.13/0.39 tptp_fun_A_5: $i)).
% 0.13/0.39 tff(subset_type, type, (
% 0.13/0.39 subset: ( $i * $i ) > $o)).
% 0.13/0.39 tff(equal_set_type, type, (
% 0.13/0.39 equal_set: ( $i * $i ) > $o)).
% 0.13/0.39 tff(1,plain,
% 0.13/0.39 (^[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))))))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(2,plain,
% 0.13/0.39 (![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)))))))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[1])).
% 0.13/0.39 tff(3,plain,
% 0.13/0.39 (^[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))))))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(4,plain,
% 0.13/0.39 (![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)))))))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[3])).
% 0.13/0.39 tff(5,plain,
% 0.13/0.39 (![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)))))))),
% 0.13/0.39 inference(transitivity,[status(thm)],[4, 2])).
% 0.13/0.39 tff(6,plain,
% 0.13/0.39 (^[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)))))))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(7,plain,
% 0.13/0.39 (![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)))))))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[6])).
% 0.13/0.40 tff(8,plain,
% 0.13/0.40 (![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)))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(9,plain,
% 0.13/0.40 (^[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))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(10,plain,
% 0.13/0.40 (![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)))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[9])).
% 0.13/0.40 tff(11,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')).
% 0.13/0.40 tff(12,plain,
% 0.13/0.40 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.13/0.40 tff(13,plain,
% 0.13/0.40 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[12, 8])).
% 0.13/0.40 tff(14,plain,(
% 0.13/0.40 ![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)))))),
% 0.13/0.40 inference(skolemize,[status(sab)],[13])).
% 0.13/0.40 tff(15,plain,
% 0.13/0.40 (![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)))))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[14, 7])).
% 0.13/0.40 tff(16,plain,
% 0.13/0.40 (![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)))))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[15, 5])).
% 0.13/0.40 tff(17,plain,
% 0.13/0.40 ((~![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(C!3, A!5)) | ![X: $i] : ((~member(X, C!3)) | member(X, A!5)))) | (~(subset(C!3, A!5) | (~((~member(tptp_fun_X_0(A!5, C!3), C!3)) | member(tptp_fun_X_0(A!5, C!3), A!5)))))))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(18,plain,
% 0.13/0.40 (~((~((~subset(C!3, A!5)) | ![X: $i] : ((~member(X, C!3)) | member(X, A!5)))) | (~(subset(C!3, A!5) | (~((~member(tptp_fun_X_0(A!5, C!3), C!3)) | member(tptp_fun_X_0(A!5, C!3), A!5))))))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.13/0.40 tff(19,plain,
% 0.13/0.40 (((~((~subset(C!3, A!5)) | ![X: $i] : ((~member(X, C!3)) | member(X, A!5)))) | (~(subset(C!3, A!5) | (~((~member(tptp_fun_X_0(A!5, C!3), C!3)) | member(tptp_fun_X_0(A!5, C!3), A!5)))))) | ((~subset(C!3, A!5)) | ![X: $i] : ((~member(X, C!3)) | member(X, A!5)))),
% 0.13/0.40 inference(tautology,[status(thm)],[])).
% 0.13/0.40 tff(20,plain,
% 0.13/0.40 ((~subset(C!3, A!5)) | ![X: $i] : ((~member(X, C!3)) | member(X, A!5))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[19, 18])).
% 0.13/0.40 tff(21,plain,
% 0.13/0.40 (^[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))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(22,plain,
% 0.13/0.40 (![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)))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[21])).
% 0.13/0.40 tff(23,plain,
% 0.13/0.40 (^[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)))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(24,plain,
% 0.13/0.40 (![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)))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[23])).
% 0.13/0.40 tff(25,plain,
% 0.13/0.40 (![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)))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(26,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')).
% 0.13/0.40 tff(27,plain,
% 0.13/0.40 (![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.13/0.40 tff(28,plain,(
% 0.13/0.40 ![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 0.13/0.40 inference(skolemize,[status(sab)],[27])).
% 0.13/0.40 tff(29,plain,
% 0.13/0.40 (![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[28, 24])).
% 0.13/0.40 tff(30,plain,
% 0.13/0.40 (![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[29, 22])).
% 0.13/0.40 tff(31,plain,
% 0.13/0.40 ((~![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))) | (~(((~subset(A!5, C!3)) | (~subset(C!3, A!5))) <=> equal_set(A!5, C!3)))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(32,plain,
% 0.13/0.40 (~(((~subset(A!5, C!3)) | (~subset(C!3, A!5))) <=> equal_set(A!5, C!3))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[31, 30])).
% 0.13/0.40 tff(33,plain,
% 0.13/0.40 ((~![A: $i, B: $i, C: $i] : ((~equal_set(A, C)) | (~(subset(A, B) & (~equal_set(A, B)) & subset(B, C) & (~equal_set(B, C)))))) <=> (~![A: $i, B: $i, C: $i] : ((~equal_set(A, C)) | (~(subset(A, B) & (~equal_set(A, B)) & subset(B, C) & (~equal_set(B, C))))))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(34,plain,
% 0.13/0.40 ((~![A: $i, B: $i, C: $i] : ((((subset(A, B) & (~equal_set(A, B))) & subset(B, C)) & (~equal_set(B, C))) => (~equal_set(A, C)))) <=> (~![A: $i, B: $i, C: $i] : ((~equal_set(A, C)) | (~(subset(A, B) & (~equal_set(A, B)) & subset(B, C) & (~equal_set(B, C))))))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(35,axiom,(~![A: $i, B: $i, C: $i] : ((((subset(A, B) & (~equal_set(A, B))) & subset(B, C)) & (~equal_set(B, C))) => (~equal_set(A, C)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thI04')).
% 0.13/0.40 tff(36,plain,
% 0.13/0.40 (~![A: $i, B: $i, C: $i] : ((~equal_set(A, C)) | (~(subset(A, B) & (~equal_set(A, B)) & subset(B, C) & (~equal_set(B, C)))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.13/0.40 tff(37,plain,
% 0.13/0.40 (~![A: $i, B: $i, C: $i] : ((~equal_set(A, C)) | (~(subset(A, B) & (~equal_set(A, B)) & subset(B, C) & (~equal_set(B, C)))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[36, 33])).
% 0.13/0.40 tff(38,plain,
% 0.13/0.40 (~![A: $i, B: $i, C: $i] : ((~equal_set(A, C)) | (~(subset(A, B) & (~equal_set(A, B)) & subset(B, C) & (~equal_set(B, C)))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[37, 33])).
% 0.13/0.40 tff(39,plain,
% 0.13/0.40 (~![A: $i, B: $i, C: $i] : ((~equal_set(A, C)) | (~(subset(A, B) & (~equal_set(A, B)) & subset(B, C) & (~equal_set(B, C)))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[38, 33])).
% 0.13/0.40 tff(40,plain,(
% 0.13/0.40 ~((~equal_set(A!5, C!3)) | (~(subset(A!5, B!4) & (~equal_set(A!5, B!4)) & subset(B!4, C!3) & (~equal_set(B!4, C!3)))))),
% 0.13/0.40 inference(skolemize,[status(sab)],[39])).
% 0.13/0.40 tff(41,plain,
% 0.13/0.40 (equal_set(A!5, C!3)),
% 0.13/0.40 inference(or_elim,[status(thm)],[40])).
% 0.13/0.40 tff(42,plain,
% 0.13/0.40 ((((~subset(A!5, C!3)) | (~subset(C!3, A!5))) <=> equal_set(A!5, C!3)) | (~((~subset(A!5, C!3)) | (~subset(C!3, A!5)))) | (~equal_set(A!5, C!3))),
% 0.13/0.40 inference(tautology,[status(thm)],[])).
% 0.13/0.40 tff(43,plain,
% 0.13/0.40 ((((~subset(A!5, C!3)) | (~subset(C!3, A!5))) <=> equal_set(A!5, C!3)) | (~((~subset(A!5, C!3)) | (~subset(C!3, A!5))))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[42, 41])).
% 0.13/0.40 tff(44,plain,
% 0.13/0.40 (~((~subset(A!5, C!3)) | (~subset(C!3, A!5)))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[43, 32])).
% 0.13/0.40 tff(45,plain,
% 0.13/0.40 (((~subset(A!5, C!3)) | (~subset(C!3, A!5))) | subset(C!3, A!5)),
% 0.13/0.40 inference(tautology,[status(thm)],[])).
% 0.13/0.40 tff(46,plain,
% 0.13/0.40 (subset(C!3, A!5)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[45, 44])).
% 0.13/0.40 tff(47,plain,
% 0.13/0.40 ((~((~subset(C!3, A!5)) | ![X: $i] : ((~member(X, C!3)) | member(X, A!5)))) | (~subset(C!3, A!5)) | ![X: $i] : ((~member(X, C!3)) | member(X, A!5))),
% 0.13/0.40 inference(tautology,[status(thm)],[])).
% 0.13/0.40 tff(48,plain,
% 0.13/0.40 ((~((~subset(C!3, A!5)) | ![X: $i] : ((~member(X, C!3)) | member(X, A!5)))) | ![X: $i] : ((~member(X, C!3)) | member(X, A!5))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[47, 46])).
% 0.13/0.40 tff(49,plain,
% 0.13/0.40 (![X: $i] : ((~member(X, C!3)) | member(X, A!5))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[48, 20])).
% 0.13/0.40 tff(50,plain,
% 0.13/0.40 ((~![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(B!4, A!5)) | ![X: $i] : ((~member(X, B!4)) | member(X, A!5)))) | (~(subset(B!4, A!5) | (~((~member(tptp_fun_X_0(A!5, B!4), B!4)) | member(tptp_fun_X_0(A!5, B!4), A!5)))))))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(51,plain,
% 0.13/0.40 (~((~((~subset(B!4, A!5)) | ![X: $i] : ((~member(X, B!4)) | member(X, A!5)))) | (~(subset(B!4, A!5) | (~((~member(tptp_fun_X_0(A!5, B!4), B!4)) | member(tptp_fun_X_0(A!5, B!4), A!5))))))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[50, 16])).
% 0.13/0.40 tff(52,plain,
% 0.13/0.40 (((~((~subset(B!4, A!5)) | ![X: $i] : ((~member(X, B!4)) | member(X, A!5)))) | (~(subset(B!4, A!5) | (~((~member(tptp_fun_X_0(A!5, B!4), B!4)) | member(tptp_fun_X_0(A!5, B!4), A!5)))))) | (subset(B!4, A!5) | (~((~member(tptp_fun_X_0(A!5, B!4), B!4)) | member(tptp_fun_X_0(A!5, B!4), A!5))))),
% 0.13/0.40 inference(tautology,[status(thm)],[])).
% 0.13/0.40 tff(53,plain,
% 0.13/0.40 (subset(B!4, A!5) | (~((~member(tptp_fun_X_0(A!5, B!4), B!4)) | member(tptp_fun_X_0(A!5, B!4), A!5)))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[52, 51])).
% 0.13/0.40 tff(54,plain,
% 0.13/0.40 ((~![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))) | (~(((~subset(A!5, B!4)) | (~subset(B!4, A!5))) <=> equal_set(A!5, B!4)))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(55,plain,
% 0.13/0.40 (~(((~subset(A!5, B!4)) | (~subset(B!4, A!5))) <=> equal_set(A!5, B!4))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[54, 30])).
% 0.13/0.40 tff(56,plain,
% 0.13/0.40 (subset(A!5, B!4) & (~equal_set(A!5, B!4)) & subset(B!4, C!3) & (~equal_set(B!4, C!3))),
% 0.13/0.40 inference(or_elim,[status(thm)],[40])).
% 0.13/0.40 tff(57,plain,
% 0.13/0.40 (~equal_set(A!5, B!4)),
% 0.13/0.40 inference(and_elim,[status(thm)],[56])).
% 0.13/0.40 tff(58,plain,
% 0.13/0.40 ((((~subset(A!5, B!4)) | (~subset(B!4, A!5))) <=> equal_set(A!5, B!4)) | ((~subset(A!5, B!4)) | (~subset(B!4, A!5))) | equal_set(A!5, B!4)),
% 0.13/0.40 inference(tautology,[status(thm)],[])).
% 0.13/0.40 tff(59,plain,
% 0.13/0.40 ((((~subset(A!5, B!4)) | (~subset(B!4, A!5))) <=> equal_set(A!5, B!4)) | ((~subset(A!5, B!4)) | (~subset(B!4, A!5)))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[58, 57])).
% 0.13/0.40 tff(60,plain,
% 0.13/0.40 ((~subset(A!5, B!4)) | (~subset(B!4, A!5))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[59, 55])).
% 0.13/0.40 tff(61,plain,
% 0.13/0.40 (subset(A!5, B!4)),
% 0.13/0.40 inference(and_elim,[status(thm)],[56])).
% 0.13/0.40 tff(62,plain,
% 0.13/0.40 ((~((~subset(A!5, B!4)) | (~subset(B!4, A!5)))) | (~subset(A!5, B!4)) | (~subset(B!4, A!5))),
% 0.13/0.40 inference(tautology,[status(thm)],[])).
% 0.13/0.40 tff(63,plain,
% 0.13/0.40 ((~((~subset(A!5, B!4)) | (~subset(B!4, A!5)))) | (~subset(B!4, A!5))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[62, 61])).
% 0.13/0.40 tff(64,plain,
% 0.13/0.40 (~subset(B!4, A!5)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[63, 60])).
% 0.13/0.40 tff(65,plain,
% 0.13/0.40 ((~(subset(B!4, A!5) | (~((~member(tptp_fun_X_0(A!5, B!4), B!4)) | member(tptp_fun_X_0(A!5, B!4), A!5))))) | subset(B!4, A!5) | (~((~member(tptp_fun_X_0(A!5, B!4), B!4)) | member(tptp_fun_X_0(A!5, B!4), A!5)))),
% 0.13/0.40 inference(tautology,[status(thm)],[])).
% 0.13/0.40 tff(66,plain,
% 0.13/0.40 ((~(subset(B!4, A!5) | (~((~member(tptp_fun_X_0(A!5, B!4), B!4)) | member(tptp_fun_X_0(A!5, B!4), A!5))))) | (~((~member(tptp_fun_X_0(A!5, B!4), B!4)) | member(tptp_fun_X_0(A!5, B!4), A!5)))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[65, 64])).
% 0.13/0.40 tff(67,plain,
% 0.13/0.40 (~((~member(tptp_fun_X_0(A!5, B!4), B!4)) | member(tptp_fun_X_0(A!5, B!4), A!5))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[66, 53])).
% 0.13/0.40 tff(68,plain,
% 0.13/0.40 (((~member(tptp_fun_X_0(A!5, B!4), B!4)) | member(tptp_fun_X_0(A!5, B!4), A!5)) | (~member(tptp_fun_X_0(A!5, B!4), A!5))),
% 0.13/0.40 inference(tautology,[status(thm)],[])).
% 0.13/0.40 tff(69,plain,
% 0.13/0.40 (~member(tptp_fun_X_0(A!5, B!4), A!5)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[68, 67])).
% 0.13/0.40 tff(70,plain,
% 0.13/0.40 (((~![X: $i] : ((~member(X, C!3)) | member(X, A!5))) | ((~member(tptp_fun_X_0(A!5, B!4), C!3)) | member(tptp_fun_X_0(A!5, B!4), A!5))) <=> ((~![X: $i] : ((~member(X, C!3)) | member(X, A!5))) | (~member(tptp_fun_X_0(A!5, B!4), C!3)) | member(tptp_fun_X_0(A!5, B!4), A!5))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(71,plain,
% 0.13/0.40 ((~![X: $i] : ((~member(X, C!3)) | member(X, A!5))) | ((~member(tptp_fun_X_0(A!5, B!4), C!3)) | member(tptp_fun_X_0(A!5, B!4), A!5))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(72,plain,
% 0.13/0.40 ((~![X: $i] : ((~member(X, C!3)) | member(X, A!5))) | (~member(tptp_fun_X_0(A!5, B!4), C!3)) | member(tptp_fun_X_0(A!5, B!4), A!5)),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.13/0.40 tff(73,plain,
% 0.13/0.40 (~member(tptp_fun_X_0(A!5, B!4), C!3)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[72, 69, 49])).
% 0.13/0.40 tff(74,plain,
% 0.13/0.40 (((~member(tptp_fun_X_0(A!5, B!4), B!4)) | member(tptp_fun_X_0(A!5, B!4), A!5)) | member(tptp_fun_X_0(A!5, B!4), B!4)),
% 0.13/0.40 inference(tautology,[status(thm)],[])).
% 0.13/0.40 tff(75,plain,
% 0.13/0.40 (member(tptp_fun_X_0(A!5, B!4), B!4)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[74, 67])).
% 0.13/0.40 tff(76,plain,
% 0.13/0.40 ((~![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(B!4, C!3)) | ![X: $i] : ((~member(X, B!4)) | member(X, C!3)))) | (~(subset(B!4, C!3) | (~((~member(tptp_fun_X_0(C!3, B!4), B!4)) | member(tptp_fun_X_0(C!3, B!4), C!3)))))))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(77,plain,
% 0.13/0.40 (~((~((~subset(B!4, C!3)) | ![X: $i] : ((~member(X, B!4)) | member(X, C!3)))) | (~(subset(B!4, C!3) | (~((~member(tptp_fun_X_0(C!3, B!4), B!4)) | member(tptp_fun_X_0(C!3, B!4), C!3))))))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[76, 16])).
% 0.13/0.40 tff(78,plain,
% 0.13/0.40 (((~((~subset(B!4, C!3)) | ![X: $i] : ((~member(X, B!4)) | member(X, C!3)))) | (~(subset(B!4, C!3) | (~((~member(tptp_fun_X_0(C!3, B!4), B!4)) | member(tptp_fun_X_0(C!3, B!4), C!3)))))) | ((~subset(B!4, C!3)) | ![X: $i] : ((~member(X, B!4)) | member(X, C!3)))),
% 0.13/0.40 inference(tautology,[status(thm)],[])).
% 0.13/0.40 tff(79,plain,
% 0.13/0.40 ((~subset(B!4, C!3)) | ![X: $i] : ((~member(X, B!4)) | member(X, C!3))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[78, 77])).
% 0.13/0.40 tff(80,plain,
% 0.13/0.40 (subset(B!4, C!3)),
% 0.13/0.40 inference(and_elim,[status(thm)],[56])).
% 0.13/0.40 tff(81,plain,
% 0.13/0.40 ((~((~subset(B!4, C!3)) | ![X: $i] : ((~member(X, B!4)) | member(X, C!3)))) | (~subset(B!4, C!3)) | ![X: $i] : ((~member(X, B!4)) | member(X, C!3))),
% 0.13/0.40 inference(tautology,[status(thm)],[])).
% 0.13/0.40 tff(82,plain,
% 0.13/0.40 ((~((~subset(B!4, C!3)) | ![X: $i] : ((~member(X, B!4)) | member(X, C!3)))) | ![X: $i] : ((~member(X, B!4)) | member(X, C!3))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[81, 80])).
% 0.13/0.40 tff(83,plain,
% 0.13/0.40 (![X: $i] : ((~member(X, B!4)) | member(X, C!3))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[82, 79])).
% 0.13/0.40 tff(84,plain,
% 0.13/0.40 (((~![X: $i] : ((~member(X, B!4)) | member(X, C!3))) | ((~member(tptp_fun_X_0(A!5, B!4), B!4)) | member(tptp_fun_X_0(A!5, B!4), C!3))) <=> ((~![X: $i] : ((~member(X, B!4)) | member(X, C!3))) | (~member(tptp_fun_X_0(A!5, B!4), B!4)) | member(tptp_fun_X_0(A!5, B!4), C!3))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(85,plain,
% 0.13/0.41 ((~![X: $i] : ((~member(X, B!4)) | member(X, C!3))) | ((~member(tptp_fun_X_0(A!5, B!4), B!4)) | member(tptp_fun_X_0(A!5, B!4), C!3))),
% 0.13/0.41 inference(quant_inst,[status(thm)],[])).
% 0.13/0.41 tff(86,plain,
% 0.13/0.41 ((~![X: $i] : ((~member(X, B!4)) | member(X, C!3))) | (~member(tptp_fun_X_0(A!5, B!4), B!4)) | member(tptp_fun_X_0(A!5, B!4), C!3)),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.13/0.41 tff(87,plain,
% 0.13/0.41 ($false),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[86, 83, 75, 73])).
% 0.13/0.41 % SZS output end Proof
% 0.13/0.41 % E exiting
%------------------------------------------------------------------------------