%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET013+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 05:24:46 AM UTC 2025
% Result : Theorem 0.20s 0.38s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SET013+4 : TPTP v9.0.0. Released v2.2.0.
% 0.03/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n003.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 04:01:24 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.20/0.38 % SZS status Theorem
% 0.20/0.38 % SZS output start Proof
% 0.20/0.38 tff(member_type, type, (
% 0.20/0.38 member: ( $i * $i ) > $o)).
% 0.20/0.38 tff(intersection_type, type, (
% 0.20/0.38 intersection: ( $i * $i ) > $i)).
% 0.20/0.38 tff(tptp_fun_A_4_type, type, (
% 0.20/0.38 tptp_fun_A_4: $i)).
% 0.20/0.38 tff(tptp_fun_B_3_type, type, (
% 0.20/0.38 tptp_fun_B_3: $i)).
% 0.20/0.38 tff(tptp_fun_X_0_type, type, (
% 0.20/0.38 tptp_fun_X_0: ( $i * $i ) > $i)).
% 0.20/0.38 tff(subset_type, type, (
% 0.20/0.38 subset: ( $i * $i ) > $o)).
% 0.20/0.38 tff(equal_set_type, type, (
% 0.20/0.38 equal_set: ( $i * $i ) > $o)).
% 0.20/0.38 tff(1,plain,
% 0.20/0.38 (^[X: $i, A: $i, B: $i] : refl((~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B)))) <=> (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B)))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(2,plain,
% 0.20/0.38 (![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B)))) <=> ![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.38 tff(3,plain,
% 0.20/0.38 (^[X: $i, A: $i, B: $i] : trans(trans(monotonicity(rewrite((member(X, A) & member(X, B)) <=> (~((~member(X, A)) | (~member(X, B))))), ((member(X, intersection(A, B)) <=> (member(X, A) & member(X, B))) <=> (member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B))))))), rewrite((member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B))))) <=> (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))), ((member(X, intersection(A, B)) <=> (member(X, A) & member(X, B))) <=> (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B)))))), rewrite((~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B)))) <=> (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))), ((member(X, intersection(A, B)) <=> (member(X, A) & member(X, B))) <=> (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(4,plain,
% 0.20/0.38 (![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (member(X, A) & member(X, B))) <=> ![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[3])).
% 0.20/0.38 tff(5,plain,
% 0.20/0.38 (![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (member(X, A) & member(X, B))) <=> ![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (member(X, A) & member(X, B)))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(6,axiom,(![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (member(X, A) & member(X, B)))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax','intersection')).
% 0.20/0.38 tff(7,plain,
% 0.20/0.38 (![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (member(X, A) & member(X, B)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.20/0.38 tff(8,plain,(
% 0.20/0.38 ![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (member(X, A) & member(X, B)))),
% 0.20/0.38 inference(skolemize,[status(sab)],[7])).
% 0.20/0.38 tff(9,plain,
% 0.20/0.38 (![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.20/0.38 tff(10,plain,
% 0.20/0.38 (![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.20/0.38 tff(11,plain,
% 0.20/0.38 (((~![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))) | (~(((~member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), A!4)) | (~member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), B!3))) <=> member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), intersection(B!3, A!4))))) <=> ((~![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))) | (~(((~member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), A!4)) | (~member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), B!3))) <=> member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), intersection(B!3, A!4)))))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(12,plain,
% 0.20/0.38 ((~(((~member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), A!4)) | (~member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), B!3))) <=> member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), intersection(B!3, A!4)))) <=> (~(((~member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), A!4)) | (~member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), B!3))) <=> member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), intersection(B!3, A!4))))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(13,plain,
% 0.20/0.38 ((((~member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), B!3)) | (~member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), A!4))) <=> member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), intersection(B!3, A!4))) <=> (((~member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), A!4)) | (~member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), B!3))) <=> member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), intersection(B!3, A!4)))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(14,plain,
% 0.20/0.38 ((~(((~member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), B!3)) | (~member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), A!4))) <=> member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), intersection(B!3, A!4)))) <=> (~(((~member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), A!4)) | (~member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), B!3))) <=> member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), intersection(B!3, A!4))))),
% 0.20/0.38 inference(monotonicity,[status(thm)],[13])).
% 0.20/0.38 tff(15,plain,
% 0.20/0.38 ((~(((~member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), B!3)) | (~member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), A!4))) <=> member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), intersection(B!3, A!4)))) <=> (~(((~member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), A!4)) | (~member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), B!3))) <=> member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), intersection(B!3, A!4))))),
% 0.20/0.38 inference(transitivity,[status(thm)],[14, 12])).
% 0.20/0.38 tff(16,plain,
% 0.20/0.38 (((~![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))) | (~(((~member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), B!3)) | (~member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), A!4))) <=> member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), intersection(B!3, A!4))))) <=> ((~![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))) | (~(((~member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), A!4)) | (~member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), B!3))) <=> member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), intersection(B!3, A!4)))))),
% 0.20/0.38 inference(monotonicity,[status(thm)],[15])).
% 0.20/0.38 tff(17,plain,
% 0.20/0.38 (((~![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))) | (~(((~member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), B!3)) | (~member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), A!4))) <=> member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), intersection(B!3, A!4))))) <=> ((~![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))) | (~(((~member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), A!4)) | (~member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), B!3))) <=> member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), intersection(B!3, A!4)))))),
% 0.20/0.38 inference(transitivity,[status(thm)],[16, 11])).
% 0.20/0.38 tff(18,plain,
% 0.20/0.38 ((~![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))) | (~(((~member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), B!3)) | (~member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), A!4))) <=> member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), intersection(B!3, A!4))))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(19,plain,
% 0.20/0.39 ((~![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))) | (~(((~member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), A!4)) | (~member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), B!3))) <=> member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), intersection(B!3, A!4))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.20/0.39 tff(20,plain,
% 0.20/0.39 (~(((~member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), A!4)) | (~member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), B!3))) <=> member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), intersection(B!3, A!4)))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[19, 10])).
% 0.20/0.39 tff(21,plain,
% 0.20/0.39 ((~![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))) | (~(((~member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), A!4)) | (~member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), B!3))) <=> member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), intersection(A!4, B!3))))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(22,plain,
% 0.20/0.39 (~(((~member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), A!4)) | (~member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), B!3))) <=> member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), intersection(A!4, B!3)))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[21, 10])).
% 0.20/0.39 tff(23,plain,
% 0.20/0.39 (^[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))))))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(24,plain,
% 0.20/0.39 (![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)))))))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[23])).
% 0.20/0.39 tff(25,plain,
% 0.20/0.39 (^[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))))))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(26,plain,
% 0.20/0.39 (![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)))))))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[25])).
% 0.20/0.39 tff(27,plain,
% 0.20/0.39 (![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)))))))),
% 0.20/0.39 inference(transitivity,[status(thm)],[26, 24])).
% 0.20/0.39 tff(28,plain,
% 0.20/0.39 (^[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)))))))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(29,plain,
% 0.20/0.39 (![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)))))))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[28])).
% 0.20/0.39 tff(30,plain,
% 0.20/0.39 (![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)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(31,plain,
% 0.20/0.39 (^[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))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(32,plain,
% 0.20/0.39 (![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)))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[31])).
% 0.20/0.39 tff(33,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')).
% 0.20/0.39 tff(34,plain,
% 0.20/0.39 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.20/0.39 tff(35,plain,
% 0.20/0.39 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[34, 30])).
% 0.20/0.39 tff(36,plain,(
% 0.20/0.39 ![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)))))),
% 0.20/0.39 inference(skolemize,[status(sab)],[35])).
% 0.20/0.39 tff(37,plain,
% 0.20/0.39 (![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)))))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[36, 29])).
% 0.20/0.39 tff(38,plain,
% 0.20/0.39 (![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)))))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[37, 27])).
% 0.20/0.39 tff(39,plain,
% 0.20/0.39 ((~![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)))))))) | (~((~((~subset(intersection(B!3, A!4), intersection(A!4, B!3))) | ![X: $i] : ((~member(X, intersection(B!3, A!4))) | member(X, intersection(A!4, B!3))))) | (~(subset(intersection(B!3, A!4), intersection(A!4, B!3)) | (~((~member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), intersection(B!3, A!4))) | member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), intersection(A!4, B!3))))))))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(40,plain,
% 0.20/0.39 (~((~((~subset(intersection(B!3, A!4), intersection(A!4, B!3))) | ![X: $i] : ((~member(X, intersection(B!3, A!4))) | member(X, intersection(A!4, B!3))))) | (~(subset(intersection(B!3, A!4), intersection(A!4, B!3)) | (~((~member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), intersection(B!3, A!4))) | member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), intersection(A!4, B!3)))))))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[39, 38])).
% 0.20/0.39 tff(41,plain,
% 0.20/0.39 (((~((~subset(intersection(B!3, A!4), intersection(A!4, B!3))) | ![X: $i] : ((~member(X, intersection(B!3, A!4))) | member(X, intersection(A!4, B!3))))) | (~(subset(intersection(B!3, A!4), intersection(A!4, B!3)) | (~((~member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), intersection(B!3, A!4))) | member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), intersection(A!4, B!3))))))) | (subset(intersection(B!3, A!4), intersection(A!4, B!3)) | (~((~member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), intersection(B!3, A!4))) | member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), intersection(A!4, B!3)))))),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(42,plain,
% 0.20/0.39 (subset(intersection(B!3, A!4), intersection(A!4, B!3)) | (~((~member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), intersection(B!3, A!4))) | member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), intersection(A!4, B!3))))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[41, 40])).
% 0.20/0.39 tff(43,assumption,((~((~subset(intersection(A!4, B!3), intersection(B!3, A!4))) | ![X: $i] : ((~member(X, intersection(A!4, B!3))) | member(X, intersection(B!3, A!4))))) | (~(subset(intersection(A!4, B!3), intersection(B!3, A!4)) | (~((~member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), intersection(A!4, B!3))) | member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), intersection(B!3, A!4))))))), introduced(assumption)).
% 0.20/0.39 tff(44,plain,
% 0.20/0.39 ((~![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)))))))) | (~((~((~subset(intersection(A!4, B!3), intersection(B!3, A!4))) | ![X: $i] : ((~member(X, intersection(A!4, B!3))) | member(X, intersection(B!3, A!4))))) | (~(subset(intersection(A!4, B!3), intersection(B!3, A!4)) | (~((~member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), intersection(A!4, B!3))) | member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), intersection(B!3, A!4))))))))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(45,plain,
% 0.20/0.39 ($false),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[44, 38, 43])).
% 0.20/0.39 tff(46,plain,(~((~((~subset(intersection(A!4, B!3), intersection(B!3, A!4))) | ![X: $i] : ((~member(X, intersection(A!4, B!3))) | member(X, intersection(B!3, A!4))))) | (~(subset(intersection(A!4, B!3), intersection(B!3, A!4)) | (~((~member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), intersection(A!4, B!3))) | member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), intersection(B!3, A!4)))))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.39 tff(47,plain,
% 0.20/0.39 (((~((~subset(intersection(A!4, B!3), intersection(B!3, A!4))) | ![X: $i] : ((~member(X, intersection(A!4, B!3))) | member(X, intersection(B!3, A!4))))) | (~(subset(intersection(A!4, B!3), intersection(B!3, A!4)) | (~((~member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), intersection(A!4, B!3))) | member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), intersection(B!3, A!4))))))) | (subset(intersection(A!4, B!3), intersection(B!3, A!4)) | (~((~member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), intersection(A!4, B!3))) | member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), intersection(B!3, A!4)))))),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(48,plain,
% 0.20/0.40 (subset(intersection(A!4, B!3), intersection(B!3, A!4)) | (~((~member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), intersection(A!4, B!3))) | member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), intersection(B!3, A!4))))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[47, 46])).
% 0.20/0.40 tff(49,plain,
% 0.20/0.40 ((~![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))) | (~(((~member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), B!3)) | (~member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), A!4))) <=> member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), intersection(B!3, A!4))))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(50,plain,
% 0.20/0.40 (~(((~member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), B!3)) | (~member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), A!4))) <=> member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), intersection(B!3, A!4)))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[49, 10])).
% 0.20/0.40 tff(51,assumption,(~((~member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), intersection(A!4, B!3))) | member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), intersection(B!3, A!4)))), introduced(assumption)).
% 0.20/0.40 tff(52,plain,
% 0.20/0.40 (((~member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), intersection(A!4, B!3))) | member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), intersection(B!3, A!4))) | (~member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), intersection(B!3, A!4)))),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(53,plain,
% 0.20/0.40 (~member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), intersection(B!3, A!4))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[52, 51])).
% 0.20/0.40 tff(54,plain,
% 0.20/0.40 ((((~member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), B!3)) | (~member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), A!4))) <=> member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), intersection(B!3, A!4))) | ((~member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), B!3)) | (~member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), A!4))) | member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), intersection(B!3, A!4))),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(55,plain,
% 0.20/0.40 ((((~member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), B!3)) | (~member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), A!4))) <=> member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), intersection(B!3, A!4))) | ((~member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), B!3)) | (~member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), A!4)))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[54, 53])).
% 0.20/0.40 tff(56,plain,
% 0.20/0.40 ((~member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), B!3)) | (~member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), A!4))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[55, 50])).
% 0.20/0.40 tff(57,plain,
% 0.20/0.40 ((~![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))) | (~(((~member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), A!4)) | (~member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), B!3))) <=> member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), intersection(A!4, B!3))))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(58,plain,
% 0.20/0.40 (~(((~member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), A!4)) | (~member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), B!3))) <=> member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), intersection(A!4, B!3)))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[57, 10])).
% 0.20/0.40 tff(59,plain,
% 0.20/0.40 (((~member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), intersection(A!4, B!3))) | member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), intersection(B!3, A!4))) | member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), intersection(A!4, B!3))),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(60,plain,
% 0.20/0.40 (member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), intersection(A!4, B!3))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[59, 51])).
% 0.20/0.40 tff(61,plain,
% 0.20/0.40 ((((~member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), A!4)) | (~member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), B!3))) <=> member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), intersection(A!4, B!3))) | (~((~member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), A!4)) | (~member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), B!3)))) | (~member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), intersection(A!4, B!3)))),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(62,plain,
% 0.20/0.40 ((((~member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), A!4)) | (~member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), B!3))) <=> member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), intersection(A!4, B!3))) | (~((~member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), A!4)) | (~member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), B!3))))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[61, 60])).
% 0.20/0.40 tff(63,plain,
% 0.20/0.40 (~((~member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), A!4)) | (~member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), B!3)))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[62, 58])).
% 0.20/0.40 tff(64,plain,
% 0.20/0.40 (((~member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), A!4)) | (~member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), B!3))) | member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), A!4)),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(65,plain,
% 0.20/0.40 (member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), A!4)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[64, 63])).
% 0.20/0.40 tff(66,plain,
% 0.20/0.40 (((~member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), A!4)) | (~member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), B!3))) | member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), B!3)),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(67,plain,
% 0.20/0.40 (member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), B!3)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[66, 63])).
% 0.20/0.40 tff(68,plain,
% 0.20/0.40 ((~((~member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), B!3)) | (~member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), A!4)))) | (~member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), B!3)) | (~member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), A!4))),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(69,plain,
% 0.20/0.40 ($false),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[68, 67, 65, 56])).
% 0.20/0.40 tff(70,plain,((~member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), intersection(A!4, B!3))) | member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), intersection(B!3, A!4))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.40 tff(71,plain,
% 0.20/0.40 ((~(subset(intersection(A!4, B!3), intersection(B!3, A!4)) | (~((~member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), intersection(A!4, B!3))) | member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), intersection(B!3, A!4)))))) | subset(intersection(A!4, B!3), intersection(B!3, A!4)) | (~((~member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), intersection(A!4, B!3))) | member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), intersection(B!3, A!4))))),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(72,plain,
% 0.20/0.40 ((~(subset(intersection(A!4, B!3), intersection(B!3, A!4)) | (~((~member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), intersection(A!4, B!3))) | member(tptp_fun_X_0(intersection(B!3, A!4), intersection(A!4, B!3)), intersection(B!3, A!4)))))) | subset(intersection(A!4, B!3), intersection(B!3, A!4))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[71, 70])).
% 0.20/0.40 tff(73,plain,
% 0.20/0.40 (subset(intersection(A!4, B!3), intersection(B!3, A!4))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[72, 48])).
% 0.20/0.40 tff(74,plain,
% 0.20/0.40 (^[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))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(75,plain,
% 0.20/0.40 (![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)))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[74])).
% 0.20/0.40 tff(76,plain,
% 0.20/0.40 (^[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)))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(77,plain,
% 0.20/0.40 (![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)))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[76])).
% 0.20/0.40 tff(78,plain,
% 0.20/0.40 (![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)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(79,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')).
% 0.20/0.40 tff(80,plain,
% 0.20/0.40 (![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.20/0.40 tff(81,plain,(
% 0.20/0.40 ![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 0.20/0.40 inference(skolemize,[status(sab)],[80])).
% 0.20/0.40 tff(82,plain,
% 0.20/0.40 (![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[81, 77])).
% 0.20/0.40 tff(83,plain,
% 0.20/0.40 (![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[82, 75])).
% 0.20/0.40 tff(84,plain,
% 0.20/0.40 ((~![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))) | (~(((~subset(intersection(A!4, B!3), intersection(B!3, A!4))) | (~subset(intersection(B!3, A!4), intersection(A!4, B!3)))) <=> equal_set(intersection(A!4, B!3), intersection(B!3, A!4))))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(85,plain,
% 0.20/0.40 (~(((~subset(intersection(A!4, B!3), intersection(B!3, A!4))) | (~subset(intersection(B!3, A!4), intersection(A!4, B!3)))) <=> equal_set(intersection(A!4, B!3), intersection(B!3, A!4)))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[84, 83])).
% 0.20/0.40 tff(86,plain,
% 0.20/0.40 ((~![A: $i, B: $i] : equal_set(intersection(A, B), intersection(B, A))) <=> (~![A: $i, B: $i] : equal_set(intersection(A, B), intersection(B, A)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(87,axiom,(~![A: $i, B: $i] : equal_set(intersection(A, B), intersection(B, A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thI06')).
% 0.20/0.40 tff(88,plain,
% 0.20/0.40 (~![A: $i, B: $i] : equal_set(intersection(A, B), intersection(B, A))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.20/0.40 tff(89,plain,
% 0.20/0.40 (~![A: $i, B: $i] : equal_set(intersection(A, B), intersection(B, A))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[88, 86])).
% 0.20/0.40 tff(90,plain,
% 0.20/0.41 (~![A: $i, B: $i] : equal_set(intersection(A, B), intersection(B, A))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[89, 86])).
% 0.20/0.41 tff(91,plain,
% 0.20/0.41 (~![A: $i, B: $i] : equal_set(intersection(A, B), intersection(B, A))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[90, 86])).
% 0.20/0.41 tff(92,plain,(
% 0.20/0.41 ~equal_set(intersection(A!4, B!3), intersection(B!3, A!4))),
% 0.20/0.41 inference(skolemize,[status(sab)],[91])).
% 0.20/0.41 tff(93,plain,
% 0.20/0.41 ((((~subset(intersection(A!4, B!3), intersection(B!3, A!4))) | (~subset(intersection(B!3, A!4), intersection(A!4, B!3)))) <=> equal_set(intersection(A!4, B!3), intersection(B!3, A!4))) | ((~subset(intersection(A!4, B!3), intersection(B!3, A!4))) | (~subset(intersection(B!3, A!4), intersection(A!4, B!3)))) | equal_set(intersection(A!4, B!3), intersection(B!3, A!4))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(94,plain,
% 0.20/0.41 ((((~subset(intersection(A!4, B!3), intersection(B!3, A!4))) | (~subset(intersection(B!3, A!4), intersection(A!4, B!3)))) <=> equal_set(intersection(A!4, B!3), intersection(B!3, A!4))) | ((~subset(intersection(A!4, B!3), intersection(B!3, A!4))) | (~subset(intersection(B!3, A!4), intersection(A!4, B!3))))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[93, 92])).
% 0.20/0.41 tff(95,plain,
% 0.20/0.41 ((~subset(intersection(A!4, B!3), intersection(B!3, A!4))) | (~subset(intersection(B!3, A!4), intersection(A!4, B!3)))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[94, 85])).
% 0.20/0.41 tff(96,plain,
% 0.20/0.41 ((~((~subset(intersection(A!4, B!3), intersection(B!3, A!4))) | (~subset(intersection(B!3, A!4), intersection(A!4, B!3))))) | (~subset(intersection(A!4, B!3), intersection(B!3, A!4))) | (~subset(intersection(B!3, A!4), intersection(A!4, B!3)))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(97,plain,
% 0.20/0.41 ((~subset(intersection(A!4, B!3), intersection(B!3, A!4))) | (~subset(intersection(B!3, A!4), intersection(A!4, B!3)))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[96, 95])).
% 0.20/0.41 tff(98,plain,
% 0.20/0.41 (~subset(intersection(B!3, A!4), intersection(A!4, B!3))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[97, 73])).
% 0.20/0.41 tff(99,plain,
% 0.20/0.41 ((~(subset(intersection(B!3, A!4), intersection(A!4, B!3)) | (~((~member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), intersection(B!3, A!4))) | member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), intersection(A!4, B!3)))))) | subset(intersection(B!3, A!4), intersection(A!4, B!3)) | (~((~member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), intersection(B!3, A!4))) | member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), intersection(A!4, B!3))))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(100,plain,
% 0.20/0.41 ((~(subset(intersection(B!3, A!4), intersection(A!4, B!3)) | (~((~member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), intersection(B!3, A!4))) | member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), intersection(A!4, B!3)))))) | (~((~member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), intersection(B!3, A!4))) | member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), intersection(A!4, B!3))))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[99, 98])).
% 0.20/0.41 tff(101,plain,
% 0.20/0.41 (~((~member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), intersection(B!3, A!4))) | member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), intersection(A!4, B!3)))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[100, 42])).
% 0.20/0.41 tff(102,plain,
% 0.20/0.41 (((~member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), intersection(B!3, A!4))) | member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), intersection(A!4, B!3))) | (~member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), intersection(A!4, B!3)))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(103,plain,
% 0.20/0.41 (~member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), intersection(A!4, B!3))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[102, 101])).
% 0.20/0.41 tff(104,plain,
% 0.20/0.41 ((((~member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), A!4)) | (~member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), B!3))) <=> member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), intersection(A!4, B!3))) | ((~member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), A!4)) | (~member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), B!3))) | member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), intersection(A!4, B!3))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(105,plain,
% 0.20/0.41 ((((~member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), A!4)) | (~member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), B!3))) <=> member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), intersection(A!4, B!3))) | ((~member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), A!4)) | (~member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), B!3)))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[104, 103])).
% 0.20/0.41 tff(106,plain,
% 0.20/0.41 ((~member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), A!4)) | (~member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), B!3))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[105, 22])).
% 0.20/0.41 tff(107,plain,
% 0.20/0.41 (((~member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), intersection(B!3, A!4))) | member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), intersection(A!4, B!3))) | member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), intersection(B!3, A!4))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(108,plain,
% 0.20/0.41 (member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), intersection(B!3, A!4))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[107, 101])).
% 0.20/0.41 tff(109,plain,
% 0.20/0.41 ((((~member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), A!4)) | (~member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), B!3))) <=> member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), intersection(B!3, A!4))) | (~((~member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), A!4)) | (~member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), B!3)))) | (~member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), intersection(B!3, A!4)))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(110,plain,
% 0.20/0.41 ((((~member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), A!4)) | (~member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), B!3))) <=> member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), intersection(B!3, A!4))) | (~((~member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), A!4)) | (~member(tptp_fun_X_0(intersection(A!4, B!3), intersection(B!3, A!4)), B!3))))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[109, 108])).
% 0.20/0.41 tff(111,plain,
% 0.20/0.41 ($false),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[110, 106, 20])).
% 0.20/0.41 % SZS output end Proof
% 0.20/0.41 % E exiting
%------------------------------------------------------------------------------