%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET700+4 : TPTP v9.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n002.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 05:26:10 AM UTC 2025
% Result : Theorem 0.12s 0.38s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET700+4 : TPTP v9.0.0. Released v2.2.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n002.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 05:39:46 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.12/0.38 % SZS status Theorem
% 0.12/0.38 % SZS output start Proof
% 0.12/0.38 tff(member_type, type, (
% 0.12/0.38 member: ( $i * $i ) > $o)).
% 0.12/0.38 tff(difference_type, type, (
% 0.12/0.38 difference: ( $i * $i ) > $i)).
% 0.12/0.38 tff(tptp_fun_B_4_type, type, (
% 0.12/0.38 tptp_fun_B_4: $i)).
% 0.12/0.38 tff(tptp_fun_E_3_type, type, (
% 0.12/0.38 tptp_fun_E_3: $i)).
% 0.12/0.38 tff(tptp_fun_X_0_type, type, (
% 0.12/0.38 tptp_fun_X_0: ( $i * $i ) > $i)).
% 0.12/0.38 tff(tptp_fun_A_5_type, type, (
% 0.12/0.38 tptp_fun_A_5: $i)).
% 0.12/0.38 tff(subset_type, type, (
% 0.12/0.38 subset: ( $i * $i ) > $o)).
% 0.12/0.38 tff(intersection_type, type, (
% 0.12/0.38 intersection: ( $i * $i ) > $i)).
% 0.12/0.38 tff(1,assumption,(((~member(tptp_fun_X_0(B!4, intersection(A!5, difference(E!3, B!4))), A!5)) | (~member(tptp_fun_X_0(B!4, intersection(A!5, difference(E!3, B!4))), difference(E!3, B!4)))) <=> member(tptp_fun_X_0(B!4, intersection(A!5, difference(E!3, B!4))), intersection(A!5, difference(E!3, B!4)))), introduced(assumption)).
% 0.12/0.38 tff(2,plain,
% 0.12/0.38 (^[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)))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(3,plain,
% 0.12/0.38 (![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))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[2])).
% 0.12/0.38 tff(4,plain,
% 0.12/0.38 (^[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))))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(5,plain,
% 0.12/0.38 (![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))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[4])).
% 0.12/0.38 tff(6,plain,
% 0.12/0.38 (![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)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(7,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')).
% 0.12/0.38 tff(8,plain,
% 0.12/0.38 (![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (member(X, A) & member(X, B)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.12/0.38 tff(9,plain,(
% 0.12/0.38 ![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (member(X, A) & member(X, B)))),
% 0.12/0.38 inference(skolemize,[status(sab)],[8])).
% 0.12/0.38 tff(10,plain,
% 0.12/0.38 (![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.12/0.38 tff(11,plain,
% 0.12/0.38 (![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[10, 3])).
% 0.12/0.38 tff(12,plain,
% 0.12/0.38 ((~![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))) | (~(((~member(tptp_fun_X_0(B!4, intersection(A!5, difference(E!3, B!4))), A!5)) | (~member(tptp_fun_X_0(B!4, intersection(A!5, difference(E!3, B!4))), difference(E!3, B!4)))) <=> member(tptp_fun_X_0(B!4, intersection(A!5, difference(E!3, B!4))), intersection(A!5, difference(E!3, B!4)))))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(13,plain,
% 0.12/0.38 ($false),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[12, 11, 1])).
% 0.12/0.38 tff(14,plain,(~(((~member(tptp_fun_X_0(B!4, intersection(A!5, difference(E!3, B!4))), A!5)) | (~member(tptp_fun_X_0(B!4, intersection(A!5, difference(E!3, B!4))), difference(E!3, B!4)))) <=> member(tptp_fun_X_0(B!4, intersection(A!5, difference(E!3, B!4))), intersection(A!5, difference(E!3, B!4))))), inference(lemma,lemma(discharge,[]))).
% 0.12/0.38 tff(15,assumption,(~subset(intersection(A!5, difference(E!3, B!4)), B!4)), introduced(assumption)).
% 0.12/0.38 tff(16,plain,
% 0.12/0.38 (^[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))))))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(17,plain,
% 0.12/0.38 (![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)))))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[16])).
% 0.12/0.38 tff(18,plain,
% 0.12/0.38 (^[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))))))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(19,plain,
% 0.12/0.38 (![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)))))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[18])).
% 0.12/0.38 tff(20,plain,
% 0.12/0.38 (![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)))))))),
% 0.12/0.38 inference(transitivity,[status(thm)],[19, 17])).
% 0.12/0.38 tff(21,plain,
% 0.12/0.38 (^[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)))))))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(22,plain,
% 0.12/0.38 (![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)))))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[21])).
% 0.12/0.38 tff(23,plain,
% 0.12/0.38 (![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)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(24,plain,
% 0.12/0.38 (^[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))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(25,plain,
% 0.12/0.38 (![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)))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[24])).
% 0.12/0.38 tff(26,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')).
% 0.12/0.38 tff(27,plain,
% 0.12/0.38 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.12/0.38 tff(28,plain,
% 0.12/0.38 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[27, 23])).
% 0.12/0.38 tff(29,plain,(
% 0.12/0.38 ![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)))))),
% 0.12/0.38 inference(skolemize,[status(sab)],[28])).
% 0.12/0.38 tff(30,plain,
% 0.12/0.38 (![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)))))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[29, 22])).
% 0.12/0.38 tff(31,plain,
% 0.12/0.38 (![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)))))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[30, 20])).
% 0.12/0.38 tff(32,plain,
% 0.12/0.38 ((~![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!5, difference(E!3, B!4)), B!4)) | ![X: $i] : ((~member(X, intersection(A!5, difference(E!3, B!4)))) | member(X, B!4)))) | (~(subset(intersection(A!5, difference(E!3, B!4)), B!4) | (~((~member(tptp_fun_X_0(B!4, intersection(A!5, difference(E!3, B!4))), intersection(A!5, difference(E!3, B!4)))) | member(tptp_fun_X_0(B!4, intersection(A!5, difference(E!3, B!4))), B!4)))))))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(33,plain,
% 0.12/0.38 (~((~((~subset(intersection(A!5, difference(E!3, B!4)), B!4)) | ![X: $i] : ((~member(X, intersection(A!5, difference(E!3, B!4)))) | member(X, B!4)))) | (~(subset(intersection(A!5, difference(E!3, B!4)), B!4) | (~((~member(tptp_fun_X_0(B!4, intersection(A!5, difference(E!3, B!4))), intersection(A!5, difference(E!3, B!4)))) | member(tptp_fun_X_0(B!4, intersection(A!5, difference(E!3, B!4))), B!4))))))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[32, 31])).
% 0.12/0.38 tff(34,plain,
% 0.12/0.38 (((~((~subset(intersection(A!5, difference(E!3, B!4)), B!4)) | ![X: $i] : ((~member(X, intersection(A!5, difference(E!3, B!4)))) | member(X, B!4)))) | (~(subset(intersection(A!5, difference(E!3, B!4)), B!4) | (~((~member(tptp_fun_X_0(B!4, intersection(A!5, difference(E!3, B!4))), intersection(A!5, difference(E!3, B!4)))) | member(tptp_fun_X_0(B!4, intersection(A!5, difference(E!3, B!4))), B!4)))))) | (subset(intersection(A!5, difference(E!3, B!4)), B!4) | (~((~member(tptp_fun_X_0(B!4, intersection(A!5, difference(E!3, B!4))), intersection(A!5, difference(E!3, B!4)))) | member(tptp_fun_X_0(B!4, intersection(A!5, difference(E!3, B!4))), B!4))))),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(35,plain,
% 0.12/0.39 (subset(intersection(A!5, difference(E!3, B!4)), B!4) | (~((~member(tptp_fun_X_0(B!4, intersection(A!5, difference(E!3, B!4))), intersection(A!5, difference(E!3, B!4)))) | member(tptp_fun_X_0(B!4, intersection(A!5, difference(E!3, B!4))), B!4)))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[34, 33])).
% 0.12/0.39 tff(36,plain,
% 0.12/0.39 ((~(subset(intersection(A!5, difference(E!3, B!4)), B!4) | (~((~member(tptp_fun_X_0(B!4, intersection(A!5, difference(E!3, B!4))), intersection(A!5, difference(E!3, B!4)))) | member(tptp_fun_X_0(B!4, intersection(A!5, difference(E!3, B!4))), B!4))))) | subset(intersection(A!5, difference(E!3, B!4)), B!4) | (~((~member(tptp_fun_X_0(B!4, intersection(A!5, difference(E!3, B!4))), intersection(A!5, difference(E!3, B!4)))) | member(tptp_fun_X_0(B!4, intersection(A!5, difference(E!3, B!4))), B!4)))),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(37,plain,
% 0.12/0.39 (subset(intersection(A!5, difference(E!3, B!4)), B!4) | (~((~member(tptp_fun_X_0(B!4, intersection(A!5, difference(E!3, B!4))), intersection(A!5, difference(E!3, B!4)))) | member(tptp_fun_X_0(B!4, intersection(A!5, difference(E!3, B!4))), B!4)))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[36, 35])).
% 0.12/0.39 tff(38,plain,
% 0.12/0.39 (~((~member(tptp_fun_X_0(B!4, intersection(A!5, difference(E!3, B!4))), intersection(A!5, difference(E!3, B!4)))) | member(tptp_fun_X_0(B!4, intersection(A!5, difference(E!3, B!4))), B!4))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[37, 15])).
% 0.12/0.39 tff(39,plain,
% 0.12/0.39 (((~member(tptp_fun_X_0(B!4, intersection(A!5, difference(E!3, B!4))), intersection(A!5, difference(E!3, B!4)))) | member(tptp_fun_X_0(B!4, intersection(A!5, difference(E!3, B!4))), B!4)) | member(tptp_fun_X_0(B!4, intersection(A!5, difference(E!3, B!4))), intersection(A!5, difference(E!3, B!4)))),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(40,plain,
% 0.12/0.39 (member(tptp_fun_X_0(B!4, intersection(A!5, difference(E!3, B!4))), intersection(A!5, difference(E!3, B!4)))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[39, 38])).
% 0.12/0.39 tff(41,plain,
% 0.12/0.39 ((((~member(tptp_fun_X_0(B!4, intersection(A!5, difference(E!3, B!4))), A!5)) | (~member(tptp_fun_X_0(B!4, intersection(A!5, difference(E!3, B!4))), difference(E!3, B!4)))) <=> member(tptp_fun_X_0(B!4, intersection(A!5, difference(E!3, B!4))), intersection(A!5, difference(E!3, B!4)))) | (~((~member(tptp_fun_X_0(B!4, intersection(A!5, difference(E!3, B!4))), A!5)) | (~member(tptp_fun_X_0(B!4, intersection(A!5, difference(E!3, B!4))), difference(E!3, B!4))))) | (~member(tptp_fun_X_0(B!4, intersection(A!5, difference(E!3, B!4))), intersection(A!5, difference(E!3, B!4))))),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(42,plain,
% 0.12/0.39 (~((~member(tptp_fun_X_0(B!4, intersection(A!5, difference(E!3, B!4))), A!5)) | (~member(tptp_fun_X_0(B!4, intersection(A!5, difference(E!3, B!4))), difference(E!3, B!4))))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[41, 40, 14])).
% 0.12/0.39 tff(43,plain,
% 0.12/0.39 (((~member(tptp_fun_X_0(B!4, intersection(A!5, difference(E!3, B!4))), A!5)) | (~member(tptp_fun_X_0(B!4, intersection(A!5, difference(E!3, B!4))), difference(E!3, B!4)))) | member(tptp_fun_X_0(B!4, intersection(A!5, difference(E!3, B!4))), A!5)),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(44,plain,
% 0.12/0.39 (member(tptp_fun_X_0(B!4, intersection(A!5, difference(E!3, B!4))), A!5)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[43, 42])).
% 0.12/0.39 tff(45,plain,
% 0.12/0.39 (((~member(tptp_fun_X_0(B!4, intersection(A!5, difference(E!3, B!4))), intersection(A!5, difference(E!3, B!4)))) | member(tptp_fun_X_0(B!4, intersection(A!5, difference(E!3, B!4))), B!4)) | (~member(tptp_fun_X_0(B!4, intersection(A!5, difference(E!3, B!4))), B!4))),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(46,plain,
% 0.12/0.39 (~member(tptp_fun_X_0(B!4, intersection(A!5, difference(E!3, B!4))), B!4)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[45, 38])).
% 0.12/0.39 tff(47,plain,
% 0.12/0.39 ((~![A: $i, B: $i, E: $i] : ((~(subset(A, E) & subset(B, E))) | (subset(A, B) <=> subset(intersection(A, difference(E, B)), B)))) <=> (~![A: $i, B: $i, E: $i] : ((~(subset(A, E) & subset(B, E))) | (subset(A, B) <=> subset(intersection(A, difference(E, B)), B))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(48,plain,
% 0.12/0.39 ((~![A: $i, B: $i, E: $i] : ((subset(A, E) & subset(B, E)) => (subset(A, B) <=> subset(intersection(A, difference(E, B)), B)))) <=> (~![A: $i, B: $i, E: $i] : ((~(subset(A, E) & subset(B, E))) | (subset(A, B) <=> subset(intersection(A, difference(E, B)), B))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(49,axiom,(~![A: $i, B: $i, E: $i] : ((subset(A, E) & subset(B, E)) => (subset(A, B) <=> subset(intersection(A, difference(E, B)), B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thI34')).
% 0.12/0.39 tff(50,plain,
% 0.12/0.39 (~![A: $i, B: $i, E: $i] : ((~(subset(A, E) & subset(B, E))) | (subset(A, B) <=> subset(intersection(A, difference(E, B)), B)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.12/0.39 tff(51,plain,
% 0.12/0.39 (~![A: $i, B: $i, E: $i] : ((~(subset(A, E) & subset(B, E))) | (subset(A, B) <=> subset(intersection(A, difference(E, B)), B)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[50, 47])).
% 0.12/0.39 tff(52,plain,
% 0.12/0.39 (~![A: $i, B: $i, E: $i] : ((~(subset(A, E) & subset(B, E))) | (subset(A, B) <=> subset(intersection(A, difference(E, B)), B)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[51, 47])).
% 0.12/0.39 tff(53,plain,
% 0.12/0.39 (~![A: $i, B: $i, E: $i] : ((~(subset(A, E) & subset(B, E))) | (subset(A, B) <=> subset(intersection(A, difference(E, B)), B)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[52, 47])).
% 0.12/0.39 tff(54,plain,(
% 0.12/0.39 ~((~(subset(A!5, E!3) & subset(B!4, E!3))) | (subset(A!5, B!4) <=> subset(intersection(A!5, difference(E!3, B!4)), B!4)))),
% 0.12/0.39 inference(skolemize,[status(sab)],[53])).
% 0.12/0.39 tff(55,plain,
% 0.12/0.39 (~(subset(A!5, B!4) <=> subset(intersection(A!5, difference(E!3, B!4)), B!4))),
% 0.12/0.39 inference(or_elim,[status(thm)],[54])).
% 0.12/0.39 tff(56,plain,
% 0.12/0.39 ((subset(A!5, B!4) <=> subset(intersection(A!5, difference(E!3, B!4)), B!4)) | subset(A!5, B!4) | subset(intersection(A!5, difference(E!3, B!4)), B!4)),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(57,plain,
% 0.12/0.39 (subset(A!5, B!4) | subset(intersection(A!5, difference(E!3, B!4)), B!4)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[56, 55])).
% 0.12/0.39 tff(58,plain,
% 0.12/0.39 (subset(A!5, B!4)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[57, 15])).
% 0.12/0.39 tff(59,plain,
% 0.12/0.39 ((~![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(A!5, B!4)) | ![X: $i] : ((~member(X, A!5)) | member(X, B!4)))) | (~(subset(A!5, B!4) | (~((~member(tptp_fun_X_0(B!4, A!5), A!5)) | member(tptp_fun_X_0(B!4, A!5), B!4)))))))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(60,plain,
% 0.12/0.39 (~((~((~subset(A!5, B!4)) | ![X: $i] : ((~member(X, A!5)) | member(X, B!4)))) | (~(subset(A!5, B!4) | (~((~member(tptp_fun_X_0(B!4, A!5), A!5)) | member(tptp_fun_X_0(B!4, A!5), B!4))))))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[59, 31])).
% 0.12/0.39 tff(61,plain,
% 0.12/0.39 (((~((~subset(A!5, B!4)) | ![X: $i] : ((~member(X, A!5)) | member(X, B!4)))) | (~(subset(A!5, B!4) | (~((~member(tptp_fun_X_0(B!4, A!5), A!5)) | member(tptp_fun_X_0(B!4, A!5), B!4)))))) | ((~subset(A!5, B!4)) | ![X: $i] : ((~member(X, A!5)) | member(X, B!4)))),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(62,plain,
% 0.12/0.39 ((~subset(A!5, B!4)) | ![X: $i] : ((~member(X, A!5)) | member(X, B!4))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[61, 60])).
% 0.12/0.39 tff(63,plain,
% 0.12/0.39 ((~((~subset(A!5, B!4)) | ![X: $i] : ((~member(X, A!5)) | member(X, B!4)))) | (~subset(A!5, B!4)) | ![X: $i] : ((~member(X, A!5)) | member(X, B!4))),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(64,plain,
% 0.12/0.39 ((~subset(A!5, B!4)) | ![X: $i] : ((~member(X, A!5)) | member(X, B!4))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[63, 62])).
% 0.12/0.39 tff(65,plain,
% 0.12/0.39 (![X: $i] : ((~member(X, A!5)) | member(X, B!4))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[64, 58])).
% 0.12/0.39 tff(66,plain,
% 0.12/0.39 (((~![X: $i] : ((~member(X, A!5)) | member(X, B!4))) | ((~member(tptp_fun_X_0(B!4, intersection(A!5, difference(E!3, B!4))), A!5)) | member(tptp_fun_X_0(B!4, intersection(A!5, difference(E!3, B!4))), B!4))) <=> ((~![X: $i] : ((~member(X, A!5)) | member(X, B!4))) | (~member(tptp_fun_X_0(B!4, intersection(A!5, difference(E!3, B!4))), A!5)) | member(tptp_fun_X_0(B!4, intersection(A!5, difference(E!3, B!4))), B!4))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(67,plain,
% 0.12/0.39 ((~![X: $i] : ((~member(X, A!5)) | member(X, B!4))) | ((~member(tptp_fun_X_0(B!4, intersection(A!5, difference(E!3, B!4))), A!5)) | member(tptp_fun_X_0(B!4, intersection(A!5, difference(E!3, B!4))), B!4))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(68,plain,
% 0.12/0.39 ((~![X: $i] : ((~member(X, A!5)) | member(X, B!4))) | (~member(tptp_fun_X_0(B!4, intersection(A!5, difference(E!3, B!4))), A!5)) | member(tptp_fun_X_0(B!4, intersection(A!5, difference(E!3, B!4))), B!4)),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.12/0.39 tff(69,plain,
% 0.12/0.39 ($false),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[68, 65, 46, 44])).
% 0.12/0.39 tff(70,plain,(subset(intersection(A!5, difference(E!3, B!4)), B!4)), inference(lemma,lemma(discharge,[]))).
% 0.12/0.39 tff(71,plain,
% 0.12/0.39 ((subset(A!5, B!4) <=> subset(intersection(A!5, difference(E!3, B!4)), B!4)) | (~subset(A!5, B!4)) | (~subset(intersection(A!5, difference(E!3, B!4)), B!4))),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(72,plain,
% 0.12/0.39 ((~subset(A!5, B!4)) | (~subset(intersection(A!5, difference(E!3, B!4)), B!4))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[71, 55])).
% 0.12/0.39 tff(73,plain,
% 0.12/0.39 (~subset(A!5, B!4)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[72, 70])).
% 0.12/0.39 tff(74,plain,
% 0.12/0.39 (((~((~subset(A!5, B!4)) | ![X: $i] : ((~member(X, A!5)) | member(X, B!4)))) | (~(subset(A!5, B!4) | (~((~member(tptp_fun_X_0(B!4, A!5), A!5)) | member(tptp_fun_X_0(B!4, A!5), B!4)))))) | (subset(A!5, B!4) | (~((~member(tptp_fun_X_0(B!4, A!5), A!5)) | member(tptp_fun_X_0(B!4, A!5), B!4))))),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(75,plain,
% 0.12/0.39 (subset(A!5, B!4) | (~((~member(tptp_fun_X_0(B!4, A!5), A!5)) | member(tptp_fun_X_0(B!4, A!5), B!4)))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[74, 60])).
% 0.12/0.39 tff(76,plain,
% 0.12/0.39 ((~(subset(A!5, B!4) | (~((~member(tptp_fun_X_0(B!4, A!5), A!5)) | member(tptp_fun_X_0(B!4, A!5), B!4))))) | subset(A!5, B!4) | (~((~member(tptp_fun_X_0(B!4, A!5), A!5)) | member(tptp_fun_X_0(B!4, A!5), B!4)))),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(77,plain,
% 0.12/0.39 (subset(A!5, B!4) | (~((~member(tptp_fun_X_0(B!4, A!5), A!5)) | member(tptp_fun_X_0(B!4, A!5), B!4)))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[76, 75])).
% 0.12/0.39 tff(78,plain,
% 0.12/0.39 (~((~member(tptp_fun_X_0(B!4, A!5), A!5)) | member(tptp_fun_X_0(B!4, A!5), B!4))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[77, 73])).
% 0.12/0.39 tff(79,plain,
% 0.12/0.39 (((~member(tptp_fun_X_0(B!4, A!5), A!5)) | member(tptp_fun_X_0(B!4, A!5), B!4)) | member(tptp_fun_X_0(B!4, A!5), A!5)),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(80,plain,
% 0.12/0.39 (member(tptp_fun_X_0(B!4, A!5), A!5)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[79, 78])).
% 0.12/0.39 tff(81,plain,
% 0.12/0.39 ((~![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(A!5, E!3)) | ![X: $i] : ((~member(X, A!5)) | member(X, E!3)))) | (~(subset(A!5, E!3) | (~((~member(tptp_fun_X_0(E!3, A!5), A!5)) | member(tptp_fun_X_0(E!3, A!5), E!3)))))))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(82,plain,
% 0.12/0.39 (~((~((~subset(A!5, E!3)) | ![X: $i] : ((~member(X, A!5)) | member(X, E!3)))) | (~(subset(A!5, E!3) | (~((~member(tptp_fun_X_0(E!3, A!5), A!5)) | member(tptp_fun_X_0(E!3, A!5), E!3))))))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[81, 31])).
% 0.12/0.39 tff(83,plain,
% 0.12/0.39 (((~((~subset(A!5, E!3)) | ![X: $i] : ((~member(X, A!5)) | member(X, E!3)))) | (~(subset(A!5, E!3) | (~((~member(tptp_fun_X_0(E!3, A!5), A!5)) | member(tptp_fun_X_0(E!3, A!5), E!3)))))) | ((~subset(A!5, E!3)) | ![X: $i] : ((~member(X, A!5)) | member(X, E!3)))),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(84,plain,
% 0.12/0.39 ((~subset(A!5, E!3)) | ![X: $i] : ((~member(X, A!5)) | member(X, E!3))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[83, 82])).
% 0.20/0.40 tff(85,plain,
% 0.20/0.40 (subset(A!5, E!3) & subset(B!4, E!3)),
% 0.20/0.40 inference(or_elim,[status(thm)],[54])).
% 0.20/0.40 tff(86,plain,
% 0.20/0.40 (subset(A!5, E!3)),
% 0.20/0.40 inference(and_elim,[status(thm)],[85])).
% 0.20/0.40 tff(87,plain,
% 0.20/0.40 ((~((~subset(A!5, E!3)) | ![X: $i] : ((~member(X, A!5)) | member(X, E!3)))) | (~subset(A!5, E!3)) | ![X: $i] : ((~member(X, A!5)) | member(X, E!3))),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(88,plain,
% 0.20/0.40 ((~((~subset(A!5, E!3)) | ![X: $i] : ((~member(X, A!5)) | member(X, E!3)))) | ![X: $i] : ((~member(X, A!5)) | member(X, E!3))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[87, 86])).
% 0.20/0.40 tff(89,plain,
% 0.20/0.40 (![X: $i] : ((~member(X, A!5)) | member(X, E!3))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[88, 84])).
% 0.20/0.40 tff(90,plain,
% 0.20/0.40 (((~![X: $i] : ((~member(X, A!5)) | member(X, E!3))) | ((~member(tptp_fun_X_0(B!4, A!5), A!5)) | member(tptp_fun_X_0(B!4, A!5), E!3))) <=> ((~![X: $i] : ((~member(X, A!5)) | member(X, E!3))) | (~member(tptp_fun_X_0(B!4, A!5), A!5)) | member(tptp_fun_X_0(B!4, A!5), E!3))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(91,plain,
% 0.20/0.40 ((~![X: $i] : ((~member(X, A!5)) | member(X, E!3))) | ((~member(tptp_fun_X_0(B!4, A!5), A!5)) | member(tptp_fun_X_0(B!4, A!5), E!3))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(92,plain,
% 0.20/0.40 ((~![X: $i] : ((~member(X, A!5)) | member(X, E!3))) | (~member(tptp_fun_X_0(B!4, A!5), A!5)) | member(tptp_fun_X_0(B!4, A!5), E!3)),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.20/0.40 tff(93,plain,
% 0.20/0.40 (member(tptp_fun_X_0(B!4, A!5), E!3)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[92, 89, 80])).
% 0.20/0.40 tff(94,plain,
% 0.20/0.40 (((~member(tptp_fun_X_0(B!4, A!5), A!5)) | member(tptp_fun_X_0(B!4, A!5), B!4)) | (~member(tptp_fun_X_0(B!4, A!5), B!4))),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(95,plain,
% 0.20/0.40 (~member(tptp_fun_X_0(B!4, A!5), B!4)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[94, 78])).
% 0.20/0.40 tff(96,plain,
% 0.20/0.40 ((~((~member(tptp_fun_X_0(B!4, A!5), E!3)) | member(tptp_fun_X_0(B!4, A!5), B!4))) | (~member(tptp_fun_X_0(B!4, A!5), E!3)) | member(tptp_fun_X_0(B!4, A!5), B!4)),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(97,plain,
% 0.20/0.40 (~((~member(tptp_fun_X_0(B!4, A!5), E!3)) | member(tptp_fun_X_0(B!4, A!5), B!4))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[96, 95, 93])).
% 0.20/0.40 tff(98,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(B!4, A!5), A!5)) | (~member(tptp_fun_X_0(B!4, A!5), difference(E!3, B!4)))) <=> member(tptp_fun_X_0(B!4, A!5), intersection(A!5, difference(E!3, B!4)))))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(99,plain,
% 0.20/0.40 (~(((~member(tptp_fun_X_0(B!4, A!5), A!5)) | (~member(tptp_fun_X_0(B!4, A!5), difference(E!3, B!4)))) <=> member(tptp_fun_X_0(B!4, A!5), intersection(A!5, difference(E!3, B!4))))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[98, 11])).
% 0.20/0.40 tff(100,plain,
% 0.20/0.40 (((~((~subset(intersection(A!5, difference(E!3, B!4)), B!4)) | ![X: $i] : ((~member(X, intersection(A!5, difference(E!3, B!4)))) | member(X, B!4)))) | (~(subset(intersection(A!5, difference(E!3, B!4)), B!4) | (~((~member(tptp_fun_X_0(B!4, intersection(A!5, difference(E!3, B!4))), intersection(A!5, difference(E!3, B!4)))) | member(tptp_fun_X_0(B!4, intersection(A!5, difference(E!3, B!4))), B!4)))))) | ((~subset(intersection(A!5, difference(E!3, B!4)), B!4)) | ![X: $i] : ((~member(X, intersection(A!5, difference(E!3, B!4)))) | member(X, B!4)))),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(101,plain,
% 0.20/0.40 ((~subset(intersection(A!5, difference(E!3, B!4)), B!4)) | ![X: $i] : ((~member(X, intersection(A!5, difference(E!3, B!4)))) | member(X, B!4))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[100, 33])).
% 0.20/0.40 tff(102,plain,
% 0.20/0.40 ((~((~subset(intersection(A!5, difference(E!3, B!4)), B!4)) | ![X: $i] : ((~member(X, intersection(A!5, difference(E!3, B!4)))) | member(X, B!4)))) | (~subset(intersection(A!5, difference(E!3, B!4)), B!4)) | ![X: $i] : ((~member(X, intersection(A!5, difference(E!3, B!4)))) | member(X, B!4))),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(103,plain,
% 0.20/0.40 ((~subset(intersection(A!5, difference(E!3, B!4)), B!4)) | ![X: $i] : ((~member(X, intersection(A!5, difference(E!3, B!4)))) | member(X, B!4))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[102, 101])).
% 0.20/0.40 tff(104,plain,
% 0.20/0.40 (![X: $i] : ((~member(X, intersection(A!5, difference(E!3, B!4)))) | member(X, B!4))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[103, 70])).
% 0.20/0.40 tff(105,plain,
% 0.20/0.40 (((~![X: $i] : ((~member(X, intersection(A!5, difference(E!3, B!4)))) | member(X, B!4))) | ((~member(tptp_fun_X_0(B!4, A!5), intersection(A!5, difference(E!3, B!4)))) | member(tptp_fun_X_0(B!4, A!5), B!4))) <=> ((~![X: $i] : ((~member(X, intersection(A!5, difference(E!3, B!4)))) | member(X, B!4))) | (~member(tptp_fun_X_0(B!4, A!5), intersection(A!5, difference(E!3, B!4)))) | member(tptp_fun_X_0(B!4, A!5), B!4))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(106,plain,
% 0.20/0.40 ((~![X: $i] : ((~member(X, intersection(A!5, difference(E!3, B!4)))) | member(X, B!4))) | ((~member(tptp_fun_X_0(B!4, A!5), intersection(A!5, difference(E!3, B!4)))) | member(tptp_fun_X_0(B!4, A!5), B!4))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(107,plain,
% 0.20/0.40 ((~![X: $i] : ((~member(X, intersection(A!5, difference(E!3, B!4)))) | member(X, B!4))) | (~member(tptp_fun_X_0(B!4, A!5), intersection(A!5, difference(E!3, B!4)))) | member(tptp_fun_X_0(B!4, A!5), B!4)),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[106, 105])).
% 0.20/0.40 tff(108,plain,
% 0.20/0.40 (~member(tptp_fun_X_0(B!4, A!5), intersection(A!5, difference(E!3, B!4)))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[107, 95, 104])).
% 0.20/0.40 tff(109,plain,
% 0.20/0.40 ((((~member(tptp_fun_X_0(B!4, A!5), A!5)) | (~member(tptp_fun_X_0(B!4, A!5), difference(E!3, B!4)))) <=> member(tptp_fun_X_0(B!4, A!5), intersection(A!5, difference(E!3, B!4)))) | ((~member(tptp_fun_X_0(B!4, A!5), A!5)) | (~member(tptp_fun_X_0(B!4, A!5), difference(E!3, B!4)))) | member(tptp_fun_X_0(B!4, A!5), intersection(A!5, difference(E!3, B!4)))),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(110,plain,
% 0.20/0.40 ((((~member(tptp_fun_X_0(B!4, A!5), A!5)) | (~member(tptp_fun_X_0(B!4, A!5), difference(E!3, B!4)))) <=> member(tptp_fun_X_0(B!4, A!5), intersection(A!5, difference(E!3, B!4)))) | ((~member(tptp_fun_X_0(B!4, A!5), A!5)) | (~member(tptp_fun_X_0(B!4, A!5), difference(E!3, B!4))))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[109, 108])).
% 0.20/0.40 tff(111,plain,
% 0.20/0.40 ((~member(tptp_fun_X_0(B!4, A!5), A!5)) | (~member(tptp_fun_X_0(B!4, A!5), difference(E!3, B!4)))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[110, 99])).
% 0.20/0.40 tff(112,plain,
% 0.20/0.40 ((~((~member(tptp_fun_X_0(B!4, A!5), A!5)) | (~member(tptp_fun_X_0(B!4, A!5), difference(E!3, B!4))))) | (~member(tptp_fun_X_0(B!4, A!5), A!5)) | (~member(tptp_fun_X_0(B!4, A!5), difference(E!3, B!4)))),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(113,plain,
% 0.20/0.40 ((~((~member(tptp_fun_X_0(B!4, A!5), A!5)) | (~member(tptp_fun_X_0(B!4, A!5), difference(E!3, B!4))))) | (~member(tptp_fun_X_0(B!4, A!5), difference(E!3, B!4)))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[112, 80])).
% 0.20/0.40 tff(114,plain,
% 0.20/0.40 (~member(tptp_fun_X_0(B!4, A!5), difference(E!3, B!4))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[113, 111])).
% 0.20/0.40 tff(115,plain,
% 0.20/0.40 ((((~member(tptp_fun_X_0(B!4, A!5), E!3)) | member(tptp_fun_X_0(B!4, A!5), B!4)) <=> member(tptp_fun_X_0(B!4, A!5), difference(E!3, B!4))) | ((~member(tptp_fun_X_0(B!4, A!5), E!3)) | member(tptp_fun_X_0(B!4, A!5), B!4)) | member(tptp_fun_X_0(B!4, A!5), difference(E!3, B!4))),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(116,plain,
% 0.20/0.40 (((~member(tptp_fun_X_0(B!4, A!5), E!3)) | member(tptp_fun_X_0(B!4, A!5), B!4)) <=> member(tptp_fun_X_0(B!4, A!5), difference(E!3, B!4))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[115, 114, 97])).
% 0.20/0.40 tff(117,plain,
% 0.20/0.40 (^[B: $i, A: $i, E: $i] : refl((~(((~member(B, E)) | member(B, A)) <=> member(B, difference(E, A)))) <=> (~(((~member(B, E)) | member(B, A)) <=> member(B, difference(E, A)))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(118,plain,
% 0.20/0.40 (![B: $i, A: $i, E: $i] : (~(((~member(B, E)) | member(B, A)) <=> member(B, difference(E, A)))) <=> ![B: $i, A: $i, E: $i] : (~(((~member(B, E)) | member(B, A)) <=> member(B, difference(E, A))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[117])).
% 0.20/0.41 tff(119,plain,
% 0.20/0.41 (^[B: $i, A: $i, E: $i] : trans(trans(monotonicity(rewrite((member(B, E) & (~member(B, A))) <=> (~((~member(B, E)) | member(B, A)))), ((member(B, difference(E, A)) <=> (member(B, E) & (~member(B, A)))) <=> (member(B, difference(E, A)) <=> (~((~member(B, E)) | member(B, A)))))), rewrite((member(B, difference(E, A)) <=> (~((~member(B, E)) | member(B, A)))) <=> (~(((~member(B, E)) | member(B, A)) <=> member(B, difference(E, A))))), ((member(B, difference(E, A)) <=> (member(B, E) & (~member(B, A)))) <=> (~(((~member(B, E)) | member(B, A)) <=> member(B, difference(E, A)))))), rewrite((~(((~member(B, E)) | member(B, A)) <=> member(B, difference(E, A)))) <=> (~(((~member(B, E)) | member(B, A)) <=> member(B, difference(E, A))))), ((member(B, difference(E, A)) <=> (member(B, E) & (~member(B, A)))) <=> (~(((~member(B, E)) | member(B, A)) <=> member(B, difference(E, A))))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(120,plain,
% 0.20/0.41 (![B: $i, A: $i, E: $i] : (member(B, difference(E, A)) <=> (member(B, E) & (~member(B, A)))) <=> ![B: $i, A: $i, E: $i] : (~(((~member(B, E)) | member(B, A)) <=> member(B, difference(E, A))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[119])).
% 0.20/0.41 tff(121,plain,
% 0.20/0.41 (![B: $i, A: $i, E: $i] : (member(B, difference(E, A)) <=> (member(B, E) & (~member(B, A)))) <=> ![B: $i, A: $i, E: $i] : (member(B, difference(E, A)) <=> (member(B, E) & (~member(B, A))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(122,axiom,(![B: $i, A: $i, E: $i] : (member(B, difference(E, A)) <=> (member(B, E) & (~member(B, A))))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax','difference')).
% 0.20/0.41 tff(123,plain,
% 0.20/0.41 (![B: $i, A: $i, E: $i] : (member(B, difference(E, A)) <=> (member(B, E) & (~member(B, A))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[122, 121])).
% 0.20/0.41 tff(124,plain,(
% 0.20/0.41 ![B: $i, A: $i, E: $i] : (member(B, difference(E, A)) <=> (member(B, E) & (~member(B, A))))),
% 0.20/0.41 inference(skolemize,[status(sab)],[123])).
% 0.20/0.41 tff(125,plain,
% 0.20/0.41 (![B: $i, A: $i, E: $i] : (~(((~member(B, E)) | member(B, A)) <=> member(B, difference(E, A))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[124, 120])).
% 0.20/0.41 tff(126,plain,
% 0.20/0.41 (![B: $i, A: $i, E: $i] : (~(((~member(B, E)) | member(B, A)) <=> member(B, difference(E, A))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[125, 118])).
% 0.20/0.41 tff(127,plain,
% 0.20/0.41 ((~![B: $i, A: $i, E: $i] : (~(((~member(B, E)) | member(B, A)) <=> member(B, difference(E, A))))) | (~(((~member(tptp_fun_X_0(B!4, A!5), E!3)) | member(tptp_fun_X_0(B!4, A!5), B!4)) <=> member(tptp_fun_X_0(B!4, A!5), difference(E!3, B!4))))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(128,plain,
% 0.20/0.41 ($false),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[127, 126, 116])).
% 0.20/0.41 % SZS output end Proof
% 0.20/0.41 % E exiting
%------------------------------------------------------------------------------