%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET701+4 : TPTP v9.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:26:10 AM UTC 2025
% Result : Theorem 0.98s 1.14s
% Output : Proof 1.01s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET701+4 : TPTP v9.0.0. Released v2.2.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.12/0.32 % Computer : n014.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 05:38:24 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.98/1.14 % SZS status Theorem
% 0.98/1.14 % SZS output start Proof
% 0.98/1.14 tff(member_type, type, (
% 0.98/1.14 member: ( $i * $i ) > $o)).
% 0.98/1.14 tff(difference_type, type, (
% 0.98/1.14 difference: ( $i * $i ) > $i)).
% 0.98/1.14 tff(tptp_fun_B_5_type, type, (
% 0.98/1.14 tptp_fun_B_5: $i)).
% 0.98/1.14 tff(tptp_fun_E_3_type, type, (
% 0.98/1.14 tptp_fun_E_3: $i)).
% 0.98/1.14 tff(tptp_fun_X_0_type, type, (
% 0.98/1.14 tptp_fun_X_0: ( $i * $i ) > $i)).
% 0.98/1.14 tff(tptp_fun_A_6_type, type, (
% 0.98/1.14 tptp_fun_A_6: $i)).
% 0.98/1.14 tff(subset_type, type, (
% 0.98/1.14 subset: ( $i * $i ) > $o)).
% 0.98/1.14 tff(intersection_type, type, (
% 0.98/1.14 intersection: ( $i * $i ) > $i)).
% 0.98/1.14 tff(tptp_fun_C_4_type, type, (
% 0.98/1.14 tptp_fun_C_4: $i)).
% 0.98/1.14 tff(sum_type, type, (
% 0.98/1.14 sum: $i > $i)).
% 0.98/1.14 tff(tptp_fun_Y_1_type, type, (
% 0.98/1.14 tptp_fun_Y_1: ( $i * $i ) > $i)).
% 0.98/1.14 tff(product_type, type, (
% 0.98/1.14 product: $i > $i)).
% 0.98/1.14 tff(tptp_fun_Y_2_type, type, (
% 0.98/1.14 tptp_fun_Y_2: ( $i * $i ) > $i)).
% 0.98/1.14 tff(1,plain,
% 0.98/1.14 (^[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)))))),
% 0.98/1.14 inference(bind,[status(th)],[])).
% 0.98/1.14 tff(2,plain,
% 0.98/1.14 (![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))))),
% 0.98/1.14 inference(quant_intro,[status(thm)],[1])).
% 0.98/1.14 tff(3,plain,
% 0.98/1.14 (^[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))))))),
% 0.98/1.14 inference(bind,[status(th)],[])).
% 0.98/1.14 tff(4,plain,
% 0.98/1.14 (![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))))),
% 0.98/1.14 inference(quant_intro,[status(thm)],[3])).
% 0.98/1.14 tff(5,plain,
% 0.98/1.14 (![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)))),
% 0.98/1.14 inference(rewrite,[status(thm)],[])).
% 0.98/1.14 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')).
% 0.98/1.14 tff(7,plain,
% 0.98/1.14 (![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (member(X, A) & member(X, B)))),
% 0.98/1.14 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.98/1.14 tff(8,plain,(
% 0.98/1.14 ![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (member(X, A) & member(X, B)))),
% 0.98/1.14 inference(skolemize,[status(sab)],[7])).
% 0.98/1.14 tff(9,plain,
% 0.98/1.14 (![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))),
% 0.98/1.14 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.98/1.14 tff(10,plain,
% 0.98/1.14 (![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))),
% 0.98/1.14 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.98/1.14 tff(11,plain,
% 0.98/1.14 ((~![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))) | (~(((~member(tptp_fun_X_0(intersection(C!4, difference(E!3, C!4)), intersection(A!6, difference(E!3, B!5))), A!6)) | (~member(tptp_fun_X_0(intersection(C!4, difference(E!3, C!4)), intersection(A!6, difference(E!3, B!5))), difference(E!3, B!5)))) <=> member(tptp_fun_X_0(intersection(C!4, difference(E!3, C!4)), intersection(A!6, difference(E!3, B!5))), intersection(A!6, difference(E!3, B!5)))))),
% 0.98/1.14 inference(quant_inst,[status(thm)],[])).
% 0.98/1.14 tff(12,plain,
% 0.98/1.14 (~(((~member(tptp_fun_X_0(intersection(C!4, difference(E!3, C!4)), intersection(A!6, difference(E!3, B!5))), A!6)) | (~member(tptp_fun_X_0(intersection(C!4, difference(E!3, C!4)), intersection(A!6, difference(E!3, B!5))), difference(E!3, B!5)))) <=> member(tptp_fun_X_0(intersection(C!4, difference(E!3, C!4)), intersection(A!6, difference(E!3, B!5))), intersection(A!6, difference(E!3, B!5))))),
% 0.98/1.14 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.98/1.14 tff(13,assumption,(~subset(intersection(A!6, difference(E!3, B!5)), intersection(C!4, difference(E!3, C!4)))), introduced(assumption)).
% 0.98/1.14 tff(14,plain,
% 0.98/1.14 (^[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))))))))),
% 0.98/1.14 inference(bind,[status(th)],[])).
% 0.98/1.14 tff(15,plain,
% 0.98/1.14 (![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)))))))),
% 0.98/1.14 inference(quant_intro,[status(thm)],[14])).
% 0.98/1.14 tff(16,plain,
% 0.98/1.14 (^[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))))))))),
% 0.98/1.14 inference(bind,[status(th)],[])).
% 0.98/1.14 tff(17,plain,
% 0.98/1.14 (![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)))))))),
% 0.98/1.14 inference(quant_intro,[status(thm)],[16])).
% 0.98/1.14 tff(18,plain,
% 0.98/1.14 (![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)))))))),
% 0.98/1.14 inference(transitivity,[status(thm)],[17, 15])).
% 0.98/1.14 tff(19,plain,
% 0.98/1.14 (^[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)))))))))),
% 0.98/1.14 inference(bind,[status(th)],[])).
% 0.98/1.14 tff(20,plain,
% 0.98/1.14 (![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)))))))),
% 0.98/1.14 inference(quant_intro,[status(thm)],[19])).
% 0.98/1.14 tff(21,plain,
% 0.98/1.14 (![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)))),
% 0.98/1.14 inference(rewrite,[status(thm)],[])).
% 0.98/1.14 tff(22,plain,
% 0.98/1.14 (^[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))))),
% 0.98/1.14 inference(bind,[status(th)],[])).
% 0.98/1.14 tff(23,plain,
% 0.98/1.14 (![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)))),
% 0.98/1.14 inference(quant_intro,[status(thm)],[22])).
% 0.98/1.14 tff(24,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')).
% 0.98/1.14 tff(25,plain,
% 0.98/1.14 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.98/1.14 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.98/1.14 tff(26,plain,
% 0.98/1.14 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.98/1.14 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.98/1.14 tff(27,plain,(
% 0.98/1.14 ![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)))))),
% 0.98/1.14 inference(skolemize,[status(sab)],[26])).
% 0.98/1.14 tff(28,plain,
% 0.98/1.14 (![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)))))))),
% 0.98/1.14 inference(modus_ponens,[status(thm)],[27, 20])).
% 0.98/1.14 tff(29,plain,
% 0.98/1.14 (![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)))))))),
% 0.98/1.14 inference(modus_ponens,[status(thm)],[28, 18])).
% 0.98/1.14 tff(30,plain,
% 0.98/1.14 ((~![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!6, difference(E!3, B!5)), intersection(C!4, difference(E!3, C!4)))) | ![X: $i] : ((~member(X, intersection(A!6, difference(E!3, B!5)))) | member(X, intersection(C!4, difference(E!3, C!4)))))) | (~(subset(intersection(A!6, difference(E!3, B!5)), intersection(C!4, difference(E!3, C!4))) | (~((~member(tptp_fun_X_0(intersection(C!4, difference(E!3, C!4)), intersection(A!6, difference(E!3, B!5))), intersection(A!6, difference(E!3, B!5)))) | member(tptp_fun_X_0(intersection(C!4, difference(E!3, C!4)), intersection(A!6, difference(E!3, B!5))), intersection(C!4, difference(E!3, C!4)))))))))),
% 0.98/1.14 inference(quant_inst,[status(thm)],[])).
% 0.98/1.14 tff(31,plain,
% 0.98/1.14 (~((~((~subset(intersection(A!6, difference(E!3, B!5)), intersection(C!4, difference(E!3, C!4)))) | ![X: $i] : ((~member(X, intersection(A!6, difference(E!3, B!5)))) | member(X, intersection(C!4, difference(E!3, C!4)))))) | (~(subset(intersection(A!6, difference(E!3, B!5)), intersection(C!4, difference(E!3, C!4))) | (~((~member(tptp_fun_X_0(intersection(C!4, difference(E!3, C!4)), intersection(A!6, difference(E!3, B!5))), intersection(A!6, difference(E!3, B!5)))) | member(tptp_fun_X_0(intersection(C!4, difference(E!3, C!4)), intersection(A!6, difference(E!3, B!5))), intersection(C!4, difference(E!3, C!4))))))))),
% 0.98/1.14 inference(unit_resolution,[status(thm)],[30, 29])).
% 0.98/1.14 tff(32,plain,
% 0.98/1.14 (((~((~subset(intersection(A!6, difference(E!3, B!5)), intersection(C!4, difference(E!3, C!4)))) | ![X: $i] : ((~member(X, intersection(A!6, difference(E!3, B!5)))) | member(X, intersection(C!4, difference(E!3, C!4)))))) | (~(subset(intersection(A!6, difference(E!3, B!5)), intersection(C!4, difference(E!3, C!4))) | (~((~member(tptp_fun_X_0(intersection(C!4, difference(E!3, C!4)), intersection(A!6, difference(E!3, B!5))), intersection(A!6, difference(E!3, B!5)))) | member(tptp_fun_X_0(intersection(C!4, difference(E!3, C!4)), intersection(A!6, difference(E!3, B!5))), intersection(C!4, difference(E!3, C!4)))))))) | (subset(intersection(A!6, difference(E!3, B!5)), intersection(C!4, difference(E!3, C!4))) | (~((~member(tptp_fun_X_0(intersection(C!4, difference(E!3, C!4)), intersection(A!6, difference(E!3, B!5))), intersection(A!6, difference(E!3, B!5)))) | member(tptp_fun_X_0(intersection(C!4, difference(E!3, C!4)), intersection(A!6, difference(E!3, B!5))), intersection(C!4, difference(E!3, C!4))))))),
% 0.98/1.14 inference(tautology,[status(thm)],[])).
% 0.98/1.14 tff(33,plain,
% 0.98/1.14 (subset(intersection(A!6, difference(E!3, B!5)), intersection(C!4, difference(E!3, C!4))) | (~((~member(tptp_fun_X_0(intersection(C!4, difference(E!3, C!4)), intersection(A!6, difference(E!3, B!5))), intersection(A!6, difference(E!3, B!5)))) | member(tptp_fun_X_0(intersection(C!4, difference(E!3, C!4)), intersection(A!6, difference(E!3, B!5))), intersection(C!4, difference(E!3, C!4)))))),
% 0.98/1.14 inference(unit_resolution,[status(thm)],[32, 31])).
% 0.98/1.14 tff(34,plain,
% 0.98/1.14 ((~(subset(intersection(A!6, difference(E!3, B!5)), intersection(C!4, difference(E!3, C!4))) | (~((~member(tptp_fun_X_0(intersection(C!4, difference(E!3, C!4)), intersection(A!6, difference(E!3, B!5))), intersection(A!6, difference(E!3, B!5)))) | member(tptp_fun_X_0(intersection(C!4, difference(E!3, C!4)), intersection(A!6, difference(E!3, B!5))), intersection(C!4, difference(E!3, C!4))))))) | subset(intersection(A!6, difference(E!3, B!5)), intersection(C!4, difference(E!3, C!4))) | (~((~member(tptp_fun_X_0(intersection(C!4, difference(E!3, C!4)), intersection(A!6, difference(E!3, B!5))), intersection(A!6, difference(E!3, B!5)))) | member(tptp_fun_X_0(intersection(C!4, difference(E!3, C!4)), intersection(A!6, difference(E!3, B!5))), intersection(C!4, difference(E!3, C!4)))))),
% 0.98/1.14 inference(tautology,[status(thm)],[])).
% 0.98/1.14 tff(35,plain,
% 0.98/1.14 (subset(intersection(A!6, difference(E!3, B!5)), intersection(C!4, difference(E!3, C!4))) | (~((~member(tptp_fun_X_0(intersection(C!4, difference(E!3, C!4)), intersection(A!6, difference(E!3, B!5))), intersection(A!6, difference(E!3, B!5)))) | member(tptp_fun_X_0(intersection(C!4, difference(E!3, C!4)), intersection(A!6, difference(E!3, B!5))), intersection(C!4, difference(E!3, C!4)))))),
% 0.98/1.14 inference(unit_resolution,[status(thm)],[34, 33])).
% 0.98/1.14 tff(36,plain,
% 0.98/1.14 (~((~member(tptp_fun_X_0(intersection(C!4, difference(E!3, C!4)), intersection(A!6, difference(E!3, B!5))), intersection(A!6, difference(E!3, B!5)))) | member(tptp_fun_X_0(intersection(C!4, difference(E!3, C!4)), intersection(A!6, difference(E!3, B!5))), intersection(C!4, difference(E!3, C!4))))),
% 0.98/1.14 inference(unit_resolution,[status(thm)],[35, 13])).
% 0.98/1.14 tff(37,plain,
% 0.98/1.14 (((~member(tptp_fun_X_0(intersection(C!4, difference(E!3, C!4)), intersection(A!6, difference(E!3, B!5))), intersection(A!6, difference(E!3, B!5)))) | member(tptp_fun_X_0(intersection(C!4, difference(E!3, C!4)), intersection(A!6, difference(E!3, B!5))), intersection(C!4, difference(E!3, C!4)))) | member(tptp_fun_X_0(intersection(C!4, difference(E!3, C!4)), intersection(A!6, difference(E!3, B!5))), intersection(A!6, difference(E!3, B!5)))),
% 0.98/1.14 inference(tautology,[status(thm)],[])).
% 0.98/1.14 tff(38,plain,
% 0.98/1.14 (member(tptp_fun_X_0(intersection(C!4, difference(E!3, C!4)), intersection(A!6, difference(E!3, B!5))), intersection(A!6, difference(E!3, B!5)))),
% 0.98/1.14 inference(unit_resolution,[status(thm)],[37, 36])).
% 0.98/1.14 tff(39,plain,
% 0.98/1.14 ((((~member(tptp_fun_X_0(intersection(C!4, difference(E!3, C!4)), intersection(A!6, difference(E!3, B!5))), A!6)) | (~member(tptp_fun_X_0(intersection(C!4, difference(E!3, C!4)), intersection(A!6, difference(E!3, B!5))), difference(E!3, B!5)))) <=> member(tptp_fun_X_0(intersection(C!4, difference(E!3, C!4)), intersection(A!6, difference(E!3, B!5))), intersection(A!6, difference(E!3, B!5)))) | (~((~member(tptp_fun_X_0(intersection(C!4, difference(E!3, C!4)), intersection(A!6, difference(E!3, B!5))), A!6)) | (~member(tptp_fun_X_0(intersection(C!4, difference(E!3, C!4)), intersection(A!6, difference(E!3, B!5))), difference(E!3, B!5))))) | (~member(tptp_fun_X_0(intersection(C!4, difference(E!3, C!4)), intersection(A!6, difference(E!3, B!5))), intersection(A!6, difference(E!3, B!5))))),
% 0.98/1.15 inference(tautology,[status(thm)],[])).
% 0.98/1.15 tff(40,plain,
% 0.98/1.15 ((((~member(tptp_fun_X_0(intersection(C!4, difference(E!3, C!4)), intersection(A!6, difference(E!3, B!5))), A!6)) | (~member(tptp_fun_X_0(intersection(C!4, difference(E!3, C!4)), intersection(A!6, difference(E!3, B!5))), difference(E!3, B!5)))) <=> member(tptp_fun_X_0(intersection(C!4, difference(E!3, C!4)), intersection(A!6, difference(E!3, B!5))), intersection(A!6, difference(E!3, B!5)))) | (~((~member(tptp_fun_X_0(intersection(C!4, difference(E!3, C!4)), intersection(A!6, difference(E!3, B!5))), A!6)) | (~member(tptp_fun_X_0(intersection(C!4, difference(E!3, C!4)), intersection(A!6, difference(E!3, B!5))), difference(E!3, B!5)))))),
% 0.98/1.15 inference(unit_resolution,[status(thm)],[39, 38])).
% 0.98/1.15 tff(41,plain,
% 0.98/1.15 (~((~member(tptp_fun_X_0(intersection(C!4, difference(E!3, C!4)), intersection(A!6, difference(E!3, B!5))), A!6)) | (~member(tptp_fun_X_0(intersection(C!4, difference(E!3, C!4)), intersection(A!6, difference(E!3, B!5))), difference(E!3, B!5))))),
% 0.98/1.15 inference(unit_resolution,[status(thm)],[40, 12])).
% 0.98/1.15 tff(42,plain,
% 0.98/1.15 (((~member(tptp_fun_X_0(intersection(C!4, difference(E!3, C!4)), intersection(A!6, difference(E!3, B!5))), A!6)) | (~member(tptp_fun_X_0(intersection(C!4, difference(E!3, C!4)), intersection(A!6, difference(E!3, B!5))), difference(E!3, B!5)))) | member(tptp_fun_X_0(intersection(C!4, difference(E!3, C!4)), intersection(A!6, difference(E!3, B!5))), A!6)),
% 0.98/1.15 inference(tautology,[status(thm)],[])).
% 0.98/1.15 tff(43,plain,
% 0.98/1.15 (member(tptp_fun_X_0(intersection(C!4, difference(E!3, C!4)), intersection(A!6, difference(E!3, B!5))), A!6)),
% 0.98/1.15 inference(unit_resolution,[status(thm)],[42, 41])).
% 0.98/1.15 tff(44,plain,
% 0.98/1.15 ((~![A: $i, B: $i, C: $i, E: $i] : ((~(subset(A, E) & subset(B, E))) | (subset(A, B) <=> subset(intersection(A, difference(E, B)), intersection(C, difference(E, C)))))) <=> (~![A: $i, B: $i, C: $i, E: $i] : ((~(subset(A, E) & subset(B, E))) | (subset(A, B) <=> subset(intersection(A, difference(E, B)), intersection(C, difference(E, C))))))),
% 0.98/1.15 inference(rewrite,[status(thm)],[])).
% 0.98/1.15 tff(45,plain,
% 0.98/1.15 ((~![A: $i, B: $i, C: $i, E: $i] : ((subset(A, E) & subset(B, E)) => (subset(A, B) <=> subset(intersection(A, difference(E, B)), intersection(C, difference(E, C)))))) <=> (~![A: $i, B: $i, C: $i, E: $i] : ((~(subset(A, E) & subset(B, E))) | (subset(A, B) <=> subset(intersection(A, difference(E, B)), intersection(C, difference(E, C))))))),
% 0.98/1.15 inference(rewrite,[status(thm)],[])).
% 0.98/1.15 tff(46,axiom,(~![A: $i, B: $i, C: $i, E: $i] : ((subset(A, E) & subset(B, E)) => (subset(A, B) <=> subset(intersection(A, difference(E, B)), intersection(C, difference(E, C)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thI35')).
% 0.98/1.15 tff(47,plain,
% 0.98/1.15 (~![A: $i, B: $i, C: $i, E: $i] : ((~(subset(A, E) & subset(B, E))) | (subset(A, B) <=> subset(intersection(A, difference(E, B)), intersection(C, difference(E, C)))))),
% 0.98/1.15 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.98/1.15 tff(48,plain,
% 0.98/1.15 (~![A: $i, B: $i, C: $i, E: $i] : ((~(subset(A, E) & subset(B, E))) | (subset(A, B) <=> subset(intersection(A, difference(E, B)), intersection(C, difference(E, C)))))),
% 0.98/1.15 inference(modus_ponens,[status(thm)],[47, 44])).
% 0.98/1.15 tff(49,plain,
% 0.98/1.15 (~![A: $i, B: $i, C: $i, E: $i] : ((~(subset(A, E) & subset(B, E))) | (subset(A, B) <=> subset(intersection(A, difference(E, B)), intersection(C, difference(E, C)))))),
% 0.98/1.15 inference(modus_ponens,[status(thm)],[48, 44])).
% 0.98/1.15 tff(50,plain,
% 0.98/1.15 (~![A: $i, B: $i, C: $i, E: $i] : ((~(subset(A, E) & subset(B, E))) | (subset(A, B) <=> subset(intersection(A, difference(E, B)), intersection(C, difference(E, C)))))),
% 0.98/1.15 inference(modus_ponens,[status(thm)],[49, 44])).
% 0.98/1.15 tff(51,plain,(
% 0.98/1.15 ~((~(subset(A!6, E!3) & subset(B!5, E!3))) | (subset(A!6, B!5) <=> subset(intersection(A!6, difference(E!3, B!5)), intersection(C!4, difference(E!3, C!4)))))),
% 0.98/1.15 inference(skolemize,[status(sab)],[50])).
% 0.98/1.15 tff(52,plain,
% 0.98/1.15 (~(subset(A!6, B!5) <=> subset(intersection(A!6, difference(E!3, B!5)), intersection(C!4, difference(E!3, C!4))))),
% 0.98/1.15 inference(or_elim,[status(thm)],[51])).
% 0.98/1.15 tff(53,plain,
% 0.98/1.15 ((subset(A!6, B!5) <=> subset(intersection(A!6, difference(E!3, B!5)), intersection(C!4, difference(E!3, C!4)))) | subset(A!6, B!5) | subset(intersection(A!6, difference(E!3, B!5)), intersection(C!4, difference(E!3, C!4)))),
% 0.98/1.15 inference(tautology,[status(thm)],[])).
% 0.98/1.15 tff(54,plain,
% 0.98/1.15 (subset(A!6, B!5) | subset(intersection(A!6, difference(E!3, B!5)), intersection(C!4, difference(E!3, C!4)))),
% 0.98/1.15 inference(unit_resolution,[status(thm)],[53, 52])).
% 0.98/1.15 tff(55,plain,
% 0.98/1.15 (subset(A!6, B!5)),
% 0.98/1.15 inference(unit_resolution,[status(thm)],[54, 13])).
% 0.98/1.15 tff(56,plain,
% 0.98/1.15 ((~![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!6, B!5)) | ![X: $i] : ((~member(X, A!6)) | member(X, B!5)))) | (~(subset(A!6, B!5) | (~((~member(tptp_fun_X_0(B!5, A!6), A!6)) | member(tptp_fun_X_0(B!5, A!6), B!5)))))))),
% 0.98/1.15 inference(quant_inst,[status(thm)],[])).
% 0.98/1.15 tff(57,plain,
% 0.98/1.15 (~((~((~subset(A!6, B!5)) | ![X: $i] : ((~member(X, A!6)) | member(X, B!5)))) | (~(subset(A!6, B!5) | (~((~member(tptp_fun_X_0(B!5, A!6), A!6)) | member(tptp_fun_X_0(B!5, A!6), B!5))))))),
% 0.98/1.15 inference(unit_resolution,[status(thm)],[56, 29])).
% 0.98/1.15 tff(58,plain,
% 0.98/1.15 (((~((~subset(A!6, B!5)) | ![X: $i] : ((~member(X, A!6)) | member(X, B!5)))) | (~(subset(A!6, B!5) | (~((~member(tptp_fun_X_0(B!5, A!6), A!6)) | member(tptp_fun_X_0(B!5, A!6), B!5)))))) | ((~subset(A!6, B!5)) | ![X: $i] : ((~member(X, A!6)) | member(X, B!5)))),
% 0.98/1.15 inference(tautology,[status(thm)],[])).
% 0.98/1.15 tff(59,plain,
% 0.98/1.15 ((~subset(A!6, B!5)) | ![X: $i] : ((~member(X, A!6)) | member(X, B!5))),
% 0.98/1.15 inference(unit_resolution,[status(thm)],[58, 57])).
% 0.98/1.15 tff(60,plain,
% 0.98/1.15 ((~((~subset(A!6, B!5)) | ![X: $i] : ((~member(X, A!6)) | member(X, B!5)))) | (~subset(A!6, B!5)) | ![X: $i] : ((~member(X, A!6)) | member(X, B!5))),
% 0.98/1.15 inference(tautology,[status(thm)],[])).
% 0.98/1.15 tff(61,plain,
% 0.98/1.15 ((~subset(A!6, B!5)) | ![X: $i] : ((~member(X, A!6)) | member(X, B!5))),
% 0.98/1.15 inference(unit_resolution,[status(thm)],[60, 59])).
% 0.98/1.15 tff(62,plain,
% 0.98/1.15 (![X: $i] : ((~member(X, A!6)) | member(X, B!5))),
% 0.98/1.15 inference(unit_resolution,[status(thm)],[61, 55])).
% 0.98/1.15 tff(63,plain,
% 0.98/1.15 (((~![X: $i] : ((~member(X, A!6)) | member(X, B!5))) | ((~member(tptp_fun_X_0(intersection(C!4, difference(E!3, C!4)), intersection(A!6, difference(E!3, B!5))), A!6)) | member(tptp_fun_X_0(intersection(C!4, difference(E!3, C!4)), intersection(A!6, difference(E!3, B!5))), B!5))) <=> ((~![X: $i] : ((~member(X, A!6)) | member(X, B!5))) | (~member(tptp_fun_X_0(intersection(C!4, difference(E!3, C!4)), intersection(A!6, difference(E!3, B!5))), A!6)) | member(tptp_fun_X_0(intersection(C!4, difference(E!3, C!4)), intersection(A!6, difference(E!3, B!5))), B!5))),
% 0.98/1.15 inference(rewrite,[status(thm)],[])).
% 0.98/1.15 tff(64,plain,
% 0.98/1.15 ((~![X: $i] : ((~member(X, A!6)) | member(X, B!5))) | ((~member(tptp_fun_X_0(intersection(C!4, difference(E!3, C!4)), intersection(A!6, difference(E!3, B!5))), A!6)) | member(tptp_fun_X_0(intersection(C!4, difference(E!3, C!4)), intersection(A!6, difference(E!3, B!5))), B!5))),
% 0.98/1.15 inference(quant_inst,[status(thm)],[])).
% 0.98/1.15 tff(65,plain,
% 0.98/1.15 ((~![X: $i] : ((~member(X, A!6)) | member(X, B!5))) | (~member(tptp_fun_X_0(intersection(C!4, difference(E!3, C!4)), intersection(A!6, difference(E!3, B!5))), A!6)) | member(tptp_fun_X_0(intersection(C!4, difference(E!3, C!4)), intersection(A!6, difference(E!3, B!5))), B!5)),
% 0.98/1.15 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.98/1.15 tff(66,plain,
% 0.98/1.15 (member(tptp_fun_X_0(intersection(C!4, difference(E!3, C!4)), intersection(A!6, difference(E!3, B!5))), B!5)),
% 0.98/1.15 inference(unit_resolution,[status(thm)],[65, 62, 43])).
% 0.98/1.15 tff(67,plain,
% 0.98/1.15 (^[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)))))),
% 0.98/1.15 inference(bind,[status(th)],[])).
% 0.98/1.15 tff(68,plain,
% 0.98/1.15 (![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))))),
% 0.98/1.15 inference(quant_intro,[status(thm)],[67])).
% 0.98/1.15 tff(69,plain,
% 0.98/1.15 (^[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))))))),
% 0.98/1.15 inference(bind,[status(th)],[])).
% 0.98/1.15 tff(70,plain,
% 0.98/1.15 (![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))))),
% 0.98/1.15 inference(quant_intro,[status(thm)],[69])).
% 0.98/1.15 tff(71,plain,
% 0.98/1.15 (![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))))),
% 0.98/1.15 inference(rewrite,[status(thm)],[])).
% 0.98/1.15 tff(72,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')).
% 0.98/1.15 tff(73,plain,
% 0.98/1.15 (![B: $i, A: $i, E: $i] : (member(B, difference(E, A)) <=> (member(B, E) & (~member(B, A))))),
% 0.98/1.15 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.98/1.15 tff(74,plain,(
% 0.98/1.15 ![B: $i, A: $i, E: $i] : (member(B, difference(E, A)) <=> (member(B, E) & (~member(B, A))))),
% 0.98/1.15 inference(skolemize,[status(sab)],[73])).
% 0.98/1.15 tff(75,plain,
% 0.98/1.15 (![B: $i, A: $i, E: $i] : (~(((~member(B, E)) | member(B, A)) <=> member(B, difference(E, A))))),
% 0.98/1.15 inference(modus_ponens,[status(thm)],[74, 70])).
% 0.98/1.15 tff(76,plain,
% 0.98/1.15 (![B: $i, A: $i, E: $i] : (~(((~member(B, E)) | member(B, A)) <=> member(B, difference(E, A))))),
% 0.98/1.15 inference(modus_ponens,[status(thm)],[75, 68])).
% 0.98/1.15 tff(77,plain,
% 0.98/1.15 ((~![B: $i, A: $i, E: $i] : (~(((~member(B, E)) | member(B, A)) <=> member(B, difference(E, A))))) | (~(((~member(tptp_fun_X_0(intersection(C!4, difference(E!3, C!4)), intersection(A!6, difference(E!3, B!5))), E!3)) | member(tptp_fun_X_0(intersection(C!4, difference(E!3, C!4)), intersection(A!6, difference(E!3, B!5))), B!5)) <=> member(tptp_fun_X_0(intersection(C!4, difference(E!3, C!4)), intersection(A!6, difference(E!3, B!5))), difference(E!3, B!5))))),
% 0.98/1.15 inference(quant_inst,[status(thm)],[])).
% 0.98/1.15 tff(78,plain,
% 0.98/1.15 (~(((~member(tptp_fun_X_0(intersection(C!4, difference(E!3, C!4)), intersection(A!6, difference(E!3, B!5))), E!3)) | member(tptp_fun_X_0(intersection(C!4, difference(E!3, C!4)), intersection(A!6, difference(E!3, B!5))), B!5)) <=> member(tptp_fun_X_0(intersection(C!4, difference(E!3, C!4)), intersection(A!6, difference(E!3, B!5))), difference(E!3, B!5)))),
% 0.98/1.15 inference(unit_resolution,[status(thm)],[77, 76])).
% 0.98/1.15 tff(79,plain,
% 0.98/1.15 (((~member(tptp_fun_X_0(intersection(C!4, difference(E!3, C!4)), intersection(A!6, difference(E!3, B!5))), A!6)) | (~member(tptp_fun_X_0(intersection(C!4, difference(E!3, C!4)), intersection(A!6, difference(E!3, B!5))), difference(E!3, B!5)))) | member(tptp_fun_X_0(intersection(C!4, difference(E!3, C!4)), intersection(A!6, difference(E!3, B!5))), difference(E!3, B!5))),
% 0.98/1.15 inference(tautology,[status(thm)],[])).
% 0.98/1.15 tff(80,plain,
% 0.98/1.15 (member(tptp_fun_X_0(intersection(C!4, difference(E!3, C!4)), intersection(A!6, difference(E!3, B!5))), difference(E!3, B!5))),
% 0.98/1.15 inference(unit_resolution,[status(thm)],[79, 41])).
% 0.98/1.15 tff(81,plain,
% 0.98/1.15 ((((~member(tptp_fun_X_0(intersection(C!4, difference(E!3, C!4)), intersection(A!6, difference(E!3, B!5))), E!3)) | member(tptp_fun_X_0(intersection(C!4, difference(E!3, C!4)), intersection(A!6, difference(E!3, B!5))), B!5)) <=> member(tptp_fun_X_0(intersection(C!4, difference(E!3, C!4)), intersection(A!6, difference(E!3, B!5))), difference(E!3, B!5))) | (~((~member(tptp_fun_X_0(intersection(C!4, difference(E!3, C!4)), intersection(A!6, difference(E!3, B!5))), E!3)) | member(tptp_fun_X_0(intersection(C!4, difference(E!3, C!4)), intersection(A!6, difference(E!3, B!5))), B!5))) | (~member(tptp_fun_X_0(intersection(C!4, difference(E!3, C!4)), intersection(A!6, difference(E!3, B!5))), difference(E!3, B!5)))),
% 0.98/1.15 inference(tautology,[status(thm)],[])).
% 0.98/1.15 tff(82,plain,
% 0.98/1.15 ((((~member(tptp_fun_X_0(intersection(C!4, difference(E!3, C!4)), intersection(A!6, difference(E!3, B!5))), E!3)) | member(tptp_fun_X_0(intersection(C!4, difference(E!3, C!4)), intersection(A!6, difference(E!3, B!5))), B!5)) <=> member(tptp_fun_X_0(intersection(C!4, difference(E!3, C!4)), intersection(A!6, difference(E!3, B!5))), difference(E!3, B!5))) | (~((~member(tptp_fun_X_0(intersection(C!4, difference(E!3, C!4)), intersection(A!6, difference(E!3, B!5))), E!3)) | member(tptp_fun_X_0(intersection(C!4, difference(E!3, C!4)), intersection(A!6, difference(E!3, B!5))), B!5)))),
% 0.98/1.15 inference(unit_resolution,[status(thm)],[81, 80])).
% 0.98/1.15 tff(83,plain,
% 0.98/1.15 (~((~member(tptp_fun_X_0(intersection(C!4, difference(E!3, C!4)), intersection(A!6, difference(E!3, B!5))), E!3)) | member(tptp_fun_X_0(intersection(C!4, difference(E!3, C!4)), intersection(A!6, difference(E!3, B!5))), B!5))),
% 0.98/1.15 inference(unit_resolution,[status(thm)],[82, 78])).
% 0.98/1.15 tff(84,plain,
% 0.98/1.15 (((~member(tptp_fun_X_0(intersection(C!4, difference(E!3, C!4)), intersection(A!6, difference(E!3, B!5))), E!3)) | member(tptp_fun_X_0(intersection(C!4, difference(E!3, C!4)), intersection(A!6, difference(E!3, B!5))), B!5)) | (~member(tptp_fun_X_0(intersection(C!4, difference(E!3, C!4)), intersection(A!6, difference(E!3, B!5))), B!5))),
% 0.98/1.15 inference(tautology,[status(thm)],[])).
% 0.98/1.15 tff(85,plain,
% 0.98/1.15 ($false),
% 0.98/1.15 inference(unit_resolution,[status(thm)],[84, 83, 66])).
% 0.98/1.15 tff(86,plain,(subset(intersection(A!6, difference(E!3, B!5)), intersection(C!4, difference(E!3, C!4)))), inference(lemma,lemma(discharge,[]))).
% 0.98/1.15 tff(87,plain,
% 0.98/1.15 ((subset(A!6, B!5) <=> subset(intersection(A!6, difference(E!3, B!5)), intersection(C!4, difference(E!3, C!4)))) | (~subset(A!6, B!5)) | (~subset(intersection(A!6, difference(E!3, B!5)), intersection(C!4, difference(E!3, C!4))))),
% 0.98/1.15 inference(tautology,[status(thm)],[])).
% 0.98/1.15 tff(88,plain,
% 0.98/1.15 ((~subset(A!6, B!5)) | (~subset(intersection(A!6, difference(E!3, B!5)), intersection(C!4, difference(E!3, C!4))))),
% 0.98/1.15 inference(unit_resolution,[status(thm)],[87, 52])).
% 0.98/1.15 tff(89,plain,
% 0.98/1.15 (~subset(A!6, B!5)),
% 0.98/1.15 inference(unit_resolution,[status(thm)],[88, 86])).
% 0.98/1.15 tff(90,plain,
% 0.98/1.15 (((~((~subset(A!6, B!5)) | ![X: $i] : ((~member(X, A!6)) | member(X, B!5)))) | (~(subset(A!6, B!5) | (~((~member(tptp_fun_X_0(B!5, A!6), A!6)) | member(tptp_fun_X_0(B!5, A!6), B!5)))))) | (subset(A!6, B!5) | (~((~member(tptp_fun_X_0(B!5, A!6), A!6)) | member(tptp_fun_X_0(B!5, A!6), B!5))))),
% 0.98/1.15 inference(tautology,[status(thm)],[])).
% 0.98/1.15 tff(91,plain,
% 0.98/1.15 (subset(A!6, B!5) | (~((~member(tptp_fun_X_0(B!5, A!6), A!6)) | member(tptp_fun_X_0(B!5, A!6), B!5)))),
% 0.98/1.15 inference(unit_resolution,[status(thm)],[90, 57])).
% 0.98/1.15 tff(92,plain,
% 0.98/1.15 ((~(subset(A!6, B!5) | (~((~member(tptp_fun_X_0(B!5, A!6), A!6)) | member(tptp_fun_X_0(B!5, A!6), B!5))))) | subset(A!6, B!5) | (~((~member(tptp_fun_X_0(B!5, A!6), A!6)) | member(tptp_fun_X_0(B!5, A!6), B!5)))),
% 0.98/1.15 inference(tautology,[status(thm)],[])).
% 0.98/1.15 tff(93,plain,
% 0.98/1.15 (subset(A!6, B!5) | (~((~member(tptp_fun_X_0(B!5, A!6), A!6)) | member(tptp_fun_X_0(B!5, A!6), B!5)))),
% 0.98/1.15 inference(unit_resolution,[status(thm)],[92, 91])).
% 0.98/1.15 tff(94,plain,
% 0.98/1.15 (~((~member(tptp_fun_X_0(B!5, A!6), A!6)) | member(tptp_fun_X_0(B!5, A!6), B!5))),
% 0.98/1.15 inference(unit_resolution,[status(thm)],[93, 89])).
% 0.98/1.15 tff(95,plain,
% 0.98/1.15 (((~member(tptp_fun_X_0(B!5, A!6), A!6)) | member(tptp_fun_X_0(B!5, A!6), B!5)) | member(tptp_fun_X_0(B!5, A!6), A!6)),
% 0.98/1.15 inference(tautology,[status(thm)],[])).
% 0.98/1.15 tff(96,plain,
% 0.98/1.15 (member(tptp_fun_X_0(B!5, A!6), A!6)),
% 0.98/1.15 inference(unit_resolution,[status(thm)],[95, 94])).
% 0.98/1.15 tff(97,plain,
% 0.98/1.15 ((~![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!6, E!3)) | ![X: $i] : ((~member(X, A!6)) | member(X, E!3)))) | (~(subset(A!6, E!3) | (~((~member(tptp_fun_X_0(E!3, A!6), A!6)) | member(tptp_fun_X_0(E!3, A!6), E!3)))))))),
% 0.98/1.15 inference(quant_inst,[status(thm)],[])).
% 0.98/1.15 tff(98,plain,
% 0.98/1.15 (~((~((~subset(A!6, E!3)) | ![X: $i] : ((~member(X, A!6)) | member(X, E!3)))) | (~(subset(A!6, E!3) | (~((~member(tptp_fun_X_0(E!3, A!6), A!6)) | member(tptp_fun_X_0(E!3, A!6), E!3))))))),
% 0.98/1.15 inference(unit_resolution,[status(thm)],[97, 29])).
% 0.98/1.15 tff(99,plain,
% 0.98/1.15 (((~((~subset(A!6, E!3)) | ![X: $i] : ((~member(X, A!6)) | member(X, E!3)))) | (~(subset(A!6, E!3) | (~((~member(tptp_fun_X_0(E!3, A!6), A!6)) | member(tptp_fun_X_0(E!3, A!6), E!3)))))) | ((~subset(A!6, E!3)) | ![X: $i] : ((~member(X, A!6)) | member(X, E!3)))),
% 0.98/1.15 inference(tautology,[status(thm)],[])).
% 0.98/1.15 tff(100,plain,
% 0.98/1.15 ((~subset(A!6, E!3)) | ![X: $i] : ((~member(X, A!6)) | member(X, E!3))),
% 0.98/1.15 inference(unit_resolution,[status(thm)],[99, 98])).
% 0.98/1.15 tff(101,plain,
% 0.98/1.15 (subset(A!6, E!3) & subset(B!5, E!3)),
% 0.98/1.15 inference(or_elim,[status(thm)],[51])).
% 0.98/1.15 tff(102,plain,
% 0.98/1.15 (subset(A!6, E!3)),
% 0.98/1.15 inference(and_elim,[status(thm)],[101])).
% 0.98/1.15 tff(103,plain,
% 0.98/1.15 ((~((~subset(A!6, E!3)) | ![X: $i] : ((~member(X, A!6)) | member(X, E!3)))) | (~subset(A!6, E!3)) | ![X: $i] : ((~member(X, A!6)) | member(X, E!3))),
% 0.98/1.15 inference(tautology,[status(thm)],[])).
% 0.98/1.15 tff(104,plain,
% 0.98/1.15 ((~((~subset(A!6, E!3)) | ![X: $i] : ((~member(X, A!6)) | member(X, E!3)))) | ![X: $i] : ((~member(X, A!6)) | member(X, E!3))),
% 0.98/1.15 inference(unit_resolution,[status(thm)],[103, 102])).
% 0.98/1.15 tff(105,plain,
% 0.98/1.15 (![X: $i] : ((~member(X, A!6)) | member(X, E!3))),
% 0.98/1.15 inference(unit_resolution,[status(thm)],[104, 100])).
% 0.98/1.15 tff(106,plain,
% 0.98/1.15 (((~![X: $i] : ((~member(X, A!6)) | member(X, E!3))) | ((~member(tptp_fun_X_0(B!5, A!6), A!6)) | member(tptp_fun_X_0(B!5, A!6), E!3))) <=> ((~![X: $i] : ((~member(X, A!6)) | member(X, E!3))) | (~member(tptp_fun_X_0(B!5, A!6), A!6)) | member(tptp_fun_X_0(B!5, A!6), E!3))),
% 0.98/1.15 inference(rewrite,[status(thm)],[])).
% 0.98/1.15 tff(107,plain,
% 0.98/1.15 ((~![X: $i] : ((~member(X, A!6)) | member(X, E!3))) | ((~member(tptp_fun_X_0(B!5, A!6), A!6)) | member(tptp_fun_X_0(B!5, A!6), E!3))),
% 0.98/1.15 inference(quant_inst,[status(thm)],[])).
% 0.98/1.15 tff(108,plain,
% 0.98/1.15 ((~![X: $i] : ((~member(X, A!6)) | member(X, E!3))) | (~member(tptp_fun_X_0(B!5, A!6), A!6)) | member(tptp_fun_X_0(B!5, A!6), E!3)),
% 0.98/1.15 inference(modus_ponens,[status(thm)],[107, 106])).
% 0.98/1.15 tff(109,plain,
% 0.98/1.15 (member(tptp_fun_X_0(B!5, A!6), E!3)),
% 0.98/1.15 inference(unit_resolution,[status(thm)],[108, 105, 96])).
% 0.98/1.15 tff(110,plain,
% 0.98/1.15 (((~member(tptp_fun_X_0(B!5, A!6), A!6)) | member(tptp_fun_X_0(B!5, A!6), B!5)) | (~member(tptp_fun_X_0(B!5, A!6), B!5))),
% 0.98/1.15 inference(tautology,[status(thm)],[])).
% 0.98/1.15 tff(111,plain,
% 0.98/1.15 (~member(tptp_fun_X_0(B!5, A!6), B!5)),
% 0.98/1.15 inference(unit_resolution,[status(thm)],[110, 94])).
% 0.98/1.15 tff(112,plain,
% 0.98/1.15 ((~((~member(tptp_fun_X_0(B!5, A!6), E!3)) | member(tptp_fun_X_0(B!5, A!6), B!5))) | (~member(tptp_fun_X_0(B!5, A!6), E!3)) | member(tptp_fun_X_0(B!5, A!6), B!5)),
% 0.98/1.15 inference(tautology,[status(thm)],[])).
% 0.98/1.15 tff(113,plain,
% 0.98/1.15 (~((~member(tptp_fun_X_0(B!5, A!6), E!3)) | member(tptp_fun_X_0(B!5, A!6), B!5))),
% 0.98/1.15 inference(unit_resolution,[status(thm)],[112, 111, 109])).
% 0.98/1.15 tff(114,plain,
% 0.98/1.15 ((~![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))) | (~(((~member(tptp_fun_X_0(B!5, A!6), A!6)) | (~member(tptp_fun_X_0(B!5, A!6), difference(E!3, B!5)))) <=> member(tptp_fun_X_0(B!5, A!6), intersection(A!6, difference(E!3, B!5)))))),
% 0.98/1.15 inference(quant_inst,[status(thm)],[])).
% 0.98/1.15 tff(115,plain,
% 0.98/1.15 (~(((~member(tptp_fun_X_0(B!5, A!6), A!6)) | (~member(tptp_fun_X_0(B!5, A!6), difference(E!3, B!5)))) <=> member(tptp_fun_X_0(B!5, A!6), intersection(A!6, difference(E!3, B!5))))),
% 0.98/1.15 inference(unit_resolution,[status(thm)],[114, 10])).
% 0.98/1.15 tff(116,assumption,(member(tptp_fun_X_0(B!5, A!6), intersection(C!4, difference(E!3, C!4)))), introduced(assumption)).
% 0.98/1.15 tff(117,assumption,((~((~subset(intersection(C!4, difference(E!3, C!4)), intersection(A!6, difference(E!3, B!5)))) | ![X: $i] : ((~member(X, intersection(C!4, difference(E!3, C!4)))) | member(X, intersection(A!6, difference(E!3, B!5)))))) | (~(subset(intersection(C!4, difference(E!3, C!4)), intersection(A!6, difference(E!3, B!5))) | (~((~member(tptp_fun_X_0(intersection(A!6, difference(E!3, B!5)), intersection(C!4, difference(E!3, C!4))), intersection(C!4, difference(E!3, C!4)))) | member(tptp_fun_X_0(intersection(A!6, difference(E!3, B!5)), intersection(C!4, difference(E!3, C!4))), intersection(A!6, difference(E!3, B!5)))))))), introduced(assumption)).
% 0.98/1.15 tff(118,plain,
% 0.98/1.15 ((~![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(C!4, difference(E!3, C!4)), intersection(A!6, difference(E!3, B!5)))) | ![X: $i] : ((~member(X, intersection(C!4, difference(E!3, C!4)))) | member(X, intersection(A!6, difference(E!3, B!5)))))) | (~(subset(intersection(C!4, difference(E!3, C!4)), intersection(A!6, difference(E!3, B!5))) | (~((~member(tptp_fun_X_0(intersection(A!6, difference(E!3, B!5)), intersection(C!4, difference(E!3, C!4))), intersection(C!4, difference(E!3, C!4)))) | member(tptp_fun_X_0(intersection(A!6, difference(E!3, B!5)), intersection(C!4, difference(E!3, C!4))), intersection(A!6, difference(E!3, B!5)))))))))),
% 0.98/1.15 inference(quant_inst,[status(thm)],[])).
% 0.98/1.15 tff(119,plain,
% 0.98/1.15 ($false),
% 0.98/1.15 inference(unit_resolution,[status(thm)],[118, 29, 117])).
% 0.98/1.15 tff(120,plain,(~((~((~subset(intersection(C!4, difference(E!3, C!4)), intersection(A!6, difference(E!3, B!5)))) | ![X: $i] : ((~member(X, intersection(C!4, difference(E!3, C!4)))) | member(X, intersection(A!6, difference(E!3, B!5)))))) | (~(subset(intersection(C!4, difference(E!3, C!4)), intersection(A!6, difference(E!3, B!5))) | (~((~member(tptp_fun_X_0(intersection(A!6, difference(E!3, B!5)), intersection(C!4, difference(E!3, C!4))), intersection(C!4, difference(E!3, C!4)))) | member(tptp_fun_X_0(intersection(A!6, difference(E!3, B!5)), intersection(C!4, difference(E!3, C!4))), intersection(A!6, difference(E!3, B!5))))))))), inference(lemma,lemma(discharge,[]))).
% 0.98/1.15 tff(121,plain,
% 0.98/1.15 (((~((~subset(intersection(C!4, difference(E!3, C!4)), intersection(A!6, difference(E!3, B!5)))) | ![X: $i] : ((~member(X, intersection(C!4, difference(E!3, C!4)))) | member(X, intersection(A!6, difference(E!3, B!5)))))) | (~(subset(intersection(C!4, difference(E!3, C!4)), intersection(A!6, difference(E!3, B!5))) | (~((~member(tptp_fun_X_0(intersection(A!6, difference(E!3, B!5)), intersection(C!4, difference(E!3, C!4))), intersection(C!4, difference(E!3, C!4)))) | member(tptp_fun_X_0(intersection(A!6, difference(E!3, B!5)), intersection(C!4, difference(E!3, C!4))), intersection(A!6, difference(E!3, B!5)))))))) | ((~subset(intersection(C!4, difference(E!3, C!4)), intersection(A!6, difference(E!3, B!5)))) | ![X: $i] : ((~member(X, intersection(C!4, difference(E!3, C!4)))) | member(X, intersection(A!6, difference(E!3, B!5)))))),
% 0.98/1.16 inference(tautology,[status(thm)],[])).
% 0.98/1.16 tff(122,plain,
% 0.98/1.16 ((~subset(intersection(C!4, difference(E!3, C!4)), intersection(A!6, difference(E!3, B!5)))) | ![X: $i] : ((~member(X, intersection(C!4, difference(E!3, C!4)))) | member(X, intersection(A!6, difference(E!3, B!5))))),
% 0.98/1.16 inference(unit_resolution,[status(thm)],[121, 120])).
% 0.98/1.16 tff(123,plain,
% 0.98/1.16 (((~((~subset(intersection(C!4, difference(E!3, C!4)), intersection(A!6, difference(E!3, B!5)))) | ![X: $i] : ((~member(X, intersection(C!4, difference(E!3, C!4)))) | member(X, intersection(A!6, difference(E!3, B!5)))))) | (~(subset(intersection(C!4, difference(E!3, C!4)), intersection(A!6, difference(E!3, B!5))) | (~((~member(tptp_fun_X_0(intersection(A!6, difference(E!3, B!5)), intersection(C!4, difference(E!3, C!4))), intersection(C!4, difference(E!3, C!4)))) | member(tptp_fun_X_0(intersection(A!6, difference(E!3, B!5)), intersection(C!4, difference(E!3, C!4))), intersection(A!6, difference(E!3, B!5)))))))) | (subset(intersection(C!4, difference(E!3, C!4)), intersection(A!6, difference(E!3, B!5))) | (~((~member(tptp_fun_X_0(intersection(A!6, difference(E!3, B!5)), intersection(C!4, difference(E!3, C!4))), intersection(C!4, difference(E!3, C!4)))) | member(tptp_fun_X_0(intersection(A!6, difference(E!3, B!5)), intersection(C!4, difference(E!3, C!4))), intersection(A!6, difference(E!3, B!5))))))),
% 0.98/1.16 inference(tautology,[status(thm)],[])).
% 0.98/1.16 tff(124,plain,
% 0.98/1.16 (subset(intersection(C!4, difference(E!3, C!4)), intersection(A!6, difference(E!3, B!5))) | (~((~member(tptp_fun_X_0(intersection(A!6, difference(E!3, B!5)), intersection(C!4, difference(E!3, C!4))), intersection(C!4, difference(E!3, C!4)))) | member(tptp_fun_X_0(intersection(A!6, difference(E!3, B!5)), intersection(C!4, difference(E!3, C!4))), intersection(A!6, difference(E!3, B!5)))))),
% 0.98/1.16 inference(unit_resolution,[status(thm)],[123, 120])).
% 0.98/1.16 tff(125,assumption,(((~member(tptp_fun_X_0(intersection(A!6, difference(E!3, B!5)), intersection(C!4, difference(E!3, C!4))), C!4)) | (~member(tptp_fun_X_0(intersection(A!6, difference(E!3, B!5)), intersection(C!4, difference(E!3, C!4))), difference(E!3, C!4)))) <=> member(tptp_fun_X_0(intersection(A!6, difference(E!3, B!5)), intersection(C!4, difference(E!3, C!4))), intersection(C!4, difference(E!3, C!4)))), introduced(assumption)).
% 0.98/1.16 tff(126,plain,
% 0.98/1.16 ((~![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))) | (~(((~member(tptp_fun_X_0(intersection(A!6, difference(E!3, B!5)), intersection(C!4, difference(E!3, C!4))), C!4)) | (~member(tptp_fun_X_0(intersection(A!6, difference(E!3, B!5)), intersection(C!4, difference(E!3, C!4))), difference(E!3, C!4)))) <=> member(tptp_fun_X_0(intersection(A!6, difference(E!3, B!5)), intersection(C!4, difference(E!3, C!4))), intersection(C!4, difference(E!3, C!4)))))),
% 0.98/1.16 inference(quant_inst,[status(thm)],[])).
% 0.98/1.16 tff(127,plain,
% 0.98/1.16 ($false),
% 0.98/1.16 inference(unit_resolution,[status(thm)],[126, 10, 125])).
% 0.98/1.16 tff(128,plain,(~(((~member(tptp_fun_X_0(intersection(A!6, difference(E!3, B!5)), intersection(C!4, difference(E!3, C!4))), C!4)) | (~member(tptp_fun_X_0(intersection(A!6, difference(E!3, B!5)), intersection(C!4, difference(E!3, C!4))), difference(E!3, C!4)))) <=> member(tptp_fun_X_0(intersection(A!6, difference(E!3, B!5)), intersection(C!4, difference(E!3, C!4))), intersection(C!4, difference(E!3, C!4))))), inference(lemma,lemma(discharge,[]))).
% 0.98/1.16 tff(129,assumption,(((~member(tptp_fun_X_0(intersection(A!6, difference(E!3, B!5)), intersection(C!4, difference(E!3, C!4))), E!3)) | member(tptp_fun_X_0(intersection(A!6, difference(E!3, B!5)), intersection(C!4, difference(E!3, C!4))), C!4)) <=> member(tptp_fun_X_0(intersection(A!6, difference(E!3, B!5)), intersection(C!4, difference(E!3, C!4))), difference(E!3, C!4))), introduced(assumption)).
% 0.98/1.16 tff(130,plain,
% 0.98/1.16 ((~![B: $i, A: $i, E: $i] : (~(((~member(B, E)) | member(B, A)) <=> member(B, difference(E, A))))) | (~(((~member(tptp_fun_X_0(intersection(A!6, difference(E!3, B!5)), intersection(C!4, difference(E!3, C!4))), E!3)) | member(tptp_fun_X_0(intersection(A!6, difference(E!3, B!5)), intersection(C!4, difference(E!3, C!4))), C!4)) <=> member(tptp_fun_X_0(intersection(A!6, difference(E!3, B!5)), intersection(C!4, difference(E!3, C!4))), difference(E!3, C!4))))),
% 0.98/1.16 inference(quant_inst,[status(thm)],[])).
% 0.98/1.16 tff(131,plain,
% 0.98/1.16 ($false),
% 0.98/1.16 inference(unit_resolution,[status(thm)],[130, 76, 129])).
% 0.98/1.16 tff(132,plain,(~(((~member(tptp_fun_X_0(intersection(A!6, difference(E!3, B!5)), intersection(C!4, difference(E!3, C!4))), E!3)) | member(tptp_fun_X_0(intersection(A!6, difference(E!3, B!5)), intersection(C!4, difference(E!3, C!4))), C!4)) <=> member(tptp_fun_X_0(intersection(A!6, difference(E!3, B!5)), intersection(C!4, difference(E!3, C!4))), difference(E!3, C!4)))), inference(lemma,lemma(discharge,[]))).
% 0.98/1.16 tff(133,assumption,(~((~member(tptp_fun_X_0(intersection(A!6, difference(E!3, B!5)), intersection(C!4, difference(E!3, C!4))), C!4)) | (~member(tptp_fun_X_0(intersection(A!6, difference(E!3, B!5)), intersection(C!4, difference(E!3, C!4))), difference(E!3, C!4))))), introduced(assumption)).
% 0.98/1.16 tff(134,plain,
% 0.98/1.16 (((~member(tptp_fun_X_0(intersection(A!6, difference(E!3, B!5)), intersection(C!4, difference(E!3, C!4))), C!4)) | (~member(tptp_fun_X_0(intersection(A!6, difference(E!3, B!5)), intersection(C!4, difference(E!3, C!4))), difference(E!3, C!4)))) | member(tptp_fun_X_0(intersection(A!6, difference(E!3, B!5)), intersection(C!4, difference(E!3, C!4))), difference(E!3, C!4))),
% 0.98/1.16 inference(tautology,[status(thm)],[])).
% 0.98/1.16 tff(135,plain,
% 0.98/1.16 (member(tptp_fun_X_0(intersection(A!6, difference(E!3, B!5)), intersection(C!4, difference(E!3, C!4))), difference(E!3, C!4))),
% 0.98/1.16 inference(unit_resolution,[status(thm)],[134, 133])).
% 0.98/1.16 tff(136,plain,
% 0.98/1.16 (((~member(tptp_fun_X_0(intersection(A!6, difference(E!3, B!5)), intersection(C!4, difference(E!3, C!4))), C!4)) | (~member(tptp_fun_X_0(intersection(A!6, difference(E!3, B!5)), intersection(C!4, difference(E!3, C!4))), difference(E!3, C!4)))) | member(tptp_fun_X_0(intersection(A!6, difference(E!3, B!5)), intersection(C!4, difference(E!3, C!4))), C!4)),
% 0.98/1.16 inference(tautology,[status(thm)],[])).
% 0.98/1.16 tff(137,plain,
% 0.98/1.16 (member(tptp_fun_X_0(intersection(A!6, difference(E!3, B!5)), intersection(C!4, difference(E!3, C!4))), C!4)),
% 0.98/1.16 inference(unit_resolution,[status(thm)],[136, 133])).
% 0.98/1.16 tff(138,plain,
% 0.98/1.16 (((~member(tptp_fun_X_0(intersection(A!6, difference(E!3, B!5)), intersection(C!4, difference(E!3, C!4))), E!3)) | member(tptp_fun_X_0(intersection(A!6, difference(E!3, B!5)), intersection(C!4, difference(E!3, C!4))), C!4)) | (~member(tptp_fun_X_0(intersection(A!6, difference(E!3, B!5)), intersection(C!4, difference(E!3, C!4))), C!4))),
% 0.98/1.16 inference(tautology,[status(thm)],[])).
% 0.98/1.16 tff(139,plain,
% 0.98/1.16 ((~member(tptp_fun_X_0(intersection(A!6, difference(E!3, B!5)), intersection(C!4, difference(E!3, C!4))), E!3)) | member(tptp_fun_X_0(intersection(A!6, difference(E!3, B!5)), intersection(C!4, difference(E!3, C!4))), C!4)),
% 0.98/1.16 inference(unit_resolution,[status(thm)],[138, 137])).
% 0.98/1.16 tff(140,plain,
% 0.98/1.16 ((((~member(tptp_fun_X_0(intersection(A!6, difference(E!3, B!5)), intersection(C!4, difference(E!3, C!4))), E!3)) | member(tptp_fun_X_0(intersection(A!6, difference(E!3, B!5)), intersection(C!4, difference(E!3, C!4))), C!4)) <=> member(tptp_fun_X_0(intersection(A!6, difference(E!3, B!5)), intersection(C!4, difference(E!3, C!4))), difference(E!3, C!4))) | (~((~member(tptp_fun_X_0(intersection(A!6, difference(E!3, B!5)), intersection(C!4, difference(E!3, C!4))), E!3)) | member(tptp_fun_X_0(intersection(A!6, difference(E!3, B!5)), intersection(C!4, difference(E!3, C!4))), C!4))) | (~member(tptp_fun_X_0(intersection(A!6, difference(E!3, B!5)), intersection(C!4, difference(E!3, C!4))), difference(E!3, C!4)))),
% 0.98/1.16 inference(tautology,[status(thm)],[])).
% 0.98/1.16 tff(141,plain,
% 0.98/1.16 ($false),
% 0.98/1.16 inference(unit_resolution,[status(thm)],[140, 139, 135, 132])).
% 0.98/1.16 tff(142,plain,((~member(tptp_fun_X_0(intersection(A!6, difference(E!3, B!5)), intersection(C!4, difference(E!3, C!4))), C!4)) | (~member(tptp_fun_X_0(intersection(A!6, difference(E!3, B!5)), intersection(C!4, difference(E!3, C!4))), difference(E!3, C!4)))), inference(lemma,lemma(discharge,[]))).
% 0.98/1.16 tff(143,plain,
% 0.98/1.16 ((((~member(tptp_fun_X_0(intersection(A!6, difference(E!3, B!5)), intersection(C!4, difference(E!3, C!4))), C!4)) | (~member(tptp_fun_X_0(intersection(A!6, difference(E!3, B!5)), intersection(C!4, difference(E!3, C!4))), difference(E!3, C!4)))) <=> member(tptp_fun_X_0(intersection(A!6, difference(E!3, B!5)), intersection(C!4, difference(E!3, C!4))), intersection(C!4, difference(E!3, C!4)))) | (~((~member(tptp_fun_X_0(intersection(A!6, difference(E!3, B!5)), intersection(C!4, difference(E!3, C!4))), C!4)) | (~member(tptp_fun_X_0(intersection(A!6, difference(E!3, B!5)), intersection(C!4, difference(E!3, C!4))), difference(E!3, C!4))))) | (~member(tptp_fun_X_0(intersection(A!6, difference(E!3, B!5)), intersection(C!4, difference(E!3, C!4))), intersection(C!4, difference(E!3, C!4))))),
% 0.98/1.16 inference(tautology,[status(thm)],[])).
% 0.98/1.16 tff(144,plain,
% 0.98/1.16 ((((~member(tptp_fun_X_0(intersection(A!6, difference(E!3, B!5)), intersection(C!4, difference(E!3, C!4))), C!4)) | (~member(tptp_fun_X_0(intersection(A!6, difference(E!3, B!5)), intersection(C!4, difference(E!3, C!4))), difference(E!3, C!4)))) <=> member(tptp_fun_X_0(intersection(A!6, difference(E!3, B!5)), intersection(C!4, difference(E!3, C!4))), intersection(C!4, difference(E!3, C!4)))) | (~member(tptp_fun_X_0(intersection(A!6, difference(E!3, B!5)), intersection(C!4, difference(E!3, C!4))), intersection(C!4, difference(E!3, C!4))))),
% 0.98/1.16 inference(unit_resolution,[status(thm)],[143, 142])).
% 0.98/1.16 tff(145,plain,
% 0.98/1.16 (~member(tptp_fun_X_0(intersection(A!6, difference(E!3, B!5)), intersection(C!4, difference(E!3, C!4))), intersection(C!4, difference(E!3, C!4)))),
% 0.98/1.16 inference(unit_resolution,[status(thm)],[144, 128])).
% 0.98/1.16 tff(146,plain,
% 0.98/1.16 (((~member(tptp_fun_X_0(intersection(A!6, difference(E!3, B!5)), intersection(C!4, difference(E!3, C!4))), intersection(C!4, difference(E!3, C!4)))) | member(tptp_fun_X_0(intersection(A!6, difference(E!3, B!5)), intersection(C!4, difference(E!3, C!4))), intersection(A!6, difference(E!3, B!5)))) | member(tptp_fun_X_0(intersection(A!6, difference(E!3, B!5)), intersection(C!4, difference(E!3, C!4))), intersection(C!4, difference(E!3, C!4)))),
% 0.98/1.16 inference(tautology,[status(thm)],[])).
% 0.98/1.16 tff(147,plain,
% 0.98/1.16 ((~member(tptp_fun_X_0(intersection(A!6, difference(E!3, B!5)), intersection(C!4, difference(E!3, C!4))), intersection(C!4, difference(E!3, C!4)))) | member(tptp_fun_X_0(intersection(A!6, difference(E!3, B!5)), intersection(C!4, difference(E!3, C!4))), intersection(A!6, difference(E!3, B!5)))),
% 0.98/1.16 inference(unit_resolution,[status(thm)],[146, 145])).
% 0.98/1.16 tff(148,plain,
% 0.98/1.16 ((~(subset(intersection(C!4, difference(E!3, C!4)), intersection(A!6, difference(E!3, B!5))) | (~((~member(tptp_fun_X_0(intersection(A!6, difference(E!3, B!5)), intersection(C!4, difference(E!3, C!4))), intersection(C!4, difference(E!3, C!4)))) | member(tptp_fun_X_0(intersection(A!6, difference(E!3, B!5)), intersection(C!4, difference(E!3, C!4))), intersection(A!6, difference(E!3, B!5))))))) | subset(intersection(C!4, difference(E!3, C!4)), intersection(A!6, difference(E!3, B!5))) | (~((~member(tptp_fun_X_0(intersection(A!6, difference(E!3, B!5)), intersection(C!4, difference(E!3, C!4))), intersection(C!4, difference(E!3, C!4)))) | member(tptp_fun_X_0(intersection(A!6, difference(E!3, B!5)), intersection(C!4, difference(E!3, C!4))), intersection(A!6, difference(E!3, B!5)))))),
% 0.98/1.16 inference(tautology,[status(thm)],[])).
% 0.98/1.16 tff(149,plain,
% 0.98/1.16 ((~(subset(intersection(C!4, difference(E!3, C!4)), intersection(A!6, difference(E!3, B!5))) | (~((~member(tptp_fun_X_0(intersection(A!6, difference(E!3, B!5)), intersection(C!4, difference(E!3, C!4))), intersection(C!4, difference(E!3, C!4)))) | member(tptp_fun_X_0(intersection(A!6, difference(E!3, B!5)), intersection(C!4, difference(E!3, C!4))), intersection(A!6, difference(E!3, B!5))))))) | subset(intersection(C!4, difference(E!3, C!4)), intersection(A!6, difference(E!3, B!5)))),
% 0.98/1.16 inference(unit_resolution,[status(thm)],[148, 147])).
% 0.98/1.16 tff(150,plain,
% 0.98/1.16 (subset(intersection(C!4, difference(E!3, C!4)), intersection(A!6, difference(E!3, B!5)))),
% 0.98/1.16 inference(unit_resolution,[status(thm)],[149, 124])).
% 0.98/1.16 tff(151,plain,
% 0.98/1.16 ((~((~subset(intersection(C!4, difference(E!3, C!4)), intersection(A!6, difference(E!3, B!5)))) | ![X: $i] : ((~member(X, intersection(C!4, difference(E!3, C!4)))) | member(X, intersection(A!6, difference(E!3, B!5)))))) | (~subset(intersection(C!4, difference(E!3, C!4)), intersection(A!6, difference(E!3, B!5)))) | ![X: $i] : ((~member(X, intersection(C!4, difference(E!3, C!4)))) | member(X, intersection(A!6, difference(E!3, B!5))))),
% 0.98/1.16 inference(tautology,[status(thm)],[])).
% 0.98/1.16 tff(152,plain,
% 0.98/1.16 (![X: $i] : ((~member(X, intersection(C!4, difference(E!3, C!4)))) | member(X, intersection(A!6, difference(E!3, B!5))))),
% 0.98/1.16 inference(unit_resolution,[status(thm)],[151, 150, 122])).
% 0.98/1.16 tff(153,plain,
% 0.98/1.16 (((~![X: $i] : ((~member(X, intersection(C!4, difference(E!3, C!4)))) | member(X, intersection(A!6, difference(E!3, B!5))))) | ((~member(tptp_fun_X_0(B!5, A!6), intersection(C!4, difference(E!3, C!4)))) | member(tptp_fun_X_0(B!5, A!6), intersection(A!6, difference(E!3, B!5))))) <=> ((~![X: $i] : ((~member(X, intersection(C!4, difference(E!3, C!4)))) | member(X, intersection(A!6, difference(E!3, B!5))))) | (~member(tptp_fun_X_0(B!5, A!6), intersection(C!4, difference(E!3, C!4)))) | member(tptp_fun_X_0(B!5, A!6), intersection(A!6, difference(E!3, B!5))))),
% 0.98/1.16 inference(rewrite,[status(thm)],[])).
% 0.98/1.16 tff(154,plain,
% 0.98/1.16 ((~![X: $i] : ((~member(X, intersection(C!4, difference(E!3, C!4)))) | member(X, intersection(A!6, difference(E!3, B!5))))) | ((~member(tptp_fun_X_0(B!5, A!6), intersection(C!4, difference(E!3, C!4)))) | member(tptp_fun_X_0(B!5, A!6), intersection(A!6, difference(E!3, B!5))))),
% 0.98/1.16 inference(quant_inst,[status(thm)],[])).
% 0.98/1.16 tff(155,plain,
% 0.98/1.16 ((~![X: $i] : ((~member(X, intersection(C!4, difference(E!3, C!4)))) | member(X, intersection(A!6, difference(E!3, B!5))))) | (~member(tptp_fun_X_0(B!5, A!6), intersection(C!4, difference(E!3, C!4)))) | member(tptp_fun_X_0(B!5, A!6), intersection(A!6, difference(E!3, B!5)))),
% 0.98/1.16 inference(modus_ponens,[status(thm)],[154, 153])).
% 0.98/1.16 tff(156,plain,
% 0.98/1.16 (member(tptp_fun_X_0(B!5, A!6), intersection(A!6, difference(E!3, B!5)))),
% 0.98/1.16 inference(unit_resolution,[status(thm)],[155, 152, 116])).
% 0.98/1.16 tff(157,assumption,(((~member(tptp_fun_Y_1(intersection(C!4, difference(E!3, C!4)), E!3), C!4)) | (~member(tptp_fun_Y_1(intersection(C!4, difference(E!3, C!4)), E!3), difference(E!3, C!4)))) <=> member(tptp_fun_Y_1(intersection(C!4, difference(E!3, C!4)), E!3), intersection(C!4, difference(E!3, C!4)))), introduced(assumption)).
% 0.98/1.16 tff(158,plain,
% 0.98/1.16 ((~![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))) | (~(((~member(tptp_fun_Y_1(intersection(C!4, difference(E!3, C!4)), E!3), C!4)) | (~member(tptp_fun_Y_1(intersection(C!4, difference(E!3, C!4)), E!3), difference(E!3, C!4)))) <=> member(tptp_fun_Y_1(intersection(C!4, difference(E!3, C!4)), E!3), intersection(C!4, difference(E!3, C!4)))))),
% 0.98/1.16 inference(quant_inst,[status(thm)],[])).
% 0.98/1.16 tff(159,plain,
% 0.98/1.16 ($false),
% 0.98/1.16 inference(unit_resolution,[status(thm)],[158, 10, 157])).
% 0.98/1.16 tff(160,plain,(~(((~member(tptp_fun_Y_1(intersection(C!4, difference(E!3, C!4)), E!3), C!4)) | (~member(tptp_fun_Y_1(intersection(C!4, difference(E!3, C!4)), E!3), difference(E!3, C!4)))) <=> member(tptp_fun_Y_1(intersection(C!4, difference(E!3, C!4)), E!3), intersection(C!4, difference(E!3, C!4))))), inference(lemma,lemma(discharge,[]))).
% 0.98/1.16 tff(161,assumption,(((~member(tptp_fun_Y_1(intersection(C!4, difference(E!3, C!4)), E!3), E!3)) | member(tptp_fun_Y_1(intersection(C!4, difference(E!3, C!4)), E!3), C!4)) <=> member(tptp_fun_Y_1(intersection(C!4, difference(E!3, C!4)), E!3), difference(E!3, C!4))), introduced(assumption)).
% 0.98/1.16 tff(162,plain,
% 0.98/1.16 ((~![B: $i, A: $i, E: $i] : (~(((~member(B, E)) | member(B, A)) <=> member(B, difference(E, A))))) | (~(((~member(tptp_fun_Y_1(intersection(C!4, difference(E!3, C!4)), E!3), E!3)) | member(tptp_fun_Y_1(intersection(C!4, difference(E!3, C!4)), E!3), C!4)) <=> member(tptp_fun_Y_1(intersection(C!4, difference(E!3, C!4)), E!3), difference(E!3, C!4))))),
% 0.98/1.16 inference(quant_inst,[status(thm)],[])).
% 0.98/1.16 tff(163,plain,
% 0.98/1.16 ($false),
% 0.98/1.16 inference(unit_resolution,[status(thm)],[162, 76, 161])).
% 0.98/1.16 tff(164,plain,(~(((~member(tptp_fun_Y_1(intersection(C!4, difference(E!3, C!4)), E!3), E!3)) | member(tptp_fun_Y_1(intersection(C!4, difference(E!3, C!4)), E!3), C!4)) <=> member(tptp_fun_Y_1(intersection(C!4, difference(E!3, C!4)), E!3), difference(E!3, C!4)))), inference(lemma,lemma(discharge,[]))).
% 0.98/1.16 tff(165,assumption,(~((~member(tptp_fun_Y_1(intersection(C!4, difference(E!3, C!4)), E!3), C!4)) | (~member(tptp_fun_Y_1(intersection(C!4, difference(E!3, C!4)), E!3), difference(E!3, C!4))))), introduced(assumption)).
% 0.98/1.16 tff(166,plain,
% 0.98/1.16 (((~member(tptp_fun_Y_1(intersection(C!4, difference(E!3, C!4)), E!3), C!4)) | (~member(tptp_fun_Y_1(intersection(C!4, difference(E!3, C!4)), E!3), difference(E!3, C!4)))) | member(tptp_fun_Y_1(intersection(C!4, difference(E!3, C!4)), E!3), difference(E!3, C!4))),
% 0.98/1.16 inference(tautology,[status(thm)],[])).
% 0.98/1.16 tff(167,plain,
% 0.98/1.16 (member(tptp_fun_Y_1(intersection(C!4, difference(E!3, C!4)), E!3), difference(E!3, C!4))),
% 0.98/1.16 inference(unit_resolution,[status(thm)],[166, 165])).
% 0.98/1.16 tff(168,plain,
% 0.98/1.16 (((~member(tptp_fun_Y_1(intersection(C!4, difference(E!3, C!4)), E!3), C!4)) | (~member(tptp_fun_Y_1(intersection(C!4, difference(E!3, C!4)), E!3), difference(E!3, C!4)))) | member(tptp_fun_Y_1(intersection(C!4, difference(E!3, C!4)), E!3), C!4)),
% 0.98/1.16 inference(tautology,[status(thm)],[])).
% 0.98/1.16 tff(169,plain,
% 0.98/1.16 (member(tptp_fun_Y_1(intersection(C!4, difference(E!3, C!4)), E!3), C!4)),
% 0.98/1.16 inference(unit_resolution,[status(thm)],[168, 165])).
% 0.98/1.16 tff(170,plain,
% 0.98/1.16 (((~member(tptp_fun_Y_1(intersection(C!4, difference(E!3, C!4)), E!3), E!3)) | member(tptp_fun_Y_1(intersection(C!4, difference(E!3, C!4)), E!3), C!4)) | (~member(tptp_fun_Y_1(intersection(C!4, difference(E!3, C!4)), E!3), C!4))),
% 0.98/1.16 inference(tautology,[status(thm)],[])).
% 0.98/1.16 tff(171,plain,
% 0.98/1.16 ((~member(tptp_fun_Y_1(intersection(C!4, difference(E!3, C!4)), E!3), E!3)) | member(tptp_fun_Y_1(intersection(C!4, difference(E!3, C!4)), E!3), C!4)),
% 0.98/1.16 inference(unit_resolution,[status(thm)],[170, 169])).
% 0.98/1.16 tff(172,plain,
% 0.98/1.16 ((((~member(tptp_fun_Y_1(intersection(C!4, difference(E!3, C!4)), E!3), E!3)) | member(tptp_fun_Y_1(intersection(C!4, difference(E!3, C!4)), E!3), C!4)) <=> member(tptp_fun_Y_1(intersection(C!4, difference(E!3, C!4)), E!3), difference(E!3, C!4))) | (~((~member(tptp_fun_Y_1(intersection(C!4, difference(E!3, C!4)), E!3), E!3)) | member(tptp_fun_Y_1(intersection(C!4, difference(E!3, C!4)), E!3), C!4))) | (~member(tptp_fun_Y_1(intersection(C!4, difference(E!3, C!4)), E!3), difference(E!3, C!4)))),
% 0.98/1.16 inference(tautology,[status(thm)],[])).
% 0.98/1.16 tff(173,plain,
% 0.98/1.16 ($false),
% 0.98/1.16 inference(unit_resolution,[status(thm)],[172, 171, 167, 164])).
% 0.98/1.16 tff(174,plain,((~member(tptp_fun_Y_1(intersection(C!4, difference(E!3, C!4)), E!3), C!4)) | (~member(tptp_fun_Y_1(intersection(C!4, difference(E!3, C!4)), E!3), difference(E!3, C!4)))), inference(lemma,lemma(discharge,[]))).
% 0.98/1.16 tff(175,plain,
% 0.98/1.16 ((((~member(tptp_fun_Y_1(intersection(C!4, difference(E!3, C!4)), E!3), C!4)) | (~member(tptp_fun_Y_1(intersection(C!4, difference(E!3, C!4)), E!3), difference(E!3, C!4)))) <=> member(tptp_fun_Y_1(intersection(C!4, difference(E!3, C!4)), E!3), intersection(C!4, difference(E!3, C!4)))) | (~((~member(tptp_fun_Y_1(intersection(C!4, difference(E!3, C!4)), E!3), C!4)) | (~member(tptp_fun_Y_1(intersection(C!4, difference(E!3, C!4)), E!3), difference(E!3, C!4))))) | (~member(tptp_fun_Y_1(intersection(C!4, difference(E!3, C!4)), E!3), intersection(C!4, difference(E!3, C!4))))),
% 0.98/1.16 inference(tautology,[status(thm)],[])).
% 0.98/1.16 tff(176,plain,
% 0.98/1.16 ((((~member(tptp_fun_Y_1(intersection(C!4, difference(E!3, C!4)), E!3), C!4)) | (~member(tptp_fun_Y_1(intersection(C!4, difference(E!3, C!4)), E!3), difference(E!3, C!4)))) <=> member(tptp_fun_Y_1(intersection(C!4, difference(E!3, C!4)), E!3), intersection(C!4, difference(E!3, C!4)))) | (~member(tptp_fun_Y_1(intersection(C!4, difference(E!3, C!4)), E!3), intersection(C!4, difference(E!3, C!4))))),
% 0.98/1.16 inference(unit_resolution,[status(thm)],[175, 174])).
% 0.98/1.16 tff(177,plain,
% 0.98/1.16 (~member(tptp_fun_Y_1(intersection(C!4, difference(E!3, C!4)), E!3), intersection(C!4, difference(E!3, C!4)))),
% 0.98/1.16 inference(unit_resolution,[status(thm)],[176, 160])).
% 0.98/1.16 tff(178,plain,
% 0.98/1.16 (((~member(E!3, tptp_fun_Y_1(intersection(C!4, difference(E!3, C!4)), E!3))) | (~member(tptp_fun_Y_1(intersection(C!4, difference(E!3, C!4)), E!3), intersection(C!4, difference(E!3, C!4))))) | member(tptp_fun_Y_1(intersection(C!4, difference(E!3, C!4)), E!3), intersection(C!4, difference(E!3, C!4)))),
% 0.98/1.16 inference(tautology,[status(thm)],[])).
% 0.98/1.16 tff(179,plain,
% 0.98/1.16 ((~member(E!3, tptp_fun_Y_1(intersection(C!4, difference(E!3, C!4)), E!3))) | (~member(tptp_fun_Y_1(intersection(C!4, difference(E!3, C!4)), E!3), intersection(C!4, difference(E!3, C!4))))),
% 0.98/1.16 inference(unit_resolution,[status(thm)],[178, 177])).
% 0.98/1.16 tff(180,plain,
% 0.98/1.16 (^[X: $i, A: $i] : refl((~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y))))))) <=> (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y))))))))),
% 0.98/1.16 inference(bind,[status(th)],[])).
% 0.98/1.16 tff(181,plain,
% 0.98/1.16 (![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y))))))) <=> ![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y)))))))),
% 0.98/1.16 inference(quant_intro,[status(thm)],[180])).
% 0.98/1.16 tff(182,plain,
% 0.98/1.16 (^[X: $i, A: $i] : rewrite((~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y))))))) <=> (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y))))))))),
% 0.98/1.16 inference(bind,[status(th)],[])).
% 0.98/1.16 tff(183,plain,
% 0.98/1.16 (![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y))))))) <=> ![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y)))))))),
% 0.98/1.16 inference(quant_intro,[status(thm)],[182])).
% 0.98/1.16 tff(184,plain,
% 0.98/1.16 (![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y))))))) <=> ![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y)))))))),
% 0.98/1.16 inference(transitivity,[status(thm)],[183, 181])).
% 0.98/1.16 tff(185,plain,
% 0.98/1.16 (^[X: $i, A: $i] : trans(monotonicity(rewrite(((~member(X, sum(A))) | (member(tptp_fun_Y_1(A, X), A) & member(X, tptp_fun_Y_1(A, X)))) <=> ((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))), rewrite((member(X, sum(A)) | ![Y: $i] : (~(member(Y, A) & member(X, Y)))) <=> (member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y))))), ((((~member(X, sum(A))) | (member(tptp_fun_Y_1(A, X), A) & member(X, tptp_fun_Y_1(A, X)))) & (member(X, sum(A)) | ![Y: $i] : (~(member(Y, A) & member(X, Y))))) <=> (((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X)))))) & (member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y))))))), rewrite((((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X)))))) & (member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y))))) <=> (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y)))))))), ((((~member(X, sum(A))) | (member(tptp_fun_Y_1(A, X), A) & member(X, tptp_fun_Y_1(A, X)))) & (member(X, sum(A)) | ![Y: $i] : (~(member(Y, A) & member(X, Y))))) <=> (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y)))))))))),
% 0.98/1.16 inference(bind,[status(th)],[])).
% 0.98/1.16 tff(186,plain,
% 0.98/1.16 (![X: $i, A: $i] : (((~member(X, sum(A))) | (member(tptp_fun_Y_1(A, X), A) & member(X, tptp_fun_Y_1(A, X)))) & (member(X, sum(A)) | ![Y: $i] : (~(member(Y, A) & member(X, Y))))) <=> ![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y)))))))),
% 0.98/1.16 inference(quant_intro,[status(thm)],[185])).
% 0.98/1.16 tff(187,plain,
% 0.98/1.16 (![X: $i, A: $i] : (member(X, sum(A)) <=> ?[Y: $i] : (member(Y, A) & member(X, Y))) <=> ![X: $i, A: $i] : (member(X, sum(A)) <=> ?[Y: $i] : (member(Y, A) & member(X, Y)))),
% 0.98/1.16 inference(rewrite,[status(thm)],[])).
% 0.98/1.16 tff(188,axiom,(![X: $i, A: $i] : (member(X, sum(A)) <=> ?[Y: $i] : (member(Y, A) & member(X, Y)))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax','sum')).
% 0.98/1.16 tff(189,plain,
% 0.98/1.16 (![X: $i, A: $i] : (member(X, sum(A)) <=> ?[Y: $i] : (member(Y, A) & member(X, Y)))),
% 0.98/1.16 inference(modus_ponens,[status(thm)],[188, 187])).
% 0.98/1.16 tff(190,plain,(
% 0.98/1.16 ![X: $i, A: $i] : (((~member(X, sum(A))) | (member(tptp_fun_Y_1(A, X), A) & member(X, tptp_fun_Y_1(A, X)))) & (member(X, sum(A)) | ![Y: $i] : (~(member(Y, A) & member(X, Y)))))),
% 0.98/1.16 inference(skolemize,[status(sab)],[189])).
% 0.98/1.16 tff(191,plain,
% 0.98/1.16 (![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y)))))))),
% 1.01/1.16 inference(modus_ponens,[status(thm)],[190, 186])).
% 1.01/1.16 tff(192,plain,
% 1.01/1.16 (![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y)))))))),
% 1.01/1.16 inference(modus_ponens,[status(thm)],[191, 184])).
% 1.01/1.16 tff(193,plain,
% 1.01/1.16 (((~![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y)))))))) | (~((~((~member(E!3, sum(intersection(C!4, difference(E!3, C!4))))) | (~((~member(E!3, tptp_fun_Y_1(intersection(C!4, difference(E!3, C!4)), E!3))) | (~member(tptp_fun_Y_1(intersection(C!4, difference(E!3, C!4)), E!3), intersection(C!4, difference(E!3, C!4)))))))) | (~(member(E!3, sum(intersection(C!4, difference(E!3, C!4)))) | ![Y: $i] : ((~member(Y, intersection(C!4, difference(E!3, C!4)))) | (~member(E!3, Y)))))))) <=> ((~![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y)))))))) | (~((~((~member(E!3, sum(intersection(C!4, difference(E!3, C!4))))) | (~((~member(E!3, tptp_fun_Y_1(intersection(C!4, difference(E!3, C!4)), E!3))) | (~member(tptp_fun_Y_1(intersection(C!4, difference(E!3, C!4)), E!3), intersection(C!4, difference(E!3, C!4)))))))) | (~(member(E!3, sum(intersection(C!4, difference(E!3, C!4)))) | ![Y: $i] : ((~member(Y, intersection(C!4, difference(E!3, C!4)))) | (~member(E!3, Y))))))))),
% 1.01/1.16 inference(rewrite,[status(thm)],[])).
% 1.01/1.16 tff(194,plain,
% 1.01/1.16 ((~((~((~member(E!3, sum(intersection(C!4, difference(E!3, C!4))))) | (~((~member(tptp_fun_Y_1(intersection(C!4, difference(E!3, C!4)), E!3), intersection(C!4, difference(E!3, C!4)))) | (~member(E!3, tptp_fun_Y_1(intersection(C!4, difference(E!3, C!4)), E!3))))))) | (~(member(E!3, sum(intersection(C!4, difference(E!3, C!4)))) | ![Y: $i] : ((~member(Y, intersection(C!4, difference(E!3, C!4)))) | (~member(E!3, Y))))))) <=> (~((~((~member(E!3, sum(intersection(C!4, difference(E!3, C!4))))) | (~((~member(E!3, tptp_fun_Y_1(intersection(C!4, difference(E!3, C!4)), E!3))) | (~member(tptp_fun_Y_1(intersection(C!4, difference(E!3, C!4)), E!3), intersection(C!4, difference(E!3, C!4)))))))) | (~(member(E!3, sum(intersection(C!4, difference(E!3, C!4)))) | ![Y: $i] : ((~member(Y, intersection(C!4, difference(E!3, C!4)))) | (~member(E!3, Y)))))))),
% 1.01/1.17 inference(rewrite,[status(thm)],[])).
% 1.01/1.17 tff(195,plain,
% 1.01/1.17 (((~![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y)))))))) | (~((~((~member(E!3, sum(intersection(C!4, difference(E!3, C!4))))) | (~((~member(tptp_fun_Y_1(intersection(C!4, difference(E!3, C!4)), E!3), intersection(C!4, difference(E!3, C!4)))) | (~member(E!3, tptp_fun_Y_1(intersection(C!4, difference(E!3, C!4)), E!3))))))) | (~(member(E!3, sum(intersection(C!4, difference(E!3, C!4)))) | ![Y: $i] : ((~member(Y, intersection(C!4, difference(E!3, C!4)))) | (~member(E!3, Y)))))))) <=> ((~![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y)))))))) | (~((~((~member(E!3, sum(intersection(C!4, difference(E!3, C!4))))) | (~((~member(E!3, tptp_fun_Y_1(intersection(C!4, difference(E!3, C!4)), E!3))) | (~member(tptp_fun_Y_1(intersection(C!4, difference(E!3, C!4)), E!3), intersection(C!4, difference(E!3, C!4)))))))) | (~(member(E!3, sum(intersection(C!4, difference(E!3, C!4)))) | ![Y: $i] : ((~member(Y, intersection(C!4, difference(E!3, C!4)))) | (~member(E!3, Y))))))))),
% 1.01/1.17 inference(monotonicity,[status(thm)],[194])).
% 1.01/1.17 tff(196,plain,
% 1.01/1.17 (((~![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y)))))))) | (~((~((~member(E!3, sum(intersection(C!4, difference(E!3, C!4))))) | (~((~member(tptp_fun_Y_1(intersection(C!4, difference(E!3, C!4)), E!3), intersection(C!4, difference(E!3, C!4)))) | (~member(E!3, tptp_fun_Y_1(intersection(C!4, difference(E!3, C!4)), E!3))))))) | (~(member(E!3, sum(intersection(C!4, difference(E!3, C!4)))) | ![Y: $i] : ((~member(Y, intersection(C!4, difference(E!3, C!4)))) | (~member(E!3, Y)))))))) <=> ((~![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y)))))))) | (~((~((~member(E!3, sum(intersection(C!4, difference(E!3, C!4))))) | (~((~member(E!3, tptp_fun_Y_1(intersection(C!4, difference(E!3, C!4)), E!3))) | (~member(tptp_fun_Y_1(intersection(C!4, difference(E!3, C!4)), E!3), intersection(C!4, difference(E!3, C!4)))))))) | (~(member(E!3, sum(intersection(C!4, difference(E!3, C!4)))) | ![Y: $i] : ((~member(Y, intersection(C!4, difference(E!3, C!4)))) | (~member(E!3, Y))))))))),
% 1.01/1.17 inference(transitivity,[status(thm)],[195, 193])).
% 1.01/1.17 tff(197,plain,
% 1.01/1.17 ((~![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y)))))))) | (~((~((~member(E!3, sum(intersection(C!4, difference(E!3, C!4))))) | (~((~member(tptp_fun_Y_1(intersection(C!4, difference(E!3, C!4)), E!3), intersection(C!4, difference(E!3, C!4)))) | (~member(E!3, tptp_fun_Y_1(intersection(C!4, difference(E!3, C!4)), E!3))))))) | (~(member(E!3, sum(intersection(C!4, difference(E!3, C!4)))) | ![Y: $i] : ((~member(Y, intersection(C!4, difference(E!3, C!4)))) | (~member(E!3, Y)))))))),
% 1.01/1.17 inference(quant_inst,[status(thm)],[])).
% 1.01/1.17 tff(198,plain,
% 1.01/1.17 ((~![X: $i, A: $i] : (~((~((~member(X, sum(A))) | (~((~member(tptp_fun_Y_1(A, X), A)) | (~member(X, tptp_fun_Y_1(A, X))))))) | (~(member(X, sum(A)) | ![Y: $i] : ((~member(Y, A)) | (~member(X, Y)))))))) | (~((~((~member(E!3, sum(intersection(C!4, difference(E!3, C!4))))) | (~((~member(E!3, tptp_fun_Y_1(intersection(C!4, difference(E!3, C!4)), E!3))) | (~member(tptp_fun_Y_1(intersection(C!4, difference(E!3, C!4)), E!3), intersection(C!4, difference(E!3, C!4)))))))) | (~(member(E!3, sum(intersection(C!4, difference(E!3, C!4)))) | ![Y: $i] : ((~member(Y, intersection(C!4, difference(E!3, C!4)))) | (~member(E!3, Y)))))))),
% 1.01/1.17 inference(modus_ponens,[status(thm)],[197, 196])).
% 1.01/1.17 tff(199,plain,
% 1.01/1.17 (~((~((~member(E!3, sum(intersection(C!4, difference(E!3, C!4))))) | (~((~member(E!3, tptp_fun_Y_1(intersection(C!4, difference(E!3, C!4)), E!3))) | (~member(tptp_fun_Y_1(intersection(C!4, difference(E!3, C!4)), E!3), intersection(C!4, difference(E!3, C!4)))))))) | (~(member(E!3, sum(intersection(C!4, difference(E!3, C!4)))) | ![Y: $i] : ((~member(Y, intersection(C!4, difference(E!3, C!4)))) | (~member(E!3, Y))))))),
% 1.01/1.17 inference(unit_resolution,[status(thm)],[198, 192])).
% 1.01/1.17 tff(200,plain,
% 1.01/1.17 (((~((~member(E!3, sum(intersection(C!4, difference(E!3, C!4))))) | (~((~member(E!3, tptp_fun_Y_1(intersection(C!4, difference(E!3, C!4)), E!3))) | (~member(tptp_fun_Y_1(intersection(C!4, difference(E!3, C!4)), E!3), intersection(C!4, difference(E!3, C!4)))))))) | (~(member(E!3, sum(intersection(C!4, difference(E!3, C!4)))) | ![Y: $i] : ((~member(Y, intersection(C!4, difference(E!3, C!4)))) | (~member(E!3, Y)))))) | ((~member(E!3, sum(intersection(C!4, difference(E!3, C!4))))) | (~((~member(E!3, tptp_fun_Y_1(intersection(C!4, difference(E!3, C!4)), E!3))) | (~member(tptp_fun_Y_1(intersection(C!4, difference(E!3, C!4)), E!3), intersection(C!4, difference(E!3, C!4)))))))),
% 1.01/1.17 inference(tautology,[status(thm)],[])).
% 1.01/1.17 tff(201,plain,
% 1.01/1.17 ((~member(E!3, sum(intersection(C!4, difference(E!3, C!4))))) | (~((~member(E!3, tptp_fun_Y_1(intersection(C!4, difference(E!3, C!4)), E!3))) | (~member(tptp_fun_Y_1(intersection(C!4, difference(E!3, C!4)), E!3), intersection(C!4, difference(E!3, C!4))))))),
% 1.01/1.17 inference(unit_resolution,[status(thm)],[200, 199])).
% 1.01/1.17 tff(202,plain,
% 1.01/1.17 ((~((~member(E!3, sum(intersection(C!4, difference(E!3, C!4))))) | (~((~member(E!3, tptp_fun_Y_1(intersection(C!4, difference(E!3, C!4)), E!3))) | (~member(tptp_fun_Y_1(intersection(C!4, difference(E!3, C!4)), E!3), intersection(C!4, difference(E!3, C!4)))))))) | (~member(E!3, sum(intersection(C!4, difference(E!3, C!4))))) | (~((~member(E!3, tptp_fun_Y_1(intersection(C!4, difference(E!3, C!4)), E!3))) | (~member(tptp_fun_Y_1(intersection(C!4, difference(E!3, C!4)), E!3), intersection(C!4, difference(E!3, C!4))))))),
% 1.01/1.17 inference(tautology,[status(thm)],[])).
% 1.01/1.17 tff(203,plain,
% 1.01/1.17 ((~member(E!3, sum(intersection(C!4, difference(E!3, C!4))))) | (~((~member(E!3, tptp_fun_Y_1(intersection(C!4, difference(E!3, C!4)), E!3))) | (~member(tptp_fun_Y_1(intersection(C!4, difference(E!3, C!4)), E!3), intersection(C!4, difference(E!3, C!4))))))),
% 1.01/1.17 inference(unit_resolution,[status(thm)],[202, 201])).
% 1.01/1.17 tff(204,plain,
% 1.01/1.17 (~member(E!3, sum(intersection(C!4, difference(E!3, C!4))))),
% 1.01/1.17 inference(unit_resolution,[status(thm)],[203, 179])).
% 1.01/1.17 tff(205,plain,
% 1.01/1.17 (((~((~member(E!3, sum(intersection(C!4, difference(E!3, C!4))))) | (~((~member(E!3, tptp_fun_Y_1(intersection(C!4, difference(E!3, C!4)), E!3))) | (~member(tptp_fun_Y_1(intersection(C!4, difference(E!3, C!4)), E!3), intersection(C!4, difference(E!3, C!4)))))))) | (~(member(E!3, sum(intersection(C!4, difference(E!3, C!4)))) | ![Y: $i] : ((~member(Y, intersection(C!4, difference(E!3, C!4)))) | (~member(E!3, Y)))))) | (member(E!3, sum(intersection(C!4, difference(E!3, C!4)))) | ![Y: $i] : ((~member(Y, intersection(C!4, difference(E!3, C!4)))) | (~member(E!3, Y))))),
% 1.01/1.17 inference(tautology,[status(thm)],[])).
% 1.01/1.17 tff(206,plain,
% 1.01/1.17 (member(E!3, sum(intersection(C!4, difference(E!3, C!4)))) | ![Y: $i] : ((~member(Y, intersection(C!4, difference(E!3, C!4)))) | (~member(E!3, Y)))),
% 1.01/1.17 inference(unit_resolution,[status(thm)],[205, 199])).
% 1.01/1.17 tff(207,plain,
% 1.01/1.17 ((~(member(E!3, sum(intersection(C!4, difference(E!3, C!4)))) | ![Y: $i] : ((~member(Y, intersection(C!4, difference(E!3, C!4)))) | (~member(E!3, Y))))) | member(E!3, sum(intersection(C!4, difference(E!3, C!4)))) | ![Y: $i] : ((~member(Y, intersection(C!4, difference(E!3, C!4)))) | (~member(E!3, Y)))),
% 1.01/1.17 inference(tautology,[status(thm)],[])).
% 1.01/1.17 tff(208,plain,
% 1.01/1.17 (member(E!3, sum(intersection(C!4, difference(E!3, C!4)))) | ![Y: $i] : ((~member(Y, intersection(C!4, difference(E!3, C!4)))) | (~member(E!3, Y)))),
% 1.01/1.17 inference(unit_resolution,[status(thm)],[207, 206])).
% 1.01/1.17 tff(209,plain,
% 1.01/1.17 (![Y: $i] : ((~member(Y, intersection(C!4, difference(E!3, C!4)))) | (~member(E!3, Y)))),
% 1.01/1.17 inference(unit_resolution,[status(thm)],[208, 204])).
% 1.01/1.17 tff(210,plain,
% 1.01/1.17 (((~![Y: $i] : ((~member(Y, intersection(C!4, difference(E!3, C!4)))) | (~member(E!3, Y)))) | ((~member(tptp_fun_X_0(B!5, A!6), intersection(C!4, difference(E!3, C!4)))) | (~member(E!3, tptp_fun_X_0(B!5, A!6))))) <=> ((~![Y: $i] : ((~member(Y, intersection(C!4, difference(E!3, C!4)))) | (~member(E!3, Y)))) | (~member(tptp_fun_X_0(B!5, A!6), intersection(C!4, difference(E!3, C!4)))) | (~member(E!3, tptp_fun_X_0(B!5, A!6))))),
% 1.01/1.17 inference(rewrite,[status(thm)],[])).
% 1.01/1.17 tff(211,plain,
% 1.01/1.17 ((~![Y: $i] : ((~member(Y, intersection(C!4, difference(E!3, C!4)))) | (~member(E!3, Y)))) | ((~member(tptp_fun_X_0(B!5, A!6), intersection(C!4, difference(E!3, C!4)))) | (~member(E!3, tptp_fun_X_0(B!5, A!6))))),
% 1.01/1.17 inference(quant_inst,[status(thm)],[])).
% 1.01/1.17 tff(212,plain,
% 1.01/1.17 ((~![Y: $i] : ((~member(Y, intersection(C!4, difference(E!3, C!4)))) | (~member(E!3, Y)))) | (~member(tptp_fun_X_0(B!5, A!6), intersection(C!4, difference(E!3, C!4)))) | (~member(E!3, tptp_fun_X_0(B!5, A!6)))),
% 1.01/1.17 inference(modus_ponens,[status(thm)],[211, 210])).
% 1.01/1.17 tff(213,plain,
% 1.01/1.17 (~member(E!3, tptp_fun_X_0(B!5, A!6))),
% 1.01/1.17 inference(unit_resolution,[status(thm)],[212, 209, 116])).
% 1.01/1.17 tff(214,assumption,(((~member(tptp_fun_Y_2(intersection(A!6, difference(E!3, B!5)), E!3), C!4)) | (~member(tptp_fun_Y_2(intersection(A!6, difference(E!3, B!5)), E!3), difference(E!3, C!4)))) <=> member(tptp_fun_Y_2(intersection(A!6, difference(E!3, B!5)), E!3), intersection(C!4, difference(E!3, C!4)))), introduced(assumption)).
% 1.01/1.17 tff(215,plain,
% 1.01/1.17 ((~![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))) | (~(((~member(tptp_fun_Y_2(intersection(A!6, difference(E!3, B!5)), E!3), C!4)) | (~member(tptp_fun_Y_2(intersection(A!6, difference(E!3, B!5)), E!3), difference(E!3, C!4)))) <=> member(tptp_fun_Y_2(intersection(A!6, difference(E!3, B!5)), E!3), intersection(C!4, difference(E!3, C!4)))))),
% 1.01/1.17 inference(quant_inst,[status(thm)],[])).
% 1.01/1.17 tff(216,plain,
% 1.01/1.17 ($false),
% 1.01/1.17 inference(unit_resolution,[status(thm)],[215, 10, 214])).
% 1.01/1.17 tff(217,plain,(~(((~member(tptp_fun_Y_2(intersection(A!6, difference(E!3, B!5)), E!3), C!4)) | (~member(tptp_fun_Y_2(intersection(A!6, difference(E!3, B!5)), E!3), difference(E!3, C!4)))) <=> member(tptp_fun_Y_2(intersection(A!6, difference(E!3, B!5)), E!3), intersection(C!4, difference(E!3, C!4))))), inference(lemma,lemma(discharge,[]))).
% 1.01/1.17 tff(218,assumption,(~((~member(tptp_fun_Y_2(intersection(A!6, difference(E!3, B!5)), E!3), C!4)) | (~member(tptp_fun_Y_2(intersection(A!6, difference(E!3, B!5)), E!3), difference(E!3, C!4))))), introduced(assumption)).
% 1.01/1.17 tff(219,plain,
% 1.01/1.17 (((~member(tptp_fun_Y_2(intersection(A!6, difference(E!3, B!5)), E!3), C!4)) | (~member(tptp_fun_Y_2(intersection(A!6, difference(E!3, B!5)), E!3), difference(E!3, C!4)))) | member(tptp_fun_Y_2(intersection(A!6, difference(E!3, B!5)), E!3), difference(E!3, C!4))),
% 1.01/1.17 inference(tautology,[status(thm)],[])).
% 1.01/1.17 tff(220,plain,
% 1.01/1.17 (member(tptp_fun_Y_2(intersection(A!6, difference(E!3, B!5)), E!3), difference(E!3, C!4))),
% 1.01/1.17 inference(unit_resolution,[status(thm)],[219, 218])).
% 1.01/1.17 tff(221,plain,
% 1.01/1.17 (((~member(tptp_fun_Y_2(intersection(A!6, difference(E!3, B!5)), E!3), C!4)) | (~member(tptp_fun_Y_2(intersection(A!6, difference(E!3, B!5)), E!3), difference(E!3, C!4)))) | member(tptp_fun_Y_2(intersection(A!6, difference(E!3, B!5)), E!3), C!4)),
% 1.01/1.17 inference(tautology,[status(thm)],[])).
% 1.01/1.17 tff(222,plain,
% 1.01/1.17 (member(tptp_fun_Y_2(intersection(A!6, difference(E!3, B!5)), E!3), C!4)),
% 1.01/1.17 inference(unit_resolution,[status(thm)],[221, 218])).
% 1.01/1.17 tff(223,plain,
% 1.01/1.17 (((~member(tptp_fun_Y_2(intersection(A!6, difference(E!3, B!5)), E!3), E!3)) | member(tptp_fun_Y_2(intersection(A!6, difference(E!3, B!5)), E!3), C!4)) | (~member(tptp_fun_Y_2(intersection(A!6, difference(E!3, B!5)), E!3), C!4))),
% 1.01/1.17 inference(tautology,[status(thm)],[])).
% 1.01/1.17 tff(224,plain,
% 1.01/1.17 ((~member(tptp_fun_Y_2(intersection(A!6, difference(E!3, B!5)), E!3), E!3)) | member(tptp_fun_Y_2(intersection(A!6, difference(E!3, B!5)), E!3), C!4)),
% 1.01/1.17 inference(unit_resolution,[status(thm)],[223, 222])).
% 1.01/1.17 tff(225,assumption,(((~member(tptp_fun_Y_2(intersection(A!6, difference(E!3, B!5)), E!3), E!3)) | member(tptp_fun_Y_2(intersection(A!6, difference(E!3, B!5)), E!3), C!4)) <=> member(tptp_fun_Y_2(intersection(A!6, difference(E!3, B!5)), E!3), difference(E!3, C!4))), introduced(assumption)).
% 1.01/1.17 tff(226,plain,
% 1.01/1.17 ((~![B: $i, A: $i, E: $i] : (~(((~member(B, E)) | member(B, A)) <=> member(B, difference(E, A))))) | (~(((~member(tptp_fun_Y_2(intersection(A!6, difference(E!3, B!5)), E!3), E!3)) | member(tptp_fun_Y_2(intersection(A!6, difference(E!3, B!5)), E!3), C!4)) <=> member(tptp_fun_Y_2(intersection(A!6, difference(E!3, B!5)), E!3), difference(E!3, C!4))))),
% 1.01/1.17 inference(quant_inst,[status(thm)],[])).
% 1.01/1.17 tff(227,plain,
% 1.01/1.17 ($false),
% 1.01/1.17 inference(unit_resolution,[status(thm)],[226, 76, 225])).
% 1.01/1.17 tff(228,plain,(~(((~member(tptp_fun_Y_2(intersection(A!6, difference(E!3, B!5)), E!3), E!3)) | member(tptp_fun_Y_2(intersection(A!6, difference(E!3, B!5)), E!3), C!4)) <=> member(tptp_fun_Y_2(intersection(A!6, difference(E!3, B!5)), E!3), difference(E!3, C!4)))), inference(lemma,lemma(discharge,[]))).
% 1.01/1.17 tff(229,plain,
% 1.01/1.17 ((((~member(tptp_fun_Y_2(intersection(A!6, difference(E!3, B!5)), E!3), E!3)) | member(tptp_fun_Y_2(intersection(A!6, difference(E!3, B!5)), E!3), C!4)) <=> member(tptp_fun_Y_2(intersection(A!6, difference(E!3, B!5)), E!3), difference(E!3, C!4))) | (~((~member(tptp_fun_Y_2(intersection(A!6, difference(E!3, B!5)), E!3), E!3)) | member(tptp_fun_Y_2(intersection(A!6, difference(E!3, B!5)), E!3), C!4))) | (~member(tptp_fun_Y_2(intersection(A!6, difference(E!3, B!5)), E!3), difference(E!3, C!4)))),
% 1.01/1.17 inference(tautology,[status(thm)],[])).
% 1.01/1.17 tff(230,plain,
% 1.01/1.17 ((~((~member(tptp_fun_Y_2(intersection(A!6, difference(E!3, B!5)), E!3), E!3)) | member(tptp_fun_Y_2(intersection(A!6, difference(E!3, B!5)), E!3), C!4))) | (~member(tptp_fun_Y_2(intersection(A!6, difference(E!3, B!5)), E!3), difference(E!3, C!4)))),
% 1.01/1.17 inference(unit_resolution,[status(thm)],[229, 228])).
% 1.01/1.17 tff(231,plain,
% 1.01/1.17 ($false),
% 1.01/1.17 inference(unit_resolution,[status(thm)],[230, 224, 220])).
% 1.01/1.17 tff(232,plain,((~member(tptp_fun_Y_2(intersection(A!6, difference(E!3, B!5)), E!3), C!4)) | (~member(tptp_fun_Y_2(intersection(A!6, difference(E!3, B!5)), E!3), difference(E!3, C!4)))), inference(lemma,lemma(discharge,[]))).
% 1.01/1.17 tff(233,plain,
% 1.01/1.17 ((((~member(tptp_fun_Y_2(intersection(A!6, difference(E!3, B!5)), E!3), C!4)) | (~member(tptp_fun_Y_2(intersection(A!6, difference(E!3, B!5)), E!3), difference(E!3, C!4)))) <=> member(tptp_fun_Y_2(intersection(A!6, difference(E!3, B!5)), E!3), intersection(C!4, difference(E!3, C!4)))) | (~((~member(tptp_fun_Y_2(intersection(A!6, difference(E!3, B!5)), E!3), C!4)) | (~member(tptp_fun_Y_2(intersection(A!6, difference(E!3, B!5)), E!3), difference(E!3, C!4))))) | (~member(tptp_fun_Y_2(intersection(A!6, difference(E!3, B!5)), E!3), intersection(C!4, difference(E!3, C!4))))),
% 1.01/1.17 inference(tautology,[status(thm)],[])).
% 1.01/1.17 tff(234,plain,
% 1.01/1.17 ((((~member(tptp_fun_Y_2(intersection(A!6, difference(E!3, B!5)), E!3), C!4)) | (~member(tptp_fun_Y_2(intersection(A!6, difference(E!3, B!5)), E!3), difference(E!3, C!4)))) <=> member(tptp_fun_Y_2(intersection(A!6, difference(E!3, B!5)), E!3), intersection(C!4, difference(E!3, C!4)))) | (~member(tptp_fun_Y_2(intersection(A!6, difference(E!3, B!5)), E!3), intersection(C!4, difference(E!3, C!4))))),
% 1.01/1.17 inference(unit_resolution,[status(thm)],[233, 232])).
% 1.01/1.17 tff(235,plain,
% 1.01/1.17 (~member(tptp_fun_Y_2(intersection(A!6, difference(E!3, B!5)), E!3), intersection(C!4, difference(E!3, C!4)))),
% 1.01/1.17 inference(unit_resolution,[status(thm)],[234, 217])).
% 1.01/1.17 tff(236,assumption,(member(tptp_fun_Y_2(intersection(A!6, difference(E!3, B!5)), E!3), intersection(A!6, difference(E!3, B!5)))), introduced(assumption)).
% 1.01/1.17 tff(237,plain,
% 1.01/1.17 (((~((~subset(intersection(A!6, difference(E!3, B!5)), intersection(C!4, difference(E!3, C!4)))) | ![X: $i] : ((~member(X, intersection(A!6, difference(E!3, B!5)))) | member(X, intersection(C!4, difference(E!3, C!4)))))) | (~(subset(intersection(A!6, difference(E!3, B!5)), intersection(C!4, difference(E!3, C!4))) | (~((~member(tptp_fun_X_0(intersection(C!4, difference(E!3, C!4)), intersection(A!6, difference(E!3, B!5))), intersection(A!6, difference(E!3, B!5)))) | member(tptp_fun_X_0(intersection(C!4, difference(E!3, C!4)), intersection(A!6, difference(E!3, B!5))), intersection(C!4, difference(E!3, C!4)))))))) | ((~subset(intersection(A!6, difference(E!3, B!5)), intersection(C!4, difference(E!3, C!4)))) | ![X: $i] : ((~member(X, intersection(A!6, difference(E!3, B!5)))) | member(X, intersection(C!4, difference(E!3, C!4)))))),
% 1.01/1.17 inference(tautology,[status(thm)],[])).
% 1.01/1.17 tff(238,plain,
% 1.01/1.17 ((~subset(intersection(A!6, difference(E!3, B!5)), intersection(C!4, difference(E!3, C!4)))) | ![X: $i] : ((~member(X, intersection(A!6, difference(E!3, B!5)))) | member(X, intersection(C!4, difference(E!3, C!4))))),
% 1.01/1.17 inference(unit_resolution,[status(thm)],[237, 31])).
% 1.01/1.17 tff(239,plain,
% 1.01/1.17 ((~((~subset(intersection(A!6, difference(E!3, B!5)), intersection(C!4, difference(E!3, C!4)))) | ![X: $i] : ((~member(X, intersection(A!6, difference(E!3, B!5)))) | member(X, intersection(C!4, difference(E!3, C!4)))))) | (~subset(intersection(A!6, difference(E!3, B!5)), intersection(C!4, difference(E!3, C!4)))) | ![X: $i] : ((~member(X, intersection(A!6, difference(E!3, B!5)))) | member(X, intersection(C!4, difference(E!3, C!4))))),
% 1.01/1.17 inference(tautology,[status(thm)],[])).
% 1.01/1.17 tff(240,plain,
% 1.01/1.17 ((~subset(intersection(A!6, difference(E!3, B!5)), intersection(C!4, difference(E!3, C!4)))) | ![X: $i] : ((~member(X, intersection(A!6, difference(E!3, B!5)))) | member(X, intersection(C!4, difference(E!3, C!4))))),
% 1.01/1.17 inference(unit_resolution,[status(thm)],[239, 238])).
% 1.01/1.17 tff(241,plain,
% 1.01/1.17 (![X: $i] : ((~member(X, intersection(A!6, difference(E!3, B!5)))) | member(X, intersection(C!4, difference(E!3, C!4))))),
% 1.01/1.17 inference(unit_resolution,[status(thm)],[240, 86])).
% 1.01/1.17 tff(242,plain,
% 1.01/1.17 (((~![X: $i] : ((~member(X, intersection(A!6, difference(E!3, B!5)))) | member(X, intersection(C!4, difference(E!3, C!4))))) | ((~member(tptp_fun_Y_2(intersection(A!6, difference(E!3, B!5)), E!3), intersection(A!6, difference(E!3, B!5)))) | member(tptp_fun_Y_2(intersection(A!6, difference(E!3, B!5)), E!3), intersection(C!4, difference(E!3, C!4))))) <=> ((~![X: $i] : ((~member(X, intersection(A!6, difference(E!3, B!5)))) | member(X, intersection(C!4, difference(E!3, C!4))))) | (~member(tptp_fun_Y_2(intersection(A!6, difference(E!3, B!5)), E!3), intersection(A!6, difference(E!3, B!5)))) | member(tptp_fun_Y_2(intersection(A!6, difference(E!3, B!5)), E!3), intersection(C!4, difference(E!3, C!4))))),
% 1.01/1.17 inference(rewrite,[status(thm)],[])).
% 1.01/1.17 tff(243,plain,
% 1.01/1.17 ((~![X: $i] : ((~member(X, intersection(A!6, difference(E!3, B!5)))) | member(X, intersection(C!4, difference(E!3, C!4))))) | ((~member(tptp_fun_Y_2(intersection(A!6, difference(E!3, B!5)), E!3), intersection(A!6, difference(E!3, B!5)))) | member(tptp_fun_Y_2(intersection(A!6, difference(E!3, B!5)), E!3), intersection(C!4, difference(E!3, C!4))))),
% 1.01/1.17 inference(quant_inst,[status(thm)],[])).
% 1.01/1.17 tff(244,plain,
% 1.01/1.17 ((~![X: $i] : ((~member(X, intersection(A!6, difference(E!3, B!5)))) | member(X, intersection(C!4, difference(E!3, C!4))))) | (~member(tptp_fun_Y_2(intersection(A!6, difference(E!3, B!5)), E!3), intersection(A!6, difference(E!3, B!5)))) | member(tptp_fun_Y_2(intersection(A!6, difference(E!3, B!5)), E!3), intersection(C!4, difference(E!3, C!4)))),
% 1.01/1.17 inference(modus_ponens,[status(thm)],[243, 242])).
% 1.01/1.17 tff(245,plain,
% 1.01/1.17 ($false),
% 1.01/1.17 inference(unit_resolution,[status(thm)],[244, 241, 236, 235])).
% 1.01/1.17 tff(246,plain,(~member(tptp_fun_Y_2(intersection(A!6, difference(E!3, B!5)), E!3), intersection(A!6, difference(E!3, B!5)))), inference(lemma,lemma(discharge,[]))).
% 1.01/1.17 tff(247,plain,
% 1.01/1.17 (((~member(tptp_fun_Y_2(intersection(A!6, difference(E!3, B!5)), E!3), intersection(A!6, difference(E!3, B!5)))) | member(E!3, tptp_fun_Y_2(intersection(A!6, difference(E!3, B!5)), E!3))) | member(tptp_fun_Y_2(intersection(A!6, difference(E!3, B!5)), E!3), intersection(A!6, difference(E!3, B!5)))),
% 1.01/1.17 inference(tautology,[status(thm)],[])).
% 1.01/1.17 tff(248,plain,
% 1.01/1.17 ((~member(tptp_fun_Y_2(intersection(A!6, difference(E!3, B!5)), E!3), intersection(A!6, difference(E!3, B!5)))) | member(E!3, tptp_fun_Y_2(intersection(A!6, difference(E!3, B!5)), E!3))),
% 1.01/1.17 inference(unit_resolution,[status(thm)],[247, 246])).
% 1.01/1.17 tff(249,plain,
% 1.01/1.17 (^[X: $i, A: $i] : refl((~((~((~member(X, product(A))) | ![Y: $i] : ((~member(Y, A)) | member(X, Y)))) | (~(member(X, product(A)) | (~((~member(tptp_fun_Y_2(A, X), A)) | member(X, tptp_fun_Y_2(A, X)))))))) <=> (~((~((~member(X, product(A))) | ![Y: $i] : ((~member(Y, A)) | member(X, Y)))) | (~(member(X, product(A)) | (~((~member(tptp_fun_Y_2(A, X), A)) | member(X, tptp_fun_Y_2(A, X)))))))))),
% 1.01/1.17 inference(bind,[status(th)],[])).
% 1.01/1.17 tff(250,plain,
% 1.01/1.17 (![X: $i, A: $i] : (~((~((~member(X, product(A))) | ![Y: $i] : ((~member(Y, A)) | member(X, Y)))) | (~(member(X, product(A)) | (~((~member(tptp_fun_Y_2(A, X), A)) | member(X, tptp_fun_Y_2(A, X)))))))) <=> ![X: $i, A: $i] : (~((~((~member(X, product(A))) | ![Y: $i] : ((~member(Y, A)) | member(X, Y)))) | (~(member(X, product(A)) | (~((~member(tptp_fun_Y_2(A, X), A)) | member(X, tptp_fun_Y_2(A, X))))))))),
% 1.01/1.17 inference(quant_intro,[status(thm)],[249])).
% 1.01/1.17 tff(251,plain,
% 1.01/1.17 (^[X: $i, A: $i] : rewrite((~((~((~member(X, product(A))) | ![Y: $i] : ((~member(Y, A)) | member(X, Y)))) | (~(member(X, product(A)) | (~((~member(tptp_fun_Y_2(A, X), A)) | member(X, tptp_fun_Y_2(A, X)))))))) <=> (~((~((~member(X, product(A))) | ![Y: $i] : ((~member(Y, A)) | member(X, Y)))) | (~(member(X, product(A)) | (~((~member(tptp_fun_Y_2(A, X), A)) | member(X, tptp_fun_Y_2(A, X)))))))))),
% 1.01/1.17 inference(bind,[status(th)],[])).
% 1.01/1.17 tff(252,plain,
% 1.01/1.17 (![X: $i, A: $i] : (~((~((~member(X, product(A))) | ![Y: $i] : ((~member(Y, A)) | member(X, Y)))) | (~(member(X, product(A)) | (~((~member(tptp_fun_Y_2(A, X), A)) | member(X, tptp_fun_Y_2(A, X)))))))) <=> ![X: $i, A: $i] : (~((~((~member(X, product(A))) | ![Y: $i] : ((~member(Y, A)) | member(X, Y)))) | (~(member(X, product(A)) | (~((~member(tptp_fun_Y_2(A, X), A)) | member(X, tptp_fun_Y_2(A, X))))))))),
% 1.01/1.17 inference(quant_intro,[status(thm)],[251])).
% 1.01/1.17 tff(253,plain,
% 1.01/1.17 (![X: $i, A: $i] : (~((~((~member(X, product(A))) | ![Y: $i] : ((~member(Y, A)) | member(X, Y)))) | (~(member(X, product(A)) | (~((~member(tptp_fun_Y_2(A, X), A)) | member(X, tptp_fun_Y_2(A, X)))))))) <=> ![X: $i, A: $i] : (~((~((~member(X, product(A))) | ![Y: $i] : ((~member(Y, A)) | member(X, Y)))) | (~(member(X, product(A)) | (~((~member(tptp_fun_Y_2(A, X), A)) | member(X, tptp_fun_Y_2(A, X))))))))),
% 1.01/1.17 inference(transitivity,[status(thm)],[252, 250])).
% 1.01/1.17 tff(254,plain,
% 1.01/1.17 (^[X: $i, A: $i] : trans(monotonicity(rewrite(((~member(X, product(A))) | ![Y: $i] : ((~member(Y, A)) | member(X, Y))) <=> ((~member(X, product(A))) | ![Y: $i] : ((~member(Y, A)) | member(X, Y)))), rewrite((member(X, product(A)) | (~((~member(tptp_fun_Y_2(A, X), A)) | member(X, tptp_fun_Y_2(A, X))))) <=> (member(X, product(A)) | (~((~member(tptp_fun_Y_2(A, X), A)) | member(X, tptp_fun_Y_2(A, X)))))), ((((~member(X, product(A))) | ![Y: $i] : ((~member(Y, A)) | member(X, Y))) & (member(X, product(A)) | (~((~member(tptp_fun_Y_2(A, X), A)) | member(X, tptp_fun_Y_2(A, X)))))) <=> (((~member(X, product(A))) | ![Y: $i] : ((~member(Y, A)) | member(X, Y))) & (member(X, product(A)) | (~((~member(tptp_fun_Y_2(A, X), A)) | member(X, tptp_fun_Y_2(A, X)))))))), rewrite((((~member(X, product(A))) | ![Y: $i] : ((~member(Y, A)) | member(X, Y))) & (member(X, product(A)) | (~((~member(tptp_fun_Y_2(A, X), A)) | member(X, tptp_fun_Y_2(A, X)))))) <=> (~((~((~member(X, product(A))) | ![Y: $i] : ((~member(Y, A)) | member(X, Y)))) | (~(member(X, product(A)) | (~((~member(tptp_fun_Y_2(A, X), A)) | member(X, tptp_fun_Y_2(A, X))))))))), ((((~member(X, product(A))) | ![Y: $i] : ((~member(Y, A)) | member(X, Y))) & (member(X, product(A)) | (~((~member(tptp_fun_Y_2(A, X), A)) | member(X, tptp_fun_Y_2(A, X)))))) <=> (~((~((~member(X, product(A))) | ![Y: $i] : ((~member(Y, A)) | member(X, Y)))) | (~(member(X, product(A)) | (~((~member(tptp_fun_Y_2(A, X), A)) | member(X, tptp_fun_Y_2(A, X))))))))))),
% 1.01/1.17 inference(bind,[status(th)],[])).
% 1.01/1.17 tff(255,plain,
% 1.01/1.17 (![X: $i, A: $i] : (((~member(X, product(A))) | ![Y: $i] : ((~member(Y, A)) | member(X, Y))) & (member(X, product(A)) | (~((~member(tptp_fun_Y_2(A, X), A)) | member(X, tptp_fun_Y_2(A, X)))))) <=> ![X: $i, A: $i] : (~((~((~member(X, product(A))) | ![Y: $i] : ((~member(Y, A)) | member(X, Y)))) | (~(member(X, product(A)) | (~((~member(tptp_fun_Y_2(A, X), A)) | member(X, tptp_fun_Y_2(A, X))))))))),
% 1.01/1.17 inference(quant_intro,[status(thm)],[254])).
% 1.01/1.17 tff(256,plain,
% 1.01/1.17 (![X: $i, A: $i] : (member(X, product(A)) <=> ![Y: $i] : ((~member(Y, A)) | member(X, Y))) <=> ![X: $i, A: $i] : (member(X, product(A)) <=> ![Y: $i] : ((~member(Y, A)) | member(X, Y)))),
% 1.01/1.17 inference(rewrite,[status(thm)],[])).
% 1.01/1.17 tff(257,plain,
% 1.01/1.17 (^[X: $i, A: $i] : rewrite((member(X, product(A)) <=> ![Y: $i] : (member(Y, A) => member(X, Y))) <=> (member(X, product(A)) <=> ![Y: $i] : ((~member(Y, A)) | member(X, Y))))),
% 1.01/1.17 inference(bind,[status(th)],[])).
% 1.01/1.17 tff(258,plain,
% 1.01/1.17 (![X: $i, A: $i] : (member(X, product(A)) <=> ![Y: $i] : (member(Y, A) => member(X, Y))) <=> ![X: $i, A: $i] : (member(X, product(A)) <=> ![Y: $i] : ((~member(Y, A)) | member(X, Y)))),
% 1.01/1.17 inference(quant_intro,[status(thm)],[257])).
% 1.01/1.17 tff(259,axiom,(![X: $i, A: $i] : (member(X, product(A)) <=> ![Y: $i] : (member(Y, A) => member(X, Y)))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax','product')).
% 1.01/1.17 tff(260,plain,
% 1.01/1.17 (![X: $i, A: $i] : (member(X, product(A)) <=> ![Y: $i] : ((~member(Y, A)) | member(X, Y)))),
% 1.01/1.17 inference(modus_ponens,[status(thm)],[259, 258])).
% 1.01/1.17 tff(261,plain,
% 1.01/1.17 (![X: $i, A: $i] : (member(X, product(A)) <=> ![Y: $i] : ((~member(Y, A)) | member(X, Y)))),
% 1.01/1.17 inference(modus_ponens,[status(thm)],[260, 256])).
% 1.01/1.17 tff(262,plain,(
% 1.01/1.17 ![X: $i, A: $i] : (((~member(X, product(A))) | ![Y: $i] : ((~member(Y, A)) | member(X, Y))) & (member(X, product(A)) | (~((~member(tptp_fun_Y_2(A, X), A)) | member(X, tptp_fun_Y_2(A, X))))))),
% 1.01/1.17 inference(skolemize,[status(sab)],[261])).
% 1.01/1.17 tff(263,plain,
% 1.01/1.17 (![X: $i, A: $i] : (~((~((~member(X, product(A))) | ![Y: $i] : ((~member(Y, A)) | member(X, Y)))) | (~(member(X, product(A)) | (~((~member(tptp_fun_Y_2(A, X), A)) | member(X, tptp_fun_Y_2(A, X))))))))),
% 1.01/1.17 inference(modus_ponens,[status(thm)],[262, 255])).
% 1.01/1.17 tff(264,plain,
% 1.01/1.17 (![X: $i, A: $i] : (~((~((~member(X, product(A))) | ![Y: $i] : ((~member(Y, A)) | member(X, Y)))) | (~(member(X, product(A)) | (~((~member(tptp_fun_Y_2(A, X), A)) | member(X, tptp_fun_Y_2(A, X))))))))),
% 1.01/1.17 inference(modus_ponens,[status(thm)],[263, 253])).
% 1.01/1.17 tff(265,plain,
% 1.01/1.17 (((~![X: $i, A: $i] : (~((~((~member(X, product(A))) | ![Y: $i] : ((~member(Y, A)) | member(X, Y)))) | (~(member(X, product(A)) | (~((~member(tptp_fun_Y_2(A, X), A)) | member(X, tptp_fun_Y_2(A, X))))))))) | (~((~((~member(E!3, product(intersection(A!6, difference(E!3, B!5))))) | ![Y: $i] : ((~member(Y, intersection(A!6, difference(E!3, B!5)))) | member(E!3, Y)))) | (~((~((~member(tptp_fun_Y_2(intersection(A!6, difference(E!3, B!5)), E!3), intersection(A!6, difference(E!3, B!5)))) | member(E!3, tptp_fun_Y_2(intersection(A!6, difference(E!3, B!5)), E!3)))) | member(E!3, product(intersection(A!6, difference(E!3, B!5))))))))) <=> ((~![X: $i, A: $i] : (~((~((~member(X, product(A))) | ![Y: $i] : ((~member(Y, A)) | member(X, Y)))) | (~(member(X, product(A)) | (~((~member(tptp_fun_Y_2(A, X), A)) | member(X, tptp_fun_Y_2(A, X))))))))) | (~((~((~member(E!3, product(intersection(A!6, difference(E!3, B!5))))) | ![Y: $i] : ((~member(Y, intersection(A!6, difference(E!3, B!5)))) | member(E!3, Y)))) | (~((~((~member(tptp_fun_Y_2(intersection(A!6, difference(E!3, B!5)), E!3), intersection(A!6, difference(E!3, B!5)))) | member(E!3, tptp_fun_Y_2(intersection(A!6, difference(E!3, B!5)), E!3)))) | member(E!3, product(intersection(A!6, difference(E!3, B!5)))))))))),
% 1.01/1.18 inference(rewrite,[status(thm)],[])).
% 1.01/1.18 tff(266,plain,
% 1.01/1.18 ((~((~((~member(E!3, product(intersection(A!6, difference(E!3, B!5))))) | ![Y: $i] : ((~member(Y, intersection(A!6, difference(E!3, B!5)))) | member(E!3, Y)))) | (~(member(E!3, product(intersection(A!6, difference(E!3, B!5)))) | (~((~member(tptp_fun_Y_2(intersection(A!6, difference(E!3, B!5)), E!3), intersection(A!6, difference(E!3, B!5)))) | member(E!3, tptp_fun_Y_2(intersection(A!6, difference(E!3, B!5)), E!3)))))))) <=> (~((~((~member(E!3, product(intersection(A!6, difference(E!3, B!5))))) | ![Y: $i] : ((~member(Y, intersection(A!6, difference(E!3, B!5)))) | member(E!3, Y)))) | (~((~((~member(tptp_fun_Y_2(intersection(A!6, difference(E!3, B!5)), E!3), intersection(A!6, difference(E!3, B!5)))) | member(E!3, tptp_fun_Y_2(intersection(A!6, difference(E!3, B!5)), E!3)))) | member(E!3, product(intersection(A!6, difference(E!3, B!5))))))))),
% 1.01/1.18 inference(rewrite,[status(thm)],[])).
% 1.01/1.18 tff(267,plain,
% 1.01/1.18 (((~![X: $i, A: $i] : (~((~((~member(X, product(A))) | ![Y: $i] : ((~member(Y, A)) | member(X, Y)))) | (~(member(X, product(A)) | (~((~member(tptp_fun_Y_2(A, X), A)) | member(X, tptp_fun_Y_2(A, X))))))))) | (~((~((~member(E!3, product(intersection(A!6, difference(E!3, B!5))))) | ![Y: $i] : ((~member(Y, intersection(A!6, difference(E!3, B!5)))) | member(E!3, Y)))) | (~(member(E!3, product(intersection(A!6, difference(E!3, B!5)))) | (~((~member(tptp_fun_Y_2(intersection(A!6, difference(E!3, B!5)), E!3), intersection(A!6, difference(E!3, B!5)))) | member(E!3, tptp_fun_Y_2(intersection(A!6, difference(E!3, B!5)), E!3))))))))) <=> ((~![X: $i, A: $i] : (~((~((~member(X, product(A))) | ![Y: $i] : ((~member(Y, A)) | member(X, Y)))) | (~(member(X, product(A)) | (~((~member(tptp_fun_Y_2(A, X), A)) | member(X, tptp_fun_Y_2(A, X))))))))) | (~((~((~member(E!3, product(intersection(A!6, difference(E!3, B!5))))) | ![Y: $i] : ((~member(Y, intersection(A!6, difference(E!3, B!5)))) | member(E!3, Y)))) | (~((~((~member(tptp_fun_Y_2(intersection(A!6, difference(E!3, B!5)), E!3), intersection(A!6, difference(E!3, B!5)))) | member(E!3, tptp_fun_Y_2(intersection(A!6, difference(E!3, B!5)), E!3)))) | member(E!3, product(intersection(A!6, difference(E!3, B!5)))))))))),
% 1.01/1.18 inference(monotonicity,[status(thm)],[266])).
% 1.01/1.18 tff(268,plain,
% 1.01/1.18 (((~![X: $i, A: $i] : (~((~((~member(X, product(A))) | ![Y: $i] : ((~member(Y, A)) | member(X, Y)))) | (~(member(X, product(A)) | (~((~member(tptp_fun_Y_2(A, X), A)) | member(X, tptp_fun_Y_2(A, X))))))))) | (~((~((~member(E!3, product(intersection(A!6, difference(E!3, B!5))))) | ![Y: $i] : ((~member(Y, intersection(A!6, difference(E!3, B!5)))) | member(E!3, Y)))) | (~(member(E!3, product(intersection(A!6, difference(E!3, B!5)))) | (~((~member(tptp_fun_Y_2(intersection(A!6, difference(E!3, B!5)), E!3), intersection(A!6, difference(E!3, B!5)))) | member(E!3, tptp_fun_Y_2(intersection(A!6, difference(E!3, B!5)), E!3))))))))) <=> ((~![X: $i, A: $i] : (~((~((~member(X, product(A))) | ![Y: $i] : ((~member(Y, A)) | member(X, Y)))) | (~(member(X, product(A)) | (~((~member(tptp_fun_Y_2(A, X), A)) | member(X, tptp_fun_Y_2(A, X))))))))) | (~((~((~member(E!3, product(intersection(A!6, difference(E!3, B!5))))) | ![Y: $i] : ((~member(Y, intersection(A!6, difference(E!3, B!5)))) | member(E!3, Y)))) | (~((~((~member(tptp_fun_Y_2(intersection(A!6, difference(E!3, B!5)), E!3), intersection(A!6, difference(E!3, B!5)))) | member(E!3, tptp_fun_Y_2(intersection(A!6, difference(E!3, B!5)), E!3)))) | member(E!3, product(intersection(A!6, difference(E!3, B!5)))))))))),
% 1.01/1.18 inference(transitivity,[status(thm)],[267, 265])).
% 1.01/1.18 tff(269,plain,
% 1.01/1.18 ((~![X: $i, A: $i] : (~((~((~member(X, product(A))) | ![Y: $i] : ((~member(Y, A)) | member(X, Y)))) | (~(member(X, product(A)) | (~((~member(tptp_fun_Y_2(A, X), A)) | member(X, tptp_fun_Y_2(A, X))))))))) | (~((~((~member(E!3, product(intersection(A!6, difference(E!3, B!5))))) | ![Y: $i] : ((~member(Y, intersection(A!6, difference(E!3, B!5)))) | member(E!3, Y)))) | (~(member(E!3, product(intersection(A!6, difference(E!3, B!5)))) | (~((~member(tptp_fun_Y_2(intersection(A!6, difference(E!3, B!5)), E!3), intersection(A!6, difference(E!3, B!5)))) | member(E!3, tptp_fun_Y_2(intersection(A!6, difference(E!3, B!5)), E!3))))))))),
% 1.01/1.18 inference(quant_inst,[status(thm)],[])).
% 1.01/1.18 tff(270,plain,
% 1.01/1.18 ((~![X: $i, A: $i] : (~((~((~member(X, product(A))) | ![Y: $i] : ((~member(Y, A)) | member(X, Y)))) | (~(member(X, product(A)) | (~((~member(tptp_fun_Y_2(A, X), A)) | member(X, tptp_fun_Y_2(A, X))))))))) | (~((~((~member(E!3, product(intersection(A!6, difference(E!3, B!5))))) | ![Y: $i] : ((~member(Y, intersection(A!6, difference(E!3, B!5)))) | member(E!3, Y)))) | (~((~((~member(tptp_fun_Y_2(intersection(A!6, difference(E!3, B!5)), E!3), intersection(A!6, difference(E!3, B!5)))) | member(E!3, tptp_fun_Y_2(intersection(A!6, difference(E!3, B!5)), E!3)))) | member(E!3, product(intersection(A!6, difference(E!3, B!5))))))))),
% 1.01/1.18 inference(modus_ponens,[status(thm)],[269, 268])).
% 1.01/1.18 tff(271,plain,
% 1.01/1.18 (~((~((~member(E!3, product(intersection(A!6, difference(E!3, B!5))))) | ![Y: $i] : ((~member(Y, intersection(A!6, difference(E!3, B!5)))) | member(E!3, Y)))) | (~((~((~member(tptp_fun_Y_2(intersection(A!6, difference(E!3, B!5)), E!3), intersection(A!6, difference(E!3, B!5)))) | member(E!3, tptp_fun_Y_2(intersection(A!6, difference(E!3, B!5)), E!3)))) | member(E!3, product(intersection(A!6, difference(E!3, B!5)))))))),
% 1.01/1.18 inference(unit_resolution,[status(thm)],[270, 264])).
% 1.01/1.18 tff(272,plain,
% 1.01/1.18 (((~((~member(E!3, product(intersection(A!6, difference(E!3, B!5))))) | ![Y: $i] : ((~member(Y, intersection(A!6, difference(E!3, B!5)))) | member(E!3, Y)))) | (~((~((~member(tptp_fun_Y_2(intersection(A!6, difference(E!3, B!5)), E!3), intersection(A!6, difference(E!3, B!5)))) | member(E!3, tptp_fun_Y_2(intersection(A!6, difference(E!3, B!5)), E!3)))) | member(E!3, product(intersection(A!6, difference(E!3, B!5))))))) | ((~((~member(tptp_fun_Y_2(intersection(A!6, difference(E!3, B!5)), E!3), intersection(A!6, difference(E!3, B!5)))) | member(E!3, tptp_fun_Y_2(intersection(A!6, difference(E!3, B!5)), E!3)))) | member(E!3, product(intersection(A!6, difference(E!3, B!5)))))),
% 1.01/1.18 inference(tautology,[status(thm)],[])).
% 1.01/1.18 tff(273,plain,
% 1.01/1.18 ((~((~member(tptp_fun_Y_2(intersection(A!6, difference(E!3, B!5)), E!3), intersection(A!6, difference(E!3, B!5)))) | member(E!3, tptp_fun_Y_2(intersection(A!6, difference(E!3, B!5)), E!3)))) | member(E!3, product(intersection(A!6, difference(E!3, B!5))))),
% 1.01/1.18 inference(unit_resolution,[status(thm)],[272, 271])).
% 1.01/1.18 tff(274,plain,
% 1.01/1.18 ((~((~((~member(tptp_fun_Y_2(intersection(A!6, difference(E!3, B!5)), E!3), intersection(A!6, difference(E!3, B!5)))) | member(E!3, tptp_fun_Y_2(intersection(A!6, difference(E!3, B!5)), E!3)))) | member(E!3, product(intersection(A!6, difference(E!3, B!5)))))) | (~((~member(tptp_fun_Y_2(intersection(A!6, difference(E!3, B!5)), E!3), intersection(A!6, difference(E!3, B!5)))) | member(E!3, tptp_fun_Y_2(intersection(A!6, difference(E!3, B!5)), E!3)))) | member(E!3, product(intersection(A!6, difference(E!3, B!5))))),
% 1.01/1.18 inference(tautology,[status(thm)],[])).
% 1.01/1.18 tff(275,plain,
% 1.01/1.18 ((~((~member(tptp_fun_Y_2(intersection(A!6, difference(E!3, B!5)), E!3), intersection(A!6, difference(E!3, B!5)))) | member(E!3, tptp_fun_Y_2(intersection(A!6, difference(E!3, B!5)), E!3)))) | member(E!3, product(intersection(A!6, difference(E!3, B!5))))),
% 1.01/1.18 inference(unit_resolution,[status(thm)],[274, 273])).
% 1.01/1.18 tff(276,plain,
% 1.01/1.18 (member(E!3, product(intersection(A!6, difference(E!3, B!5))))),
% 1.01/1.18 inference(unit_resolution,[status(thm)],[275, 248])).
% 1.01/1.18 tff(277,plain,
% 1.01/1.18 (((~((~member(E!3, product(intersection(A!6, difference(E!3, B!5))))) | ![Y: $i] : ((~member(Y, intersection(A!6, difference(E!3, B!5)))) | member(E!3, Y)))) | (~((~((~member(tptp_fun_Y_2(intersection(A!6, difference(E!3, B!5)), E!3), intersection(A!6, difference(E!3, B!5)))) | member(E!3, tptp_fun_Y_2(intersection(A!6, difference(E!3, B!5)), E!3)))) | member(E!3, product(intersection(A!6, difference(E!3, B!5))))))) | ((~member(E!3, product(intersection(A!6, difference(E!3, B!5))))) | ![Y: $i] : ((~member(Y, intersection(A!6, difference(E!3, B!5)))) | member(E!3, Y)))),
% 1.01/1.18 inference(tautology,[status(thm)],[])).
% 1.01/1.18 tff(278,plain,
% 1.01/1.18 ((~member(E!3, product(intersection(A!6, difference(E!3, B!5))))) | ![Y: $i] : ((~member(Y, intersection(A!6, difference(E!3, B!5)))) | member(E!3, Y))),
% 1.01/1.18 inference(unit_resolution,[status(thm)],[277, 271])).
% 1.01/1.18 tff(279,plain,
% 1.01/1.18 ((~((~member(E!3, product(intersection(A!6, difference(E!3, B!5))))) | ![Y: $i] : ((~member(Y, intersection(A!6, difference(E!3, B!5)))) | member(E!3, Y)))) | (~member(E!3, product(intersection(A!6, difference(E!3, B!5))))) | ![Y: $i] : ((~member(Y, intersection(A!6, difference(E!3, B!5)))) | member(E!3, Y))),
% 1.01/1.18 inference(tautology,[status(thm)],[])).
% 1.01/1.18 tff(280,plain,
% 1.01/1.18 ((~member(E!3, product(intersection(A!6, difference(E!3, B!5))))) | ![Y: $i] : ((~member(Y, intersection(A!6, difference(E!3, B!5)))) | member(E!3, Y))),
% 1.01/1.18 inference(unit_resolution,[status(thm)],[279, 278])).
% 1.01/1.18 tff(281,plain,
% 1.01/1.18 (![Y: $i] : ((~member(Y, intersection(A!6, difference(E!3, B!5)))) | member(E!3, Y))),
% 1.01/1.18 inference(unit_resolution,[status(thm)],[280, 276])).
% 1.01/1.18 tff(282,plain,
% 1.01/1.18 (((~![Y: $i] : ((~member(Y, intersection(A!6, difference(E!3, B!5)))) | member(E!3, Y))) | ((~member(tptp_fun_X_0(B!5, A!6), intersection(A!6, difference(E!3, B!5)))) | member(E!3, tptp_fun_X_0(B!5, A!6)))) <=> ((~![Y: $i] : ((~member(Y, intersection(A!6, difference(E!3, B!5)))) | member(E!3, Y))) | (~member(tptp_fun_X_0(B!5, A!6), intersection(A!6, difference(E!3, B!5)))) | member(E!3, tptp_fun_X_0(B!5, A!6)))),
% 1.01/1.18 inference(rewrite,[status(thm)],[])).
% 1.01/1.18 tff(283,plain,
% 1.01/1.18 ((~![Y: $i] : ((~member(Y, intersection(A!6, difference(E!3, B!5)))) | member(E!3, Y))) | ((~member(tptp_fun_X_0(B!5, A!6), intersection(A!6, difference(E!3, B!5)))) | member(E!3, tptp_fun_X_0(B!5, A!6)))),
% 1.01/1.18 inference(quant_inst,[status(thm)],[])).
% 1.01/1.18 tff(284,plain,
% 1.01/1.18 ((~![Y: $i] : ((~member(Y, intersection(A!6, difference(E!3, B!5)))) | member(E!3, Y))) | (~member(tptp_fun_X_0(B!5, A!6), intersection(A!6, difference(E!3, B!5)))) | member(E!3, tptp_fun_X_0(B!5, A!6))),
% 1.01/1.18 inference(modus_ponens,[status(thm)],[283, 282])).
% 1.01/1.18 tff(285,plain,
% 1.01/1.18 ($false),
% 1.01/1.18 inference(unit_resolution,[status(thm)],[284, 281, 213, 156])).
% 1.01/1.18 tff(286,plain,(~member(tptp_fun_X_0(B!5, A!6), intersection(C!4, difference(E!3, C!4)))), inference(lemma,lemma(discharge,[]))).
% 1.01/1.18 tff(287,plain,
% 1.01/1.18 (((~![X: $i] : ((~member(X, intersection(A!6, difference(E!3, B!5)))) | member(X, intersection(C!4, difference(E!3, C!4))))) | ((~member(tptp_fun_X_0(B!5, A!6), intersection(A!6, difference(E!3, B!5)))) | member(tptp_fun_X_0(B!5, A!6), intersection(C!4, difference(E!3, C!4))))) <=> ((~![X: $i] : ((~member(X, intersection(A!6, difference(E!3, B!5)))) | member(X, intersection(C!4, difference(E!3, C!4))))) | (~member(tptp_fun_X_0(B!5, A!6), intersection(A!6, difference(E!3, B!5)))) | member(tptp_fun_X_0(B!5, A!6), intersection(C!4, difference(E!3, C!4))))),
% 1.01/1.18 inference(rewrite,[status(thm)],[])).
% 1.01/1.18 tff(288,plain,
% 1.01/1.18 ((~![X: $i] : ((~member(X, intersection(A!6, difference(E!3, B!5)))) | member(X, intersection(C!4, difference(E!3, C!4))))) | ((~member(tptp_fun_X_0(B!5, A!6), intersection(A!6, difference(E!3, B!5)))) | member(tptp_fun_X_0(B!5, A!6), intersection(C!4, difference(E!3, C!4))))),
% 1.01/1.18 inference(quant_inst,[status(thm)],[])).
% 1.01/1.18 tff(289,plain,
% 1.01/1.18 ((~![X: $i] : ((~member(X, intersection(A!6, difference(E!3, B!5)))) | member(X, intersection(C!4, difference(E!3, C!4))))) | (~member(tptp_fun_X_0(B!5, A!6), intersection(A!6, difference(E!3, B!5)))) | member(tptp_fun_X_0(B!5, A!6), intersection(C!4, difference(E!3, C!4)))),
% 1.01/1.18 inference(modus_ponens,[status(thm)],[288, 287])).
% 1.01/1.18 tff(290,plain,
% 1.01/1.18 (~member(tptp_fun_X_0(B!5, A!6), intersection(A!6, difference(E!3, B!5)))),
% 1.01/1.18 inference(unit_resolution,[status(thm)],[289, 241, 286])).
% 1.01/1.18 tff(291,plain,
% 1.01/1.18 ((((~member(tptp_fun_X_0(B!5, A!6), A!6)) | (~member(tptp_fun_X_0(B!5, A!6), difference(E!3, B!5)))) <=> member(tptp_fun_X_0(B!5, A!6), intersection(A!6, difference(E!3, B!5)))) | ((~member(tptp_fun_X_0(B!5, A!6), A!6)) | (~member(tptp_fun_X_0(B!5, A!6), difference(E!3, B!5)))) | member(tptp_fun_X_0(B!5, A!6), intersection(A!6, difference(E!3, B!5)))),
% 1.01/1.18 inference(tautology,[status(thm)],[])).
% 1.01/1.18 tff(292,plain,
% 1.01/1.18 ((((~member(tptp_fun_X_0(B!5, A!6), A!6)) | (~member(tptp_fun_X_0(B!5, A!6), difference(E!3, B!5)))) <=> member(tptp_fun_X_0(B!5, A!6), intersection(A!6, difference(E!3, B!5)))) | ((~member(tptp_fun_X_0(B!5, A!6), A!6)) | (~member(tptp_fun_X_0(B!5, A!6), difference(E!3, B!5))))),
% 1.01/1.18 inference(unit_resolution,[status(thm)],[291, 290])).
% 1.01/1.18 tff(293,plain,
% 1.01/1.18 ((~member(tptp_fun_X_0(B!5, A!6), A!6)) | (~member(tptp_fun_X_0(B!5, A!6), difference(E!3, B!5)))),
% 1.01/1.18 inference(unit_resolution,[status(thm)],[292, 115])).
% 1.01/1.18 tff(294,plain,
% 1.01/1.18 ((~((~member(tptp_fun_X_0(B!5, A!6), A!6)) | (~member(tptp_fun_X_0(B!5, A!6), difference(E!3, B!5))))) | (~member(tptp_fun_X_0(B!5, A!6), A!6)) | (~member(tptp_fun_X_0(B!5, A!6), difference(E!3, B!5)))),
% 1.01/1.18 inference(tautology,[status(thm)],[])).
% 1.01/1.18 tff(295,plain,
% 1.01/1.18 ((~((~member(tptp_fun_X_0(B!5, A!6), A!6)) | (~member(tptp_fun_X_0(B!5, A!6), difference(E!3, B!5))))) | (~member(tptp_fun_X_0(B!5, A!6), difference(E!3, B!5)))),
% 1.01/1.18 inference(unit_resolution,[status(thm)],[294, 96])).
% 1.01/1.18 tff(296,plain,
% 1.01/1.18 (~member(tptp_fun_X_0(B!5, A!6), difference(E!3, B!5))),
% 1.01/1.18 inference(unit_resolution,[status(thm)],[295, 293])).
% 1.01/1.18 tff(297,plain,
% 1.01/1.18 ((((~member(tptp_fun_X_0(B!5, A!6), E!3)) | member(tptp_fun_X_0(B!5, A!6), B!5)) <=> member(tptp_fun_X_0(B!5, A!6), difference(E!3, B!5))) | ((~member(tptp_fun_X_0(B!5, A!6), E!3)) | member(tptp_fun_X_0(B!5, A!6), B!5)) | member(tptp_fun_X_0(B!5, A!6), difference(E!3, B!5))),
% 1.01/1.18 inference(tautology,[status(thm)],[])).
% 1.01/1.18 tff(298,plain,
% 1.01/1.18 (((~member(tptp_fun_X_0(B!5, A!6), E!3)) | member(tptp_fun_X_0(B!5, A!6), B!5)) <=> member(tptp_fun_X_0(B!5, A!6), difference(E!3, B!5))),
% 1.01/1.18 inference(unit_resolution,[status(thm)],[297, 296, 113])).
% 1.01/1.18 tff(299,plain,
% 1.01/1.18 ((~![B: $i, A: $i, E: $i] : (~(((~member(B, E)) | member(B, A)) <=> member(B, difference(E, A))))) | (~(((~member(tptp_fun_X_0(B!5, A!6), E!3)) | member(tptp_fun_X_0(B!5, A!6), B!5)) <=> member(tptp_fun_X_0(B!5, A!6), difference(E!3, B!5))))),
% 1.01/1.18 inference(quant_inst,[status(thm)],[])).
% 1.01/1.18 tff(300,plain,
% 1.01/1.18 ($false),
% 1.01/1.18 inference(unit_resolution,[status(thm)],[299, 76, 298])).
% 1.01/1.18 % SZS output end Proof
% 1.01/1.18 % E exiting
%------------------------------------------------------------------------------