%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET702+4 : TPTP v9.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n011.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 0.20s 0.38s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SET702+4 : TPTP v9.0.0. Released v2.2.0.
% 0.04/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n011.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 05:38:41 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.20/0.38 % SZS status Theorem
% 0.20/0.38 % SZS output start Proof
% 0.20/0.38 tff(member_type, type, (
% 0.20/0.38 member: ( $i * $i ) > $o)).
% 0.20/0.38 tff(tptp_fun_B_3_type, type, (
% 0.20/0.38 tptp_fun_B_3: $i)).
% 0.20/0.38 tff(tptp_fun_Y_2_type, type, (
% 0.20/0.38 tptp_fun_Y_2: ( $i * $i ) > $i)).
% 0.20/0.38 tff(tptp_fun_X_0_type, type, (
% 0.20/0.38 tptp_fun_X_0: ( $i * $i ) > $i)).
% 0.20/0.38 tff(intersection_type, type, (
% 0.20/0.38 intersection: ( $i * $i ) > $i)).
% 0.20/0.38 tff(product_type, type, (
% 0.20/0.38 product: $i > $i)).
% 0.20/0.38 tff(tptp_fun_A_4_type, type, (
% 0.20/0.38 tptp_fun_A_4: $i)).
% 0.20/0.38 tff(subset_type, type, (
% 0.20/0.38 subset: ( $i * $i ) > $o)).
% 0.20/0.38 tff(1,plain,
% 0.20/0.38 (^[X: $i, A: $i, B: $i] : refl((~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B)))) <=> (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B)))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(2,plain,
% 0.20/0.38 (![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B)))) <=> ![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.38 tff(3,plain,
% 0.20/0.38 (^[X: $i, A: $i, B: $i] : trans(trans(monotonicity(rewrite((member(X, A) & member(X, B)) <=> (~((~member(X, A)) | (~member(X, B))))), ((member(X, intersection(A, B)) <=> (member(X, A) & member(X, B))) <=> (member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B))))))), rewrite((member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B))))) <=> (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))), ((member(X, intersection(A, B)) <=> (member(X, A) & member(X, B))) <=> (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B)))))), rewrite((~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B)))) <=> (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))), ((member(X, intersection(A, B)) <=> (member(X, A) & member(X, B))) <=> (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(4,plain,
% 0.20/0.38 (![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (member(X, A) & member(X, B))) <=> ![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[3])).
% 0.20/0.38 tff(5,plain,
% 0.20/0.38 (![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (member(X, A) & member(X, B))) <=> ![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (member(X, A) & member(X, B)))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(6,axiom,(![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (member(X, A) & member(X, B)))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax','intersection')).
% 0.20/0.38 tff(7,plain,
% 0.20/0.38 (![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (member(X, A) & member(X, B)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.20/0.38 tff(8,plain,(
% 0.20/0.38 ![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (member(X, A) & member(X, B)))),
% 0.20/0.38 inference(skolemize,[status(sab)],[7])).
% 0.20/0.38 tff(9,plain,
% 0.20/0.38 (![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.20/0.38 tff(10,plain,
% 0.20/0.38 (![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.20/0.38 tff(11,plain,
% 0.20/0.38 ((~![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))) | (~(((~member(tptp_fun_Y_2(intersection(A!4, B!3), tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3)))), A!4)) | (~member(tptp_fun_Y_2(intersection(A!4, B!3), tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3)))), B!3))) <=> member(tptp_fun_Y_2(intersection(A!4, B!3), tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3)))), intersection(A!4, B!3))))),
% 0.20/0.38 inference(quant_inst,[status(thm)],[])).
% 0.20/0.38 tff(12,plain,
% 0.20/0.38 (~(((~member(tptp_fun_Y_2(intersection(A!4, B!3), tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3)))), A!4)) | (~member(tptp_fun_Y_2(intersection(A!4, B!3), tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3)))), B!3))) <=> member(tptp_fun_Y_2(intersection(A!4, B!3), tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3)))), intersection(A!4, B!3)))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.20/0.38 tff(13,plain,
% 0.20/0.38 (^[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)))))))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(14,plain,
% 0.20/0.38 (![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))))))))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[13])).
% 0.20/0.38 tff(15,plain,
% 0.20/0.38 (^[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)))))))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(16,plain,
% 0.20/0.38 (![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))))))))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[15])).
% 0.20/0.38 tff(17,plain,
% 0.20/0.38 (![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))))))))),
% 0.20/0.38 inference(transitivity,[status(thm)],[16, 14])).
% 0.20/0.38 tff(18,plain,
% 0.20/0.38 (^[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))))))))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(19,plain,
% 0.20/0.38 (![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))))))))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[18])).
% 0.20/0.38 tff(20,plain,
% 0.20/0.38 (![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)))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(21,plain,
% 0.20/0.38 (^[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))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(22,plain,
% 0.20/0.38 (![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)))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[21])).
% 0.20/0.38 tff(23,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')).
% 0.20/0.38 tff(24,plain,
% 0.20/0.38 (![X: $i, A: $i] : (member(X, product(A)) <=> ![Y: $i] : ((~member(Y, A)) | member(X, Y)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.20/0.38 tff(25,plain,
% 0.20/0.38 (![X: $i, A: $i] : (member(X, product(A)) <=> ![Y: $i] : ((~member(Y, A)) | member(X, Y)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[24, 20])).
% 0.20/0.38 tff(26,plain,(
% 0.20/0.38 ![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))))))),
% 0.20/0.38 inference(skolemize,[status(sab)],[25])).
% 0.20/0.38 tff(27,plain,
% 0.20/0.38 (![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))))))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[26, 19])).
% 0.20/0.38 tff(28,plain,
% 0.20/0.38 (![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))))))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[27, 17])).
% 0.20/0.38 tff(29,plain,
% 0.20/0.38 ((~![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(tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3))), product(intersection(A!4, B!3)))) | ![Y: $i] : ((~member(Y, intersection(A!4, B!3))) | member(tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3))), Y)))) | (~(member(tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3))), product(intersection(A!4, B!3))) | (~((~member(tptp_fun_Y_2(intersection(A!4, B!3), tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3)))), intersection(A!4, B!3))) | member(tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3))), tptp_fun_Y_2(intersection(A!4, B!3), tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3)))))))))))),
% 0.20/0.38 inference(quant_inst,[status(thm)],[])).
% 0.20/0.38 tff(30,plain,
% 0.20/0.38 (~((~((~member(tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3))), product(intersection(A!4, B!3)))) | ![Y: $i] : ((~member(Y, intersection(A!4, B!3))) | member(tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3))), Y)))) | (~(member(tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3))), product(intersection(A!4, B!3))) | (~((~member(tptp_fun_Y_2(intersection(A!4, B!3), tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3)))), intersection(A!4, B!3))) | member(tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3))), tptp_fun_Y_2(intersection(A!4, B!3), tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3))))))))))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[29, 28])).
% 0.20/0.38 tff(31,plain,
% 0.20/0.38 (((~((~member(tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3))), product(intersection(A!4, B!3)))) | ![Y: $i] : ((~member(Y, intersection(A!4, B!3))) | member(tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3))), Y)))) | (~(member(tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3))), product(intersection(A!4, B!3))) | (~((~member(tptp_fun_Y_2(intersection(A!4, B!3), tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3)))), intersection(A!4, B!3))) | member(tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3))), tptp_fun_Y_2(intersection(A!4, B!3), tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3)))))))))) | (member(tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3))), product(intersection(A!4, B!3))) | (~((~member(tptp_fun_Y_2(intersection(A!4, B!3), tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3)))), intersection(A!4, B!3))) | member(tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3))), tptp_fun_Y_2(intersection(A!4, B!3), tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3))))))))),
% 0.20/0.38 inference(tautology,[status(thm)],[])).
% 0.20/0.38 tff(32,plain,
% 0.20/0.38 (member(tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3))), product(intersection(A!4, B!3))) | (~((~member(tptp_fun_Y_2(intersection(A!4, B!3), tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3)))), intersection(A!4, B!3))) | member(tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3))), tptp_fun_Y_2(intersection(A!4, B!3), tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3)))))))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[31, 30])).
% 0.20/0.38 tff(33,plain,
% 0.20/0.38 (^[A: $i, B: $i] : refl((~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(34,plain,
% 0.20/0.38 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[33])).
% 0.20/0.38 tff(35,plain,
% 0.20/0.38 (^[A: $i, B: $i] : rewrite((~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(36,plain,
% 0.20/0.38 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[35])).
% 0.20/0.39 tff(37,plain,
% 0.20/0.39 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.20/0.39 inference(transitivity,[status(thm)],[36, 34])).
% 0.20/0.39 tff(38,plain,
% 0.20/0.39 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) <=> ((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))), rewrite((subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))) <=> (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))), ((((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> (((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))), rewrite((((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))), ((((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(39,plain,
% 0.20/0.39 (![A: $i, B: $i] : (((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[38])).
% 0.20/0.39 tff(40,plain,
% 0.20/0.39 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(41,plain,
% 0.20/0.39 (^[A: $i, B: $i] : rewrite((subset(A, B) <=> ![X: $i] : (member(X, A) => member(X, B))) <=> (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(42,plain,
% 0.20/0.39 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : (member(X, A) => member(X, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[41])).
% 0.20/0.39 tff(43,axiom,(![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : (member(X, A) => member(X, B)))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax','subset')).
% 0.20/0.39 tff(44,plain,
% 0.20/0.39 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.20/0.39 tff(45,plain,
% 0.20/0.39 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[44, 40])).
% 0.20/0.39 tff(46,plain,(
% 0.20/0.39 ![A: $i, B: $i] : (((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))),
% 0.20/0.39 inference(skolemize,[status(sab)],[45])).
% 0.20/0.39 tff(47,plain,
% 0.20/0.39 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[46, 39])).
% 0.20/0.39 tff(48,plain,
% 0.20/0.39 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[47, 37])).
% 0.20/0.39 tff(49,plain,
% 0.20/0.39 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))) | (~((~((~subset(intersection(product(A!4), product(B!3)), product(intersection(A!4, B!3)))) | ![X: $i] : ((~member(X, intersection(product(A!4), product(B!3)))) | member(X, product(intersection(A!4, B!3)))))) | (~(subset(intersection(product(A!4), product(B!3)), product(intersection(A!4, B!3))) | (~((~member(tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3))), intersection(product(A!4), product(B!3)))) | member(tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3))), product(intersection(A!4, B!3)))))))))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(50,plain,
% 0.20/0.39 (~((~((~subset(intersection(product(A!4), product(B!3)), product(intersection(A!4, B!3)))) | ![X: $i] : ((~member(X, intersection(product(A!4), product(B!3)))) | member(X, product(intersection(A!4, B!3)))))) | (~(subset(intersection(product(A!4), product(B!3)), product(intersection(A!4, B!3))) | (~((~member(tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3))), intersection(product(A!4), product(B!3)))) | member(tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3))), product(intersection(A!4, B!3))))))))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[49, 48])).
% 0.20/0.39 tff(51,plain,
% 0.20/0.39 (((~((~subset(intersection(product(A!4), product(B!3)), product(intersection(A!4, B!3)))) | ![X: $i] : ((~member(X, intersection(product(A!4), product(B!3)))) | member(X, product(intersection(A!4, B!3)))))) | (~(subset(intersection(product(A!4), product(B!3)), product(intersection(A!4, B!3))) | (~((~member(tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3))), intersection(product(A!4), product(B!3)))) | member(tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3))), product(intersection(A!4, B!3)))))))) | (subset(intersection(product(A!4), product(B!3)), product(intersection(A!4, B!3))) | (~((~member(tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3))), intersection(product(A!4), product(B!3)))) | member(tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3))), product(intersection(A!4, B!3))))))),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(52,plain,
% 0.20/0.39 (subset(intersection(product(A!4), product(B!3)), product(intersection(A!4, B!3))) | (~((~member(tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3))), intersection(product(A!4), product(B!3)))) | member(tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3))), product(intersection(A!4, B!3)))))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[51, 50])).
% 0.20/0.39 tff(53,plain,
% 0.20/0.39 ((~![A: $i, B: $i] : subset(intersection(product(A), product(B)), product(intersection(A, B)))) <=> (~![A: $i, B: $i] : subset(intersection(product(A), product(B)), product(intersection(A, B))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(54,axiom,(~![A: $i, B: $i] : subset(intersection(product(A), product(B)), product(intersection(A, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thI36')).
% 0.20/0.39 tff(55,plain,
% 0.20/0.39 (~![A: $i, B: $i] : subset(intersection(product(A), product(B)), product(intersection(A, B)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.20/0.39 tff(56,plain,
% 0.20/0.39 (~![A: $i, B: $i] : subset(intersection(product(A), product(B)), product(intersection(A, B)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[55, 53])).
% 0.20/0.39 tff(57,plain,
% 0.20/0.39 (~![A: $i, B: $i] : subset(intersection(product(A), product(B)), product(intersection(A, B)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[56, 53])).
% 0.20/0.39 tff(58,plain,
% 0.20/0.39 (~![A: $i, B: $i] : subset(intersection(product(A), product(B)), product(intersection(A, B)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[57, 53])).
% 0.20/0.39 tff(59,plain,(
% 0.20/0.39 ~subset(intersection(product(A!4), product(B!3)), product(intersection(A!4, B!3)))),
% 0.20/0.39 inference(skolemize,[status(sab)],[58])).
% 0.20/0.39 tff(60,plain,
% 0.20/0.39 ((~(subset(intersection(product(A!4), product(B!3)), product(intersection(A!4, B!3))) | (~((~member(tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3))), intersection(product(A!4), product(B!3)))) | member(tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3))), product(intersection(A!4, B!3))))))) | subset(intersection(product(A!4), product(B!3)), product(intersection(A!4, B!3))) | (~((~member(tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3))), intersection(product(A!4), product(B!3)))) | member(tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3))), product(intersection(A!4, B!3)))))),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(61,plain,
% 0.20/0.39 ((~(subset(intersection(product(A!4), product(B!3)), product(intersection(A!4, B!3))) | (~((~member(tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3))), intersection(product(A!4), product(B!3)))) | member(tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3))), product(intersection(A!4, B!3))))))) | (~((~member(tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3))), intersection(product(A!4), product(B!3)))) | member(tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3))), product(intersection(A!4, B!3)))))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[60, 59])).
% 0.20/0.39 tff(62,plain,
% 0.20/0.39 (~((~member(tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3))), intersection(product(A!4), product(B!3)))) | member(tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3))), product(intersection(A!4, B!3))))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[61, 52])).
% 0.20/0.39 tff(63,plain,
% 0.20/0.39 (((~member(tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3))), intersection(product(A!4), product(B!3)))) | member(tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3))), product(intersection(A!4, B!3)))) | (~member(tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3))), product(intersection(A!4, B!3))))),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(64,plain,
% 0.20/0.39 (~member(tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3))), product(intersection(A!4, B!3)))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[63, 62])).
% 0.20/0.39 tff(65,plain,
% 0.20/0.39 ((~(member(tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3))), product(intersection(A!4, B!3))) | (~((~member(tptp_fun_Y_2(intersection(A!4, B!3), tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3)))), intersection(A!4, B!3))) | member(tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3))), tptp_fun_Y_2(intersection(A!4, B!3), tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3))))))))) | member(tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3))), product(intersection(A!4, B!3))) | (~((~member(tptp_fun_Y_2(intersection(A!4, B!3), tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3)))), intersection(A!4, B!3))) | member(tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3))), tptp_fun_Y_2(intersection(A!4, B!3), tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3)))))))),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(66,plain,
% 0.20/0.39 ((~(member(tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3))), product(intersection(A!4, B!3))) | (~((~member(tptp_fun_Y_2(intersection(A!4, B!3), tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3)))), intersection(A!4, B!3))) | member(tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3))), tptp_fun_Y_2(intersection(A!4, B!3), tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3))))))))) | (~((~member(tptp_fun_Y_2(intersection(A!4, B!3), tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3)))), intersection(A!4, B!3))) | member(tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3))), tptp_fun_Y_2(intersection(A!4, B!3), tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3)))))))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[65, 64])).
% 0.20/0.40 tff(67,plain,
% 0.20/0.40 (~((~member(tptp_fun_Y_2(intersection(A!4, B!3), tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3)))), intersection(A!4, B!3))) | member(tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3))), tptp_fun_Y_2(intersection(A!4, B!3), tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3))))))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[66, 32])).
% 0.20/0.40 tff(68,plain,
% 0.20/0.40 (((~member(tptp_fun_Y_2(intersection(A!4, B!3), tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3)))), intersection(A!4, B!3))) | member(tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3))), tptp_fun_Y_2(intersection(A!4, B!3), tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3)))))) | member(tptp_fun_Y_2(intersection(A!4, B!3), tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3)))), intersection(A!4, B!3))),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(69,plain,
% 0.20/0.40 (member(tptp_fun_Y_2(intersection(A!4, B!3), tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3)))), intersection(A!4, B!3))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[68, 67])).
% 0.20/0.40 tff(70,plain,
% 0.20/0.40 ((((~member(tptp_fun_Y_2(intersection(A!4, B!3), tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3)))), A!4)) | (~member(tptp_fun_Y_2(intersection(A!4, B!3), tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3)))), B!3))) <=> member(tptp_fun_Y_2(intersection(A!4, B!3), tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3)))), intersection(A!4, B!3))) | (~((~member(tptp_fun_Y_2(intersection(A!4, B!3), tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3)))), A!4)) | (~member(tptp_fun_Y_2(intersection(A!4, B!3), tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3)))), B!3)))) | (~member(tptp_fun_Y_2(intersection(A!4, B!3), tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3)))), intersection(A!4, B!3)))),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(71,plain,
% 0.20/0.40 ((((~member(tptp_fun_Y_2(intersection(A!4, B!3), tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3)))), A!4)) | (~member(tptp_fun_Y_2(intersection(A!4, B!3), tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3)))), B!3))) <=> member(tptp_fun_Y_2(intersection(A!4, B!3), tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3)))), intersection(A!4, B!3))) | (~((~member(tptp_fun_Y_2(intersection(A!4, B!3), tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3)))), A!4)) | (~member(tptp_fun_Y_2(intersection(A!4, B!3), tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3)))), B!3))))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[70, 69])).
% 0.20/0.40 tff(72,plain,
% 0.20/0.40 (~((~member(tptp_fun_Y_2(intersection(A!4, B!3), tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3)))), A!4)) | (~member(tptp_fun_Y_2(intersection(A!4, B!3), tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3)))), B!3)))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[71, 12])).
% 0.20/0.40 tff(73,plain,
% 0.20/0.40 (((~member(tptp_fun_Y_2(intersection(A!4, B!3), tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3)))), A!4)) | (~member(tptp_fun_Y_2(intersection(A!4, B!3), tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3)))), B!3))) | member(tptp_fun_Y_2(intersection(A!4, B!3), tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3)))), B!3)),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(74,plain,
% 0.20/0.40 (member(tptp_fun_Y_2(intersection(A!4, B!3), tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3)))), B!3)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[73, 72])).
% 0.20/0.40 tff(75,plain,
% 0.20/0.40 ((~![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(tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3))), product(B!3))) | ![Y: $i] : ((~member(Y, B!3)) | member(tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3))), Y)))) | (~(member(tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3))), product(B!3)) | (~((~member(tptp_fun_Y_2(B!3, tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3)))), B!3)) | member(tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3))), tptp_fun_Y_2(B!3, tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3)))))))))))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(76,plain,
% 0.20/0.40 (~((~((~member(tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3))), product(B!3))) | ![Y: $i] : ((~member(Y, B!3)) | member(tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3))), Y)))) | (~(member(tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3))), product(B!3)) | (~((~member(tptp_fun_Y_2(B!3, tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3)))), B!3)) | member(tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3))), tptp_fun_Y_2(B!3, tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3))))))))))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[75, 28])).
% 0.20/0.40 tff(77,plain,
% 0.20/0.40 (((~((~member(tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3))), product(B!3))) | ![Y: $i] : ((~member(Y, B!3)) | member(tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3))), Y)))) | (~(member(tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3))), product(B!3)) | (~((~member(tptp_fun_Y_2(B!3, tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3)))), B!3)) | member(tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3))), tptp_fun_Y_2(B!3, tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3)))))))))) | ((~member(tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3))), product(B!3))) | ![Y: $i] : ((~member(Y, B!3)) | member(tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3))), Y)))),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(78,plain,
% 0.20/0.40 ((~member(tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3))), product(B!3))) | ![Y: $i] : ((~member(Y, B!3)) | member(tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3))), Y))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[77, 76])).
% 0.20/0.40 tff(79,plain,
% 0.20/0.40 ((~![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))) | (~(((~member(tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3))), product(A!4))) | (~member(tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3))), product(B!3)))) <=> member(tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3))), intersection(product(A!4), product(B!3)))))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(80,plain,
% 0.20/0.40 (~(((~member(tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3))), product(A!4))) | (~member(tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3))), product(B!3)))) <=> member(tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3))), intersection(product(A!4), product(B!3))))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[79, 10])).
% 0.20/0.40 tff(81,plain,
% 0.20/0.40 (((~member(tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3))), intersection(product(A!4), product(B!3)))) | member(tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3))), product(intersection(A!4, B!3)))) | member(tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3))), intersection(product(A!4), product(B!3)))),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(82,plain,
% 0.20/0.40 (member(tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3))), intersection(product(A!4), product(B!3)))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[81, 62])).
% 0.20/0.40 tff(83,plain,
% 0.20/0.40 ((((~member(tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3))), product(A!4))) | (~member(tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3))), product(B!3)))) <=> member(tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3))), intersection(product(A!4), product(B!3)))) | (~((~member(tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3))), product(A!4))) | (~member(tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3))), product(B!3))))) | (~member(tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3))), intersection(product(A!4), product(B!3))))),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(84,plain,
% 0.20/0.40 ((((~member(tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3))), product(A!4))) | (~member(tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3))), product(B!3)))) <=> member(tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3))), intersection(product(A!4), product(B!3)))) | (~((~member(tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3))), product(A!4))) | (~member(tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3))), product(B!3)))))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[83, 82])).
% 0.20/0.40 tff(85,plain,
% 0.20/0.40 (~((~member(tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3))), product(A!4))) | (~member(tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3))), product(B!3))))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[84, 80])).
% 0.20/0.40 tff(86,plain,
% 0.20/0.40 (((~member(tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3))), product(A!4))) | (~member(tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3))), product(B!3)))) | member(tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3))), product(B!3))),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(87,plain,
% 0.20/0.40 (member(tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3))), product(B!3))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[86, 85])).
% 0.20/0.41 tff(88,plain,
% 0.20/0.41 ((~((~member(tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3))), product(B!3))) | ![Y: $i] : ((~member(Y, B!3)) | member(tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3))), Y)))) | (~member(tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3))), product(B!3))) | ![Y: $i] : ((~member(Y, B!3)) | member(tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3))), Y))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(89,plain,
% 0.20/0.41 ((~((~member(tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3))), product(B!3))) | ![Y: $i] : ((~member(Y, B!3)) | member(tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3))), Y)))) | ![Y: $i] : ((~member(Y, B!3)) | member(tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3))), Y))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[88, 87])).
% 0.20/0.41 tff(90,plain,
% 0.20/0.41 (![Y: $i] : ((~member(Y, B!3)) | member(tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3))), Y))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[89, 78])).
% 0.20/0.41 tff(91,plain,
% 0.20/0.41 (((~member(tptp_fun_Y_2(intersection(A!4, B!3), tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3)))), intersection(A!4, B!3))) | member(tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3))), tptp_fun_Y_2(intersection(A!4, B!3), tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3)))))) | (~member(tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3))), tptp_fun_Y_2(intersection(A!4, B!3), tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3))))))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(92,plain,
% 0.20/0.41 (~member(tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3))), tptp_fun_Y_2(intersection(A!4, B!3), tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3)))))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[91, 67])).
% 0.20/0.41 tff(93,plain,
% 0.20/0.41 (((~![Y: $i] : ((~member(Y, B!3)) | member(tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3))), Y))) | ((~member(tptp_fun_Y_2(intersection(A!4, B!3), tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3)))), B!3)) | member(tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3))), tptp_fun_Y_2(intersection(A!4, B!3), tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3))))))) <=> ((~![Y: $i] : ((~member(Y, B!3)) | member(tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3))), Y))) | (~member(tptp_fun_Y_2(intersection(A!4, B!3), tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3)))), B!3)) | member(tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3))), tptp_fun_Y_2(intersection(A!4, B!3), tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3))))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(94,plain,
% 0.20/0.41 ((~![Y: $i] : ((~member(Y, B!3)) | member(tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3))), Y))) | ((~member(tptp_fun_Y_2(intersection(A!4, B!3), tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3)))), B!3)) | member(tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3))), tptp_fun_Y_2(intersection(A!4, B!3), tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3))))))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(95,plain,
% 0.20/0.41 ((~![Y: $i] : ((~member(Y, B!3)) | member(tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3))), Y))) | (~member(tptp_fun_Y_2(intersection(A!4, B!3), tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3)))), B!3)) | member(tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3))), tptp_fun_Y_2(intersection(A!4, B!3), tptp_fun_X_0(product(intersection(A!4, B!3)), intersection(product(A!4), product(B!3)))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.20/0.41 tff(96,plain,
% 0.20/0.41 ($false),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[95, 92, 90, 74])).
% 0.20/0.41 % SZS output end Proof
% 0.20/0.41 % E exiting
%------------------------------------------------------------------------------