%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET704+4 : TPTP v9.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n010.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 05:26:11 AM UTC 2025
% Result : Theorem 0.12s 0.38s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : SET704+4 : TPTP v9.0.0. Released v2.2.0.
% 0.08/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n010.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 05:40:11 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.12/0.38 % SZS status Theorem
% 0.12/0.38 % SZS output start Proof
% 0.12/0.38 tff(member_type, type, (
% 0.12/0.38 member: ( $i * $i ) > $o)).
% 0.12/0.38 tff(tptp_fun_X_0_type, type, (
% 0.12/0.38 tptp_fun_X_0: ( $i * $i ) > $i)).
% 0.12/0.38 tff(product_type, type, (
% 0.12/0.38 product: $i > $i)).
% 0.12/0.38 tff(tptp_fun_A_4_type, type, (
% 0.12/0.38 tptp_fun_A_4: $i)).
% 0.12/0.38 tff(tptp_fun_X_3_type, type, (
% 0.12/0.38 tptp_fun_X_3: $i)).
% 0.12/0.38 tff(tptp_fun_Y_2_type, type, (
% 0.12/0.38 tptp_fun_Y_2: ( $i * $i ) > $i)).
% 0.12/0.38 tff(subset_type, type, (
% 0.12/0.38 subset: ( $i * $i ) > $o)).
% 0.12/0.38 tff(1,plain,
% 0.12/0.38 (^[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)))))))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(2,plain,
% 0.12/0.38 (![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))))))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[1])).
% 0.12/0.38 tff(3,plain,
% 0.12/0.38 (^[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)))))))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(4,plain,
% 0.12/0.38 (![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))))))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[3])).
% 0.12/0.38 tff(5,plain,
% 0.12/0.38 (![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))))))))),
% 0.12/0.38 inference(transitivity,[status(thm)],[4, 2])).
% 0.12/0.38 tff(6,plain,
% 0.12/0.38 (^[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))))))))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(7,plain,
% 0.12/0.38 (![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))))))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[6])).
% 0.12/0.38 tff(8,plain,
% 0.12/0.38 (![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)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(9,plain,
% 0.12/0.38 (^[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))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(10,plain,
% 0.12/0.38 (![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)))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[9])).
% 0.12/0.38 tff(11,axiom,(![X: $i, A: $i] : (member(X, product(A)) <=> ![Y: $i] : (member(Y, A) => member(X, Y)))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax','product')).
% 0.12/0.38 tff(12,plain,
% 0.12/0.38 (![X: $i, A: $i] : (member(X, product(A)) <=> ![Y: $i] : ((~member(Y, A)) | member(X, Y)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.12/0.38 tff(13,plain,
% 0.12/0.38 (![X: $i, A: $i] : (member(X, product(A)) <=> ![Y: $i] : ((~member(Y, A)) | member(X, Y)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[12, 8])).
% 0.12/0.38 tff(14,plain,(
% 0.12/0.38 ![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))))))),
% 0.12/0.38 inference(skolemize,[status(sab)],[13])).
% 0.12/0.38 tff(15,plain,
% 0.12/0.38 (![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))))))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[14, 7])).
% 0.12/0.38 tff(16,plain,
% 0.12/0.38 (![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))))))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[15, 5])).
% 0.12/0.38 tff(17,plain,
% 0.12/0.38 ((~![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(X!3, product(A!4)), product(A!4))) | ![Y: $i] : ((~member(Y, A!4)) | member(tptp_fun_X_0(X!3, product(A!4)), Y)))) | (~(member(tptp_fun_X_0(X!3, product(A!4)), product(A!4)) | (~((~member(tptp_fun_Y_2(A!4, tptp_fun_X_0(X!3, product(A!4))), A!4)) | member(tptp_fun_X_0(X!3, product(A!4)), tptp_fun_Y_2(A!4, tptp_fun_X_0(X!3, product(A!4))))))))))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(18,plain,
% 0.12/0.38 (~((~((~member(tptp_fun_X_0(X!3, product(A!4)), product(A!4))) | ![Y: $i] : ((~member(Y, A!4)) | member(tptp_fun_X_0(X!3, product(A!4)), Y)))) | (~(member(tptp_fun_X_0(X!3, product(A!4)), product(A!4)) | (~((~member(tptp_fun_Y_2(A!4, tptp_fun_X_0(X!3, product(A!4))), A!4)) | member(tptp_fun_X_0(X!3, product(A!4)), tptp_fun_Y_2(A!4, tptp_fun_X_0(X!3, product(A!4)))))))))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.12/0.38 tff(19,plain,
% 0.12/0.38 (((~((~member(tptp_fun_X_0(X!3, product(A!4)), product(A!4))) | ![Y: $i] : ((~member(Y, A!4)) | member(tptp_fun_X_0(X!3, product(A!4)), Y)))) | (~(member(tptp_fun_X_0(X!3, product(A!4)), product(A!4)) | (~((~member(tptp_fun_Y_2(A!4, tptp_fun_X_0(X!3, product(A!4))), A!4)) | member(tptp_fun_X_0(X!3, product(A!4)), tptp_fun_Y_2(A!4, tptp_fun_X_0(X!3, product(A!4))))))))) | ((~member(tptp_fun_X_0(X!3, product(A!4)), product(A!4))) | ![Y: $i] : ((~member(Y, A!4)) | member(tptp_fun_X_0(X!3, product(A!4)), Y)))),
% 0.12/0.38 inference(tautology,[status(thm)],[])).
% 0.12/0.38 tff(20,plain,
% 0.12/0.38 ((~member(tptp_fun_X_0(X!3, product(A!4)), product(A!4))) | ![Y: $i] : ((~member(Y, A!4)) | member(tptp_fun_X_0(X!3, product(A!4)), Y))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[19, 18])).
% 0.12/0.38 tff(21,plain,
% 0.12/0.38 (^[A: $i, B: $i] : refl((~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(22,plain,
% 0.12/0.38 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[21])).
% 0.12/0.38 tff(23,plain,
% 0.12/0.38 (^[A: $i, B: $i] : rewrite((~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(24,plain,
% 0.12/0.38 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[23])).
% 0.12/0.38 tff(25,plain,
% 0.12/0.38 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.12/0.38 inference(transitivity,[status(thm)],[24, 22])).
% 0.12/0.38 tff(26,plain,
% 0.12/0.38 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) <=> ((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))), rewrite((subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))) <=> (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))), ((((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> (((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))), rewrite((((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))), ((((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(27,plain,
% 0.12/0.38 (![A: $i, B: $i] : (((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[26])).
% 0.12/0.38 tff(28,plain,
% 0.12/0.38 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(29,plain,
% 0.12/0.38 (^[A: $i, B: $i] : rewrite((subset(A, B) <=> ![X: $i] : (member(X, A) => member(X, B))) <=> (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(30,plain,
% 0.12/0.38 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : (member(X, A) => member(X, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[29])).
% 0.12/0.38 tff(31,axiom,(![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : (member(X, A) => member(X, B)))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax','subset')).
% 0.12/0.38 tff(32,plain,
% 0.12/0.38 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.12/0.38 tff(33,plain,
% 0.12/0.38 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[32, 28])).
% 0.12/0.38 tff(34,plain,(
% 0.12/0.38 ![A: $i, B: $i] : (((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))),
% 0.12/0.38 inference(skolemize,[status(sab)],[33])).
% 0.12/0.38 tff(35,plain,
% 0.12/0.38 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[34, 27])).
% 0.12/0.38 tff(36,plain,
% 0.12/0.38 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[35, 25])).
% 0.12/0.38 tff(37,plain,
% 0.12/0.38 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))) | (~((~((~subset(product(A!4), X!3)) | ![X: $i] : ((~member(X, product(A!4))) | member(X, X!3)))) | (~(subset(product(A!4), X!3) | (~((~member(tptp_fun_X_0(X!3, product(A!4)), product(A!4))) | member(tptp_fun_X_0(X!3, product(A!4)), X!3)))))))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(38,plain,
% 0.12/0.38 (~((~((~subset(product(A!4), X!3)) | ![X: $i] : ((~member(X, product(A!4))) | member(X, X!3)))) | (~(subset(product(A!4), X!3) | (~((~member(tptp_fun_X_0(X!3, product(A!4)), product(A!4))) | member(tptp_fun_X_0(X!3, product(A!4)), X!3))))))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[37, 36])).
% 0.12/0.38 tff(39,plain,
% 0.12/0.38 (((~((~subset(product(A!4), X!3)) | ![X: $i] : ((~member(X, product(A!4))) | member(X, X!3)))) | (~(subset(product(A!4), X!3) | (~((~member(tptp_fun_X_0(X!3, product(A!4)), product(A!4))) | member(tptp_fun_X_0(X!3, product(A!4)), X!3)))))) | (subset(product(A!4), X!3) | (~((~member(tptp_fun_X_0(X!3, product(A!4)), product(A!4))) | member(tptp_fun_X_0(X!3, product(A!4)), X!3))))),
% 0.12/0.38 inference(tautology,[status(thm)],[])).
% 0.12/0.38 tff(40,plain,
% 0.12/0.38 (subset(product(A!4), X!3) | (~((~member(tptp_fun_X_0(X!3, product(A!4)), product(A!4))) | member(tptp_fun_X_0(X!3, product(A!4)), X!3)))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[39, 38])).
% 0.12/0.38 tff(41,plain,
% 0.12/0.38 ((~![A: $i, X: $i] : ((~member(X, A)) | subset(product(A), X))) <=> (~![A: $i, X: $i] : ((~member(X, A)) | subset(product(A), X)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(42,plain,
% 0.12/0.38 ((~![A: $i, X: $i] : (member(X, A) => subset(product(A), X))) <=> (~![A: $i, X: $i] : ((~member(X, A)) | subset(product(A), X)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(43,axiom,(~![A: $i, X: $i] : (member(X, A) => subset(product(A), X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','thI42')).
% 0.20/0.39 tff(44,plain,
% 0.20/0.39 (~![A: $i, X: $i] : ((~member(X, A)) | subset(product(A), X))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.20/0.39 tff(45,plain,
% 0.20/0.39 (~![A: $i, X: $i] : ((~member(X, A)) | subset(product(A), X))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[44, 41])).
% 0.20/0.39 tff(46,plain,
% 0.20/0.39 (~![A: $i, X: $i] : ((~member(X, A)) | subset(product(A), X))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[45, 41])).
% 0.20/0.39 tff(47,plain,
% 0.20/0.39 (~![A: $i, X: $i] : ((~member(X, A)) | subset(product(A), X))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[46, 41])).
% 0.20/0.39 tff(48,plain,(
% 0.20/0.39 ~((~member(X!3, A!4)) | subset(product(A!4), X!3))),
% 0.20/0.39 inference(skolemize,[status(sab)],[47])).
% 0.20/0.39 tff(49,plain,
% 0.20/0.39 (~subset(product(A!4), X!3)),
% 0.20/0.39 inference(or_elim,[status(thm)],[48])).
% 0.20/0.39 tff(50,plain,
% 0.20/0.39 ((~(subset(product(A!4), X!3) | (~((~member(tptp_fun_X_0(X!3, product(A!4)), product(A!4))) | member(tptp_fun_X_0(X!3, product(A!4)), X!3))))) | subset(product(A!4), X!3) | (~((~member(tptp_fun_X_0(X!3, product(A!4)), product(A!4))) | member(tptp_fun_X_0(X!3, product(A!4)), X!3)))),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(51,plain,
% 0.20/0.39 ((~(subset(product(A!4), X!3) | (~((~member(tptp_fun_X_0(X!3, product(A!4)), product(A!4))) | member(tptp_fun_X_0(X!3, product(A!4)), X!3))))) | (~((~member(tptp_fun_X_0(X!3, product(A!4)), product(A!4))) | member(tptp_fun_X_0(X!3, product(A!4)), X!3)))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[50, 49])).
% 0.20/0.39 tff(52,plain,
% 0.20/0.39 (~((~member(tptp_fun_X_0(X!3, product(A!4)), product(A!4))) | member(tptp_fun_X_0(X!3, product(A!4)), X!3))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[51, 40])).
% 0.20/0.39 tff(53,plain,
% 0.20/0.39 (((~member(tptp_fun_X_0(X!3, product(A!4)), product(A!4))) | member(tptp_fun_X_0(X!3, product(A!4)), X!3)) | member(tptp_fun_X_0(X!3, product(A!4)), product(A!4))),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(54,plain,
% 0.20/0.39 (member(tptp_fun_X_0(X!3, product(A!4)), product(A!4))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[53, 52])).
% 0.20/0.39 tff(55,plain,
% 0.20/0.39 ((~((~member(tptp_fun_X_0(X!3, product(A!4)), product(A!4))) | ![Y: $i] : ((~member(Y, A!4)) | member(tptp_fun_X_0(X!3, product(A!4)), Y)))) | (~member(tptp_fun_X_0(X!3, product(A!4)), product(A!4))) | ![Y: $i] : ((~member(Y, A!4)) | member(tptp_fun_X_0(X!3, product(A!4)), Y))),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(56,plain,
% 0.20/0.39 ((~((~member(tptp_fun_X_0(X!3, product(A!4)), product(A!4))) | ![Y: $i] : ((~member(Y, A!4)) | member(tptp_fun_X_0(X!3, product(A!4)), Y)))) | ![Y: $i] : ((~member(Y, A!4)) | member(tptp_fun_X_0(X!3, product(A!4)), Y))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[55, 54])).
% 0.20/0.39 tff(57,plain,
% 0.20/0.39 (![Y: $i] : ((~member(Y, A!4)) | member(tptp_fun_X_0(X!3, product(A!4)), Y))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[56, 20])).
% 0.20/0.39 tff(58,plain,
% 0.20/0.39 (((~member(tptp_fun_X_0(X!3, product(A!4)), product(A!4))) | member(tptp_fun_X_0(X!3, product(A!4)), X!3)) | (~member(tptp_fun_X_0(X!3, product(A!4)), X!3))),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(59,plain,
% 0.20/0.39 (~member(tptp_fun_X_0(X!3, product(A!4)), X!3)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[58, 52])).
% 0.20/0.39 tff(60,plain,
% 0.20/0.39 (member(X!3, A!4)),
% 0.20/0.39 inference(or_elim,[status(thm)],[48])).
% 0.20/0.39 tff(61,plain,
% 0.20/0.39 (((~![Y: $i] : ((~member(Y, A!4)) | member(tptp_fun_X_0(X!3, product(A!4)), Y))) | ((~member(X!3, A!4)) | member(tptp_fun_X_0(X!3, product(A!4)), X!3))) <=> ((~![Y: $i] : ((~member(Y, A!4)) | member(tptp_fun_X_0(X!3, product(A!4)), Y))) | (~member(X!3, A!4)) | member(tptp_fun_X_0(X!3, product(A!4)), X!3))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(62,plain,
% 0.20/0.39 ((~![Y: $i] : ((~member(Y, A!4)) | member(tptp_fun_X_0(X!3, product(A!4)), Y))) | ((~member(X!3, A!4)) | member(tptp_fun_X_0(X!3, product(A!4)), X!3))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(63,plain,
% 0.20/0.39 ((~![Y: $i] : ((~member(Y, A!4)) | member(tptp_fun_X_0(X!3, product(A!4)), Y))) | (~member(X!3, A!4)) | member(tptp_fun_X_0(X!3, product(A!4)), X!3)),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.20/0.39 tff(64,plain,
% 0.20/0.39 ($false),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[63, 60, 59, 57])).
% 0.20/0.39 % SZS output end Proof
% 0.20/0.39 % E exiting
%------------------------------------------------------------------------------