%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET355+4 : TPTP v9.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n015.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 05:25:39 AM UTC 2025
% Result : Theorem 0.19s 0.38s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SET355+4 : TPTP v9.0.0. Released v2.2.0.
% 0.12/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n015.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Jun 20 04:55:11 EDT 2025
% 0.19/0.34 % CPUTime :
% 0.19/0.38 % SZS status Theorem
% 0.19/0.38 % SZS output start Proof
% 0.19/0.38 tff(member_type, type, (
% 0.19/0.38 member: ( $i * $i ) > $o)).
% 0.19/0.38 tff(tptp_fun_X_0_type, type, (
% 0.19/0.38 tptp_fun_X_0: ( $i * $i ) > $i)).
% 0.19/0.38 tff(tptp_fun_X_3_type, type, (
% 0.19/0.38 tptp_fun_X_3: $i)).
% 0.19/0.38 tff(sum_type, type, (
% 0.19/0.38 sum: $i > $i)).
% 0.19/0.38 tff(tptp_fun_A_4_type, type, (
% 0.19/0.38 tptp_fun_A_4: $i)).
% 0.19/0.38 tff(tptp_fun_Y_1_type, type, (
% 0.19/0.38 tptp_fun_Y_1: ( $i * $i ) > $i)).
% 0.19/0.38 tff(subset_type, type, (
% 0.19/0.38 subset: ( $i * $i ) > $o)).
% 0.19/0.38 tff(1,plain,
% 0.19/0.38 (^[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))))))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(2,plain,
% 0.19/0.38 (![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)))))))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.38 tff(3,plain,
% 0.19/0.38 (^[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))))))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(4,plain,
% 0.19/0.38 (![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)))))))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[3])).
% 0.19/0.38 tff(5,plain,
% 0.19/0.38 (![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)))))))),
% 0.19/0.38 inference(transitivity,[status(thm)],[4, 2])).
% 0.19/0.38 tff(6,plain,
% 0.19/0.38 (^[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)))))))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(7,plain,
% 0.19/0.38 (![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)))))))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[6])).
% 0.19/0.38 tff(8,plain,
% 0.19/0.38 (![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)))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(9,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')).
% 0.19/0.38 tff(10,plain,
% 0.19/0.38 (![X: $i, A: $i] : (member(X, sum(A)) <=> ?[Y: $i] : (member(Y, A) & member(X, Y)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[9, 8])).
% 0.19/0.38 tff(11,plain,(
% 0.19/0.38 ![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)))))),
% 0.19/0.38 inference(skolemize,[status(sab)],[10])).
% 0.19/0.38 tff(12,plain,
% 0.19/0.38 (![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)))))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[11, 7])).
% 0.19/0.38 tff(13,plain,
% 0.19/0.38 (![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)))))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[12, 5])).
% 0.19/0.38 tff(14,plain,
% 0.19/0.38 (((~![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(tptp_fun_X_0(sum(A!4), X!3), sum(A!4)) | ![Y: $i] : ((~member(Y, A!4)) | (~member(tptp_fun_X_0(sum(A!4), X!3), Y))))) | (~((~member(tptp_fun_X_0(sum(A!4), X!3), sum(A!4))) | (~((~member(tptp_fun_X_0(sum(A!4), X!3), tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(A!4), X!3)))) | (~member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(A!4), X!3)), A!4))))))))) <=> ((~![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(tptp_fun_X_0(sum(A!4), X!3), sum(A!4)) | ![Y: $i] : ((~member(Y, A!4)) | (~member(tptp_fun_X_0(sum(A!4), X!3), Y))))) | (~((~member(tptp_fun_X_0(sum(A!4), X!3), sum(A!4))) | (~((~member(tptp_fun_X_0(sum(A!4), X!3), tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(A!4), X!3)))) | (~member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(A!4), X!3)), A!4)))))))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(15,plain,
% 0.19/0.38 ((~((~((~member(tptp_fun_X_0(sum(A!4), X!3), sum(A!4))) | (~((~member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(A!4), X!3)), A!4)) | (~member(tptp_fun_X_0(sum(A!4), X!3), tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(A!4), X!3)))))))) | (~(member(tptp_fun_X_0(sum(A!4), X!3), sum(A!4)) | ![Y: $i] : ((~member(Y, A!4)) | (~member(tptp_fun_X_0(sum(A!4), X!3), Y))))))) <=> (~((~(member(tptp_fun_X_0(sum(A!4), X!3), sum(A!4)) | ![Y: $i] : ((~member(Y, A!4)) | (~member(tptp_fun_X_0(sum(A!4), X!3), Y))))) | (~((~member(tptp_fun_X_0(sum(A!4), X!3), sum(A!4))) | (~((~member(tptp_fun_X_0(sum(A!4), X!3), tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(A!4), X!3)))) | (~member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(A!4), X!3)), A!4))))))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(16,plain,
% 0.19/0.38 (((~![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(tptp_fun_X_0(sum(A!4), X!3), sum(A!4))) | (~((~member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(A!4), X!3)), A!4)) | (~member(tptp_fun_X_0(sum(A!4), X!3), tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(A!4), X!3)))))))) | (~(member(tptp_fun_X_0(sum(A!4), X!3), sum(A!4)) | ![Y: $i] : ((~member(Y, A!4)) | (~member(tptp_fun_X_0(sum(A!4), X!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(tptp_fun_X_0(sum(A!4), X!3), sum(A!4)) | ![Y: $i] : ((~member(Y, A!4)) | (~member(tptp_fun_X_0(sum(A!4), X!3), Y))))) | (~((~member(tptp_fun_X_0(sum(A!4), X!3), sum(A!4))) | (~((~member(tptp_fun_X_0(sum(A!4), X!3), tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(A!4), X!3)))) | (~member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(A!4), X!3)), A!4)))))))))),
% 0.19/0.39 inference(monotonicity,[status(thm)],[15])).
% 0.19/0.39 tff(17,plain,
% 0.19/0.39 (((~![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(tptp_fun_X_0(sum(A!4), X!3), sum(A!4))) | (~((~member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(A!4), X!3)), A!4)) | (~member(tptp_fun_X_0(sum(A!4), X!3), tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(A!4), X!3)))))))) | (~(member(tptp_fun_X_0(sum(A!4), X!3), sum(A!4)) | ![Y: $i] : ((~member(Y, A!4)) | (~member(tptp_fun_X_0(sum(A!4), X!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(tptp_fun_X_0(sum(A!4), X!3), sum(A!4)) | ![Y: $i] : ((~member(Y, A!4)) | (~member(tptp_fun_X_0(sum(A!4), X!3), Y))))) | (~((~member(tptp_fun_X_0(sum(A!4), X!3), sum(A!4))) | (~((~member(tptp_fun_X_0(sum(A!4), X!3), tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(A!4), X!3)))) | (~member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(A!4), X!3)), A!4)))))))))),
% 0.19/0.39 inference(transitivity,[status(thm)],[16, 14])).
% 0.19/0.39 tff(18,plain,
% 0.19/0.39 ((~![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(tptp_fun_X_0(sum(A!4), X!3), sum(A!4))) | (~((~member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(A!4), X!3)), A!4)) | (~member(tptp_fun_X_0(sum(A!4), X!3), tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(A!4), X!3)))))))) | (~(member(tptp_fun_X_0(sum(A!4), X!3), sum(A!4)) | ![Y: $i] : ((~member(Y, A!4)) | (~member(tptp_fun_X_0(sum(A!4), X!3), Y)))))))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(19,plain,
% 0.19/0.39 ((~![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(tptp_fun_X_0(sum(A!4), X!3), sum(A!4)) | ![Y: $i] : ((~member(Y, A!4)) | (~member(tptp_fun_X_0(sum(A!4), X!3), Y))))) | (~((~member(tptp_fun_X_0(sum(A!4), X!3), sum(A!4))) | (~((~member(tptp_fun_X_0(sum(A!4), X!3), tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(A!4), X!3)))) | (~member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(A!4), X!3)), A!4))))))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.19/0.39 tff(20,plain,
% 0.19/0.39 (~((~(member(tptp_fun_X_0(sum(A!4), X!3), sum(A!4)) | ![Y: $i] : ((~member(Y, A!4)) | (~member(tptp_fun_X_0(sum(A!4), X!3), Y))))) | (~((~member(tptp_fun_X_0(sum(A!4), X!3), sum(A!4))) | (~((~member(tptp_fun_X_0(sum(A!4), X!3), tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(A!4), X!3)))) | (~member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(A!4), X!3)), A!4)))))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[19, 13])).
% 0.19/0.39 tff(21,plain,
% 0.19/0.39 (((~(member(tptp_fun_X_0(sum(A!4), X!3), sum(A!4)) | ![Y: $i] : ((~member(Y, A!4)) | (~member(tptp_fun_X_0(sum(A!4), X!3), Y))))) | (~((~member(tptp_fun_X_0(sum(A!4), X!3), sum(A!4))) | (~((~member(tptp_fun_X_0(sum(A!4), X!3), tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(A!4), X!3)))) | (~member(tptp_fun_Y_1(A!4, tptp_fun_X_0(sum(A!4), X!3)), A!4))))))) | (member(tptp_fun_X_0(sum(A!4), X!3), sum(A!4)) | ![Y: $i] : ((~member(Y, A!4)) | (~member(tptp_fun_X_0(sum(A!4), X!3), Y))))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(22,plain,
% 0.19/0.39 (member(tptp_fun_X_0(sum(A!4), X!3), sum(A!4)) | ![Y: $i] : ((~member(Y, A!4)) | (~member(tptp_fun_X_0(sum(A!4), X!3), Y)))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[21, 20])).
% 0.19/0.39 tff(23,plain,
% 0.19/0.39 (^[A: $i, B: $i] : refl((~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(24,plain,
% 0.19/0.39 (![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)))))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[23])).
% 0.19/0.39 tff(25,plain,
% 0.19/0.39 (^[A: $i, B: $i] : rewrite((~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(26,plain,
% 0.19/0.39 (![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)))))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[25])).
% 0.19/0.39 tff(27,plain,
% 0.19/0.39 (![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)))))))),
% 0.19/0.39 inference(transitivity,[status(thm)],[26, 24])).
% 0.19/0.39 tff(28,plain,
% 0.19/0.39 (^[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)))))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(29,plain,
% 0.19/0.39 (![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)))))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[28])).
% 0.19/0.39 tff(30,plain,
% 0.19/0.39 (![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)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(31,plain,
% 0.19/0.39 (^[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))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(32,plain,
% 0.19/0.39 (![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)))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[31])).
% 0.19/0.39 tff(33,axiom,(![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : (member(X, A) => member(X, B)))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax','subset')).
% 0.19/0.39 tff(34,plain,
% 0.19/0.39 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.19/0.39 tff(35,plain,
% 0.19/0.39 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[34, 30])).
% 0.19/0.39 tff(36,plain,(
% 0.19/0.39 ![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)))))),
% 0.19/0.39 inference(skolemize,[status(sab)],[35])).
% 0.19/0.39 tff(37,plain,
% 0.19/0.39 (![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)))))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[36, 29])).
% 0.19/0.39 tff(38,plain,
% 0.19/0.39 (![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)))))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[37, 27])).
% 0.19/0.39 tff(39,plain,
% 0.19/0.39 ((~![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(X!3, sum(A!4))) | ![X: $i] : ((~member(X, X!3)) | member(X, sum(A!4))))) | (~(subset(X!3, sum(A!4)) | (~((~member(tptp_fun_X_0(sum(A!4), X!3), X!3)) | member(tptp_fun_X_0(sum(A!4), X!3), sum(A!4))))))))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(40,plain,
% 0.19/0.39 (~((~((~subset(X!3, sum(A!4))) | ![X: $i] : ((~member(X, X!3)) | member(X, sum(A!4))))) | (~(subset(X!3, sum(A!4)) | (~((~member(tptp_fun_X_0(sum(A!4), X!3), X!3)) | member(tptp_fun_X_0(sum(A!4), X!3), sum(A!4)))))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[39, 38])).
% 0.19/0.39 tff(41,plain,
% 0.19/0.39 (((~((~subset(X!3, sum(A!4))) | ![X: $i] : ((~member(X, X!3)) | member(X, sum(A!4))))) | (~(subset(X!3, sum(A!4)) | (~((~member(tptp_fun_X_0(sum(A!4), X!3), X!3)) | member(tptp_fun_X_0(sum(A!4), X!3), sum(A!4))))))) | (subset(X!3, sum(A!4)) | (~((~member(tptp_fun_X_0(sum(A!4), X!3), X!3)) | member(tptp_fun_X_0(sum(A!4), X!3), sum(A!4)))))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(42,plain,
% 0.19/0.39 (subset(X!3, sum(A!4)) | (~((~member(tptp_fun_X_0(sum(A!4), X!3), X!3)) | member(tptp_fun_X_0(sum(A!4), X!3), sum(A!4))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[41, 40])).
% 0.19/0.39 tff(43,plain,
% 0.19/0.39 ((~![A: $i, X: $i] : ((~member(X, A)) | subset(X, sum(A)))) <=> (~![A: $i, X: $i] : ((~member(X, A)) | subset(X, sum(A))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(44,plain,
% 0.19/0.39 ((~![A: $i, X: $i] : (member(X, A) => subset(X, sum(A)))) <=> (~![A: $i, X: $i] : ((~member(X, A)) | subset(X, sum(A))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(45,axiom,(~![A: $i, X: $i] : (member(X, A) => subset(X, sum(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thI43')).
% 0.19/0.40 tff(46,plain,
% 0.19/0.40 (~![A: $i, X: $i] : ((~member(X, A)) | subset(X, sum(A)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.19/0.40 tff(47,plain,
% 0.19/0.40 (~![A: $i, X: $i] : ((~member(X, A)) | subset(X, sum(A)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[46, 43])).
% 0.19/0.40 tff(48,plain,
% 0.19/0.40 (~![A: $i, X: $i] : ((~member(X, A)) | subset(X, sum(A)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[47, 43])).
% 0.19/0.40 tff(49,plain,
% 0.19/0.40 (~![A: $i, X: $i] : ((~member(X, A)) | subset(X, sum(A)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[48, 43])).
% 0.19/0.40 tff(50,plain,(
% 0.19/0.40 ~((~member(X!3, A!4)) | subset(X!3, sum(A!4)))),
% 0.19/0.40 inference(skolemize,[status(sab)],[49])).
% 0.19/0.40 tff(51,plain,
% 0.19/0.40 (~subset(X!3, sum(A!4))),
% 0.19/0.40 inference(or_elim,[status(thm)],[50])).
% 0.19/0.40 tff(52,plain,
% 0.19/0.40 ((~(subset(X!3, sum(A!4)) | (~((~member(tptp_fun_X_0(sum(A!4), X!3), X!3)) | member(tptp_fun_X_0(sum(A!4), X!3), sum(A!4)))))) | subset(X!3, sum(A!4)) | (~((~member(tptp_fun_X_0(sum(A!4), X!3), X!3)) | member(tptp_fun_X_0(sum(A!4), X!3), sum(A!4))))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(53,plain,
% 0.19/0.40 ((~(subset(X!3, sum(A!4)) | (~((~member(tptp_fun_X_0(sum(A!4), X!3), X!3)) | member(tptp_fun_X_0(sum(A!4), X!3), sum(A!4)))))) | (~((~member(tptp_fun_X_0(sum(A!4), X!3), X!3)) | member(tptp_fun_X_0(sum(A!4), X!3), sum(A!4))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[52, 51])).
% 0.19/0.40 tff(54,plain,
% 0.19/0.40 (~((~member(tptp_fun_X_0(sum(A!4), X!3), X!3)) | member(tptp_fun_X_0(sum(A!4), X!3), sum(A!4)))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[53, 42])).
% 0.19/0.40 tff(55,plain,
% 0.19/0.40 (((~member(tptp_fun_X_0(sum(A!4), X!3), X!3)) | member(tptp_fun_X_0(sum(A!4), X!3), sum(A!4))) | (~member(tptp_fun_X_0(sum(A!4), X!3), sum(A!4)))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(56,plain,
% 0.19/0.40 (~member(tptp_fun_X_0(sum(A!4), X!3), sum(A!4))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[55, 54])).
% 0.19/0.40 tff(57,plain,
% 0.19/0.40 ((~(member(tptp_fun_X_0(sum(A!4), X!3), sum(A!4)) | ![Y: $i] : ((~member(Y, A!4)) | (~member(tptp_fun_X_0(sum(A!4), X!3), Y))))) | member(tptp_fun_X_0(sum(A!4), X!3), sum(A!4)) | ![Y: $i] : ((~member(Y, A!4)) | (~member(tptp_fun_X_0(sum(A!4), X!3), Y)))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(58,plain,
% 0.19/0.40 ((~(member(tptp_fun_X_0(sum(A!4), X!3), sum(A!4)) | ![Y: $i] : ((~member(Y, A!4)) | (~member(tptp_fun_X_0(sum(A!4), X!3), Y))))) | ![Y: $i] : ((~member(Y, A!4)) | (~member(tptp_fun_X_0(sum(A!4), X!3), Y)))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[57, 56])).
% 0.19/0.40 tff(59,plain,
% 0.19/0.40 (![Y: $i] : ((~member(Y, A!4)) | (~member(tptp_fun_X_0(sum(A!4), X!3), Y)))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[58, 22])).
% 0.19/0.40 tff(60,plain,
% 0.19/0.40 (((~member(tptp_fun_X_0(sum(A!4), X!3), X!3)) | member(tptp_fun_X_0(sum(A!4), X!3), sum(A!4))) | member(tptp_fun_X_0(sum(A!4), X!3), X!3)),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(61,plain,
% 0.19/0.40 (member(tptp_fun_X_0(sum(A!4), X!3), X!3)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[60, 54])).
% 0.19/0.40 tff(62,plain,
% 0.19/0.40 (member(X!3, A!4)),
% 0.19/0.40 inference(or_elim,[status(thm)],[50])).
% 0.19/0.40 tff(63,plain,
% 0.19/0.40 (((~![Y: $i] : ((~member(Y, A!4)) | (~member(tptp_fun_X_0(sum(A!4), X!3), Y)))) | ((~member(X!3, A!4)) | (~member(tptp_fun_X_0(sum(A!4), X!3), X!3)))) <=> ((~![Y: $i] : ((~member(Y, A!4)) | (~member(tptp_fun_X_0(sum(A!4), X!3), Y)))) | (~member(X!3, A!4)) | (~member(tptp_fun_X_0(sum(A!4), X!3), X!3)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(64,plain,
% 0.19/0.40 ((~![Y: $i] : ((~member(Y, A!4)) | (~member(tptp_fun_X_0(sum(A!4), X!3), Y)))) | ((~member(X!3, A!4)) | (~member(tptp_fun_X_0(sum(A!4), X!3), X!3)))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(65,plain,
% 0.19/0.40 ((~![Y: $i] : ((~member(Y, A!4)) | (~member(tptp_fun_X_0(sum(A!4), X!3), Y)))) | (~member(X!3, A!4)) | (~member(tptp_fun_X_0(sum(A!4), X!3), X!3))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.19/0.40 tff(66,plain,
% 0.19/0.40 ($false),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[65, 62, 61, 59])).
% 0.19/0.40 % SZS output end Proof
% 0.19/0.40 % E exiting
%------------------------------------------------------------------------------