%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET751+4 : TPTP v9.0.0. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n004.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 05:26:16 AM UTC 2025
% Result : Theorem 0.12s 0.39s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SET751+4 : TPTP v9.0.0. Bugfixed v2.2.1.
% 0.12/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n004.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 05:39:22 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.39 % SZS status Theorem
% 0.12/0.39 % SZS output start Proof
% 0.12/0.39 tff(member_type, type, (
% 0.12/0.39 member: ( $i * $i ) > $o)).
% 0.12/0.39 tff(tptp_fun_Y_39_type, type, (
% 0.12/0.39 tptp_fun_Y_39: $i)).
% 0.12/0.39 tff(tptp_fun_X_23_type, type, (
% 0.12/0.39 tptp_fun_X_23: ( $i * $i * $i ) > $i)).
% 0.12/0.39 tff(tptp_fun_F_43_type, type, (
% 0.12/0.39 tptp_fun_F_43: $i)).
% 0.12/0.39 tff(tptp_fun_X_40_type, type, (
% 0.12/0.39 tptp_fun_X_40: $i)).
% 0.12/0.39 tff(tptp_fun_X_0_type, type, (
% 0.12/0.39 tptp_fun_X_0: ( $i * $i ) > $i)).
% 0.12/0.39 tff(image2_type, type, (
% 0.12/0.39 image2: ( $i * $i ) > $i)).
% 0.12/0.39 tff(apply_type, type, (
% 0.12/0.39 apply: ( $i * $i * $i ) > $o)).
% 0.12/0.39 tff(subset_type, type, (
% 0.12/0.39 subset: ( $i * $i ) > $o)).
% 0.12/0.39 tff(tptp_fun_A_42_type, type, (
% 0.12/0.39 tptp_fun_A_42: $i)).
% 0.12/0.39 tff(maps_type, type, (
% 0.12/0.39 maps: ( $i * $i * $i ) > $o)).
% 0.12/0.39 tff(tptp_fun_B_41_type, type, (
% 0.12/0.39 tptp_fun_B_41: $i)).
% 0.12/0.39 tff(1,plain,
% 0.12/0.39 (^[F: $i, A: $i, Y: $i] : refl((~((~((~member(Y, image2(F, A))) | (~((~member(tptp_fun_X_23(Y, A, F), A)) | (~apply(F, tptp_fun_X_23(Y, A, F), Y)))))) | (~(member(Y, image2(F, A)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y))))))) <=> (~((~((~member(Y, image2(F, A))) | (~((~member(tptp_fun_X_23(Y, A, F), A)) | (~apply(F, tptp_fun_X_23(Y, A, F), Y)))))) | (~(member(Y, image2(F, A)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y))))))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(2,plain,
% 0.12/0.39 (![F: $i, A: $i, Y: $i] : (~((~((~member(Y, image2(F, A))) | (~((~member(tptp_fun_X_23(Y, A, F), A)) | (~apply(F, tptp_fun_X_23(Y, A, F), Y)))))) | (~(member(Y, image2(F, A)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y))))))) <=> ![F: $i, A: $i, Y: $i] : (~((~((~member(Y, image2(F, A))) | (~((~member(tptp_fun_X_23(Y, A, F), A)) | (~apply(F, tptp_fun_X_23(Y, A, F), Y)))))) | (~(member(Y, image2(F, A)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[1])).
% 0.12/0.39 tff(3,plain,
% 0.12/0.39 (^[F: $i, A: $i, Y: $i] : rewrite((~((~((~member(Y, image2(F, A))) | (~((~member(tptp_fun_X_23(Y, A, F), A)) | (~apply(F, tptp_fun_X_23(Y, A, F), Y)))))) | (~(member(Y, image2(F, A)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y))))))) <=> (~((~((~member(Y, image2(F, A))) | (~((~member(tptp_fun_X_23(Y, A, F), A)) | (~apply(F, tptp_fun_X_23(Y, A, F), Y)))))) | (~(member(Y, image2(F, A)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y))))))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(4,plain,
% 0.12/0.39 (![F: $i, A: $i, Y: $i] : (~((~((~member(Y, image2(F, A))) | (~((~member(tptp_fun_X_23(Y, A, F), A)) | (~apply(F, tptp_fun_X_23(Y, A, F), Y)))))) | (~(member(Y, image2(F, A)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y))))))) <=> ![F: $i, A: $i, Y: $i] : (~((~((~member(Y, image2(F, A))) | (~((~member(tptp_fun_X_23(Y, A, F), A)) | (~apply(F, tptp_fun_X_23(Y, A, F), Y)))))) | (~(member(Y, image2(F, A)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[3])).
% 0.12/0.39 tff(5,plain,
% 0.12/0.39 (![F: $i, A: $i, Y: $i] : (~((~((~member(Y, image2(F, A))) | (~((~member(tptp_fun_X_23(Y, A, F), A)) | (~apply(F, tptp_fun_X_23(Y, A, F), Y)))))) | (~(member(Y, image2(F, A)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y))))))) <=> ![F: $i, A: $i, Y: $i] : (~((~((~member(Y, image2(F, A))) | (~((~member(tptp_fun_X_23(Y, A, F), A)) | (~apply(F, tptp_fun_X_23(Y, A, F), Y)))))) | (~(member(Y, image2(F, A)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))),
% 0.12/0.39 inference(transitivity,[status(thm)],[4, 2])).
% 0.12/0.39 tff(6,plain,
% 0.12/0.39 (^[F: $i, A: $i, Y: $i] : trans(monotonicity(rewrite(((~member(Y, image2(F, A))) | (member(tptp_fun_X_23(Y, A, F), A) & apply(F, tptp_fun_X_23(Y, A, F), Y))) <=> ((~member(Y, image2(F, A))) | (~((~member(tptp_fun_X_23(Y, A, F), A)) | (~apply(F, tptp_fun_X_23(Y, A, F), Y)))))), rewrite((member(Y, image2(F, A)) | ![X: $i] : (~(member(X, A) & apply(F, X, Y)))) <=> (member(Y, image2(F, A)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y))))), ((((~member(Y, image2(F, A))) | (member(tptp_fun_X_23(Y, A, F), A) & apply(F, tptp_fun_X_23(Y, A, F), Y))) & (member(Y, image2(F, A)) | ![X: $i] : (~(member(X, A) & apply(F, X, Y))))) <=> (((~member(Y, image2(F, A))) | (~((~member(tptp_fun_X_23(Y, A, F), A)) | (~apply(F, tptp_fun_X_23(Y, A, F), Y))))) & (member(Y, image2(F, A)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y))))))), rewrite((((~member(Y, image2(F, A))) | (~((~member(tptp_fun_X_23(Y, A, F), A)) | (~apply(F, tptp_fun_X_23(Y, A, F), Y))))) & (member(Y, image2(F, A)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y))))) <=> (~((~((~member(Y, image2(F, A))) | (~((~member(tptp_fun_X_23(Y, A, F), A)) | (~apply(F, tptp_fun_X_23(Y, A, F), Y)))))) | (~(member(Y, image2(F, A)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))), ((((~member(Y, image2(F, A))) | (member(tptp_fun_X_23(Y, A, F), A) & apply(F, tptp_fun_X_23(Y, A, F), Y))) & (member(Y, image2(F, A)) | ![X: $i] : (~(member(X, A) & apply(F, X, Y))))) <=> (~((~((~member(Y, image2(F, A))) | (~((~member(tptp_fun_X_23(Y, A, F), A)) | (~apply(F, tptp_fun_X_23(Y, A, F), Y)))))) | (~(member(Y, image2(F, A)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(7,plain,
% 0.12/0.39 (![F: $i, A: $i, Y: $i] : (((~member(Y, image2(F, A))) | (member(tptp_fun_X_23(Y, A, F), A) & apply(F, tptp_fun_X_23(Y, A, F), Y))) & (member(Y, image2(F, A)) | ![X: $i] : (~(member(X, A) & apply(F, X, Y))))) <=> ![F: $i, A: $i, Y: $i] : (~((~((~member(Y, image2(F, A))) | (~((~member(tptp_fun_X_23(Y, A, F), A)) | (~apply(F, tptp_fun_X_23(Y, A, F), Y)))))) | (~(member(Y, image2(F, A)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[6])).
% 0.12/0.39 tff(8,plain,
% 0.12/0.39 (![F: $i, A: $i, Y: $i] : (member(Y, image2(F, A)) <=> ?[X: $i] : (member(X, A) & apply(F, X, Y))) <=> ![F: $i, A: $i, Y: $i] : (member(Y, image2(F, A)) <=> ?[X: $i] : (member(X, A) & apply(F, X, Y)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(9,axiom,(![F: $i, A: $i, Y: $i] : (member(Y, image2(F, A)) <=> ?[X: $i] : (member(X, A) & apply(F, X, Y)))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+1.ax','image2')).
% 0.12/0.39 tff(10,plain,
% 0.12/0.39 (![F: $i, A: $i, Y: $i] : (member(Y, image2(F, A)) <=> ?[X: $i] : (member(X, A) & apply(F, X, Y)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[9, 8])).
% 0.12/0.39 tff(11,plain,(
% 0.12/0.39 ![F: $i, A: $i, Y: $i] : (((~member(Y, image2(F, A))) | (member(tptp_fun_X_23(Y, A, F), A) & apply(F, tptp_fun_X_23(Y, A, F), Y))) & (member(Y, image2(F, A)) | ![X: $i] : (~(member(X, A) & apply(F, X, Y)))))),
% 0.12/0.39 inference(skolemize,[status(sab)],[10])).
% 0.12/0.39 tff(12,plain,
% 0.12/0.39 (![F: $i, A: $i, Y: $i] : (~((~((~member(Y, image2(F, A))) | (~((~member(tptp_fun_X_23(Y, A, F), A)) | (~apply(F, tptp_fun_X_23(Y, A, F), Y)))))) | (~(member(Y, image2(F, A)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[11, 7])).
% 0.12/0.39 tff(13,plain,
% 0.12/0.39 (![F: $i, A: $i, Y: $i] : (~((~((~member(Y, image2(F, A))) | (~((~member(tptp_fun_X_23(Y, A, F), A)) | (~apply(F, tptp_fun_X_23(Y, A, F), Y)))))) | (~(member(Y, image2(F, A)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[12, 5])).
% 0.12/0.39 tff(14,plain,
% 0.12/0.39 (((~![F: $i, A: $i, Y: $i] : (~((~((~member(Y, image2(F, A))) | (~((~member(tptp_fun_X_23(Y, A, F), A)) | (~apply(F, tptp_fun_X_23(Y, A, F), Y)))))) | (~(member(Y, image2(F, A)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))) | (~((~(member(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), image2(F!43, X!40)) | ![X: $i] : ((~member(X, X!40)) | (~apply(F!43, X, tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40))))))) | (~((~member(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), image2(F!43, X!40))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), X!40, F!43), tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40))))))))))) <=> ((~![F: $i, A: $i, Y: $i] : (~((~((~member(Y, image2(F, A))) | (~((~member(tptp_fun_X_23(Y, A, F), A)) | (~apply(F, tptp_fun_X_23(Y, A, F), Y)))))) | (~(member(Y, image2(F, A)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))) | (~((~(member(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), image2(F!43, X!40)) | ![X: $i] : ((~member(X, X!40)) | (~apply(F!43, X, tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40))))))) | (~((~member(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), image2(F!43, X!40))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), X!40, F!43), tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)))))))))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(15,plain,
% 0.12/0.40 ((~((~((~member(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), image2(F!43, X!40))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), X!40, F!43), tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)))))))) | (~(member(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), image2(F!43, X!40)) | ![X: $i] : ((~member(X, X!40)) | (~apply(F!43, X, tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40))))))))) <=> (~((~(member(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), image2(F!43, X!40)) | ![X: $i] : ((~member(X, X!40)) | (~apply(F!43, X, tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40))))))) | (~((~member(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), image2(F!43, X!40))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), X!40, F!43), tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40))))))))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(16,plain,
% 0.12/0.40 (((~![F: $i, A: $i, Y: $i] : (~((~((~member(Y, image2(F, A))) | (~((~member(tptp_fun_X_23(Y, A, F), A)) | (~apply(F, tptp_fun_X_23(Y, A, F), Y)))))) | (~(member(Y, image2(F, A)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), image2(F!43, X!40))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), X!40, F!43), tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)))))))) | (~(member(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), image2(F!43, X!40)) | ![X: $i] : ((~member(X, X!40)) | (~apply(F!43, X, tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)))))))))) <=> ((~![F: $i, A: $i, Y: $i] : (~((~((~member(Y, image2(F, A))) | (~((~member(tptp_fun_X_23(Y, A, F), A)) | (~apply(F, tptp_fun_X_23(Y, A, F), Y)))))) | (~(member(Y, image2(F, A)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))) | (~((~(member(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), image2(F!43, X!40)) | ![X: $i] : ((~member(X, X!40)) | (~apply(F!43, X, tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40))))))) | (~((~member(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), image2(F!43, X!40))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), X!40, F!43), tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)))))))))))),
% 0.12/0.40 inference(monotonicity,[status(thm)],[15])).
% 0.12/0.40 tff(17,plain,
% 0.12/0.40 (((~![F: $i, A: $i, Y: $i] : (~((~((~member(Y, image2(F, A))) | (~((~member(tptp_fun_X_23(Y, A, F), A)) | (~apply(F, tptp_fun_X_23(Y, A, F), Y)))))) | (~(member(Y, image2(F, A)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), image2(F!43, X!40))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), X!40, F!43), tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)))))))) | (~(member(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), image2(F!43, X!40)) | ![X: $i] : ((~member(X, X!40)) | (~apply(F!43, X, tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)))))))))) <=> ((~![F: $i, A: $i, Y: $i] : (~((~((~member(Y, image2(F, A))) | (~((~member(tptp_fun_X_23(Y, A, F), A)) | (~apply(F, tptp_fun_X_23(Y, A, F), Y)))))) | (~(member(Y, image2(F, A)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))) | (~((~(member(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), image2(F!43, X!40)) | ![X: $i] : ((~member(X, X!40)) | (~apply(F!43, X, tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40))))))) | (~((~member(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), image2(F!43, X!40))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), X!40, F!43), tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)))))))))))),
% 0.12/0.40 inference(transitivity,[status(thm)],[16, 14])).
% 0.12/0.40 tff(18,plain,
% 0.12/0.40 ((~![F: $i, A: $i, Y: $i] : (~((~((~member(Y, image2(F, A))) | (~((~member(tptp_fun_X_23(Y, A, F), A)) | (~apply(F, tptp_fun_X_23(Y, A, F), Y)))))) | (~(member(Y, image2(F, A)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), image2(F!43, X!40))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), X!40, F!43), tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)))))))) | (~(member(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), image2(F!43, X!40)) | ![X: $i] : ((~member(X, X!40)) | (~apply(F!43, X, tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)))))))))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(19,plain,
% 0.12/0.40 ((~![F: $i, A: $i, Y: $i] : (~((~((~member(Y, image2(F, A))) | (~((~member(tptp_fun_X_23(Y, A, F), A)) | (~apply(F, tptp_fun_X_23(Y, A, F), Y)))))) | (~(member(Y, image2(F, A)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))) | (~((~(member(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), image2(F!43, X!40)) | ![X: $i] : ((~member(X, X!40)) | (~apply(F!43, X, tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40))))))) | (~((~member(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), image2(F!43, X!40))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), X!40, F!43), tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40))))))))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.12/0.40 tff(20,plain,
% 0.12/0.40 (~((~(member(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), image2(F!43, X!40)) | ![X: $i] : ((~member(X, X!40)) | (~apply(F!43, X, tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40))))))) | (~((~member(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), image2(F!43, X!40))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), X!40, F!43), tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)))))))))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[19, 13])).
% 0.12/0.40 tff(21,plain,
% 0.12/0.40 (((~(member(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), image2(F!43, X!40)) | ![X: $i] : ((~member(X, X!40)) | (~apply(F!43, X, tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40))))))) | (~((~member(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), image2(F!43, X!40))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), X!40, F!43), tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40))))))))) | ((~member(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), image2(F!43, X!40))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), X!40, F!43), tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)))))))),
% 0.12/0.40 inference(tautology,[status(thm)],[])).
% 0.12/0.40 tff(22,plain,
% 0.12/0.40 ((~member(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), image2(F!43, X!40))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), X!40, F!43), tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40))))))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[21, 20])).
% 0.12/0.40 tff(23,plain,
% 0.12/0.40 (^[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))))))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(24,plain,
% 0.12/0.40 (![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)))))))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[23])).
% 0.12/0.40 tff(25,plain,
% 0.12/0.40 (^[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))))))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(26,plain,
% 0.12/0.40 (![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)))))))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[25])).
% 0.12/0.40 tff(27,plain,
% 0.12/0.40 (![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)))))))),
% 0.12/0.40 inference(transitivity,[status(thm)],[26, 24])).
% 0.12/0.40 tff(28,plain,
% 0.12/0.40 (^[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)))))))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(29,plain,
% 0.12/0.40 (![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)))))))),
% 0.12/0.41 inference(quant_intro,[status(thm)],[28])).
% 0.12/0.41 tff(30,plain,
% 0.12/0.41 (![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)))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(31,plain,
% 0.12/0.41 (^[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))))),
% 0.12/0.41 inference(bind,[status(th)],[])).
% 0.12/0.41 tff(32,plain,
% 0.12/0.41 (![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)))),
% 0.12/0.41 inference(quant_intro,[status(thm)],[31])).
% 0.12/0.41 tff(33,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')).
% 0.12/0.41 tff(34,plain,
% 0.12/0.41 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.12/0.41 tff(35,plain,
% 0.12/0.41 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[34, 30])).
% 0.12/0.41 tff(36,plain,(
% 0.12/0.41 ![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)))))),
% 0.12/0.41 inference(skolemize,[status(sab)],[35])).
% 0.12/0.41 tff(37,plain,
% 0.12/0.41 (![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)))))))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[36, 29])).
% 0.12/0.41 tff(38,plain,
% 0.12/0.41 (![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)))))))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[37, 27])).
% 0.12/0.41 tff(39,plain,
% 0.12/0.41 ((~![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(image2(F!43, X!40), image2(F!43, Y!39))) | ![X: $i] : ((~member(X, image2(F!43, X!40))) | member(X, image2(F!43, Y!39))))) | (~(subset(image2(F!43, X!40), image2(F!43, Y!39)) | (~((~member(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), image2(F!43, X!40))) | member(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), image2(F!43, Y!39))))))))),
% 0.12/0.41 inference(quant_inst,[status(thm)],[])).
% 0.12/0.41 tff(40,plain,
% 0.12/0.41 (~((~((~subset(image2(F!43, X!40), image2(F!43, Y!39))) | ![X: $i] : ((~member(X, image2(F!43, X!40))) | member(X, image2(F!43, Y!39))))) | (~(subset(image2(F!43, X!40), image2(F!43, Y!39)) | (~((~member(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), image2(F!43, X!40))) | member(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), image2(F!43, Y!39)))))))),
% 0.12/0.41 inference(unit_resolution,[status(thm)],[39, 38])).
% 0.12/0.41 tff(41,plain,
% 0.12/0.41 (((~((~subset(image2(F!43, X!40), image2(F!43, Y!39))) | ![X: $i] : ((~member(X, image2(F!43, X!40))) | member(X, image2(F!43, Y!39))))) | (~(subset(image2(F!43, X!40), image2(F!43, Y!39)) | (~((~member(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), image2(F!43, X!40))) | member(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), image2(F!43, Y!39))))))) | (subset(image2(F!43, X!40), image2(F!43, Y!39)) | (~((~member(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), image2(F!43, X!40))) | member(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), image2(F!43, Y!39)))))),
% 0.12/0.41 inference(tautology,[status(thm)],[])).
% 0.12/0.41 tff(42,plain,
% 0.12/0.41 (subset(image2(F!43, X!40), image2(F!43, Y!39)) | (~((~member(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), image2(F!43, X!40))) | member(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), image2(F!43, Y!39))))),
% 0.12/0.41 inference(unit_resolution,[status(thm)],[41, 40])).
% 0.12/0.41 tff(43,plain,
% 0.12/0.41 ((~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((~(maps(F, A, B) & subset(X, A) & subset(Y, A) & subset(X, Y))) | subset(image2(F, X), image2(F, Y)))) <=> (~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((~(maps(F, A, B) & subset(X, A) & subset(Y, A) & subset(X, Y))) | subset(image2(F, X), image2(F, Y))))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(44,plain,
% 0.12/0.41 ((~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((((maps(F, A, B) & subset(X, A)) & subset(Y, A)) & subset(X, Y)) => subset(image2(F, X), image2(F, Y)))) <=> (~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((~(maps(F, A, B) & subset(X, A) & subset(Y, A) & subset(X, Y))) | subset(image2(F, X), image2(F, Y))))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(45,axiom,(~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((((maps(F, A, B) & subset(X, A)) & subset(Y, A)) & subset(X, Y)) => subset(image2(F, X), image2(F, Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','thIIa01')).
% 0.12/0.41 tff(46,plain,
% 0.12/0.41 (~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((~(maps(F, A, B) & subset(X, A) & subset(Y, A) & subset(X, Y))) | subset(image2(F, X), image2(F, Y)))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.12/0.41 tff(47,plain,
% 0.12/0.41 (~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((~(maps(F, A, B) & subset(X, A) & subset(Y, A) & subset(X, Y))) | subset(image2(F, X), image2(F, Y)))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[46, 43])).
% 0.12/0.41 tff(48,plain,
% 0.12/0.41 (~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((~(maps(F, A, B) & subset(X, A) & subset(Y, A) & subset(X, Y))) | subset(image2(F, X), image2(F, Y)))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[47, 43])).
% 0.12/0.41 tff(49,plain,
% 0.12/0.41 (~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((~(maps(F, A, B) & subset(X, A) & subset(Y, A) & subset(X, Y))) | subset(image2(F, X), image2(F, Y)))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[48, 43])).
% 0.12/0.41 tff(50,plain,(
% 0.12/0.41 ~((~(maps(F!43, A!42, B!41) & subset(X!40, A!42) & subset(Y!39, A!42) & subset(X!40, Y!39))) | subset(image2(F!43, X!40), image2(F!43, Y!39)))),
% 0.12/0.41 inference(skolemize,[status(sab)],[49])).
% 0.12/0.41 tff(51,plain,
% 0.12/0.41 (~subset(image2(F!43, X!40), image2(F!43, Y!39))),
% 0.12/0.41 inference(or_elim,[status(thm)],[50])).
% 0.12/0.41 tff(52,plain,
% 0.12/0.41 ((~(subset(image2(F!43, X!40), image2(F!43, Y!39)) | (~((~member(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), image2(F!43, X!40))) | member(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), image2(F!43, Y!39)))))) | subset(image2(F!43, X!40), image2(F!43, Y!39)) | (~((~member(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), image2(F!43, X!40))) | member(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), image2(F!43, Y!39))))),
% 0.12/0.41 inference(tautology,[status(thm)],[])).
% 0.12/0.41 tff(53,plain,
% 0.12/0.41 ((~(subset(image2(F!43, X!40), image2(F!43, Y!39)) | (~((~member(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), image2(F!43, X!40))) | member(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), image2(F!43, Y!39)))))) | (~((~member(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), image2(F!43, X!40))) | member(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), image2(F!43, Y!39))))),
% 0.12/0.41 inference(unit_resolution,[status(thm)],[52, 51])).
% 0.12/0.41 tff(54,plain,
% 0.12/0.41 (~((~member(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), image2(F!43, X!40))) | member(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), image2(F!43, Y!39)))),
% 0.12/0.41 inference(unit_resolution,[status(thm)],[53, 42])).
% 0.12/0.41 tff(55,plain,
% 0.12/0.41 (((~member(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), image2(F!43, X!40))) | member(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), image2(F!43, Y!39))) | member(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), image2(F!43, X!40))),
% 0.12/0.41 inference(tautology,[status(thm)],[])).
% 0.12/0.41 tff(56,plain,
% 0.12/0.41 (member(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), image2(F!43, X!40))),
% 0.12/0.41 inference(unit_resolution,[status(thm)],[55, 54])).
% 0.12/0.41 tff(57,plain,
% 0.12/0.41 ((~((~member(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), image2(F!43, X!40))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), X!40, F!43), tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)))))))) | (~member(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), image2(F!43, X!40))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), X!40, F!43), tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40))))))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(58,plain,
% 0.20/0.41 ((~((~member(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), image2(F!43, X!40))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), X!40, F!43), tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)))))))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), X!40, F!43), tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40))))))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[57, 56])).
% 0.20/0.41 tff(59,plain,
% 0.20/0.41 (~((~member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), X!40, F!43), tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)))))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[58, 22])).
% 0.20/0.41 tff(60,plain,
% 0.20/0.41 (((~member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), X!40, F!43), tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40))))) | apply(F!43, tptp_fun_X_23(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), X!40, F!43), tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(61,plain,
% 0.20/0.41 (apply(F!43, tptp_fun_X_23(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), X!40, F!43), tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[60, 59])).
% 0.20/0.41 tff(62,plain,
% 0.20/0.41 (((~![F: $i, A: $i, Y: $i] : (~((~((~member(Y, image2(F, A))) | (~((~member(tptp_fun_X_23(Y, A, F), A)) | (~apply(F, tptp_fun_X_23(Y, A, F), Y)))))) | (~(member(Y, image2(F, A)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))) | (~((~(member(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), image2(F!43, Y!39)) | ![X: $i] : ((~member(X, Y!39)) | (~apply(F!43, X, tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40))))))) | (~((~member(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), image2(F!43, Y!39))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), Y!39, F!43), tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40))))))))))) <=> ((~![F: $i, A: $i, Y: $i] : (~((~((~member(Y, image2(F, A))) | (~((~member(tptp_fun_X_23(Y, A, F), A)) | (~apply(F, tptp_fun_X_23(Y, A, F), Y)))))) | (~(member(Y, image2(F, A)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))) | (~((~(member(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), image2(F!43, Y!39)) | ![X: $i] : ((~member(X, Y!39)) | (~apply(F!43, X, tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40))))))) | (~((~member(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), image2(F!43, Y!39))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), Y!39, F!43), tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)))))))))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(63,plain,
% 0.20/0.41 ((~((~((~member(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), image2(F!43, Y!39))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), Y!39, F!43), tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)))))))) | (~(member(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), image2(F!43, Y!39)) | ![X: $i] : ((~member(X, Y!39)) | (~apply(F!43, X, tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40))))))))) <=> (~((~(member(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), image2(F!43, Y!39)) | ![X: $i] : ((~member(X, Y!39)) | (~apply(F!43, X, tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40))))))) | (~((~member(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), image2(F!43, Y!39))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), Y!39, F!43), tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40))))))))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(64,plain,
% 0.20/0.42 (((~![F: $i, A: $i, Y: $i] : (~((~((~member(Y, image2(F, A))) | (~((~member(tptp_fun_X_23(Y, A, F), A)) | (~apply(F, tptp_fun_X_23(Y, A, F), Y)))))) | (~(member(Y, image2(F, A)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), image2(F!43, Y!39))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), Y!39, F!43), tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)))))))) | (~(member(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), image2(F!43, Y!39)) | ![X: $i] : ((~member(X, Y!39)) | (~apply(F!43, X, tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)))))))))) <=> ((~![F: $i, A: $i, Y: $i] : (~((~((~member(Y, image2(F, A))) | (~((~member(tptp_fun_X_23(Y, A, F), A)) | (~apply(F, tptp_fun_X_23(Y, A, F), Y)))))) | (~(member(Y, image2(F, A)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))) | (~((~(member(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), image2(F!43, Y!39)) | ![X: $i] : ((~member(X, Y!39)) | (~apply(F!43, X, tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40))))))) | (~((~member(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), image2(F!43, Y!39))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), Y!39, F!43), tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)))))))))))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[63])).
% 0.20/0.42 tff(65,plain,
% 0.20/0.42 (((~![F: $i, A: $i, Y: $i] : (~((~((~member(Y, image2(F, A))) | (~((~member(tptp_fun_X_23(Y, A, F), A)) | (~apply(F, tptp_fun_X_23(Y, A, F), Y)))))) | (~(member(Y, image2(F, A)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), image2(F!43, Y!39))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), Y!39, F!43), tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)))))))) | (~(member(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), image2(F!43, Y!39)) | ![X: $i] : ((~member(X, Y!39)) | (~apply(F!43, X, tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)))))))))) <=> ((~![F: $i, A: $i, Y: $i] : (~((~((~member(Y, image2(F, A))) | (~((~member(tptp_fun_X_23(Y, A, F), A)) | (~apply(F, tptp_fun_X_23(Y, A, F), Y)))))) | (~(member(Y, image2(F, A)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))) | (~((~(member(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), image2(F!43, Y!39)) | ![X: $i] : ((~member(X, Y!39)) | (~apply(F!43, X, tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40))))))) | (~((~member(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), image2(F!43, Y!39))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), Y!39, F!43), tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)))))))))))),
% 0.20/0.42 inference(transitivity,[status(thm)],[64, 62])).
% 0.20/0.42 tff(66,plain,
% 0.20/0.42 ((~![F: $i, A: $i, Y: $i] : (~((~((~member(Y, image2(F, A))) | (~((~member(tptp_fun_X_23(Y, A, F), A)) | (~apply(F, tptp_fun_X_23(Y, A, F), Y)))))) | (~(member(Y, image2(F, A)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), image2(F!43, Y!39))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), Y!39, F!43), tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)))))))) | (~(member(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), image2(F!43, Y!39)) | ![X: $i] : ((~member(X, Y!39)) | (~apply(F!43, X, tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)))))))))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(67,plain,
% 0.20/0.42 ((~![F: $i, A: $i, Y: $i] : (~((~((~member(Y, image2(F, A))) | (~((~member(tptp_fun_X_23(Y, A, F), A)) | (~apply(F, tptp_fun_X_23(Y, A, F), Y)))))) | (~(member(Y, image2(F, A)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))) | (~((~(member(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), image2(F!43, Y!39)) | ![X: $i] : ((~member(X, Y!39)) | (~apply(F!43, X, tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40))))))) | (~((~member(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), image2(F!43, Y!39))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), Y!39, F!43), tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40))))))))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.20/0.42 tff(68,plain,
% 0.20/0.42 (~((~(member(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), image2(F!43, Y!39)) | ![X: $i] : ((~member(X, Y!39)) | (~apply(F!43, X, tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40))))))) | (~((~member(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), image2(F!43, Y!39))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), Y!39, F!43), tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)))))))))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[67, 13])).
% 0.20/0.42 tff(69,plain,
% 0.20/0.42 (((~(member(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), image2(F!43, Y!39)) | ![X: $i] : ((~member(X, Y!39)) | (~apply(F!43, X, tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40))))))) | (~((~member(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), image2(F!43, Y!39))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), Y!39, F!43), tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40))))))))) | (member(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), image2(F!43, Y!39)) | ![X: $i] : ((~member(X, Y!39)) | (~apply(F!43, X, tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40))))))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(70,plain,
% 0.20/0.42 (member(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), image2(F!43, Y!39)) | ![X: $i] : ((~member(X, Y!39)) | (~apply(F!43, X, tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)))))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[69, 68])).
% 0.20/0.42 tff(71,plain,
% 0.20/0.42 (((~member(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), image2(F!43, X!40))) | member(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), image2(F!43, Y!39))) | (~member(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), image2(F!43, Y!39)))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(72,plain,
% 0.20/0.42 (~member(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), image2(F!43, Y!39))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[71, 54])).
% 0.20/0.42 tff(73,plain,
% 0.20/0.43 ((~(member(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), image2(F!43, Y!39)) | ![X: $i] : ((~member(X, Y!39)) | (~apply(F!43, X, tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40))))))) | member(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), image2(F!43, Y!39)) | ![X: $i] : ((~member(X, Y!39)) | (~apply(F!43, X, tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)))))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(74,plain,
% 0.20/0.43 ((~(member(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), image2(F!43, Y!39)) | ![X: $i] : ((~member(X, Y!39)) | (~apply(F!43, X, tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40))))))) | ![X: $i] : ((~member(X, Y!39)) | (~apply(F!43, X, tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)))))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[73, 72])).
% 0.20/0.43 tff(75,plain,
% 0.20/0.43 (![X: $i] : ((~member(X, Y!39)) | (~apply(F!43, X, tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)))))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[74, 70])).
% 0.20/0.43 tff(76,plain,
% 0.20/0.43 (((~![X: $i] : ((~member(X, Y!39)) | (~apply(F!43, X, tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)))))) | ((~member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), X!40, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), X!40, F!43), tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)))))) <=> ((~![X: $i] : ((~member(X, Y!39)) | (~apply(F!43, X, tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)))))) | (~member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), X!40, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), X!40, F!43), tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(77,plain,
% 0.20/0.43 ((~![X: $i] : ((~member(X, Y!39)) | (~apply(F!43, X, tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)))))) | ((~member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), X!40, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), X!40, F!43), tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)))))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(78,plain,
% 0.20/0.43 ((~![X: $i] : ((~member(X, Y!39)) | (~apply(F!43, X, tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)))))) | (~member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), X!40, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), X!40, F!43), tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.20/0.43 tff(79,plain,
% 0.20/0.43 (~member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), X!40, F!43), Y!39)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[78, 75, 61])).
% 0.20/0.43 tff(80,plain,
% 0.20/0.43 (((~member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), X!40, F!43), tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40))))) | member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), X!40, F!43), X!40)),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(81,plain,
% 0.20/0.43 (member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), X!40, F!43), X!40)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[80, 59])).
% 0.20/0.43 tff(82,plain,
% 0.20/0.43 ((~![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!40, Y!39)) | ![X: $i] : ((~member(X, X!40)) | member(X, Y!39)))) | (~(subset(X!40, Y!39) | (~((~member(tptp_fun_X_0(Y!39, X!40), X!40)) | member(tptp_fun_X_0(Y!39, X!40), Y!39)))))))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(83,plain,
% 0.20/0.43 (~((~((~subset(X!40, Y!39)) | ![X: $i] : ((~member(X, X!40)) | member(X, Y!39)))) | (~(subset(X!40, Y!39) | (~((~member(tptp_fun_X_0(Y!39, X!40), X!40)) | member(tptp_fun_X_0(Y!39, X!40), Y!39))))))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[82, 38])).
% 0.20/0.43 tff(84,plain,
% 0.20/0.43 (((~((~subset(X!40, Y!39)) | ![X: $i] : ((~member(X, X!40)) | member(X, Y!39)))) | (~(subset(X!40, Y!39) | (~((~member(tptp_fun_X_0(Y!39, X!40), X!40)) | member(tptp_fun_X_0(Y!39, X!40), Y!39)))))) | ((~subset(X!40, Y!39)) | ![X: $i] : ((~member(X, X!40)) | member(X, Y!39)))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(85,plain,
% 0.20/0.43 ((~subset(X!40, Y!39)) | ![X: $i] : ((~member(X, X!40)) | member(X, Y!39))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[84, 83])).
% 0.20/0.43 tff(86,plain,
% 0.20/0.43 (maps(F!43, A!42, B!41) & subset(X!40, A!42) & subset(Y!39, A!42) & subset(X!40, Y!39)),
% 0.20/0.43 inference(or_elim,[status(thm)],[50])).
% 0.20/0.43 tff(87,plain,
% 0.20/0.43 (subset(X!40, Y!39)),
% 0.20/0.43 inference(and_elim,[status(thm)],[86])).
% 0.20/0.43 tff(88,plain,
% 0.20/0.43 ((~((~subset(X!40, Y!39)) | ![X: $i] : ((~member(X, X!40)) | member(X, Y!39)))) | (~subset(X!40, Y!39)) | ![X: $i] : ((~member(X, X!40)) | member(X, Y!39))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(89,plain,
% 0.20/0.43 ((~((~subset(X!40, Y!39)) | ![X: $i] : ((~member(X, X!40)) | member(X, Y!39)))) | ![X: $i] : ((~member(X, X!40)) | member(X, Y!39))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[88, 87])).
% 0.20/0.43 tff(90,plain,
% 0.20/0.43 (![X: $i] : ((~member(X, X!40)) | member(X, Y!39))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[89, 85])).
% 0.20/0.43 tff(91,plain,
% 0.20/0.43 (((~![X: $i] : ((~member(X, X!40)) | member(X, Y!39))) | ((~member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), X!40, F!43), X!40)) | member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), X!40, F!43), Y!39))) <=> ((~![X: $i] : ((~member(X, X!40)) | member(X, Y!39))) | (~member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), X!40, F!43), X!40)) | member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), X!40, F!43), Y!39))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(92,plain,
% 0.20/0.43 ((~![X: $i] : ((~member(X, X!40)) | member(X, Y!39))) | ((~member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), X!40, F!43), X!40)) | member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), X!40, F!43), Y!39))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(93,plain,
% 0.20/0.43 ((~![X: $i] : ((~member(X, X!40)) | member(X, Y!39))) | (~member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), X!40, F!43), X!40)) | member(tptp_fun_X_23(tptp_fun_X_0(image2(F!43, Y!39), image2(F!43, X!40)), X!40, F!43), Y!39)),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.20/0.43 tff(94,plain,
% 0.20/0.43 ($false),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[93, 90, 81, 79])).
% 0.20/0.43 % SZS output end Proof
% 0.20/0.43 % E exiting
%------------------------------------------------------------------------------