%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET753+4 : TPTP v9.0.0. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n008.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
% 0.11/0.12 % Problem : SET753+4 : TPTP v9.0.0. Bugfixed v2.2.1.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n008.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 05:40:48 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(apply_type, type, (
% 0.12/0.39 apply: ( $i * $i * $i ) > $o)).
% 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(intersection_type, type, (
% 0.12/0.39 intersection: ( $i * $i ) > $i)).
% 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_40_type, type, (
% 0.12/0.39 tptp_fun_X_40: $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(member_type, type, (
% 0.12/0.39 member: ( $i * $i ) > $o)).
% 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(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(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), image2(F!43, Y!39)) | ![X: $i] : ((~member(X, Y!39)) | (~apply(F!43, X, tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39)))))))) | (~((~member(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), image2(F!43, Y!39))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), Y!39, F!43), tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!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(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), image2(F!43, Y!39)) | ![X: $i] : ((~member(X, Y!39)) | (~apply(F!43, X, tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39)))))))) | (~((~member(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), image2(F!43, Y!39))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), Y!39, F!43), tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))))))))))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(15,plain,
% 0.12/0.39 ((~((~((~member(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), image2(F!43, Y!39))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), Y!39, F!43), tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))))))))) | (~(member(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), image2(F!43, Y!39)) | ![X: $i] : ((~member(X, Y!39)) | (~apply(F!43, X, tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39)))))))))) <=> (~((~(member(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), image2(F!43, Y!39)) | ![X: $i] : ((~member(X, Y!39)) | (~apply(F!43, X, tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39)))))))) | (~((~member(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), image2(F!43, Y!39))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), Y!39, F!43), tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39)))))))))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(16,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(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), image2(F!43, Y!39))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), Y!39, F!43), tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))))))))) | (~(member(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), image2(F!43, Y!39)) | ![X: $i] : ((~member(X, Y!39)) | (~apply(F!43, X, tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!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(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), image2(F!43, Y!39)) | ![X: $i] : ((~member(X, Y!39)) | (~apply(F!43, X, tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39)))))))) | (~((~member(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), image2(F!43, Y!39))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), Y!39, F!43), tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))))))))))))),
% 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(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), image2(F!43, Y!39))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), Y!39, F!43), tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))))))))) | (~(member(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), image2(F!43, Y!39)) | ![X: $i] : ((~member(X, Y!39)) | (~apply(F!43, X, tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!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(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), image2(F!43, Y!39)) | ![X: $i] : ((~member(X, Y!39)) | (~apply(F!43, X, tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39)))))))) | (~((~member(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), image2(F!43, Y!39))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), Y!39, F!43), tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))))))))))))),
% 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(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), image2(F!43, Y!39))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), Y!39, F!43), tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))))))))) | (~(member(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), image2(F!43, Y!39)) | ![X: $i] : ((~member(X, Y!39)) | (~apply(F!43, X, tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))))))))))),
% 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(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), image2(F!43, Y!39)) | ![X: $i] : ((~member(X, Y!39)) | (~apply(F!43, X, tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39)))))))) | (~((~member(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), image2(F!43, Y!39))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), Y!39, F!43), tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39)))))))))))),
% 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(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), image2(F!43, Y!39)) | ![X: $i] : ((~member(X, Y!39)) | (~apply(F!43, X, tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39)))))))) | (~((~member(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), image2(F!43, Y!39))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), Y!39, F!43), tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))))))))))),
% 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(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), image2(F!43, Y!39)) | ![X: $i] : ((~member(X, Y!39)) | (~apply(F!43, X, tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39)))))))) | (~((~member(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), image2(F!43, Y!39))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), Y!39, F!43), tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39)))))))))) | (member(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), image2(F!43, Y!39)) | ![X: $i] : ((~member(X, Y!39)) | (~apply(F!43, X, tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39)))))))),
% 0.12/0.40 inference(tautology,[status(thm)],[])).
% 0.12/0.40 tff(22,plain,
% 0.12/0.40 (member(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), image2(F!43, Y!39)) | ![X: $i] : ((~member(X, Y!39)) | (~apply(F!43, X, tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))))))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[21, 20])).
% 0.20/0.40 tff(23,assumption,((~(member(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), image2(F!43, X!40)) | ![X: $i] : ((~member(X, X!40)) | (~apply(F!43, X, tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39)))))))) | (~((~member(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), image2(F!43, X!40))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), X!40, F!43), tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39)))))))))), introduced(assumption)).
% 0.20/0.40 tff(24,plain,
% 0.20/0.40 (((~![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(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), image2(F!43, X!40)) | ![X: $i] : ((~member(X, X!40)) | (~apply(F!43, X, tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39)))))))) | (~((~member(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), image2(F!43, X!40))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), X!40, F!43), tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!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(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), image2(F!43, X!40)) | ![X: $i] : ((~member(X, X!40)) | (~apply(F!43, X, tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39)))))))) | (~((~member(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), image2(F!43, X!40))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), X!40, F!43), tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))))))))))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(25,plain,
% 0.20/0.40 ((~((~((~member(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), image2(F!43, X!40))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), X!40, F!43), tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))))))))) | (~(member(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), image2(F!43, X!40)) | ![X: $i] : ((~member(X, X!40)) | (~apply(F!43, X, tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39)))))))))) <=> (~((~(member(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), image2(F!43, X!40)) | ![X: $i] : ((~member(X, X!40)) | (~apply(F!43, X, tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39)))))))) | (~((~member(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), image2(F!43, X!40))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), X!40, F!43), tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39)))))))))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(26,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(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), image2(F!43, X!40))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), X!40, F!43), tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))))))))) | (~(member(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), image2(F!43, X!40)) | ![X: $i] : ((~member(X, X!40)) | (~apply(F!43, X, tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!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(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), image2(F!43, X!40)) | ![X: $i] : ((~member(X, X!40)) | (~apply(F!43, X, tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39)))))))) | (~((~member(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), image2(F!43, X!40))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), X!40, F!43), tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))))))))))))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[25])).
% 0.20/0.41 tff(27,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(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), image2(F!43, X!40))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), X!40, F!43), tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))))))))) | (~(member(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), image2(F!43, X!40)) | ![X: $i] : ((~member(X, X!40)) | (~apply(F!43, X, tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!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(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), image2(F!43, X!40)) | ![X: $i] : ((~member(X, X!40)) | (~apply(F!43, X, tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39)))))))) | (~((~member(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), image2(F!43, X!40))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), X!40, F!43), tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))))))))))))),
% 0.20/0.41 inference(transitivity,[status(thm)],[26, 24])).
% 0.20/0.41 tff(28,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(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), image2(F!43, X!40))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), X!40, F!43), tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))))))))) | (~(member(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), image2(F!43, X!40)) | ![X: $i] : ((~member(X, X!40)) | (~apply(F!43, X, tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))))))))))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(29,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(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), image2(F!43, X!40)) | ![X: $i] : ((~member(X, X!40)) | (~apply(F!43, X, tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39)))))))) | (~((~member(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), image2(F!43, X!40))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), X!40, F!43), tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39)))))))))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.20/0.41 tff(30,plain,
% 0.20/0.41 ($false),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[29, 13, 23])).
% 0.20/0.41 tff(31,plain,(~((~(member(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), image2(F!43, X!40)) | ![X: $i] : ((~member(X, X!40)) | (~apply(F!43, X, tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39)))))))) | (~((~member(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), image2(F!43, X!40))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), X!40, F!43), tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))))))))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.42 tff(32,plain,
% 0.20/0.42 (((~(member(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), image2(F!43, X!40)) | ![X: $i] : ((~member(X, X!40)) | (~apply(F!43, X, tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39)))))))) | (~((~member(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), image2(F!43, X!40))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), X!40, F!43), tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39)))))))))) | (member(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), image2(F!43, X!40)) | ![X: $i] : ((~member(X, X!40)) | (~apply(F!43, X, tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39)))))))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(33,plain,
% 0.20/0.42 (member(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), image2(F!43, X!40)) | ![X: $i] : ((~member(X, X!40)) | (~apply(F!43, X, tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))))))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[32, 31])).
% 0.20/0.42 tff(34,assumption,(![X: $i] : ((~member(X, X!40)) | (~apply(F!43, X, tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))))))), introduced(assumption)).
% 0.20/0.42 tff(35,plain,
% 0.20/0.42 (^[X: $i, A: $i, B: $i] : refl((~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B)))) <=> (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B)))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(36,plain,
% 0.20/0.42 (![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B)))) <=> ![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[35])).
% 0.20/0.42 tff(37,plain,
% 0.20/0.42 (^[X: $i, A: $i, B: $i] : trans(trans(monotonicity(rewrite((member(X, A) & member(X, B)) <=> (~((~member(X, A)) | (~member(X, B))))), ((member(X, intersection(A, B)) <=> (member(X, A) & member(X, B))) <=> (member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B))))))), rewrite((member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B))))) <=> (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))), ((member(X, intersection(A, B)) <=> (member(X, A) & member(X, B))) <=> (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B)))))), rewrite((~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B)))) <=> (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))), ((member(X, intersection(A, B)) <=> (member(X, A) & member(X, B))) <=> (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(38,plain,
% 0.20/0.42 (![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (member(X, A) & member(X, B))) <=> ![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[37])).
% 0.20/0.42 tff(39,plain,
% 0.20/0.42 (![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (member(X, A) & member(X, B))) <=> ![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (member(X, A) & member(X, B)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(40,axiom,(![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (member(X, A) & member(X, B)))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax','intersection')).
% 0.20/0.42 tff(41,plain,
% 0.20/0.42 (![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (member(X, A) & member(X, B)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.20/0.42 tff(42,plain,(
% 0.20/0.42 ![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (member(X, A) & member(X, B)))),
% 0.20/0.42 inference(skolemize,[status(sab)],[41])).
% 0.20/0.42 tff(43,plain,
% 0.20/0.42 (![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[42, 38])).
% 0.20/0.42 tff(44,plain,
% 0.20/0.42 (![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[43, 36])).
% 0.20/0.42 tff(45,plain,
% 0.20/0.42 ((~![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))) | (~(((~member(tptp_fun_X_23(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), intersection(X!40, Y!39), F!43), X!40)) | (~member(tptp_fun_X_23(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), intersection(X!40, Y!39), F!43), Y!39))) <=> member(tptp_fun_X_23(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), intersection(X!40, Y!39), F!43), intersection(X!40, Y!39))))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(46,plain,
% 0.20/0.42 (~(((~member(tptp_fun_X_23(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), intersection(X!40, Y!39), F!43), X!40)) | (~member(tptp_fun_X_23(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), intersection(X!40, Y!39), F!43), Y!39))) <=> member(tptp_fun_X_23(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), intersection(X!40, Y!39), F!43), intersection(X!40, Y!39)))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[45, 44])).
% 0.20/0.42 tff(47,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(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), image2(F!43, intersection(X!40, Y!39))) | ![X: $i] : ((~member(X, intersection(X!40, Y!39))) | (~apply(F!43, X, tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39)))))))) | (~((~member(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), image2(F!43, intersection(X!40, Y!39)))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), intersection(X!40, Y!39), F!43), intersection(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), intersection(X!40, Y!39), F!43), tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!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(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), image2(F!43, intersection(X!40, Y!39))) | ![X: $i] : ((~member(X, intersection(X!40, Y!39))) | (~apply(F!43, X, tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39)))))))) | (~((~member(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), image2(F!43, intersection(X!40, Y!39)))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), intersection(X!40, Y!39), F!43), intersection(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), intersection(X!40, Y!39), F!43), tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))))))))))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(48,plain,
% 0.20/0.42 ((~((~((~member(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), image2(F!43, intersection(X!40, Y!39)))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), intersection(X!40, Y!39), F!43), intersection(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), intersection(X!40, Y!39), F!43), tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))))))))) | (~(member(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), image2(F!43, intersection(X!40, Y!39))) | ![X: $i] : ((~member(X, intersection(X!40, Y!39))) | (~apply(F!43, X, tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39)))))))))) <=> (~((~(member(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), image2(F!43, intersection(X!40, Y!39))) | ![X: $i] : ((~member(X, intersection(X!40, Y!39))) | (~apply(F!43, X, tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39)))))))) | (~((~member(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), image2(F!43, intersection(X!40, Y!39)))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), intersection(X!40, Y!39), F!43), intersection(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), intersection(X!40, Y!39), F!43), tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39)))))))))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(49,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(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), image2(F!43, intersection(X!40, Y!39)))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), intersection(X!40, Y!39), F!43), intersection(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), intersection(X!40, Y!39), F!43), tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))))))))) | (~(member(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), image2(F!43, intersection(X!40, Y!39))) | ![X: $i] : ((~member(X, intersection(X!40, Y!39))) | (~apply(F!43, X, tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!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(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), image2(F!43, intersection(X!40, Y!39))) | ![X: $i] : ((~member(X, intersection(X!40, Y!39))) | (~apply(F!43, X, tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39)))))))) | (~((~member(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), image2(F!43, intersection(X!40, Y!39)))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), intersection(X!40, Y!39), F!43), intersection(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), intersection(X!40, Y!39), F!43), tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))))))))))))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[48])).
% 0.20/0.43 tff(50,plain,
% 0.20/0.43 (((~![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(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), image2(F!43, intersection(X!40, Y!39)))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), intersection(X!40, Y!39), F!43), intersection(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), intersection(X!40, Y!39), F!43), tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))))))))) | (~(member(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), image2(F!43, intersection(X!40, Y!39))) | ![X: $i] : ((~member(X, intersection(X!40, Y!39))) | (~apply(F!43, X, tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!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(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), image2(F!43, intersection(X!40, Y!39))) | ![X: $i] : ((~member(X, intersection(X!40, Y!39))) | (~apply(F!43, X, tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39)))))))) | (~((~member(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), image2(F!43, intersection(X!40, Y!39)))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), intersection(X!40, Y!39), F!43), intersection(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), intersection(X!40, Y!39), F!43), tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))))))))))))),
% 0.20/0.43 inference(transitivity,[status(thm)],[49, 47])).
% 0.20/0.43 tff(51,plain,
% 0.20/0.43 ((~![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(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), image2(F!43, intersection(X!40, Y!39)))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), intersection(X!40, Y!39), F!43), intersection(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), intersection(X!40, Y!39), F!43), tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))))))))) | (~(member(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), image2(F!43, intersection(X!40, Y!39))) | ![X: $i] : ((~member(X, intersection(X!40, Y!39))) | (~apply(F!43, X, tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))))))))))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(52,plain,
% 0.20/0.43 ((~![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(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), image2(F!43, intersection(X!40, Y!39))) | ![X: $i] : ((~member(X, intersection(X!40, Y!39))) | (~apply(F!43, X, tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39)))))))) | (~((~member(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), image2(F!43, intersection(X!40, Y!39)))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), intersection(X!40, Y!39), F!43), intersection(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), intersection(X!40, Y!39), F!43), tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39)))))))))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.20/0.43 tff(53,plain,
% 0.20/0.43 (~((~(member(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), image2(F!43, intersection(X!40, Y!39))) | ![X: $i] : ((~member(X, intersection(X!40, Y!39))) | (~apply(F!43, X, tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39)))))))) | (~((~member(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), image2(F!43, intersection(X!40, Y!39)))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), intersection(X!40, Y!39), F!43), intersection(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), intersection(X!40, Y!39), F!43), tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))))))))))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[52, 13])).
% 0.20/0.43 tff(54,plain,
% 0.20/0.43 (((~(member(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), image2(F!43, intersection(X!40, Y!39))) | ![X: $i] : ((~member(X, intersection(X!40, Y!39))) | (~apply(F!43, X, tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39)))))))) | (~((~member(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), image2(F!43, intersection(X!40, Y!39)))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), intersection(X!40, Y!39), F!43), intersection(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), intersection(X!40, Y!39), F!43), tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39)))))))))) | ((~member(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), image2(F!43, intersection(X!40, Y!39)))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), intersection(X!40, Y!39), F!43), intersection(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), intersection(X!40, Y!39), F!43), tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))))))))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(55,plain,
% 0.20/0.43 ((~member(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), image2(F!43, intersection(X!40, Y!39)))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), intersection(X!40, Y!39), F!43), intersection(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), intersection(X!40, Y!39), F!43), tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39)))))))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[54, 53])).
% 0.20/0.43 tff(56,plain,
% 0.20/0.43 (^[A: $i, B: $i] : refl((~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(57,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))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[56])).
% 0.20/0.43 tff(58,plain,
% 0.20/0.43 (^[A: $i, B: $i] : rewrite((~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(59,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))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[58])).
% 0.20/0.43 tff(60,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))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.20/0.44 inference(transitivity,[status(thm)],[59, 57])).
% 0.20/0.44 tff(61,plain,
% 0.20/0.44 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) <=> ((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))), rewrite((subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))) <=> (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))), ((((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> (((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))), rewrite((((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))), ((((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(62,plain,
% 0.20/0.44 (![A: $i, B: $i] : (((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[61])).
% 0.20/0.44 tff(63,plain,
% 0.20/0.44 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(64,plain,
% 0.20/0.44 (^[A: $i, B: $i] : rewrite((subset(A, B) <=> ![X: $i] : (member(X, A) => member(X, B))) <=> (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(65,plain,
% 0.20/0.44 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : (member(X, A) => member(X, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[64])).
% 0.20/0.44 tff(66,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')).
% 0.20/0.44 tff(67,plain,
% 0.20/0.44 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.20/0.44 tff(68,plain,
% 0.20/0.44 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[67, 63])).
% 0.20/0.44 tff(69,plain,(
% 0.20/0.44 ![A: $i, B: $i] : (((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))),
% 0.20/0.44 inference(skolemize,[status(sab)],[68])).
% 0.20/0.44 tff(70,plain,
% 0.20/0.44 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[69, 62])).
% 0.20/0.44 tff(71,plain,
% 0.20/0.44 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[70, 60])).
% 0.20/0.44 tff(72,plain,
% 0.20/0.44 ((~![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, intersection(X!40, Y!39)), intersection(image2(F!43, X!40), image2(F!43, Y!39)))) | ![X: $i] : ((~member(X, image2(F!43, intersection(X!40, Y!39)))) | member(X, intersection(image2(F!43, X!40), image2(F!43, Y!39)))))) | (~(subset(image2(F!43, intersection(X!40, Y!39)), intersection(image2(F!43, X!40), image2(F!43, Y!39))) | (~((~member(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), image2(F!43, intersection(X!40, Y!39)))) | member(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), intersection(image2(F!43, X!40), image2(F!43, Y!39)))))))))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(73,plain,
% 0.20/0.44 (~((~((~subset(image2(F!43, intersection(X!40, Y!39)), intersection(image2(F!43, X!40), image2(F!43, Y!39)))) | ![X: $i] : ((~member(X, image2(F!43, intersection(X!40, Y!39)))) | member(X, intersection(image2(F!43, X!40), image2(F!43, Y!39)))))) | (~(subset(image2(F!43, intersection(X!40, Y!39)), intersection(image2(F!43, X!40), image2(F!43, Y!39))) | (~((~member(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), image2(F!43, intersection(X!40, Y!39)))) | member(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), intersection(image2(F!43, X!40), image2(F!43, Y!39))))))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[72, 71])).
% 0.20/0.44 tff(74,plain,
% 0.20/0.44 (((~((~subset(image2(F!43, intersection(X!40, Y!39)), intersection(image2(F!43, X!40), image2(F!43, Y!39)))) | ![X: $i] : ((~member(X, image2(F!43, intersection(X!40, Y!39)))) | member(X, intersection(image2(F!43, X!40), image2(F!43, Y!39)))))) | (~(subset(image2(F!43, intersection(X!40, Y!39)), intersection(image2(F!43, X!40), image2(F!43, Y!39))) | (~((~member(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), image2(F!43, intersection(X!40, Y!39)))) | member(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), intersection(image2(F!43, X!40), image2(F!43, Y!39)))))))) | (subset(image2(F!43, intersection(X!40, Y!39)), intersection(image2(F!43, X!40), image2(F!43, Y!39))) | (~((~member(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), image2(F!43, intersection(X!40, Y!39)))) | member(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), intersection(image2(F!43, X!40), image2(F!43, Y!39))))))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(75,plain,
% 0.20/0.44 (subset(image2(F!43, intersection(X!40, Y!39)), intersection(image2(F!43, X!40), image2(F!43, Y!39))) | (~((~member(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), image2(F!43, intersection(X!40, Y!39)))) | member(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), intersection(image2(F!43, X!40), image2(F!43, Y!39)))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[74, 73])).
% 0.20/0.44 tff(76,plain,
% 0.20/0.44 ((~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((~(maps(F, A, B) & subset(X, A) & subset(Y, A))) | subset(image2(F, intersection(X, Y)), intersection(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(image2(F, intersection(X, Y)), intersection(image2(F, X), image2(F, Y)))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(77,plain,
% 0.20/0.44 ((~![F: $i, A: $i, B: $i, X: $i, Y: $i] : (((maps(F, A, B) & subset(X, A)) & subset(Y, A)) => subset(image2(F, intersection(X, Y)), intersection(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(image2(F, intersection(X, Y)), intersection(image2(F, X), image2(F, Y)))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(78,axiom,(~![F: $i, A: $i, B: $i, X: $i, Y: $i] : (((maps(F, A, B) & subset(X, A)) & subset(Y, A)) => subset(image2(F, intersection(X, Y)), intersection(image2(F, X), image2(F, Y))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','thIIa03')).
% 0.20/0.44 tff(79,plain,
% 0.20/0.44 (~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((~(maps(F, A, B) & subset(X, A) & subset(Y, A))) | subset(image2(F, intersection(X, Y)), intersection(image2(F, X), image2(F, Y))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.20/0.44 tff(80,plain,
% 0.20/0.44 (~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((~(maps(F, A, B) & subset(X, A) & subset(Y, A))) | subset(image2(F, intersection(X, Y)), intersection(image2(F, X), image2(F, Y))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[79, 76])).
% 0.20/0.44 tff(81,plain,
% 0.20/0.44 (~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((~(maps(F, A, B) & subset(X, A) & subset(Y, A))) | subset(image2(F, intersection(X, Y)), intersection(image2(F, X), image2(F, Y))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[80, 76])).
% 0.20/0.44 tff(82,plain,
% 0.20/0.44 (~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((~(maps(F, A, B) & subset(X, A) & subset(Y, A))) | subset(image2(F, intersection(X, Y)), intersection(image2(F, X), image2(F, Y))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[81, 76])).
% 0.20/0.44 tff(83,plain,(
% 0.20/0.44 ~((~(maps(F!43, A!42, B!41) & subset(X!40, A!42) & subset(Y!39, A!42))) | subset(image2(F!43, intersection(X!40, Y!39)), intersection(image2(F!43, X!40), image2(F!43, Y!39))))),
% 0.20/0.44 inference(skolemize,[status(sab)],[82])).
% 0.20/0.44 tff(84,plain,
% 0.20/0.44 (~subset(image2(F!43, intersection(X!40, Y!39)), intersection(image2(F!43, X!40), image2(F!43, Y!39)))),
% 0.20/0.44 inference(or_elim,[status(thm)],[83])).
% 0.20/0.44 tff(85,plain,
% 0.20/0.44 ((~(subset(image2(F!43, intersection(X!40, Y!39)), intersection(image2(F!43, X!40), image2(F!43, Y!39))) | (~((~member(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), image2(F!43, intersection(X!40, Y!39)))) | member(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), intersection(image2(F!43, X!40), image2(F!43, Y!39))))))) | subset(image2(F!43, intersection(X!40, Y!39)), intersection(image2(F!43, X!40), image2(F!43, Y!39))) | (~((~member(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), image2(F!43, intersection(X!40, Y!39)))) | member(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), intersection(image2(F!43, X!40), image2(F!43, Y!39)))))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(86,plain,
% 0.20/0.44 ((~(subset(image2(F!43, intersection(X!40, Y!39)), intersection(image2(F!43, X!40), image2(F!43, Y!39))) | (~((~member(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), image2(F!43, intersection(X!40, Y!39)))) | member(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), intersection(image2(F!43, X!40), image2(F!43, Y!39))))))) | (~((~member(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), image2(F!43, intersection(X!40, Y!39)))) | member(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), intersection(image2(F!43, X!40), image2(F!43, Y!39)))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[85, 84])).
% 0.20/0.44 tff(87,plain,
% 0.20/0.44 (~((~member(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), image2(F!43, intersection(X!40, Y!39)))) | member(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), intersection(image2(F!43, X!40), image2(F!43, Y!39))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[86, 75])).
% 0.20/0.44 tff(88,plain,
% 0.20/0.44 (((~member(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), image2(F!43, intersection(X!40, Y!39)))) | member(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), intersection(image2(F!43, X!40), image2(F!43, Y!39)))) | member(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), image2(F!43, intersection(X!40, Y!39)))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(89,plain,
% 0.20/0.45 (member(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), image2(F!43, intersection(X!40, Y!39)))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[88, 87])).
% 0.20/0.45 tff(90,plain,
% 0.20/0.45 ((~((~member(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), image2(F!43, intersection(X!40, Y!39)))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), intersection(X!40, Y!39), F!43), intersection(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), intersection(X!40, Y!39), F!43), tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))))))))) | (~member(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), image2(F!43, intersection(X!40, Y!39)))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), intersection(X!40, Y!39), F!43), intersection(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), intersection(X!40, Y!39), F!43), tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39)))))))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(91,plain,
% 0.20/0.45 ((~((~member(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), image2(F!43, intersection(X!40, Y!39)))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), intersection(X!40, Y!39), F!43), intersection(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), intersection(X!40, Y!39), F!43), tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))))))))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), intersection(X!40, Y!39), F!43), intersection(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), intersection(X!40, Y!39), F!43), tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39)))))))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[90, 89])).
% 0.20/0.45 tff(92,plain,
% 0.20/0.45 (~((~member(tptp_fun_X_23(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), intersection(X!40, Y!39), F!43), intersection(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), intersection(X!40, Y!39), F!43), tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))))))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[91, 55])).
% 0.20/0.45 tff(93,plain,
% 0.20/0.45 (((~member(tptp_fun_X_23(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), intersection(X!40, Y!39), F!43), intersection(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), intersection(X!40, Y!39), F!43), tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39)))))) | member(tptp_fun_X_23(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), intersection(X!40, Y!39), F!43), intersection(X!40, Y!39))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(94,plain,
% 0.20/0.45 (member(tptp_fun_X_23(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), intersection(X!40, Y!39), F!43), intersection(X!40, Y!39))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[93, 92])).
% 0.20/0.45 tff(95,plain,
% 0.20/0.45 ((((~member(tptp_fun_X_23(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), intersection(X!40, Y!39), F!43), X!40)) | (~member(tptp_fun_X_23(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), intersection(X!40, Y!39), F!43), Y!39))) <=> member(tptp_fun_X_23(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), intersection(X!40, Y!39), F!43), intersection(X!40, Y!39))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), intersection(X!40, Y!39), F!43), X!40)) | (~member(tptp_fun_X_23(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), intersection(X!40, Y!39), F!43), Y!39)))) | (~member(tptp_fun_X_23(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), intersection(X!40, Y!39), F!43), intersection(X!40, Y!39)))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(96,plain,
% 0.20/0.45 ((((~member(tptp_fun_X_23(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), intersection(X!40, Y!39), F!43), X!40)) | (~member(tptp_fun_X_23(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), intersection(X!40, Y!39), F!43), Y!39))) <=> member(tptp_fun_X_23(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), intersection(X!40, Y!39), F!43), intersection(X!40, Y!39))) | (~((~member(tptp_fun_X_23(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), intersection(X!40, Y!39), F!43), X!40)) | (~member(tptp_fun_X_23(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), intersection(X!40, Y!39), F!43), Y!39))))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[95, 94])).
% 0.20/0.45 tff(97,plain,
% 0.20/0.45 (~((~member(tptp_fun_X_23(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), intersection(X!40, Y!39), F!43), X!40)) | (~member(tptp_fun_X_23(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), intersection(X!40, Y!39), F!43), Y!39)))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[96, 46])).
% 0.20/0.45 tff(98,plain,
% 0.20/0.45 (((~member(tptp_fun_X_23(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), intersection(X!40, Y!39), F!43), X!40)) | (~member(tptp_fun_X_23(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), intersection(X!40, Y!39), F!43), Y!39))) | member(tptp_fun_X_23(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), intersection(X!40, Y!39), F!43), X!40)),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(99,plain,
% 0.20/0.45 (member(tptp_fun_X_23(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), intersection(X!40, Y!39), F!43), X!40)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[98, 97])).
% 0.20/0.45 tff(100,plain,
% 0.20/0.45 (((~member(tptp_fun_X_23(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), intersection(X!40, Y!39), F!43), intersection(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), intersection(X!40, Y!39), F!43), tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39)))))) | apply(F!43, tptp_fun_X_23(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), intersection(X!40, Y!39), F!43), tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))))),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(101,plain,
% 0.20/0.46 (apply(F!43, tptp_fun_X_23(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), intersection(X!40, Y!39), F!43), tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[100, 92])).
% 0.20/0.46 tff(102,plain,
% 0.20/0.46 (((~![X: $i] : ((~member(X, X!40)) | (~apply(F!43, X, tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))))))) | ((~member(tptp_fun_X_23(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), intersection(X!40, Y!39), F!43), X!40)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), intersection(X!40, Y!39), F!43), tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))))))) <=> ((~![X: $i] : ((~member(X, X!40)) | (~apply(F!43, X, tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))))))) | (~member(tptp_fun_X_23(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), intersection(X!40, Y!39), F!43), X!40)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), intersection(X!40, Y!39), F!43), tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(103,plain,
% 0.20/0.46 ((~![X: $i] : ((~member(X, X!40)) | (~apply(F!43, X, tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))))))) | ((~member(tptp_fun_X_23(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), intersection(X!40, Y!39), F!43), X!40)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), intersection(X!40, Y!39), F!43), tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))))))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(104,plain,
% 0.20/0.46 ((~![X: $i] : ((~member(X, X!40)) | (~apply(F!43, X, tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))))))) | (~member(tptp_fun_X_23(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), intersection(X!40, Y!39), F!43), X!40)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), intersection(X!40, Y!39), F!43), tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39)))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.20/0.46 tff(105,plain,
% 0.20/0.46 ($false),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[104, 101, 99, 34])).
% 0.20/0.46 tff(106,plain,(~![X: $i] : ((~member(X, X!40)) | (~apply(F!43, X, tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.46 tff(107,plain,
% 0.20/0.46 ((~(member(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), image2(F!43, X!40)) | ![X: $i] : ((~member(X, X!40)) | (~apply(F!43, X, tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39)))))))) | member(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), image2(F!43, X!40)) | ![X: $i] : ((~member(X, X!40)) | (~apply(F!43, X, tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))))))),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(108,plain,
% 0.20/0.46 ((~(member(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), image2(F!43, X!40)) | ![X: $i] : ((~member(X, X!40)) | (~apply(F!43, X, tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39)))))))) | member(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), image2(F!43, X!40))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[107, 106])).
% 0.20/0.46 tff(109,plain,
% 0.20/0.46 (member(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), image2(F!43, X!40))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[108, 33])).
% 0.20/0.46 tff(110,plain,
% 0.20/0.46 ((~![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))) | (~(((~member(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), image2(F!43, X!40))) | (~member(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), image2(F!43, Y!39)))) <=> member(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), intersection(image2(F!43, X!40), image2(F!43, Y!39)))))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(111,plain,
% 0.20/0.46 (~(((~member(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), image2(F!43, X!40))) | (~member(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), image2(F!43, Y!39)))) <=> member(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), intersection(image2(F!43, X!40), image2(F!43, Y!39))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[110, 44])).
% 0.20/0.46 tff(112,plain,
% 0.20/0.46 (((~member(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), image2(F!43, intersection(X!40, Y!39)))) | member(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), intersection(image2(F!43, X!40), image2(F!43, Y!39)))) | (~member(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), intersection(image2(F!43, X!40), image2(F!43, Y!39))))),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(113,plain,
% 0.20/0.46 (~member(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), intersection(image2(F!43, X!40), image2(F!43, Y!39)))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[112, 87])).
% 0.20/0.46 tff(114,plain,
% 0.20/0.46 ((((~member(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), image2(F!43, X!40))) | (~member(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), image2(F!43, Y!39)))) <=> member(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), intersection(image2(F!43, X!40), image2(F!43, Y!39)))) | ((~member(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), image2(F!43, X!40))) | (~member(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), image2(F!43, Y!39)))) | member(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), intersection(image2(F!43, X!40), image2(F!43, Y!39)))),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(115,plain,
% 0.20/0.46 ((((~member(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), image2(F!43, X!40))) | (~member(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), image2(F!43, Y!39)))) <=> member(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), intersection(image2(F!43, X!40), image2(F!43, Y!39)))) | ((~member(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), image2(F!43, X!40))) | (~member(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), image2(F!43, Y!39))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[114, 113])).
% 0.20/0.46 tff(116,plain,
% 0.20/0.46 ((~member(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), image2(F!43, X!40))) | (~member(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), image2(F!43, Y!39)))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[115, 111])).
% 0.20/0.46 tff(117,plain,
% 0.20/0.46 ((~((~member(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), image2(F!43, X!40))) | (~member(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), image2(F!43, Y!39))))) | (~member(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), image2(F!43, X!40))) | (~member(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), image2(F!43, Y!39)))),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(118,plain,
% 0.20/0.46 ((~member(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), image2(F!43, X!40))) | (~member(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), image2(F!43, Y!39)))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[117, 116])).
% 0.20/0.46 tff(119,plain,
% 0.20/0.46 (~member(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), image2(F!43, Y!39))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[118, 109])).
% 0.20/0.46 tff(120,plain,
% 0.20/0.46 ((~(member(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), image2(F!43, Y!39)) | ![X: $i] : ((~member(X, Y!39)) | (~apply(F!43, X, tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39)))))))) | member(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), image2(F!43, Y!39)) | ![X: $i] : ((~member(X, Y!39)) | (~apply(F!43, X, tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))))))),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(121,plain,
% 0.20/0.46 ((~(member(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), image2(F!43, Y!39)) | ![X: $i] : ((~member(X, Y!39)) | (~apply(F!43, X, tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39)))))))) | ![X: $i] : ((~member(X, Y!39)) | (~apply(F!43, X, tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[120, 119])).
% 0.20/0.46 tff(122,plain,
% 0.20/0.46 (![X: $i] : ((~member(X, Y!39)) | (~apply(F!43, X, tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[121, 22])).
% 0.20/0.46 tff(123,plain,
% 0.20/0.46 (((~member(tptp_fun_X_23(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), intersection(X!40, Y!39), F!43), X!40)) | (~member(tptp_fun_X_23(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), intersection(X!40, Y!39), F!43), Y!39))) | member(tptp_fun_X_23(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), intersection(X!40, Y!39), F!43), Y!39)),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(124,plain,
% 0.20/0.47 (member(tptp_fun_X_23(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), intersection(X!40, Y!39), F!43), Y!39)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[123, 97])).
% 0.20/0.47 tff(125,plain,
% 0.20/0.47 (((~![X: $i] : ((~member(X, Y!39)) | (~apply(F!43, X, tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))))))) | ((~member(tptp_fun_X_23(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), intersection(X!40, Y!39), F!43), Y!39)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), intersection(X!40, Y!39), F!43), tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))))))) <=> ((~![X: $i] : ((~member(X, Y!39)) | (~apply(F!43, X, tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))))))) | (~member(tptp_fun_X_23(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), intersection(X!40, Y!39), F!43), Y!39)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), intersection(X!40, Y!39), F!43), tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(126,plain,
% 0.20/0.47 ((~![X: $i] : ((~member(X, Y!39)) | (~apply(F!43, X, tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))))))) | ((~member(tptp_fun_X_23(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), intersection(X!40, Y!39), F!43), Y!39)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), intersection(X!40, Y!39), F!43), tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))))))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(127,plain,
% 0.20/0.47 ((~![X: $i] : ((~member(X, Y!39)) | (~apply(F!43, X, tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))))))) | (~member(tptp_fun_X_23(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), intersection(X!40, Y!39), F!43), Y!39)) | (~apply(F!43, tptp_fun_X_23(tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39))), intersection(X!40, Y!39), F!43), tptp_fun_X_0(intersection(image2(F!43, X!40), image2(F!43, Y!39)), image2(F!43, intersection(X!40, Y!39)))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[126, 125])).
% 0.20/0.47 tff(128,plain,
% 0.20/0.47 ($false),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[127, 101, 124, 122])).
% 0.20/0.47 % SZS output end Proof
% 0.20/0.47 % E exiting
%------------------------------------------------------------------------------