%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET756+4 : TPTP v9.0.0. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n003.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 05:26:17 AM UTC 2025
% Result : Theorem 0.14s 0.42s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.14/0.14 % Problem : SET756+4 : TPTP v9.0.0. Bugfixed v2.2.1.
% 0.14/0.14 % Command : run_E %s %d THM
% 0.14/0.36 % Computer : n003.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Fri Jun 20 05:40:39 EDT 2025
% 0.14/0.36 % CPUTime :
% 0.14/0.42 % SZS status Theorem
% 0.14/0.42 % SZS output start Proof
% 0.14/0.42 tff(member_type, type, (
% 0.14/0.42 member: ( $i * $i ) > $o)).
% 0.14/0.42 tff(tptp_fun_Y_39_type, type, (
% 0.14/0.42 tptp_fun_Y_39: $i)).
% 0.14/0.42 tff(tptp_fun_Y_25_type, type, (
% 0.14/0.42 tptp_fun_Y_25: ( $i * $i * $i ) > $i)).
% 0.14/0.42 tff(tptp_fun_F_43_type, type, (
% 0.14/0.42 tptp_fun_F_43: $i)).
% 0.14/0.42 tff(tptp_fun_X_40_type, type, (
% 0.14/0.42 tptp_fun_X_40: $i)).
% 0.14/0.42 tff(tptp_fun_X_0_type, type, (
% 0.14/0.42 tptp_fun_X_0: ( $i * $i ) > $i)).
% 0.14/0.42 tff(union_type, type, (
% 0.14/0.42 union: ( $i * $i ) > $i)).
% 0.14/0.42 tff(inverse_image2_type, type, (
% 0.14/0.42 inverse_image2: ( $i * $i ) > $i)).
% 0.14/0.42 tff(apply_type, type, (
% 0.14/0.42 apply: ( $i * $i * $i ) > $o)).
% 0.14/0.42 tff(subset_type, type, (
% 0.14/0.42 subset: ( $i * $i ) > $o)).
% 0.14/0.42 tff(equal_set_type, type, (
% 0.14/0.42 equal_set: ( $i * $i ) > $o)).
% 0.14/0.42 tff(tptp_fun_B_41_type, type, (
% 0.14/0.42 tptp_fun_B_41: $i)).
% 0.14/0.42 tff(maps_type, type, (
% 0.14/0.42 maps: ( $i * $i * $i ) > $o)).
% 0.14/0.42 tff(tptp_fun_A_42_type, type, (
% 0.14/0.42 tptp_fun_A_42: $i)).
% 0.14/0.42 tff(1,plain,
% 0.14/0.42 (^[F: $i, B: $i, X: $i] : refl((~((~((~member(X, inverse_image2(F, B))) | (~((~member(tptp_fun_Y_25(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_25(X, B, F))))))) | (~(member(X, inverse_image2(F, B)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y))))))) <=> (~((~((~member(X, inverse_image2(F, B))) | (~((~member(tptp_fun_Y_25(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_25(X, B, F))))))) | (~(member(X, inverse_image2(F, B)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y))))))))),
% 0.14/0.42 inference(bind,[status(th)],[])).
% 0.14/0.42 tff(2,plain,
% 0.14/0.42 (![F: $i, B: $i, X: $i] : (~((~((~member(X, inverse_image2(F, B))) | (~((~member(tptp_fun_Y_25(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_25(X, B, F))))))) | (~(member(X, inverse_image2(F, B)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y))))))) <=> ![F: $i, B: $i, X: $i] : (~((~((~member(X, inverse_image2(F, B))) | (~((~member(tptp_fun_Y_25(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_25(X, B, F))))))) | (~(member(X, inverse_image2(F, B)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))),
% 0.14/0.42 inference(quant_intro,[status(thm)],[1])).
% 0.14/0.42 tff(3,plain,
% 0.14/0.42 (^[F: $i, B: $i, X: $i] : rewrite((~((~((~member(X, inverse_image2(F, B))) | (~((~member(tptp_fun_Y_25(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_25(X, B, F))))))) | (~(member(X, inverse_image2(F, B)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y))))))) <=> (~((~((~member(X, inverse_image2(F, B))) | (~((~member(tptp_fun_Y_25(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_25(X, B, F))))))) | (~(member(X, inverse_image2(F, B)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y))))))))),
% 0.14/0.42 inference(bind,[status(th)],[])).
% 0.14/0.42 tff(4,plain,
% 0.14/0.42 (![F: $i, B: $i, X: $i] : (~((~((~member(X, inverse_image2(F, B))) | (~((~member(tptp_fun_Y_25(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_25(X, B, F))))))) | (~(member(X, inverse_image2(F, B)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y))))))) <=> ![F: $i, B: $i, X: $i] : (~((~((~member(X, inverse_image2(F, B))) | (~((~member(tptp_fun_Y_25(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_25(X, B, F))))))) | (~(member(X, inverse_image2(F, B)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))),
% 0.14/0.42 inference(quant_intro,[status(thm)],[3])).
% 0.14/0.42 tff(5,plain,
% 0.14/0.42 (![F: $i, B: $i, X: $i] : (~((~((~member(X, inverse_image2(F, B))) | (~((~member(tptp_fun_Y_25(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_25(X, B, F))))))) | (~(member(X, inverse_image2(F, B)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y))))))) <=> ![F: $i, B: $i, X: $i] : (~((~((~member(X, inverse_image2(F, B))) | (~((~member(tptp_fun_Y_25(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_25(X, B, F))))))) | (~(member(X, inverse_image2(F, B)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))),
% 0.14/0.42 inference(transitivity,[status(thm)],[4, 2])).
% 0.14/0.42 tff(6,plain,
% 0.14/0.42 (^[F: $i, B: $i, X: $i] : trans(monotonicity(rewrite(((~member(X, inverse_image2(F, B))) | (member(tptp_fun_Y_25(X, B, F), B) & apply(F, X, tptp_fun_Y_25(X, B, F)))) <=> ((~member(X, inverse_image2(F, B))) | (~((~member(tptp_fun_Y_25(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_25(X, B, F))))))), rewrite((member(X, inverse_image2(F, B)) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y)))) <=> (member(X, inverse_image2(F, B)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y))))), ((((~member(X, inverse_image2(F, B))) | (member(tptp_fun_Y_25(X, B, F), B) & apply(F, X, tptp_fun_Y_25(X, B, F)))) & (member(X, inverse_image2(F, B)) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y))))) <=> (((~member(X, inverse_image2(F, B))) | (~((~member(tptp_fun_Y_25(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_25(X, B, F)))))) & (member(X, inverse_image2(F, B)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y))))))), rewrite((((~member(X, inverse_image2(F, B))) | (~((~member(tptp_fun_Y_25(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_25(X, B, F)))))) & (member(X, inverse_image2(F, B)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y))))) <=> (~((~((~member(X, inverse_image2(F, B))) | (~((~member(tptp_fun_Y_25(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_25(X, B, F))))))) | (~(member(X, inverse_image2(F, B)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))), ((((~member(X, inverse_image2(F, B))) | (member(tptp_fun_Y_25(X, B, F), B) & apply(F, X, tptp_fun_Y_25(X, B, F)))) & (member(X, inverse_image2(F, B)) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y))))) <=> (~((~((~member(X, inverse_image2(F, B))) | (~((~member(tptp_fun_Y_25(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_25(X, B, F))))))) | (~(member(X, inverse_image2(F, B)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))))),
% 0.14/0.43 inference(bind,[status(th)],[])).
% 0.14/0.43 tff(7,plain,
% 0.14/0.43 (![F: $i, B: $i, X: $i] : (((~member(X, inverse_image2(F, B))) | (member(tptp_fun_Y_25(X, B, F), B) & apply(F, X, tptp_fun_Y_25(X, B, F)))) & (member(X, inverse_image2(F, B)) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y))))) <=> ![F: $i, B: $i, X: $i] : (~((~((~member(X, inverse_image2(F, B))) | (~((~member(tptp_fun_Y_25(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_25(X, B, F))))))) | (~(member(X, inverse_image2(F, B)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))),
% 0.14/0.43 inference(quant_intro,[status(thm)],[6])).
% 0.14/0.43 tff(8,plain,
% 0.14/0.43 (![F: $i, B: $i, X: $i] : (member(X, inverse_image2(F, B)) <=> ?[Y: $i] : (member(Y, B) & apply(F, X, Y))) <=> ![F: $i, B: $i, X: $i] : (member(X, inverse_image2(F, B)) <=> ?[Y: $i] : (member(Y, B) & apply(F, X, Y)))),
% 0.14/0.43 inference(rewrite,[status(thm)],[])).
% 0.14/0.43 tff(9,axiom,(![F: $i, B: $i, X: $i] : (member(X, inverse_image2(F, B)) <=> ?[Y: $i] : (member(Y, B) & apply(F, X, Y)))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+1.ax','inverse_image2')).
% 0.14/0.43 tff(10,plain,
% 0.14/0.43 (![F: $i, B: $i, X: $i] : (member(X, inverse_image2(F, B)) <=> ?[Y: $i] : (member(Y, B) & apply(F, X, Y)))),
% 0.14/0.43 inference(modus_ponens,[status(thm)],[9, 8])).
% 0.14/0.43 tff(11,plain,(
% 0.14/0.43 ![F: $i, B: $i, X: $i] : (((~member(X, inverse_image2(F, B))) | (member(tptp_fun_Y_25(X, B, F), B) & apply(F, X, tptp_fun_Y_25(X, B, F)))) & (member(X, inverse_image2(F, B)) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y)))))),
% 0.14/0.43 inference(skolemize,[status(sab)],[10])).
% 0.14/0.43 tff(12,plain,
% 0.14/0.43 (![F: $i, B: $i, X: $i] : (~((~((~member(X, inverse_image2(F, B))) | (~((~member(tptp_fun_Y_25(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_25(X, B, F))))))) | (~(member(X, inverse_image2(F, B)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))),
% 0.14/0.43 inference(modus_ponens,[status(thm)],[11, 7])).
% 0.14/0.43 tff(13,plain,
% 0.14/0.43 (![F: $i, B: $i, X: $i] : (~((~((~member(X, inverse_image2(F, B))) | (~((~member(tptp_fun_Y_25(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_25(X, B, F))))))) | (~(member(X, inverse_image2(F, B)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))),
% 0.14/0.43 inference(modus_ponens,[status(thm)],[12, 5])).
% 0.14/0.43 tff(14,plain,
% 0.14/0.43 (((~![F: $i, B: $i, X: $i] : (~((~((~member(X, inverse_image2(F, B))) | (~((~member(tptp_fun_Y_25(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_25(X, B, F))))))) | (~(member(X, inverse_image2(F, B)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))) | (~((~(member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), inverse_image2(F!43, X!40)) | ![Y: $i] : ((~member(Y, X!40)) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), Y))))) | (~((~member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), inverse_image2(F!43, X!40))) | (~((~member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), X!40, F!43)))))))))) <=> ((~![F: $i, B: $i, X: $i] : (~((~((~member(X, inverse_image2(F, B))) | (~((~member(tptp_fun_Y_25(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_25(X, B, F))))))) | (~(member(X, inverse_image2(F, B)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))) | (~((~(member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), inverse_image2(F!43, X!40)) | ![Y: $i] : ((~member(Y, X!40)) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), Y))))) | (~((~member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), inverse_image2(F!43, X!40))) | (~((~member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), X!40, F!43))))))))))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(15,plain,
% 0.22/0.43 ((~((~((~member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), inverse_image2(F!43, X!40))) | (~((~member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), X!40, F!43))))))) | (~(member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), inverse_image2(F!43, X!40)) | ![Y: $i] : ((~member(Y, X!40)) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), Y))))))) <=> (~((~(member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), inverse_image2(F!43, X!40)) | ![Y: $i] : ((~member(Y, X!40)) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), Y))))) | (~((~member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), inverse_image2(F!43, X!40))) | (~((~member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), X!40, F!43)))))))))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(16,plain,
% 0.22/0.43 (((~![F: $i, B: $i, X: $i] : (~((~((~member(X, inverse_image2(F, B))) | (~((~member(tptp_fun_Y_25(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_25(X, B, F))))))) | (~(member(X, inverse_image2(F, B)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), inverse_image2(F!43, X!40))) | (~((~member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), X!40, F!43))))))) | (~(member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), inverse_image2(F!43, X!40)) | ![Y: $i] : ((~member(Y, X!40)) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), Y)))))))) <=> ((~![F: $i, B: $i, X: $i] : (~((~((~member(X, inverse_image2(F, B))) | (~((~member(tptp_fun_Y_25(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_25(X, B, F))))))) | (~(member(X, inverse_image2(F, B)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))) | (~((~(member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), inverse_image2(F!43, X!40)) | ![Y: $i] : ((~member(Y, X!40)) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), Y))))) | (~((~member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), inverse_image2(F!43, X!40))) | (~((~member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), X!40, F!43))))))))))),
% 0.22/0.43 inference(monotonicity,[status(thm)],[15])).
% 0.22/0.43 tff(17,plain,
% 0.22/0.43 (((~![F: $i, B: $i, X: $i] : (~((~((~member(X, inverse_image2(F, B))) | (~((~member(tptp_fun_Y_25(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_25(X, B, F))))))) | (~(member(X, inverse_image2(F, B)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), inverse_image2(F!43, X!40))) | (~((~member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), X!40, F!43))))))) | (~(member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), inverse_image2(F!43, X!40)) | ![Y: $i] : ((~member(Y, X!40)) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), Y)))))))) <=> ((~![F: $i, B: $i, X: $i] : (~((~((~member(X, inverse_image2(F, B))) | (~((~member(tptp_fun_Y_25(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_25(X, B, F))))))) | (~(member(X, inverse_image2(F, B)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))) | (~((~(member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), inverse_image2(F!43, X!40)) | ![Y: $i] : ((~member(Y, X!40)) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), Y))))) | (~((~member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), inverse_image2(F!43, X!40))) | (~((~member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), X!40, F!43))))))))))),
% 0.22/0.44 inference(transitivity,[status(thm)],[16, 14])).
% 0.22/0.44 tff(18,plain,
% 0.22/0.44 ((~![F: $i, B: $i, X: $i] : (~((~((~member(X, inverse_image2(F, B))) | (~((~member(tptp_fun_Y_25(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_25(X, B, F))))))) | (~(member(X, inverse_image2(F, B)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), inverse_image2(F!43, X!40))) | (~((~member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), X!40, F!43))))))) | (~(member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), inverse_image2(F!43, X!40)) | ![Y: $i] : ((~member(Y, X!40)) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), Y)))))))),
% 0.22/0.44 inference(quant_inst,[status(thm)],[])).
% 0.22/0.44 tff(19,plain,
% 0.22/0.44 ((~![F: $i, B: $i, X: $i] : (~((~((~member(X, inverse_image2(F, B))) | (~((~member(tptp_fun_Y_25(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_25(X, B, F))))))) | (~(member(X, inverse_image2(F, B)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))) | (~((~(member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), inverse_image2(F!43, X!40)) | ![Y: $i] : ((~member(Y, X!40)) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), Y))))) | (~((~member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), inverse_image2(F!43, X!40))) | (~((~member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), X!40, F!43)))))))))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.22/0.44 tff(20,plain,
% 0.22/0.44 (~((~(member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), inverse_image2(F!43, X!40)) | ![Y: $i] : ((~member(Y, X!40)) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), Y))))) | (~((~member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), inverse_image2(F!43, X!40))) | (~((~member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), X!40, F!43))))))))),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[19, 13])).
% 0.22/0.44 tff(21,plain,
% 0.22/0.44 (((~(member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), inverse_image2(F!43, X!40)) | ![Y: $i] : ((~member(Y, X!40)) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), Y))))) | (~((~member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), inverse_image2(F!43, X!40))) | (~((~member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), X!40, F!43)))))))) | ((~member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), inverse_image2(F!43, X!40))) | (~((~member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), X!40, F!43))))))),
% 0.22/0.44 inference(tautology,[status(thm)],[])).
% 0.22/0.44 tff(22,plain,
% 0.22/0.44 ((~member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), inverse_image2(F!43, X!40))) | (~((~member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), X!40, F!43)))))),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[21, 20])).
% 0.22/0.44 tff(23,assumption,((~(member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), inverse_image2(F!43, Y!39)) | ![Y: $i] : ((~member(Y, Y!39)) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), Y))))) | (~((~member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), inverse_image2(F!43, Y!39))) | (~((~member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), Y!39, F!43)))))))), introduced(assumption)).
% 0.22/0.44 tff(24,plain,
% 0.22/0.44 (((~![F: $i, B: $i, X: $i] : (~((~((~member(X, inverse_image2(F, B))) | (~((~member(tptp_fun_Y_25(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_25(X, B, F))))))) | (~(member(X, inverse_image2(F, B)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))) | (~((~(member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), inverse_image2(F!43, Y!39)) | ![Y: $i] : ((~member(Y, Y!39)) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), Y))))) | (~((~member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), inverse_image2(F!43, Y!39))) | (~((~member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), Y!39, F!43)))))))))) <=> ((~![F: $i, B: $i, X: $i] : (~((~((~member(X, inverse_image2(F, B))) | (~((~member(tptp_fun_Y_25(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_25(X, B, F))))))) | (~(member(X, inverse_image2(F, B)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))) | (~((~(member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), inverse_image2(F!43, Y!39)) | ![Y: $i] : ((~member(Y, Y!39)) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), Y))))) | (~((~member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), inverse_image2(F!43, Y!39))) | (~((~member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), Y!39, F!43))))))))))),
% 0.22/0.45 inference(rewrite,[status(thm)],[])).
% 0.22/0.45 tff(25,plain,
% 0.22/0.45 ((~((~((~member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), inverse_image2(F!43, Y!39))) | (~((~member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), Y!39, F!43))))))) | (~(member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), inverse_image2(F!43, Y!39)) | ![Y: $i] : ((~member(Y, Y!39)) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), Y))))))) <=> (~((~(member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), inverse_image2(F!43, Y!39)) | ![Y: $i] : ((~member(Y, Y!39)) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), Y))))) | (~((~member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), inverse_image2(F!43, Y!39))) | (~((~member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), Y!39, F!43)))))))))),
% 0.22/0.45 inference(rewrite,[status(thm)],[])).
% 0.22/0.45 tff(26,plain,
% 0.22/0.45 (((~![F: $i, B: $i, X: $i] : (~((~((~member(X, inverse_image2(F, B))) | (~((~member(tptp_fun_Y_25(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_25(X, B, F))))))) | (~(member(X, inverse_image2(F, B)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), inverse_image2(F!43, Y!39))) | (~((~member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), Y!39, F!43))))))) | (~(member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), inverse_image2(F!43, Y!39)) | ![Y: $i] : ((~member(Y, Y!39)) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), Y)))))))) <=> ((~![F: $i, B: $i, X: $i] : (~((~((~member(X, inverse_image2(F, B))) | (~((~member(tptp_fun_Y_25(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_25(X, B, F))))))) | (~(member(X, inverse_image2(F, B)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))) | (~((~(member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), inverse_image2(F!43, Y!39)) | ![Y: $i] : ((~member(Y, Y!39)) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), Y))))) | (~((~member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), inverse_image2(F!43, Y!39))) | (~((~member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), Y!39, F!43))))))))))),
% 0.22/0.45 inference(monotonicity,[status(thm)],[25])).
% 0.22/0.45 tff(27,plain,
% 0.22/0.45 (((~![F: $i, B: $i, X: $i] : (~((~((~member(X, inverse_image2(F, B))) | (~((~member(tptp_fun_Y_25(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_25(X, B, F))))))) | (~(member(X, inverse_image2(F, B)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), inverse_image2(F!43, Y!39))) | (~((~member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), Y!39, F!43))))))) | (~(member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), inverse_image2(F!43, Y!39)) | ![Y: $i] : ((~member(Y, Y!39)) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), Y)))))))) <=> ((~![F: $i, B: $i, X: $i] : (~((~((~member(X, inverse_image2(F, B))) | (~((~member(tptp_fun_Y_25(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_25(X, B, F))))))) | (~(member(X, inverse_image2(F, B)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))) | (~((~(member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), inverse_image2(F!43, Y!39)) | ![Y: $i] : ((~member(Y, Y!39)) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), Y))))) | (~((~member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), inverse_image2(F!43, Y!39))) | (~((~member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), Y!39, F!43))))))))))),
% 0.22/0.45 inference(transitivity,[status(thm)],[26, 24])).
% 0.22/0.45 tff(28,plain,
% 0.22/0.45 ((~![F: $i, B: $i, X: $i] : (~((~((~member(X, inverse_image2(F, B))) | (~((~member(tptp_fun_Y_25(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_25(X, B, F))))))) | (~(member(X, inverse_image2(F, B)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), inverse_image2(F!43, Y!39))) | (~((~member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), Y!39, F!43))))))) | (~(member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), inverse_image2(F!43, Y!39)) | ![Y: $i] : ((~member(Y, Y!39)) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), Y)))))))),
% 0.22/0.45 inference(quant_inst,[status(thm)],[])).
% 0.22/0.45 tff(29,plain,
% 0.22/0.45 ((~![F: $i, B: $i, X: $i] : (~((~((~member(X, inverse_image2(F, B))) | (~((~member(tptp_fun_Y_25(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_25(X, B, F))))))) | (~(member(X, inverse_image2(F, B)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))) | (~((~(member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), inverse_image2(F!43, Y!39)) | ![Y: $i] : ((~member(Y, Y!39)) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), Y))))) | (~((~member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), inverse_image2(F!43, Y!39))) | (~((~member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), Y!39, F!43)))))))))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.22/0.45 tff(30,plain,
% 0.22/0.45 ($false),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[29, 13, 23])).
% 0.22/0.45 tff(31,plain,(~((~(member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), inverse_image2(F!43, Y!39)) | ![Y: $i] : ((~member(Y, Y!39)) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), Y))))) | (~((~member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), inverse_image2(F!43, Y!39))) | (~((~member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), Y!39, F!43))))))))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.45 tff(32,plain,
% 0.22/0.45 (((~(member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), inverse_image2(F!43, Y!39)) | ![Y: $i] : ((~member(Y, Y!39)) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), Y))))) | (~((~member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), inverse_image2(F!43, Y!39))) | (~((~member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), Y!39, F!43)))))))) | ((~member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), inverse_image2(F!43, Y!39))) | (~((~member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), Y!39, F!43))))))),
% 0.22/0.46 inference(tautology,[status(thm)],[])).
% 0.22/0.46 tff(33,plain,
% 0.22/0.46 ((~member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), inverse_image2(F!43, Y!39))) | (~((~member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), Y!39, F!43)))))),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[32, 31])).
% 0.22/0.46 tff(34,assumption,(~((~member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), Y!39, F!43))))), introduced(assumption)).
% 0.22/0.46 tff(35,plain,
% 0.22/0.46 (((~member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), Y!39, F!43)))) | apply(F!43, tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), Y!39, F!43))),
% 0.22/0.46 inference(tautology,[status(thm)],[])).
% 0.22/0.46 tff(36,plain,
% 0.22/0.46 (apply(F!43, tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), Y!39, F!43))),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[35, 34])).
% 0.22/0.46 tff(37,plain,
% 0.22/0.46 (((~member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), Y!39, F!43)))) | member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), Y!39, F!43), Y!39)),
% 0.22/0.46 inference(tautology,[status(thm)],[])).
% 0.22/0.46 tff(38,plain,
% 0.22/0.46 (member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), Y!39, F!43), Y!39)),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[37, 34])).
% 0.22/0.46 tff(39,plain,
% 0.22/0.46 ((member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), Y!39, F!43), Y!39) | member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), Y!39, F!43), X!40)) | (~member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), Y!39, F!43), Y!39))),
% 0.22/0.46 inference(tautology,[status(thm)],[])).
% 0.22/0.46 tff(40,plain,
% 0.22/0.46 (member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), Y!39, F!43), Y!39) | member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), Y!39, F!43), X!40)),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[39, 38])).
% 0.22/0.46 tff(41,assumption,(~(member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), Y!39, F!43), union(X!40, Y!39)) <=> (member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), Y!39, F!43), Y!39) | member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), Y!39, F!43), X!40)))), introduced(assumption)).
% 0.22/0.46 tff(42,plain,
% 0.22/0.46 (^[X: $i, A: $i, B: $i] : refl((member(X, union(A, B)) <=> (member(X, B) | member(X, A))) <=> (member(X, union(A, B)) <=> (member(X, B) | member(X, A))))),
% 0.22/0.46 inference(bind,[status(th)],[])).
% 0.22/0.46 tff(43,plain,
% 0.22/0.46 (![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A))) <=> ![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 0.22/0.46 inference(quant_intro,[status(thm)],[42])).
% 0.22/0.46 tff(44,plain,
% 0.22/0.46 (![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A))) <=> ![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 0.22/0.46 inference(rewrite,[status(thm)],[])).
% 0.22/0.46 tff(45,plain,
% 0.22/0.46 (^[X: $i, A: $i, B: $i] : rewrite((member(X, union(A, B)) <=> (member(X, A) | member(X, B))) <=> (member(X, union(A, B)) <=> (member(X, B) | member(X, A))))),
% 0.22/0.46 inference(bind,[status(th)],[])).
% 0.22/0.46 tff(46,plain,
% 0.22/0.46 (![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, A) | member(X, B))) <=> ![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 0.22/0.46 inference(quant_intro,[status(thm)],[45])).
% 0.22/0.46 tff(47,axiom,(![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, A) | member(X, B)))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax','union')).
% 0.22/0.46 tff(48,plain,
% 0.22/0.46 (![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.22/0.46 tff(49,plain,
% 0.22/0.46 (![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[48, 44])).
% 0.22/0.46 tff(50,plain,(
% 0.22/0.46 ![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 0.22/0.46 inference(skolemize,[status(sab)],[49])).
% 0.22/0.46 tff(51,plain,
% 0.22/0.46 (![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[50, 43])).
% 0.22/0.46 tff(52,plain,
% 0.22/0.46 ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), Y!39, F!43), union(X!40, Y!39)) <=> (member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), Y!39, F!43), Y!39) | member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), Y!39, F!43), X!40)))),
% 0.22/0.46 inference(quant_inst,[status(thm)],[])).
% 0.22/0.46 tff(53,plain,
% 0.22/0.46 ($false),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[52, 51, 41])).
% 0.22/0.46 tff(54,plain,(member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), Y!39, F!43), union(X!40, Y!39)) <=> (member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), Y!39, F!43), Y!39) | member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), Y!39, F!43), X!40))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.46 tff(55,plain,
% 0.22/0.46 ((~(member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), Y!39, F!43), union(X!40, Y!39)) <=> (member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), Y!39, F!43), Y!39) | member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), Y!39, F!43), X!40)))) | member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), Y!39, F!43), union(X!40, Y!39)) | (~(member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), Y!39, F!43), Y!39) | member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), Y!39, F!43), X!40)))),
% 0.22/0.46 inference(tautology,[status(thm)],[])).
% 0.22/0.46 tff(56,plain,
% 0.22/0.46 (member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), Y!39, F!43), union(X!40, Y!39)) | (~(member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), Y!39, F!43), Y!39) | member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), Y!39, F!43), X!40)))),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[55, 54])).
% 0.22/0.46 tff(57,plain,
% 0.22/0.46 (member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), Y!39, F!43), union(X!40, Y!39))),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[56, 40])).
% 0.22/0.46 tff(58,plain,
% 0.22/0.46 (((~![F: $i, B: $i, X: $i] : (~((~((~member(X, inverse_image2(F, B))) | (~((~member(tptp_fun_Y_25(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_25(X, B, F))))))) | (~(member(X, inverse_image2(F, B)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))) | (~((~(member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), inverse_image2(F!43, union(X!40, Y!39))) | ![Y: $i] : ((~member(Y, union(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), Y))))) | (~((~member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), inverse_image2(F!43, union(X!40, Y!39)))) | (~((~member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), union(X!40, Y!39), F!43), union(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), union(X!40, Y!39), F!43)))))))))) <=> ((~![F: $i, B: $i, X: $i] : (~((~((~member(X, inverse_image2(F, B))) | (~((~member(tptp_fun_Y_25(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_25(X, B, F))))))) | (~(member(X, inverse_image2(F, B)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))) | (~((~(member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), inverse_image2(F!43, union(X!40, Y!39))) | ![Y: $i] : ((~member(Y, union(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), Y))))) | (~((~member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), inverse_image2(F!43, union(X!40, Y!39)))) | (~((~member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), union(X!40, Y!39), F!43), union(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), union(X!40, Y!39), F!43))))))))))),
% 0.22/0.47 inference(rewrite,[status(thm)],[])).
% 0.22/0.47 tff(59,plain,
% 0.22/0.47 ((~((~((~member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), inverse_image2(F!43, union(X!40, Y!39)))) | (~((~member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), union(X!40, Y!39), F!43), union(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), union(X!40, Y!39), F!43))))))) | (~(member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), inverse_image2(F!43, union(X!40, Y!39))) | ![Y: $i] : ((~member(Y, union(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), Y))))))) <=> (~((~(member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), inverse_image2(F!43, union(X!40, Y!39))) | ![Y: $i] : ((~member(Y, union(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), Y))))) | (~((~member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), inverse_image2(F!43, union(X!40, Y!39)))) | (~((~member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), union(X!40, Y!39), F!43), union(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), union(X!40, Y!39), F!43)))))))))),
% 0.22/0.47 inference(rewrite,[status(thm)],[])).
% 0.22/0.47 tff(60,plain,
% 0.22/0.47 (((~![F: $i, B: $i, X: $i] : (~((~((~member(X, inverse_image2(F, B))) | (~((~member(tptp_fun_Y_25(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_25(X, B, F))))))) | (~(member(X, inverse_image2(F, B)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), inverse_image2(F!43, union(X!40, Y!39)))) | (~((~member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), union(X!40, Y!39), F!43), union(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), union(X!40, Y!39), F!43))))))) | (~(member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), inverse_image2(F!43, union(X!40, Y!39))) | ![Y: $i] : ((~member(Y, union(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), Y)))))))) <=> ((~![F: $i, B: $i, X: $i] : (~((~((~member(X, inverse_image2(F, B))) | (~((~member(tptp_fun_Y_25(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_25(X, B, F))))))) | (~(member(X, inverse_image2(F, B)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))) | (~((~(member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), inverse_image2(F!43, union(X!40, Y!39))) | ![Y: $i] : ((~member(Y, union(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), Y))))) | (~((~member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), inverse_image2(F!43, union(X!40, Y!39)))) | (~((~member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), union(X!40, Y!39), F!43), union(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), union(X!40, Y!39), F!43))))))))))),
% 0.22/0.47 inference(monotonicity,[status(thm)],[59])).
% 0.22/0.47 tff(61,plain,
% 0.22/0.47 (((~![F: $i, B: $i, X: $i] : (~((~((~member(X, inverse_image2(F, B))) | (~((~member(tptp_fun_Y_25(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_25(X, B, F))))))) | (~(member(X, inverse_image2(F, B)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), inverse_image2(F!43, union(X!40, Y!39)))) | (~((~member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), union(X!40, Y!39), F!43), union(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), union(X!40, Y!39), F!43))))))) | (~(member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), inverse_image2(F!43, union(X!40, Y!39))) | ![Y: $i] : ((~member(Y, union(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), Y)))))))) <=> ((~![F: $i, B: $i, X: $i] : (~((~((~member(X, inverse_image2(F, B))) | (~((~member(tptp_fun_Y_25(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_25(X, B, F))))))) | (~(member(X, inverse_image2(F, B)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))) | (~((~(member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), inverse_image2(F!43, union(X!40, Y!39))) | ![Y: $i] : ((~member(Y, union(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), Y))))) | (~((~member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), inverse_image2(F!43, union(X!40, Y!39)))) | (~((~member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), union(X!40, Y!39), F!43), union(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), union(X!40, Y!39), F!43))))))))))),
% 0.22/0.48 inference(transitivity,[status(thm)],[60, 58])).
% 0.22/0.48 tff(62,plain,
% 0.22/0.48 ((~![F: $i, B: $i, X: $i] : (~((~((~member(X, inverse_image2(F, B))) | (~((~member(tptp_fun_Y_25(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_25(X, B, F))))))) | (~(member(X, inverse_image2(F, B)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), inverse_image2(F!43, union(X!40, Y!39)))) | (~((~member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), union(X!40, Y!39), F!43), union(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), union(X!40, Y!39), F!43))))))) | (~(member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), inverse_image2(F!43, union(X!40, Y!39))) | ![Y: $i] : ((~member(Y, union(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), Y)))))))),
% 0.22/0.48 inference(quant_inst,[status(thm)],[])).
% 0.22/0.48 tff(63,plain,
% 0.22/0.48 ((~![F: $i, B: $i, X: $i] : (~((~((~member(X, inverse_image2(F, B))) | (~((~member(tptp_fun_Y_25(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_25(X, B, F))))))) | (~(member(X, inverse_image2(F, B)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))) | (~((~(member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), inverse_image2(F!43, union(X!40, Y!39))) | ![Y: $i] : ((~member(Y, union(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), Y))))) | (~((~member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), inverse_image2(F!43, union(X!40, Y!39)))) | (~((~member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), union(X!40, Y!39), F!43), union(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), union(X!40, Y!39), F!43)))))))))),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.22/0.48 tff(64,plain,
% 0.22/0.48 (~((~(member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), inverse_image2(F!43, union(X!40, Y!39))) | ![Y: $i] : ((~member(Y, union(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), Y))))) | (~((~member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), inverse_image2(F!43, union(X!40, Y!39)))) | (~((~member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), union(X!40, Y!39), F!43), union(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), union(X!40, Y!39), F!43))))))))),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[63, 13])).
% 0.22/0.48 tff(65,plain,
% 0.22/0.48 (((~(member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), inverse_image2(F!43, union(X!40, Y!39))) | ![Y: $i] : ((~member(Y, union(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), Y))))) | (~((~member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), inverse_image2(F!43, union(X!40, Y!39)))) | (~((~member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), union(X!40, Y!39), F!43), union(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), union(X!40, Y!39), F!43)))))))) | (member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), inverse_image2(F!43, union(X!40, Y!39))) | ![Y: $i] : ((~member(Y, union(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), Y))))),
% 0.22/0.48 inference(tautology,[status(thm)],[])).
% 0.22/0.48 tff(66,plain,
% 0.22/0.48 (member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), inverse_image2(F!43, union(X!40, Y!39))) | ![Y: $i] : ((~member(Y, union(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), Y)))),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[65, 64])).
% 0.22/0.48 tff(67,plain,
% 0.22/0.48 (^[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))))))))),
% 0.22/0.48 inference(bind,[status(th)],[])).
% 0.22/0.48 tff(68,plain,
% 0.22/0.48 (![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)))))))),
% 0.22/0.48 inference(quant_intro,[status(thm)],[67])).
% 0.22/0.48 tff(69,plain,
% 0.22/0.48 (^[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))))))))),
% 0.22/0.48 inference(bind,[status(th)],[])).
% 0.22/0.48 tff(70,plain,
% 0.22/0.48 (![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)))))))),
% 0.22/0.48 inference(quant_intro,[status(thm)],[69])).
% 0.22/0.48 tff(71,plain,
% 0.22/0.48 (![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)))))))),
% 0.22/0.48 inference(transitivity,[status(thm)],[70, 68])).
% 0.22/0.48 tff(72,plain,
% 0.22/0.48 (^[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)))))))))),
% 0.22/0.48 inference(bind,[status(th)],[])).
% 0.22/0.48 tff(73,plain,
% 0.22/0.48 (![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)))))))),
% 0.22/0.48 inference(quant_intro,[status(thm)],[72])).
% 0.22/0.48 tff(74,plain,
% 0.22/0.48 (![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)))),
% 0.22/0.48 inference(rewrite,[status(thm)],[])).
% 0.22/0.48 tff(75,plain,
% 0.22/0.48 (^[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))))),
% 0.22/0.48 inference(bind,[status(th)],[])).
% 0.22/0.48 tff(76,plain,
% 0.22/0.48 (![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)))),
% 0.22/0.48 inference(quant_intro,[status(thm)],[75])).
% 0.22/0.48 tff(77,axiom,(![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : (member(X, A) => member(X, B)))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax','subset')).
% 0.22/0.48 tff(78,plain,
% 0.22/0.48 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.22/0.48 tff(79,plain,
% 0.22/0.48 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[78, 74])).
% 0.22/0.48 tff(80,plain,(
% 0.22/0.48 ![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)))))),
% 0.22/0.48 inference(skolemize,[status(sab)],[79])).
% 0.22/0.48 tff(81,plain,
% 0.22/0.48 (![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)))))))),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[80, 73])).
% 0.22/0.48 tff(82,plain,
% 0.22/0.48 (![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)))))))),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[81, 71])).
% 0.22/0.48 tff(83,plain,
% 0.22/0.48 ((~![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(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39)))) | ![X: $i] : ((~member(X, union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)))) | member(X, inverse_image2(F!43, union(X!40, Y!39)))))) | (~(subset(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))) | (~((~member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)))) | member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), inverse_image2(F!43, union(X!40, Y!39)))))))))),
% 0.22/0.48 inference(quant_inst,[status(thm)],[])).
% 0.22/0.48 tff(84,plain,
% 0.22/0.48 (~((~((~subset(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39)))) | ![X: $i] : ((~member(X, union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)))) | member(X, inverse_image2(F!43, union(X!40, Y!39)))))) | (~(subset(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))) | (~((~member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)))) | member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), inverse_image2(F!43, union(X!40, Y!39))))))))),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[83, 82])).
% 0.22/0.48 tff(85,plain,
% 0.22/0.48 (((~((~subset(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39)))) | ![X: $i] : ((~member(X, union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)))) | member(X, inverse_image2(F!43, union(X!40, Y!39)))))) | (~(subset(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))) | (~((~member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)))) | member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), inverse_image2(F!43, union(X!40, Y!39)))))))) | (subset(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))) | (~((~member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)))) | member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), inverse_image2(F!43, union(X!40, Y!39))))))),
% 0.22/0.48 inference(tautology,[status(thm)],[])).
% 0.22/0.48 tff(86,plain,
% 0.22/0.48 (subset(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))) | (~((~member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)))) | member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), inverse_image2(F!43, union(X!40, Y!39)))))),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[85, 84])).
% 0.22/0.48 tff(87,assumption,((~((~subset(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)))) | ![X: $i] : ((~member(X, inverse_image2(F!43, union(X!40, Y!39)))) | member(X, union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)))))) | (~(subset(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))) | (~((~member(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), inverse_image2(F!43, union(X!40, Y!39)))) | member(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)))))))), introduced(assumption)).
% 0.22/0.49 tff(88,plain,
% 0.22/0.49 ((~![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(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)))) | ![X: $i] : ((~member(X, inverse_image2(F!43, union(X!40, Y!39)))) | member(X, union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)))))) | (~(subset(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))) | (~((~member(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), inverse_image2(F!43, union(X!40, Y!39)))) | member(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)))))))))),
% 0.22/0.49 inference(quant_inst,[status(thm)],[])).
% 0.22/0.49 tff(89,plain,
% 0.22/0.49 ($false),
% 0.22/0.49 inference(unit_resolution,[status(thm)],[88, 82, 87])).
% 0.22/0.49 tff(90,plain,(~((~((~subset(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)))) | ![X: $i] : ((~member(X, inverse_image2(F!43, union(X!40, Y!39)))) | member(X, union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)))))) | (~(subset(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))) | (~((~member(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), inverse_image2(F!43, union(X!40, Y!39)))) | member(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))))))))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.49 tff(91,plain,
% 0.22/0.49 (((~((~subset(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)))) | ![X: $i] : ((~member(X, inverse_image2(F!43, union(X!40, Y!39)))) | member(X, union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)))))) | (~(subset(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))) | (~((~member(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), inverse_image2(F!43, union(X!40, Y!39)))) | member(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)))))))) | (subset(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))) | (~((~member(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), inverse_image2(F!43, union(X!40, Y!39)))) | member(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))))))),
% 0.22/0.49 inference(tautology,[status(thm)],[])).
% 0.22/0.49 tff(92,plain,
% 0.22/0.49 (subset(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))) | (~((~member(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), inverse_image2(F!43, union(X!40, Y!39)))) | member(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)))))),
% 0.22/0.49 inference(unit_resolution,[status(thm)],[91, 90])).
% 0.22/0.49 tff(93,plain,
% 0.22/0.49 ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_Y_25(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43), union(X!40, Y!39)) <=> (member(tptp_fun_Y_25(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43), Y!39) | member(tptp_fun_Y_25(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43), X!40)))),
% 0.22/0.49 inference(quant_inst,[status(thm)],[])).
% 0.22/0.49 tff(94,plain,
% 0.22/0.49 (member(tptp_fun_Y_25(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43), union(X!40, Y!39)) <=> (member(tptp_fun_Y_25(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43), Y!39) | member(tptp_fun_Y_25(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43), X!40))),
% 0.22/0.49 inference(unit_resolution,[status(thm)],[93, 51])).
% 0.22/0.49 tff(95,plain,
% 0.22/0.49 (((~![F: $i, B: $i, X: $i] : (~((~((~member(X, inverse_image2(F, B))) | (~((~member(tptp_fun_Y_25(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_25(X, B, F))))))) | (~(member(X, inverse_image2(F, B)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))) | (~((~(member(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), inverse_image2(F!43, union(X!40, Y!39))) | ![Y: $i] : ((~member(Y, union(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), Y))))) | (~((~member(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), inverse_image2(F!43, union(X!40, Y!39)))) | (~((~member(tptp_fun_Y_25(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43), union(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), tptp_fun_Y_25(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43)))))))))) <=> ((~![F: $i, B: $i, X: $i] : (~((~((~member(X, inverse_image2(F, B))) | (~((~member(tptp_fun_Y_25(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_25(X, B, F))))))) | (~(member(X, inverse_image2(F, B)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))) | (~((~(member(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), inverse_image2(F!43, union(X!40, Y!39))) | ![Y: $i] : ((~member(Y, union(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), Y))))) | (~((~member(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), inverse_image2(F!43, union(X!40, Y!39)))) | (~((~member(tptp_fun_Y_25(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43), union(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), tptp_fun_Y_25(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43))))))))))),
% 0.22/0.49 inference(rewrite,[status(thm)],[])).
% 0.22/0.49 tff(96,plain,
% 0.22/0.49 ((~((~((~member(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), inverse_image2(F!43, union(X!40, Y!39)))) | (~((~member(tptp_fun_Y_25(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43), union(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), tptp_fun_Y_25(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43))))))) | (~(member(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), inverse_image2(F!43, union(X!40, Y!39))) | ![Y: $i] : ((~member(Y, union(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), Y))))))) <=> (~((~(member(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), inverse_image2(F!43, union(X!40, Y!39))) | ![Y: $i] : ((~member(Y, union(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), Y))))) | (~((~member(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), inverse_image2(F!43, union(X!40, Y!39)))) | (~((~member(tptp_fun_Y_25(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43), union(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), tptp_fun_Y_25(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43)))))))))),
% 0.22/0.49 inference(rewrite,[status(thm)],[])).
% 0.22/0.49 tff(97,plain,
% 0.22/0.49 (((~![F: $i, B: $i, X: $i] : (~((~((~member(X, inverse_image2(F, B))) | (~((~member(tptp_fun_Y_25(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_25(X, B, F))))))) | (~(member(X, inverse_image2(F, B)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), inverse_image2(F!43, union(X!40, Y!39)))) | (~((~member(tptp_fun_Y_25(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43), union(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), tptp_fun_Y_25(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43))))))) | (~(member(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), inverse_image2(F!43, union(X!40, Y!39))) | ![Y: $i] : ((~member(Y, union(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), Y)))))))) <=> ((~![F: $i, B: $i, X: $i] : (~((~((~member(X, inverse_image2(F, B))) | (~((~member(tptp_fun_Y_25(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_25(X, B, F))))))) | (~(member(X, inverse_image2(F, B)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))) | (~((~(member(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), inverse_image2(F!43, union(X!40, Y!39))) | ![Y: $i] : ((~member(Y, union(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), Y))))) | (~((~member(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), inverse_image2(F!43, union(X!40, Y!39)))) | (~((~member(tptp_fun_Y_25(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43), union(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), tptp_fun_Y_25(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43))))))))))),
% 0.22/0.50 inference(monotonicity,[status(thm)],[96])).
% 0.22/0.50 tff(98,plain,
% 0.22/0.50 (((~![F: $i, B: $i, X: $i] : (~((~((~member(X, inverse_image2(F, B))) | (~((~member(tptp_fun_Y_25(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_25(X, B, F))))))) | (~(member(X, inverse_image2(F, B)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), inverse_image2(F!43, union(X!40, Y!39)))) | (~((~member(tptp_fun_Y_25(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43), union(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), tptp_fun_Y_25(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43))))))) | (~(member(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), inverse_image2(F!43, union(X!40, Y!39))) | ![Y: $i] : ((~member(Y, union(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), Y)))))))) <=> ((~![F: $i, B: $i, X: $i] : (~((~((~member(X, inverse_image2(F, B))) | (~((~member(tptp_fun_Y_25(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_25(X, B, F))))))) | (~(member(X, inverse_image2(F, B)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))) | (~((~(member(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), inverse_image2(F!43, union(X!40, Y!39))) | ![Y: $i] : ((~member(Y, union(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), Y))))) | (~((~member(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), inverse_image2(F!43, union(X!40, Y!39)))) | (~((~member(tptp_fun_Y_25(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43), union(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), tptp_fun_Y_25(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43))))))))))),
% 0.22/0.50 inference(transitivity,[status(thm)],[97, 95])).
% 0.22/0.50 tff(99,plain,
% 0.22/0.50 ((~![F: $i, B: $i, X: $i] : (~((~((~member(X, inverse_image2(F, B))) | (~((~member(tptp_fun_Y_25(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_25(X, B, F))))))) | (~(member(X, inverse_image2(F, B)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), inverse_image2(F!43, union(X!40, Y!39)))) | (~((~member(tptp_fun_Y_25(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43), union(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), tptp_fun_Y_25(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43))))))) | (~(member(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), inverse_image2(F!43, union(X!40, Y!39))) | ![Y: $i] : ((~member(Y, union(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), Y)))))))),
% 0.22/0.50 inference(quant_inst,[status(thm)],[])).
% 0.22/0.50 tff(100,plain,
% 0.22/0.50 ((~![F: $i, B: $i, X: $i] : (~((~((~member(X, inverse_image2(F, B))) | (~((~member(tptp_fun_Y_25(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_25(X, B, F))))))) | (~(member(X, inverse_image2(F, B)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))) | (~((~(member(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), inverse_image2(F!43, union(X!40, Y!39))) | ![Y: $i] : ((~member(Y, union(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), Y))))) | (~((~member(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), inverse_image2(F!43, union(X!40, Y!39)))) | (~((~member(tptp_fun_Y_25(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43), union(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), tptp_fun_Y_25(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43)))))))))),
% 0.22/0.50 inference(modus_ponens,[status(thm)],[99, 98])).
% 0.22/0.50 tff(101,plain,
% 0.22/0.50 (~((~(member(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), inverse_image2(F!43, union(X!40, Y!39))) | ![Y: $i] : ((~member(Y, union(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), Y))))) | (~((~member(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), inverse_image2(F!43, union(X!40, Y!39)))) | (~((~member(tptp_fun_Y_25(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43), union(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), tptp_fun_Y_25(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43))))))))),
% 0.22/0.50 inference(unit_resolution,[status(thm)],[100, 13])).
% 0.22/0.50 tff(102,plain,
% 0.22/0.50 (((~(member(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), inverse_image2(F!43, union(X!40, Y!39))) | ![Y: $i] : ((~member(Y, union(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), Y))))) | (~((~member(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), inverse_image2(F!43, union(X!40, Y!39)))) | (~((~member(tptp_fun_Y_25(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43), union(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), tptp_fun_Y_25(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43)))))))) | ((~member(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), inverse_image2(F!43, union(X!40, Y!39)))) | (~((~member(tptp_fun_Y_25(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43), union(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), tptp_fun_Y_25(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43))))))),
% 0.22/0.50 inference(tautology,[status(thm)],[])).
% 0.22/0.50 tff(103,plain,
% 0.22/0.50 ((~member(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), inverse_image2(F!43, union(X!40, Y!39)))) | (~((~member(tptp_fun_Y_25(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43), union(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), tptp_fun_Y_25(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43)))))),
% 0.22/0.50 inference(unit_resolution,[status(thm)],[102, 101])).
% 0.22/0.50 tff(104,assumption,(~((~member(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), inverse_image2(F!43, union(X!40, Y!39)))) | member(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))))), introduced(assumption)).
% 0.22/0.50 tff(105,plain,
% 0.22/0.50 (((~member(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), inverse_image2(F!43, union(X!40, Y!39)))) | member(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)))) | member(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), inverse_image2(F!43, union(X!40, Y!39)))),
% 0.22/0.50 inference(tautology,[status(thm)],[])).
% 0.22/0.50 tff(106,plain,
% 0.22/0.50 (member(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), inverse_image2(F!43, union(X!40, Y!39)))),
% 0.22/0.50 inference(unit_resolution,[status(thm)],[105, 104])).
% 0.22/0.50 tff(107,plain,
% 0.22/0.50 ((~((~member(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), inverse_image2(F!43, union(X!40, Y!39)))) | (~((~member(tptp_fun_Y_25(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43), union(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), tptp_fun_Y_25(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43))))))) | (~member(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), inverse_image2(F!43, union(X!40, Y!39)))) | (~((~member(tptp_fun_Y_25(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43), union(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), tptp_fun_Y_25(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43)))))),
% 0.22/0.50 inference(tautology,[status(thm)],[])).
% 0.22/0.50 tff(108,plain,
% 0.22/0.50 ((~((~member(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), inverse_image2(F!43, union(X!40, Y!39)))) | (~((~member(tptp_fun_Y_25(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43), union(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), tptp_fun_Y_25(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43))))))) | (~((~member(tptp_fun_Y_25(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43), union(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), tptp_fun_Y_25(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43)))))),
% 0.22/0.50 inference(unit_resolution,[status(thm)],[107, 106])).
% 0.22/0.50 tff(109,plain,
% 0.22/0.50 (~((~member(tptp_fun_Y_25(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43), union(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), tptp_fun_Y_25(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43))))),
% 0.22/0.50 inference(unit_resolution,[status(thm)],[108, 103])).
% 0.22/0.50 tff(110,plain,
% 0.22/0.50 (((~member(tptp_fun_Y_25(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43), union(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), tptp_fun_Y_25(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43)))) | member(tptp_fun_Y_25(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43), union(X!40, Y!39))),
% 0.22/0.50 inference(tautology,[status(thm)],[])).
% 0.22/0.50 tff(111,plain,
% 0.22/0.50 (member(tptp_fun_Y_25(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43), union(X!40, Y!39))),
% 0.22/0.50 inference(unit_resolution,[status(thm)],[110, 109])).
% 0.22/0.50 tff(112,plain,
% 0.22/0.50 ((~(member(tptp_fun_Y_25(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43), union(X!40, Y!39)) <=> (member(tptp_fun_Y_25(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43), Y!39) | member(tptp_fun_Y_25(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43), X!40)))) | (~member(tptp_fun_Y_25(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43), union(X!40, Y!39))) | (member(tptp_fun_Y_25(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43), Y!39) | member(tptp_fun_Y_25(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43), X!40))),
% 0.22/0.50 inference(tautology,[status(thm)],[])).
% 0.22/0.50 tff(113,plain,
% 0.22/0.50 ((~(member(tptp_fun_Y_25(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43), union(X!40, Y!39)) <=> (member(tptp_fun_Y_25(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43), Y!39) | member(tptp_fun_Y_25(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43), X!40)))) | (member(tptp_fun_Y_25(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43), Y!39) | member(tptp_fun_Y_25(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43), X!40))),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[112, 111])).
% 0.22/0.51 tff(114,plain,
% 0.22/0.51 (member(tptp_fun_Y_25(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43), Y!39) | member(tptp_fun_Y_25(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43), X!40)),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[113, 94])).
% 0.22/0.51 tff(115,plain,
% 0.22/0.51 (((~![F: $i, B: $i, X: $i] : (~((~((~member(X, inverse_image2(F, B))) | (~((~member(tptp_fun_Y_25(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_25(X, B, F))))))) | (~(member(X, inverse_image2(F, B)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))) | (~((~(member(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), inverse_image2(F!43, X!40)) | ![Y: $i] : ((~member(Y, X!40)) | (~apply(F!43, tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), Y))))) | (~((~member(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), inverse_image2(F!43, X!40))) | (~((~member(tptp_fun_Y_25(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), tptp_fun_Y_25(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), X!40, F!43)))))))))) <=> ((~![F: $i, B: $i, X: $i] : (~((~((~member(X, inverse_image2(F, B))) | (~((~member(tptp_fun_Y_25(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_25(X, B, F))))))) | (~(member(X, inverse_image2(F, B)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))) | (~((~(member(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), inverse_image2(F!43, X!40)) | ![Y: $i] : ((~member(Y, X!40)) | (~apply(F!43, tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), Y))))) | (~((~member(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), inverse_image2(F!43, X!40))) | (~((~member(tptp_fun_Y_25(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), tptp_fun_Y_25(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), X!40, F!43))))))))))),
% 0.22/0.51 inference(rewrite,[status(thm)],[])).
% 0.22/0.51 tff(116,plain,
% 0.22/0.51 ((~((~((~member(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), inverse_image2(F!43, X!40))) | (~((~member(tptp_fun_Y_25(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), tptp_fun_Y_25(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), X!40, F!43))))))) | (~(member(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), inverse_image2(F!43, X!40)) | ![Y: $i] : ((~member(Y, X!40)) | (~apply(F!43, tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), Y))))))) <=> (~((~(member(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), inverse_image2(F!43, X!40)) | ![Y: $i] : ((~member(Y, X!40)) | (~apply(F!43, tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), Y))))) | (~((~member(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), inverse_image2(F!43, X!40))) | (~((~member(tptp_fun_Y_25(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), tptp_fun_Y_25(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), X!40, F!43)))))))))),
% 0.22/0.51 inference(rewrite,[status(thm)],[])).
% 0.22/0.51 tff(117,plain,
% 0.22/0.51 (((~![F: $i, B: $i, X: $i] : (~((~((~member(X, inverse_image2(F, B))) | (~((~member(tptp_fun_Y_25(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_25(X, B, F))))))) | (~(member(X, inverse_image2(F, B)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), inverse_image2(F!43, X!40))) | (~((~member(tptp_fun_Y_25(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), tptp_fun_Y_25(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), X!40, F!43))))))) | (~(member(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), inverse_image2(F!43, X!40)) | ![Y: $i] : ((~member(Y, X!40)) | (~apply(F!43, tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), Y)))))))) <=> ((~![F: $i, B: $i, X: $i] : (~((~((~member(X, inverse_image2(F, B))) | (~((~member(tptp_fun_Y_25(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_25(X, B, F))))))) | (~(member(X, inverse_image2(F, B)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))) | (~((~(member(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), inverse_image2(F!43, X!40)) | ![Y: $i] : ((~member(Y, X!40)) | (~apply(F!43, tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), Y))))) | (~((~member(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), inverse_image2(F!43, X!40))) | (~((~member(tptp_fun_Y_25(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), tptp_fun_Y_25(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), X!40, F!43))))))))))),
% 0.22/0.51 inference(monotonicity,[status(thm)],[116])).
% 0.22/0.51 tff(118,plain,
% 0.22/0.51 (((~![F: $i, B: $i, X: $i] : (~((~((~member(X, inverse_image2(F, B))) | (~((~member(tptp_fun_Y_25(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_25(X, B, F))))))) | (~(member(X, inverse_image2(F, B)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), inverse_image2(F!43, X!40))) | (~((~member(tptp_fun_Y_25(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), tptp_fun_Y_25(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), X!40, F!43))))))) | (~(member(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), inverse_image2(F!43, X!40)) | ![Y: $i] : ((~member(Y, X!40)) | (~apply(F!43, tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), Y)))))))) <=> ((~![F: $i, B: $i, X: $i] : (~((~((~member(X, inverse_image2(F, B))) | (~((~member(tptp_fun_Y_25(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_25(X, B, F))))))) | (~(member(X, inverse_image2(F, B)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))) | (~((~(member(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), inverse_image2(F!43, X!40)) | ![Y: $i] : ((~member(Y, X!40)) | (~apply(F!43, tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), Y))))) | (~((~member(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), inverse_image2(F!43, X!40))) | (~((~member(tptp_fun_Y_25(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), tptp_fun_Y_25(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), X!40, F!43))))))))))),
% 0.22/0.51 inference(transitivity,[status(thm)],[117, 115])).
% 0.22/0.51 tff(119,plain,
% 0.22/0.51 ((~![F: $i, B: $i, X: $i] : (~((~((~member(X, inverse_image2(F, B))) | (~((~member(tptp_fun_Y_25(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_25(X, B, F))))))) | (~(member(X, inverse_image2(F, B)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), inverse_image2(F!43, X!40))) | (~((~member(tptp_fun_Y_25(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), tptp_fun_Y_25(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), X!40, F!43))))))) | (~(member(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), inverse_image2(F!43, X!40)) | ![Y: $i] : ((~member(Y, X!40)) | (~apply(F!43, tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), Y)))))))),
% 0.22/0.51 inference(quant_inst,[status(thm)],[])).
% 0.22/0.51 tff(120,plain,
% 0.22/0.51 ((~![F: $i, B: $i, X: $i] : (~((~((~member(X, inverse_image2(F, B))) | (~((~member(tptp_fun_Y_25(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_25(X, B, F))))))) | (~(member(X, inverse_image2(F, B)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))) | (~((~(member(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), inverse_image2(F!43, X!40)) | ![Y: $i] : ((~member(Y, X!40)) | (~apply(F!43, tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), Y))))) | (~((~member(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), inverse_image2(F!43, X!40))) | (~((~member(tptp_fun_Y_25(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), tptp_fun_Y_25(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), X!40, F!43)))))))))),
% 0.22/0.51 inference(modus_ponens,[status(thm)],[119, 118])).
% 0.22/0.51 tff(121,plain,
% 0.22/0.51 (~((~(member(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), inverse_image2(F!43, X!40)) | ![Y: $i] : ((~member(Y, X!40)) | (~apply(F!43, tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), Y))))) | (~((~member(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), inverse_image2(F!43, X!40))) | (~((~member(tptp_fun_Y_25(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), tptp_fun_Y_25(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), X!40, F!43))))))))),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[120, 13])).
% 0.22/0.51 tff(122,plain,
% 0.22/0.51 (((~(member(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), inverse_image2(F!43, X!40)) | ![Y: $i] : ((~member(Y, X!40)) | (~apply(F!43, tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), Y))))) | (~((~member(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), inverse_image2(F!43, X!40))) | (~((~member(tptp_fun_Y_25(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), tptp_fun_Y_25(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), X!40, F!43)))))))) | (member(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), inverse_image2(F!43, X!40)) | ![Y: $i] : ((~member(Y, X!40)) | (~apply(F!43, tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), Y))))),
% 0.22/0.51 inference(tautology,[status(thm)],[])).
% 0.22/0.51 tff(123,plain,
% 0.22/0.51 (member(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), inverse_image2(F!43, X!40)) | ![Y: $i] : ((~member(Y, X!40)) | (~apply(F!43, tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), Y)))),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[122, 121])).
% 0.22/0.51 tff(124,plain,
% 0.22/0.51 ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))) <=> (member(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), inverse_image2(F!43, Y!39)) | member(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), inverse_image2(F!43, X!40))))),
% 0.22/0.51 inference(quant_inst,[status(thm)],[])).
% 0.22/0.51 tff(125,plain,
% 0.22/0.51 (member(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))) <=> (member(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), inverse_image2(F!43, Y!39)) | member(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), inverse_image2(F!43, X!40)))),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[124, 51])).
% 0.22/0.51 tff(126,plain,
% 0.22/0.51 (((~member(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), inverse_image2(F!43, union(X!40, Y!39)))) | member(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)))) | (~member(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))))),
% 0.22/0.51 inference(tautology,[status(thm)],[])).
% 0.22/0.51 tff(127,plain,
% 0.22/0.51 (~member(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)))),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[126, 104])).
% 0.22/0.51 tff(128,plain,
% 0.22/0.51 ((~(member(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))) <=> (member(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), inverse_image2(F!43, Y!39)) | member(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), inverse_image2(F!43, X!40))))) | member(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))) | (~(member(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), inverse_image2(F!43, Y!39)) | member(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), inverse_image2(F!43, X!40))))),
% 0.22/0.51 inference(tautology,[status(thm)],[])).
% 0.22/0.51 tff(129,plain,
% 0.22/0.51 ((~(member(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))) <=> (member(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), inverse_image2(F!43, Y!39)) | member(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), inverse_image2(F!43, X!40))))) | (~(member(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), inverse_image2(F!43, Y!39)) | member(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), inverse_image2(F!43, X!40))))),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[128, 127])).
% 0.22/0.51 tff(130,plain,
% 0.22/0.51 (~(member(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), inverse_image2(F!43, Y!39)) | member(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), inverse_image2(F!43, X!40)))),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[129, 125])).
% 0.22/0.51 tff(131,plain,
% 0.22/0.51 ((member(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), inverse_image2(F!43, Y!39)) | member(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), inverse_image2(F!43, X!40))) | (~member(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), inverse_image2(F!43, X!40)))),
% 0.22/0.52 inference(tautology,[status(thm)],[])).
% 0.22/0.52 tff(132,plain,
% 0.22/0.52 (~member(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), inverse_image2(F!43, X!40))),
% 0.22/0.52 inference(unit_resolution,[status(thm)],[131, 130])).
% 0.22/0.52 tff(133,plain,
% 0.22/0.52 ((~(member(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), inverse_image2(F!43, X!40)) | ![Y: $i] : ((~member(Y, X!40)) | (~apply(F!43, tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), Y))))) | member(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), inverse_image2(F!43, X!40)) | ![Y: $i] : ((~member(Y, X!40)) | (~apply(F!43, tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), Y)))),
% 0.22/0.52 inference(tautology,[status(thm)],[])).
% 0.22/0.52 tff(134,plain,
% 0.22/0.52 ((~(member(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), inverse_image2(F!43, X!40)) | ![Y: $i] : ((~member(Y, X!40)) | (~apply(F!43, tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), Y))))) | ![Y: $i] : ((~member(Y, X!40)) | (~apply(F!43, tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), Y)))),
% 0.22/0.52 inference(unit_resolution,[status(thm)],[133, 132])).
% 0.22/0.52 tff(135,plain,
% 0.22/0.52 (![Y: $i] : ((~member(Y, X!40)) | (~apply(F!43, tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), Y)))),
% 0.22/0.52 inference(unit_resolution,[status(thm)],[134, 123])).
% 0.22/0.52 tff(136,plain,
% 0.22/0.52 (((~member(tptp_fun_Y_25(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43), union(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), tptp_fun_Y_25(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43)))) | apply(F!43, tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), tptp_fun_Y_25(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43))),
% 0.22/0.52 inference(tautology,[status(thm)],[])).
% 0.22/0.52 tff(137,plain,
% 0.22/0.52 (apply(F!43, tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), tptp_fun_Y_25(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43))),
% 0.22/0.52 inference(unit_resolution,[status(thm)],[136, 109])).
% 0.22/0.52 tff(138,plain,
% 0.22/0.52 (((~![Y: $i] : ((~member(Y, X!40)) | (~apply(F!43, tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), Y)))) | ((~member(tptp_fun_Y_25(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43), X!40)) | (~apply(F!43, tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), tptp_fun_Y_25(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43))))) <=> ((~![Y: $i] : ((~member(Y, X!40)) | (~apply(F!43, tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), Y)))) | (~member(tptp_fun_Y_25(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43), X!40)) | (~apply(F!43, tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), tptp_fun_Y_25(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43))))),
% 0.22/0.52 inference(rewrite,[status(thm)],[])).
% 0.22/0.52 tff(139,plain,
% 0.22/0.52 ((~![Y: $i] : ((~member(Y, X!40)) | (~apply(F!43, tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), Y)))) | ((~member(tptp_fun_Y_25(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43), X!40)) | (~apply(F!43, tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), tptp_fun_Y_25(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43))))),
% 0.22/0.52 inference(quant_inst,[status(thm)],[])).
% 0.22/0.52 tff(140,plain,
% 0.22/0.52 ((~![Y: $i] : ((~member(Y, X!40)) | (~apply(F!43, tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), Y)))) | (~member(tptp_fun_Y_25(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43), X!40)) | (~apply(F!43, tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), tptp_fun_Y_25(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43)))),
% 0.22/0.52 inference(modus_ponens,[status(thm)],[139, 138])).
% 0.22/0.52 tff(141,plain,
% 0.22/0.52 (~member(tptp_fun_Y_25(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43), X!40)),
% 0.22/0.52 inference(unit_resolution,[status(thm)],[140, 137, 135])).
% 0.22/0.52 tff(142,plain,
% 0.22/0.52 (((~![F: $i, B: $i, X: $i] : (~((~((~member(X, inverse_image2(F, B))) | (~((~member(tptp_fun_Y_25(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_25(X, B, F))))))) | (~(member(X, inverse_image2(F, B)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))) | (~((~(member(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), inverse_image2(F!43, Y!39)) | ![Y: $i] : ((~member(Y, Y!39)) | (~apply(F!43, tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), Y))))) | (~((~member(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), inverse_image2(F!43, Y!39))) | (~((~member(tptp_fun_Y_25(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), tptp_fun_Y_25(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), Y!39, F!43)))))))))) <=> ((~![F: $i, B: $i, X: $i] : (~((~((~member(X, inverse_image2(F, B))) | (~((~member(tptp_fun_Y_25(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_25(X, B, F))))))) | (~(member(X, inverse_image2(F, B)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))) | (~((~(member(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), inverse_image2(F!43, Y!39)) | ![Y: $i] : ((~member(Y, Y!39)) | (~apply(F!43, tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), Y))))) | (~((~member(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), inverse_image2(F!43, Y!39))) | (~((~member(tptp_fun_Y_25(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), tptp_fun_Y_25(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), Y!39, F!43))))))))))),
% 0.22/0.52 inference(rewrite,[status(thm)],[])).
% 0.22/0.52 tff(143,plain,
% 0.22/0.52 ((~((~((~member(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), inverse_image2(F!43, Y!39))) | (~((~member(tptp_fun_Y_25(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), tptp_fun_Y_25(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), Y!39, F!43))))))) | (~(member(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), inverse_image2(F!43, Y!39)) | ![Y: $i] : ((~member(Y, Y!39)) | (~apply(F!43, tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), Y))))))) <=> (~((~(member(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), inverse_image2(F!43, Y!39)) | ![Y: $i] : ((~member(Y, Y!39)) | (~apply(F!43, tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), Y))))) | (~((~member(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), inverse_image2(F!43, Y!39))) | (~((~member(tptp_fun_Y_25(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), tptp_fun_Y_25(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), Y!39, F!43)))))))))),
% 0.22/0.52 inference(rewrite,[status(thm)],[])).
% 0.22/0.52 tff(144,plain,
% 0.22/0.52 (((~![F: $i, B: $i, X: $i] : (~((~((~member(X, inverse_image2(F, B))) | (~((~member(tptp_fun_Y_25(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_25(X, B, F))))))) | (~(member(X, inverse_image2(F, B)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), inverse_image2(F!43, Y!39))) | (~((~member(tptp_fun_Y_25(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), tptp_fun_Y_25(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), Y!39, F!43))))))) | (~(member(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), inverse_image2(F!43, Y!39)) | ![Y: $i] : ((~member(Y, Y!39)) | (~apply(F!43, tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), Y)))))))) <=> ((~![F: $i, B: $i, X: $i] : (~((~((~member(X, inverse_image2(F, B))) | (~((~member(tptp_fun_Y_25(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_25(X, B, F))))))) | (~(member(X, inverse_image2(F, B)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))) | (~((~(member(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), inverse_image2(F!43, Y!39)) | ![Y: $i] : ((~member(Y, Y!39)) | (~apply(F!43, tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), Y))))) | (~((~member(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), inverse_image2(F!43, Y!39))) | (~((~member(tptp_fun_Y_25(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), tptp_fun_Y_25(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), Y!39, F!43))))))))))),
% 0.22/0.52 inference(monotonicity,[status(thm)],[143])).
% 0.22/0.52 tff(145,plain,
% 0.22/0.52 (((~![F: $i, B: $i, X: $i] : (~((~((~member(X, inverse_image2(F, B))) | (~((~member(tptp_fun_Y_25(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_25(X, B, F))))))) | (~(member(X, inverse_image2(F, B)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), inverse_image2(F!43, Y!39))) | (~((~member(tptp_fun_Y_25(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), tptp_fun_Y_25(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), Y!39, F!43))))))) | (~(member(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), inverse_image2(F!43, Y!39)) | ![Y: $i] : ((~member(Y, Y!39)) | (~apply(F!43, tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), Y)))))))) <=> ((~![F: $i, B: $i, X: $i] : (~((~((~member(X, inverse_image2(F, B))) | (~((~member(tptp_fun_Y_25(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_25(X, B, F))))))) | (~(member(X, inverse_image2(F, B)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))) | (~((~(member(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), inverse_image2(F!43, Y!39)) | ![Y: $i] : ((~member(Y, Y!39)) | (~apply(F!43, tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), Y))))) | (~((~member(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), inverse_image2(F!43, Y!39))) | (~((~member(tptp_fun_Y_25(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), tptp_fun_Y_25(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), Y!39, F!43))))))))))),
% 0.22/0.52 inference(transitivity,[status(thm)],[144, 142])).
% 0.22/0.52 tff(146,plain,
% 0.22/0.52 ((~![F: $i, B: $i, X: $i] : (~((~((~member(X, inverse_image2(F, B))) | (~((~member(tptp_fun_Y_25(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_25(X, B, F))))))) | (~(member(X, inverse_image2(F, B)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), inverse_image2(F!43, Y!39))) | (~((~member(tptp_fun_Y_25(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), tptp_fun_Y_25(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), Y!39, F!43))))))) | (~(member(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), inverse_image2(F!43, Y!39)) | ![Y: $i] : ((~member(Y, Y!39)) | (~apply(F!43, tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), Y)))))))),
% 0.22/0.53 inference(quant_inst,[status(thm)],[])).
% 0.22/0.53 tff(147,plain,
% 0.22/0.53 ((~![F: $i, B: $i, X: $i] : (~((~((~member(X, inverse_image2(F, B))) | (~((~member(tptp_fun_Y_25(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_25(X, B, F))))))) | (~(member(X, inverse_image2(F, B)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))) | (~((~(member(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), inverse_image2(F!43, Y!39)) | ![Y: $i] : ((~member(Y, Y!39)) | (~apply(F!43, tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), Y))))) | (~((~member(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), inverse_image2(F!43, Y!39))) | (~((~member(tptp_fun_Y_25(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), tptp_fun_Y_25(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), Y!39, F!43)))))))))),
% 0.22/0.53 inference(modus_ponens,[status(thm)],[146, 145])).
% 0.22/0.53 tff(148,plain,
% 0.22/0.53 (~((~(member(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), inverse_image2(F!43, Y!39)) | ![Y: $i] : ((~member(Y, Y!39)) | (~apply(F!43, tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), Y))))) | (~((~member(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), inverse_image2(F!43, Y!39))) | (~((~member(tptp_fun_Y_25(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), tptp_fun_Y_25(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), Y!39, F!43))))))))),
% 0.22/0.53 inference(unit_resolution,[status(thm)],[147, 13])).
% 0.22/0.53 tff(149,plain,
% 0.22/0.53 (((~(member(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), inverse_image2(F!43, Y!39)) | ![Y: $i] : ((~member(Y, Y!39)) | (~apply(F!43, tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), Y))))) | (~((~member(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), inverse_image2(F!43, Y!39))) | (~((~member(tptp_fun_Y_25(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), tptp_fun_Y_25(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), Y!39, F!43)))))))) | (member(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), inverse_image2(F!43, Y!39)) | ![Y: $i] : ((~member(Y, Y!39)) | (~apply(F!43, tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), Y))))),
% 0.22/0.53 inference(tautology,[status(thm)],[])).
% 0.22/0.53 tff(150,plain,
% 0.22/0.53 (member(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), inverse_image2(F!43, Y!39)) | ![Y: $i] : ((~member(Y, Y!39)) | (~apply(F!43, tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), Y)))),
% 0.22/0.53 inference(unit_resolution,[status(thm)],[149, 148])).
% 0.22/0.53 tff(151,plain,
% 0.22/0.53 ((member(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), inverse_image2(F!43, Y!39)) | member(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), inverse_image2(F!43, X!40))) | (~member(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), inverse_image2(F!43, Y!39)))),
% 0.22/0.53 inference(tautology,[status(thm)],[])).
% 0.22/0.53 tff(152,plain,
% 0.22/0.53 (~member(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), inverse_image2(F!43, Y!39))),
% 0.22/0.53 inference(unit_resolution,[status(thm)],[151, 130])).
% 0.22/0.53 tff(153,plain,
% 0.22/0.53 ((~(member(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), inverse_image2(F!43, Y!39)) | ![Y: $i] : ((~member(Y, Y!39)) | (~apply(F!43, tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), Y))))) | member(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), inverse_image2(F!43, Y!39)) | ![Y: $i] : ((~member(Y, Y!39)) | (~apply(F!43, tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), Y)))),
% 0.22/0.53 inference(tautology,[status(thm)],[])).
% 0.22/0.53 tff(154,plain,
% 0.22/0.53 ((~(member(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), inverse_image2(F!43, Y!39)) | ![Y: $i] : ((~member(Y, Y!39)) | (~apply(F!43, tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), Y))))) | ![Y: $i] : ((~member(Y, Y!39)) | (~apply(F!43, tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), Y)))),
% 0.22/0.53 inference(unit_resolution,[status(thm)],[153, 152])).
% 0.22/0.53 tff(155,plain,
% 0.22/0.53 (![Y: $i] : ((~member(Y, Y!39)) | (~apply(F!43, tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), Y)))),
% 0.22/0.53 inference(unit_resolution,[status(thm)],[154, 150])).
% 0.22/0.53 tff(156,plain,
% 0.22/0.53 (((~![Y: $i] : ((~member(Y, Y!39)) | (~apply(F!43, tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), Y)))) | ((~member(tptp_fun_Y_25(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43), Y!39)) | (~apply(F!43, tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), tptp_fun_Y_25(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43))))) <=> ((~![Y: $i] : ((~member(Y, Y!39)) | (~apply(F!43, tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), Y)))) | (~member(tptp_fun_Y_25(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43), Y!39)) | (~apply(F!43, tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), tptp_fun_Y_25(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43))))),
% 0.22/0.53 inference(rewrite,[status(thm)],[])).
% 0.22/0.53 tff(157,plain,
% 0.22/0.53 ((~![Y: $i] : ((~member(Y, Y!39)) | (~apply(F!43, tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), Y)))) | ((~member(tptp_fun_Y_25(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43), Y!39)) | (~apply(F!43, tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), tptp_fun_Y_25(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43))))),
% 0.22/0.53 inference(quant_inst,[status(thm)],[])).
% 0.22/0.53 tff(158,plain,
% 0.22/0.53 ((~![Y: $i] : ((~member(Y, Y!39)) | (~apply(F!43, tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), Y)))) | (~member(tptp_fun_Y_25(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43), Y!39)) | (~apply(F!43, tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), tptp_fun_Y_25(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43)))),
% 0.22/0.53 inference(modus_ponens,[status(thm)],[157, 156])).
% 0.22/0.53 tff(159,plain,
% 0.22/0.53 (~member(tptp_fun_Y_25(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43), Y!39)),
% 0.22/0.53 inference(unit_resolution,[status(thm)],[158, 137, 155])).
% 0.22/0.53 tff(160,plain,
% 0.22/0.53 ((~(member(tptp_fun_Y_25(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43), Y!39) | member(tptp_fun_Y_25(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43), X!40))) | member(tptp_fun_Y_25(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43), Y!39) | member(tptp_fun_Y_25(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), union(X!40, Y!39), F!43), X!40)),
% 0.22/0.53 inference(tautology,[status(thm)],[])).
% 0.22/0.53 tff(161,plain,
% 0.22/0.53 ($false),
% 0.22/0.53 inference(unit_resolution,[status(thm)],[160, 159, 141, 114])).
% 0.22/0.53 tff(162,plain,((~member(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), inverse_image2(F!43, union(X!40, Y!39)))) | member(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.53 tff(163,plain,
% 0.22/0.53 ((~(subset(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))) | (~((~member(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), inverse_image2(F!43, union(X!40, Y!39)))) | member(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))))))) | subset(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))) | (~((~member(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), inverse_image2(F!43, union(X!40, Y!39)))) | member(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)))))),
% 0.22/0.53 inference(tautology,[status(thm)],[])).
% 0.22/0.53 tff(164,plain,
% 0.22/0.53 ((~(subset(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))) | (~((~member(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), inverse_image2(F!43, union(X!40, Y!39)))) | member(tptp_fun_X_0(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))))))) | subset(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)))),
% 0.22/0.53 inference(unit_resolution,[status(thm)],[163, 162])).
% 0.22/0.53 tff(165,plain,
% 0.22/0.53 (subset(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)))),
% 0.22/0.53 inference(unit_resolution,[status(thm)],[164, 92])).
% 0.22/0.53 tff(166,plain,
% 0.22/0.53 (^[A: $i, B: $i] : refl((~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B))) <=> (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B))))),
% 0.22/0.53 inference(bind,[status(th)],[])).
% 0.22/0.53 tff(167,plain,
% 0.22/0.53 (![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B))) <=> ![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))),
% 0.22/0.53 inference(quant_intro,[status(thm)],[166])).
% 0.22/0.53 tff(168,plain,
% 0.22/0.53 (^[A: $i, B: $i] : trans(trans(monotonicity(rewrite((subset(A, B) & subset(B, A)) <=> (~((~subset(A, B)) | (~subset(B, A))))), ((equal_set(A, B) <=> (subset(A, B) & subset(B, A))) <=> (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A))))))), rewrite((equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A))))) <=> (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))), ((equal_set(A, B) <=> (subset(A, B) & subset(B, A))) <=> (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B))))), rewrite((~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B))) <=> (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))), ((equal_set(A, B) <=> (subset(A, B) & subset(B, A))) <=> (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))))),
% 0.22/0.53 inference(bind,[status(th)],[])).
% 0.22/0.53 tff(169,plain,
% 0.22/0.53 (![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A))) <=> ![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))),
% 0.22/0.53 inference(quant_intro,[status(thm)],[168])).
% 0.22/0.53 tff(170,plain,
% 0.22/0.53 (![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A))) <=> ![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 0.22/0.53 inference(rewrite,[status(thm)],[])).
% 0.22/0.53 tff(171,axiom,(![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax','equal_set')).
% 0.22/0.53 tff(172,plain,
% 0.22/0.53 (![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 0.22/0.53 inference(modus_ponens,[status(thm)],[171, 170])).
% 0.22/0.53 tff(173,plain,(
% 0.22/0.53 ![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 0.22/0.53 inference(skolemize,[status(sab)],[172])).
% 0.22/0.53 tff(174,plain,
% 0.22/0.53 (![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))),
% 0.22/0.53 inference(modus_ponens,[status(thm)],[173, 169])).
% 0.22/0.53 tff(175,plain,
% 0.22/0.53 (![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))),
% 0.22/0.53 inference(modus_ponens,[status(thm)],[174, 167])).
% 0.22/0.53 tff(176,plain,
% 0.22/0.53 ((~![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))) | (~(((~subset(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)))) | (~subset(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))))) <=> equal_set(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)))))),
% 0.22/0.53 inference(quant_inst,[status(thm)],[])).
% 0.22/0.53 tff(177,plain,
% 0.22/0.53 (~(((~subset(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)))) | (~subset(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))))) <=> equal_set(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))))),
% 0.22/0.53 inference(unit_resolution,[status(thm)],[176, 175])).
% 0.22/0.53 tff(178,plain,
% 0.22/0.53 ((~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((~(maps(F, A, B) & subset(X, B) & subset(Y, B))) | equal_set(inverse_image2(F, union(X, Y)), union(inverse_image2(F, X), inverse_image2(F, Y))))) <=> (~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((~(maps(F, A, B) & subset(X, B) & subset(Y, B))) | equal_set(inverse_image2(F, union(X, Y)), union(inverse_image2(F, X), inverse_image2(F, Y)))))),
% 0.22/0.53 inference(rewrite,[status(thm)],[])).
% 0.22/0.53 tff(179,plain,
% 0.22/0.53 ((~![F: $i, A: $i, B: $i, X: $i, Y: $i] : (((maps(F, A, B) & subset(X, B)) & subset(Y, B)) => equal_set(inverse_image2(F, union(X, Y)), union(inverse_image2(F, X), inverse_image2(F, Y))))) <=> (~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((~(maps(F, A, B) & subset(X, B) & subset(Y, B))) | equal_set(inverse_image2(F, union(X, Y)), union(inverse_image2(F, X), inverse_image2(F, Y)))))),
% 0.22/0.53 inference(rewrite,[status(thm)],[])).
% 0.22/0.53 tff(180,axiom,(~![F: $i, A: $i, B: $i, X: $i, Y: $i] : (((maps(F, A, B) & subset(X, B)) & subset(Y, B)) => equal_set(inverse_image2(F, union(X, Y)), union(inverse_image2(F, X), inverse_image2(F, Y))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thIIa06')).
% 0.22/0.53 tff(181,plain,
% 0.22/0.53 (~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((~(maps(F, A, B) & subset(X, B) & subset(Y, B))) | equal_set(inverse_image2(F, union(X, Y)), union(inverse_image2(F, X), inverse_image2(F, Y))))),
% 0.22/0.53 inference(modus_ponens,[status(thm)],[180, 179])).
% 0.22/0.53 tff(182,plain,
% 0.22/0.53 (~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((~(maps(F, A, B) & subset(X, B) & subset(Y, B))) | equal_set(inverse_image2(F, union(X, Y)), union(inverse_image2(F, X), inverse_image2(F, Y))))),
% 0.22/0.53 inference(modus_ponens,[status(thm)],[181, 178])).
% 0.22/0.53 tff(183,plain,
% 0.22/0.53 (~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((~(maps(F, A, B) & subset(X, B) & subset(Y, B))) | equal_set(inverse_image2(F, union(X, Y)), union(inverse_image2(F, X), inverse_image2(F, Y))))),
% 0.22/0.53 inference(modus_ponens,[status(thm)],[182, 178])).
% 0.22/0.53 tff(184,plain,
% 0.22/0.53 (~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((~(maps(F, A, B) & subset(X, B) & subset(Y, B))) | equal_set(inverse_image2(F, union(X, Y)), union(inverse_image2(F, X), inverse_image2(F, Y))))),
% 0.22/0.53 inference(modus_ponens,[status(thm)],[183, 178])).
% 0.22/0.53 tff(185,plain,(
% 0.22/0.53 ~((~(maps(F!43, A!42, B!41) & subset(X!40, B!41) & subset(Y!39, B!41))) | equal_set(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))))),
% 0.22/0.53 inference(skolemize,[status(sab)],[184])).
% 0.22/0.53 tff(186,plain,
% 0.22/0.53 (~equal_set(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)))),
% 0.22/0.53 inference(or_elim,[status(thm)],[185])).
% 0.22/0.53 tff(187,plain,
% 0.22/0.53 ((((~subset(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)))) | (~subset(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))))) <=> equal_set(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)))) | ((~subset(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)))) | (~subset(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))))) | equal_set(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)))),
% 0.22/0.53 inference(tautology,[status(thm)],[])).
% 0.22/0.53 tff(188,plain,
% 0.22/0.53 ((((~subset(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)))) | (~subset(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))))) <=> equal_set(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)))) | ((~subset(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)))) | (~subset(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39)))))),
% 0.22/0.53 inference(unit_resolution,[status(thm)],[187, 186])).
% 0.22/0.53 tff(189,plain,
% 0.22/0.53 ((~subset(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)))) | (~subset(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))))),
% 0.22/0.53 inference(unit_resolution,[status(thm)],[188, 177])).
% 0.22/0.53 tff(190,plain,
% 0.22/0.53 ((~((~subset(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)))) | (~subset(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39)))))) | (~subset(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)))) | (~subset(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))))),
% 0.22/0.53 inference(tautology,[status(thm)],[])).
% 0.22/0.53 tff(191,plain,
% 0.22/0.54 ((~subset(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)))) | (~subset(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))))),
% 0.22/0.54 inference(unit_resolution,[status(thm)],[190, 189])).
% 0.22/0.54 tff(192,plain,
% 0.22/0.54 (~subset(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39)))),
% 0.22/0.54 inference(unit_resolution,[status(thm)],[191, 165])).
% 0.22/0.54 tff(193,plain,
% 0.22/0.54 ((~(subset(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))) | (~((~member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)))) | member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), inverse_image2(F!43, union(X!40, Y!39))))))) | subset(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))) | (~((~member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)))) | member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), inverse_image2(F!43, union(X!40, Y!39)))))),
% 0.22/0.54 inference(tautology,[status(thm)],[])).
% 0.22/0.54 tff(194,plain,
% 0.22/0.54 ((~(subset(union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)), inverse_image2(F!43, union(X!40, Y!39))) | (~((~member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)))) | member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), inverse_image2(F!43, union(X!40, Y!39))))))) | (~((~member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)))) | member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), inverse_image2(F!43, union(X!40, Y!39)))))),
% 0.22/0.54 inference(unit_resolution,[status(thm)],[193, 192])).
% 0.22/0.54 tff(195,plain,
% 0.22/0.54 (~((~member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)))) | member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), inverse_image2(F!43, union(X!40, Y!39))))),
% 0.22/0.54 inference(unit_resolution,[status(thm)],[194, 86])).
% 0.22/0.54 tff(196,plain,
% 0.22/0.54 (((~member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)))) | member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), inverse_image2(F!43, union(X!40, Y!39)))) | (~member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), inverse_image2(F!43, union(X!40, Y!39))))),
% 0.22/0.54 inference(tautology,[status(thm)],[])).
% 0.22/0.54 tff(197,plain,
% 0.22/0.54 (~member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), inverse_image2(F!43, union(X!40, Y!39)))),
% 0.22/0.54 inference(unit_resolution,[status(thm)],[196, 195])).
% 0.22/0.54 tff(198,plain,
% 0.22/0.54 ((~(member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), inverse_image2(F!43, union(X!40, Y!39))) | ![Y: $i] : ((~member(Y, union(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), Y))))) | member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), inverse_image2(F!43, union(X!40, Y!39))) | ![Y: $i] : ((~member(Y, union(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), Y)))),
% 0.22/0.54 inference(tautology,[status(thm)],[])).
% 0.22/0.54 tff(199,plain,
% 0.22/0.54 ((~(member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), inverse_image2(F!43, union(X!40, Y!39))) | ![Y: $i] : ((~member(Y, union(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), Y))))) | ![Y: $i] : ((~member(Y, union(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), Y)))),
% 0.22/0.54 inference(unit_resolution,[status(thm)],[198, 197])).
% 0.22/0.54 tff(200,plain,
% 0.22/0.54 (![Y: $i] : ((~member(Y, union(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), Y)))),
% 0.22/0.54 inference(unit_resolution,[status(thm)],[199, 66])).
% 0.22/0.54 tff(201,plain,
% 0.22/0.54 (((~![Y: $i] : ((~member(Y, union(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), Y)))) | ((~member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), Y!39, F!43), union(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), Y!39, F!43))))) <=> ((~![Y: $i] : ((~member(Y, union(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), Y)))) | (~member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), Y!39, F!43), union(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), Y!39, F!43))))),
% 0.22/0.54 inference(rewrite,[status(thm)],[])).
% 0.22/0.54 tff(202,plain,
% 0.22/0.54 ((~![Y: $i] : ((~member(Y, union(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), Y)))) | ((~member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), Y!39, F!43), union(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), Y!39, F!43))))),
% 0.22/0.54 inference(quant_inst,[status(thm)],[])).
% 0.22/0.54 tff(203,plain,
% 0.22/0.54 ((~![Y: $i] : ((~member(Y, union(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), Y)))) | (~member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), Y!39, F!43), union(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), Y!39, F!43)))),
% 0.22/0.54 inference(modus_ponens,[status(thm)],[202, 201])).
% 0.22/0.54 tff(204,plain,
% 0.22/0.54 ($false),
% 0.22/0.54 inference(unit_resolution,[status(thm)],[203, 200, 57, 36])).
% 0.22/0.54 tff(205,plain,((~member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), Y!39, F!43)))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.54 tff(206,plain,
% 0.22/0.54 ((~((~member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), inverse_image2(F!43, Y!39))) | (~((~member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), Y!39, F!43))))))) | (~member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), inverse_image2(F!43, Y!39))) | (~((~member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), Y!39, F!43)))))),
% 0.22/0.54 inference(tautology,[status(thm)],[])).
% 0.22/0.54 tff(207,plain,
% 0.22/0.54 ((~((~member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), inverse_image2(F!43, Y!39))) | (~((~member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), Y!39, F!43))))))) | (~member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), inverse_image2(F!43, Y!39)))),
% 0.22/0.54 inference(unit_resolution,[status(thm)],[206, 205])).
% 0.22/0.54 tff(208,plain,
% 0.22/0.54 (~member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), inverse_image2(F!43, Y!39))),
% 0.22/0.54 inference(unit_resolution,[status(thm)],[207, 33])).
% 0.22/0.54 tff(209,plain,
% 0.22/0.54 ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))) <=> (member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), inverse_image2(F!43, Y!39)) | member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), inverse_image2(F!43, X!40))))),
% 0.22/0.54 inference(quant_inst,[status(thm)],[])).
% 0.22/0.54 tff(210,plain,
% 0.22/0.54 (member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))) <=> (member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), inverse_image2(F!43, Y!39)) | member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), inverse_image2(F!43, X!40)))),
% 0.22/0.54 inference(unit_resolution,[status(thm)],[209, 51])).
% 0.22/0.54 tff(211,plain,
% 0.22/0.54 (((~member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)))) | member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), inverse_image2(F!43, union(X!40, Y!39)))) | member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)))),
% 0.22/0.54 inference(tautology,[status(thm)],[])).
% 0.22/0.54 tff(212,plain,
% 0.22/0.54 (member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)))),
% 0.22/0.54 inference(unit_resolution,[status(thm)],[211, 195])).
% 0.22/0.54 tff(213,plain,
% 0.22/0.54 ((~(member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))) <=> (member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), inverse_image2(F!43, Y!39)) | member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), inverse_image2(F!43, X!40))))) | (~member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39)))) | (member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), inverse_image2(F!43, Y!39)) | member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), inverse_image2(F!43, X!40)))),
% 0.22/0.54 inference(tautology,[status(thm)],[])).
% 0.22/0.54 tff(214,plain,
% 0.22/0.54 ((~(member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))) <=> (member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), inverse_image2(F!43, Y!39)) | member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), inverse_image2(F!43, X!40))))) | (member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), inverse_image2(F!43, Y!39)) | member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), inverse_image2(F!43, X!40)))),
% 0.22/0.54 inference(unit_resolution,[status(thm)],[213, 212])).
% 0.22/0.54 tff(215,plain,
% 0.22/0.54 (member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), inverse_image2(F!43, Y!39)) | member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), inverse_image2(F!43, X!40))),
% 0.22/0.54 inference(unit_resolution,[status(thm)],[214, 210])).
% 0.22/0.54 tff(216,plain,
% 0.22/0.54 ((~(member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), inverse_image2(F!43, Y!39)) | member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), inverse_image2(F!43, X!40)))) | member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), inverse_image2(F!43, Y!39)) | member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), inverse_image2(F!43, X!40))),
% 0.22/0.54 inference(tautology,[status(thm)],[])).
% 0.22/0.54 tff(217,plain,
% 0.22/0.54 (member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), inverse_image2(F!43, Y!39)) | member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), inverse_image2(F!43, X!40))),
% 0.22/0.54 inference(unit_resolution,[status(thm)],[216, 215])).
% 0.22/0.54 tff(218,plain,
% 0.22/0.54 (member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), inverse_image2(F!43, X!40))),
% 0.22/0.54 inference(unit_resolution,[status(thm)],[217, 208])).
% 0.22/0.54 tff(219,plain,
% 0.22/0.54 ((~((~member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), inverse_image2(F!43, X!40))) | (~((~member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), X!40, F!43))))))) | (~member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), inverse_image2(F!43, X!40))) | (~((~member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), X!40, F!43)))))),
% 0.22/0.54 inference(tautology,[status(thm)],[])).
% 0.22/0.54 tff(220,plain,
% 0.22/0.54 ((~((~member(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), inverse_image2(F!43, X!40))) | (~((~member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), X!40, F!43))))))) | (~((~member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), X!40, F!43)))))),
% 0.22/0.54 inference(unit_resolution,[status(thm)],[219, 218])).
% 0.22/0.54 tff(221,plain,
% 0.22/0.54 (~((~member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), X!40, F!43))))),
% 0.22/0.55 inference(unit_resolution,[status(thm)],[220, 22])).
% 0.22/0.55 tff(222,plain,
% 0.22/0.55 (((~member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), X!40, F!43)))) | member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), X!40, F!43), X!40)),
% 0.22/0.55 inference(tautology,[status(thm)],[])).
% 0.22/0.55 tff(223,plain,
% 0.22/0.55 (member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), X!40, F!43), X!40)),
% 0.22/0.55 inference(unit_resolution,[status(thm)],[222, 221])).
% 0.22/0.55 tff(224,plain,
% 0.22/0.55 ((member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), X!40, F!43), X!40) | member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), X!40, F!43), Y!39)) | (~member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), X!40, F!43), X!40))),
% 0.22/0.55 inference(tautology,[status(thm)],[])).
% 0.22/0.55 tff(225,plain,
% 0.22/0.55 (member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), X!40, F!43), X!40) | member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), X!40, F!43), Y!39)),
% 0.22/0.55 inference(unit_resolution,[status(thm)],[224, 223])).
% 0.22/0.55 tff(226,plain,
% 0.22/0.55 (((~member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), X!40, F!43)))) | apply(F!43, tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), X!40, F!43))),
% 0.22/0.55 inference(tautology,[status(thm)],[])).
% 0.22/0.55 tff(227,plain,
% 0.22/0.55 (apply(F!43, tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), X!40, F!43))),
% 0.22/0.55 inference(unit_resolution,[status(thm)],[226, 221])).
% 0.22/0.55 tff(228,plain,
% 0.22/0.55 (((~![Y: $i] : ((~member(Y, union(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), Y)))) | ((~member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), X!40, F!43), union(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), X!40, F!43))))) <=> ((~![Y: $i] : ((~member(Y, union(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), Y)))) | (~member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), X!40, F!43), union(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), X!40, F!43))))),
% 0.22/0.55 inference(rewrite,[status(thm)],[])).
% 0.22/0.55 tff(229,plain,
% 0.22/0.55 ((~![Y: $i] : ((~member(Y, union(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), Y)))) | ((~member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), X!40, F!43), union(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), X!40, F!43))))),
% 0.22/0.55 inference(quant_inst,[status(thm)],[])).
% 0.22/0.55 tff(230,plain,
% 0.22/0.55 ((~![Y: $i] : ((~member(Y, union(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), Y)))) | (~member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), X!40, F!43), union(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), X!40, F!43)))),
% 0.22/0.55 inference(modus_ponens,[status(thm)],[229, 228])).
% 0.22/0.55 tff(231,plain,
% 0.22/0.55 (~member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), X!40, F!43), union(X!40, Y!39))),
% 0.22/0.55 inference(unit_resolution,[status(thm)],[230, 200, 227])).
% 0.22/0.55 tff(232,plain,
% 0.22/0.55 ((~(member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), X!40, F!43), union(X!40, Y!39)) <=> (member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), X!40, F!43), X!40) | member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), X!40, F!43), Y!39)))) | member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), X!40, F!43), union(X!40, Y!39)) | (~(member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), X!40, F!43), X!40) | member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), X!40, F!43), Y!39)))),
% 0.22/0.55 inference(tautology,[status(thm)],[])).
% 0.22/0.55 tff(233,plain,
% 0.22/0.55 (~(member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), X!40, F!43), union(X!40, Y!39)) <=> (member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), X!40, F!43), X!40) | member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), X!40, F!43), Y!39)))),
% 0.22/0.55 inference(unit_resolution,[status(thm)],[232, 231, 225])).
% 0.22/0.55 tff(234,plain,
% 0.22/0.55 (((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), X!40, F!43), union(X!40, Y!39)) <=> (member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), X!40, F!43), X!40) | member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), X!40, F!43), Y!39)))) <=> ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), X!40, F!43), union(X!40, Y!39)) <=> (member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), X!40, F!43), X!40) | member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), X!40, F!43), Y!39))))),
% 0.22/0.55 inference(rewrite,[status(thm)],[])).
% 0.22/0.55 tff(235,plain,
% 0.22/0.55 ((member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), X!40, F!43), union(X!40, Y!39)) <=> (member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), X!40, F!43), Y!39) | member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), X!40, F!43), X!40))) <=> (member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), X!40, F!43), union(X!40, Y!39)) <=> (member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), X!40, F!43), X!40) | member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), X!40, F!43), Y!39)))),
% 0.22/0.55 inference(rewrite,[status(thm)],[])).
% 0.22/0.55 tff(236,plain,
% 0.22/0.55 (((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), X!40, F!43), union(X!40, Y!39)) <=> (member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), X!40, F!43), Y!39) | member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), X!40, F!43), X!40)))) <=> ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), X!40, F!43), union(X!40, Y!39)) <=> (member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), X!40, F!43), X!40) | member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), X!40, F!43), Y!39))))),
% 0.22/0.55 inference(monotonicity,[status(thm)],[235])).
% 0.22/0.55 tff(237,plain,
% 0.22/0.55 (((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), X!40, F!43), union(X!40, Y!39)) <=> (member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), X!40, F!43), Y!39) | member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), X!40, F!43), X!40)))) <=> ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), X!40, F!43), union(X!40, Y!39)) <=> (member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), X!40, F!43), X!40) | member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), X!40, F!43), Y!39))))),
% 0.22/0.55 inference(transitivity,[status(thm)],[236, 234])).
% 0.22/0.55 tff(238,plain,
% 0.22/0.55 ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), X!40, F!43), union(X!40, Y!39)) <=> (member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), X!40, F!43), Y!39) | member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), X!40, F!43), X!40)))),
% 0.22/0.55 inference(quant_inst,[status(thm)],[])).
% 0.22/0.55 tff(239,plain,
% 0.22/0.55 ((~![X: $i, A: $i, B: $i] : (member(X, union(A, B)) <=> (member(X, B) | member(X, A)))) | (member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), X!40, F!43), union(X!40, Y!39)) <=> (member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), X!40, F!43), X!40) | member(tptp_fun_Y_25(tptp_fun_X_0(inverse_image2(F!43, union(X!40, Y!39)), union(inverse_image2(F!43, X!40), inverse_image2(F!43, Y!39))), X!40, F!43), Y!39)))),
% 0.22/0.55 inference(modus_ponens,[status(thm)],[238, 237])).
% 0.22/0.55 tff(240,plain,
% 0.22/0.55 ($false),
% 0.22/0.55 inference(unit_resolution,[status(thm)],[239, 51, 233])).
% 0.22/0.55 % SZS output end Proof
% 0.22/0.56 % E exiting
%------------------------------------------------------------------------------