%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET758+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 0.15s 0.42s
% Output : Proof 0.24s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.14 % Problem : SET758+4 : TPTP v9.0.0. Bugfixed v2.2.1.
% 0.13/0.14 % Command : run_E %s %d THM
% 0.15/0.36 % Computer : n003.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Fri Jun 20 05:40:24 EDT 2025
% 0.15/0.37 % CPUTime :
% 0.15/0.42 % SZS status Theorem
% 0.15/0.42 % SZS output start Proof
% 0.15/0.42 tff(member_type, type, (
% 0.15/0.42 member: ( $i * $i ) > $o)).
% 0.15/0.42 tff(tptp_fun_Y_39_type, type, (
% 0.15/0.42 tptp_fun_Y_39: $i)).
% 0.15/0.42 tff(tptp_fun_Y_26_type, type, (
% 0.15/0.42 tptp_fun_Y_26: ( $i * $i * $i ) > $i)).
% 0.15/0.42 tff(tptp_fun_F_42_type, type, (
% 0.15/0.42 tptp_fun_F_42: $i)).
% 0.15/0.42 tff(tptp_fun_X_24_type, type, (
% 0.15/0.42 tptp_fun_X_24: ( $i * $i * $i ) > $i)).
% 0.15/0.42 tff(inverse_image3_type, type, (
% 0.15/0.42 inverse_image3: ( $i * $i * $i ) > $i)).
% 0.15/0.42 tff(tptp_fun_A_41_type, type, (
% 0.15/0.42 tptp_fun_A_41: $i)).
% 0.15/0.42 tff(tptp_fun_X_0_type, type, (
% 0.15/0.42 tptp_fun_X_0: ( $i * $i ) > $i)).
% 0.15/0.42 tff(image3_type, type, (
% 0.15/0.42 image3: ( $i * $i * $i ) > $i)).
% 0.15/0.42 tff(tptp_fun_B_40_type, type, (
% 0.15/0.42 tptp_fun_B_40: $i)).
% 0.15/0.42 tff(apply_type, type, (
% 0.15/0.42 apply: ( $i * $i * $i ) > $o)).
% 0.15/0.42 tff(subset_type, type, (
% 0.15/0.42 subset: ( $i * $i ) > $o)).
% 0.15/0.42 tff(maps_type, type, (
% 0.15/0.42 maps: ( $i * $i * $i ) > $o)).
% 0.15/0.42 tff(tptp_fun_Y_3_type, type, (
% 0.15/0.42 tptp_fun_Y_3: ( $i * $i * $i ) > $i)).
% 0.15/0.42 tff(tptp_fun_Y2_5_type, type, (
% 0.15/0.42 tptp_fun_Y2_5: ( $i * $i * $i ) > $i)).
% 0.15/0.42 tff(tptp_fun_Y1_6_type, type, (
% 0.15/0.42 tptp_fun_Y1_6: ( $i * $i * $i ) > $i)).
% 0.15/0.42 tff(tptp_fun_X_7_type, type, (
% 0.15/0.42 tptp_fun_X_7: ( $i * $i * $i ) > $i)).
% 0.15/0.42 tff(tptp_fun_X_4_type, type, (
% 0.15/0.42 tptp_fun_X_4: ( $i * $i * $i ) > $i)).
% 0.15/0.42 tff(1,plain,
% 0.15/0.42 (^[F: $i, B: $i, A: $i, X: $i] : refl((~((~((~member(X, inverse_image3(F, B, A))) | (~((~member(X, A)) | (~member(tptp_fun_Y_26(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_26(X, B, F))))))) | (~(member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y))))))) <=> (~((~((~member(X, inverse_image3(F, B, A))) | (~((~member(X, A)) | (~member(tptp_fun_Y_26(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_26(X, B, F))))))) | (~(member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y))))))))),
% 0.15/0.42 inference(bind,[status(th)],[])).
% 0.15/0.42 tff(2,plain,
% 0.15/0.42 (![F: $i, B: $i, A: $i, X: $i] : (~((~((~member(X, inverse_image3(F, B, A))) | (~((~member(X, A)) | (~member(tptp_fun_Y_26(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_26(X, B, F))))))) | (~(member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y))))))) <=> ![F: $i, B: $i, A: $i, X: $i] : (~((~((~member(X, inverse_image3(F, B, A))) | (~((~member(X, A)) | (~member(tptp_fun_Y_26(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_26(X, B, F))))))) | (~(member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))),
% 0.15/0.42 inference(quant_intro,[status(thm)],[1])).
% 0.15/0.42 tff(3,plain,
% 0.15/0.42 (^[F: $i, B: $i, A: $i, X: $i] : rewrite((~((~((~member(X, inverse_image3(F, B, A))) | (~((~member(X, A)) | (~member(tptp_fun_Y_26(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_26(X, B, F))))))) | (~(member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y))))))) <=> (~((~((~member(X, inverse_image3(F, B, A))) | (~((~member(X, A)) | (~member(tptp_fun_Y_26(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_26(X, B, F))))))) | (~(member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y))))))))),
% 0.15/0.42 inference(bind,[status(th)],[])).
% 0.15/0.42 tff(4,plain,
% 0.15/0.42 (![F: $i, B: $i, A: $i, X: $i] : (~((~((~member(X, inverse_image3(F, B, A))) | (~((~member(X, A)) | (~member(tptp_fun_Y_26(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_26(X, B, F))))))) | (~(member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y))))))) <=> ![F: $i, B: $i, A: $i, X: $i] : (~((~((~member(X, inverse_image3(F, B, A))) | (~((~member(X, A)) | (~member(tptp_fun_Y_26(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_26(X, B, F))))))) | (~(member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))),
% 0.15/0.42 inference(quant_intro,[status(thm)],[3])).
% 0.15/0.42 tff(5,plain,
% 0.15/0.42 (![F: $i, B: $i, A: $i, X: $i] : (~((~((~member(X, inverse_image3(F, B, A))) | (~((~member(X, A)) | (~member(tptp_fun_Y_26(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_26(X, B, F))))))) | (~(member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y))))))) <=> ![F: $i, B: $i, A: $i, X: $i] : (~((~((~member(X, inverse_image3(F, B, A))) | (~((~member(X, A)) | (~member(tptp_fun_Y_26(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_26(X, B, F))))))) | (~(member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))),
% 0.15/0.43 inference(transitivity,[status(thm)],[4, 2])).
% 0.15/0.43 tff(6,plain,
% 0.15/0.43 (^[F: $i, B: $i, A: $i, X: $i] : trans(monotonicity(rewrite(((~member(X, inverse_image3(F, B, A))) | (member(X, A) & member(tptp_fun_Y_26(X, B, F), B) & apply(F, X, tptp_fun_Y_26(X, B, F)))) <=> ((~member(X, inverse_image3(F, B, A))) | (~((~member(X, A)) | (~member(tptp_fun_Y_26(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_26(X, B, F))))))), trans(monotonicity(quant_intro(proof_bind(^[Y: $i] : trans(monotonicity(rewrite((member(Y, B) & apply(F, X, Y)) <=> (~((~member(Y, B)) | (~apply(F, X, Y))))), ((~(member(Y, B) & apply(F, X, Y))) <=> (~(~((~member(Y, B)) | (~apply(F, X, Y))))))), rewrite((~(~((~member(Y, B)) | (~apply(F, X, Y))))) <=> ((~member(Y, B)) | (~apply(F, X, Y)))), ((~(member(Y, B) & apply(F, X, Y))) <=> ((~member(Y, B)) | (~apply(F, X, Y)))))), (![Y: $i] : (~(member(Y, B) & apply(F, X, Y))) <=> ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y))))), ((member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y)))) <=> (member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))), rewrite((member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))) <=> (member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y))))), ((member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y)))) <=> (member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))), ((((~member(X, inverse_image3(F, B, A))) | (member(X, A) & member(tptp_fun_Y_26(X, B, F), B) & apply(F, X, tptp_fun_Y_26(X, B, F)))) & (member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y))))) <=> (((~member(X, inverse_image3(F, B, A))) | (~((~member(X, A)) | (~member(tptp_fun_Y_26(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_26(X, B, F)))))) & (member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y))))))), rewrite((((~member(X, inverse_image3(F, B, A))) | (~((~member(X, A)) | (~member(tptp_fun_Y_26(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_26(X, B, F)))))) & (member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y))))) <=> (~((~((~member(X, inverse_image3(F, B, A))) | (~((~member(X, A)) | (~member(tptp_fun_Y_26(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_26(X, B, F))))))) | (~(member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))), ((((~member(X, inverse_image3(F, B, A))) | (member(X, A) & member(tptp_fun_Y_26(X, B, F), B) & apply(F, X, tptp_fun_Y_26(X, B, F)))) & (member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y))))) <=> (~((~((~member(X, inverse_image3(F, B, A))) | (~((~member(X, A)) | (~member(tptp_fun_Y_26(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_26(X, B, F))))))) | (~(member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))))),
% 0.15/0.43 inference(bind,[status(th)],[])).
% 0.15/0.43 tff(7,plain,
% 0.15/0.43 (![F: $i, B: $i, A: $i, X: $i] : (((~member(X, inverse_image3(F, B, A))) | (member(X, A) & member(tptp_fun_Y_26(X, B, F), B) & apply(F, X, tptp_fun_Y_26(X, B, F)))) & (member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y))))) <=> ![F: $i, B: $i, A: $i, X: $i] : (~((~((~member(X, inverse_image3(F, B, A))) | (~((~member(X, A)) | (~member(tptp_fun_Y_26(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_26(X, B, F))))))) | (~(member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))),
% 0.15/0.43 inference(quant_intro,[status(thm)],[6])).
% 0.15/0.43 tff(8,plain,
% 0.15/0.43 (^[F: $i, B: $i, A: $i, X: $i] : rewrite((((~member(X, inverse_image3(F, B, A))) | (member(X, A) & (member(tptp_fun_Y_26(X, B, F), B) & apply(F, X, tptp_fun_Y_26(X, B, F))))) & (member(X, inverse_image3(F, B, A)) | ((~member(X, A)) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y)))))) <=> (((~member(X, inverse_image3(F, B, A))) | (member(X, A) & member(tptp_fun_Y_26(X, B, F), B) & apply(F, X, tptp_fun_Y_26(X, B, F)))) & (member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y))))))),
% 0.15/0.43 inference(bind,[status(th)],[])).
% 0.15/0.43 tff(9,plain,
% 0.15/0.43 (![F: $i, B: $i, A: $i, X: $i] : (((~member(X, inverse_image3(F, B, A))) | (member(X, A) & (member(tptp_fun_Y_26(X, B, F), B) & apply(F, X, tptp_fun_Y_26(X, B, F))))) & (member(X, inverse_image3(F, B, A)) | ((~member(X, A)) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y)))))) <=> ![F: $i, B: $i, A: $i, X: $i] : (((~member(X, inverse_image3(F, B, A))) | (member(X, A) & member(tptp_fun_Y_26(X, B, F), B) & apply(F, X, tptp_fun_Y_26(X, B, F)))) & (member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y)))))),
% 0.15/0.43 inference(quant_intro,[status(thm)],[8])).
% 0.15/0.43 tff(10,plain,
% 0.15/0.43 (![F: $i, B: $i, A: $i, X: $i] : (member(X, inverse_image3(F, B, A)) <=> (member(X, A) & ?[Y: $i] : (member(Y, B) & apply(F, X, Y)))) <=> ![F: $i, B: $i, A: $i, X: $i] : (member(X, inverse_image3(F, B, A)) <=> (member(X, A) & ?[Y: $i] : (member(Y, B) & apply(F, X, Y))))),
% 0.15/0.43 inference(rewrite,[status(thm)],[])).
% 0.15/0.43 tff(11,axiom,(![F: $i, B: $i, A: $i, X: $i] : (member(X, inverse_image3(F, B, A)) <=> (member(X, A) & ?[Y: $i] : (member(Y, B) & apply(F, X, Y))))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+1.ax','inverse_image3')).
% 0.15/0.43 tff(12,plain,
% 0.15/0.43 (![F: $i, B: $i, A: $i, X: $i] : (member(X, inverse_image3(F, B, A)) <=> (member(X, A) & ?[Y: $i] : (member(Y, B) & apply(F, X, Y))))),
% 0.15/0.43 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.15/0.43 tff(13,plain,(
% 0.15/0.43 ![F: $i, B: $i, A: $i, X: $i] : (((~member(X, inverse_image3(F, B, A))) | (member(X, A) & (member(tptp_fun_Y_26(X, B, F), B) & apply(F, X, tptp_fun_Y_26(X, B, F))))) & (member(X, inverse_image3(F, B, A)) | ((~member(X, A)) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y))))))),
% 0.15/0.43 inference(skolemize,[status(sab)],[12])).
% 0.15/0.43 tff(14,plain,
% 0.15/0.43 (![F: $i, B: $i, A: $i, X: $i] : (((~member(X, inverse_image3(F, B, A))) | (member(X, A) & member(tptp_fun_Y_26(X, B, F), B) & apply(F, X, tptp_fun_Y_26(X, B, F)))) & (member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y)))))),
% 0.15/0.43 inference(modus_ponens,[status(thm)],[13, 9])).
% 0.15/0.43 tff(15,plain,
% 0.15/0.43 (![F: $i, B: $i, A: $i, X: $i] : (~((~((~member(X, inverse_image3(F, B, A))) | (~((~member(X, A)) | (~member(tptp_fun_Y_26(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_26(X, B, F))))))) | (~(member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))),
% 0.15/0.43 inference(modus_ponens,[status(thm)],[14, 7])).
% 0.15/0.43 tff(16,plain,
% 0.15/0.43 (![F: $i, B: $i, A: $i, X: $i] : (~((~((~member(X, inverse_image3(F, B, A))) | (~((~member(X, A)) | (~member(tptp_fun_Y_26(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_26(X, B, F))))))) | (~(member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))),
% 0.15/0.43 inference(modus_ponens,[status(thm)],[15, 5])).
% 0.15/0.43 tff(17,plain,
% 0.15/0.43 (((~![F: $i, B: $i, A: $i, X: $i] : (~((~((~member(X, inverse_image3(F, B, A))) | (~((~member(X, A)) | (~member(tptp_fun_Y_26(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_26(X, B, F))))))) | (~(member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), inverse_image3(F!42, Y!39, A!41))) | (~((~member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), A!41)) | (~member(tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42), Y!39)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42))))))) | (~(member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), inverse_image3(F!42, Y!39, A!41)) | ![Y: $i] : ((~member(Y, Y!39)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y))) | (~member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), A!41))))))) <=> ((~![F: $i, B: $i, A: $i, X: $i] : (~((~((~member(X, inverse_image3(F, B, A))) | (~((~member(X, A)) | (~member(tptp_fun_Y_26(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_26(X, B, F))))))) | (~(member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), inverse_image3(F!42, Y!39, A!41))) | (~((~member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), A!41)) | (~member(tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42), Y!39)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42))))))) | (~(member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), inverse_image3(F!42, Y!39, A!41)) | ![Y: $i] : ((~member(Y, Y!39)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y))) | (~member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), A!41)))))))),
% 0.15/0.43 inference(rewrite,[status(thm)],[])).
% 0.15/0.43 tff(18,plain,
% 0.15/0.43 ((~((~((~member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), inverse_image3(F!42, Y!39, A!41))) | (~((~member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), A!41)) | (~member(tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42), Y!39)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42))))))) | (~(member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), inverse_image3(F!42, Y!39, A!41)) | (~member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), A!41)) | ![Y: $i] : ((~member(Y, Y!39)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y))))))) <=> (~((~((~member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), inverse_image3(F!42, Y!39, A!41))) | (~((~member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), A!41)) | (~member(tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42), Y!39)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42))))))) | (~(member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), inverse_image3(F!42, Y!39, A!41)) | ![Y: $i] : ((~member(Y, Y!39)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y))) | (~member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), A!41))))))),
% 0.15/0.44 inference(rewrite,[status(thm)],[])).
% 0.15/0.44 tff(19,plain,
% 0.15/0.44 (((~![F: $i, B: $i, A: $i, X: $i] : (~((~((~member(X, inverse_image3(F, B, A))) | (~((~member(X, A)) | (~member(tptp_fun_Y_26(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_26(X, B, F))))))) | (~(member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), inverse_image3(F!42, Y!39, A!41))) | (~((~member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), A!41)) | (~member(tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42), Y!39)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42))))))) | (~(member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), inverse_image3(F!42, Y!39, A!41)) | (~member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), A!41)) | ![Y: $i] : ((~member(Y, Y!39)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y)))))))) <=> ((~![F: $i, B: $i, A: $i, X: $i] : (~((~((~member(X, inverse_image3(F, B, A))) | (~((~member(X, A)) | (~member(tptp_fun_Y_26(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_26(X, B, F))))))) | (~(member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), inverse_image3(F!42, Y!39, A!41))) | (~((~member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), A!41)) | (~member(tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42), Y!39)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42))))))) | (~(member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), inverse_image3(F!42, Y!39, A!41)) | ![Y: $i] : ((~member(Y, Y!39)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y))) | (~member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), A!41)))))))),
% 0.24/0.44 inference(monotonicity,[status(thm)],[18])).
% 0.24/0.44 tff(20,plain,
% 0.24/0.44 (((~![F: $i, B: $i, A: $i, X: $i] : (~((~((~member(X, inverse_image3(F, B, A))) | (~((~member(X, A)) | (~member(tptp_fun_Y_26(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_26(X, B, F))))))) | (~(member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), inverse_image3(F!42, Y!39, A!41))) | (~((~member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), A!41)) | (~member(tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42), Y!39)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42))))))) | (~(member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), inverse_image3(F!42, Y!39, A!41)) | (~member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), A!41)) | ![Y: $i] : ((~member(Y, Y!39)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y)))))))) <=> ((~![F: $i, B: $i, A: $i, X: $i] : (~((~((~member(X, inverse_image3(F, B, A))) | (~((~member(X, A)) | (~member(tptp_fun_Y_26(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_26(X, B, F))))))) | (~(member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), inverse_image3(F!42, Y!39, A!41))) | (~((~member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), A!41)) | (~member(tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42), Y!39)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42))))))) | (~(member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), inverse_image3(F!42, Y!39, A!41)) | ![Y: $i] : ((~member(Y, Y!39)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y))) | (~member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), A!41)))))))),
% 0.24/0.44 inference(transitivity,[status(thm)],[19, 17])).
% 0.24/0.44 tff(21,plain,
% 0.24/0.44 ((~![F: $i, B: $i, A: $i, X: $i] : (~((~((~member(X, inverse_image3(F, B, A))) | (~((~member(X, A)) | (~member(tptp_fun_Y_26(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_26(X, B, F))))))) | (~(member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), inverse_image3(F!42, Y!39, A!41))) | (~((~member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), A!41)) | (~member(tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42), Y!39)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42))))))) | (~(member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), inverse_image3(F!42, Y!39, A!41)) | (~member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), A!41)) | ![Y: $i] : ((~member(Y, Y!39)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y)))))))),
% 0.24/0.45 inference(quant_inst,[status(thm)],[])).
% 0.24/0.45 tff(22,plain,
% 0.24/0.45 ((~![F: $i, B: $i, A: $i, X: $i] : (~((~((~member(X, inverse_image3(F, B, A))) | (~((~member(X, A)) | (~member(tptp_fun_Y_26(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_26(X, B, F))))))) | (~(member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), inverse_image3(F!42, Y!39, A!41))) | (~((~member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), A!41)) | (~member(tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42), Y!39)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42))))))) | (~(member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), inverse_image3(F!42, Y!39, A!41)) | ![Y: $i] : ((~member(Y, Y!39)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y))) | (~member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), A!41))))))),
% 0.24/0.45 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.24/0.45 tff(23,plain,
% 0.24/0.45 (~((~((~member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), inverse_image3(F!42, Y!39, A!41))) | (~((~member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), A!41)) | (~member(tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42), Y!39)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42))))))) | (~(member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), inverse_image3(F!42, Y!39, A!41)) | ![Y: $i] : ((~member(Y, Y!39)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y))) | (~member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), A!41)))))),
% 0.24/0.45 inference(unit_resolution,[status(thm)],[22, 16])).
% 0.24/0.45 tff(24,plain,
% 0.24/0.45 (((~((~member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), inverse_image3(F!42, Y!39, A!41))) | (~((~member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), A!41)) | (~member(tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42), Y!39)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42))))))) | (~(member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), inverse_image3(F!42, Y!39, A!41)) | ![Y: $i] : ((~member(Y, Y!39)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y))) | (~member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), A!41))))) | ((~member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), inverse_image3(F!42, Y!39, A!41))) | (~((~member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), A!41)) | (~member(tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42), Y!39)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42))))))),
% 0.24/0.45 inference(tautology,[status(thm)],[])).
% 0.24/0.45 tff(25,plain,
% 0.24/0.45 ((~member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), inverse_image3(F!42, Y!39, A!41))) | (~((~member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), A!41)) | (~member(tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42), Y!39)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42)))))),
% 0.24/0.45 inference(unit_resolution,[status(thm)],[24, 23])).
% 0.24/0.45 tff(26,plain,
% 0.24/0.45 (^[F: $i, A: $i, B: $i, Y: $i] : refl((~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y))))))) <=> (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y))))))))),
% 0.24/0.45 inference(bind,[status(th)],[])).
% 0.24/0.45 tff(27,plain,
% 0.24/0.45 (![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y))))))) <=> ![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))),
% 0.24/0.45 inference(quant_intro,[status(thm)],[26])).
% 0.24/0.45 tff(28,plain,
% 0.24/0.45 (^[F: $i, A: $i, B: $i, Y: $i] : rewrite((~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y))))))) <=> (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y))))))))),
% 0.24/0.45 inference(bind,[status(th)],[])).
% 0.24/0.45 tff(29,plain,
% 0.24/0.45 (![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y))))))) <=> ![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))),
% 0.24/0.45 inference(quant_intro,[status(thm)],[28])).
% 0.24/0.45 tff(30,plain,
% 0.24/0.45 (![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y))))))) <=> ![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))),
% 0.24/0.45 inference(transitivity,[status(thm)],[29, 27])).
% 0.24/0.45 tff(31,plain,
% 0.24/0.45 (^[F: $i, A: $i, B: $i, Y: $i] : trans(monotonicity(rewrite(((~member(Y, image3(F, A, B))) | (member(Y, B) & member(tptp_fun_X_24(Y, A, F), A) & apply(F, tptp_fun_X_24(Y, A, F), Y))) <=> ((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))), trans(monotonicity(quant_intro(proof_bind(^[X: $i] : trans(monotonicity(rewrite((member(X, A) & apply(F, X, Y)) <=> (~((~member(X, A)) | (~apply(F, X, Y))))), ((~(member(X, A) & apply(F, X, Y))) <=> (~(~((~member(X, A)) | (~apply(F, X, Y))))))), rewrite((~(~((~member(X, A)) | (~apply(F, X, Y))))) <=> ((~member(X, A)) | (~apply(F, X, Y)))), ((~(member(X, A) & apply(F, X, Y))) <=> ((~member(X, A)) | (~apply(F, X, Y)))))), (![X: $i] : (~(member(X, A) & apply(F, X, Y))) <=> ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y))))), ((member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : (~(member(X, A) & apply(F, X, Y)))) <=> (member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))), rewrite((member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))) <=> (member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y))))), ((member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : (~(member(X, A) & apply(F, X, Y)))) <=> (member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))), ((((~member(Y, image3(F, A, B))) | (member(Y, B) & member(tptp_fun_X_24(Y, A, F), A) & apply(F, tptp_fun_X_24(Y, A, F), Y))) & (member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : (~(member(X, A) & apply(F, X, Y))))) <=> (((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y))))) & (member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y))))))), rewrite((((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y))))) & (member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y))))) <=> (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))), ((((~member(Y, image3(F, A, B))) | (member(Y, B) & member(tptp_fun_X_24(Y, A, F), A) & apply(F, tptp_fun_X_24(Y, A, F), Y))) & (member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : (~(member(X, A) & apply(F, X, Y))))) <=> (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))))),
% 0.24/0.46 inference(bind,[status(th)],[])).
% 0.24/0.46 tff(32,plain,
% 0.24/0.46 (![F: $i, A: $i, B: $i, Y: $i] : (((~member(Y, image3(F, A, B))) | (member(Y, B) & member(tptp_fun_X_24(Y, A, F), A) & apply(F, tptp_fun_X_24(Y, A, F), Y))) & (member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : (~(member(X, A) & apply(F, X, Y))))) <=> ![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))),
% 0.24/0.46 inference(quant_intro,[status(thm)],[31])).
% 0.24/0.46 tff(33,plain,
% 0.24/0.46 (^[F: $i, A: $i, B: $i, Y: $i] : rewrite((((~member(Y, image3(F, A, B))) | (member(Y, B) & (member(tptp_fun_X_24(Y, A, F), A) & apply(F, tptp_fun_X_24(Y, A, F), Y)))) & (member(Y, image3(F, A, B)) | ((~member(Y, B)) | ![X: $i] : (~(member(X, A) & apply(F, X, Y)))))) <=> (((~member(Y, image3(F, A, B))) | (member(Y, B) & member(tptp_fun_X_24(Y, A, F), A) & apply(F, tptp_fun_X_24(Y, A, F), Y))) & (member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : (~(member(X, A) & apply(F, X, Y))))))),
% 0.24/0.46 inference(bind,[status(th)],[])).
% 0.24/0.46 tff(34,plain,
% 0.24/0.46 (![F: $i, A: $i, B: $i, Y: $i] : (((~member(Y, image3(F, A, B))) | (member(Y, B) & (member(tptp_fun_X_24(Y, A, F), A) & apply(F, tptp_fun_X_24(Y, A, F), Y)))) & (member(Y, image3(F, A, B)) | ((~member(Y, B)) | ![X: $i] : (~(member(X, A) & apply(F, X, Y)))))) <=> ![F: $i, A: $i, B: $i, Y: $i] : (((~member(Y, image3(F, A, B))) | (member(Y, B) & member(tptp_fun_X_24(Y, A, F), A) & apply(F, tptp_fun_X_24(Y, A, F), Y))) & (member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : (~(member(X, A) & apply(F, X, Y)))))),
% 0.24/0.46 inference(quant_intro,[status(thm)],[33])).
% 0.24/0.46 tff(35,plain,
% 0.24/0.46 (![F: $i, A: $i, B: $i, Y: $i] : (member(Y, image3(F, A, B)) <=> (member(Y, B) & ?[X: $i] : (member(X, A) & apply(F, X, Y)))) <=> ![F: $i, A: $i, B: $i, Y: $i] : (member(Y, image3(F, A, B)) <=> (member(Y, B) & ?[X: $i] : (member(X, A) & apply(F, X, Y))))),
% 0.24/0.46 inference(rewrite,[status(thm)],[])).
% 0.24/0.46 tff(36,axiom,(![F: $i, A: $i, B: $i, Y: $i] : (member(Y, image3(F, A, B)) <=> (member(Y, B) & ?[X: $i] : (member(X, A) & apply(F, X, Y))))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+1.ax','image3')).
% 0.24/0.46 tff(37,plain,
% 0.24/0.46 (![F: $i, A: $i, B: $i, Y: $i] : (member(Y, image3(F, A, B)) <=> (member(Y, B) & ?[X: $i] : (member(X, A) & apply(F, X, Y))))),
% 0.24/0.46 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.24/0.46 tff(38,plain,(
% 0.24/0.46 ![F: $i, A: $i, B: $i, Y: $i] : (((~member(Y, image3(F, A, B))) | (member(Y, B) & (member(tptp_fun_X_24(Y, A, F), A) & apply(F, tptp_fun_X_24(Y, A, F), Y)))) & (member(Y, image3(F, A, B)) | ((~member(Y, B)) | ![X: $i] : (~(member(X, A) & apply(F, X, Y))))))),
% 0.24/0.46 inference(skolemize,[status(sab)],[37])).
% 0.24/0.46 tff(39,plain,
% 0.24/0.46 (![F: $i, A: $i, B: $i, Y: $i] : (((~member(Y, image3(F, A, B))) | (member(Y, B) & member(tptp_fun_X_24(Y, A, F), A) & apply(F, tptp_fun_X_24(Y, A, F), Y))) & (member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : (~(member(X, A) & apply(F, X, Y)))))),
% 0.24/0.46 inference(modus_ponens,[status(thm)],[38, 34])).
% 0.24/0.46 tff(40,plain,
% 0.24/0.46 (![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))),
% 0.24/0.46 inference(modus_ponens,[status(thm)],[39, 32])).
% 0.24/0.46 tff(41,plain,
% 0.24/0.46 (![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))),
% 0.24/0.46 inference(modus_ponens,[status(thm)],[40, 30])).
% 0.24/0.46 tff(42,plain,
% 0.24/0.46 (((~![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))) | (~((~member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), B!40)) | (~member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), inverse_image3(F!42, Y!39, A!41))) | (~apply(F!42, tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)))))))) | (~(member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)) | ![X: $i] : ((~member(X, inverse_image3(F!42, Y!39, A!41))) | (~apply(F!42, X, tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))))) | (~member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), B!40))))))) <=> ((~![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))) | (~((~member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), B!40)) | (~member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), inverse_image3(F!42, Y!39, A!41))) | (~apply(F!42, tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)))))))) | (~(member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)) | ![X: $i] : ((~member(X, inverse_image3(F!42, Y!39, A!41))) | (~apply(F!42, X, tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))))) | (~member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), B!40)))))))),
% 0.24/0.46 inference(rewrite,[status(thm)],[])).
% 0.24/0.46 tff(43,plain,
% 0.24/0.46 ((~((~((~member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))) | (~((~member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), B!40)) | (~member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), inverse_image3(F!42, Y!39, A!41))) | (~apply(F!42, tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)))))))) | (~(member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)) | (~member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), B!40)) | ![X: $i] : ((~member(X, inverse_image3(F!42, Y!39, A!41))) | (~apply(F!42, X, tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))))))))) <=> (~((~((~member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))) | (~((~member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), B!40)) | (~member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), inverse_image3(F!42, Y!39, A!41))) | (~apply(F!42, tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)))))))) | (~(member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)) | ![X: $i] : ((~member(X, inverse_image3(F!42, Y!39, A!41))) | (~apply(F!42, X, tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))))) | (~member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), B!40))))))),
% 0.24/0.46 inference(rewrite,[status(thm)],[])).
% 0.24/0.46 tff(44,plain,
% 0.24/0.46 (((~![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))) | (~((~member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), B!40)) | (~member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), inverse_image3(F!42, Y!39, A!41))) | (~apply(F!42, tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)))))))) | (~(member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)) | (~member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), B!40)) | ![X: $i] : ((~member(X, inverse_image3(F!42, Y!39, A!41))) | (~apply(F!42, X, tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)))))))))) <=> ((~![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))) | (~((~member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), B!40)) | (~member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), inverse_image3(F!42, Y!39, A!41))) | (~apply(F!42, tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)))))))) | (~(member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)) | ![X: $i] : ((~member(X, inverse_image3(F!42, Y!39, A!41))) | (~apply(F!42, X, tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))))) | (~member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), B!40)))))))),
% 0.24/0.47 inference(monotonicity,[status(thm)],[43])).
% 0.24/0.47 tff(45,plain,
% 0.24/0.47 (((~![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))) | (~((~member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), B!40)) | (~member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), inverse_image3(F!42, Y!39, A!41))) | (~apply(F!42, tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)))))))) | (~(member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)) | (~member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), B!40)) | ![X: $i] : ((~member(X, inverse_image3(F!42, Y!39, A!41))) | (~apply(F!42, X, tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)))))))))) <=> ((~![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))) | (~((~member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), B!40)) | (~member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), inverse_image3(F!42, Y!39, A!41))) | (~apply(F!42, tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)))))))) | (~(member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)) | ![X: $i] : ((~member(X, inverse_image3(F!42, Y!39, A!41))) | (~apply(F!42, X, tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))))) | (~member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), B!40)))))))),
% 0.24/0.47 inference(transitivity,[status(thm)],[44, 42])).
% 0.24/0.47 tff(46,plain,
% 0.24/0.47 ((~![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))) | (~((~member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), B!40)) | (~member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), inverse_image3(F!42, Y!39, A!41))) | (~apply(F!42, tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)))))))) | (~(member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)) | (~member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), B!40)) | ![X: $i] : ((~member(X, inverse_image3(F!42, Y!39, A!41))) | (~apply(F!42, X, tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)))))))))),
% 0.24/0.47 inference(quant_inst,[status(thm)],[])).
% 0.24/0.47 tff(47,plain,
% 0.24/0.47 ((~![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))) | (~((~member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), B!40)) | (~member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), inverse_image3(F!42, Y!39, A!41))) | (~apply(F!42, tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)))))))) | (~(member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)) | ![X: $i] : ((~member(X, inverse_image3(F!42, Y!39, A!41))) | (~apply(F!42, X, tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))))) | (~member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), B!40))))))),
% 0.24/0.47 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.24/0.47 tff(48,plain,
% 0.24/0.47 (~((~((~member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))) | (~((~member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), B!40)) | (~member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), inverse_image3(F!42, Y!39, A!41))) | (~apply(F!42, tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)))))))) | (~(member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)) | ![X: $i] : ((~member(X, inverse_image3(F!42, Y!39, A!41))) | (~apply(F!42, X, tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))))) | (~member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), B!40)))))),
% 0.24/0.47 inference(unit_resolution,[status(thm)],[47, 41])).
% 0.24/0.47 tff(49,plain,
% 0.24/0.47 (((~((~member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))) | (~((~member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), B!40)) | (~member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), inverse_image3(F!42, Y!39, A!41))) | (~apply(F!42, tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)))))))) | (~(member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)) | ![X: $i] : ((~member(X, inverse_image3(F!42, Y!39, A!41))) | (~apply(F!42, X, tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))))) | (~member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), B!40))))) | ((~member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))) | (~((~member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), B!40)) | (~member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), inverse_image3(F!42, Y!39, A!41))) | (~apply(F!42, tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)))))))),
% 0.24/0.48 inference(tautology,[status(thm)],[])).
% 0.24/0.48 tff(50,plain,
% 0.24/0.48 ((~member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))) | (~((~member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), B!40)) | (~member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), inverse_image3(F!42, Y!39, A!41))) | (~apply(F!42, tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))))))),
% 0.24/0.48 inference(unit_resolution,[status(thm)],[49, 48])).
% 0.24/0.48 tff(51,plain,
% 0.24/0.48 (^[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))))))))),
% 0.24/0.48 inference(bind,[status(th)],[])).
% 0.24/0.48 tff(52,plain,
% 0.24/0.48 (![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)))))))),
% 0.24/0.48 inference(quant_intro,[status(thm)],[51])).
% 0.24/0.48 tff(53,plain,
% 0.24/0.48 (^[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))))))))),
% 0.24/0.48 inference(bind,[status(th)],[])).
% 0.24/0.48 tff(54,plain,
% 0.24/0.48 (![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)))))))),
% 0.24/0.48 inference(quant_intro,[status(thm)],[53])).
% 0.24/0.48 tff(55,plain,
% 0.24/0.48 (![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)))))))),
% 0.24/0.48 inference(transitivity,[status(thm)],[54, 52])).
% 0.24/0.48 tff(56,plain,
% 0.24/0.48 (^[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)))))))))),
% 0.24/0.48 inference(bind,[status(th)],[])).
% 0.24/0.48 tff(57,plain,
% 0.24/0.48 (![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)))))))),
% 0.24/0.48 inference(quant_intro,[status(thm)],[56])).
% 0.24/0.48 tff(58,plain,
% 0.24/0.48 (![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)))),
% 0.24/0.48 inference(rewrite,[status(thm)],[])).
% 0.24/0.48 tff(59,plain,
% 0.24/0.48 (^[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))))),
% 0.24/0.48 inference(bind,[status(th)],[])).
% 0.24/0.48 tff(60,plain,
% 0.24/0.48 (![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)))),
% 0.24/0.48 inference(quant_intro,[status(thm)],[59])).
% 0.24/0.48 tff(61,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')).
% 0.24/0.48 tff(62,plain,
% 0.24/0.48 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.24/0.48 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.24/0.48 tff(63,plain,
% 0.24/0.48 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.24/0.48 inference(modus_ponens,[status(thm)],[62, 58])).
% 0.24/0.48 tff(64,plain,(
% 0.24/0.48 ![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)))))),
% 0.24/0.48 inference(skolemize,[status(sab)],[63])).
% 0.24/0.48 tff(65,plain,
% 0.24/0.48 (![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)))))))),
% 0.24/0.48 inference(modus_ponens,[status(thm)],[64, 57])).
% 0.24/0.48 tff(66,plain,
% 0.24/0.48 (![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)))))))),
% 0.24/0.48 inference(modus_ponens,[status(thm)],[65, 55])).
% 0.24/0.48 tff(67,plain,
% 0.24/0.48 ((~![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(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39)) | ![X: $i] : ((~member(X, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))) | member(X, Y!39)))) | (~(subset(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39) | (~((~member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))) | member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), Y!39)))))))),
% 0.24/0.48 inference(quant_inst,[status(thm)],[])).
% 0.24/0.48 tff(68,plain,
% 0.24/0.48 (~((~((~subset(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39)) | ![X: $i] : ((~member(X, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))) | member(X, Y!39)))) | (~(subset(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39) | (~((~member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))) | member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), Y!39))))))),
% 0.24/0.48 inference(unit_resolution,[status(thm)],[67, 66])).
% 0.24/0.48 tff(69,plain,
% 0.24/0.48 (((~((~subset(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39)) | ![X: $i] : ((~member(X, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))) | member(X, Y!39)))) | (~(subset(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39) | (~((~member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))) | member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), Y!39)))))) | (subset(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39) | (~((~member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))) | member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), Y!39))))),
% 0.24/0.48 inference(tautology,[status(thm)],[])).
% 0.24/0.48 tff(70,plain,
% 0.24/0.48 (subset(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39) | (~((~member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))) | member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), Y!39)))),
% 0.24/0.48 inference(unit_resolution,[status(thm)],[69, 68])).
% 0.24/0.48 tff(71,plain,
% 0.24/0.48 ((~![F: $i, A: $i, B: $i, Y: $i] : ((~(maps(F, A, B) & subset(Y, B))) | subset(image3(F, inverse_image3(F, Y, A), B), Y))) <=> (~![F: $i, A: $i, B: $i, Y: $i] : ((~(maps(F, A, B) & subset(Y, B))) | subset(image3(F, inverse_image3(F, Y, A), B), Y)))),
% 0.24/0.48 inference(rewrite,[status(thm)],[])).
% 0.24/0.48 tff(72,plain,
% 0.24/0.48 ((~![F: $i, A: $i, B: $i, Y: $i] : ((maps(F, A, B) & subset(Y, B)) => subset(image3(F, inverse_image3(F, Y, A), B), Y))) <=> (~![F: $i, A: $i, B: $i, Y: $i] : ((~(maps(F, A, B) & subset(Y, B))) | subset(image3(F, inverse_image3(F, Y, A), B), Y)))),
% 0.24/0.48 inference(rewrite,[status(thm)],[])).
% 0.24/0.48 tff(73,axiom,(~![F: $i, A: $i, B: $i, Y: $i] : ((maps(F, A, B) & subset(Y, B)) => subset(image3(F, inverse_image3(F, Y, A), B), Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thIIa08')).
% 0.24/0.48 tff(74,plain,
% 0.24/0.48 (~![F: $i, A: $i, B: $i, Y: $i] : ((~(maps(F, A, B) & subset(Y, B))) | subset(image3(F, inverse_image3(F, Y, A), B), Y))),
% 0.24/0.48 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.24/0.48 tff(75,plain,
% 0.24/0.48 (~![F: $i, A: $i, B: $i, Y: $i] : ((~(maps(F, A, B) & subset(Y, B))) | subset(image3(F, inverse_image3(F, Y, A), B), Y))),
% 0.24/0.48 inference(modus_ponens,[status(thm)],[74, 71])).
% 0.24/0.48 tff(76,plain,
% 0.24/0.48 (~![F: $i, A: $i, B: $i, Y: $i] : ((~(maps(F, A, B) & subset(Y, B))) | subset(image3(F, inverse_image3(F, Y, A), B), Y))),
% 0.24/0.48 inference(modus_ponens,[status(thm)],[75, 71])).
% 0.24/0.48 tff(77,plain,
% 0.24/0.48 (~![F: $i, A: $i, B: $i, Y: $i] : ((~(maps(F, A, B) & subset(Y, B))) | subset(image3(F, inverse_image3(F, Y, A), B), Y))),
% 0.24/0.48 inference(modus_ponens,[status(thm)],[76, 71])).
% 0.24/0.48 tff(78,plain,(
% 0.24/0.48 ~((~(maps(F!42, A!41, B!40) & subset(Y!39, B!40))) | subset(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39))),
% 0.24/0.48 inference(skolemize,[status(sab)],[77])).
% 0.24/0.48 tff(79,plain,
% 0.24/0.48 (~subset(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39)),
% 0.24/0.48 inference(or_elim,[status(thm)],[78])).
% 0.24/0.48 tff(80,plain,
% 0.24/0.48 ((~(subset(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39) | (~((~member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))) | member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), Y!39))))) | subset(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39) | (~((~member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))) | member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), Y!39)))),
% 0.24/0.48 inference(tautology,[status(thm)],[])).
% 0.24/0.48 tff(81,plain,
% 0.24/0.48 ((~(subset(image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40), Y!39) | (~((~member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))) | member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), Y!39))))) | (~((~member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))) | member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), Y!39)))),
% 0.24/0.48 inference(unit_resolution,[status(thm)],[80, 79])).
% 0.24/0.48 tff(82,plain,
% 0.24/0.48 (~((~member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))) | member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), Y!39))),
% 0.24/0.48 inference(unit_resolution,[status(thm)],[81, 70])).
% 0.24/0.48 tff(83,plain,
% 0.24/0.48 (((~member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))) | member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), Y!39)) | member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))),
% 0.24/0.48 inference(tautology,[status(thm)],[])).
% 0.24/0.48 tff(84,plain,
% 0.24/0.48 (member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))),
% 0.24/0.48 inference(unit_resolution,[status(thm)],[83, 82])).
% 0.24/0.48 tff(85,plain,
% 0.24/0.48 ((~((~member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))) | (~((~member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), B!40)) | (~member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), inverse_image3(F!42, Y!39, A!41))) | (~apply(F!42, tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)))))))) | (~member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))) | (~((~member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), B!40)) | (~member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), inverse_image3(F!42, Y!39, A!41))) | (~apply(F!42, tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))))))),
% 0.24/0.48 inference(tautology,[status(thm)],[])).
% 0.24/0.48 tff(86,plain,
% 0.24/0.48 ((~((~member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))) | (~((~member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), B!40)) | (~member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), inverse_image3(F!42, Y!39, A!41))) | (~apply(F!42, tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)))))))) | (~((~member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), B!40)) | (~member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), inverse_image3(F!42, Y!39, A!41))) | (~apply(F!42, tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))))))),
% 0.24/0.48 inference(unit_resolution,[status(thm)],[85, 84])).
% 0.24/0.48 tff(87,plain,
% 0.24/0.48 (~((~member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), B!40)) | (~member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), inverse_image3(F!42, Y!39, A!41))) | (~apply(F!42, tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)))))),
% 0.24/0.49 inference(unit_resolution,[status(thm)],[86, 50])).
% 0.24/0.49 tff(88,plain,
% 0.24/0.49 (((~member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), B!40)) | (~member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), inverse_image3(F!42, Y!39, A!41))) | (~apply(F!42, tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))))) | member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), inverse_image3(F!42, Y!39, A!41))),
% 0.24/0.49 inference(tautology,[status(thm)],[])).
% 0.24/0.49 tff(89,plain,
% 0.24/0.49 (member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), inverse_image3(F!42, Y!39, A!41))),
% 0.24/0.49 inference(unit_resolution,[status(thm)],[88, 87])).
% 0.24/0.49 tff(90,plain,
% 0.24/0.49 ((~((~member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), inverse_image3(F!42, Y!39, A!41))) | (~((~member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), A!41)) | (~member(tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42), Y!39)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42))))))) | (~member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), inverse_image3(F!42, Y!39, A!41))) | (~((~member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), A!41)) | (~member(tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42), Y!39)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42)))))),
% 0.24/0.49 inference(tautology,[status(thm)],[])).
% 0.24/0.49 tff(91,plain,
% 0.24/0.49 ((~((~member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), inverse_image3(F!42, Y!39, A!41))) | (~((~member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), A!41)) | (~member(tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42), Y!39)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42))))))) | (~((~member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), A!41)) | (~member(tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42), Y!39)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42)))))),
% 0.24/0.49 inference(unit_resolution,[status(thm)],[90, 89])).
% 0.24/0.49 tff(92,plain,
% 0.24/0.49 (~((~member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), A!41)) | (~member(tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42), Y!39)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42))))),
% 0.24/0.49 inference(unit_resolution,[status(thm)],[91, 25])).
% 0.24/0.49 tff(93,plain,
% 0.24/0.49 (((~member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), A!41)) | (~member(tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42), Y!39)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42)))) | member(tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42), Y!39)),
% 0.24/0.49 inference(tautology,[status(thm)],[])).
% 0.24/0.49 tff(94,plain,
% 0.24/0.49 (member(tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42), Y!39)),
% 0.24/0.49 inference(unit_resolution,[status(thm)],[93, 92])).
% 0.24/0.49 tff(95,plain,
% 0.24/0.49 ((~![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(Y!39, B!40)) | ![X: $i] : ((~member(X, Y!39)) | member(X, B!40)))) | (~(subset(Y!39, B!40) | (~((~member(tptp_fun_X_0(B!40, Y!39), Y!39)) | member(tptp_fun_X_0(B!40, Y!39), B!40)))))))),
% 0.24/0.49 inference(quant_inst,[status(thm)],[])).
% 0.24/0.49 tff(96,plain,
% 0.24/0.49 (~((~((~subset(Y!39, B!40)) | ![X: $i] : ((~member(X, Y!39)) | member(X, B!40)))) | (~(subset(Y!39, B!40) | (~((~member(tptp_fun_X_0(B!40, Y!39), Y!39)) | member(tptp_fun_X_0(B!40, Y!39), B!40))))))),
% 0.24/0.49 inference(unit_resolution,[status(thm)],[95, 66])).
% 0.24/0.49 tff(97,plain,
% 0.24/0.49 (((~((~subset(Y!39, B!40)) | ![X: $i] : ((~member(X, Y!39)) | member(X, B!40)))) | (~(subset(Y!39, B!40) | (~((~member(tptp_fun_X_0(B!40, Y!39), Y!39)) | member(tptp_fun_X_0(B!40, Y!39), B!40)))))) | ((~subset(Y!39, B!40)) | ![X: $i] : ((~member(X, Y!39)) | member(X, B!40)))),
% 0.24/0.49 inference(tautology,[status(thm)],[])).
% 0.24/0.49 tff(98,plain,
% 0.24/0.49 ((~subset(Y!39, B!40)) | ![X: $i] : ((~member(X, Y!39)) | member(X, B!40))),
% 0.24/0.49 inference(unit_resolution,[status(thm)],[97, 96])).
% 0.24/0.49 tff(99,plain,
% 0.24/0.49 (maps(F!42, A!41, B!40) & subset(Y!39, B!40)),
% 0.24/0.49 inference(or_elim,[status(thm)],[78])).
% 0.24/0.49 tff(100,plain,
% 0.24/0.49 (subset(Y!39, B!40)),
% 0.24/0.49 inference(and_elim,[status(thm)],[99])).
% 0.24/0.49 tff(101,plain,
% 0.24/0.49 ((~((~subset(Y!39, B!40)) | ![X: $i] : ((~member(X, Y!39)) | member(X, B!40)))) | (~subset(Y!39, B!40)) | ![X: $i] : ((~member(X, Y!39)) | member(X, B!40))),
% 0.24/0.49 inference(tautology,[status(thm)],[])).
% 0.24/0.49 tff(102,plain,
% 0.24/0.49 ((~((~subset(Y!39, B!40)) | ![X: $i] : ((~member(X, Y!39)) | member(X, B!40)))) | ![X: $i] : ((~member(X, Y!39)) | member(X, B!40))),
% 0.24/0.49 inference(unit_resolution,[status(thm)],[101, 100])).
% 0.24/0.49 tff(103,plain,
% 0.24/0.49 (![X: $i] : ((~member(X, Y!39)) | member(X, B!40))),
% 0.24/0.49 inference(unit_resolution,[status(thm)],[102, 98])).
% 0.24/0.49 tff(104,plain,
% 0.24/0.49 (((~![X: $i] : ((~member(X, Y!39)) | member(X, B!40))) | ((~member(tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42), Y!39)) | member(tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42), B!40))) <=> ((~![X: $i] : ((~member(X, Y!39)) | member(X, B!40))) | (~member(tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42), Y!39)) | member(tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42), B!40))),
% 0.24/0.49 inference(rewrite,[status(thm)],[])).
% 0.24/0.49 tff(105,plain,
% 0.24/0.49 ((~![X: $i] : ((~member(X, Y!39)) | member(X, B!40))) | ((~member(tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42), Y!39)) | member(tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42), B!40))),
% 0.24/0.49 inference(quant_inst,[status(thm)],[])).
% 0.24/0.49 tff(106,plain,
% 0.24/0.49 ((~![X: $i] : ((~member(X, Y!39)) | member(X, B!40))) | (~member(tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42), Y!39)) | member(tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42), B!40)),
% 0.24/0.49 inference(modus_ponens,[status(thm)],[105, 104])).
% 0.24/0.49 tff(107,plain,
% 0.24/0.49 (member(tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42), B!40)),
% 0.24/0.49 inference(unit_resolution,[status(thm)],[106, 103, 94])).
% 0.24/0.49 tff(108,plain,
% 0.24/0.49 (((~member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), A!41)) | (~member(tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42), Y!39)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42)))) | apply(F!42, tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42))),
% 0.24/0.49 inference(tautology,[status(thm)],[])).
% 0.24/0.49 tff(109,plain,
% 0.24/0.49 (apply(F!42, tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42))),
% 0.24/0.49 inference(unit_resolution,[status(thm)],[108, 92])).
% 0.24/0.49 tff(110,plain,
% 0.24/0.49 (((~member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), A!41)) | (~member(tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42), Y!39)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42)))) | member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), A!41)),
% 0.24/0.49 inference(tautology,[status(thm)],[])).
% 0.24/0.49 tff(111,plain,
% 0.24/0.49 (member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), A!41)),
% 0.24/0.49 inference(unit_resolution,[status(thm)],[110, 92])).
% 0.24/0.49 tff(112,plain,
% 0.24/0.49 (((~member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), B!40)) | (~member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), inverse_image3(F!42, Y!39, A!41))) | (~apply(F!42, tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))))) | apply(F!42, tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)))),
% 0.24/0.49 inference(tautology,[status(thm)],[])).
% 0.24/0.49 tff(113,plain,
% 0.24/0.49 (apply(F!42, tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)))),
% 0.24/0.49 inference(unit_resolution,[status(thm)],[112, 87])).
% 0.24/0.49 tff(114,plain,
% 0.24/0.49 (((~member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), B!40)) | (~member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), inverse_image3(F!42, Y!39, A!41))) | (~apply(F!42, tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))))) | member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), B!40)),
% 0.24/0.49 inference(tautology,[status(thm)],[])).
% 0.24/0.49 tff(115,plain,
% 0.24/0.49 (member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), B!40)),
% 0.24/0.49 inference(unit_resolution,[status(thm)],[114, 87])).
% 0.24/0.49 tff(116,plain,
% 0.24/0.49 (^[F: $i, A: $i, B: $i] : rewrite((~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))) <=> (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))))))))),
% 0.24/0.49 inference(bind,[status(th)],[])).
% 0.24/0.49 tff(117,plain,
% 0.24/0.49 (![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))),
% 0.24/0.50 inference(quant_intro,[status(thm)],[116])).
% 0.24/0.50 tff(118,plain,
% 0.24/0.50 (^[F: $i, A: $i, B: $i] : refl((~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))) <=> (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))))),
% 0.24/0.50 inference(bind,[status(th)],[])).
% 0.24/0.50 tff(119,plain,
% 0.24/0.50 (![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))))))),
% 0.24/0.50 inference(quant_intro,[status(thm)],[118])).
% 0.24/0.50 tff(120,plain,
% 0.24/0.50 (^[F: $i, A: $i, B: $i] : rewrite((~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))) <=> (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))))),
% 0.24/0.50 inference(bind,[status(th)],[])).
% 0.24/0.50 tff(121,plain,
% 0.24/0.50 (![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))))))),
% 0.24/0.50 inference(quant_intro,[status(thm)],[120])).
% 0.24/0.50 tff(122,plain,
% 0.24/0.50 (![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))))))),
% 0.24/0.50 inference(transitivity,[status(thm)],[121, 119])).
% 0.24/0.50 tff(123,plain,
% 0.24/0.50 (^[F: $i, A: $i, B: $i] : trans(monotonicity(rewrite(((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) <=> ((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))), trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[Y: $i] : trans(monotonicity(rewrite((member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)) <=> (~((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))), ((~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y))) <=> (~(~((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))), rewrite((~(~((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))) <=> ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))), ((~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y))) <=> ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))), (![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y))) <=> ![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))), ((member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) <=> (member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))), rewrite((member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))) <=> (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))), ((member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) <=> (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))))), rewrite((~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B))))) <=> (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))), ((maps(F, A, B) | (member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B)))))) <=> (maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))))), rewrite((maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))) <=> (maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))), ((maps(F, A, B) | (member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B)))))) <=> (maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))))), ((((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) & (maps(F, A, B) | (member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B))))))) <=> (((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B))))))) & (maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))), rewrite((((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B))))))) & (maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))) <=> (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))))))), ((((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) & (maps(F, A, B) | (member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B))))))) <=> (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))))))))),
% 0.24/0.50 inference(bind,[status(th)],[])).
% 0.24/0.50 tff(124,plain,
% 0.24/0.50 (![F: $i, A: $i, B: $i] : (((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) & (maps(F, A, B) | (member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))))))),
% 0.24/0.50 inference(quant_intro,[status(thm)],[123])).
% 0.24/0.50 tff(125,plain,
% 0.24/0.50 (^[F: $i, A: $i, B: $i] : rewrite((((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) & (maps(F, A, B) | ((member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B)))))))) <=> (((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) & (maps(F, A, B) | (member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B))))))))),
% 0.24/0.50 inference(bind,[status(th)],[])).
% 0.24/0.50 tff(126,plain,
% 0.24/0.50 (![F: $i, A: $i, B: $i] : (((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) & (maps(F, A, B) | ((member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B)))))))) <=> ![F: $i, A: $i, B: $i] : (((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) & (maps(F, A, B) | (member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B)))))))),
% 0.24/0.50 inference(quant_intro,[status(thm)],[125])).
% 0.24/0.50 tff(127,plain,
% 0.24/0.50 (![F: $i, A: $i, B: $i] : (maps(F, A, B) <=> (![X: $i] : ((~member(X, A)) | ?[Y: $i] : (member(Y, B) & apply(F, X, Y))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) <=> ![F: $i, A: $i, B: $i] : (maps(F, A, B) <=> (![X: $i] : ((~member(X, A)) | ?[Y: $i] : (member(Y, B) & apply(F, X, Y))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B))))))),
% 0.24/0.50 inference(rewrite,[status(thm)],[])).
% 0.24/0.50 tff(128,plain,
% 0.24/0.50 (^[F: $i, A: $i, B: $i] : rewrite((maps(F, A, B) <=> (![X: $i] : (member(X, A) => ?[Y: $i] : (member(Y, B) & apply(F, X, Y))) & ![X: $i, Y1: $i, Y2: $i] : (((member(X, A) & member(Y1, B)) & member(Y2, B)) => ((apply(F, X, Y1) & apply(F, X, Y2)) => (Y1 = Y2))))) <=> (maps(F, A, B) <=> (![X: $i] : ((~member(X, A)) | ?[Y: $i] : (member(Y, B) & apply(F, X, Y))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))))),
% 0.24/0.50 inference(bind,[status(th)],[])).
% 0.24/0.50 tff(129,plain,
% 0.24/0.50 (![F: $i, A: $i, B: $i] : (maps(F, A, B) <=> (![X: $i] : (member(X, A) => ?[Y: $i] : (member(Y, B) & apply(F, X, Y))) & ![X: $i, Y1: $i, Y2: $i] : (((member(X, A) & member(Y1, B)) & member(Y2, B)) => ((apply(F, X, Y1) & apply(F, X, Y2)) => (Y1 = Y2))))) <=> ![F: $i, A: $i, B: $i] : (maps(F, A, B) <=> (![X: $i] : ((~member(X, A)) | ?[Y: $i] : (member(Y, B) & apply(F, X, Y))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B))))))),
% 0.24/0.50 inference(quant_intro,[status(thm)],[128])).
% 0.24/0.50 tff(130,axiom,(![F: $i, A: $i, B: $i] : (maps(F, A, B) <=> (![X: $i] : (member(X, A) => ?[Y: $i] : (member(Y, B) & apply(F, X, Y))) & ![X: $i, Y1: $i, Y2: $i] : (((member(X, A) & member(Y1, B)) & member(Y2, B)) => ((apply(F, X, Y1) & apply(F, X, Y2)) => (Y1 = Y2)))))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+1.ax','maps')).
% 0.24/0.50 tff(131,plain,
% 0.24/0.50 (![F: $i, A: $i, B: $i] : (maps(F, A, B) <=> (![X: $i] : ((~member(X, A)) | ?[Y: $i] : (member(Y, B) & apply(F, X, Y))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B))))))),
% 0.24/0.50 inference(modus_ponens,[status(thm)],[130, 129])).
% 0.24/0.50 tff(132,plain,
% 0.24/0.50 (![F: $i, A: $i, B: $i] : (maps(F, A, B) <=> (![X: $i] : ((~member(X, A)) | ?[Y: $i] : (member(Y, B) & apply(F, X, Y))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B))))))),
% 0.24/0.50 inference(modus_ponens,[status(thm)],[131, 127])).
% 0.24/0.50 tff(133,plain,(
% 0.24/0.50 ![F: $i, A: $i, B: $i] : (((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) & (maps(F, A, B) | ((member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B))))))))),
% 0.24/0.50 inference(skolemize,[status(sab)],[132])).
% 0.24/0.50 tff(134,plain,
% 0.24/0.50 (![F: $i, A: $i, B: $i] : (((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) & (maps(F, A, B) | (member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B)))))))),
% 0.24/0.50 inference(modus_ponens,[status(thm)],[133, 126])).
% 0.24/0.50 tff(135,plain,
% 0.24/0.50 (![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))))))),
% 0.24/0.50 inference(modus_ponens,[status(thm)],[134, 124])).
% 0.24/0.50 tff(136,plain,
% 0.24/0.50 (![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))))))),
% 0.24/0.50 inference(modus_ponens,[status(thm)],[135, 122])).
% 0.24/0.50 tff(137,plain,
% 0.24/0.50 (![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))),
% 0.24/0.50 inference(modus_ponens,[status(thm)],[136, 117])).
% 0.24/0.50 tff(138,plain,
% 0.24/0.50 (((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(F!42, A!41, B!40)) | (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!42), B!40)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!40, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)))))))) | (~(maps(F!42, A!41, B!40) | (~((~member(tptp_fun_X_4(B!40, A!41, F!42), A!41)) | (~![Y: $i] : ((~member(Y, B!40)) | (~apply(F!42, tptp_fun_X_4(B!40, A!41, F!42), Y)))))) | (~((~member(tptp_fun_Y2_5(B!40, A!41, F!42), B!40)) | (~member(tptp_fun_Y1_6(B!40, A!41, F!42), B!40)) | (~member(tptp_fun_X_7(B!40, A!41, F!42), A!41)) | (~apply(F!42, tptp_fun_X_7(B!40, A!41, F!42), tptp_fun_Y2_5(B!40, A!41, F!42))) | (~apply(F!42, tptp_fun_X_7(B!40, A!41, F!42), tptp_fun_Y1_6(B!40, A!41, F!42))) | (tptp_fun_Y1_6(B!40, A!41, F!42) = tptp_fun_Y2_5(B!40, A!41, F!42))))))))) <=> ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(F!42, A!41, B!40)) | (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!42), B!40)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!40, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)))))))) | (~(maps(F!42, A!41, B!40) | (~((~member(tptp_fun_X_4(B!40, A!41, F!42), A!41)) | (~![Y: $i] : ((~member(Y, B!40)) | (~apply(F!42, tptp_fun_X_4(B!40, A!41, F!42), Y)))))) | (~((~member(tptp_fun_Y2_5(B!40, A!41, F!42), B!40)) | (~member(tptp_fun_Y1_6(B!40, A!41, F!42), B!40)) | (~member(tptp_fun_X_7(B!40, A!41, F!42), A!41)) | (~apply(F!42, tptp_fun_X_7(B!40, A!41, F!42), tptp_fun_Y2_5(B!40, A!41, F!42))) | (~apply(F!42, tptp_fun_X_7(B!40, A!41, F!42), tptp_fun_Y1_6(B!40, A!41, F!42))) | (tptp_fun_Y1_6(B!40, A!41, F!42) = tptp_fun_Y2_5(B!40, A!41, F!42)))))))))),
% 0.24/0.51 inference(rewrite,[status(thm)],[])).
% 0.24/0.51 tff(139,plain,
% 0.24/0.51 ((~((~((~maps(F!42, A!41, B!40)) | (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!42), B!40)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!40, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)) | (~member(Y2, B!40)))))))) | (~(maps(F!42, A!41, B!40) | (~((tptp_fun_Y1_6(B!40, A!41, F!42) = tptp_fun_Y2_5(B!40, A!41, F!42)) | (~apply(F!42, tptp_fun_X_7(B!40, A!41, F!42), tptp_fun_Y1_6(B!40, A!41, F!42))) | (~apply(F!42, tptp_fun_X_7(B!40, A!41, F!42), tptp_fun_Y2_5(B!40, A!41, F!42))) | (~member(tptp_fun_X_7(B!40, A!41, F!42), A!41)) | (~member(tptp_fun_Y1_6(B!40, A!41, F!42), B!40)) | (~member(tptp_fun_Y2_5(B!40, A!41, F!42), B!40)))) | (~((~member(tptp_fun_X_4(B!40, A!41, F!42), A!41)) | (~![Y: $i] : ((~member(Y, B!40)) | (~apply(F!42, tptp_fun_X_4(B!40, A!41, F!42), Y)))))))))) <=> (~((~((~maps(F!42, A!41, B!40)) | (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!42), B!40)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!40, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)))))))) | (~(maps(F!42, A!41, B!40) | (~((~member(tptp_fun_X_4(B!40, A!41, F!42), A!41)) | (~![Y: $i] : ((~member(Y, B!40)) | (~apply(F!42, tptp_fun_X_4(B!40, A!41, F!42), Y)))))) | (~((~member(tptp_fun_Y2_5(B!40, A!41, F!42), B!40)) | (~member(tptp_fun_Y1_6(B!40, A!41, F!42), B!40)) | (~member(tptp_fun_X_7(B!40, A!41, F!42), A!41)) | (~apply(F!42, tptp_fun_X_7(B!40, A!41, F!42), tptp_fun_Y2_5(B!40, A!41, F!42))) | (~apply(F!42, tptp_fun_X_7(B!40, A!41, F!42), tptp_fun_Y1_6(B!40, A!41, F!42))) | (tptp_fun_Y1_6(B!40, A!41, F!42) = tptp_fun_Y2_5(B!40, A!41, F!42))))))))),
% 0.24/0.51 inference(rewrite,[status(thm)],[])).
% 0.24/0.51 tff(140,plain,
% 0.24/0.51 (((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(F!42, A!41, B!40)) | (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!42), B!40)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!40, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)) | (~member(Y2, B!40)))))))) | (~(maps(F!42, A!41, B!40) | (~((tptp_fun_Y1_6(B!40, A!41, F!42) = tptp_fun_Y2_5(B!40, A!41, F!42)) | (~apply(F!42, tptp_fun_X_7(B!40, A!41, F!42), tptp_fun_Y1_6(B!40, A!41, F!42))) | (~apply(F!42, tptp_fun_X_7(B!40, A!41, F!42), tptp_fun_Y2_5(B!40, A!41, F!42))) | (~member(tptp_fun_X_7(B!40, A!41, F!42), A!41)) | (~member(tptp_fun_Y1_6(B!40, A!41, F!42), B!40)) | (~member(tptp_fun_Y2_5(B!40, A!41, F!42), B!40)))) | (~((~member(tptp_fun_X_4(B!40, A!41, F!42), A!41)) | (~![Y: $i] : ((~member(Y, B!40)) | (~apply(F!42, tptp_fun_X_4(B!40, A!41, F!42), Y))))))))))) <=> ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(F!42, A!41, B!40)) | (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!42), B!40)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!40, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)))))))) | (~(maps(F!42, A!41, B!40) | (~((~member(tptp_fun_X_4(B!40, A!41, F!42), A!41)) | (~![Y: $i] : ((~member(Y, B!40)) | (~apply(F!42, tptp_fun_X_4(B!40, A!41, F!42), Y)))))) | (~((~member(tptp_fun_Y2_5(B!40, A!41, F!42), B!40)) | (~member(tptp_fun_Y1_6(B!40, A!41, F!42), B!40)) | (~member(tptp_fun_X_7(B!40, A!41, F!42), A!41)) | (~apply(F!42, tptp_fun_X_7(B!40, A!41, F!42), tptp_fun_Y2_5(B!40, A!41, F!42))) | (~apply(F!42, tptp_fun_X_7(B!40, A!41, F!42), tptp_fun_Y1_6(B!40, A!41, F!42))) | (tptp_fun_Y1_6(B!40, A!41, F!42) = tptp_fun_Y2_5(B!40, A!41, F!42)))))))))),
% 0.24/0.51 inference(monotonicity,[status(thm)],[139])).
% 0.24/0.51 tff(141,plain,
% 0.24/0.51 (((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(F!42, A!41, B!40)) | (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!42), B!40)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!40, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)) | (~member(Y2, B!40)))))))) | (~(maps(F!42, A!41, B!40) | (~((tptp_fun_Y1_6(B!40, A!41, F!42) = tptp_fun_Y2_5(B!40, A!41, F!42)) | (~apply(F!42, tptp_fun_X_7(B!40, A!41, F!42), tptp_fun_Y1_6(B!40, A!41, F!42))) | (~apply(F!42, tptp_fun_X_7(B!40, A!41, F!42), tptp_fun_Y2_5(B!40, A!41, F!42))) | (~member(tptp_fun_X_7(B!40, A!41, F!42), A!41)) | (~member(tptp_fun_Y1_6(B!40, A!41, F!42), B!40)) | (~member(tptp_fun_Y2_5(B!40, A!41, F!42), B!40)))) | (~((~member(tptp_fun_X_4(B!40, A!41, F!42), A!41)) | (~![Y: $i] : ((~member(Y, B!40)) | (~apply(F!42, tptp_fun_X_4(B!40, A!41, F!42), Y))))))))))) <=> ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(F!42, A!41, B!40)) | (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!42), B!40)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!40, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)))))))) | (~(maps(F!42, A!41, B!40) | (~((~member(tptp_fun_X_4(B!40, A!41, F!42), A!41)) | (~![Y: $i] : ((~member(Y, B!40)) | (~apply(F!42, tptp_fun_X_4(B!40, A!41, F!42), Y)))))) | (~((~member(tptp_fun_Y2_5(B!40, A!41, F!42), B!40)) | (~member(tptp_fun_Y1_6(B!40, A!41, F!42), B!40)) | (~member(tptp_fun_X_7(B!40, A!41, F!42), A!41)) | (~apply(F!42, tptp_fun_X_7(B!40, A!41, F!42), tptp_fun_Y2_5(B!40, A!41, F!42))) | (~apply(F!42, tptp_fun_X_7(B!40, A!41, F!42), tptp_fun_Y1_6(B!40, A!41, F!42))) | (tptp_fun_Y1_6(B!40, A!41, F!42) = tptp_fun_Y2_5(B!40, A!41, F!42)))))))))),
% 0.24/0.51 inference(transitivity,[status(thm)],[140, 138])).
% 0.24/0.51 tff(142,plain,
% 0.24/0.51 ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(F!42, A!41, B!40)) | (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!42), B!40)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!40, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)) | (~member(Y2, B!40)))))))) | (~(maps(F!42, A!41, B!40) | (~((tptp_fun_Y1_6(B!40, A!41, F!42) = tptp_fun_Y2_5(B!40, A!41, F!42)) | (~apply(F!42, tptp_fun_X_7(B!40, A!41, F!42), tptp_fun_Y1_6(B!40, A!41, F!42))) | (~apply(F!42, tptp_fun_X_7(B!40, A!41, F!42), tptp_fun_Y2_5(B!40, A!41, F!42))) | (~member(tptp_fun_X_7(B!40, A!41, F!42), A!41)) | (~member(tptp_fun_Y1_6(B!40, A!41, F!42), B!40)) | (~member(tptp_fun_Y2_5(B!40, A!41, F!42), B!40)))) | (~((~member(tptp_fun_X_4(B!40, A!41, F!42), A!41)) | (~![Y: $i] : ((~member(Y, B!40)) | (~apply(F!42, tptp_fun_X_4(B!40, A!41, F!42), Y))))))))))),
% 0.24/0.51 inference(quant_inst,[status(thm)],[])).
% 0.24/0.51 tff(143,plain,
% 0.24/0.51 ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(F!42, A!41, B!40)) | (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!42), B!40)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!40, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)))))))) | (~(maps(F!42, A!41, B!40) | (~((~member(tptp_fun_X_4(B!40, A!41, F!42), A!41)) | (~![Y: $i] : ((~member(Y, B!40)) | (~apply(F!42, tptp_fun_X_4(B!40, A!41, F!42), Y)))))) | (~((~member(tptp_fun_Y2_5(B!40, A!41, F!42), B!40)) | (~member(tptp_fun_Y1_6(B!40, A!41, F!42), B!40)) | (~member(tptp_fun_X_7(B!40, A!41, F!42), A!41)) | (~apply(F!42, tptp_fun_X_7(B!40, A!41, F!42), tptp_fun_Y2_5(B!40, A!41, F!42))) | (~apply(F!42, tptp_fun_X_7(B!40, A!41, F!42), tptp_fun_Y1_6(B!40, A!41, F!42))) | (tptp_fun_Y1_6(B!40, A!41, F!42) = tptp_fun_Y2_5(B!40, A!41, F!42))))))))),
% 0.24/0.51 inference(modus_ponens,[status(thm)],[142, 141])).
% 0.24/0.51 tff(144,plain,
% 0.24/0.51 (~((~((~maps(F!42, A!41, B!40)) | (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!42), B!40)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!40, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)))))))) | (~(maps(F!42, A!41, B!40) | (~((~member(tptp_fun_X_4(B!40, A!41, F!42), A!41)) | (~![Y: $i] : ((~member(Y, B!40)) | (~apply(F!42, tptp_fun_X_4(B!40, A!41, F!42), Y)))))) | (~((~member(tptp_fun_Y2_5(B!40, A!41, F!42), B!40)) | (~member(tptp_fun_Y1_6(B!40, A!41, F!42), B!40)) | (~member(tptp_fun_X_7(B!40, A!41, F!42), A!41)) | (~apply(F!42, tptp_fun_X_7(B!40, A!41, F!42), tptp_fun_Y2_5(B!40, A!41, F!42))) | (~apply(F!42, tptp_fun_X_7(B!40, A!41, F!42), tptp_fun_Y1_6(B!40, A!41, F!42))) | (tptp_fun_Y1_6(B!40, A!41, F!42) = tptp_fun_Y2_5(B!40, A!41, F!42)))))))),
% 0.24/0.51 inference(unit_resolution,[status(thm)],[143, 137])).
% 0.24/0.51 tff(145,plain,
% 0.24/0.51 (((~((~maps(F!42, A!41, B!40)) | (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!42), B!40)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!40, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)))))))) | (~(maps(F!42, A!41, B!40) | (~((~member(tptp_fun_X_4(B!40, A!41, F!42), A!41)) | (~![Y: $i] : ((~member(Y, B!40)) | (~apply(F!42, tptp_fun_X_4(B!40, A!41, F!42), Y)))))) | (~((~member(tptp_fun_Y2_5(B!40, A!41, F!42), B!40)) | (~member(tptp_fun_Y1_6(B!40, A!41, F!42), B!40)) | (~member(tptp_fun_X_7(B!40, A!41, F!42), A!41)) | (~apply(F!42, tptp_fun_X_7(B!40, A!41, F!42), tptp_fun_Y2_5(B!40, A!41, F!42))) | (~apply(F!42, tptp_fun_X_7(B!40, A!41, F!42), tptp_fun_Y1_6(B!40, A!41, F!42))) | (tptp_fun_Y1_6(B!40, A!41, F!42) = tptp_fun_Y2_5(B!40, A!41, F!42))))))) | ((~maps(F!42, A!41, B!40)) | (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!42), B!40)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!40, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)))))))),
% 0.24/0.51 inference(tautology,[status(thm)],[])).
% 0.24/0.51 tff(146,plain,
% 0.24/0.51 ((~maps(F!42, A!41, B!40)) | (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!42), B!40)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!40, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40))))))),
% 0.24/0.51 inference(unit_resolution,[status(thm)],[145, 144])).
% 0.24/0.51 tff(147,plain,
% 0.24/0.51 (maps(F!42, A!41, B!40)),
% 0.24/0.51 inference(and_elim,[status(thm)],[99])).
% 0.24/0.51 tff(148,plain,
% 0.24/0.51 ((~((~maps(F!42, A!41, B!40)) | (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!42), B!40)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!40, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)))))))) | (~maps(F!42, A!41, B!40)) | (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!42), B!40)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!40, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40))))))),
% 0.24/0.51 inference(tautology,[status(thm)],[])).
% 0.24/0.51 tff(149,plain,
% 0.24/0.51 ((~((~maps(F!42, A!41, B!40)) | (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!42), B!40)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!40, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)))))))) | (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!42), B!40)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!40, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40))))))),
% 0.24/0.51 inference(unit_resolution,[status(thm)],[148, 147])).
% 0.24/0.51 tff(150,plain,
% 0.24/0.51 (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!42), B!40)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!40, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)))))),
% 0.24/0.51 inference(unit_resolution,[status(thm)],[149, 146])).
% 0.24/0.51 tff(151,plain,
% 0.24/0.51 (((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!42), B!40)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!40, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40))))) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)))),
% 0.24/0.51 inference(tautology,[status(thm)],[])).
% 0.24/0.51 tff(152,plain,
% 0.24/0.51 (![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)))),
% 0.24/0.51 inference(unit_resolution,[status(thm)],[151, 150])).
% 0.24/0.51 tff(153,plain,
% 0.24/0.51 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)))) | ((~member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), B!40)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)))) | (~member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), A!41)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42))) | (tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42) = tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))) | (~member(tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42), B!40)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)))) | (~member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), B!40)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)))) | (~member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), A!41)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42))) | (tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42) = tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))) | (~member(tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42), B!40)))),
% 0.24/0.52 inference(rewrite,[status(thm)],[])).
% 0.24/0.52 tff(154,plain,
% 0.24/0.52 (((tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42) = tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))) | (~member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), B!40)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42))) | (~apply(F!42, tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)))) | (~member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), A!41)) | (~member(tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42), B!40))) <=> ((~member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), B!40)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)))) | (~member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), A!41)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42))) | (tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42) = tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))) | (~member(tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42), B!40)))),
% 0.24/0.52 inference(rewrite,[status(thm)],[])).
% 0.24/0.52 tff(155,plain,
% 0.24/0.52 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)))) | ((tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42) = tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))) | (~member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), B!40)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42))) | (~apply(F!42, tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)))) | (~member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), A!41)) | (~member(tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42), B!40)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)))) | ((~member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), B!40)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)))) | (~member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), A!41)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42))) | (tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42) = tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))) | (~member(tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42), B!40))))),
% 0.24/0.52 inference(monotonicity,[status(thm)],[154])).
% 0.24/0.52 tff(156,plain,
% 0.24/0.52 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)))) | ((tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42) = tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))) | (~member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), B!40)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42))) | (~apply(F!42, tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)))) | (~member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), A!41)) | (~member(tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42), B!40)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)))) | (~member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), B!40)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)))) | (~member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), A!41)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42))) | (tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42) = tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))) | (~member(tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42), B!40)))),
% 0.24/0.52 inference(transitivity,[status(thm)],[155, 153])).
% 0.24/0.52 tff(157,plain,
% 0.24/0.52 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)))) | ((tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42) = tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))) | (~member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), B!40)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42))) | (~apply(F!42, tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)))) | (~member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), A!41)) | (~member(tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42), B!40)))),
% 0.24/0.52 inference(quant_inst,[status(thm)],[])).
% 0.24/0.52 tff(158,plain,
% 0.24/0.52 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)))) | (~member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), B!40)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)))) | (~member(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), A!41)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42))) | (tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42) = tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))) | (~member(tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42), B!40))),
% 0.24/0.52 inference(modus_ponens,[status(thm)],[157, 156])).
% 0.24/0.52 tff(159,plain,
% 0.24/0.52 ((tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42) = tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))) | (~member(tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42), B!40))),
% 0.24/0.52 inference(unit_resolution,[status(thm)],[158, 152, 115, 113, 111, 109])).
% 0.24/0.52 tff(160,plain,
% 0.24/0.52 (tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42) = tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))),
% 0.24/0.52 inference(unit_resolution,[status(thm)],[159, 107])).
% 0.24/0.52 tff(161,plain,
% 0.24/0.52 (member(tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42), Y!39) <=> member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), Y!39)),
% 0.24/0.52 inference(monotonicity,[status(thm)],[160])).
% 0.24/0.52 tff(162,plain,
% 0.24/0.52 (member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), Y!39) <=> member(tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42), Y!39)),
% 0.24/0.53 inference(symmetry,[status(thm)],[161])).
% 0.24/0.53 tff(163,plain,
% 0.24/0.53 ((~member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), Y!39)) <=> (~member(tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42), Y!39))),
% 0.24/0.53 inference(monotonicity,[status(thm)],[162])).
% 0.24/0.53 tff(164,plain,
% 0.24/0.53 (((~member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40))) | member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), Y!39)) | (~member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), Y!39))),
% 0.24/0.53 inference(tautology,[status(thm)],[])).
% 0.24/0.53 tff(165,plain,
% 0.24/0.53 (~member(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), Y!39)),
% 0.24/0.53 inference(unit_resolution,[status(thm)],[164, 82])).
% 0.24/0.53 tff(166,plain,
% 0.24/0.53 (~member(tptp_fun_Y_26(tptp_fun_X_24(tptp_fun_X_0(Y!39, image3(F!42, inverse_image3(F!42, Y!39, A!41), B!40)), inverse_image3(F!42, Y!39, A!41), F!42), Y!39, F!42), Y!39)),
% 0.24/0.53 inference(modus_ponens,[status(thm)],[165, 163])).
% 0.24/0.53 tff(167,plain,
% 0.24/0.53 ($false),
% 0.24/0.53 inference(unit_resolution,[status(thm)],[94, 166])).
% 0.24/0.53 % SZS output end Proof
% 0.24/0.53 % E exiting
%------------------------------------------------------------------------------