%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET757+4 : TPTP v9.0.0. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n002.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 0.21s 0.42s
% Output : Proof 0.48s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.14 % Problem : SET757+4 : TPTP v9.0.0. Bugfixed v2.2.1.
% 0.03/0.14 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n002.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Jun 20 05:42:01 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.21/0.42 % SZS status Theorem
% 0.21/0.42 % SZS output start Proof
% 0.21/0.42 tff(member_type, type, (
% 0.21/0.42 member: ( $i * $i ) > $o)).
% 0.21/0.42 tff(tptp_fun_Y_39_type, type, (
% 0.21/0.42 tptp_fun_Y_39: $i)).
% 0.21/0.42 tff(tptp_fun_Y_26_type, type, (
% 0.21/0.42 tptp_fun_Y_26: ( $i * $i * $i ) > $i)).
% 0.21/0.42 tff(tptp_fun_F_43_type, type, (
% 0.21/0.42 tptp_fun_F_43: $i)).
% 0.21/0.42 tff(tptp_fun_X_40_type, type, (
% 0.21/0.42 tptp_fun_X_40: $i)).
% 0.21/0.42 tff(tptp_fun_X_0_type, type, (
% 0.21/0.42 tptp_fun_X_0: ( $i * $i ) > $i)).
% 0.21/0.42 tff(intersection_type, type, (
% 0.21/0.42 intersection: ( $i * $i ) > $i)).
% 0.21/0.42 tff(inverse_image3_type, type, (
% 0.21/0.42 inverse_image3: ( $i * $i * $i ) > $i)).
% 0.21/0.42 tff(tptp_fun_A_42_type, type, (
% 0.21/0.42 tptp_fun_A_42: $i)).
% 0.21/0.42 tff(tptp_fun_B_41_type, type, (
% 0.21/0.42 tptp_fun_B_41: $i)).
% 0.21/0.42 tff(apply_type, type, (
% 0.21/0.42 apply: ( $i * $i * $i ) > $o)).
% 0.21/0.42 tff(subset_type, type, (
% 0.21/0.42 subset: ( $i * $i ) > $o)).
% 0.21/0.42 tff(equal_set_type, type, (
% 0.21/0.42 equal_set: ( $i * $i ) > $o)).
% 0.21/0.42 tff(maps_type, type, (
% 0.21/0.42 maps: ( $i * $i * $i ) > $o)).
% 0.21/0.42 tff(tptp_fun_Y_3_type, type, (
% 0.21/0.42 tptp_fun_Y_3: ( $i * $i * $i ) > $i)).
% 0.21/0.42 tff(tptp_fun_Y2_5_type, type, (
% 0.21/0.42 tptp_fun_Y2_5: ( $i * $i * $i ) > $i)).
% 0.21/0.42 tff(tptp_fun_Y1_6_type, type, (
% 0.21/0.42 tptp_fun_Y1_6: ( $i * $i * $i ) > $i)).
% 0.21/0.42 tff(tptp_fun_X_7_type, type, (
% 0.21/0.42 tptp_fun_X_7: ( $i * $i * $i ) > $i)).
% 0.21/0.42 tff(tptp_fun_X_4_type, type, (
% 0.21/0.42 tptp_fun_X_4: ( $i * $i * $i ) > $i)).
% 0.21/0.42 tff(1,plain,
% 0.21/0.42 (^[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))))))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(2,plain,
% 0.21/0.42 (![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)))))))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[1])).
% 0.21/0.42 tff(3,plain,
% 0.21/0.42 (^[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))))))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(4,plain,
% 0.21/0.42 (![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)))))))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[3])).
% 0.21/0.42 tff(5,plain,
% 0.21/0.42 (![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)))))))),
% 0.21/0.42 inference(transitivity,[status(thm)],[4, 2])).
% 0.21/0.42 tff(6,plain,
% 0.21/0.42 (^[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)))))))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(7,plain,
% 0.21/0.42 (![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)))))))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[6])).
% 0.21/0.42 tff(8,plain,
% 0.21/0.42 (^[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))))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(9,plain,
% 0.21/0.42 (![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)))))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[8])).
% 0.21/0.42 tff(10,plain,
% 0.21/0.42 (![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))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 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')).
% 0.21/0.42 tff(12,plain,
% 0.21/0.42 (![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))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.21/0.42 tff(13,plain,(
% 0.21/0.42 ![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))))))),
% 0.21/0.42 inference(skolemize,[status(sab)],[12])).
% 0.21/0.42 tff(14,plain,
% 0.21/0.42 (![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)))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[13, 9])).
% 0.21/0.42 tff(15,plain,
% 0.21/0.42 (![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)))))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[14, 7])).
% 0.21/0.42 tff(16,plain,
% 0.21/0.42 (![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)))))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[15, 5])).
% 0.21/0.42 tff(17,plain,
% 0.21/0.42 (((~![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)))))))) | (~((~((~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), A!42)) | member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), inverse_image3(F!43, Y!39, A!42)) | ![Y: $i] : ((~member(Y, Y!39)) | (~apply(F!43, tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), Y))))) | (~((~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), inverse_image3(F!43, Y!39, A!42))) | (~((~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), A!42)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), Y!39, F!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_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), A!42)) | member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), inverse_image3(F!43, Y!39, A!42)) | ![Y: $i] : ((~member(Y, Y!39)) | (~apply(F!43, tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), Y))))) | (~((~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), inverse_image3(F!43, Y!39, A!42))) | (~((~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), A!42)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), Y!39, F!43))))))))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(18,plain,
% 0.21/0.43 ((~((~((~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), inverse_image3(F!43, Y!39, A!42))) | (~((~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), A!42)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), Y!39, F!43))))))) | (~(member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), inverse_image3(F!43, Y!39, A!42)) | (~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), A!42)) | ![Y: $i] : ((~member(Y, Y!39)) | (~apply(F!43, tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), Y))))))) <=> (~((~((~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), A!42)) | member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), inverse_image3(F!43, Y!39, A!42)) | ![Y: $i] : ((~member(Y, Y!39)) | (~apply(F!43, tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), Y))))) | (~((~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), inverse_image3(F!43, Y!39, A!42))) | (~((~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), A!42)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), Y!39, F!43)))))))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(19,plain,
% 0.21/0.43 (((~![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_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), inverse_image3(F!43, Y!39, A!42))) | (~((~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), A!42)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), Y!39, F!43))))))) | (~(member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), inverse_image3(F!43, Y!39, A!42)) | (~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), A!42)) | ![Y: $i] : ((~member(Y, Y!39)) | (~apply(F!43, tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!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_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), A!42)) | member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), inverse_image3(F!43, Y!39, A!42)) | ![Y: $i] : ((~member(Y, Y!39)) | (~apply(F!43, tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), Y))))) | (~((~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), inverse_image3(F!43, Y!39, A!42))) | (~((~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), A!42)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), Y!39, F!43))))))))))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[18])).
% 0.21/0.43 tff(20,plain,
% 0.21/0.43 (((~![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_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), inverse_image3(F!43, Y!39, A!42))) | (~((~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), A!42)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), Y!39, F!43))))))) | (~(member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), inverse_image3(F!43, Y!39, A!42)) | (~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), A!42)) | ![Y: $i] : ((~member(Y, Y!39)) | (~apply(F!43, tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!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_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), A!42)) | member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), inverse_image3(F!43, Y!39, A!42)) | ![Y: $i] : ((~member(Y, Y!39)) | (~apply(F!43, tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), Y))))) | (~((~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), inverse_image3(F!43, Y!39, A!42))) | (~((~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), A!42)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), Y!39, F!43))))))))))),
% 0.21/0.44 inference(transitivity,[status(thm)],[19, 17])).
% 0.21/0.44 tff(21,plain,
% 0.21/0.44 ((~![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_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), inverse_image3(F!43, Y!39, A!42))) | (~((~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), A!42)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), Y!39, F!43))))))) | (~(member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), inverse_image3(F!43, Y!39, A!42)) | (~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), A!42)) | ![Y: $i] : ((~member(Y, Y!39)) | (~apply(F!43, tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), Y)))))))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(22,plain,
% 0.21/0.44 ((~![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_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), A!42)) | member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), inverse_image3(F!43, Y!39, A!42)) | ![Y: $i] : ((~member(Y, Y!39)) | (~apply(F!43, tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), Y))))) | (~((~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), inverse_image3(F!43, Y!39, A!42))) | (~((~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), A!42)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), Y!39, F!43)))))))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.21/0.44 tff(23,plain,
% 0.21/0.44 (~((~((~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), A!42)) | member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), inverse_image3(F!43, Y!39, A!42)) | ![Y: $i] : ((~member(Y, Y!39)) | (~apply(F!43, tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), Y))))) | (~((~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), inverse_image3(F!43, Y!39, A!42))) | (~((~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), A!42)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), Y!39, F!43))))))))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[22, 16])).
% 0.21/0.44 tff(24,plain,
% 0.21/0.44 (((~((~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), A!42)) | member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), inverse_image3(F!43, Y!39, A!42)) | ![Y: $i] : ((~member(Y, Y!39)) | (~apply(F!43, tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), Y))))) | (~((~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), inverse_image3(F!43, Y!39, A!42))) | (~((~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), A!42)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), Y!39, F!43)))))))) | ((~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), inverse_image3(F!43, Y!39, A!42))) | (~((~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), A!42)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), Y!39, F!43))))))),
% 0.22/0.45 inference(tautology,[status(thm)],[])).
% 0.22/0.45 tff(25,plain,
% 0.22/0.45 ((~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), inverse_image3(F!43, Y!39, A!42))) | (~((~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), A!42)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), Y!39, F!43)))))),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[24, 23])).
% 0.22/0.45 tff(26,plain,
% 0.22/0.45 (^[X: $i, A: $i, B: $i] : refl((~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B)))) <=> (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B)))))),
% 0.22/0.45 inference(bind,[status(th)],[])).
% 0.22/0.45 tff(27,plain,
% 0.22/0.45 (![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B)))) <=> ![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))),
% 0.22/0.45 inference(quant_intro,[status(thm)],[26])).
% 0.22/0.45 tff(28,plain,
% 0.22/0.45 (^[X: $i, A: $i, B: $i] : trans(trans(monotonicity(rewrite((member(X, A) & member(X, B)) <=> (~((~member(X, A)) | (~member(X, B))))), ((member(X, intersection(A, B)) <=> (member(X, A) & member(X, B))) <=> (member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B))))))), rewrite((member(X, intersection(A, B)) <=> (~((~member(X, A)) | (~member(X, B))))) <=> (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))), ((member(X, intersection(A, B)) <=> (member(X, A) & member(X, B))) <=> (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B)))))), rewrite((~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B)))) <=> (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))), ((member(X, intersection(A, B)) <=> (member(X, A) & member(X, B))) <=> (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))))),
% 0.22/0.45 inference(bind,[status(th)],[])).
% 0.22/0.45 tff(29,plain,
% 0.22/0.45 (![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (member(X, A) & member(X, B))) <=> ![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))),
% 0.22/0.45 inference(quant_intro,[status(thm)],[28])).
% 0.22/0.45 tff(30,plain,
% 0.22/0.45 (![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (member(X, A) & member(X, B))) <=> ![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (member(X, A) & member(X, B)))),
% 0.22/0.45 inference(rewrite,[status(thm)],[])).
% 0.22/0.45 tff(31,axiom,(![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (member(X, A) & member(X, B)))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax','intersection')).
% 0.22/0.45 tff(32,plain,
% 0.22/0.45 (![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (member(X, A) & member(X, B)))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.22/0.45 tff(33,plain,(
% 0.22/0.45 ![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (member(X, A) & member(X, B)))),
% 0.22/0.45 inference(skolemize,[status(sab)],[32])).
% 0.22/0.45 tff(34,plain,
% 0.22/0.45 (![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[33, 29])).
% 0.22/0.45 tff(35,plain,
% 0.22/0.45 (![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[34, 27])).
% 0.22/0.45 tff(36,plain,
% 0.22/0.45 ((~![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))) | (~(((~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), inverse_image3(F!43, X!40, A!42))) | (~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), inverse_image3(F!43, Y!39, A!42)))) <=> member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)))))),
% 0.22/0.45 inference(quant_inst,[status(thm)],[])).
% 0.22/0.45 tff(37,plain,
% 0.22/0.45 (~(((~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), inverse_image3(F!43, X!40, A!42))) | (~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), inverse_image3(F!43, Y!39, A!42)))) <=> member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))))),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[36, 35])).
% 0.22/0.45 tff(38,plain,
% 0.22/0.45 (^[A: $i, B: $i] : refl((~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))))),
% 0.22/0.45 inference(bind,[status(th)],[])).
% 0.22/0.45 tff(39,plain,
% 0.22/0.45 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.22/0.45 inference(quant_intro,[status(thm)],[38])).
% 0.22/0.45 tff(40,plain,
% 0.22/0.45 (^[A: $i, B: $i] : rewrite((~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))))),
% 0.22/0.45 inference(bind,[status(th)],[])).
% 0.22/0.45 tff(41,plain,
% 0.22/0.45 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.22/0.45 inference(quant_intro,[status(thm)],[40])).
% 0.22/0.45 tff(42,plain,
% 0.22/0.45 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.22/0.45 inference(transitivity,[status(thm)],[41, 39])).
% 0.22/0.45 tff(43,plain,
% 0.22/0.45 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) <=> ((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))), rewrite((subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))) <=> (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))), ((((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> (((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))))), rewrite((((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))), ((((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))))),
% 0.22/0.45 inference(bind,[status(th)],[])).
% 0.22/0.45 tff(44,plain,
% 0.22/0.45 (![A: $i, B: $i] : (((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.22/0.45 inference(quant_intro,[status(thm)],[43])).
% 0.22/0.45 tff(45,plain,
% 0.22/0.45 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.22/0.45 inference(rewrite,[status(thm)],[])).
% 0.22/0.45 tff(46,plain,
% 0.22/0.45 (^[A: $i, B: $i] : rewrite((subset(A, B) <=> ![X: $i] : (member(X, A) => member(X, B))) <=> (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B))))),
% 0.22/0.45 inference(bind,[status(th)],[])).
% 0.22/0.45 tff(47,plain,
% 0.22/0.45 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : (member(X, A) => member(X, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.22/0.45 inference(quant_intro,[status(thm)],[46])).
% 0.22/0.45 tff(48,axiom,(![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : (member(X, A) => member(X, B)))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax','subset')).
% 0.22/0.45 tff(49,plain,
% 0.22/0.45 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.22/0.45 tff(50,plain,
% 0.22/0.45 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[49, 45])).
% 0.22/0.45 tff(51,plain,(
% 0.22/0.45 ![A: $i, B: $i] : (((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B))) & (subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))),
% 0.22/0.45 inference(skolemize,[status(sab)],[50])).
% 0.22/0.45 tff(52,plain,
% 0.22/0.45 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[51, 44])).
% 0.22/0.45 tff(53,plain,
% 0.22/0.45 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[52, 42])).
% 0.22/0.45 tff(54,plain,
% 0.22/0.45 ((~![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(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42))) | ![X: $i] : ((~member(X, intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)))) | member(X, inverse_image3(F!43, intersection(X!40, Y!39), A!42))))) | (~(subset(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)) | (~((~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)))) | member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), inverse_image3(F!43, intersection(X!40, Y!39), A!42))))))))),
% 0.22/0.45 inference(quant_inst,[status(thm)],[])).
% 0.22/0.45 tff(55,plain,
% 0.22/0.45 (~((~((~subset(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42))) | ![X: $i] : ((~member(X, intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)))) | member(X, inverse_image3(F!43, intersection(X!40, Y!39), A!42))))) | (~(subset(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)) | (~((~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)))) | member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), inverse_image3(F!43, intersection(X!40, Y!39), A!42)))))))),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[54, 53])).
% 0.22/0.45 tff(56,plain,
% 0.22/0.45 (((~((~subset(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42))) | ![X: $i] : ((~member(X, intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)))) | member(X, inverse_image3(F!43, intersection(X!40, Y!39), A!42))))) | (~(subset(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)) | (~((~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)))) | member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), inverse_image3(F!43, intersection(X!40, Y!39), A!42))))))) | (subset(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)) | (~((~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)))) | member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), inverse_image3(F!43, intersection(X!40, Y!39), A!42)))))),
% 0.22/0.45 inference(tautology,[status(thm)],[])).
% 0.22/0.45 tff(57,plain,
% 0.22/0.45 (subset(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)) | (~((~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)))) | member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), inverse_image3(F!43, intersection(X!40, Y!39), A!42))))),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[56, 55])).
% 0.22/0.45 tff(58,assumption,((~((~subset(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)))) | ![X: $i] : ((~member(X, inverse_image3(F!43, intersection(X!40, Y!39), A!42))) | member(X, intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)))))) | (~(subset(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))) | (~((~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42))) | member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)))))))), introduced(assumption)).
% 0.22/0.46 tff(59,plain,
% 0.22/0.46 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))) | (~((~((~subset(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)))) | ![X: $i] : ((~member(X, inverse_image3(F!43, intersection(X!40, Y!39), A!42))) | member(X, intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)))))) | (~(subset(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))) | (~((~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42))) | member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)))))))))),
% 0.22/0.46 inference(quant_inst,[status(thm)],[])).
% 0.22/0.46 tff(60,plain,
% 0.22/0.46 ($false),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[59, 53, 58])).
% 0.22/0.46 tff(61,plain,(~((~((~subset(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)))) | ![X: $i] : ((~member(X, inverse_image3(F!43, intersection(X!40, Y!39), A!42))) | member(X, intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)))))) | (~(subset(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))) | (~((~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42))) | member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))))))))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.46 tff(62,plain,
% 0.22/0.46 (((~((~subset(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)))) | ![X: $i] : ((~member(X, inverse_image3(F!43, intersection(X!40, Y!39), A!42))) | member(X, intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)))))) | (~(subset(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))) | (~((~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42))) | member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)))))))) | (subset(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))) | (~((~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42))) | member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))))))),
% 0.22/0.46 inference(tautology,[status(thm)],[])).
% 0.22/0.46 tff(63,plain,
% 0.22/0.46 (subset(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))) | (~((~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42))) | member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)))))),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[62, 61])).
% 0.22/0.46 tff(64,plain,
% 0.22/0.46 (((~![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_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), inverse_image3(F!43, Y!39, A!42)) | (~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), A!42)) | ![Y: $i] : ((~member(Y, Y!39)) | (~apply(F!43, tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), Y))))) | (~((~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), inverse_image3(F!43, Y!39, A!42))) | (~((~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), A!42)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), Y!39, F!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_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), inverse_image3(F!43, Y!39, A!42)) | (~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), A!42)) | ![Y: $i] : ((~member(Y, Y!39)) | (~apply(F!43, tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), Y))))) | (~((~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), inverse_image3(F!43, Y!39, A!42))) | (~((~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), A!42)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), Y!39, F!43))))))))))),
% 0.22/0.47 inference(rewrite,[status(thm)],[])).
% 0.22/0.47 tff(65,plain,
% 0.22/0.47 ((~((~((~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), inverse_image3(F!43, Y!39, A!42))) | (~((~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), A!42)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), Y!39, F!43))))))) | (~(member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), inverse_image3(F!43, Y!39, A!42)) | (~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), A!42)) | ![Y: $i] : ((~member(Y, Y!39)) | (~apply(F!43, tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), Y))))))) <=> (~((~(member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), inverse_image3(F!43, Y!39, A!42)) | (~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), A!42)) | ![Y: $i] : ((~member(Y, Y!39)) | (~apply(F!43, tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), Y))))) | (~((~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), inverse_image3(F!43, Y!39, A!42))) | (~((~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), A!42)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), Y!39, F!43)))))))))),
% 0.22/0.47 inference(rewrite,[status(thm)],[])).
% 0.22/0.47 tff(66,plain,
% 0.22/0.47 (((~![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_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), inverse_image3(F!43, Y!39, A!42))) | (~((~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), A!42)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), Y!39, F!43))))))) | (~(member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), inverse_image3(F!43, Y!39, A!42)) | (~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), A!42)) | ![Y: $i] : ((~member(Y, Y!39)) | (~apply(F!43, tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!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_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), inverse_image3(F!43, Y!39, A!42)) | (~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), A!42)) | ![Y: $i] : ((~member(Y, Y!39)) | (~apply(F!43, tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), Y))))) | (~((~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), inverse_image3(F!43, Y!39, A!42))) | (~((~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), A!42)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), Y!39, F!43))))))))))),
% 0.22/0.47 inference(monotonicity,[status(thm)],[65])).
% 0.22/0.47 tff(67,plain,
% 0.22/0.47 (((~![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_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), inverse_image3(F!43, Y!39, A!42))) | (~((~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), A!42)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), Y!39, F!43))))))) | (~(member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), inverse_image3(F!43, Y!39, A!42)) | (~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), A!42)) | ![Y: $i] : ((~member(Y, Y!39)) | (~apply(F!43, tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!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_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), inverse_image3(F!43, Y!39, A!42)) | (~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), A!42)) | ![Y: $i] : ((~member(Y, Y!39)) | (~apply(F!43, tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), Y))))) | (~((~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), inverse_image3(F!43, Y!39, A!42))) | (~((~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), A!42)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), Y!39, F!43))))))))))),
% 0.22/0.48 inference(transitivity,[status(thm)],[66, 64])).
% 0.22/0.48 tff(68,plain,
% 0.22/0.48 ((~![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_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), inverse_image3(F!43, Y!39, A!42))) | (~((~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), A!42)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), Y!39, F!43))))))) | (~(member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), inverse_image3(F!43, Y!39, A!42)) | (~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), A!42)) | ![Y: $i] : ((~member(Y, Y!39)) | (~apply(F!43, tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), Y)))))))),
% 0.22/0.48 inference(quant_inst,[status(thm)],[])).
% 0.22/0.48 tff(69,plain,
% 0.22/0.48 ((~![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_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), inverse_image3(F!43, Y!39, A!42)) | (~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), A!42)) | ![Y: $i] : ((~member(Y, Y!39)) | (~apply(F!43, tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), Y))))) | (~((~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), inverse_image3(F!43, Y!39, A!42))) | (~((~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), A!42)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), Y!39, F!43)))))))))),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.22/0.48 tff(70,plain,
% 0.22/0.48 (~((~(member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), inverse_image3(F!43, Y!39, A!42)) | (~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), A!42)) | ![Y: $i] : ((~member(Y, Y!39)) | (~apply(F!43, tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), Y))))) | (~((~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), inverse_image3(F!43, Y!39, A!42))) | (~((~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), A!42)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), Y!39, F!43))))))))),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[69, 16])).
% 0.22/0.48 tff(71,plain,
% 0.22/0.48 (((~(member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), inverse_image3(F!43, Y!39, A!42)) | (~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), A!42)) | ![Y: $i] : ((~member(Y, Y!39)) | (~apply(F!43, tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), Y))))) | (~((~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), inverse_image3(F!43, Y!39, A!42))) | (~((~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), A!42)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), Y!39, F!43)))))))) | (member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), inverse_image3(F!43, Y!39, A!42)) | (~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), A!42)) | ![Y: $i] : ((~member(Y, Y!39)) | (~apply(F!43, tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), Y))))),
% 0.22/0.48 inference(tautology,[status(thm)],[])).
% 0.22/0.48 tff(72,plain,
% 0.22/0.48 (member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), inverse_image3(F!43, Y!39, A!42)) | (~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), A!42)) | ![Y: $i] : ((~member(Y, Y!39)) | (~apply(F!43, tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), Y)))),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[71, 70])).
% 0.22/0.48 tff(73,plain,
% 0.22/0.48 ((~![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))) | (~(((~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), inverse_image3(F!43, X!40, A!42))) | (~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), inverse_image3(F!43, Y!39, A!42)))) <=> member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)))))),
% 0.22/0.48 inference(quant_inst,[status(thm)],[])).
% 0.22/0.48 tff(74,plain,
% 0.22/0.48 (~(((~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), inverse_image3(F!43, X!40, A!42))) | (~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), inverse_image3(F!43, Y!39, A!42)))) <=> member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))))),
% 0.22/0.49 inference(unit_resolution,[status(thm)],[73, 35])).
% 0.22/0.49 tff(75,assumption,(~((~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42))) | member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))))), introduced(assumption)).
% 0.22/0.49 tff(76,plain,
% 0.22/0.49 (((~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42))) | member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)))) | (~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))))),
% 0.22/0.49 inference(tautology,[status(thm)],[])).
% 0.22/0.49 tff(77,plain,
% 0.22/0.49 (~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)))),
% 0.22/0.49 inference(unit_resolution,[status(thm)],[76, 75])).
% 0.22/0.49 tff(78,plain,
% 0.22/0.49 ((((~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), inverse_image3(F!43, X!40, A!42))) | (~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), inverse_image3(F!43, Y!39, A!42)))) <=> member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)))) | ((~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), inverse_image3(F!43, X!40, A!42))) | (~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), inverse_image3(F!43, Y!39, A!42)))) | member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)))),
% 0.22/0.49 inference(tautology,[status(thm)],[])).
% 0.22/0.49 tff(79,plain,
% 0.22/0.49 ((((~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), inverse_image3(F!43, X!40, A!42))) | (~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), inverse_image3(F!43, Y!39, A!42)))) <=> member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)))) | ((~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), inverse_image3(F!43, X!40, A!42))) | (~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), inverse_image3(F!43, Y!39, A!42))))),
% 0.22/0.49 inference(unit_resolution,[status(thm)],[78, 77])).
% 0.22/0.49 tff(80,plain,
% 0.22/0.49 ((~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), inverse_image3(F!43, X!40, A!42))) | (~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), inverse_image3(F!43, Y!39, A!42)))),
% 0.22/0.49 inference(unit_resolution,[status(thm)],[79, 74])).
% 0.22/0.49 tff(81,plain,
% 0.22/0.49 (((~![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_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42))) | (~((~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), A!42)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), intersection(X!40, Y!39), F!43), intersection(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), intersection(X!40, Y!39), F!43))))))) | (~(member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)) | ![Y: $i] : ((~member(Y, intersection(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), Y))) | (~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), A!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)))))))) | (~((~((~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42))) | (~((~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), A!42)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), intersection(X!40, Y!39), F!43), intersection(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), intersection(X!40, Y!39), F!43))))))) | (~(member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)) | ![Y: $i] : ((~member(Y, intersection(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), Y))) | (~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), A!42)))))))),
% 0.22/0.50 inference(rewrite,[status(thm)],[])).
% 0.22/0.50 tff(82,plain,
% 0.22/0.50 ((~((~((~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42))) | (~((~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), A!42)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), intersection(X!40, Y!39), F!43), intersection(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), intersection(X!40, Y!39), F!43))))))) | (~(member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)) | (~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), A!42)) | ![Y: $i] : ((~member(Y, intersection(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), Y))))))) <=> (~((~((~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42))) | (~((~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), A!42)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), intersection(X!40, Y!39), F!43), intersection(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), intersection(X!40, Y!39), F!43))))))) | (~(member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)) | ![Y: $i] : ((~member(Y, intersection(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), Y))) | (~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), A!42))))))),
% 0.22/0.50 inference(rewrite,[status(thm)],[])).
% 0.22/0.50 tff(83,plain,
% 0.22/0.50 (((~![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_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42))) | (~((~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), A!42)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), intersection(X!40, Y!39), F!43), intersection(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), intersection(X!40, Y!39), F!43))))))) | (~(member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)) | (~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), A!42)) | ![Y: $i] : ((~member(Y, intersection(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!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_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42))) | (~((~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), A!42)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), intersection(X!40, Y!39), F!43), intersection(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), intersection(X!40, Y!39), F!43))))))) | (~(member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)) | ![Y: $i] : ((~member(Y, intersection(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), Y))) | (~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), A!42)))))))),
% 0.22/0.50 inference(monotonicity,[status(thm)],[82])).
% 0.22/0.50 tff(84,plain,
% 0.22/0.50 (((~![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_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42))) | (~((~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), A!42)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), intersection(X!40, Y!39), F!43), intersection(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), intersection(X!40, Y!39), F!43))))))) | (~(member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)) | (~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), A!42)) | ![Y: $i] : ((~member(Y, intersection(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!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_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42))) | (~((~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), A!42)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), intersection(X!40, Y!39), F!43), intersection(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), intersection(X!40, Y!39), F!43))))))) | (~(member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)) | ![Y: $i] : ((~member(Y, intersection(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), Y))) | (~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), A!42)))))))),
% 0.22/0.50 inference(transitivity,[status(thm)],[83, 81])).
% 0.22/0.50 tff(85,plain,
% 0.22/0.50 ((~![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_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42))) | (~((~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), A!42)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), intersection(X!40, Y!39), F!43), intersection(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), intersection(X!40, Y!39), F!43))))))) | (~(member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)) | (~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), A!42)) | ![Y: $i] : ((~member(Y, intersection(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), Y)))))))),
% 0.22/0.51 inference(quant_inst,[status(thm)],[])).
% 0.22/0.51 tff(86,plain,
% 0.22/0.51 ((~![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_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42))) | (~((~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), A!42)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), intersection(X!40, Y!39), F!43), intersection(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), intersection(X!40, Y!39), F!43))))))) | (~(member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)) | ![Y: $i] : ((~member(Y, intersection(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), Y))) | (~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), A!42))))))),
% 0.22/0.51 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.22/0.51 tff(87,plain,
% 0.22/0.51 (~((~((~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42))) | (~((~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), A!42)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), intersection(X!40, Y!39), F!43), intersection(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), intersection(X!40, Y!39), F!43))))))) | (~(member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)) | ![Y: $i] : ((~member(Y, intersection(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), Y))) | (~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), A!42)))))),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[86, 16])).
% 0.22/0.51 tff(88,plain,
% 0.22/0.51 (((~((~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42))) | (~((~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), A!42)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), intersection(X!40, Y!39), F!43), intersection(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), intersection(X!40, Y!39), F!43))))))) | (~(member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)) | ![Y: $i] : ((~member(Y, intersection(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), Y))) | (~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), A!42))))) | ((~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42))) | (~((~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), A!42)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), intersection(X!40, Y!39), F!43), intersection(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), intersection(X!40, Y!39), F!43))))))),
% 0.22/0.51 inference(tautology,[status(thm)],[])).
% 0.22/0.51 tff(89,plain,
% 0.22/0.51 ((~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42))) | (~((~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), A!42)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), intersection(X!40, Y!39), F!43), intersection(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), intersection(X!40, Y!39), F!43)))))),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[88, 87])).
% 0.22/0.51 tff(90,plain,
% 0.22/0.51 (((~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42))) | member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)))) | member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42))),
% 0.22/0.51 inference(tautology,[status(thm)],[])).
% 0.22/0.51 tff(91,plain,
% 0.22/0.51 (member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42))),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[90, 75])).
% 0.22/0.51 tff(92,plain,
% 0.22/0.51 ((~((~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42))) | (~((~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), A!42)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), intersection(X!40, Y!39), F!43), intersection(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), intersection(X!40, Y!39), F!43))))))) | (~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42))) | (~((~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), A!42)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), intersection(X!40, Y!39), F!43), intersection(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), intersection(X!40, Y!39), F!43)))))),
% 0.22/0.51 inference(tautology,[status(thm)],[])).
% 0.22/0.51 tff(93,plain,
% 0.22/0.51 ((~((~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42))) | (~((~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), A!42)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), intersection(X!40, Y!39), F!43), intersection(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), intersection(X!40, Y!39), F!43))))))) | (~((~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), A!42)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), intersection(X!40, Y!39), F!43), intersection(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), intersection(X!40, Y!39), F!43)))))),
% 0.22/0.52 inference(unit_resolution,[status(thm)],[92, 91])).
% 0.22/0.52 tff(94,plain,
% 0.22/0.52 (~((~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), A!42)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), intersection(X!40, Y!39), F!43), intersection(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), intersection(X!40, Y!39), F!43))))),
% 0.22/0.52 inference(unit_resolution,[status(thm)],[93, 89])).
% 0.22/0.52 tff(95,plain,
% 0.22/0.52 (((~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), A!42)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), intersection(X!40, Y!39), F!43), intersection(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), intersection(X!40, Y!39), F!43)))) | member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), A!42)),
% 0.22/0.52 inference(tautology,[status(thm)],[])).
% 0.22/0.52 tff(96,plain,
% 0.22/0.52 (member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), A!42)),
% 0.22/0.52 inference(unit_resolution,[status(thm)],[95, 94])).
% 0.22/0.52 tff(97,plain,
% 0.22/0.52 (((~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), A!42)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), intersection(X!40, Y!39), F!43), intersection(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), intersection(X!40, Y!39), F!43)))) | apply(F!43, tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), intersection(X!40, Y!39), F!43))),
% 0.22/0.52 inference(tautology,[status(thm)],[])).
% 0.22/0.52 tff(98,plain,
% 0.22/0.52 (apply(F!43, tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), intersection(X!40, Y!39), F!43))),
% 0.22/0.52 inference(unit_resolution,[status(thm)],[97, 94])).
% 0.22/0.52 tff(99,plain,
% 0.22/0.52 ((~![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))) | (~(((~member(tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), intersection(X!40, Y!39), F!43), X!40)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), intersection(X!40, Y!39), F!43), Y!39))) <=> member(tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), intersection(X!40, Y!39), F!43), intersection(X!40, Y!39))))),
% 0.22/0.52 inference(quant_inst,[status(thm)],[])).
% 0.22/0.52 tff(100,plain,
% 0.22/0.52 (~(((~member(tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), intersection(X!40, Y!39), F!43), X!40)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), intersection(X!40, Y!39), F!43), Y!39))) <=> member(tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), intersection(X!40, Y!39), F!43), intersection(X!40, Y!39)))),
% 0.22/0.52 inference(unit_resolution,[status(thm)],[99, 35])).
% 0.22/0.52 tff(101,plain,
% 0.22/0.52 (((~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), A!42)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), intersection(X!40, Y!39), F!43), intersection(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), intersection(X!40, Y!39), F!43)))) | member(tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), intersection(X!40, Y!39), F!43), intersection(X!40, Y!39))),
% 0.22/0.52 inference(tautology,[status(thm)],[])).
% 0.22/0.52 tff(102,plain,
% 0.22/0.52 (member(tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), intersection(X!40, Y!39), F!43), intersection(X!40, Y!39))),
% 0.22/0.52 inference(unit_resolution,[status(thm)],[101, 94])).
% 0.22/0.52 tff(103,plain,
% 0.22/0.52 ((((~member(tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), intersection(X!40, Y!39), F!43), X!40)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), intersection(X!40, Y!39), F!43), Y!39))) <=> member(tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), intersection(X!40, Y!39), F!43), intersection(X!40, Y!39))) | (~((~member(tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), intersection(X!40, Y!39), F!43), X!40)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), intersection(X!40, Y!39), F!43), Y!39)))) | (~member(tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), intersection(X!40, Y!39), F!43), intersection(X!40, Y!39)))),
% 0.22/0.52 inference(tautology,[status(thm)],[])).
% 0.22/0.52 tff(104,plain,
% 0.22/0.52 ((((~member(tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), intersection(X!40, Y!39), F!43), X!40)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), intersection(X!40, Y!39), F!43), Y!39))) <=> member(tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), intersection(X!40, Y!39), F!43), intersection(X!40, Y!39))) | (~((~member(tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), intersection(X!40, Y!39), F!43), X!40)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), intersection(X!40, Y!39), F!43), Y!39))))),
% 0.22/0.52 inference(unit_resolution,[status(thm)],[103, 102])).
% 0.22/0.52 tff(105,plain,
% 0.22/0.52 (~((~member(tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), intersection(X!40, Y!39), F!43), X!40)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), intersection(X!40, Y!39), F!43), Y!39)))),
% 0.22/0.52 inference(unit_resolution,[status(thm)],[104, 100])).
% 0.22/0.52 tff(106,plain,
% 0.22/0.52 (((~member(tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), intersection(X!40, Y!39), F!43), X!40)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), intersection(X!40, Y!39), F!43), Y!39))) | member(tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), intersection(X!40, Y!39), F!43), X!40)),
% 0.22/0.52 inference(tautology,[status(thm)],[])).
% 0.22/0.52 tff(107,plain,
% 0.22/0.52 (member(tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), intersection(X!40, Y!39), F!43), X!40)),
% 0.22/0.52 inference(unit_resolution,[status(thm)],[106, 105])).
% 0.22/0.52 tff(108,assumption,(![Y: $i] : ((~member(Y, X!40)) | (~apply(F!43, tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), Y)))), introduced(assumption)).
% 0.22/0.52 tff(109,assumption,(member(tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), intersection(X!40, Y!39), F!43), X!40)), introduced(assumption)).
% 0.22/0.52 tff(110,assumption,(apply(F!43, tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), intersection(X!40, Y!39), F!43))), introduced(assumption)).
% 0.22/0.52 tff(111,plain,
% 0.22/0.52 (((~![Y: $i] : ((~member(Y, X!40)) | (~apply(F!43, tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), Y)))) | ((~member(tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), intersection(X!40, Y!39), F!43), X!40)) | (~apply(F!43, tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), intersection(X!40, Y!39), F!43))))) <=> ((~![Y: $i] : ((~member(Y, X!40)) | (~apply(F!43, tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), Y)))) | (~member(tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), intersection(X!40, Y!39), F!43), X!40)) | (~apply(F!43, tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), intersection(X!40, Y!39), F!43))))),
% 0.22/0.52 inference(rewrite,[status(thm)],[])).
% 0.22/0.52 tff(112,plain,
% 0.22/0.52 ((~![Y: $i] : ((~member(Y, X!40)) | (~apply(F!43, tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), Y)))) | ((~member(tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), intersection(X!40, Y!39), F!43), X!40)) | (~apply(F!43, tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), intersection(X!40, Y!39), F!43))))),
% 0.22/0.52 inference(quant_inst,[status(thm)],[])).
% 0.22/0.52 tff(113,plain,
% 0.22/0.52 ((~![Y: $i] : ((~member(Y, X!40)) | (~apply(F!43, tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), Y)))) | (~member(tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), intersection(X!40, Y!39), F!43), X!40)) | (~apply(F!43, tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), intersection(X!40, Y!39), F!43)))),
% 0.22/0.52 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.22/0.52 tff(114,plain,
% 0.22/0.52 ($false),
% 0.22/0.52 inference(unit_resolution,[status(thm)],[113, 110, 109, 108])).
% 0.22/0.53 tff(115,plain,((~![Y: $i] : ((~member(Y, X!40)) | (~apply(F!43, tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), Y)))) | (~apply(F!43, tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), intersection(X!40, Y!39), F!43))) | (~member(tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), intersection(X!40, Y!39), F!43), X!40))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.53 tff(116,plain,
% 0.22/0.53 (~![Y: $i] : ((~member(Y, X!40)) | (~apply(F!43, tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), Y)))),
% 0.22/0.53 inference(unit_resolution,[status(thm)],[115, 107, 98])).
% 0.22/0.53 tff(117,assumption,((~(member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), inverse_image3(F!43, X!40, A!42)) | (~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), A!42)) | ![Y: $i] : ((~member(Y, X!40)) | (~apply(F!43, tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), Y))))) | (~((~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), inverse_image3(F!43, X!40, A!42))) | (~((~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), A!42)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), X!40, F!43)))))))), introduced(assumption)).
% 0.22/0.53 tff(118,plain,
% 0.22/0.53 (((~![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_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), inverse_image3(F!43, X!40, A!42)) | (~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), A!42)) | ![Y: $i] : ((~member(Y, X!40)) | (~apply(F!43, tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), Y))))) | (~((~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), inverse_image3(F!43, X!40, A!42))) | (~((~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), A!42)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), X!40, F!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_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), inverse_image3(F!43, X!40, A!42)) | (~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), A!42)) | ![Y: $i] : ((~member(Y, X!40)) | (~apply(F!43, tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), Y))))) | (~((~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), inverse_image3(F!43, X!40, A!42))) | (~((~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), A!42)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), X!40, F!43))))))))))),
% 0.22/0.53 inference(rewrite,[status(thm)],[])).
% 0.22/0.53 tff(119,plain,
% 0.22/0.53 ((~((~((~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), inverse_image3(F!43, X!40, A!42))) | (~((~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), A!42)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), X!40, F!43))))))) | (~(member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), inverse_image3(F!43, X!40, A!42)) | (~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), A!42)) | ![Y: $i] : ((~member(Y, X!40)) | (~apply(F!43, tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), Y))))))) <=> (~((~(member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), inverse_image3(F!43, X!40, A!42)) | (~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), A!42)) | ![Y: $i] : ((~member(Y, X!40)) | (~apply(F!43, tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), Y))))) | (~((~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), inverse_image3(F!43, X!40, A!42))) | (~((~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), A!42)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), X!40, F!43)))))))))),
% 0.22/0.53 inference(rewrite,[status(thm)],[])).
% 0.22/0.53 tff(120,plain,
% 0.22/0.53 (((~![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_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), inverse_image3(F!43, X!40, A!42))) | (~((~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), A!42)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), X!40, F!43))))))) | (~(member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), inverse_image3(F!43, X!40, A!42)) | (~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), A!42)) | ![Y: $i] : ((~member(Y, X!40)) | (~apply(F!43, tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!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_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), inverse_image3(F!43, X!40, A!42)) | (~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), A!42)) | ![Y: $i] : ((~member(Y, X!40)) | (~apply(F!43, tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), Y))))) | (~((~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), inverse_image3(F!43, X!40, A!42))) | (~((~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), A!42)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), X!40, F!43))))))))))),
% 0.22/0.53 inference(monotonicity,[status(thm)],[119])).
% 0.22/0.53 tff(121,plain,
% 0.22/0.53 (((~![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_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), inverse_image3(F!43, X!40, A!42))) | (~((~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), A!42)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), X!40, F!43))))))) | (~(member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), inverse_image3(F!43, X!40, A!42)) | (~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), A!42)) | ![Y: $i] : ((~member(Y, X!40)) | (~apply(F!43, tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!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_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), inverse_image3(F!43, X!40, A!42)) | (~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), A!42)) | ![Y: $i] : ((~member(Y, X!40)) | (~apply(F!43, tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), Y))))) | (~((~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), inverse_image3(F!43, X!40, A!42))) | (~((~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), A!42)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), X!40, F!43))))))))))),
% 0.22/0.54 inference(transitivity,[status(thm)],[120, 118])).
% 0.22/0.54 tff(122,plain,
% 0.22/0.54 ((~![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_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), inverse_image3(F!43, X!40, A!42))) | (~((~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), A!42)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), X!40, F!43))))))) | (~(member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), inverse_image3(F!43, X!40, A!42)) | (~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), A!42)) | ![Y: $i] : ((~member(Y, X!40)) | (~apply(F!43, tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), Y)))))))),
% 0.22/0.54 inference(quant_inst,[status(thm)],[])).
% 0.22/0.54 tff(123,plain,
% 0.22/0.54 ((~![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_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), inverse_image3(F!43, X!40, A!42)) | (~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), A!42)) | ![Y: $i] : ((~member(Y, X!40)) | (~apply(F!43, tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), Y))))) | (~((~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), inverse_image3(F!43, X!40, A!42))) | (~((~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), A!42)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), X!40, F!43)))))))))),
% 0.22/0.54 inference(modus_ponens,[status(thm)],[122, 121])).
% 0.22/0.54 tff(124,plain,
% 0.22/0.54 ($false),
% 0.22/0.54 inference(unit_resolution,[status(thm)],[123, 16, 117])).
% 0.22/0.54 tff(125,plain,(~((~(member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), inverse_image3(F!43, X!40, A!42)) | (~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), A!42)) | ![Y: $i] : ((~member(Y, X!40)) | (~apply(F!43, tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), Y))))) | (~((~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), inverse_image3(F!43, X!40, A!42))) | (~((~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), A!42)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), X!40, F!43))))))))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.54 tff(126,plain,
% 0.22/0.54 (((~(member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), inverse_image3(F!43, X!40, A!42)) | (~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), A!42)) | ![Y: $i] : ((~member(Y, X!40)) | (~apply(F!43, tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), Y))))) | (~((~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), inverse_image3(F!43, X!40, A!42))) | (~((~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), A!42)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), X!40, F!43)))))))) | (member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), inverse_image3(F!43, X!40, A!42)) | (~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), A!42)) | ![Y: $i] : ((~member(Y, X!40)) | (~apply(F!43, tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), Y))))),
% 0.22/0.54 inference(tautology,[status(thm)],[])).
% 0.22/0.54 tff(127,plain,
% 0.22/0.54 (member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), inverse_image3(F!43, X!40, A!42)) | (~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), A!42)) | ![Y: $i] : ((~member(Y, X!40)) | (~apply(F!43, tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), Y)))),
% 0.22/0.54 inference(unit_resolution,[status(thm)],[126, 125])).
% 0.22/0.54 tff(128,plain,
% 0.22/0.54 ((~(member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), inverse_image3(F!43, X!40, A!42)) | (~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), A!42)) | ![Y: $i] : ((~member(Y, X!40)) | (~apply(F!43, tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), Y))))) | member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), inverse_image3(F!43, X!40, A!42)) | (~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), A!42)) | ![Y: $i] : ((~member(Y, X!40)) | (~apply(F!43, tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), Y)))),
% 0.22/0.54 inference(tautology,[status(thm)],[])).
% 0.22/0.54 tff(129,plain,
% 0.22/0.54 (member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), inverse_image3(F!43, X!40, A!42)) | (~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), A!42)) | ![Y: $i] : ((~member(Y, X!40)) | (~apply(F!43, tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), Y)))),
% 0.22/0.54 inference(unit_resolution,[status(thm)],[128, 127])).
% 0.22/0.54 tff(130,plain,
% 0.22/0.54 (member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), inverse_image3(F!43, X!40, A!42))),
% 0.22/0.54 inference(unit_resolution,[status(thm)],[129, 116, 96])).
% 0.22/0.54 tff(131,plain,
% 0.22/0.54 ((~((~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), inverse_image3(F!43, X!40, A!42))) | (~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), inverse_image3(F!43, Y!39, A!42))))) | (~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), inverse_image3(F!43, X!40, A!42))) | (~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), inverse_image3(F!43, Y!39, A!42)))),
% 0.22/0.54 inference(tautology,[status(thm)],[])).
% 0.22/0.54 tff(132,plain,
% 0.22/0.54 (~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), inverse_image3(F!43, Y!39, A!42))),
% 0.22/0.54 inference(unit_resolution,[status(thm)],[131, 130, 80])).
% 0.22/0.54 tff(133,plain,
% 0.22/0.54 ((~(member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), inverse_image3(F!43, Y!39, A!42)) | (~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), A!42)) | ![Y: $i] : ((~member(Y, Y!39)) | (~apply(F!43, tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), Y))))) | member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), inverse_image3(F!43, Y!39, A!42)) | (~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), A!42)) | ![Y: $i] : ((~member(Y, Y!39)) | (~apply(F!43, tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), Y)))),
% 0.22/0.54 inference(tautology,[status(thm)],[])).
% 0.22/0.54 tff(134,plain,
% 0.22/0.54 ((~(member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), inverse_image3(F!43, Y!39, A!42)) | (~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), A!42)) | ![Y: $i] : ((~member(Y, Y!39)) | (~apply(F!43, tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), Y))))) | ![Y: $i] : ((~member(Y, Y!39)) | (~apply(F!43, tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), Y)))),
% 0.22/0.54 inference(unit_resolution,[status(thm)],[133, 96, 132])).
% 0.22/0.54 tff(135,plain,
% 0.22/0.54 (![Y: $i] : ((~member(Y, Y!39)) | (~apply(F!43, tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), Y)))),
% 0.22/0.54 inference(unit_resolution,[status(thm)],[134, 72])).
% 0.22/0.54 tff(136,plain,
% 0.22/0.54 (((~member(tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), intersection(X!40, Y!39), F!43), X!40)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), intersection(X!40, Y!39), F!43), Y!39))) | member(tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), intersection(X!40, Y!39), F!43), Y!39)),
% 0.22/0.54 inference(tautology,[status(thm)],[])).
% 0.22/0.54 tff(137,plain,
% 0.22/0.54 (member(tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), intersection(X!40, Y!39), F!43), Y!39)),
% 0.22/0.54 inference(unit_resolution,[status(thm)],[136, 105])).
% 0.22/0.54 tff(138,plain,
% 0.22/0.54 (((~![Y: $i] : ((~member(Y, Y!39)) | (~apply(F!43, tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), Y)))) | ((~member(tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), intersection(X!40, Y!39), F!43), Y!39)) | (~apply(F!43, tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), intersection(X!40, Y!39), F!43))))) <=> ((~![Y: $i] : ((~member(Y, Y!39)) | (~apply(F!43, tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), Y)))) | (~member(tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), intersection(X!40, Y!39), F!43), Y!39)) | (~apply(F!43, tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), intersection(X!40, Y!39), F!43))))),
% 0.22/0.55 inference(rewrite,[status(thm)],[])).
% 0.22/0.55 tff(139,plain,
% 0.22/0.55 ((~![Y: $i] : ((~member(Y, Y!39)) | (~apply(F!43, tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), Y)))) | ((~member(tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), intersection(X!40, Y!39), F!43), Y!39)) | (~apply(F!43, tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), intersection(X!40, Y!39), F!43))))),
% 0.22/0.55 inference(quant_inst,[status(thm)],[])).
% 0.22/0.55 tff(140,plain,
% 0.22/0.55 ((~![Y: $i] : ((~member(Y, Y!39)) | (~apply(F!43, tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), Y)))) | (~member(tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), intersection(X!40, Y!39), F!43), Y!39)) | (~apply(F!43, tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), tptp_fun_Y_26(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), intersection(X!40, Y!39), F!43)))),
% 0.22/0.55 inference(modus_ponens,[status(thm)],[139, 138])).
% 0.22/0.55 tff(141,plain,
% 0.22/0.55 ($false),
% 0.22/0.55 inference(unit_resolution,[status(thm)],[140, 98, 137, 135])).
% 0.22/0.55 tff(142,plain,((~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42))) | member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.55 tff(143,plain,
% 0.22/0.55 ((~(subset(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))) | (~((~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42))) | member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))))))) | subset(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))) | (~((~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42))) | member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)))))),
% 0.22/0.55 inference(tautology,[status(thm)],[])).
% 0.22/0.55 tff(144,plain,
% 0.22/0.55 ((~(subset(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))) | (~((~member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42))) | member(tptp_fun_X_0(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))))))) | subset(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)))),
% 0.39/0.55 inference(unit_resolution,[status(thm)],[143, 142])).
% 0.39/0.55 tff(145,plain,
% 0.39/0.55 (subset(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)))),
% 0.39/0.55 inference(unit_resolution,[status(thm)],[144, 63])).
% 0.39/0.55 tff(146,plain,
% 0.39/0.55 (^[A: $i, B: $i] : refl((~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B))) <=> (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B))))),
% 0.39/0.55 inference(bind,[status(th)],[])).
% 0.39/0.55 tff(147,plain,
% 0.39/0.55 (![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B))) <=> ![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))),
% 0.39/0.55 inference(quant_intro,[status(thm)],[146])).
% 0.39/0.55 tff(148,plain,
% 0.39/0.55 (^[A: $i, B: $i] : trans(trans(monotonicity(rewrite((subset(A, B) & subset(B, A)) <=> (~((~subset(A, B)) | (~subset(B, A))))), ((equal_set(A, B) <=> (subset(A, B) & subset(B, A))) <=> (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A))))))), rewrite((equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A))))) <=> (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))), ((equal_set(A, B) <=> (subset(A, B) & subset(B, A))) <=> (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B))))), rewrite((~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B))) <=> (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))), ((equal_set(A, B) <=> (subset(A, B) & subset(B, A))) <=> (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))))),
% 0.39/0.55 inference(bind,[status(th)],[])).
% 0.39/0.55 tff(149,plain,
% 0.39/0.55 (![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A))) <=> ![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))),
% 0.39/0.55 inference(quant_intro,[status(thm)],[148])).
% 0.39/0.55 tff(150,plain,
% 0.39/0.55 (![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A))) <=> ![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 0.39/0.55 inference(rewrite,[status(thm)],[])).
% 0.39/0.55 tff(151,axiom,(![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax','equal_set')).
% 0.39/0.55 tff(152,plain,
% 0.39/0.55 (![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 0.39/0.55 inference(modus_ponens,[status(thm)],[151, 150])).
% 0.39/0.55 tff(153,plain,(
% 0.39/0.55 ![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 0.39/0.55 inference(skolemize,[status(sab)],[152])).
% 0.39/0.55 tff(154,plain,
% 0.39/0.55 (![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))),
% 0.39/0.55 inference(modus_ponens,[status(thm)],[153, 149])).
% 0.39/0.55 tff(155,plain,
% 0.39/0.55 (![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))),
% 0.39/0.55 inference(modus_ponens,[status(thm)],[154, 147])).
% 0.39/0.55 tff(156,plain,
% 0.39/0.55 ((~![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))) | (~(((~subset(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)))) | (~subset(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)))) <=> equal_set(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)))))),
% 0.39/0.55 inference(quant_inst,[status(thm)],[])).
% 0.39/0.55 tff(157,plain,
% 0.39/0.55 (~(((~subset(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)))) | (~subset(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)))) <=> equal_set(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))))),
% 0.39/0.55 inference(unit_resolution,[status(thm)],[156, 155])).
% 0.39/0.55 tff(158,plain,
% 0.39/0.55 ((~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((~(maps(F, A, B) & subset(X, B) & subset(Y, B))) | equal_set(inverse_image3(F, intersection(X, Y), A), intersection(inverse_image3(F, X, A), inverse_image3(F, Y, A))))) <=> (~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((~(maps(F, A, B) & subset(X, B) & subset(Y, B))) | equal_set(inverse_image3(F, intersection(X, Y), A), intersection(inverse_image3(F, X, A), inverse_image3(F, Y, A)))))),
% 0.39/0.55 inference(rewrite,[status(thm)],[])).
% 0.39/0.55 tff(159,plain,
% 0.39/0.55 ((~![F: $i, A: $i, B: $i, X: $i, Y: $i] : (((maps(F, A, B) & subset(X, B)) & subset(Y, B)) => equal_set(inverse_image3(F, intersection(X, Y), A), intersection(inverse_image3(F, X, A), inverse_image3(F, Y, A))))) <=> (~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((~(maps(F, A, B) & subset(X, B) & subset(Y, B))) | equal_set(inverse_image3(F, intersection(X, Y), A), intersection(inverse_image3(F, X, A), inverse_image3(F, Y, A)))))),
% 0.39/0.55 inference(rewrite,[status(thm)],[])).
% 0.39/0.55 tff(160,axiom,(~![F: $i, A: $i, B: $i, X: $i, Y: $i] : (((maps(F, A, B) & subset(X, B)) & subset(Y, B)) => equal_set(inverse_image3(F, intersection(X, Y), A), intersection(inverse_image3(F, X, A), inverse_image3(F, Y, A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thIIa07')).
% 0.39/0.55 tff(161,plain,
% 0.39/0.55 (~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((~(maps(F, A, B) & subset(X, B) & subset(Y, B))) | equal_set(inverse_image3(F, intersection(X, Y), A), intersection(inverse_image3(F, X, A), inverse_image3(F, Y, A))))),
% 0.39/0.55 inference(modus_ponens,[status(thm)],[160, 159])).
% 0.39/0.55 tff(162,plain,
% 0.39/0.55 (~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((~(maps(F, A, B) & subset(X, B) & subset(Y, B))) | equal_set(inverse_image3(F, intersection(X, Y), A), intersection(inverse_image3(F, X, A), inverse_image3(F, Y, A))))),
% 0.39/0.55 inference(modus_ponens,[status(thm)],[161, 158])).
% 0.39/0.55 tff(163,plain,
% 0.39/0.55 (~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((~(maps(F, A, B) & subset(X, B) & subset(Y, B))) | equal_set(inverse_image3(F, intersection(X, Y), A), intersection(inverse_image3(F, X, A), inverse_image3(F, Y, A))))),
% 0.39/0.55 inference(modus_ponens,[status(thm)],[162, 158])).
% 0.39/0.55 tff(164,plain,
% 0.39/0.55 (~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((~(maps(F, A, B) & subset(X, B) & subset(Y, B))) | equal_set(inverse_image3(F, intersection(X, Y), A), intersection(inverse_image3(F, X, A), inverse_image3(F, Y, A))))),
% 0.39/0.55 inference(modus_ponens,[status(thm)],[163, 158])).
% 0.39/0.55 tff(165,plain,(
% 0.39/0.55 ~((~(maps(F!43, A!42, B!41) & subset(X!40, B!41) & subset(Y!39, B!41))) | equal_set(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))))),
% 0.39/0.55 inference(skolemize,[status(sab)],[164])).
% 0.39/0.55 tff(166,plain,
% 0.39/0.55 (~equal_set(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)))),
% 0.39/0.55 inference(or_elim,[status(thm)],[165])).
% 0.39/0.55 tff(167,plain,
% 0.39/0.55 ((((~subset(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)))) | (~subset(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)))) <=> equal_set(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)))) | ((~subset(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)))) | (~subset(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)))) | equal_set(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)))),
% 0.39/0.55 inference(tautology,[status(thm)],[])).
% 0.39/0.55 tff(168,plain,
% 0.39/0.55 ((((~subset(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)))) | (~subset(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)))) <=> equal_set(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)))) | ((~subset(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)))) | (~subset(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42))))),
% 0.39/0.55 inference(unit_resolution,[status(thm)],[167, 166])).
% 0.39/0.55 tff(169,plain,
% 0.39/0.55 ((~subset(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)))) | (~subset(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)))),
% 0.39/0.55 inference(unit_resolution,[status(thm)],[168, 157])).
% 0.39/0.55 tff(170,plain,
% 0.39/0.55 ((~((~subset(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)))) | (~subset(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42))))) | (~subset(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)))) | (~subset(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)))),
% 0.39/0.55 inference(tautology,[status(thm)],[])).
% 0.39/0.55 tff(171,plain,
% 0.39/0.55 ((~subset(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)))) | (~subset(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)))),
% 0.39/0.55 inference(unit_resolution,[status(thm)],[170, 169])).
% 0.39/0.55 tff(172,plain,
% 0.39/0.55 (~subset(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42))),
% 0.39/0.55 inference(unit_resolution,[status(thm)],[171, 145])).
% 0.39/0.55 tff(173,plain,
% 0.39/0.55 ((~(subset(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)) | (~((~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)))) | member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), inverse_image3(F!43, intersection(X!40, Y!39), A!42)))))) | subset(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)) | (~((~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)))) | member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), inverse_image3(F!43, intersection(X!40, Y!39), A!42))))),
% 0.39/0.55 inference(tautology,[status(thm)],[])).
% 0.39/0.55 tff(174,plain,
% 0.39/0.55 ((~(subset(intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)), inverse_image3(F!43, intersection(X!40, Y!39), A!42)) | (~((~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)))) | member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), inverse_image3(F!43, intersection(X!40, Y!39), A!42)))))) | (~((~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)))) | member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), inverse_image3(F!43, intersection(X!40, Y!39), A!42))))),
% 0.39/0.55 inference(unit_resolution,[status(thm)],[173, 172])).
% 0.39/0.55 tff(175,plain,
% 0.39/0.55 (~((~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)))) | member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), inverse_image3(F!43, intersection(X!40, Y!39), A!42)))),
% 0.39/0.55 inference(unit_resolution,[status(thm)],[174, 57])).
% 0.39/0.55 tff(176,plain,
% 0.39/0.55 (((~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)))) | member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), inverse_image3(F!43, intersection(X!40, Y!39), A!42))) | member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)))),
% 0.39/0.55 inference(tautology,[status(thm)],[])).
% 0.39/0.55 tff(177,plain,
% 0.39/0.55 (member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)))),
% 0.39/0.55 inference(unit_resolution,[status(thm)],[176, 175])).
% 0.39/0.55 tff(178,plain,
% 0.39/0.55 ((((~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), inverse_image3(F!43, X!40, A!42))) | (~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), inverse_image3(F!43, Y!39, A!42)))) <=> member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)))) | (~((~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), inverse_image3(F!43, X!40, A!42))) | (~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), inverse_image3(F!43, Y!39, A!42))))) | (~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))))),
% 0.39/0.55 inference(tautology,[status(thm)],[])).
% 0.39/0.55 tff(179,plain,
% 0.39/0.55 ((((~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), inverse_image3(F!43, X!40, A!42))) | (~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), inverse_image3(F!43, Y!39, A!42)))) <=> member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)))) | (~((~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), inverse_image3(F!43, X!40, A!42))) | (~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), inverse_image3(F!43, Y!39, A!42)))))),
% 0.39/0.56 inference(unit_resolution,[status(thm)],[178, 177])).
% 0.39/0.56 tff(180,plain,
% 0.39/0.56 (~((~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), inverse_image3(F!43, X!40, A!42))) | (~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), inverse_image3(F!43, Y!39, A!42))))),
% 0.39/0.56 inference(unit_resolution,[status(thm)],[179, 37])).
% 0.39/0.56 tff(181,plain,
% 0.39/0.56 (((~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), inverse_image3(F!43, X!40, A!42))) | (~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), inverse_image3(F!43, Y!39, A!42)))) | member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), inverse_image3(F!43, Y!39, A!42))),
% 0.39/0.56 inference(tautology,[status(thm)],[])).
% 0.39/0.56 tff(182,plain,
% 0.39/0.56 (member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), inverse_image3(F!43, Y!39, A!42))),
% 0.39/0.56 inference(unit_resolution,[status(thm)],[181, 180])).
% 0.39/0.56 tff(183,plain,
% 0.39/0.56 ((~((~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), inverse_image3(F!43, Y!39, A!42))) | (~((~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), A!42)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), Y!39, F!43))))))) | (~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), inverse_image3(F!43, Y!39, A!42))) | (~((~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), A!42)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), Y!39, F!43)))))),
% 0.39/0.56 inference(tautology,[status(thm)],[])).
% 0.39/0.56 tff(184,plain,
% 0.39/0.56 ((~((~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), inverse_image3(F!43, Y!39, A!42))) | (~((~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), A!42)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), Y!39, F!43))))))) | (~((~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), A!42)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), Y!39, F!43)))))),
% 0.39/0.56 inference(unit_resolution,[status(thm)],[183, 182])).
% 0.39/0.56 tff(185,plain,
% 0.39/0.56 (~((~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), A!42)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), Y!39, F!43))))),
% 0.39/0.56 inference(unit_resolution,[status(thm)],[184, 25])).
% 0.39/0.56 tff(186,plain,
% 0.39/0.56 (((~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), A!42)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), Y!39, F!43)))) | member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), Y!39, F!43), Y!39)),
% 0.39/0.56 inference(tautology,[status(thm)],[])).
% 0.39/0.56 tff(187,plain,
% 0.39/0.56 (member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), Y!39, F!43), Y!39)),
% 0.39/0.56 inference(unit_resolution,[status(thm)],[186, 185])).
% 0.39/0.56 tff(188,plain,
% 0.39/0.56 ((~![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!41)) | ![X: $i] : ((~member(X, Y!39)) | member(X, B!41)))) | (~(subset(Y!39, B!41) | (~((~member(tptp_fun_X_0(B!41, Y!39), Y!39)) | member(tptp_fun_X_0(B!41, Y!39), B!41)))))))),
% 0.39/0.56 inference(quant_inst,[status(thm)],[])).
% 0.39/0.56 tff(189,plain,
% 0.39/0.56 (~((~((~subset(Y!39, B!41)) | ![X: $i] : ((~member(X, Y!39)) | member(X, B!41)))) | (~(subset(Y!39, B!41) | (~((~member(tptp_fun_X_0(B!41, Y!39), Y!39)) | member(tptp_fun_X_0(B!41, Y!39), B!41))))))),
% 0.39/0.56 inference(unit_resolution,[status(thm)],[188, 53])).
% 0.39/0.56 tff(190,plain,
% 0.39/0.56 (((~((~subset(Y!39, B!41)) | ![X: $i] : ((~member(X, Y!39)) | member(X, B!41)))) | (~(subset(Y!39, B!41) | (~((~member(tptp_fun_X_0(B!41, Y!39), Y!39)) | member(tptp_fun_X_0(B!41, Y!39), B!41)))))) | ((~subset(Y!39, B!41)) | ![X: $i] : ((~member(X, Y!39)) | member(X, B!41)))),
% 0.39/0.56 inference(tautology,[status(thm)],[])).
% 0.39/0.56 tff(191,plain,
% 0.39/0.56 ((~subset(Y!39, B!41)) | ![X: $i] : ((~member(X, Y!39)) | member(X, B!41))),
% 0.39/0.56 inference(unit_resolution,[status(thm)],[190, 189])).
% 0.39/0.56 tff(192,plain,
% 0.39/0.56 (maps(F!43, A!42, B!41) & subset(X!40, B!41) & subset(Y!39, B!41)),
% 0.39/0.56 inference(or_elim,[status(thm)],[165])).
% 0.39/0.56 tff(193,plain,
% 0.39/0.56 (subset(Y!39, B!41)),
% 0.39/0.56 inference(and_elim,[status(thm)],[192])).
% 0.39/0.56 tff(194,plain,
% 0.39/0.56 ((~((~subset(Y!39, B!41)) | ![X: $i] : ((~member(X, Y!39)) | member(X, B!41)))) | (~subset(Y!39, B!41)) | ![X: $i] : ((~member(X, Y!39)) | member(X, B!41))),
% 0.39/0.56 inference(tautology,[status(thm)],[])).
% 0.39/0.56 tff(195,plain,
% 0.39/0.56 ((~((~subset(Y!39, B!41)) | ![X: $i] : ((~member(X, Y!39)) | member(X, B!41)))) | ![X: $i] : ((~member(X, Y!39)) | member(X, B!41))),
% 0.39/0.56 inference(unit_resolution,[status(thm)],[194, 193])).
% 0.39/0.56 tff(196,plain,
% 0.39/0.56 (![X: $i] : ((~member(X, Y!39)) | member(X, B!41))),
% 0.39/0.56 inference(unit_resolution,[status(thm)],[195, 191])).
% 0.39/0.56 tff(197,plain,
% 0.39/0.56 (((~![X: $i] : ((~member(X, Y!39)) | member(X, B!41))) | ((~member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), Y!39, F!43), Y!39)) | member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), Y!39, F!43), B!41))) <=> ((~![X: $i] : ((~member(X, Y!39)) | member(X, B!41))) | (~member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), Y!39, F!43), Y!39)) | member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), Y!39, F!43), B!41))),
% 0.39/0.56 inference(rewrite,[status(thm)],[])).
% 0.39/0.56 tff(198,plain,
% 0.39/0.56 ((~![X: $i] : ((~member(X, Y!39)) | member(X, B!41))) | ((~member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), Y!39, F!43), Y!39)) | member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), Y!39, F!43), B!41))),
% 0.39/0.56 inference(quant_inst,[status(thm)],[])).
% 0.39/0.56 tff(199,plain,
% 0.39/0.56 ((~![X: $i] : ((~member(X, Y!39)) | member(X, B!41))) | (~member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), Y!39, F!43), Y!39)) | member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), Y!39, F!43), B!41)),
% 0.39/0.56 inference(modus_ponens,[status(thm)],[198, 197])).
% 0.39/0.56 tff(200,plain,
% 0.39/0.56 (member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), Y!39, F!43), B!41)),
% 0.39/0.56 inference(unit_resolution,[status(thm)],[199, 196, 187])).
% 0.39/0.56 tff(201,plain,
% 0.39/0.56 (((~![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_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), inverse_image3(F!43, X!40, A!42))) | (~((~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), A!42)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), X!40, F!43))))))) | (~((~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), A!42)) | member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), inverse_image3(F!43, X!40, A!42)) | ![Y: $i] : ((~member(Y, X!40)) | (~apply(F!43, tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!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_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), inverse_image3(F!43, X!40, A!42))) | (~((~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), A!42)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), X!40, F!43))))))) | (~((~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), A!42)) | member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), inverse_image3(F!43, X!40, A!42)) | ![Y: $i] : ((~member(Y, X!40)) | (~apply(F!43, tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), Y))))))))),
% 0.39/0.56 inference(rewrite,[status(thm)],[])).
% 0.39/0.56 tff(202,plain,
% 0.39/0.56 ((~((~((~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), inverse_image3(F!43, X!40, A!42))) | (~((~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), A!42)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), X!40, F!43))))))) | (~(member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), inverse_image3(F!43, X!40, A!42)) | (~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), A!42)) | ![Y: $i] : ((~member(Y, X!40)) | (~apply(F!43, tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), Y))))))) <=> (~((~((~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), inverse_image3(F!43, X!40, A!42))) | (~((~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), A!42)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), X!40, F!43))))))) | (~((~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), A!42)) | member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), inverse_image3(F!43, X!40, A!42)) | ![Y: $i] : ((~member(Y, X!40)) | (~apply(F!43, tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), Y)))))))),
% 0.41/0.57 inference(rewrite,[status(thm)],[])).
% 0.41/0.57 tff(203,plain,
% 0.41/0.57 (((~![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_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), inverse_image3(F!43, X!40, A!42))) | (~((~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), A!42)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), X!40, F!43))))))) | (~(member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), inverse_image3(F!43, X!40, A!42)) | (~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), A!42)) | ![Y: $i] : ((~member(Y, X!40)) | (~apply(F!43, tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!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_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), inverse_image3(F!43, X!40, A!42))) | (~((~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), A!42)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), X!40, F!43))))))) | (~((~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), A!42)) | member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), inverse_image3(F!43, X!40, A!42)) | ![Y: $i] : ((~member(Y, X!40)) | (~apply(F!43, tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), Y))))))))),
% 0.41/0.57 inference(monotonicity,[status(thm)],[202])).
% 0.41/0.57 tff(204,plain,
% 0.41/0.57 (((~![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_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), inverse_image3(F!43, X!40, A!42))) | (~((~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), A!42)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), X!40, F!43))))))) | (~(member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), inverse_image3(F!43, X!40, A!42)) | (~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), A!42)) | ![Y: $i] : ((~member(Y, X!40)) | (~apply(F!43, tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!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_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), inverse_image3(F!43, X!40, A!42))) | (~((~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), A!42)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), X!40, F!43))))))) | (~((~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), A!42)) | member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), inverse_image3(F!43, X!40, A!42)) | ![Y: $i] : ((~member(Y, X!40)) | (~apply(F!43, tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), Y))))))))),
% 0.41/0.57 inference(transitivity,[status(thm)],[203, 201])).
% 0.41/0.57 tff(205,plain,
% 0.41/0.57 ((~![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_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), inverse_image3(F!43, X!40, A!42))) | (~((~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), A!42)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), X!40, F!43))))))) | (~(member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), inverse_image3(F!43, X!40, A!42)) | (~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), A!42)) | ![Y: $i] : ((~member(Y, X!40)) | (~apply(F!43, tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), Y)))))))),
% 0.41/0.57 inference(quant_inst,[status(thm)],[])).
% 0.41/0.57 tff(206,plain,
% 0.41/0.57 ((~![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_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), inverse_image3(F!43, X!40, A!42))) | (~((~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), A!42)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), X!40, F!43))))))) | (~((~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), A!42)) | member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), inverse_image3(F!43, X!40, A!42)) | ![Y: $i] : ((~member(Y, X!40)) | (~apply(F!43, tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), Y)))))))),
% 0.41/0.57 inference(modus_ponens,[status(thm)],[205, 204])).
% 0.41/0.57 tff(207,plain,
% 0.41/0.57 (~((~((~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), inverse_image3(F!43, X!40, A!42))) | (~((~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), A!42)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), X!40, F!43))))))) | (~((~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), A!42)) | member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), inverse_image3(F!43, X!40, A!42)) | ![Y: $i] : ((~member(Y, X!40)) | (~apply(F!43, tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), Y))))))),
% 0.41/0.57 inference(unit_resolution,[status(thm)],[206, 16])).
% 0.41/0.57 tff(208,plain,
% 0.41/0.57 (((~((~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), inverse_image3(F!43, X!40, A!42))) | (~((~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), A!42)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), X!40, F!43))))))) | (~((~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), A!42)) | member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), inverse_image3(F!43, X!40, A!42)) | ![Y: $i] : ((~member(Y, X!40)) | (~apply(F!43, tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), Y)))))) | ((~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), inverse_image3(F!43, X!40, A!42))) | (~((~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), A!42)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), X!40, F!43))))))),
% 0.41/0.58 inference(tautology,[status(thm)],[])).
% 0.41/0.58 tff(209,plain,
% 0.41/0.58 ((~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), inverse_image3(F!43, X!40, A!42))) | (~((~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), A!42)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), X!40, F!43)))))),
% 0.41/0.58 inference(unit_resolution,[status(thm)],[208, 207])).
% 0.41/0.58 tff(210,plain,
% 0.41/0.58 (((~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), inverse_image3(F!43, X!40, A!42))) | (~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), inverse_image3(F!43, Y!39, A!42)))) | member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), inverse_image3(F!43, X!40, A!42))),
% 0.41/0.58 inference(tautology,[status(thm)],[])).
% 0.41/0.58 tff(211,plain,
% 0.41/0.58 (member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), inverse_image3(F!43, X!40, A!42))),
% 0.41/0.58 inference(unit_resolution,[status(thm)],[210, 180])).
% 0.41/0.58 tff(212,plain,
% 0.41/0.58 ((~((~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), inverse_image3(F!43, X!40, A!42))) | (~((~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), A!42)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), X!40, F!43))))))) | (~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), inverse_image3(F!43, X!40, A!42))) | (~((~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), A!42)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), X!40, F!43)))))),
% 0.41/0.58 inference(tautology,[status(thm)],[])).
% 0.41/0.58 tff(213,plain,
% 0.41/0.58 ((~((~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), inverse_image3(F!43, X!40, A!42))) | (~((~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), A!42)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), X!40, F!43))))))) | (~((~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), A!42)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), X!40, F!43)))))),
% 0.41/0.58 inference(unit_resolution,[status(thm)],[212, 211])).
% 0.41/0.58 tff(214,plain,
% 0.41/0.58 (~((~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), A!42)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), X!40, F!43))))),
% 0.41/0.58 inference(unit_resolution,[status(thm)],[213, 209])).
% 0.41/0.58 tff(215,plain,
% 0.41/0.58 (((~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), A!42)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), X!40, F!43)))) | member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), X!40, F!43), X!40)),
% 0.41/0.58 inference(tautology,[status(thm)],[])).
% 0.41/0.58 tff(216,plain,
% 0.41/0.58 (member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), X!40, F!43), X!40)),
% 0.41/0.58 inference(unit_resolution,[status(thm)],[215, 214])).
% 0.41/0.58 tff(217,plain,
% 0.41/0.58 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))) | (~((~((~subset(X!40, B!41)) | ![X: $i] : ((~member(X, X!40)) | member(X, B!41)))) | (~(subset(X!40, B!41) | (~((~member(tptp_fun_X_0(B!41, X!40), X!40)) | member(tptp_fun_X_0(B!41, X!40), B!41)))))))),
% 0.41/0.58 inference(quant_inst,[status(thm)],[])).
% 0.41/0.58 tff(218,plain,
% 0.41/0.58 (~((~((~subset(X!40, B!41)) | ![X: $i] : ((~member(X, X!40)) | member(X, B!41)))) | (~(subset(X!40, B!41) | (~((~member(tptp_fun_X_0(B!41, X!40), X!40)) | member(tptp_fun_X_0(B!41, X!40), B!41))))))),
% 0.41/0.58 inference(unit_resolution,[status(thm)],[217, 53])).
% 0.41/0.58 tff(219,plain,
% 0.41/0.58 (((~((~subset(X!40, B!41)) | ![X: $i] : ((~member(X, X!40)) | member(X, B!41)))) | (~(subset(X!40, B!41) | (~((~member(tptp_fun_X_0(B!41, X!40), X!40)) | member(tptp_fun_X_0(B!41, X!40), B!41)))))) | ((~subset(X!40, B!41)) | ![X: $i] : ((~member(X, X!40)) | member(X, B!41)))),
% 0.41/0.58 inference(tautology,[status(thm)],[])).
% 0.41/0.58 tff(220,plain,
% 0.41/0.58 ((~subset(X!40, B!41)) | ![X: $i] : ((~member(X, X!40)) | member(X, B!41))),
% 0.41/0.58 inference(unit_resolution,[status(thm)],[219, 218])).
% 0.41/0.58 tff(221,plain,
% 0.41/0.58 (subset(X!40, B!41)),
% 0.41/0.58 inference(and_elim,[status(thm)],[192])).
% 0.41/0.58 tff(222,plain,
% 0.41/0.58 ((~((~subset(X!40, B!41)) | ![X: $i] : ((~member(X, X!40)) | member(X, B!41)))) | (~subset(X!40, B!41)) | ![X: $i] : ((~member(X, X!40)) | member(X, B!41))),
% 0.41/0.58 inference(tautology,[status(thm)],[])).
% 0.41/0.58 tff(223,plain,
% 0.41/0.58 ((~((~subset(X!40, B!41)) | ![X: $i] : ((~member(X, X!40)) | member(X, B!41)))) | ![X: $i] : ((~member(X, X!40)) | member(X, B!41))),
% 0.41/0.58 inference(unit_resolution,[status(thm)],[222, 221])).
% 0.41/0.58 tff(224,plain,
% 0.41/0.58 (![X: $i] : ((~member(X, X!40)) | member(X, B!41))),
% 0.41/0.58 inference(unit_resolution,[status(thm)],[223, 220])).
% 0.41/0.58 tff(225,plain,
% 0.41/0.58 (((~![X: $i] : ((~member(X, X!40)) | member(X, B!41))) | ((~member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), X!40, F!43), X!40)) | member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), X!40, F!43), B!41))) <=> ((~![X: $i] : ((~member(X, X!40)) | member(X, B!41))) | (~member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), X!40, F!43), X!40)) | member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), X!40, F!43), B!41))),
% 0.41/0.58 inference(rewrite,[status(thm)],[])).
% 0.41/0.58 tff(226,plain,
% 0.41/0.58 ((~![X: $i] : ((~member(X, X!40)) | member(X, B!41))) | ((~member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), X!40, F!43), X!40)) | member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), X!40, F!43), B!41))),
% 0.41/0.58 inference(quant_inst,[status(thm)],[])).
% 0.41/0.58 tff(227,plain,
% 0.41/0.58 ((~![X: $i] : ((~member(X, X!40)) | member(X, B!41))) | (~member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), X!40, F!43), X!40)) | member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), X!40, F!43), B!41)),
% 0.41/0.58 inference(modus_ponens,[status(thm)],[226, 225])).
% 0.41/0.58 tff(228,plain,
% 0.41/0.58 (member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), X!40, F!43), B!41)),
% 0.41/0.58 inference(unit_resolution,[status(thm)],[227, 224, 216])).
% 0.41/0.58 tff(229,plain,
% 0.41/0.58 (((~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), A!42)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), X!40, F!43)))) | apply(F!43, tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), X!40, F!43))),
% 0.41/0.58 inference(tautology,[status(thm)],[])).
% 0.41/0.58 tff(230,plain,
% 0.41/0.58 (apply(F!43, tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), X!40, F!43))),
% 0.41/0.58 inference(unit_resolution,[status(thm)],[229, 214])).
% 0.41/0.58 tff(231,plain,
% 0.41/0.58 (((~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), A!42)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), Y!39, F!43)))) | apply(F!43, tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), Y!39, F!43))),
% 0.41/0.58 inference(tautology,[status(thm)],[])).
% 0.41/0.58 tff(232,plain,
% 0.41/0.58 (apply(F!43, tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), Y!39, F!43))),
% 0.41/0.58 inference(unit_resolution,[status(thm)],[231, 185])).
% 0.41/0.58 tff(233,plain,
% 0.41/0.58 (((~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), A!42)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), Y!39, F!43)))) | member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), A!42)),
% 0.41/0.58 inference(tautology,[status(thm)],[])).
% 0.41/0.58 tff(234,plain,
% 0.41/0.58 (member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), A!42)),
% 0.41/0.58 inference(unit_resolution,[status(thm)],[233, 185])).
% 0.41/0.58 tff(235,plain,
% 0.41/0.58 (^[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)))))))))))),
% 0.41/0.58 inference(bind,[status(th)],[])).
% 0.41/0.58 tff(236,plain,
% 0.41/0.58 (![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))))))))))),
% 0.41/0.58 inference(quant_intro,[status(thm)],[235])).
% 0.41/0.58 tff(237,plain,
% 0.41/0.58 (^[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)))))))))),
% 0.41/0.59 inference(bind,[status(th)],[])).
% 0.41/0.59 tff(238,plain,
% 0.41/0.59 (![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))))))))),
% 0.41/0.59 inference(quant_intro,[status(thm)],[237])).
% 0.41/0.59 tff(239,plain,
% 0.41/0.59 (^[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)))))))))),
% 0.41/0.59 inference(bind,[status(th)],[])).
% 0.41/0.59 tff(240,plain,
% 0.41/0.59 (![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))))))))),
% 0.41/0.59 inference(quant_intro,[status(thm)],[239])).
% 0.41/0.59 tff(241,plain,
% 0.41/0.59 (![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))))))))),
% 0.41/0.59 inference(transitivity,[status(thm)],[240, 238])).
% 0.41/0.59 tff(242,plain,
% 0.41/0.59 (^[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))))))))))),
% 0.41/0.59 inference(bind,[status(th)],[])).
% 0.41/0.59 tff(243,plain,
% 0.41/0.59 (![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))))))))),
% 0.41/0.59 inference(quant_intro,[status(thm)],[242])).
% 0.41/0.59 tff(244,plain,
% 0.41/0.59 (^[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))))))))),
% 0.41/0.59 inference(bind,[status(th)],[])).
% 0.41/0.59 tff(245,plain,
% 0.41/0.59 (![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)))))))),
% 0.41/0.59 inference(quant_intro,[status(thm)],[244])).
% 0.41/0.59 tff(246,plain,
% 0.41/0.59 (![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))))))),
% 0.41/0.59 inference(rewrite,[status(thm)],[])).
% 0.41/0.59 tff(247,plain,
% 0.41/0.59 (^[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)))))))),
% 0.41/0.59 inference(bind,[status(th)],[])).
% 0.41/0.59 tff(248,plain,
% 0.41/0.59 (![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))))))),
% 0.41/0.59 inference(quant_intro,[status(thm)],[247])).
% 0.41/0.59 tff(249,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')).
% 0.41/0.59 tff(250,plain,
% 0.41/0.59 (![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))))))),
% 0.41/0.59 inference(modus_ponens,[status(thm)],[249, 248])).
% 0.41/0.59 tff(251,plain,
% 0.41/0.59 (![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))))))),
% 0.41/0.59 inference(modus_ponens,[status(thm)],[250, 246])).
% 0.41/0.59 tff(252,plain,(
% 0.41/0.59 ![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))))))))),
% 0.41/0.59 inference(skolemize,[status(sab)],[251])).
% 0.41/0.59 tff(253,plain,
% 0.41/0.59 (![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)))))))),
% 0.41/0.59 inference(modus_ponens,[status(thm)],[252, 245])).
% 0.41/0.59 tff(254,plain,
% 0.41/0.59 (![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))))))))),
% 0.41/0.59 inference(modus_ponens,[status(thm)],[253, 243])).
% 0.41/0.59 tff(255,plain,
% 0.41/0.59 (![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))))))))),
% 0.41/0.59 inference(modus_ponens,[status(thm)],[254, 241])).
% 0.41/0.59 tff(256,plain,
% 0.41/0.59 (![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))))))))))),
% 0.41/0.59 inference(modus_ponens,[status(thm)],[255, 236])).
% 0.41/0.59 tff(257,plain,
% 0.41/0.59 (((~![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!43, A!42, B!41)) | (~((~![X: $i] : ((~member(X, A!42)) | (~((~member(tptp_fun_Y_3(X, B!41, F!43), B!41)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!41, F!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!41)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!42)) | (~member(Y1, B!41)))))))) | (~(maps(F!43, A!42, B!41) | (~((~member(tptp_fun_X_4(B!41, A!42, F!43), A!42)) | (~![Y: $i] : ((~member(Y, B!41)) | (~apply(F!43, tptp_fun_X_4(B!41, A!42, F!43), Y)))))) | (~((~member(tptp_fun_Y2_5(B!41, A!42, F!43), B!41)) | (~member(tptp_fun_Y1_6(B!41, A!42, F!43), B!41)) | (~member(tptp_fun_X_7(B!41, A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_X_7(B!41, A!42, F!43), tptp_fun_Y2_5(B!41, A!42, F!43))) | (~apply(F!43, tptp_fun_X_7(B!41, A!42, F!43), tptp_fun_Y1_6(B!41, A!42, F!43))) | (tptp_fun_Y1_6(B!41, A!42, F!43) = tptp_fun_Y2_5(B!41, A!42, F!43))))))))) <=> ((~![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!43, A!42, B!41)) | (~((~![X: $i] : ((~member(X, A!42)) | (~((~member(tptp_fun_Y_3(X, B!41, F!43), B!41)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!41, F!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!41)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!42)) | (~member(Y1, B!41)))))))) | (~(maps(F!43, A!42, B!41) | (~((~member(tptp_fun_X_4(B!41, A!42, F!43), A!42)) | (~![Y: $i] : ((~member(Y, B!41)) | (~apply(F!43, tptp_fun_X_4(B!41, A!42, F!43), Y)))))) | (~((~member(tptp_fun_Y2_5(B!41, A!42, F!43), B!41)) | (~member(tptp_fun_Y1_6(B!41, A!42, F!43), B!41)) | (~member(tptp_fun_X_7(B!41, A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_X_7(B!41, A!42, F!43), tptp_fun_Y2_5(B!41, A!42, F!43))) | (~apply(F!43, tptp_fun_X_7(B!41, A!42, F!43), tptp_fun_Y1_6(B!41, A!42, F!43))) | (tptp_fun_Y1_6(B!41, A!42, F!43) = tptp_fun_Y2_5(B!41, A!42, F!43)))))))))),
% 0.41/0.59 inference(rewrite,[status(thm)],[])).
% 0.41/0.59 tff(258,plain,
% 0.41/0.59 ((~((~((~maps(F!43, A!42, B!41)) | (~((~![X: $i] : ((~member(X, A!42)) | (~((~member(tptp_fun_Y_3(X, B!41, F!43), B!41)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!41, F!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!42)) | (~member(Y1, B!41)) | (~member(Y2, B!41)))))))) | (~(maps(F!43, A!42, B!41) | (~((tptp_fun_Y1_6(B!41, A!42, F!43) = tptp_fun_Y2_5(B!41, A!42, F!43)) | (~apply(F!43, tptp_fun_X_7(B!41, A!42, F!43), tptp_fun_Y1_6(B!41, A!42, F!43))) | (~apply(F!43, tptp_fun_X_7(B!41, A!42, F!43), tptp_fun_Y2_5(B!41, A!42, F!43))) | (~member(tptp_fun_X_7(B!41, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_6(B!41, A!42, F!43), B!41)) | (~member(tptp_fun_Y2_5(B!41, A!42, F!43), B!41)))) | (~((~member(tptp_fun_X_4(B!41, A!42, F!43), A!42)) | (~![Y: $i] : ((~member(Y, B!41)) | (~apply(F!43, tptp_fun_X_4(B!41, A!42, F!43), Y)))))))))) <=> (~((~((~maps(F!43, A!42, B!41)) | (~((~![X: $i] : ((~member(X, A!42)) | (~((~member(tptp_fun_Y_3(X, B!41, F!43), B!41)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!41, F!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!41)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!42)) | (~member(Y1, B!41)))))))) | (~(maps(F!43, A!42, B!41) | (~((~member(tptp_fun_X_4(B!41, A!42, F!43), A!42)) | (~![Y: $i] : ((~member(Y, B!41)) | (~apply(F!43, tptp_fun_X_4(B!41, A!42, F!43), Y)))))) | (~((~member(tptp_fun_Y2_5(B!41, A!42, F!43), B!41)) | (~member(tptp_fun_Y1_6(B!41, A!42, F!43), B!41)) | (~member(tptp_fun_X_7(B!41, A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_X_7(B!41, A!42, F!43), tptp_fun_Y2_5(B!41, A!42, F!43))) | (~apply(F!43, tptp_fun_X_7(B!41, A!42, F!43), tptp_fun_Y1_6(B!41, A!42, F!43))) | (tptp_fun_Y1_6(B!41, A!42, F!43) = tptp_fun_Y2_5(B!41, A!42, F!43))))))))),
% 0.41/0.60 inference(rewrite,[status(thm)],[])).
% 0.41/0.60 tff(259,plain,
% 0.41/0.60 (((~![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!43, A!42, B!41)) | (~((~![X: $i] : ((~member(X, A!42)) | (~((~member(tptp_fun_Y_3(X, B!41, F!43), B!41)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!41, F!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!42)) | (~member(Y1, B!41)) | (~member(Y2, B!41)))))))) | (~(maps(F!43, A!42, B!41) | (~((tptp_fun_Y1_6(B!41, A!42, F!43) = tptp_fun_Y2_5(B!41, A!42, F!43)) | (~apply(F!43, tptp_fun_X_7(B!41, A!42, F!43), tptp_fun_Y1_6(B!41, A!42, F!43))) | (~apply(F!43, tptp_fun_X_7(B!41, A!42, F!43), tptp_fun_Y2_5(B!41, A!42, F!43))) | (~member(tptp_fun_X_7(B!41, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_6(B!41, A!42, F!43), B!41)) | (~member(tptp_fun_Y2_5(B!41, A!42, F!43), B!41)))) | (~((~member(tptp_fun_X_4(B!41, A!42, F!43), A!42)) | (~![Y: $i] : ((~member(Y, B!41)) | (~apply(F!43, tptp_fun_X_4(B!41, A!42, F!43), 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!43, A!42, B!41)) | (~((~![X: $i] : ((~member(X, A!42)) | (~((~member(tptp_fun_Y_3(X, B!41, F!43), B!41)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!41, F!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!41)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!42)) | (~member(Y1, B!41)))))))) | (~(maps(F!43, A!42, B!41) | (~((~member(tptp_fun_X_4(B!41, A!42, F!43), A!42)) | (~![Y: $i] : ((~member(Y, B!41)) | (~apply(F!43, tptp_fun_X_4(B!41, A!42, F!43), Y)))))) | (~((~member(tptp_fun_Y2_5(B!41, A!42, F!43), B!41)) | (~member(tptp_fun_Y1_6(B!41, A!42, F!43), B!41)) | (~member(tptp_fun_X_7(B!41, A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_X_7(B!41, A!42, F!43), tptp_fun_Y2_5(B!41, A!42, F!43))) | (~apply(F!43, tptp_fun_X_7(B!41, A!42, F!43), tptp_fun_Y1_6(B!41, A!42, F!43))) | (tptp_fun_Y1_6(B!41, A!42, F!43) = tptp_fun_Y2_5(B!41, A!42, F!43)))))))))),
% 0.41/0.60 inference(monotonicity,[status(thm)],[258])).
% 0.41/0.60 tff(260,plain,
% 0.41/0.60 (((~![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!43, A!42, B!41)) | (~((~![X: $i] : ((~member(X, A!42)) | (~((~member(tptp_fun_Y_3(X, B!41, F!43), B!41)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!41, F!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!42)) | (~member(Y1, B!41)) | (~member(Y2, B!41)))))))) | (~(maps(F!43, A!42, B!41) | (~((tptp_fun_Y1_6(B!41, A!42, F!43) = tptp_fun_Y2_5(B!41, A!42, F!43)) | (~apply(F!43, tptp_fun_X_7(B!41, A!42, F!43), tptp_fun_Y1_6(B!41, A!42, F!43))) | (~apply(F!43, tptp_fun_X_7(B!41, A!42, F!43), tptp_fun_Y2_5(B!41, A!42, F!43))) | (~member(tptp_fun_X_7(B!41, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_6(B!41, A!42, F!43), B!41)) | (~member(tptp_fun_Y2_5(B!41, A!42, F!43), B!41)))) | (~((~member(tptp_fun_X_4(B!41, A!42, F!43), A!42)) | (~![Y: $i] : ((~member(Y, B!41)) | (~apply(F!43, tptp_fun_X_4(B!41, A!42, F!43), 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!43, A!42, B!41)) | (~((~![X: $i] : ((~member(X, A!42)) | (~((~member(tptp_fun_Y_3(X, B!41, F!43), B!41)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!41, F!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!41)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!42)) | (~member(Y1, B!41)))))))) | (~(maps(F!43, A!42, B!41) | (~((~member(tptp_fun_X_4(B!41, A!42, F!43), A!42)) | (~![Y: $i] : ((~member(Y, B!41)) | (~apply(F!43, tptp_fun_X_4(B!41, A!42, F!43), Y)))))) | (~((~member(tptp_fun_Y2_5(B!41, A!42, F!43), B!41)) | (~member(tptp_fun_Y1_6(B!41, A!42, F!43), B!41)) | (~member(tptp_fun_X_7(B!41, A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_X_7(B!41, A!42, F!43), tptp_fun_Y2_5(B!41, A!42, F!43))) | (~apply(F!43, tptp_fun_X_7(B!41, A!42, F!43), tptp_fun_Y1_6(B!41, A!42, F!43))) | (tptp_fun_Y1_6(B!41, A!42, F!43) = tptp_fun_Y2_5(B!41, A!42, F!43)))))))))),
% 0.41/0.60 inference(transitivity,[status(thm)],[259, 257])).
% 0.41/0.60 tff(261,plain,
% 0.41/0.60 ((~![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!43, A!42, B!41)) | (~((~![X: $i] : ((~member(X, A!42)) | (~((~member(tptp_fun_Y_3(X, B!41, F!43), B!41)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!41, F!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!42)) | (~member(Y1, B!41)) | (~member(Y2, B!41)))))))) | (~(maps(F!43, A!42, B!41) | (~((tptp_fun_Y1_6(B!41, A!42, F!43) = tptp_fun_Y2_5(B!41, A!42, F!43)) | (~apply(F!43, tptp_fun_X_7(B!41, A!42, F!43), tptp_fun_Y1_6(B!41, A!42, F!43))) | (~apply(F!43, tptp_fun_X_7(B!41, A!42, F!43), tptp_fun_Y2_5(B!41, A!42, F!43))) | (~member(tptp_fun_X_7(B!41, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_6(B!41, A!42, F!43), B!41)) | (~member(tptp_fun_Y2_5(B!41, A!42, F!43), B!41)))) | (~((~member(tptp_fun_X_4(B!41, A!42, F!43), A!42)) | (~![Y: $i] : ((~member(Y, B!41)) | (~apply(F!43, tptp_fun_X_4(B!41, A!42, F!43), Y))))))))))),
% 0.41/0.60 inference(quant_inst,[status(thm)],[])).
% 0.41/0.60 tff(262,plain,
% 0.41/0.60 ((~![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!43, A!42, B!41)) | (~((~![X: $i] : ((~member(X, A!42)) | (~((~member(tptp_fun_Y_3(X, B!41, F!43), B!41)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!41, F!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!41)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!42)) | (~member(Y1, B!41)))))))) | (~(maps(F!43, A!42, B!41) | (~((~member(tptp_fun_X_4(B!41, A!42, F!43), A!42)) | (~![Y: $i] : ((~member(Y, B!41)) | (~apply(F!43, tptp_fun_X_4(B!41, A!42, F!43), Y)))))) | (~((~member(tptp_fun_Y2_5(B!41, A!42, F!43), B!41)) | (~member(tptp_fun_Y1_6(B!41, A!42, F!43), B!41)) | (~member(tptp_fun_X_7(B!41, A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_X_7(B!41, A!42, F!43), tptp_fun_Y2_5(B!41, A!42, F!43))) | (~apply(F!43, tptp_fun_X_7(B!41, A!42, F!43), tptp_fun_Y1_6(B!41, A!42, F!43))) | (tptp_fun_Y1_6(B!41, A!42, F!43) = tptp_fun_Y2_5(B!41, A!42, F!43))))))))),
% 0.41/0.60 inference(modus_ponens,[status(thm)],[261, 260])).
% 0.41/0.60 tff(263,plain,
% 0.41/0.60 (~((~((~maps(F!43, A!42, B!41)) | (~((~![X: $i] : ((~member(X, A!42)) | (~((~member(tptp_fun_Y_3(X, B!41, F!43), B!41)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!41, F!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!41)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!42)) | (~member(Y1, B!41)))))))) | (~(maps(F!43, A!42, B!41) | (~((~member(tptp_fun_X_4(B!41, A!42, F!43), A!42)) | (~![Y: $i] : ((~member(Y, B!41)) | (~apply(F!43, tptp_fun_X_4(B!41, A!42, F!43), Y)))))) | (~((~member(tptp_fun_Y2_5(B!41, A!42, F!43), B!41)) | (~member(tptp_fun_Y1_6(B!41, A!42, F!43), B!41)) | (~member(tptp_fun_X_7(B!41, A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_X_7(B!41, A!42, F!43), tptp_fun_Y2_5(B!41, A!42, F!43))) | (~apply(F!43, tptp_fun_X_7(B!41, A!42, F!43), tptp_fun_Y1_6(B!41, A!42, F!43))) | (tptp_fun_Y1_6(B!41, A!42, F!43) = tptp_fun_Y2_5(B!41, A!42, F!43)))))))),
% 0.41/0.60 inference(unit_resolution,[status(thm)],[262, 256])).
% 0.41/0.60 tff(264,plain,
% 0.41/0.60 (((~((~maps(F!43, A!42, B!41)) | (~((~![X: $i] : ((~member(X, A!42)) | (~((~member(tptp_fun_Y_3(X, B!41, F!43), B!41)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!41, F!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!41)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!42)) | (~member(Y1, B!41)))))))) | (~(maps(F!43, A!42, B!41) | (~((~member(tptp_fun_X_4(B!41, A!42, F!43), A!42)) | (~![Y: $i] : ((~member(Y, B!41)) | (~apply(F!43, tptp_fun_X_4(B!41, A!42, F!43), Y)))))) | (~((~member(tptp_fun_Y2_5(B!41, A!42, F!43), B!41)) | (~member(tptp_fun_Y1_6(B!41, A!42, F!43), B!41)) | (~member(tptp_fun_X_7(B!41, A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_X_7(B!41, A!42, F!43), tptp_fun_Y2_5(B!41, A!42, F!43))) | (~apply(F!43, tptp_fun_X_7(B!41, A!42, F!43), tptp_fun_Y1_6(B!41, A!42, F!43))) | (tptp_fun_Y1_6(B!41, A!42, F!43) = tptp_fun_Y2_5(B!41, A!42, F!43))))))) | ((~maps(F!43, A!42, B!41)) | (~((~![X: $i] : ((~member(X, A!42)) | (~((~member(tptp_fun_Y_3(X, B!41, F!43), B!41)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!41, F!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!41)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!42)) | (~member(Y1, B!41)))))))),
% 0.41/0.60 inference(tautology,[status(thm)],[])).
% 0.41/0.60 tff(265,plain,
% 0.41/0.60 ((~maps(F!43, A!42, B!41)) | (~((~![X: $i] : ((~member(X, A!42)) | (~((~member(tptp_fun_Y_3(X, B!41, F!43), B!41)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!41, F!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!41)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!42)) | (~member(Y1, B!41))))))),
% 0.41/0.60 inference(unit_resolution,[status(thm)],[264, 263])).
% 0.41/0.60 tff(266,plain,
% 0.41/0.60 (maps(F!43, A!42, B!41)),
% 0.41/0.60 inference(and_elim,[status(thm)],[192])).
% 0.41/0.60 tff(267,plain,
% 0.41/0.60 ((~((~maps(F!43, A!42, B!41)) | (~((~![X: $i] : ((~member(X, A!42)) | (~((~member(tptp_fun_Y_3(X, B!41, F!43), B!41)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!41, F!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!41)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!42)) | (~member(Y1, B!41)))))))) | (~maps(F!43, A!42, B!41)) | (~((~![X: $i] : ((~member(X, A!42)) | (~((~member(tptp_fun_Y_3(X, B!41, F!43), B!41)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!41, F!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!41)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!42)) | (~member(Y1, B!41))))))),
% 0.41/0.60 inference(tautology,[status(thm)],[])).
% 0.41/0.60 tff(268,plain,
% 0.41/0.60 ((~((~maps(F!43, A!42, B!41)) | (~((~![X: $i] : ((~member(X, A!42)) | (~((~member(tptp_fun_Y_3(X, B!41, F!43), B!41)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!41, F!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!41)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!42)) | (~member(Y1, B!41)))))))) | (~((~![X: $i] : ((~member(X, A!42)) | (~((~member(tptp_fun_Y_3(X, B!41, F!43), B!41)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!41, F!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!41)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!42)) | (~member(Y1, B!41))))))),
% 0.41/0.60 inference(unit_resolution,[status(thm)],[267, 266])).
% 0.41/0.60 tff(269,plain,
% 0.41/0.60 (~((~![X: $i] : ((~member(X, A!42)) | (~((~member(tptp_fun_Y_3(X, B!41, F!43), B!41)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!41, F!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!41)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!42)) | (~member(Y1, B!41)))))),
% 0.41/0.60 inference(unit_resolution,[status(thm)],[268, 265])).
% 0.41/0.60 tff(270,plain,
% 0.41/0.60 (((~![X: $i] : ((~member(X, A!42)) | (~((~member(tptp_fun_Y_3(X, B!41, F!43), B!41)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!41, F!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!41)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!42)) | (~member(Y1, B!41))))) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!41)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!42)) | (~member(Y1, B!41)))),
% 0.41/0.60 inference(tautology,[status(thm)],[])).
% 0.41/0.60 tff(271,plain,
% 0.41/0.60 (![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!41)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!42)) | (~member(Y1, B!41)))),
% 0.41/0.60 inference(unit_resolution,[status(thm)],[270, 269])).
% 0.41/0.60 tff(272,plain,
% 0.41/0.60 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!41)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!42)) | (~member(Y1, B!41)))) | ((~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), A!42)) | (~apply(F!43, tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), Y!39, F!43))) | (~apply(F!43, tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), X!40, F!43))) | (tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), Y!39, F!43) = tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), X!40, F!43)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), X!40, F!43), B!41)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), Y!39, F!43), B!41)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!41)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!42)) | (~member(Y1, B!41)))) | (~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), A!42)) | (~apply(F!43, tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), Y!39, F!43))) | (~apply(F!43, tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), X!40, F!43))) | (tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), Y!39, F!43) = tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), X!40, F!43)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), X!40, F!43), B!41)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), Y!39, F!43), B!41)))),
% 0.41/0.61 inference(rewrite,[status(thm)],[])).
% 0.41/0.61 tff(273,plain,
% 0.41/0.61 (((tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), Y!39, F!43) = tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), X!40, F!43)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), X!40, F!43), B!41)) | (~apply(F!43, tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), Y!39, F!43))) | (~apply(F!43, tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), X!40, F!43))) | (~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), A!42)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), Y!39, F!43), B!41))) <=> ((~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), A!42)) | (~apply(F!43, tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), Y!39, F!43))) | (~apply(F!43, tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), X!40, F!43))) | (tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), Y!39, F!43) = tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), X!40, F!43)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), X!40, F!43), B!41)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), Y!39, F!43), B!41)))),
% 0.41/0.61 inference(rewrite,[status(thm)],[])).
% 0.41/0.61 tff(274,plain,
% 0.41/0.61 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!41)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!42)) | (~member(Y1, B!41)))) | ((tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), Y!39, F!43) = tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), X!40, F!43)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), X!40, F!43), B!41)) | (~apply(F!43, tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), Y!39, F!43))) | (~apply(F!43, tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), X!40, F!43))) | (~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), A!42)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), Y!39, F!43), B!41)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!41)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!42)) | (~member(Y1, B!41)))) | ((~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), A!42)) | (~apply(F!43, tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), Y!39, F!43))) | (~apply(F!43, tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), X!40, F!43))) | (tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), Y!39, F!43) = tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), X!40, F!43)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), X!40, F!43), B!41)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), Y!39, F!43), B!41))))),
% 0.41/0.61 inference(monotonicity,[status(thm)],[273])).
% 0.41/0.61 tff(275,plain,
% 0.41/0.61 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!41)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!42)) | (~member(Y1, B!41)))) | ((tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), Y!39, F!43) = tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), X!40, F!43)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), X!40, F!43), B!41)) | (~apply(F!43, tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), Y!39, F!43))) | (~apply(F!43, tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), X!40, F!43))) | (~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), A!42)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), Y!39, F!43), B!41)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!41)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!42)) | (~member(Y1, B!41)))) | (~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), A!42)) | (~apply(F!43, tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), Y!39, F!43))) | (~apply(F!43, tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), X!40, F!43))) | (tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), Y!39, F!43) = tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), X!40, F!43)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), X!40, F!43), B!41)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), Y!39, F!43), B!41)))),
% 0.41/0.61 inference(transitivity,[status(thm)],[274, 272])).
% 0.41/0.61 tff(276,plain,
% 0.41/0.61 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!41)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!42)) | (~member(Y1, B!41)))) | ((tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), Y!39, F!43) = tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), X!40, F!43)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), X!40, F!43), B!41)) | (~apply(F!43, tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), Y!39, F!43))) | (~apply(F!43, tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), X!40, F!43))) | (~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), A!42)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), Y!39, F!43), B!41)))),
% 0.41/0.61 inference(quant_inst,[status(thm)],[])).
% 0.41/0.61 tff(277,plain,
% 0.41/0.61 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!41)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!42)) | (~member(Y1, B!41)))) | (~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), A!42)) | (~apply(F!43, tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), Y!39, F!43))) | (~apply(F!43, tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), X!40, F!43))) | (tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), Y!39, F!43) = tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), X!40, F!43)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), X!40, F!43), B!41)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), Y!39, F!43), B!41))),
% 0.41/0.62 inference(modus_ponens,[status(thm)],[276, 275])).
% 0.41/0.62 tff(278,plain,
% 0.41/0.62 ((tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), Y!39, F!43) = tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), X!40, F!43)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), X!40, F!43), B!41)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), Y!39, F!43), B!41))),
% 0.41/0.62 inference(unit_resolution,[status(thm)],[277, 271, 234, 232, 230])).
% 0.41/0.62 tff(279,plain,
% 0.41/0.62 (tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), Y!39, F!43) = tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), X!40, F!43)),
% 0.41/0.62 inference(unit_resolution,[status(thm)],[278, 228, 200])).
% 0.41/0.62 tff(280,plain,
% 0.41/0.62 (tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), X!40, F!43) = tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), Y!39, F!43)),
% 0.41/0.62 inference(symmetry,[status(thm)],[279])).
% 0.41/0.62 tff(281,plain,
% 0.41/0.62 (member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), X!40, F!43), Y!39) <=> member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), Y!39, F!43), Y!39)),
% 0.41/0.62 inference(monotonicity,[status(thm)],[280])).
% 0.41/0.62 tff(282,plain,
% 0.41/0.62 (member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), Y!39, F!43), Y!39) <=> member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), X!40, F!43), Y!39)),
% 0.41/0.62 inference(symmetry,[status(thm)],[281])).
% 0.41/0.62 tff(283,plain,
% 0.41/0.62 (member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), X!40, F!43), Y!39)),
% 0.41/0.62 inference(modus_ponens,[status(thm)],[187, 282])).
% 0.41/0.62 tff(284,plain,
% 0.41/0.62 ((~![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))) | (~(((~member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), X!40, F!43), X!40)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), X!40, F!43), Y!39))) <=> member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), X!40, F!43), intersection(X!40, Y!39))))),
% 0.41/0.62 inference(quant_inst,[status(thm)],[])).
% 0.41/0.62 tff(285,plain,
% 0.41/0.62 (~(((~member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), X!40, F!43), X!40)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), X!40, F!43), Y!39))) <=> member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), X!40, F!43), intersection(X!40, Y!39)))),
% 0.41/0.62 inference(unit_resolution,[status(thm)],[284, 35])).
% 0.41/0.62 tff(286,plain,
% 0.41/0.62 (((~![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_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), inverse_image3(F!43, intersection(X!40, Y!39), A!42)) | ![Y: $i] : ((~member(Y, intersection(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), Y))) | (~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), A!42)))) | (~((~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), inverse_image3(F!43, intersection(X!40, Y!39), A!42))) | (~((~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), A!42)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), intersection(X!40, Y!39), F!43), intersection(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), intersection(X!40, Y!39), F!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_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), inverse_image3(F!43, intersection(X!40, Y!39), A!42)) | ![Y: $i] : ((~member(Y, intersection(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), Y))) | (~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), A!42)))) | (~((~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), inverse_image3(F!43, intersection(X!40, Y!39), A!42))) | (~((~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), A!42)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), intersection(X!40, Y!39), F!43), intersection(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), intersection(X!40, Y!39), F!43))))))))))),
% 0.41/0.62 inference(rewrite,[status(thm)],[])).
% 0.41/0.62 tff(287,plain,
% 0.41/0.62 ((~((~((~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), inverse_image3(F!43, intersection(X!40, Y!39), A!42))) | (~((~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), A!42)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), intersection(X!40, Y!39), F!43), intersection(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), intersection(X!40, Y!39), F!43))))))) | (~(member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), inverse_image3(F!43, intersection(X!40, Y!39), A!42)) | (~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), A!42)) | ![Y: $i] : ((~member(Y, intersection(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), Y))))))) <=> (~((~(member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), inverse_image3(F!43, intersection(X!40, Y!39), A!42)) | ![Y: $i] : ((~member(Y, intersection(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), Y))) | (~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), A!42)))) | (~((~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), inverse_image3(F!43, intersection(X!40, Y!39), A!42))) | (~((~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), A!42)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), intersection(X!40, Y!39), F!43), intersection(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), intersection(X!40, Y!39), F!43)))))))))),
% 0.41/0.62 inference(rewrite,[status(thm)],[])).
% 0.41/0.62 tff(288,plain,
% 0.41/0.62 (((~![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_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), inverse_image3(F!43, intersection(X!40, Y!39), A!42))) | (~((~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), A!42)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), intersection(X!40, Y!39), F!43), intersection(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), intersection(X!40, Y!39), F!43))))))) | (~(member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), inverse_image3(F!43, intersection(X!40, Y!39), A!42)) | (~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), A!42)) | ![Y: $i] : ((~member(Y, intersection(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!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_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), inverse_image3(F!43, intersection(X!40, Y!39), A!42)) | ![Y: $i] : ((~member(Y, intersection(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), Y))) | (~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), A!42)))) | (~((~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), inverse_image3(F!43, intersection(X!40, Y!39), A!42))) | (~((~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), A!42)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), intersection(X!40, Y!39), F!43), intersection(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), intersection(X!40, Y!39), F!43))))))))))),
% 0.41/0.63 inference(monotonicity,[status(thm)],[287])).
% 0.41/0.63 tff(289,plain,
% 0.41/0.63 (((~![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_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), inverse_image3(F!43, intersection(X!40, Y!39), A!42))) | (~((~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), A!42)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), intersection(X!40, Y!39), F!43), intersection(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), intersection(X!40, Y!39), F!43))))))) | (~(member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), inverse_image3(F!43, intersection(X!40, Y!39), A!42)) | (~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), A!42)) | ![Y: $i] : ((~member(Y, intersection(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!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_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), inverse_image3(F!43, intersection(X!40, Y!39), A!42)) | ![Y: $i] : ((~member(Y, intersection(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), Y))) | (~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), A!42)))) | (~((~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), inverse_image3(F!43, intersection(X!40, Y!39), A!42))) | (~((~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), A!42)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), intersection(X!40, Y!39), F!43), intersection(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), intersection(X!40, Y!39), F!43))))))))))),
% 0.41/0.63 inference(transitivity,[status(thm)],[288, 286])).
% 0.41/0.63 tff(290,plain,
% 0.41/0.63 ((~![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_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), inverse_image3(F!43, intersection(X!40, Y!39), A!42))) | (~((~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), A!42)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), intersection(X!40, Y!39), F!43), intersection(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), intersection(X!40, Y!39), F!43))))))) | (~(member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), inverse_image3(F!43, intersection(X!40, Y!39), A!42)) | (~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), A!42)) | ![Y: $i] : ((~member(Y, intersection(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), Y)))))))),
% 0.41/0.63 inference(quant_inst,[status(thm)],[])).
% 0.41/0.63 tff(291,plain,
% 0.41/0.63 ((~![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_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), inverse_image3(F!43, intersection(X!40, Y!39), A!42)) | ![Y: $i] : ((~member(Y, intersection(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), Y))) | (~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), A!42)))) | (~((~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), inverse_image3(F!43, intersection(X!40, Y!39), A!42))) | (~((~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), A!42)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), intersection(X!40, Y!39), F!43), intersection(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), intersection(X!40, Y!39), F!43)))))))))),
% 0.41/0.63 inference(modus_ponens,[status(thm)],[290, 289])).
% 0.41/0.63 tff(292,plain,
% 0.41/0.63 (~((~(member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), inverse_image3(F!43, intersection(X!40, Y!39), A!42)) | ![Y: $i] : ((~member(Y, intersection(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), Y))) | (~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), A!42)))) | (~((~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), inverse_image3(F!43, intersection(X!40, Y!39), A!42))) | (~((~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), A!42)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), intersection(X!40, Y!39), F!43), intersection(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), intersection(X!40, Y!39), F!43))))))))),
% 0.41/0.63 inference(unit_resolution,[status(thm)],[291, 16])).
% 0.41/0.63 tff(293,plain,
% 0.41/0.63 (((~(member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), inverse_image3(F!43, intersection(X!40, Y!39), A!42)) | ![Y: $i] : ((~member(Y, intersection(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), Y))) | (~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), A!42)))) | (~((~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), inverse_image3(F!43, intersection(X!40, Y!39), A!42))) | (~((~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), A!42)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), intersection(X!40, Y!39), F!43), intersection(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), intersection(X!40, Y!39), F!43)))))))) | (member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), inverse_image3(F!43, intersection(X!40, Y!39), A!42)) | ![Y: $i] : ((~member(Y, intersection(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), Y))) | (~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), A!42)))),
% 0.41/0.63 inference(tautology,[status(thm)],[])).
% 0.41/0.63 tff(294,plain,
% 0.41/0.63 (member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), inverse_image3(F!43, intersection(X!40, Y!39), A!42)) | ![Y: $i] : ((~member(Y, intersection(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), Y))) | (~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), A!42))),
% 0.41/0.63 inference(unit_resolution,[status(thm)],[293, 292])).
% 0.41/0.63 tff(295,plain,
% 0.41/0.63 (((~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42)))) | member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), inverse_image3(F!43, intersection(X!40, Y!39), A!42))) | (~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), inverse_image3(F!43, intersection(X!40, Y!39), A!42)))),
% 0.41/0.63 inference(tautology,[status(thm)],[])).
% 0.41/0.63 tff(296,plain,
% 0.41/0.63 (~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), inverse_image3(F!43, intersection(X!40, Y!39), A!42))),
% 0.41/0.63 inference(unit_resolution,[status(thm)],[295, 175])).
% 0.41/0.63 tff(297,plain,
% 0.41/0.63 ((~(member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), inverse_image3(F!43, intersection(X!40, Y!39), A!42)) | ![Y: $i] : ((~member(Y, intersection(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), Y))) | (~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), A!42)))) | member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), inverse_image3(F!43, intersection(X!40, Y!39), A!42)) | ![Y: $i] : ((~member(Y, intersection(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), Y))) | (~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), A!42))),
% 0.41/0.63 inference(tautology,[status(thm)],[])).
% 0.41/0.63 tff(298,plain,
% 0.41/0.63 ((~(member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), inverse_image3(F!43, intersection(X!40, Y!39), A!42)) | ![Y: $i] : ((~member(Y, intersection(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), Y))) | (~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), A!42)))) | ![Y: $i] : ((~member(Y, intersection(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), Y))) | (~member(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), A!42))),
% 0.41/0.63 inference(unit_resolution,[status(thm)],[297, 296])).
% 0.41/0.63 tff(299,plain,
% 0.41/0.63 (![Y: $i] : ((~member(Y, intersection(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), Y)))),
% 0.41/0.63 inference(unit_resolution,[status(thm)],[298, 234, 294])).
% 0.41/0.63 tff(300,plain,
% 0.48/0.63 (((~![Y: $i] : ((~member(Y, intersection(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), Y)))) | ((~member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), X!40, F!43), intersection(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), X!40, F!43))))) <=> ((~![Y: $i] : ((~member(Y, intersection(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), Y)))) | (~member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), X!40, F!43), intersection(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), X!40, F!43))))),
% 0.48/0.63 inference(rewrite,[status(thm)],[])).
% 0.48/0.63 tff(301,plain,
% 0.48/0.63 ((~![Y: $i] : ((~member(Y, intersection(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), Y)))) | ((~member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), X!40, F!43), intersection(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), X!40, F!43))))),
% 0.48/0.63 inference(quant_inst,[status(thm)],[])).
% 0.48/0.63 tff(302,plain,
% 0.48/0.63 ((~![Y: $i] : ((~member(Y, intersection(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), Y)))) | (~member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), X!40, F!43), intersection(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), X!40, F!43)))),
% 0.48/0.63 inference(modus_ponens,[status(thm)],[301, 300])).
% 0.48/0.63 tff(303,plain,
% 0.48/0.63 (~member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), X!40, F!43), intersection(X!40, Y!39))),
% 0.48/0.63 inference(unit_resolution,[status(thm)],[302, 299, 230])).
% 0.48/0.63 tff(304,plain,
% 0.48/0.63 ((((~member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), X!40, F!43), X!40)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), X!40, F!43), Y!39))) <=> member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), X!40, F!43), intersection(X!40, Y!39))) | ((~member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), X!40, F!43), X!40)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), X!40, F!43), Y!39))) | member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), X!40, F!43), intersection(X!40, Y!39))),
% 0.48/0.64 inference(tautology,[status(thm)],[])).
% 0.48/0.64 tff(305,plain,
% 0.48/0.64 ((((~member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), X!40, F!43), X!40)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), X!40, F!43), Y!39))) <=> member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), X!40, F!43), intersection(X!40, Y!39))) | ((~member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), X!40, F!43), X!40)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), X!40, F!43), Y!39)))),
% 0.48/0.64 inference(unit_resolution,[status(thm)],[304, 303])).
% 0.48/0.64 tff(306,plain,
% 0.48/0.64 ((~member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), X!40, F!43), X!40)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), X!40, F!43), Y!39))),
% 0.48/0.64 inference(unit_resolution,[status(thm)],[305, 285])).
% 0.48/0.64 tff(307,plain,
% 0.48/0.64 ((~((~member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), X!40, F!43), X!40)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), X!40, F!43), Y!39)))) | (~member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), X!40, F!43), X!40)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), X!40, F!43), Y!39))),
% 0.48/0.64 inference(tautology,[status(thm)],[])).
% 0.48/0.64 tff(308,plain,
% 0.48/0.64 ((~((~member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), X!40, F!43), X!40)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), X!40, F!43), Y!39)))) | (~member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), X!40, F!43), Y!39))),
% 0.48/0.64 inference(unit_resolution,[status(thm)],[307, 216])).
% 0.48/0.64 tff(309,plain,
% 0.48/0.64 (~member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!43, intersection(X!40, Y!39), A!42), intersection(inverse_image3(F!43, X!40, A!42), inverse_image3(F!43, Y!39, A!42))), X!40, F!43), Y!39)),
% 0.48/0.64 inference(unit_resolution,[status(thm)],[308, 306])).
% 0.48/0.64 tff(310,plain,
% 0.48/0.64 ($false),
% 0.48/0.64 inference(unit_resolution,[status(thm)],[309, 283])).
% 0.48/0.64 % SZS output end Proof
% 0.48/0.64 % E exiting
%------------------------------------------------------------------------------