%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET761+4 : TPTP v9.0.0. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n001.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 0.47s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SET761+4 : TPTP v9.0.0. Bugfixed v2.2.1.
% 0.08/0.13 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n001.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 05:45:20 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_X_24_type, type, (
% 0.21/0.42 tptp_fun_X_24: ( $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(image3_type, type, (
% 0.21/0.42 image3: ( $i * $i * $i ) > $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(tptp_fun_A_42_type, type, (
% 0.21/0.42 tptp_fun_A_42: $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(tptp_fun_Y_3_type, type, (
% 0.21/0.42 tptp_fun_Y_3: ( $i * $i * $i ) > $i)).
% 0.21/0.42 tff(injective_type, type, (
% 0.21/0.42 injective: ( $i * $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(equal_set_type, type, (
% 0.21/0.42 equal_set: ( $i * $i ) > $o)).
% 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(tptp_fun_X2_17_type, type, (
% 0.21/0.42 tptp_fun_X2_17: ( $i * $i * $i ) > $i)).
% 0.21/0.42 tff(tptp_fun_X1_18_type, type, (
% 0.21/0.42 tptp_fun_X1_18: ( $i * $i * $i ) > $i)).
% 0.21/0.42 tff(tptp_fun_Y_16_type, type, (
% 0.21/0.42 tptp_fun_Y_16: ( $i * $i * $i ) > $i)).
% 0.21/0.42 tff(1,plain,
% 0.21/0.42 (^[F: $i, A: $i, B: $i, Y: $i] : refl((~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y))))))) <=> (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y))))))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(2,plain,
% 0.21/0.42 (![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y))))))) <=> ![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[1])).
% 0.21/0.42 tff(3,plain,
% 0.21/0.42 (^[F: $i, A: $i, B: $i, Y: $i] : rewrite((~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y))))))) <=> (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y))))))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(4,plain,
% 0.21/0.42 (![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y))))))) <=> ![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[3])).
% 0.21/0.42 tff(5,plain,
% 0.21/0.42 (![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y))))))) <=> ![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))),
% 0.21/0.42 inference(transitivity,[status(thm)],[4, 2])).
% 0.21/0.42 tff(6,plain,
% 0.21/0.42 (^[F: $i, A: $i, B: $i, Y: $i] : trans(monotonicity(rewrite(((~member(Y, image3(F, A, B))) | (member(Y, B) & member(tptp_fun_X_24(Y, A, F), A) & apply(F, tptp_fun_X_24(Y, A, F), Y))) <=> ((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))), trans(monotonicity(quant_intro(proof_bind(^[X: $i] : trans(monotonicity(rewrite((member(X, A) & apply(F, X, Y)) <=> (~((~member(X, A)) | (~apply(F, X, Y))))), ((~(member(X, A) & apply(F, X, Y))) <=> (~(~((~member(X, A)) | (~apply(F, X, Y))))))), rewrite((~(~((~member(X, A)) | (~apply(F, X, Y))))) <=> ((~member(X, A)) | (~apply(F, X, Y)))), ((~(member(X, A) & apply(F, X, Y))) <=> ((~member(X, A)) | (~apply(F, X, Y)))))), (![X: $i] : (~(member(X, A) & apply(F, X, Y))) <=> ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y))))), ((member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : (~(member(X, A) & apply(F, X, Y)))) <=> (member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))), rewrite((member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))) <=> (member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y))))), ((member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : (~(member(X, A) & apply(F, X, Y)))) <=> (member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))), ((((~member(Y, image3(F, A, B))) | (member(Y, B) & member(tptp_fun_X_24(Y, A, F), A) & apply(F, tptp_fun_X_24(Y, A, F), Y))) & (member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : (~(member(X, A) & apply(F, X, Y))))) <=> (((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y))))) & (member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y))))))), rewrite((((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y))))) & (member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y))))) <=> (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))), ((((~member(Y, image3(F, A, B))) | (member(Y, B) & member(tptp_fun_X_24(Y, A, F), A) & apply(F, tptp_fun_X_24(Y, A, F), Y))) & (member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : (~(member(X, A) & apply(F, X, Y))))) <=> (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(7,plain,
% 0.21/0.42 (![F: $i, A: $i, B: $i, Y: $i] : (((~member(Y, image3(F, A, B))) | (member(Y, B) & member(tptp_fun_X_24(Y, A, F), A) & apply(F, tptp_fun_X_24(Y, A, F), Y))) & (member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : (~(member(X, A) & apply(F, X, Y))))) <=> ![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[6])).
% 0.21/0.42 tff(8,plain,
% 0.21/0.42 (^[F: $i, A: $i, B: $i, Y: $i] : rewrite((((~member(Y, image3(F, A, B))) | (member(Y, B) & (member(tptp_fun_X_24(Y, A, F), A) & apply(F, tptp_fun_X_24(Y, A, F), Y)))) & (member(Y, image3(F, A, B)) | ((~member(Y, B)) | ![X: $i] : (~(member(X, A) & apply(F, X, Y)))))) <=> (((~member(Y, image3(F, A, B))) | (member(Y, B) & member(tptp_fun_X_24(Y, A, F), A) & apply(F, tptp_fun_X_24(Y, A, F), Y))) & (member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : (~(member(X, A) & apply(F, X, Y))))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(9,plain,
% 0.21/0.42 (![F: $i, A: $i, B: $i, Y: $i] : (((~member(Y, image3(F, A, B))) | (member(Y, B) & (member(tptp_fun_X_24(Y, A, F), A) & apply(F, tptp_fun_X_24(Y, A, F), Y)))) & (member(Y, image3(F, A, B)) | ((~member(Y, B)) | ![X: $i] : (~(member(X, A) & apply(F, X, Y)))))) <=> ![F: $i, A: $i, B: $i, Y: $i] : (((~member(Y, image3(F, A, B))) | (member(Y, B) & member(tptp_fun_X_24(Y, A, F), A) & apply(F, tptp_fun_X_24(Y, A, F), Y))) & (member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : (~(member(X, A) & apply(F, X, Y)))))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[8])).
% 0.21/0.42 tff(10,plain,
% 0.21/0.42 (![F: $i, A: $i, B: $i, Y: $i] : (member(Y, image3(F, A, B)) <=> (member(Y, B) & ?[X: $i] : (member(X, A) & apply(F, X, Y)))) <=> ![F: $i, A: $i, B: $i, Y: $i] : (member(Y, image3(F, A, B)) <=> (member(Y, B) & ?[X: $i] : (member(X, A) & apply(F, X, Y))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(11,axiom,(![F: $i, A: $i, B: $i, Y: $i] : (member(Y, image3(F, A, B)) <=> (member(Y, B) & ?[X: $i] : (member(X, A) & apply(F, X, Y))))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+1.ax','image3')).
% 0.21/0.42 tff(12,plain,
% 0.21/0.42 (![F: $i, A: $i, B: $i, Y: $i] : (member(Y, image3(F, A, B)) <=> (member(Y, B) & ?[X: $i] : (member(X, A) & apply(F, X, Y))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.21/0.42 tff(13,plain,(
% 0.21/0.42 ![F: $i, A: $i, B: $i, Y: $i] : (((~member(Y, image3(F, A, B))) | (member(Y, B) & (member(tptp_fun_X_24(Y, A, F), A) & apply(F, tptp_fun_X_24(Y, A, F), Y)))) & (member(Y, image3(F, A, B)) | ((~member(Y, B)) | ![X: $i] : (~(member(X, A) & apply(F, X, Y))))))),
% 0.21/0.42 inference(skolemize,[status(sab)],[12])).
% 0.21/0.42 tff(14,plain,
% 0.21/0.42 (![F: $i, A: $i, B: $i, Y: $i] : (((~member(Y, image3(F, A, B))) | (member(Y, B) & member(tptp_fun_X_24(Y, A, F), A) & apply(F, tptp_fun_X_24(Y, A, F), Y))) & (member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : (~(member(X, A) & apply(F, X, Y)))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[13, 9])).
% 0.21/0.42 tff(15,plain,
% 0.21/0.42 (![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[14, 7])).
% 0.21/0.42 tff(16,plain,
% 0.21/0.42 (![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[15, 5])).
% 0.21/0.42 tff(17,plain,
% 0.21/0.42 (((~![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), image3(F!43, X!40, B!41))) | (~((~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), B!41)) | (~member(tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), X!40, F!43), tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))))))))) | (~((~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), B!41)) | member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), image3(F!43, X!40, B!41)) | ![X: $i] : ((~member(X, X!40)) | (~apply(F!43, X, tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))))))))))) <=> ((~![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), image3(F!43, X!40, B!41))) | (~((~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), B!41)) | (~member(tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), X!40, F!43), tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))))))))) | (~((~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), B!41)) | member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), image3(F!43, X!40, B!41)) | ![X: $i] : ((~member(X, X!40)) | (~apply(F!43, X, tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)))))))))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(18,plain,
% 0.21/0.43 ((~((~((~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), image3(F!43, X!40, B!41))) | (~((~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), B!41)) | (~member(tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), X!40, F!43), tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))))))))) | (~(member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), image3(F!43, X!40, B!41)) | (~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), B!41)) | ![X: $i] : ((~member(X, X!40)) | (~apply(F!43, X, tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)))))))))) <=> (~((~((~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), image3(F!43, X!40, B!41))) | (~((~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), B!41)) | (~member(tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), X!40, F!43), tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))))))))) | (~((~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), B!41)) | member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), image3(F!43, X!40, B!41)) | ![X: $i] : ((~member(X, X!40)) | (~apply(F!43, X, tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))))))))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(19,plain,
% 0.21/0.43 (((~![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), image3(F!43, X!40, B!41))) | (~((~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), B!41)) | (~member(tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), X!40, F!43), tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))))))))) | (~(member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), image3(F!43, X!40, B!41)) | (~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), B!41)) | ![X: $i] : ((~member(X, X!40)) | (~apply(F!43, X, tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))))))))))) <=> ((~![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), image3(F!43, X!40, B!41))) | (~((~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), B!41)) | (~member(tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), X!40, F!43), tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))))))))) | (~((~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), B!41)) | member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), image3(F!43, X!40, B!41)) | ![X: $i] : ((~member(X, X!40)) | (~apply(F!43, X, tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)))))))))))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[18])).
% 0.21/0.43 tff(20,plain,
% 0.21/0.43 (((~![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), image3(F!43, X!40, B!41))) | (~((~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), B!41)) | (~member(tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), X!40, F!43), tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))))))))) | (~(member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), image3(F!43, X!40, B!41)) | (~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), B!41)) | ![X: $i] : ((~member(X, X!40)) | (~apply(F!43, X, tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))))))))))) <=> ((~![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), image3(F!43, X!40, B!41))) | (~((~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), B!41)) | (~member(tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), X!40, F!43), tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))))))))) | (~((~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), B!41)) | member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), image3(F!43, X!40, B!41)) | ![X: $i] : ((~member(X, X!40)) | (~apply(F!43, X, tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)))))))))))),
% 0.21/0.44 inference(transitivity,[status(thm)],[19, 17])).
% 0.21/0.44 tff(21,plain,
% 0.21/0.44 ((~![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), image3(F!43, X!40, B!41))) | (~((~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), B!41)) | (~member(tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), X!40, F!43), tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))))))))) | (~(member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), image3(F!43, X!40, B!41)) | (~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), B!41)) | ![X: $i] : ((~member(X, X!40)) | (~apply(F!43, X, tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))))))))))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(22,plain,
% 0.21/0.44 ((~![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), image3(F!43, X!40, B!41))) | (~((~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), B!41)) | (~member(tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), X!40, F!43), tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))))))))) | (~((~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), B!41)) | member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), image3(F!43, X!40, B!41)) | ![X: $i] : ((~member(X, X!40)) | (~apply(F!43, X, tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))))))))))),
% 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(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), image3(F!43, X!40, B!41))) | (~((~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), B!41)) | (~member(tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), X!40, F!43), tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))))))))) | (~((~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), B!41)) | member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), image3(F!43, X!40, B!41)) | ![X: $i] : ((~member(X, X!40)) | (~apply(F!43, X, tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)))))))))),
% 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(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), image3(F!43, X!40, B!41))) | (~((~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), B!41)) | (~member(tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), X!40, F!43), tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))))))))) | (~((~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), B!41)) | member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), image3(F!43, X!40, B!41)) | ![X: $i] : ((~member(X, X!40)) | (~apply(F!43, X, tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))))))))) | ((~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), image3(F!43, X!40, B!41))) | (~((~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), B!41)) | (~member(tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), X!40, F!43), tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))))))))),
% 0.21/0.45 inference(tautology,[status(thm)],[])).
% 0.21/0.45 tff(25,plain,
% 0.21/0.45 ((~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), image3(F!43, X!40, B!41))) | (~((~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), B!41)) | (~member(tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), X!40, F!43), tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)))))))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[24, 23])).
% 0.21/0.45 tff(26,plain,
% 0.21/0.45 (^[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)))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(27,plain,
% 0.21/0.45 (![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))))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[26])).
% 0.21/0.45 tff(28,plain,
% 0.21/0.45 (^[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))))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(29,plain,
% 0.21/0.45 (![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))))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[28])).
% 0.21/0.45 tff(30,plain,
% 0.21/0.45 (![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)))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(31,axiom,(![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (member(X, A) & member(X, B)))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax','intersection')).
% 0.21/0.45 tff(32,plain,
% 0.21/0.45 (![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (member(X, A) & member(X, B)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.21/0.45 tff(33,plain,(
% 0.21/0.45 ![X: $i, A: $i, B: $i] : (member(X, intersection(A, B)) <=> (member(X, A) & member(X, B)))),
% 0.21/0.45 inference(skolemize,[status(sab)],[32])).
% 0.21/0.45 tff(34,plain,
% 0.21/0.45 (![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[33, 29])).
% 0.21/0.45 tff(35,plain,
% 0.21/0.45 (![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[34, 27])).
% 0.21/0.45 tff(36,plain,
% 0.21/0.45 ((~![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))) | (~(((~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), image3(F!43, X!40, B!41))) | (~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), image3(F!43, Y!39, B!41)))) <=> member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)))))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(37,plain,
% 0.21/0.45 (~(((~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), image3(F!43, X!40, B!41))) | (~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), image3(F!43, Y!39, B!41)))) <=> member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[36, 35])).
% 0.21/0.45 tff(38,plain,
% 0.21/0.45 (^[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))))))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(39,plain,
% 0.21/0.45 (![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)))))))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[38])).
% 0.21/0.45 tff(40,plain,
% 0.21/0.45 (^[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))))))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(41,plain,
% 0.21/0.45 (![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)))))))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[40])).
% 0.21/0.45 tff(42,plain,
% 0.21/0.45 (![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)))))))),
% 0.21/0.45 inference(transitivity,[status(thm)],[41, 39])).
% 0.21/0.45 tff(43,plain,
% 0.21/0.45 (^[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)))))))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(44,plain,
% 0.21/0.45 (![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)))))))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[43])).
% 0.21/0.45 tff(45,plain,
% 0.21/0.45 (![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)))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(46,plain,
% 0.21/0.45 (^[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))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(47,plain,
% 0.21/0.45 (![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)))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[46])).
% 0.21/0.45 tff(48,axiom,(![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : (member(X, A) => member(X, B)))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax','subset')).
% 0.21/0.45 tff(49,plain,
% 0.21/0.45 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.21/0.45 tff(50,plain,
% 0.21/0.45 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[49, 45])).
% 0.21/0.45 tff(51,plain,(
% 0.21/0.45 ![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)))))),
% 0.21/0.45 inference(skolemize,[status(sab)],[50])).
% 0.21/0.45 tff(52,plain,
% 0.21/0.45 (![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)))))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[51, 44])).
% 0.21/0.45 tff(53,plain,
% 0.21/0.45 (![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)))))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[52, 42])).
% 0.21/0.45 tff(54,plain,
% 0.21/0.45 ((~![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(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41))) | ![X: $i] : ((~member(X, intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)))) | member(X, image3(F!43, intersection(X!40, Y!39), B!41))))) | (~(subset(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)) | (~((~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)))) | member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), image3(F!43, intersection(X!40, Y!39), B!41))))))))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(55,plain,
% 0.21/0.45 (~((~((~subset(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41))) | ![X: $i] : ((~member(X, intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)))) | member(X, image3(F!43, intersection(X!40, Y!39), B!41))))) | (~(subset(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)) | (~((~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)))) | member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), image3(F!43, intersection(X!40, Y!39), B!41)))))))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[54, 53])).
% 0.21/0.45 tff(56,plain,
% 0.21/0.45 (((~((~subset(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41))) | ![X: $i] : ((~member(X, intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)))) | member(X, image3(F!43, intersection(X!40, Y!39), B!41))))) | (~(subset(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)) | (~((~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)))) | member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), image3(F!43, intersection(X!40, Y!39), B!41))))))) | (subset(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)) | (~((~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)))) | member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), image3(F!43, intersection(X!40, Y!39), B!41)))))),
% 0.21/0.45 inference(tautology,[status(thm)],[])).
% 0.21/0.45 tff(57,plain,
% 0.21/0.45 (subset(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)) | (~((~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)))) | member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), image3(F!43, intersection(X!40, Y!39), B!41))))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[56, 55])).
% 0.21/0.46 tff(58,assumption,((~((~subset(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)))) | ![X: $i] : ((~member(X, image3(F!43, intersection(X!40, Y!39), B!41))) | member(X, intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)))))) | (~(subset(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))) | (~((~member(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), image3(F!43, intersection(X!40, Y!39), B!41))) | member(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)))))))), introduced(assumption)).
% 0.21/0.46 tff(59,plain,
% 0.21/0.46 ((~![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(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)))) | ![X: $i] : ((~member(X, image3(F!43, intersection(X!40, Y!39), B!41))) | member(X, intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)))))) | (~(subset(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))) | (~((~member(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), image3(F!43, intersection(X!40, Y!39), B!41))) | member(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)))))))))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(60,plain,
% 0.21/0.46 ($false),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[59, 53, 58])).
% 0.21/0.46 tff(61,plain,(~((~((~subset(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)))) | ![X: $i] : ((~member(X, image3(F!43, intersection(X!40, Y!39), B!41))) | member(X, intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)))))) | (~(subset(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))) | (~((~member(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), image3(F!43, intersection(X!40, Y!39), B!41))) | member(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))))))))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.46 tff(62,plain,
% 0.21/0.46 (((~((~subset(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)))) | ![X: $i] : ((~member(X, image3(F!43, intersection(X!40, Y!39), B!41))) | member(X, intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)))))) | (~(subset(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))) | (~((~member(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), image3(F!43, intersection(X!40, Y!39), B!41))) | member(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)))))))) | (subset(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))) | (~((~member(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), image3(F!43, intersection(X!40, Y!39), B!41))) | member(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))))))),
% 0.21/0.46 inference(tautology,[status(thm)],[])).
% 0.21/0.46 tff(63,plain,
% 0.21/0.46 (subset(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))) | (~((~member(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), image3(F!43, intersection(X!40, Y!39), B!41))) | member(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)))))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[62, 61])).
% 0.21/0.46 tff(64,plain,
% 0.21/0.46 (((~![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43), image3(F!43, Y!39, B!41))) | (~((~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43), B!41)) | (~member(tptp_fun_X_24(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_24(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43), Y!39, F!43), tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43))))))) | (~((~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43), B!41)) | ![X: $i] : ((~member(X, Y!39)) | (~apply(F!43, X, tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43)))) | member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43), image3(F!43, Y!39, B!41))))))) <=> ((~![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43), image3(F!43, Y!39, B!41))) | (~((~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43), B!41)) | (~member(tptp_fun_X_24(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_24(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43), Y!39, F!43), tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43))))))) | (~((~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43), B!41)) | ![X: $i] : ((~member(X, Y!39)) | (~apply(F!43, X, tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43)))) | member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43), image3(F!43, Y!39, B!41)))))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(65,plain,
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% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(66,plain,
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% 0.21/0.47 inference(monotonicity,[status(thm)],[65])).
% 0.21/0.47 tff(67,plain,
% 0.21/0.47 (((~![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43), image3(F!43, Y!39, B!41))) | (~((~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43), B!41)) | (~member(tptp_fun_X_24(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_24(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43), Y!39, F!43), tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43))))))) | (~(member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43), image3(F!43, Y!39, B!41)) | (~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43), B!41)) | ![X: $i] : ((~member(X, Y!39)) | (~apply(F!43, X, tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43))))))))) <=> ((~![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43), image3(F!43, Y!39, B!41))) | (~((~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43), B!41)) | (~member(tptp_fun_X_24(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_24(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43), Y!39, F!43), tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43))))))) | (~((~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43), B!41)) | ![X: $i] : ((~member(X, Y!39)) | (~apply(F!43, X, tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43)))) | member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43), image3(F!43, Y!39, B!41)))))))),
% 0.21/0.48 inference(transitivity,[status(thm)],[66, 64])).
% 0.21/0.48 tff(68,plain,
% 0.21/0.48 ((~![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43), image3(F!43, Y!39, B!41))) | (~((~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43), B!41)) | (~member(tptp_fun_X_24(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_24(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43), Y!39, F!43), tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43))))))) | (~(member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43), image3(F!43, Y!39, B!41)) | (~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43), B!41)) | ![X: $i] : ((~member(X, Y!39)) | (~apply(F!43, X, tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43))))))))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(69,plain,
% 0.21/0.48 ((~![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43), image3(F!43, Y!39, B!41))) | (~((~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43), B!41)) | (~member(tptp_fun_X_24(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_24(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43), Y!39, F!43), tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43))))))) | (~((~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43), B!41)) | ![X: $i] : ((~member(X, Y!39)) | (~apply(F!43, X, tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43)))) | member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43), image3(F!43, Y!39, B!41))))))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.21/0.48 tff(70,plain,
% 0.21/0.48 (~((~((~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43), image3(F!43, Y!39, B!41))) | (~((~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43), B!41)) | (~member(tptp_fun_X_24(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_24(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43), Y!39, F!43), tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43))))))) | (~((~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43), B!41)) | ![X: $i] : ((~member(X, Y!39)) | (~apply(F!43, X, tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43)))) | member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43), image3(F!43, Y!39, B!41)))))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[69, 16])).
% 0.21/0.48 tff(71,plain,
% 0.21/0.48 (((~((~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43), image3(F!43, Y!39, B!41))) | (~((~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43), B!41)) | (~member(tptp_fun_X_24(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_24(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43), Y!39, F!43), tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43))))))) | (~((~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43), B!41)) | ![X: $i] : ((~member(X, Y!39)) | (~apply(F!43, X, tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43)))) | member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43), image3(F!43, Y!39, B!41))))) | ((~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43), B!41)) | ![X: $i] : ((~member(X, Y!39)) | (~apply(F!43, X, tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43)))) | member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43), image3(F!43, Y!39, B!41)))),
% 0.21/0.48 inference(tautology,[status(thm)],[])).
% 0.21/0.48 tff(72,plain,
% 0.21/0.48 ((~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43), B!41)) | ![X: $i] : ((~member(X, Y!39)) | (~apply(F!43, X, tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43)))) | member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43), image3(F!43, Y!39, B!41))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[71, 70])).
% 0.21/0.48 tff(73,plain,
% 0.21/0.48 ((~![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))) | (~(((~member(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), X!40)) | (~member(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), Y!39))) <=> member(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), intersection(X!40, Y!39))))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(74,plain,
% 0.21/0.48 (~(((~member(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), X!40)) | (~member(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), Y!39))) <=> member(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), intersection(X!40, Y!39)))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[73, 35])).
% 0.21/0.48 tff(75,plain,
% 0.21/0.48 (((~![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), image3(F!43, intersection(X!40, Y!39), B!41))) | (~((~member(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), B!41)) | (~member(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), intersection(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)))))))) | (~(member(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), image3(F!43, intersection(X!40, Y!39), B!41)) | ![X: $i] : ((~member(X, intersection(X!40, Y!39))) | (~apply(F!43, X, tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41))))) | (~member(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), B!41))))))) <=> ((~![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), image3(F!43, intersection(X!40, Y!39), B!41))) | (~((~member(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), B!41)) | (~member(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), intersection(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)))))))) | (~(member(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), image3(F!43, intersection(X!40, Y!39), B!41)) | ![X: $i] : ((~member(X, intersection(X!40, Y!39))) | (~apply(F!43, X, tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41))))) | (~member(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), B!41)))))))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(76,plain,
% 0.21/0.48 ((~((~((~member(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), image3(F!43, intersection(X!40, Y!39), B!41))) | (~((~member(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), B!41)) | (~member(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), intersection(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)))))))) | (~(member(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), image3(F!43, intersection(X!40, Y!39), B!41)) | (~member(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), B!41)) | ![X: $i] : ((~member(X, intersection(X!40, Y!39))) | (~apply(F!43, X, tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41))))))))) <=> (~((~((~member(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), image3(F!43, intersection(X!40, Y!39), B!41))) | (~((~member(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), B!41)) | (~member(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), intersection(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)))))))) | (~(member(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), image3(F!43, intersection(X!40, Y!39), B!41)) | ![X: $i] : ((~member(X, intersection(X!40, Y!39))) | (~apply(F!43, X, tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41))))) | (~member(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), B!41))))))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(77,plain,
% 0.21/0.49 (((~![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), image3(F!43, intersection(X!40, Y!39), B!41))) | (~((~member(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), B!41)) | (~member(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), intersection(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)))))))) | (~(member(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), image3(F!43, intersection(X!40, Y!39), B!41)) | (~member(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), B!41)) | ![X: $i] : ((~member(X, intersection(X!40, Y!39))) | (~apply(F!43, X, tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)))))))))) <=> ((~![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), image3(F!43, intersection(X!40, Y!39), B!41))) | (~((~member(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), B!41)) | (~member(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), intersection(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)))))))) | (~(member(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), image3(F!43, intersection(X!40, Y!39), B!41)) | ![X: $i] : ((~member(X, intersection(X!40, Y!39))) | (~apply(F!43, X, tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41))))) | (~member(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), B!41)))))))),
% 0.21/0.49 inference(monotonicity,[status(thm)],[76])).
% 0.21/0.49 tff(78,plain,
% 0.21/0.49 (((~![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), image3(F!43, intersection(X!40, Y!39), B!41))) | (~((~member(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), B!41)) | (~member(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), intersection(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)))))))) | (~(member(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), image3(F!43, intersection(X!40, Y!39), B!41)) | (~member(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), B!41)) | ![X: $i] : ((~member(X, intersection(X!40, Y!39))) | (~apply(F!43, X, tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)))))))))) <=> ((~![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), image3(F!43, intersection(X!40, Y!39), B!41))) | (~((~member(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), B!41)) | (~member(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), intersection(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)))))))) | (~(member(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), image3(F!43, intersection(X!40, Y!39), B!41)) | ![X: $i] : ((~member(X, intersection(X!40, Y!39))) | (~apply(F!43, X, tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41))))) | (~member(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), B!41)))))))),
% 0.21/0.49 inference(transitivity,[status(thm)],[77, 75])).
% 0.21/0.49 tff(79,plain,
% 0.21/0.49 ((~![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), image3(F!43, intersection(X!40, Y!39), B!41))) | (~((~member(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), B!41)) | (~member(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), intersection(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)))))))) | (~(member(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), image3(F!43, intersection(X!40, Y!39), B!41)) | (~member(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), B!41)) | ![X: $i] : ((~member(X, intersection(X!40, Y!39))) | (~apply(F!43, X, tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)))))))))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(80,plain,
% 0.21/0.49 ((~![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), image3(F!43, intersection(X!40, Y!39), B!41))) | (~((~member(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), B!41)) | (~member(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), intersection(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)))))))) | (~(member(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), image3(F!43, intersection(X!40, Y!39), B!41)) | ![X: $i] : ((~member(X, intersection(X!40, Y!39))) | (~apply(F!43, X, tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41))))) | (~member(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), B!41))))))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.21/0.49 tff(81,plain,
% 0.21/0.49 (~((~((~member(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), image3(F!43, intersection(X!40, Y!39), B!41))) | (~((~member(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), B!41)) | (~member(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), intersection(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)))))))) | (~(member(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), image3(F!43, intersection(X!40, Y!39), B!41)) | ![X: $i] : ((~member(X, intersection(X!40, Y!39))) | (~apply(F!43, X, tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41))))) | (~member(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), B!41)))))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[80, 16])).
% 0.21/0.49 tff(82,plain,
% 0.21/0.49 (((~((~member(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), image3(F!43, intersection(X!40, Y!39), B!41))) | (~((~member(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), B!41)) | (~member(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), intersection(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)))))))) | (~(member(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), image3(F!43, intersection(X!40, Y!39), B!41)) | ![X: $i] : ((~member(X, intersection(X!40, Y!39))) | (~apply(F!43, X, tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41))))) | (~member(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), B!41))))) | ((~member(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), image3(F!43, intersection(X!40, Y!39), B!41))) | (~((~member(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), B!41)) | (~member(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), intersection(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)))))))),
% 0.21/0.50 inference(tautology,[status(thm)],[])).
% 0.21/0.50 tff(83,plain,
% 0.21/0.50 ((~member(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), image3(F!43, intersection(X!40, Y!39), B!41))) | (~((~member(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), B!41)) | (~member(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), intersection(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41))))))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[82, 81])).
% 0.21/0.50 tff(84,assumption,(~((~member(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), image3(F!43, intersection(X!40, Y!39), B!41))) | member(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))))), introduced(assumption)).
% 0.21/0.50 tff(85,plain,
% 0.21/0.50 (((~member(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), image3(F!43, intersection(X!40, Y!39), B!41))) | member(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)))) | member(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), image3(F!43, intersection(X!40, Y!39), B!41))),
% 0.21/0.50 inference(tautology,[status(thm)],[])).
% 0.21/0.50 tff(86,plain,
% 0.21/0.50 (member(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), image3(F!43, intersection(X!40, Y!39), B!41))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[85, 84])).
% 0.21/0.50 tff(87,plain,
% 0.21/0.50 ((~((~member(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), image3(F!43, intersection(X!40, Y!39), B!41))) | (~((~member(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), B!41)) | (~member(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), intersection(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)))))))) | (~member(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), image3(F!43, intersection(X!40, Y!39), B!41))) | (~((~member(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), B!41)) | (~member(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), intersection(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41))))))),
% 0.21/0.50 inference(tautology,[status(thm)],[])).
% 0.21/0.50 tff(88,plain,
% 0.21/0.50 ((~((~member(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), image3(F!43, intersection(X!40, Y!39), B!41))) | (~((~member(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), B!41)) | (~member(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), intersection(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)))))))) | (~((~member(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), B!41)) | (~member(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), intersection(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41))))))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[87, 86])).
% 0.21/0.50 tff(89,plain,
% 0.21/0.50 (~((~member(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), B!41)) | (~member(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), intersection(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)))))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[88, 83])).
% 0.21/0.50 tff(90,plain,
% 0.21/0.50 (((~member(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), B!41)) | (~member(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), intersection(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41))))) | member(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), intersection(X!40, Y!39))),
% 0.21/0.50 inference(tautology,[status(thm)],[])).
% 0.21/0.50 tff(91,plain,
% 0.21/0.50 (member(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), intersection(X!40, Y!39))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[90, 89])).
% 0.21/0.50 tff(92,plain,
% 0.21/0.50 ((((~member(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), X!40)) | (~member(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), Y!39))) <=> member(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), intersection(X!40, Y!39))) | (~((~member(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), X!40)) | (~member(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), Y!39)))) | (~member(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), intersection(X!40, Y!39)))),
% 0.21/0.50 inference(tautology,[status(thm)],[])).
% 0.21/0.50 tff(93,plain,
% 0.21/0.50 ((((~member(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), X!40)) | (~member(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), Y!39))) <=> member(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), intersection(X!40, Y!39))) | (~((~member(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), X!40)) | (~member(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), Y!39))))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[92, 91])).
% 0.21/0.50 tff(94,plain,
% 0.21/0.50 (~((~member(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), X!40)) | (~member(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), Y!39)))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[93, 74])).
% 0.21/0.50 tff(95,plain,
% 0.21/0.50 (((~member(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), X!40)) | (~member(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), Y!39))) | member(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), Y!39)),
% 0.21/0.50 inference(tautology,[status(thm)],[])).
% 0.21/0.50 tff(96,plain,
% 0.21/0.50 (member(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), Y!39)),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[95, 94])).
% 0.21/0.50 tff(97,plain,
% 0.21/0.50 ((~![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, A!42)) | ![X: $i] : ((~member(X, Y!39)) | member(X, A!42)))) | (~(subset(Y!39, A!42) | (~((~member(tptp_fun_X_0(A!42, Y!39), Y!39)) | member(tptp_fun_X_0(A!42, Y!39), A!42)))))))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(98,plain,
% 0.21/0.50 (~((~((~subset(Y!39, A!42)) | ![X: $i] : ((~member(X, Y!39)) | member(X, A!42)))) | (~(subset(Y!39, A!42) | (~((~member(tptp_fun_X_0(A!42, Y!39), Y!39)) | member(tptp_fun_X_0(A!42, Y!39), A!42))))))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[97, 53])).
% 0.21/0.50 tff(99,plain,
% 0.21/0.50 (((~((~subset(Y!39, A!42)) | ![X: $i] : ((~member(X, Y!39)) | member(X, A!42)))) | (~(subset(Y!39, A!42) | (~((~member(tptp_fun_X_0(A!42, Y!39), Y!39)) | member(tptp_fun_X_0(A!42, Y!39), A!42)))))) | ((~subset(Y!39, A!42)) | ![X: $i] : ((~member(X, Y!39)) | member(X, A!42)))),
% 0.21/0.50 inference(tautology,[status(thm)],[])).
% 0.21/0.50 tff(100,plain,
% 0.21/0.50 ((~subset(Y!39, A!42)) | ![X: $i] : ((~member(X, Y!39)) | member(X, A!42))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[99, 98])).
% 0.21/0.50 tff(101,plain,
% 0.21/0.50 ((~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((~(maps(F, A, B) & injective(F, A, B) & subset(X, A) & subset(Y, A))) | equal_set(image3(F, intersection(X, Y), B), intersection(image3(F, X, B), image3(F, Y, B))))) <=> (~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((~(maps(F, A, B) & injective(F, A, B) & subset(X, A) & subset(Y, A))) | equal_set(image3(F, intersection(X, Y), B), intersection(image3(F, X, B), image3(F, Y, B)))))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(102,plain,
% 0.21/0.50 ((~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((((maps(F, A, B) & injective(F, A, B)) & subset(X, A)) & subset(Y, A)) => equal_set(image3(F, intersection(X, Y), B), intersection(image3(F, X, B), image3(F, Y, B))))) <=> (~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((~(maps(F, A, B) & injective(F, A, B) & subset(X, A) & subset(Y, A))) | equal_set(image3(F, intersection(X, Y), B), intersection(image3(F, X, B), image3(F, Y, B)))))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(103,axiom,(~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((((maps(F, A, B) & injective(F, A, B)) & subset(X, A)) & subset(Y, A)) => equal_set(image3(F, intersection(X, Y), B), intersection(image3(F, X, B), image3(F, Y, B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','thIIa11')).
% 0.21/0.50 tff(104,plain,
% 0.21/0.50 (~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((~(maps(F, A, B) & injective(F, A, B) & subset(X, A) & subset(Y, A))) | equal_set(image3(F, intersection(X, Y), B), intersection(image3(F, X, B), image3(F, Y, B))))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.21/0.50 tff(105,plain,
% 0.21/0.50 (~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((~(maps(F, A, B) & injective(F, A, B) & subset(X, A) & subset(Y, A))) | equal_set(image3(F, intersection(X, Y), B), intersection(image3(F, X, B), image3(F, Y, B))))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[104, 101])).
% 0.21/0.50 tff(106,plain,
% 0.21/0.50 (~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((~(maps(F, A, B) & injective(F, A, B) & subset(X, A) & subset(Y, A))) | equal_set(image3(F, intersection(X, Y), B), intersection(image3(F, X, B), image3(F, Y, B))))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[105, 101])).
% 0.21/0.50 tff(107,plain,
% 0.21/0.50 (~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((~(maps(F, A, B) & injective(F, A, B) & subset(X, A) & subset(Y, A))) | equal_set(image3(F, intersection(X, Y), B), intersection(image3(F, X, B), image3(F, Y, B))))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[106, 101])).
% 0.21/0.50 tff(108,plain,(
% 0.21/0.50 ~((~(maps(F!43, A!42, B!41) & injective(F!43, A!42, B!41) & subset(X!40, A!42) & subset(Y!39, A!42))) | equal_set(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))))),
% 0.21/0.50 inference(skolemize,[status(sab)],[107])).
% 0.21/0.50 tff(109,plain,
% 0.21/0.50 (maps(F!43, A!42, B!41) & injective(F!43, A!42, B!41) & subset(X!40, A!42) & subset(Y!39, A!42)),
% 0.21/0.50 inference(or_elim,[status(thm)],[108])).
% 0.21/0.50 tff(110,plain,
% 0.21/0.50 (subset(Y!39, A!42)),
% 0.21/0.50 inference(and_elim,[status(thm)],[109])).
% 0.21/0.50 tff(111,plain,
% 0.21/0.50 ((~((~subset(Y!39, A!42)) | ![X: $i] : ((~member(X, Y!39)) | member(X, A!42)))) | (~subset(Y!39, A!42)) | ![X: $i] : ((~member(X, Y!39)) | member(X, A!42))),
% 0.21/0.50 inference(tautology,[status(thm)],[])).
% 0.21/0.50 tff(112,plain,
% 0.21/0.50 ((~((~subset(Y!39, A!42)) | ![X: $i] : ((~member(X, Y!39)) | member(X, A!42)))) | ![X: $i] : ((~member(X, Y!39)) | member(X, A!42))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[111, 110])).
% 0.21/0.50 tff(113,plain,
% 0.21/0.50 (![X: $i] : ((~member(X, Y!39)) | member(X, A!42))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[112, 100])).
% 0.21/0.50 tff(114,plain,
% 0.21/0.50 (((~![X: $i] : ((~member(X, Y!39)) | member(X, A!42))) | ((~member(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), Y!39)) | member(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), A!42))) <=> ((~![X: $i] : ((~member(X, Y!39)) | member(X, A!42))) | (~member(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), Y!39)) | member(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), A!42))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(115,plain,
% 0.21/0.51 ((~![X: $i] : ((~member(X, Y!39)) | member(X, A!42))) | ((~member(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), Y!39)) | member(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), A!42))),
% 0.21/0.51 inference(quant_inst,[status(thm)],[])).
% 0.21/0.51 tff(116,plain,
% 0.21/0.51 ((~![X: $i] : ((~member(X, Y!39)) | member(X, A!42))) | (~member(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), Y!39)) | member(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), A!42)),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[115, 114])).
% 0.21/0.51 tff(117,plain,
% 0.21/0.51 (member(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), A!42)),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[116, 113, 96])).
% 0.21/0.51 tff(118,plain,
% 0.21/0.51 (^[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)))))))))))),
% 0.21/0.51 inference(bind,[status(th)],[])).
% 0.21/0.51 tff(119,plain,
% 0.21/0.51 (![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~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))))))))))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[118])).
% 0.21/0.51 tff(120,plain,
% 0.21/0.51 (^[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)))))))))),
% 0.21/0.51 inference(bind,[status(th)],[])).
% 0.21/0.51 tff(121,plain,
% 0.21/0.51 (![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~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))))))))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[120])).
% 0.21/0.51 tff(122,plain,
% 0.21/0.51 (^[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)))))))))),
% 0.21/0.51 inference(bind,[status(th)],[])).
% 0.21/0.51 tff(123,plain,
% 0.21/0.51 (![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~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))))))))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[122])).
% 0.21/0.51 tff(124,plain,
% 0.21/0.51 (![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~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))))))))),
% 0.21/0.51 inference(transitivity,[status(thm)],[123, 121])).
% 0.21/0.51 tff(125,plain,
% 0.21/0.51 (^[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))))))))))),
% 0.21/0.51 inference(bind,[status(th)],[])).
% 0.21/0.51 tff(126,plain,
% 0.21/0.51 (![F: $i, A: $i, B: $i] : (((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) & (maps(F, A, B) | (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))))))))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[125])).
% 0.21/0.51 tff(127,plain,
% 0.21/0.51 (^[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))))))))),
% 0.21/0.51 inference(bind,[status(th)],[])).
% 0.21/0.51 tff(128,plain,
% 0.21/0.51 (![F: $i, A: $i, B: $i] : (((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) & (maps(F, A, B) | ((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)))))))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[127])).
% 0.21/0.51 tff(129,plain,
% 0.21/0.51 (![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))))))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(130,plain,
% 0.21/0.51 (^[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)))))))),
% 0.21/0.51 inference(bind,[status(th)],[])).
% 0.21/0.51 tff(131,plain,
% 0.21/0.51 (![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))))))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[130])).
% 0.21/0.51 tff(132,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/sandbox/benchmark/Axioms/SET006+1.ax','maps')).
% 0.21/0.51 tff(133,plain,
% 0.21/0.51 (![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))))))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[132, 131])).
% 0.21/0.51 tff(134,plain,
% 0.21/0.51 (![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))))))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[133, 129])).
% 0.21/0.51 tff(135,plain,(
% 0.21/0.51 ![F: $i, A: $i, B: $i] : (((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) & (maps(F, A, B) | ((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))))))))),
% 0.21/0.51 inference(skolemize,[status(sab)],[134])).
% 0.21/0.51 tff(136,plain,
% 0.21/0.51 (![F: $i, A: $i, B: $i] : (((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) & (maps(F, A, B) | (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)))))))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[135, 128])).
% 0.21/0.51 tff(137,plain,
% 0.21/0.51 (![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~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))))))))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[136, 126])).
% 0.21/0.51 tff(138,plain,
% 0.21/0.51 (![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~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))))))))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[137, 124])).
% 0.21/0.52 tff(139,plain,
% 0.21/0.52 (![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))))))))))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[138, 119])).
% 0.21/0.52 tff(140,plain,
% 0.21/0.52 (((~![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)))))))))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(141,plain,
% 0.21/0.52 ((~((~((~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))))))))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(142,plain,
% 0.21/0.52 (((~![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)))))))))),
% 0.21/0.52 inference(monotonicity,[status(thm)],[141])).
% 0.21/0.52 tff(143,plain,
% 0.21/0.52 (((~![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)))))))))),
% 0.21/0.52 inference(transitivity,[status(thm)],[142, 140])).
% 0.21/0.52 tff(144,plain,
% 0.21/0.52 ((~![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))))))))))),
% 0.21/0.52 inference(quant_inst,[status(thm)],[])).
% 0.21/0.52 tff(145,plain,
% 0.21/0.52 ((~![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))))))))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[144, 143])).
% 0.21/0.52 tff(146,plain,
% 0.21/0.52 (~((~((~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)))))))),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[145, 139])).
% 0.21/0.52 tff(147,plain,
% 0.21/0.52 (((~((~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)))))))),
% 0.21/0.52 inference(tautology,[status(thm)],[])).
% 0.21/0.52 tff(148,plain,
% 0.21/0.52 ((~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))))))),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[147, 146])).
% 0.21/0.52 tff(149,plain,
% 0.21/0.52 (maps(F!43, A!42, B!41)),
% 0.21/0.52 inference(and_elim,[status(thm)],[109])).
% 0.21/0.52 tff(150,plain,
% 0.21/0.52 ((~((~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))))))),
% 0.21/0.52 inference(tautology,[status(thm)],[])).
% 0.21/0.52 tff(151,plain,
% 0.21/0.52 ((~((~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))))))),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[150, 149])).
% 0.21/0.53 tff(152,plain,
% 0.21/0.53 (~((~![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)))))),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[151, 148])).
% 0.21/0.53 tff(153,plain,
% 0.21/0.53 (((~![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))))))),
% 0.21/0.53 inference(tautology,[status(thm)],[])).
% 0.21/0.53 tff(154,plain,
% 0.21/0.53 (![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))))))),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[153, 152])).
% 0.21/0.53 tff(155,plain,
% 0.21/0.53 (((~![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))))))) | ((~member(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), A!42)) | (~((~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43), B!41)) | (~apply(F!43, tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43))))))) <=> ((~![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))))))) | (~member(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), A!42)) | (~((~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43), B!41)) | (~apply(F!43, tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43))))))),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(156,plain,
% 0.21/0.53 ((~![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))))))) | ((~member(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), A!42)) | (~((~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43), B!41)) | (~apply(F!43, tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43))))))),
% 0.21/0.53 inference(quant_inst,[status(thm)],[])).
% 0.21/0.53 tff(157,plain,
% 0.21/0.53 ((~![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))))))) | (~member(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), A!42)) | (~((~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43), B!41)) | (~apply(F!43, tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43)))))),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[156, 155])).
% 0.21/0.53 tff(158,plain,
% 0.21/0.53 (~((~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43), B!41)) | (~apply(F!43, tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43))))),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[157, 154, 117])).
% 0.21/0.53 tff(159,plain,
% 0.21/0.53 (((~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43), B!41)) | (~apply(F!43, tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43)))) | apply(F!43, tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43))),
% 0.21/0.53 inference(tautology,[status(thm)],[])).
% 0.21/0.53 tff(160,plain,
% 0.21/0.53 (apply(F!43, tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43))),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[159, 158])).
% 0.21/0.53 tff(161,plain,
% 0.21/0.53 (((~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43), B!41)) | (~apply(F!43, tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43)))) | member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43), B!41)),
% 0.21/0.53 inference(tautology,[status(thm)],[])).
% 0.21/0.53 tff(162,plain,
% 0.21/0.53 (member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43), B!41)),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[161, 158])).
% 0.21/0.53 tff(163,plain,
% 0.21/0.53 (((~member(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), B!41)) | (~member(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), intersection(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41))))) | apply(F!43, tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)))),
% 0.21/0.53 inference(tautology,[status(thm)],[])).
% 0.21/0.53 tff(164,plain,
% 0.21/0.53 (apply(F!43, tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)))),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[163, 89])).
% 0.21/0.53 tff(165,plain,
% 0.21/0.53 (((~member(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), B!41)) | (~member(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), intersection(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41))))) | member(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), B!41)),
% 0.21/0.53 inference(tautology,[status(thm)],[])).
% 0.21/0.53 tff(166,plain,
% 0.21/0.53 (member(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), B!41)),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[165, 89])).
% 0.21/0.53 tff(167,plain,
% 0.21/0.53 (((~![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)))),
% 0.21/0.53 inference(tautology,[status(thm)],[])).
% 0.21/0.53 tff(168,plain,
% 0.21/0.53 (![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)))),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[167, 152])).
% 0.21/0.53 tff(169,plain,
% 0.21/0.53 (((~![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(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), B!41)) | (~apply(F!43, tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)))) | (~member(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), A!42)) | (~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43), B!41)) | (~apply(F!43, tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43))) | (tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)) = tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), 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)))) | (~member(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), B!41)) | (~apply(F!43, tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)))) | (~member(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), A!42)) | (~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43), B!41)) | (~apply(F!43, tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43))) | (tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)) = tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43)))),
% 0.21/0.54 inference(rewrite,[status(thm)],[])).
% 0.21/0.54 tff(170,plain,
% 0.21/0.54 (((tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)) = tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43)) | (~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43), B!41)) | (~apply(F!43, tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)))) | (~apply(F!43, tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43))) | (~member(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), A!42)) | (~member(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), B!41))) <=> ((~member(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), B!41)) | (~apply(F!43, tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)))) | (~member(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), A!42)) | (~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43), B!41)) | (~apply(F!43, tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43))) | (tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)) = tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43)))),
% 0.21/0.54 inference(rewrite,[status(thm)],[])).
% 0.21/0.54 tff(171,plain,
% 0.21/0.54 (((~![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_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)) = tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43)) | (~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43), B!41)) | (~apply(F!43, tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)))) | (~apply(F!43, tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43))) | (~member(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), A!42)) | (~member(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), 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(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), B!41)) | (~apply(F!43, tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)))) | (~member(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), A!42)) | (~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43), B!41)) | (~apply(F!43, tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43))) | (tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)) = tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43))))),
% 0.21/0.54 inference(monotonicity,[status(thm)],[170])).
% 0.21/0.54 tff(172,plain,
% 0.21/0.54 (((~![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_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)) = tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43)) | (~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43), B!41)) | (~apply(F!43, tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)))) | (~apply(F!43, tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43))) | (~member(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), A!42)) | (~member(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), 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(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), B!41)) | (~apply(F!43, tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)))) | (~member(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), A!42)) | (~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43), B!41)) | (~apply(F!43, tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43))) | (tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)) = tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43)))),
% 0.21/0.54 inference(transitivity,[status(thm)],[171, 169])).
% 0.21/0.54 tff(173,plain,
% 0.21/0.54 ((~![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_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)) = tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43)) | (~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43), B!41)) | (~apply(F!43, tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)))) | (~apply(F!43, tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43))) | (~member(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), A!42)) | (~member(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), B!41)))),
% 0.21/0.54 inference(quant_inst,[status(thm)],[])).
% 0.21/0.54 tff(174,plain,
% 0.21/0.54 ((~![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(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), B!41)) | (~apply(F!43, tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)))) | (~member(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), A!42)) | (~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43), B!41)) | (~apply(F!43, tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43))) | (tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)) = tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43))),
% 0.21/0.55 inference(modus_ponens,[status(thm)],[173, 172])).
% 0.21/0.55 tff(175,plain,
% 0.21/0.55 (tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)) = tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43)),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[174, 168, 166, 164, 117, 162, 160])).
% 0.21/0.55 tff(176,plain,
% 0.21/0.55 (tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43) = tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41))),
% 0.21/0.55 inference(symmetry,[status(thm)],[175])).
% 0.21/0.55 tff(177,plain,
% 0.21/0.55 (member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43), image3(F!43, Y!39, B!41)) <=> member(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), image3(F!43, Y!39, B!41))),
% 0.21/0.55 inference(monotonicity,[status(thm)],[176])).
% 0.21/0.55 tff(178,plain,
% 0.21/0.55 (member(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), image3(F!43, Y!39, B!41)) <=> member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43), image3(F!43, Y!39, B!41))),
% 0.21/0.55 inference(symmetry,[status(thm)],[177])).
% 0.21/0.55 tff(179,plain,
% 0.21/0.55 ((~member(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), image3(F!43, Y!39, B!41))) <=> (~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43), image3(F!43, Y!39, B!41)))),
% 0.21/0.55 inference(monotonicity,[status(thm)],[178])).
% 0.21/0.55 tff(180,plain,
% 0.21/0.55 ((~![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))) | (~(((~member(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), image3(F!43, X!40, B!41))) | (~member(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), image3(F!43, Y!39, B!41)))) <=> member(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)))))),
% 0.21/0.55 inference(quant_inst,[status(thm)],[])).
% 0.21/0.55 tff(181,plain,
% 0.21/0.55 (~(((~member(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), image3(F!43, X!40, B!41))) | (~member(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), image3(F!43, Y!39, B!41)))) <=> member(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))))),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[180, 35])).
% 0.21/0.55 tff(182,plain,
% 0.21/0.55 (((~member(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), image3(F!43, intersection(X!40, Y!39), B!41))) | member(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)))) | (~member(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))))),
% 0.21/0.55 inference(tautology,[status(thm)],[])).
% 0.21/0.55 tff(183,plain,
% 0.21/0.55 (~member(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)))),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[182, 84])).
% 0.21/0.55 tff(184,plain,
% 0.21/0.55 ((((~member(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), image3(F!43, X!40, B!41))) | (~member(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), image3(F!43, Y!39, B!41)))) <=> member(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)))) | ((~member(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), image3(F!43, X!40, B!41))) | (~member(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), image3(F!43, Y!39, B!41)))) | member(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)))),
% 0.21/0.55 inference(tautology,[status(thm)],[])).
% 0.21/0.55 tff(185,plain,
% 0.21/0.55 ((((~member(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), image3(F!43, X!40, B!41))) | (~member(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), image3(F!43, Y!39, B!41)))) <=> member(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)))) | ((~member(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), image3(F!43, X!40, B!41))) | (~member(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), image3(F!43, Y!39, B!41))))),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[184, 183])).
% 0.21/0.55 tff(186,plain,
% 0.21/0.55 ((~member(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), image3(F!43, X!40, B!41))) | (~member(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), image3(F!43, Y!39, B!41)))),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[185, 181])).
% 0.21/0.55 tff(187,plain,
% 0.21/0.55 (((~member(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), X!40)) | (~member(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), Y!39))) | member(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), X!40)),
% 0.21/0.55 inference(tautology,[status(thm)],[])).
% 0.21/0.55 tff(188,plain,
% 0.21/0.55 (member(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), X!40)),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[187, 94])).
% 0.21/0.55 tff(189,assumption,(![X: $i] : ((~member(X, X!40)) | (~apply(F!43, X, tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43))))), introduced(assumption)).
% 0.21/0.55 tff(190,assumption,(apply(F!43, tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43))), introduced(assumption)).
% 0.21/0.55 tff(191,assumption,(member(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), X!40)), introduced(assumption)).
% 0.21/0.55 tff(192,plain,
% 0.21/0.55 (((~![X: $i] : ((~member(X, X!40)) | (~apply(F!43, X, tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43))))) | ((~member(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), X!40)) | (~apply(F!43, tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43))))) <=> ((~![X: $i] : ((~member(X, X!40)) | (~apply(F!43, X, tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43))))) | (~member(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), X!40)) | (~apply(F!43, tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43))))),
% 0.21/0.55 inference(rewrite,[status(thm)],[])).
% 0.21/0.55 tff(193,plain,
% 0.21/0.55 ((~![X: $i] : ((~member(X, X!40)) | (~apply(F!43, X, tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43))))) | ((~member(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), X!40)) | (~apply(F!43, tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43))))),
% 0.21/0.55 inference(quant_inst,[status(thm)],[])).
% 0.21/0.55 tff(194,plain,
% 0.21/0.56 ((~![X: $i] : ((~member(X, X!40)) | (~apply(F!43, X, tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43))))) | (~member(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), X!40)) | (~apply(F!43, tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43)))),
% 0.21/0.56 inference(modus_ponens,[status(thm)],[193, 192])).
% 0.21/0.56 tff(195,plain,
% 0.21/0.56 ($false),
% 0.21/0.56 inference(unit_resolution,[status(thm)],[194, 191, 190, 189])).
% 0.21/0.56 tff(196,plain,((~![X: $i] : ((~member(X, X!40)) | (~apply(F!43, X, tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43))))) | (~member(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), X!40)) | (~apply(F!43, tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43)))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.56 tff(197,plain,
% 0.21/0.56 (~![X: $i] : ((~member(X, X!40)) | (~apply(F!43, X, tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43))))),
% 0.21/0.56 inference(unit_resolution,[status(thm)],[196, 188, 160])).
% 0.21/0.56 tff(198,assumption,(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)) = tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43)), introduced(assumption)).
% 0.21/0.56 tff(199,plain,
% 0.21/0.56 (tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43) = tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41))),
% 0.21/0.56 inference(symmetry,[status(thm)],[198])).
% 0.21/0.56 tff(200,plain,
% 0.21/0.56 (member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43), image3(F!43, X!40, B!41)) <=> member(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), image3(F!43, X!40, B!41))),
% 0.21/0.56 inference(monotonicity,[status(thm)],[199])).
% 0.21/0.56 tff(201,plain,
% 0.21/0.56 (member(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), image3(F!43, X!40, B!41)) <=> member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43), image3(F!43, X!40, B!41))),
% 0.21/0.56 inference(symmetry,[status(thm)],[200])).
% 0.21/0.56 tff(202,plain,
% 0.21/0.56 ((~member(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), image3(F!43, X!40, B!41))) <=> (~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43), image3(F!43, X!40, B!41)))),
% 0.21/0.56 inference(monotonicity,[status(thm)],[201])).
% 0.21/0.56 tff(203,assumption,(~member(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), image3(F!43, X!40, B!41))), introduced(assumption)).
% 0.21/0.56 tff(204,plain,
% 0.21/0.56 (~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43), image3(F!43, X!40, B!41))),
% 0.21/0.56 inference(modus_ponens,[status(thm)],[203, 202])).
% 0.21/0.56 tff(205,plain,
% 0.21/0.56 (((~![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43), image3(F!43, X!40, B!41))) | (~((~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43), B!41)) | (~member(tptp_fun_X_24(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_24(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43), X!40, F!43), tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43))))))) | (~((~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43), B!41)) | ![X: $i] : ((~member(X, X!40)) | (~apply(F!43, X, tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43)))) | member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43), image3(F!43, X!40, B!41))))))) <=> ((~![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43), image3(F!43, X!40, B!41))) | (~((~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43), B!41)) | (~member(tptp_fun_X_24(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_24(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43), X!40, F!43), tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43))))))) | (~((~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43), B!41)) | ![X: $i] : ((~member(X, X!40)) | (~apply(F!43, X, tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43)))) | member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43), image3(F!43, X!40, B!41)))))))),
% 0.21/0.56 inference(rewrite,[status(thm)],[])).
% 0.21/0.56 tff(206,plain,
% 0.21/0.56 ((~((~((~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43), image3(F!43, X!40, B!41))) | (~((~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43), B!41)) | (~member(tptp_fun_X_24(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_24(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43), X!40, F!43), tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43))))))) | (~(member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43), image3(F!43, X!40, B!41)) | (~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43), B!41)) | ![X: $i] : ((~member(X, X!40)) | (~apply(F!43, X, tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43)))))))) <=> (~((~((~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43), image3(F!43, X!40, B!41))) | (~((~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43), B!41)) | (~member(tptp_fun_X_24(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_24(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43), X!40, F!43), tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43))))))) | (~((~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43), B!41)) | ![X: $i] : ((~member(X, X!40)) | (~apply(F!43, X, tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43)))) | member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43), image3(F!43, X!40, B!41))))))),
% 0.21/0.56 inference(rewrite,[status(thm)],[])).
% 0.21/0.56 tff(207,plain,
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% 0.21/0.57 inference(monotonicity,[status(thm)],[206])).
% 0.21/0.57 tff(208,plain,
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% 0.21/0.57 inference(transitivity,[status(thm)],[207, 205])).
% 0.21/0.57 tff(209,plain,
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% 0.21/0.57 inference(quant_inst,[status(thm)],[])).
% 0.21/0.57 tff(210,plain,
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% 0.21/0.57 inference(modus_ponens,[status(thm)],[209, 208])).
% 0.21/0.57 tff(211,plain,
% 0.21/0.57 (~((~((~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43), image3(F!43, X!40, B!41))) | (~((~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43), B!41)) | (~member(tptp_fun_X_24(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_24(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43), X!40, F!43), tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43))))))) | (~((~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43), B!41)) | ![X: $i] : ((~member(X, X!40)) | (~apply(F!43, X, tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43)))) | member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43), image3(F!43, X!40, B!41)))))),
% 0.21/0.57 inference(unit_resolution,[status(thm)],[210, 16])).
% 0.21/0.57 tff(212,plain,
% 0.21/0.57 (((~((~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43), image3(F!43, X!40, B!41))) | (~((~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43), B!41)) | (~member(tptp_fun_X_24(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_24(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43), X!40, F!43), tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43))))))) | (~((~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43), B!41)) | ![X: $i] : ((~member(X, X!40)) | (~apply(F!43, X, tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43)))) | member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43), image3(F!43, X!40, B!41))))) | ((~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43), B!41)) | ![X: $i] : ((~member(X, X!40)) | (~apply(F!43, X, tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43)))) | member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43), image3(F!43, X!40, B!41)))),
% 0.21/0.57 inference(tautology,[status(thm)],[])).
% 0.21/0.57 tff(213,plain,
% 0.21/0.57 ((~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43), B!41)) | ![X: $i] : ((~member(X, X!40)) | (~apply(F!43, X, tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43)))) | member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43), image3(F!43, X!40, B!41))),
% 0.21/0.57 inference(unit_resolution,[status(thm)],[212, 211])).
% 0.21/0.57 tff(214,assumption,(~![X: $i] : ((~member(X, X!40)) | (~apply(F!43, X, tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43))))), introduced(assumption)).
% 0.21/0.57 tff(215,assumption,(member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43), B!41)), introduced(assumption)).
% 0.21/0.57 tff(216,plain,
% 0.21/0.57 ((~((~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43), B!41)) | ![X: $i] : ((~member(X, X!40)) | (~apply(F!43, X, tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43)))) | member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43), image3(F!43, X!40, B!41)))) | (~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43), B!41)) | ![X: $i] : ((~member(X, X!40)) | (~apply(F!43, X, tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43)))) | member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43), image3(F!43, X!40, B!41))),
% 0.21/0.58 inference(tautology,[status(thm)],[])).
% 0.21/0.58 tff(217,plain,
% 0.21/0.58 ((~((~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43), B!41)) | ![X: $i] : ((~member(X, X!40)) | (~apply(F!43, X, tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43)))) | member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43), image3(F!43, X!40, B!41)))) | member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43), image3(F!43, X!40, B!41))),
% 0.21/0.58 inference(unit_resolution,[status(thm)],[216, 215, 214])).
% 0.21/0.58 tff(218,plain,
% 0.21/0.58 (member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43), image3(F!43, X!40, B!41))),
% 0.21/0.58 inference(unit_resolution,[status(thm)],[217, 213])).
% 0.21/0.58 tff(219,plain,
% 0.21/0.58 ($false),
% 0.21/0.58 inference(unit_resolution,[status(thm)],[218, 204])).
% 0.21/0.58 tff(220,plain,(member(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), image3(F!43, X!40, B!41)) | (~(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)) = tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43))) | (~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43), B!41)) | ![X: $i] : ((~member(X, X!40)) | (~apply(F!43, X, tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43))))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.58 tff(221,plain,
% 0.21/0.58 (member(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), image3(F!43, X!40, B!41))),
% 0.21/0.58 inference(unit_resolution,[status(thm)],[220, 175, 162, 197])).
% 0.21/0.58 tff(222,plain,
% 0.21/0.58 ((~((~member(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), image3(F!43, X!40, B!41))) | (~member(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), image3(F!43, Y!39, B!41))))) | (~member(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), image3(F!43, X!40, B!41))) | (~member(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), image3(F!43, Y!39, B!41)))),
% 0.21/0.58 inference(tautology,[status(thm)],[])).
% 0.21/0.58 tff(223,plain,
% 0.21/0.58 (~member(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), image3(F!43, Y!39, B!41))),
% 0.21/0.58 inference(unit_resolution,[status(thm)],[222, 221, 186])).
% 0.21/0.58 tff(224,plain,
% 0.21/0.58 (~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43), image3(F!43, Y!39, B!41))),
% 0.21/0.58 inference(modus_ponens,[status(thm)],[223, 179])).
% 0.21/0.58 tff(225,plain,
% 0.21/0.58 ((~((~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43), B!41)) | ![X: $i] : ((~member(X, Y!39)) | (~apply(F!43, X, tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43)))) | member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43), image3(F!43, Y!39, B!41)))) | (~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43), B!41)) | ![X: $i] : ((~member(X, Y!39)) | (~apply(F!43, X, tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43)))) | member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43), image3(F!43, Y!39, B!41))),
% 0.21/0.58 inference(tautology,[status(thm)],[])).
% 0.21/0.58 tff(226,plain,
% 0.21/0.58 ((~((~member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43), B!41)) | ![X: $i] : ((~member(X, Y!39)) | (~apply(F!43, X, tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43)))) | member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43), image3(F!43, Y!39, B!41)))) | ![X: $i] : ((~member(X, Y!39)) | (~apply(F!43, X, tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43)))) | member(tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43), image3(F!43, Y!39, B!41))),
% 0.21/0.58 inference(unit_resolution,[status(thm)],[225, 162])).
% 0.21/0.58 tff(227,plain,
% 0.21/0.58 (![X: $i] : ((~member(X, Y!39)) | (~apply(F!43, X, tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43))))),
% 0.21/0.58 inference(unit_resolution,[status(thm)],[226, 224, 72])).
% 0.21/0.58 tff(228,plain,
% 0.21/0.58 (((~![X: $i] : ((~member(X, Y!39)) | (~apply(F!43, X, tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43))))) | ((~member(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), Y!39)) | (~apply(F!43, tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43))))) <=> ((~![X: $i] : ((~member(X, Y!39)) | (~apply(F!43, X, tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43))))) | (~member(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), Y!39)) | (~apply(F!43, tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43))))),
% 0.21/0.58 inference(rewrite,[status(thm)],[])).
% 0.21/0.58 tff(229,plain,
% 0.21/0.58 ((~![X: $i] : ((~member(X, Y!39)) | (~apply(F!43, X, tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43))))) | ((~member(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), Y!39)) | (~apply(F!43, tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43))))),
% 0.21/0.58 inference(quant_inst,[status(thm)],[])).
% 0.21/0.58 tff(230,plain,
% 0.21/0.58 ((~![X: $i] : ((~member(X, Y!39)) | (~apply(F!43, X, tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43))))) | (~member(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), Y!39)) | (~apply(F!43, tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), tptp_fun_Y_3(tptp_fun_X_24(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(X!40, Y!39), F!43), B!41, F!43)))),
% 0.21/0.58 inference(modus_ponens,[status(thm)],[229, 228])).
% 0.21/0.58 tff(231,plain,
% 0.21/0.58 ($false),
% 0.21/0.58 inference(unit_resolution,[status(thm)],[230, 96, 160, 227])).
% 0.21/0.58 tff(232,plain,((~member(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), image3(F!43, intersection(X!40, Y!39), B!41))) | member(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.58 tff(233,plain,
% 0.21/0.58 ((~(subset(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))) | (~((~member(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), image3(F!43, intersection(X!40, Y!39), B!41))) | member(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))))))) | subset(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))) | (~((~member(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), image3(F!43, intersection(X!40, Y!39), B!41))) | member(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)))))),
% 0.21/0.58 inference(tautology,[status(thm)],[])).
% 0.21/0.58 tff(234,plain,
% 0.21/0.58 ((~(subset(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))) | (~((~member(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), image3(F!43, intersection(X!40, Y!39), B!41))) | member(tptp_fun_X_0(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))))))) | subset(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)))),
% 0.21/0.58 inference(unit_resolution,[status(thm)],[233, 232])).
% 0.21/0.58 tff(235,plain,
% 0.21/0.58 (subset(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)))),
% 0.21/0.58 inference(unit_resolution,[status(thm)],[234, 63])).
% 0.21/0.58 tff(236,plain,
% 0.21/0.58 (^[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))))),
% 0.21/0.58 inference(bind,[status(th)],[])).
% 0.21/0.58 tff(237,plain,
% 0.21/0.58 (![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)))),
% 0.21/0.58 inference(quant_intro,[status(thm)],[236])).
% 0.21/0.58 tff(238,plain,
% 0.21/0.58 (^[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)))))),
% 0.21/0.58 inference(bind,[status(th)],[])).
% 0.21/0.58 tff(239,plain,
% 0.21/0.58 (![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)))),
% 0.21/0.58 inference(quant_intro,[status(thm)],[238])).
% 0.21/0.58 tff(240,plain,
% 0.21/0.58 (![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)))),
% 0.21/0.58 inference(rewrite,[status(thm)],[])).
% 0.21/0.58 tff(241,axiom,(![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax','equal_set')).
% 0.21/0.58 tff(242,plain,
% 0.21/0.58 (![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 0.21/0.58 inference(modus_ponens,[status(thm)],[241, 240])).
% 0.21/0.58 tff(243,plain,(
% 0.21/0.58 ![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 0.21/0.58 inference(skolemize,[status(sab)],[242])).
% 0.21/0.58 tff(244,plain,
% 0.21/0.58 (![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))),
% 0.21/0.58 inference(modus_ponens,[status(thm)],[243, 239])).
% 0.21/0.58 tff(245,plain,
% 0.21/0.58 (![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))),
% 0.21/0.59 inference(modus_ponens,[status(thm)],[244, 237])).
% 0.21/0.59 tff(246,plain,
% 0.21/0.59 ((~![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))) | (~(((~subset(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)))) | (~subset(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)))) <=> equal_set(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)))))),
% 0.21/0.59 inference(quant_inst,[status(thm)],[])).
% 0.21/0.59 tff(247,plain,
% 0.21/0.59 (~(((~subset(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)))) | (~subset(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)))) <=> equal_set(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))))),
% 0.21/0.59 inference(unit_resolution,[status(thm)],[246, 245])).
% 0.21/0.59 tff(248,plain,
% 0.21/0.59 (~equal_set(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)))),
% 0.21/0.59 inference(or_elim,[status(thm)],[108])).
% 0.21/0.59 tff(249,plain,
% 0.21/0.59 ((((~subset(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)))) | (~subset(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)))) <=> equal_set(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)))) | ((~subset(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)))) | (~subset(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)))) | equal_set(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)))),
% 0.21/0.59 inference(tautology,[status(thm)],[])).
% 0.21/0.59 tff(250,plain,
% 0.21/0.59 ((((~subset(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)))) | (~subset(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)))) <=> equal_set(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)))) | ((~subset(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)))) | (~subset(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41))))),
% 0.21/0.59 inference(unit_resolution,[status(thm)],[249, 248])).
% 0.21/0.59 tff(251,plain,
% 0.21/0.59 ((~subset(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)))) | (~subset(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)))),
% 0.21/0.59 inference(unit_resolution,[status(thm)],[250, 247])).
% 0.21/0.59 tff(252,plain,
% 0.21/0.59 ((~((~subset(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)))) | (~subset(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41))))) | (~subset(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)))) | (~subset(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)))),
% 0.21/0.59 inference(tautology,[status(thm)],[])).
% 0.21/0.59 tff(253,plain,
% 0.21/0.59 ((~subset(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)))) | (~subset(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)))),
% 0.21/0.59 inference(unit_resolution,[status(thm)],[252, 251])).
% 0.21/0.59 tff(254,plain,
% 0.21/0.59 (~subset(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41))),
% 0.21/0.59 inference(unit_resolution,[status(thm)],[253, 235])).
% 0.21/0.59 tff(255,plain,
% 0.21/0.59 ((~(subset(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)) | (~((~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)))) | member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), image3(F!43, intersection(X!40, Y!39), B!41)))))) | subset(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)) | (~((~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)))) | member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), image3(F!43, intersection(X!40, Y!39), B!41))))),
% 0.21/0.59 inference(tautology,[status(thm)],[])).
% 0.21/0.59 tff(256,plain,
% 0.21/0.59 ((~(subset(intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)), image3(F!43, intersection(X!40, Y!39), B!41)) | (~((~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)))) | member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), image3(F!43, intersection(X!40, Y!39), B!41)))))) | (~((~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)))) | member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), image3(F!43, intersection(X!40, Y!39), B!41))))),
% 0.21/0.59 inference(unit_resolution,[status(thm)],[255, 254])).
% 0.21/0.59 tff(257,plain,
% 0.21/0.59 (~((~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)))) | member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), image3(F!43, intersection(X!40, Y!39), B!41)))),
% 0.21/0.59 inference(unit_resolution,[status(thm)],[256, 57])).
% 0.21/0.59 tff(258,plain,
% 0.21/0.59 (((~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)))) | member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), image3(F!43, intersection(X!40, Y!39), B!41))) | member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)))),
% 0.21/0.59 inference(tautology,[status(thm)],[])).
% 0.21/0.59 tff(259,plain,
% 0.21/0.59 (member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)))),
% 0.21/0.59 inference(unit_resolution,[status(thm)],[258, 257])).
% 0.21/0.59 tff(260,plain,
% 0.21/0.59 ((((~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), image3(F!43, X!40, B!41))) | (~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), image3(F!43, Y!39, B!41)))) <=> member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)))) | (~((~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), image3(F!43, X!40, B!41))) | (~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), image3(F!43, Y!39, B!41))))) | (~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))))),
% 0.21/0.59 inference(tautology,[status(thm)],[])).
% 0.21/0.59 tff(261,plain,
% 0.21/0.59 ((((~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), image3(F!43, X!40, B!41))) | (~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), image3(F!43, Y!39, B!41)))) <=> member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)))) | (~((~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), image3(F!43, X!40, B!41))) | (~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), image3(F!43, Y!39, B!41)))))),
% 0.21/0.59 inference(unit_resolution,[status(thm)],[260, 259])).
% 0.21/0.59 tff(262,plain,
% 0.21/0.59 (~((~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), image3(F!43, X!40, B!41))) | (~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), image3(F!43, Y!39, B!41))))),
% 0.21/0.59 inference(unit_resolution,[status(thm)],[261, 37])).
% 0.21/0.59 tff(263,plain,
% 0.21/0.59 (((~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), image3(F!43, X!40, B!41))) | (~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), image3(F!43, Y!39, B!41)))) | member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), image3(F!43, X!40, B!41))),
% 0.21/0.59 inference(tautology,[status(thm)],[])).
% 0.21/0.59 tff(264,plain,
% 0.21/0.59 (member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), image3(F!43, X!40, B!41))),
% 0.21/0.59 inference(unit_resolution,[status(thm)],[263, 262])).
% 0.21/0.59 tff(265,plain,
% 0.21/0.59 ((~((~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), image3(F!43, X!40, B!41))) | (~((~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), B!41)) | (~member(tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), X!40, F!43), tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))))))))) | (~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), image3(F!43, X!40, B!41))) | (~((~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), B!41)) | (~member(tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), X!40, F!43), tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)))))))),
% 0.21/0.60 inference(tautology,[status(thm)],[])).
% 0.21/0.60 tff(266,plain,
% 0.21/0.60 ((~((~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), image3(F!43, X!40, B!41))) | (~((~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), B!41)) | (~member(tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), X!40, F!43), tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))))))))) | (~((~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), B!41)) | (~member(tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), X!40, F!43), tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)))))))),
% 0.21/0.60 inference(unit_resolution,[status(thm)],[265, 264])).
% 0.21/0.60 tff(267,plain,
% 0.21/0.60 (~((~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), B!41)) | (~member(tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), X!40, F!43), tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))))))),
% 0.21/0.60 inference(unit_resolution,[status(thm)],[266, 25])).
% 0.21/0.60 tff(268,plain,
% 0.21/0.60 (((~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), B!41)) | (~member(tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), X!40, F!43), tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)))))) | member(tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), X!40, F!43), X!40)),
% 0.21/0.60 inference(tautology,[status(thm)],[])).
% 0.21/0.60 tff(269,plain,
% 0.21/0.60 (member(tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), X!40, F!43), X!40)),
% 0.21/0.60 inference(unit_resolution,[status(thm)],[268, 267])).
% 0.21/0.60 tff(270,plain,
% 0.21/0.60 ((~![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, A!42)) | ![X: $i] : ((~member(X, X!40)) | member(X, A!42)))) | (~(subset(X!40, A!42) | (~((~member(tptp_fun_X_0(A!42, X!40), X!40)) | member(tptp_fun_X_0(A!42, X!40), A!42)))))))),
% 0.21/0.60 inference(quant_inst,[status(thm)],[])).
% 0.21/0.60 tff(271,plain,
% 0.21/0.60 (~((~((~subset(X!40, A!42)) | ![X: $i] : ((~member(X, X!40)) | member(X, A!42)))) | (~(subset(X!40, A!42) | (~((~member(tptp_fun_X_0(A!42, X!40), X!40)) | member(tptp_fun_X_0(A!42, X!40), A!42))))))),
% 0.43/0.60 inference(unit_resolution,[status(thm)],[270, 53])).
% 0.43/0.60 tff(272,plain,
% 0.43/0.60 (((~((~subset(X!40, A!42)) | ![X: $i] : ((~member(X, X!40)) | member(X, A!42)))) | (~(subset(X!40, A!42) | (~((~member(tptp_fun_X_0(A!42, X!40), X!40)) | member(tptp_fun_X_0(A!42, X!40), A!42)))))) | ((~subset(X!40, A!42)) | ![X: $i] : ((~member(X, X!40)) | member(X, A!42)))),
% 0.43/0.60 inference(tautology,[status(thm)],[])).
% 0.43/0.60 tff(273,plain,
% 0.43/0.60 ((~subset(X!40, A!42)) | ![X: $i] : ((~member(X, X!40)) | member(X, A!42))),
% 0.43/0.60 inference(unit_resolution,[status(thm)],[272, 271])).
% 0.43/0.60 tff(274,plain,
% 0.43/0.60 (subset(X!40, A!42)),
% 0.43/0.60 inference(and_elim,[status(thm)],[109])).
% 0.43/0.60 tff(275,plain,
% 0.43/0.60 ((~((~subset(X!40, A!42)) | ![X: $i] : ((~member(X, X!40)) | member(X, A!42)))) | (~subset(X!40, A!42)) | ![X: $i] : ((~member(X, X!40)) | member(X, A!42))),
% 0.43/0.60 inference(tautology,[status(thm)],[])).
% 0.43/0.60 tff(276,plain,
% 0.43/0.60 ((~((~subset(X!40, A!42)) | ![X: $i] : ((~member(X, X!40)) | member(X, A!42)))) | ![X: $i] : ((~member(X, X!40)) | member(X, A!42))),
% 0.43/0.60 inference(unit_resolution,[status(thm)],[275, 274])).
% 0.43/0.60 tff(277,plain,
% 0.43/0.60 (![X: $i] : ((~member(X, X!40)) | member(X, A!42))),
% 0.43/0.60 inference(unit_resolution,[status(thm)],[276, 273])).
% 0.43/0.60 tff(278,plain,
% 0.43/0.60 (((~![X: $i] : ((~member(X, X!40)) | member(X, A!42))) | ((~member(tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), X!40, F!43), X!40)) | member(tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), X!40, F!43), A!42))) <=> ((~![X: $i] : ((~member(X, X!40)) | member(X, A!42))) | (~member(tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), X!40, F!43), X!40)) | member(tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), X!40, F!43), A!42))),
% 0.43/0.60 inference(rewrite,[status(thm)],[])).
% 0.43/0.60 tff(279,plain,
% 0.43/0.60 ((~![X: $i] : ((~member(X, X!40)) | member(X, A!42))) | ((~member(tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), X!40, F!43), X!40)) | member(tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), X!40, F!43), A!42))),
% 0.43/0.60 inference(quant_inst,[status(thm)],[])).
% 0.43/0.60 tff(280,plain,
% 0.43/0.60 ((~![X: $i] : ((~member(X, X!40)) | member(X, A!42))) | (~member(tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), X!40, F!43), X!40)) | member(tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), X!40, F!43), A!42)),
% 0.43/0.60 inference(modus_ponens,[status(thm)],[279, 278])).
% 0.43/0.60 tff(281,plain,
% 0.43/0.60 (member(tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), X!40, F!43), A!42)),
% 0.43/0.60 inference(unit_resolution,[status(thm)],[280, 277, 269])).
% 0.43/0.60 tff(282,plain,
% 0.43/0.60 (((~![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), image3(F!43, Y!39, B!41))) | (~((~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), B!41)) | (~member(tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), Y!39, F!43), tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))))))))) | (~((~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), B!41)) | ![X: $i] : ((~member(X, Y!39)) | (~apply(F!43, X, tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)))))) | member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), image3(F!43, Y!39, B!41))))))) <=> ((~![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), image3(F!43, Y!39, B!41))) | (~((~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), B!41)) | (~member(tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), Y!39, F!43), tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))))))))) | (~((~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), B!41)) | ![X: $i] : ((~member(X, Y!39)) | (~apply(F!43, X, tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)))))) | member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), image3(F!43, Y!39, B!41)))))))),
% 0.43/0.60 inference(rewrite,[status(thm)],[])).
% 0.43/0.60 tff(283,plain,
% 0.43/0.60 ((~((~((~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), image3(F!43, Y!39, B!41))) | (~((~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), B!41)) | (~member(tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), Y!39, F!43), tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))))))))) | (~(member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), image3(F!43, Y!39, B!41)) | (~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), B!41)) | ![X: $i] : ((~member(X, Y!39)) | (~apply(F!43, X, tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)))))))))) <=> (~((~((~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), image3(F!43, Y!39, B!41))) | (~((~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), B!41)) | (~member(tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), Y!39, F!43), tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))))))))) | (~((~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), B!41)) | ![X: $i] : ((~member(X, Y!39)) | (~apply(F!43, X, tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)))))) | member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), image3(F!43, Y!39, B!41))))))),
% 0.43/0.60 inference(rewrite,[status(thm)],[])).
% 0.43/0.60 tff(284,plain,
% 0.43/0.60 (((~![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), image3(F!43, Y!39, B!41))) | (~((~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), B!41)) | (~member(tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), Y!39, F!43), tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))))))))) | (~(member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), image3(F!43, Y!39, B!41)) | (~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), B!41)) | ![X: $i] : ((~member(X, Y!39)) | (~apply(F!43, X, tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))))))))))) <=> ((~![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), image3(F!43, Y!39, B!41))) | (~((~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), B!41)) | (~member(tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), Y!39, F!43), tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))))))))) | (~((~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), B!41)) | ![X: $i] : ((~member(X, Y!39)) | (~apply(F!43, X, tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)))))) | member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), image3(F!43, Y!39, B!41)))))))),
% 0.43/0.61 inference(monotonicity,[status(thm)],[283])).
% 0.43/0.61 tff(285,plain,
% 0.43/0.61 (((~![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), image3(F!43, Y!39, B!41))) | (~((~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), B!41)) | (~member(tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), Y!39, F!43), tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))))))))) | (~(member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), image3(F!43, Y!39, B!41)) | (~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), B!41)) | ![X: $i] : ((~member(X, Y!39)) | (~apply(F!43, X, tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))))))))))) <=> ((~![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), image3(F!43, Y!39, B!41))) | (~((~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), B!41)) | (~member(tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), Y!39, F!43), tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))))))))) | (~((~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), B!41)) | ![X: $i] : ((~member(X, Y!39)) | (~apply(F!43, X, tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)))))) | member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), image3(F!43, Y!39, B!41)))))))),
% 0.43/0.61 inference(transitivity,[status(thm)],[284, 282])).
% 0.43/0.61 tff(286,plain,
% 0.43/0.61 ((~![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), image3(F!43, Y!39, B!41))) | (~((~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), B!41)) | (~member(tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), Y!39, F!43), tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))))))))) | (~(member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), image3(F!43, Y!39, B!41)) | (~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), B!41)) | ![X: $i] : ((~member(X, Y!39)) | (~apply(F!43, X, tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))))))))))),
% 0.43/0.61 inference(quant_inst,[status(thm)],[])).
% 0.43/0.61 tff(287,plain,
% 0.43/0.61 ((~![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), image3(F!43, Y!39, B!41))) | (~((~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), B!41)) | (~member(tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), Y!39, F!43), tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))))))))) | (~((~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), B!41)) | ![X: $i] : ((~member(X, Y!39)) | (~apply(F!43, X, tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)))))) | member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), image3(F!43, Y!39, B!41))))))),
% 0.43/0.61 inference(modus_ponens,[status(thm)],[286, 285])).
% 0.43/0.61 tff(288,plain,
% 0.43/0.61 (~((~((~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), image3(F!43, Y!39, B!41))) | (~((~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), B!41)) | (~member(tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), Y!39, F!43), tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))))))))) | (~((~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), B!41)) | ![X: $i] : ((~member(X, Y!39)) | (~apply(F!43, X, tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)))))) | member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), image3(F!43, Y!39, B!41)))))),
% 0.43/0.61 inference(unit_resolution,[status(thm)],[287, 16])).
% 0.43/0.61 tff(289,plain,
% 0.43/0.61 (((~((~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), image3(F!43, Y!39, B!41))) | (~((~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), B!41)) | (~member(tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), Y!39, F!43), tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))))))))) | (~((~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), B!41)) | ![X: $i] : ((~member(X, Y!39)) | (~apply(F!43, X, tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)))))) | member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), image3(F!43, Y!39, B!41))))) | ((~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), image3(F!43, Y!39, B!41))) | (~((~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), B!41)) | (~member(tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), Y!39, F!43), tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))))))))),
% 0.43/0.61 inference(tautology,[status(thm)],[])).
% 0.43/0.61 tff(290,plain,
% 0.43/0.61 ((~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), image3(F!43, Y!39, B!41))) | (~((~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), B!41)) | (~member(tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), Y!39, F!43), tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)))))))),
% 0.43/0.61 inference(unit_resolution,[status(thm)],[289, 288])).
% 0.43/0.61 tff(291,plain,
% 0.43/0.61 (((~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), image3(F!43, X!40, B!41))) | (~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), image3(F!43, Y!39, B!41)))) | member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), image3(F!43, Y!39, B!41))),
% 0.43/0.61 inference(tautology,[status(thm)],[])).
% 0.43/0.61 tff(292,plain,
% 0.43/0.61 (member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), image3(F!43, Y!39, B!41))),
% 0.43/0.61 inference(unit_resolution,[status(thm)],[291, 262])).
% 0.43/0.61 tff(293,plain,
% 0.43/0.61 ((~((~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), image3(F!43, Y!39, B!41))) | (~((~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), B!41)) | (~member(tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), Y!39, F!43), tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))))))))) | (~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), image3(F!43, Y!39, B!41))) | (~((~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), B!41)) | (~member(tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), Y!39, F!43), tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)))))))),
% 0.45/0.62 inference(tautology,[status(thm)],[])).
% 0.45/0.62 tff(294,plain,
% 0.45/0.62 ((~((~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), image3(F!43, Y!39, B!41))) | (~((~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), B!41)) | (~member(tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), Y!39, F!43), tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))))))))) | (~((~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), B!41)) | (~member(tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), Y!39, F!43), tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)))))))),
% 0.45/0.62 inference(unit_resolution,[status(thm)],[293, 292])).
% 0.45/0.62 tff(295,plain,
% 0.45/0.62 (~((~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), B!41)) | (~member(tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), Y!39, F!43), tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))))))),
% 0.45/0.62 inference(unit_resolution,[status(thm)],[294, 290])).
% 0.45/0.62 tff(296,plain,
% 0.45/0.62 (((~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), B!41)) | (~member(tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), Y!39, F!43), tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)))))) | member(tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), Y!39, F!43), Y!39)),
% 0.45/0.62 inference(tautology,[status(thm)],[])).
% 0.45/0.62 tff(297,plain,
% 0.45/0.62 (member(tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), Y!39, F!43), Y!39)),
% 0.45/0.62 inference(unit_resolution,[status(thm)],[296, 295])).
% 0.45/0.62 tff(298,plain,
% 0.45/0.62 (((~![X: $i] : ((~member(X, Y!39)) | member(X, A!42))) | ((~member(tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), Y!39, F!43), Y!39)) | member(tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), Y!39, F!43), A!42))) <=> ((~![X: $i] : ((~member(X, Y!39)) | member(X, A!42))) | (~member(tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), Y!39, F!43), Y!39)) | member(tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), Y!39, F!43), A!42))),
% 0.45/0.62 inference(rewrite,[status(thm)],[])).
% 0.45/0.62 tff(299,plain,
% 0.45/0.62 ((~![X: $i] : ((~member(X, Y!39)) | member(X, A!42))) | ((~member(tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), Y!39, F!43), Y!39)) | member(tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), Y!39, F!43), A!42))),
% 0.45/0.62 inference(quant_inst,[status(thm)],[])).
% 0.45/0.62 tff(300,plain,
% 0.45/0.62 ((~![X: $i] : ((~member(X, Y!39)) | member(X, A!42))) | (~member(tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), Y!39, F!43), Y!39)) | member(tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), Y!39, F!43), A!42)),
% 0.45/0.62 inference(modus_ponens,[status(thm)],[299, 298])).
% 0.45/0.62 tff(301,plain,
% 0.45/0.62 (member(tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), Y!39, F!43), A!42)),
% 0.45/0.62 inference(unit_resolution,[status(thm)],[300, 113, 297])).
% 0.45/0.62 tff(302,plain,
% 0.45/0.62 (((~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), B!41)) | (~member(tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), X!40, F!43), X!40)) | (~apply(F!43, tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), X!40, F!43), tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)))))) | apply(F!43, tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), X!40, F!43), tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))))),
% 0.45/0.62 inference(tautology,[status(thm)],[])).
% 0.45/0.62 tff(303,plain,
% 0.45/0.62 (apply(F!43, tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), X!40, F!43), tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))))),
% 0.45/0.62 inference(unit_resolution,[status(thm)],[302, 267])).
% 0.45/0.62 tff(304,plain,
% 0.45/0.62 (((~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), B!41)) | (~member(tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), Y!39, F!43), tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)))))) | apply(F!43, tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), Y!39, F!43), tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))))),
% 0.45/0.62 inference(tautology,[status(thm)],[])).
% 0.45/0.62 tff(305,plain,
% 0.45/0.62 (apply(F!43, tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), Y!39, F!43), tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))))),
% 0.45/0.62 inference(unit_resolution,[status(thm)],[304, 295])).
% 0.45/0.62 tff(306,plain,
% 0.45/0.62 (((~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), B!41)) | (~member(tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), Y!39, F!43), Y!39)) | (~apply(F!43, tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), Y!39, F!43), tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)))))) | member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), B!41)),
% 0.45/0.62 inference(tautology,[status(thm)],[])).
% 0.45/0.62 tff(307,plain,
% 0.45/0.62 (member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), B!41)),
% 0.45/0.62 inference(unit_resolution,[status(thm)],[306, 295])).
% 0.45/0.62 tff(308,plain,
% 0.45/0.62 (^[F: $i, A: $i, B: $i] : refl((~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B)))))))) <=> (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B)))))))))),
% 0.45/0.62 inference(bind,[status(th)],[])).
% 0.45/0.62 tff(309,plain,
% 0.45/0.62 (![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B)))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))),
% 0.45/0.62 inference(quant_intro,[status(thm)],[308])).
% 0.45/0.62 tff(310,plain,
% 0.45/0.62 (^[F: $i, A: $i, B: $i] : rewrite((~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B)))))))) <=> (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B)))))))))),
% 0.45/0.62 inference(bind,[status(th)],[])).
% 0.45/0.62 tff(311,plain,
% 0.45/0.62 (![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B)))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))),
% 0.45/0.62 inference(quant_intro,[status(thm)],[310])).
% 0.45/0.62 tff(312,plain,
% 0.45/0.62 (![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B)))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))),
% 0.45/0.62 inference(transitivity,[status(thm)],[311, 309])).
% 0.45/0.62 tff(313,plain,
% 0.45/0.62 (^[F: $i, A: $i, B: $i] : trans(monotonicity(rewrite(((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~(apply(F, X1, Y) & apply(F, X2, Y))) | (~(member(X1, A) & member(X2, A) & member(Y, B))))) <=> ((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))), trans(monotonicity(rewrite((~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~(apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F)) & apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F)))) | (~(member(tptp_fun_X1_18(B, A, F), A) & member(tptp_fun_X2_17(B, A, F), A) & member(tptp_fun_Y_16(B, A, F), B))))) <=> (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))), ((injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~(apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F)) & apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F)))) | (~(member(tptp_fun_X1_18(B, A, F), A) & member(tptp_fun_X2_17(B, A, F), A) & member(tptp_fun_Y_16(B, A, F), B)))))) <=> (injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))), rewrite((injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))) <=> (injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B)))))), ((injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~(apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F)) & apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F)))) | (~(member(tptp_fun_X1_18(B, A, F), A) & member(tptp_fun_X2_17(B, A, F), A) & member(tptp_fun_Y_16(B, A, F), B)))))) <=> (injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))), ((((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~(apply(F, X1, Y) & apply(F, X2, Y))) | (~(member(X1, A) & member(X2, A) & member(Y, B))))) & (injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~(apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F)) & apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F)))) | (~(member(tptp_fun_X1_18(B, A, F), A) & member(tptp_fun_X2_17(B, A, F), A) & member(tptp_fun_Y_16(B, A, F), B))))))) <=> (((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y)))) & (injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B)))))))), rewrite((((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y)))) & (injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B)))))) <=> (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))), ((((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~(apply(F, X1, Y) & apply(F, X2, Y))) | (~(member(X1, A) & member(X2, A) & member(Y, B))))) & (injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~(apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F)) & apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F)))) | (~(member(tptp_fun_X1_18(B, A, F), A) & member(tptp_fun_X2_17(B, A, F), A) & member(tptp_fun_Y_16(B, A, F), B))))))) <=> (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))))),
% 0.45/0.62 inference(bind,[status(th)],[])).
% 0.45/0.62 tff(314,plain,
% 0.45/0.62 (![F: $i, A: $i, B: $i] : (((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~(apply(F, X1, Y) & apply(F, X2, Y))) | (~(member(X1, A) & member(X2, A) & member(Y, B))))) & (injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~(apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F)) & apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F)))) | (~(member(tptp_fun_X1_18(B, A, F), A) & member(tptp_fun_X2_17(B, A, F), A) & member(tptp_fun_Y_16(B, A, F), B))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))),
% 0.45/0.62 inference(quant_intro,[status(thm)],[313])).
% 0.45/0.62 tff(315,plain,
% 0.45/0.62 (![F: $i, A: $i, B: $i] : (injective(F, A, B) <=> ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~(apply(F, X1, Y) & apply(F, X2, Y))) | (~(member(X1, A) & member(X2, A) & member(Y, B))))) <=> ![F: $i, A: $i, B: $i] : (injective(F, A, B) <=> ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~(apply(F, X1, Y) & apply(F, X2, Y))) | (~(member(X1, A) & member(X2, A) & member(Y, B)))))),
% 0.45/0.62 inference(rewrite,[status(thm)],[])).
% 0.45/0.62 tff(316,plain,
% 0.45/0.62 (^[F: $i, A: $i, B: $i] : rewrite((injective(F, A, B) <=> ![X1: $i, X2: $i, Y: $i] : (((member(X1, A) & member(X2, A)) & member(Y, B)) => ((apply(F, X1, Y) & apply(F, X2, Y)) => (X1 = X2)))) <=> (injective(F, A, B) <=> ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~(apply(F, X1, Y) & apply(F, X2, Y))) | (~(member(X1, A) & member(X2, A) & member(Y, B))))))),
% 0.45/0.62 inference(bind,[status(th)],[])).
% 0.45/0.62 tff(317,plain,
% 0.45/0.62 (![F: $i, A: $i, B: $i] : (injective(F, A, B) <=> ![X1: $i, X2: $i, Y: $i] : (((member(X1, A) & member(X2, A)) & member(Y, B)) => ((apply(F, X1, Y) & apply(F, X2, Y)) => (X1 = X2)))) <=> ![F: $i, A: $i, B: $i] : (injective(F, A, B) <=> ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~(apply(F, X1, Y) & apply(F, X2, Y))) | (~(member(X1, A) & member(X2, A) & member(Y, B)))))),
% 0.45/0.62 inference(quant_intro,[status(thm)],[316])).
% 0.45/0.62 tff(318,axiom,(![F: $i, A: $i, B: $i] : (injective(F, A, B) <=> ![X1: $i, X2: $i, Y: $i] : (((member(X1, A) & member(X2, A)) & member(Y, B)) => ((apply(F, X1, Y) & apply(F, X2, Y)) => (X1 = X2))))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+1.ax','injective')).
% 0.45/0.62 tff(319,plain,
% 0.45/0.62 (![F: $i, A: $i, B: $i] : (injective(F, A, B) <=> ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~(apply(F, X1, Y) & apply(F, X2, Y))) | (~(member(X1, A) & member(X2, A) & member(Y, B)))))),
% 0.45/0.62 inference(modus_ponens,[status(thm)],[318, 317])).
% 0.45/0.62 tff(320,plain,
% 0.45/0.62 (![F: $i, A: $i, B: $i] : (injective(F, A, B) <=> ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~(apply(F, X1, Y) & apply(F, X2, Y))) | (~(member(X1, A) & member(X2, A) & member(Y, B)))))),
% 0.45/0.62 inference(modus_ponens,[status(thm)],[319, 315])).
% 0.45/0.62 tff(321,plain,(
% 0.45/0.62 ![F: $i, A: $i, B: $i] : (((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~(apply(F, X1, Y) & apply(F, X2, Y))) | (~(member(X1, A) & member(X2, A) & member(Y, B))))) & (injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~(apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F)) & apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F)))) | (~(member(tptp_fun_X1_18(B, A, F), A) & member(tptp_fun_X2_17(B, A, F), A) & member(tptp_fun_Y_16(B, A, F), B)))))))),
% 0.45/0.62 inference(skolemize,[status(sab)],[320])).
% 0.45/0.62 tff(322,plain,
% 0.45/0.62 (![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))),
% 0.45/0.62 inference(modus_ponens,[status(thm)],[321, 314])).
% 0.45/0.62 tff(323,plain,
% 0.45/0.62 (![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))),
% 0.45/0.62 inference(modus_ponens,[status(thm)],[322, 312])).
% 0.45/0.62 tff(324,plain,
% 0.45/0.62 (((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(F!43, A!42, B!41)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!41)) | (~apply(F!43, X1, Y)) | (~member(X1, A!42)) | (~member(X2, A!42)) | (~apply(F!43, X2, Y))))) | (~(injective(F!43, A!42, B!41) | (~((~member(tptp_fun_Y_16(B!41, A!42, F!43), B!41)) | (~member(tptp_fun_X2_17(B!41, A!42, F!43), A!42)) | (~member(tptp_fun_X1_18(B!41, A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_X2_17(B!41, A!42, F!43), tptp_fun_Y_16(B!41, A!42, F!43))) | (~apply(F!43, tptp_fun_X1_18(B!41, A!42, F!43), tptp_fun_Y_16(B!41, A!42, F!43))) | (tptp_fun_X1_18(B!41, A!42, F!43) = tptp_fun_X2_17(B!41, A!42, F!43))))))))) <=> ((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(F!43, A!42, B!41)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!41)) | (~apply(F!43, X1, Y)) | (~member(X1, A!42)) | (~member(X2, A!42)) | (~apply(F!43, X2, Y))))) | (~(injective(F!43, A!42, B!41) | (~((~member(tptp_fun_Y_16(B!41, A!42, F!43), B!41)) | (~member(tptp_fun_X2_17(B!41, A!42, F!43), A!42)) | (~member(tptp_fun_X1_18(B!41, A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_X2_17(B!41, A!42, F!43), tptp_fun_Y_16(B!41, A!42, F!43))) | (~apply(F!43, tptp_fun_X1_18(B!41, A!42, F!43), tptp_fun_Y_16(B!41, A!42, F!43))) | (tptp_fun_X1_18(B!41, A!42, F!43) = tptp_fun_X2_17(B!41, A!42, F!43)))))))))),
% 0.45/0.63 inference(rewrite,[status(thm)],[])).
% 0.45/0.63 tff(325,plain,
% 0.45/0.63 ((~((~((~injective(F!43, A!42, B!41)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!43, X1, Y)) | (~member(X2, A!42)) | (~member(X1, A!42)) | (~member(Y, B!41)) | (~apply(F!43, X2, Y))))) | (~(injective(F!43, A!42, B!41) | (~((tptp_fun_X1_18(B!41, A!42, F!43) = tptp_fun_X2_17(B!41, A!42, F!43)) | (~apply(F!43, tptp_fun_X1_18(B!41, A!42, F!43), tptp_fun_Y_16(B!41, A!42, F!43))) | (~apply(F!43, tptp_fun_X2_17(B!41, A!42, F!43), tptp_fun_Y_16(B!41, A!42, F!43))) | (~member(tptp_fun_X1_18(B!41, A!42, F!43), A!42)) | (~member(tptp_fun_X2_17(B!41, A!42, F!43), A!42)) | (~member(tptp_fun_Y_16(B!41, A!42, F!43), B!41)))))))) <=> (~((~((~injective(F!43, A!42, B!41)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!41)) | (~apply(F!43, X1, Y)) | (~member(X1, A!42)) | (~member(X2, A!42)) | (~apply(F!43, X2, Y))))) | (~(injective(F!43, A!42, B!41) | (~((~member(tptp_fun_Y_16(B!41, A!42, F!43), B!41)) | (~member(tptp_fun_X2_17(B!41, A!42, F!43), A!42)) | (~member(tptp_fun_X1_18(B!41, A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_X2_17(B!41, A!42, F!43), tptp_fun_Y_16(B!41, A!42, F!43))) | (~apply(F!43, tptp_fun_X1_18(B!41, A!42, F!43), tptp_fun_Y_16(B!41, A!42, F!43))) | (tptp_fun_X1_18(B!41, A!42, F!43) = tptp_fun_X2_17(B!41, A!42, F!43))))))))),
% 0.45/0.63 inference(rewrite,[status(thm)],[])).
% 0.45/0.63 tff(326,plain,
% 0.45/0.63 (((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(F!43, A!42, B!41)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!43, X1, Y)) | (~member(X2, A!42)) | (~member(X1, A!42)) | (~member(Y, B!41)) | (~apply(F!43, X2, Y))))) | (~(injective(F!43, A!42, B!41) | (~((tptp_fun_X1_18(B!41, A!42, F!43) = tptp_fun_X2_17(B!41, A!42, F!43)) | (~apply(F!43, tptp_fun_X1_18(B!41, A!42, F!43), tptp_fun_Y_16(B!41, A!42, F!43))) | (~apply(F!43, tptp_fun_X2_17(B!41, A!42, F!43), tptp_fun_Y_16(B!41, A!42, F!43))) | (~member(tptp_fun_X1_18(B!41, A!42, F!43), A!42)) | (~member(tptp_fun_X2_17(B!41, A!42, F!43), A!42)) | (~member(tptp_fun_Y_16(B!41, A!42, F!43), B!41))))))))) <=> ((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(F!43, A!42, B!41)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!41)) | (~apply(F!43, X1, Y)) | (~member(X1, A!42)) | (~member(X2, A!42)) | (~apply(F!43, X2, Y))))) | (~(injective(F!43, A!42, B!41) | (~((~member(tptp_fun_Y_16(B!41, A!42, F!43), B!41)) | (~member(tptp_fun_X2_17(B!41, A!42, F!43), A!42)) | (~member(tptp_fun_X1_18(B!41, A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_X2_17(B!41, A!42, F!43), tptp_fun_Y_16(B!41, A!42, F!43))) | (~apply(F!43, tptp_fun_X1_18(B!41, A!42, F!43), tptp_fun_Y_16(B!41, A!42, F!43))) | (tptp_fun_X1_18(B!41, A!42, F!43) = tptp_fun_X2_17(B!41, A!42, F!43)))))))))),
% 0.45/0.63 inference(monotonicity,[status(thm)],[325])).
% 0.45/0.63 tff(327,plain,
% 0.45/0.63 (((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(F!43, A!42, B!41)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!43, X1, Y)) | (~member(X2, A!42)) | (~member(X1, A!42)) | (~member(Y, B!41)) | (~apply(F!43, X2, Y))))) | (~(injective(F!43, A!42, B!41) | (~((tptp_fun_X1_18(B!41, A!42, F!43) = tptp_fun_X2_17(B!41, A!42, F!43)) | (~apply(F!43, tptp_fun_X1_18(B!41, A!42, F!43), tptp_fun_Y_16(B!41, A!42, F!43))) | (~apply(F!43, tptp_fun_X2_17(B!41, A!42, F!43), tptp_fun_Y_16(B!41, A!42, F!43))) | (~member(tptp_fun_X1_18(B!41, A!42, F!43), A!42)) | (~member(tptp_fun_X2_17(B!41, A!42, F!43), A!42)) | (~member(tptp_fun_Y_16(B!41, A!42, F!43), B!41))))))))) <=> ((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(F!43, A!42, B!41)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!41)) | (~apply(F!43, X1, Y)) | (~member(X1, A!42)) | (~member(X2, A!42)) | (~apply(F!43, X2, Y))))) | (~(injective(F!43, A!42, B!41) | (~((~member(tptp_fun_Y_16(B!41, A!42, F!43), B!41)) | (~member(tptp_fun_X2_17(B!41, A!42, F!43), A!42)) | (~member(tptp_fun_X1_18(B!41, A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_X2_17(B!41, A!42, F!43), tptp_fun_Y_16(B!41, A!42, F!43))) | (~apply(F!43, tptp_fun_X1_18(B!41, A!42, F!43), tptp_fun_Y_16(B!41, A!42, F!43))) | (tptp_fun_X1_18(B!41, A!42, F!43) = tptp_fun_X2_17(B!41, A!42, F!43)))))))))),
% 0.45/0.63 inference(transitivity,[status(thm)],[326, 324])).
% 0.45/0.63 tff(328,plain,
% 0.45/0.63 ((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(F!43, A!42, B!41)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!43, X1, Y)) | (~member(X2, A!42)) | (~member(X1, A!42)) | (~member(Y, B!41)) | (~apply(F!43, X2, Y))))) | (~(injective(F!43, A!42, B!41) | (~((tptp_fun_X1_18(B!41, A!42, F!43) = tptp_fun_X2_17(B!41, A!42, F!43)) | (~apply(F!43, tptp_fun_X1_18(B!41, A!42, F!43), tptp_fun_Y_16(B!41, A!42, F!43))) | (~apply(F!43, tptp_fun_X2_17(B!41, A!42, F!43), tptp_fun_Y_16(B!41, A!42, F!43))) | (~member(tptp_fun_X1_18(B!41, A!42, F!43), A!42)) | (~member(tptp_fun_X2_17(B!41, A!42, F!43), A!42)) | (~member(tptp_fun_Y_16(B!41, A!42, F!43), B!41))))))))),
% 0.45/0.63 inference(quant_inst,[status(thm)],[])).
% 0.45/0.63 tff(329,plain,
% 0.45/0.63 ((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(F!43, A!42, B!41)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!41)) | (~apply(F!43, X1, Y)) | (~member(X1, A!42)) | (~member(X2, A!42)) | (~apply(F!43, X2, Y))))) | (~(injective(F!43, A!42, B!41) | (~((~member(tptp_fun_Y_16(B!41, A!42, F!43), B!41)) | (~member(tptp_fun_X2_17(B!41, A!42, F!43), A!42)) | (~member(tptp_fun_X1_18(B!41, A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_X2_17(B!41, A!42, F!43), tptp_fun_Y_16(B!41, A!42, F!43))) | (~apply(F!43, tptp_fun_X1_18(B!41, A!42, F!43), tptp_fun_Y_16(B!41, A!42, F!43))) | (tptp_fun_X1_18(B!41, A!42, F!43) = tptp_fun_X2_17(B!41, A!42, F!43))))))))),
% 0.47/0.63 inference(modus_ponens,[status(thm)],[328, 327])).
% 0.47/0.63 tff(330,plain,
% 0.47/0.63 (~((~((~injective(F!43, A!42, B!41)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!41)) | (~apply(F!43, X1, Y)) | (~member(X1, A!42)) | (~member(X2, A!42)) | (~apply(F!43, X2, Y))))) | (~(injective(F!43, A!42, B!41) | (~((~member(tptp_fun_Y_16(B!41, A!42, F!43), B!41)) | (~member(tptp_fun_X2_17(B!41, A!42, F!43), A!42)) | (~member(tptp_fun_X1_18(B!41, A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_X2_17(B!41, A!42, F!43), tptp_fun_Y_16(B!41, A!42, F!43))) | (~apply(F!43, tptp_fun_X1_18(B!41, A!42, F!43), tptp_fun_Y_16(B!41, A!42, F!43))) | (tptp_fun_X1_18(B!41, A!42, F!43) = tptp_fun_X2_17(B!41, A!42, F!43)))))))),
% 0.47/0.63 inference(unit_resolution,[status(thm)],[329, 323])).
% 0.47/0.63 tff(331,plain,
% 0.47/0.63 (((~((~injective(F!43, A!42, B!41)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!41)) | (~apply(F!43, X1, Y)) | (~member(X1, A!42)) | (~member(X2, A!42)) | (~apply(F!43, X2, Y))))) | (~(injective(F!43, A!42, B!41) | (~((~member(tptp_fun_Y_16(B!41, A!42, F!43), B!41)) | (~member(tptp_fun_X2_17(B!41, A!42, F!43), A!42)) | (~member(tptp_fun_X1_18(B!41, A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_X2_17(B!41, A!42, F!43), tptp_fun_Y_16(B!41, A!42, F!43))) | (~apply(F!43, tptp_fun_X1_18(B!41, A!42, F!43), tptp_fun_Y_16(B!41, A!42, F!43))) | (tptp_fun_X1_18(B!41, A!42, F!43) = tptp_fun_X2_17(B!41, A!42, F!43))))))) | ((~injective(F!43, A!42, B!41)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!41)) | (~apply(F!43, X1, Y)) | (~member(X1, A!42)) | (~member(X2, A!42)) | (~apply(F!43, X2, Y))))),
% 0.47/0.63 inference(tautology,[status(thm)],[])).
% 0.47/0.63 tff(332,plain,
% 0.47/0.63 ((~injective(F!43, A!42, B!41)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!41)) | (~apply(F!43, X1, Y)) | (~member(X1, A!42)) | (~member(X2, A!42)) | (~apply(F!43, X2, Y)))),
% 0.47/0.63 inference(unit_resolution,[status(thm)],[331, 330])).
% 0.47/0.63 tff(333,plain,
% 0.47/0.63 (injective(F!43, A!42, B!41)),
% 0.47/0.63 inference(and_elim,[status(thm)],[109])).
% 0.47/0.63 tff(334,plain,
% 0.47/0.63 ((~((~injective(F!43, A!42, B!41)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!41)) | (~apply(F!43, X1, Y)) | (~member(X1, A!42)) | (~member(X2, A!42)) | (~apply(F!43, X2, Y))))) | (~injective(F!43, A!42, B!41)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!41)) | (~apply(F!43, X1, Y)) | (~member(X1, A!42)) | (~member(X2, A!42)) | (~apply(F!43, X2, Y)))),
% 0.47/0.63 inference(tautology,[status(thm)],[])).
% 0.47/0.63 tff(335,plain,
% 0.47/0.63 ((~((~injective(F!43, A!42, B!41)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!41)) | (~apply(F!43, X1, Y)) | (~member(X1, A!42)) | (~member(X2, A!42)) | (~apply(F!43, X2, Y))))) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!41)) | (~apply(F!43, X1, Y)) | (~member(X1, A!42)) | (~member(X2, A!42)) | (~apply(F!43, X2, Y)))),
% 0.47/0.63 inference(unit_resolution,[status(thm)],[334, 333])).
% 0.47/0.63 tff(336,plain,
% 0.47/0.63 (![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!41)) | (~apply(F!43, X1, Y)) | (~member(X1, A!42)) | (~member(X2, A!42)) | (~apply(F!43, X2, Y)))),
% 0.47/0.63 inference(unit_resolution,[status(thm)],[335, 332])).
% 0.47/0.63 tff(337,plain,
% 0.47/0.63 (((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!41)) | (~apply(F!43, X1, Y)) | (~member(X1, A!42)) | (~member(X2, A!42)) | (~apply(F!43, X2, Y)))) | ((~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), B!41)) | (~apply(F!43, tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), Y!39, F!43), tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))))) | (~apply(F!43, tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), X!40, F!43), tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))))) | (tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), Y!39, F!43) = tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), X!40, F!43)) | (~member(tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), Y!39, F!43), A!42)) | (~member(tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), X!40, F!43), A!42)))) <=> ((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!41)) | (~apply(F!43, X1, Y)) | (~member(X1, A!42)) | (~member(X2, A!42)) | (~apply(F!43, X2, Y)))) | (~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), B!41)) | (~apply(F!43, tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), Y!39, F!43), tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))))) | (~apply(F!43, tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), X!40, F!43), tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))))) | (tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), Y!39, F!43) = tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), X!40, F!43)) | (~member(tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), Y!39, F!43), A!42)) | (~member(tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), X!40, F!43), A!42)))),
% 0.47/0.63 inference(rewrite,[status(thm)],[])).
% 0.47/0.63 tff(338,plain,
% 0.47/0.63 (((tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), Y!39, F!43) = tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), X!40, F!43)) | (~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), B!41)) | (~apply(F!43, tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), Y!39, F!43), tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))))) | (~member(tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), Y!39, F!43), A!42)) | (~member(tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), X!40, F!43), A!42)) | (~apply(F!43, tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), X!40, F!43), tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)))))) <=> ((~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), B!41)) | (~apply(F!43, tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), Y!39, F!43), tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))))) | (~apply(F!43, tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), X!40, F!43), tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))))) | (tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), Y!39, F!43) = tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), X!40, F!43)) | (~member(tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), Y!39, F!43), A!42)) | (~member(tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), X!40, F!43), A!42)))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(339,plain,
% 0.47/0.64 (((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!41)) | (~apply(F!43, X1, Y)) | (~member(X1, A!42)) | (~member(X2, A!42)) | (~apply(F!43, X2, Y)))) | ((tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), Y!39, F!43) = tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), X!40, F!43)) | (~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), B!41)) | (~apply(F!43, tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), Y!39, F!43), tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))))) | (~member(tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), Y!39, F!43), A!42)) | (~member(tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), X!40, F!43), A!42)) | (~apply(F!43, tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), X!40, F!43), tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))))))) <=> ((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!41)) | (~apply(F!43, X1, Y)) | (~member(X1, A!42)) | (~member(X2, A!42)) | (~apply(F!43, X2, Y)))) | ((~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), B!41)) | (~apply(F!43, tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), Y!39, F!43), tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))))) | (~apply(F!43, tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), X!40, F!43), tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))))) | (tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), Y!39, F!43) = tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), X!40, F!43)) | (~member(tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), Y!39, F!43), A!42)) | (~member(tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), X!40, F!43), A!42))))),
% 0.47/0.64 inference(monotonicity,[status(thm)],[338])).
% 0.47/0.64 tff(340,plain,
% 0.47/0.64 (((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!41)) | (~apply(F!43, X1, Y)) | (~member(X1, A!42)) | (~member(X2, A!42)) | (~apply(F!43, X2, Y)))) | ((tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), Y!39, F!43) = tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), X!40, F!43)) | (~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), B!41)) | (~apply(F!43, tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), Y!39, F!43), tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))))) | (~member(tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), Y!39, F!43), A!42)) | (~member(tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), X!40, F!43), A!42)) | (~apply(F!43, tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), X!40, F!43), tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))))))) <=> ((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!41)) | (~apply(F!43, X1, Y)) | (~member(X1, A!42)) | (~member(X2, A!42)) | (~apply(F!43, X2, Y)))) | (~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), B!41)) | (~apply(F!43, tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), Y!39, F!43), tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))))) | (~apply(F!43, tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), X!40, F!43), tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))))) | (tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), Y!39, F!43) = tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), X!40, F!43)) | (~member(tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), Y!39, F!43), A!42)) | (~member(tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), X!40, F!43), A!42)))),
% 0.47/0.64 inference(transitivity,[status(thm)],[339, 337])).
% 0.47/0.64 tff(341,plain,
% 0.47/0.64 ((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!41)) | (~apply(F!43, X1, Y)) | (~member(X1, A!42)) | (~member(X2, A!42)) | (~apply(F!43, X2, Y)))) | ((tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), Y!39, F!43) = tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), X!40, F!43)) | (~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), B!41)) | (~apply(F!43, tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), Y!39, F!43), tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))))) | (~member(tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), Y!39, F!43), A!42)) | (~member(tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), X!40, F!43), A!42)) | (~apply(F!43, tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), X!40, F!43), tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))))))),
% 0.47/0.64 inference(quant_inst,[status(thm)],[])).
% 0.47/0.64 tff(342,plain,
% 0.47/0.64 ((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!41)) | (~apply(F!43, X1, Y)) | (~member(X1, A!42)) | (~member(X2, A!42)) | (~apply(F!43, X2, Y)))) | (~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), B!41)) | (~apply(F!43, tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), Y!39, F!43), tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))))) | (~apply(F!43, tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), X!40, F!43), tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))))) | (tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), Y!39, F!43) = tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), X!40, F!43)) | (~member(tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), Y!39, F!43), A!42)) | (~member(tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), X!40, F!43), A!42))),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[341, 340])).
% 0.47/0.64 tff(343,plain,
% 0.47/0.64 ((tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), Y!39, F!43) = tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), X!40, F!43)) | (~member(tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), Y!39, F!43), A!42)) | (~member(tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), X!40, F!43), A!42))),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[342, 336, 307, 305, 303])).
% 0.47/0.64 tff(344,plain,
% 0.47/0.64 (tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), Y!39, F!43) = tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), X!40, F!43)),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[343, 301, 281])).
% 0.47/0.65 tff(345,plain,
% 0.47/0.65 (tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), X!40, F!43) = tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), Y!39, F!43)),
% 0.47/0.65 inference(symmetry,[status(thm)],[344])).
% 0.47/0.65 tff(346,plain,
% 0.47/0.65 (member(tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), X!40, F!43), Y!39) <=> member(tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), Y!39, F!43), Y!39)),
% 0.47/0.65 inference(monotonicity,[status(thm)],[345])).
% 0.47/0.65 tff(347,plain,
% 0.47/0.65 (member(tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), Y!39, F!43), Y!39) <=> member(tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), X!40, F!43), Y!39)),
% 0.47/0.65 inference(symmetry,[status(thm)],[346])).
% 0.47/0.65 tff(348,plain,
% 0.47/0.65 (member(tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), X!40, F!43), Y!39)),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[297, 347])).
% 0.47/0.65 tff(349,plain,
% 0.47/0.65 ((~![X: $i, A: $i, B: $i] : (~(((~member(X, A)) | (~member(X, B))) <=> member(X, intersection(A, B))))) | (~(((~member(tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), X!40, F!43), X!40)) | (~member(tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), X!40, F!43), Y!39))) <=> member(tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), X!40, F!43), intersection(X!40, Y!39))))),
% 0.47/0.65 inference(quant_inst,[status(thm)],[])).
% 0.47/0.65 tff(350,plain,
% 0.47/0.65 (~(((~member(tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), X!40, F!43), X!40)) | (~member(tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), X!40, F!43), Y!39))) <=> member(tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), X!40, F!43), intersection(X!40, Y!39)))),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[349, 35])).
% 0.47/0.65 tff(351,plain,
% 0.47/0.65 (((~![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), image3(F!43, intersection(X!40, Y!39), B!41))) | (~((~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), B!41)) | (~member(tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), intersection(X!40, Y!39), F!43), intersection(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), intersection(X!40, Y!39), F!43), tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))))))))) | (~(member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), image3(F!43, intersection(X!40, Y!39), B!41)) | ![X: $i] : ((~member(X, intersection(X!40, Y!39))) | (~apply(F!43, X, tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)))))) | (~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), B!41))))))) <=> ((~![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), image3(F!43, intersection(X!40, Y!39), B!41))) | (~((~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), B!41)) | (~member(tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), intersection(X!40, Y!39), F!43), intersection(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), intersection(X!40, Y!39), F!43), tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))))))))) | (~(member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), image3(F!43, intersection(X!40, Y!39), B!41)) | ![X: $i] : ((~member(X, intersection(X!40, Y!39))) | (~apply(F!43, X, tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)))))) | (~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), B!41)))))))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(352,plain,
% 0.47/0.65 ((~((~((~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), image3(F!43, intersection(X!40, Y!39), B!41))) | (~((~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), B!41)) | (~member(tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), intersection(X!40, Y!39), F!43), intersection(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), intersection(X!40, Y!39), F!43), tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))))))))) | (~(member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), image3(F!43, intersection(X!40, Y!39), B!41)) | (~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), B!41)) | ![X: $i] : ((~member(X, intersection(X!40, Y!39))) | (~apply(F!43, X, tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)))))))))) <=> (~((~((~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), image3(F!43, intersection(X!40, Y!39), B!41))) | (~((~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), B!41)) | (~member(tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), intersection(X!40, Y!39), F!43), intersection(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), intersection(X!40, Y!39), F!43), tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))))))))) | (~(member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), image3(F!43, intersection(X!40, Y!39), B!41)) | ![X: $i] : ((~member(X, intersection(X!40, Y!39))) | (~apply(F!43, X, tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)))))) | (~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), B!41))))))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(353,plain,
% 0.47/0.65 (((~![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), image3(F!43, intersection(X!40, Y!39), B!41))) | (~((~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), B!41)) | (~member(tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), intersection(X!40, Y!39), F!43), intersection(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), intersection(X!40, Y!39), F!43), tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))))))))) | (~(member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), image3(F!43, intersection(X!40, Y!39), B!41)) | (~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), B!41)) | ![X: $i] : ((~member(X, intersection(X!40, Y!39))) | (~apply(F!43, X, tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))))))))))) <=> ((~![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), image3(F!43, intersection(X!40, Y!39), B!41))) | (~((~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), B!41)) | (~member(tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), intersection(X!40, Y!39), F!43), intersection(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), intersection(X!40, Y!39), F!43), tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))))))))) | (~(member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), image3(F!43, intersection(X!40, Y!39), B!41)) | ![X: $i] : ((~member(X, intersection(X!40, Y!39))) | (~apply(F!43, X, tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)))))) | (~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), B!41)))))))),
% 0.47/0.65 inference(monotonicity,[status(thm)],[352])).
% 0.47/0.65 tff(354,plain,
% 0.47/0.65 (((~![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), image3(F!43, intersection(X!40, Y!39), B!41))) | (~((~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), B!41)) | (~member(tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), intersection(X!40, Y!39), F!43), intersection(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), intersection(X!40, Y!39), F!43), tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))))))))) | (~(member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), image3(F!43, intersection(X!40, Y!39), B!41)) | (~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), B!41)) | ![X: $i] : ((~member(X, intersection(X!40, Y!39))) | (~apply(F!43, X, tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))))))))))) <=> ((~![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), image3(F!43, intersection(X!40, Y!39), B!41))) | (~((~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), B!41)) | (~member(tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), intersection(X!40, Y!39), F!43), intersection(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), intersection(X!40, Y!39), F!43), tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))))))))) | (~(member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), image3(F!43, intersection(X!40, Y!39), B!41)) | ![X: $i] : ((~member(X, intersection(X!40, Y!39))) | (~apply(F!43, X, tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)))))) | (~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), B!41)))))))),
% 0.47/0.65 inference(transitivity,[status(thm)],[353, 351])).
% 0.47/0.65 tff(355,plain,
% 0.47/0.65 ((~![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), image3(F!43, intersection(X!40, Y!39), B!41))) | (~((~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), B!41)) | (~member(tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), intersection(X!40, Y!39), F!43), intersection(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), intersection(X!40, Y!39), F!43), tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))))))))) | (~(member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), image3(F!43, intersection(X!40, Y!39), B!41)) | (~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), B!41)) | ![X: $i] : ((~member(X, intersection(X!40, Y!39))) | (~apply(F!43, X, tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))))))))))),
% 0.47/0.66 inference(quant_inst,[status(thm)],[])).
% 0.47/0.66 tff(356,plain,
% 0.47/0.66 ((~![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), image3(F!43, intersection(X!40, Y!39), B!41))) | (~((~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), B!41)) | (~member(tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), intersection(X!40, Y!39), F!43), intersection(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), intersection(X!40, Y!39), F!43), tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))))))))) | (~(member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), image3(F!43, intersection(X!40, Y!39), B!41)) | ![X: $i] : ((~member(X, intersection(X!40, Y!39))) | (~apply(F!43, X, tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)))))) | (~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), B!41))))))),
% 0.47/0.66 inference(modus_ponens,[status(thm)],[355, 354])).
% 0.47/0.66 tff(357,plain,
% 0.47/0.66 (~((~((~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), image3(F!43, intersection(X!40, Y!39), B!41))) | (~((~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), B!41)) | (~member(tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), intersection(X!40, Y!39), F!43), intersection(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), intersection(X!40, Y!39), F!43), tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))))))))) | (~(member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), image3(F!43, intersection(X!40, Y!39), B!41)) | ![X: $i] : ((~member(X, intersection(X!40, Y!39))) | (~apply(F!43, X, tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)))))) | (~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), B!41)))))),
% 0.47/0.66 inference(unit_resolution,[status(thm)],[356, 16])).
% 0.47/0.66 tff(358,plain,
% 0.47/0.66 (((~((~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), image3(F!43, intersection(X!40, Y!39), B!41))) | (~((~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), B!41)) | (~member(tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), intersection(X!40, Y!39), F!43), intersection(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), intersection(X!40, Y!39), F!43), tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))))))))) | (~(member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), image3(F!43, intersection(X!40, Y!39), B!41)) | ![X: $i] : ((~member(X, intersection(X!40, Y!39))) | (~apply(F!43, X, tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)))))) | (~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), B!41))))) | (member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), image3(F!43, intersection(X!40, Y!39), B!41)) | ![X: $i] : ((~member(X, intersection(X!40, Y!39))) | (~apply(F!43, X, tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)))))) | (~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), B!41)))),
% 0.47/0.66 inference(tautology,[status(thm)],[])).
% 0.47/0.66 tff(359,plain,
% 0.47/0.66 (member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), image3(F!43, intersection(X!40, Y!39), B!41)) | ![X: $i] : ((~member(X, intersection(X!40, Y!39))) | (~apply(F!43, X, tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)))))) | (~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), B!41))),
% 0.47/0.66 inference(unit_resolution,[status(thm)],[358, 357])).
% 0.47/0.66 tff(360,plain,
% 0.47/0.66 (((~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)))) | member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), image3(F!43, intersection(X!40, Y!39), B!41))) | (~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), image3(F!43, intersection(X!40, Y!39), B!41)))),
% 0.47/0.66 inference(tautology,[status(thm)],[])).
% 0.47/0.66 tff(361,plain,
% 0.47/0.66 (~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), image3(F!43, intersection(X!40, Y!39), B!41))),
% 0.47/0.66 inference(unit_resolution,[status(thm)],[360, 257])).
% 0.47/0.66 tff(362,plain,
% 0.47/0.66 ((~(member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), image3(F!43, intersection(X!40, Y!39), B!41)) | ![X: $i] : ((~member(X, intersection(X!40, Y!39))) | (~apply(F!43, X, tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)))))) | (~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), B!41)))) | member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), image3(F!43, intersection(X!40, Y!39), B!41)) | ![X: $i] : ((~member(X, intersection(X!40, Y!39))) | (~apply(F!43, X, tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)))))) | (~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), B!41))),
% 0.47/0.66 inference(tautology,[status(thm)],[])).
% 0.47/0.66 tff(363,plain,
% 0.47/0.66 ((~(member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), image3(F!43, intersection(X!40, Y!39), B!41)) | ![X: $i] : ((~member(X, intersection(X!40, Y!39))) | (~apply(F!43, X, tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)))))) | (~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), B!41)))) | ![X: $i] : ((~member(X, intersection(X!40, Y!39))) | (~apply(F!43, X, tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)))))) | (~member(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), B!41))),
% 0.47/0.66 inference(unit_resolution,[status(thm)],[362, 361])).
% 0.47/0.66 tff(364,plain,
% 0.47/0.66 (![X: $i] : ((~member(X, intersection(X!40, Y!39))) | (~apply(F!43, X, tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))))))),
% 0.47/0.66 inference(unit_resolution,[status(thm)],[363, 307, 359])).
% 0.47/0.66 tff(365,plain,
% 0.47/0.66 (((~![X: $i] : ((~member(X, intersection(X!40, Y!39))) | (~apply(F!43, X, tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))))))) | ((~member(tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), X!40, F!43), intersection(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), X!40, F!43), tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))))))) <=> ((~![X: $i] : ((~member(X, intersection(X!40, Y!39))) | (~apply(F!43, X, tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))))))) | (~member(tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), X!40, F!43), intersection(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), X!40, F!43), tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))))))),
% 0.47/0.66 inference(rewrite,[status(thm)],[])).
% 0.47/0.66 tff(366,plain,
% 0.47/0.66 ((~![X: $i] : ((~member(X, intersection(X!40, Y!39))) | (~apply(F!43, X, tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))))))) | ((~member(tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), X!40, F!43), intersection(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), X!40, F!43), tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))))))),
% 0.47/0.66 inference(quant_inst,[status(thm)],[])).
% 0.47/0.66 tff(367,plain,
% 0.47/0.66 ((~![X: $i] : ((~member(X, intersection(X!40, Y!39))) | (~apply(F!43, X, tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))))))) | (~member(tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), X!40, F!43), intersection(X!40, Y!39))) | (~apply(F!43, tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), X!40, F!43), tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41)))))),
% 0.47/0.66 inference(modus_ponens,[status(thm)],[366, 365])).
% 0.47/0.66 tff(368,plain,
% 0.47/0.66 (~member(tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), X!40, F!43), intersection(X!40, Y!39))),
% 0.47/0.66 inference(unit_resolution,[status(thm)],[367, 364, 303])).
% 0.47/0.66 tff(369,plain,
% 0.47/0.66 ((((~member(tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), X!40, F!43), X!40)) | (~member(tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), X!40, F!43), Y!39))) <=> member(tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), X!40, F!43), intersection(X!40, Y!39))) | ((~member(tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), X!40, F!43), X!40)) | (~member(tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), X!40, F!43), Y!39))) | member(tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), X!40, F!43), intersection(X!40, Y!39))),
% 0.47/0.66 inference(tautology,[status(thm)],[])).
% 0.47/0.66 tff(370,plain,
% 0.47/0.66 ((((~member(tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), X!40, F!43), X!40)) | (~member(tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), X!40, F!43), Y!39))) <=> member(tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), X!40, F!43), intersection(X!40, Y!39))) | ((~member(tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), X!40, F!43), X!40)) | (~member(tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), X!40, F!43), Y!39)))),
% 0.47/0.66 inference(unit_resolution,[status(thm)],[369, 368])).
% 0.47/0.66 tff(371,plain,
% 0.47/0.66 ((~member(tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), X!40, F!43), X!40)) | (~member(tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), X!40, F!43), Y!39))),
% 0.47/0.66 inference(unit_resolution,[status(thm)],[370, 350])).
% 0.47/0.66 tff(372,plain,
% 0.47/0.66 ((~((~member(tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), X!40, F!43), X!40)) | (~member(tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), X!40, F!43), Y!39)))) | (~member(tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), X!40, F!43), X!40)) | (~member(tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), X!40, F!43), Y!39))),
% 0.47/0.67 inference(tautology,[status(thm)],[])).
% 0.47/0.67 tff(373,plain,
% 0.47/0.67 ((~((~member(tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), X!40, F!43), X!40)) | (~member(tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), X!40, F!43), Y!39)))) | (~member(tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), X!40, F!43), Y!39))),
% 0.47/0.67 inference(unit_resolution,[status(thm)],[372, 269])).
% 0.47/0.67 tff(374,plain,
% 0.47/0.67 (~member(tptp_fun_X_24(tptp_fun_X_0(image3(F!43, intersection(X!40, Y!39), B!41), intersection(image3(F!43, X!40, B!41), image3(F!43, Y!39, B!41))), X!40, F!43), Y!39)),
% 0.47/0.67 inference(unit_resolution,[status(thm)],[373, 371])).
% 0.47/0.67 tff(375,plain,
% 0.47/0.67 ($false),
% 0.47/0.67 inference(unit_resolution,[status(thm)],[374, 348])).
% 0.47/0.67 % SZS output end Proof
% 0.47/0.67 % E exiting
%------------------------------------------------------------------------------