%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET759+4 : TPTP v9.0.0. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:26:17 AM UTC 2025
% Result : Theorem 0.23s 0.42s
% Output : Proof 0.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : SET759+4 : TPTP v9.0.0. Bugfixed v2.2.1.
% 0.08/0.14 % Command : run_E %s %d THM
% 0.14/0.36 % Computer : n003.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Fri Jun 20 05:41:39 EDT 2025
% 0.14/0.36 % CPUTime :
% 0.23/0.42 % SZS status Theorem
% 0.23/0.42 % SZS output start Proof
% 0.23/0.42 tff(apply_type, type, (
% 0.23/0.42 apply: ( $i * $i * $i ) > $o)).
% 0.23/0.42 tff(tptp_fun_Y_3_type, type, (
% 0.23/0.42 tptp_fun_Y_3: ( $i * $i * $i ) > $i)).
% 0.23/0.42 tff(tptp_fun_F_42_type, type, (
% 0.23/0.42 tptp_fun_F_42: $i)).
% 0.23/0.42 tff(tptp_fun_B_40_type, type, (
% 0.23/0.42 tptp_fun_B_40: $i)).
% 0.23/0.42 tff(tptp_fun_X_0_type, type, (
% 0.23/0.42 tptp_fun_X_0: ( $i * $i ) > $i)).
% 0.23/0.42 tff(tptp_fun_X_39_type, type, (
% 0.23/0.42 tptp_fun_X_39: $i)).
% 0.23/0.42 tff(inverse_image3_type, type, (
% 0.23/0.42 inverse_image3: ( $i * $i * $i ) > $i)).
% 0.23/0.42 tff(tptp_fun_A_41_type, type, (
% 0.23/0.42 tptp_fun_A_41: $i)).
% 0.23/0.42 tff(image3_type, type, (
% 0.23/0.42 image3: ( $i * $i * $i ) > $i)).
% 0.23/0.42 tff(member_type, type, (
% 0.23/0.42 member: ( $i * $i ) > $o)).
% 0.23/0.42 tff(tptp_fun_X_24_type, type, (
% 0.23/0.42 tptp_fun_X_24: ( $i * $i * $i ) > $i)).
% 0.23/0.42 tff(subset_type, type, (
% 0.23/0.42 subset: ( $i * $i ) > $o)).
% 0.23/0.42 tff(tptp_fun_Y_26_type, type, (
% 0.23/0.42 tptp_fun_Y_26: ( $i * $i * $i ) > $i)).
% 0.23/0.42 tff(injective_type, type, (
% 0.23/0.42 injective: ( $i * $i * $i ) > $o)).
% 0.23/0.42 tff(maps_type, type, (
% 0.23/0.42 maps: ( $i * $i * $i ) > $o)).
% 0.23/0.42 tff(equal_set_type, type, (
% 0.23/0.42 equal_set: ( $i * $i ) > $o)).
% 0.23/0.42 tff(tptp_fun_X2_17_type, type, (
% 0.23/0.42 tptp_fun_X2_17: ( $i * $i * $i ) > $i)).
% 0.23/0.42 tff(tptp_fun_X1_18_type, type, (
% 0.23/0.42 tptp_fun_X1_18: ( $i * $i * $i ) > $i)).
% 0.23/0.42 tff(tptp_fun_Y_16_type, type, (
% 0.23/0.42 tptp_fun_Y_16: ( $i * $i * $i ) > $i)).
% 0.23/0.42 tff(tptp_fun_Y2_5_type, type, (
% 0.23/0.42 tptp_fun_Y2_5: ( $i * $i * $i ) > $i)).
% 0.23/0.42 tff(tptp_fun_Y1_6_type, type, (
% 0.23/0.42 tptp_fun_Y1_6: ( $i * $i * $i ) > $i)).
% 0.23/0.42 tff(tptp_fun_X_7_type, type, (
% 0.23/0.42 tptp_fun_X_7: ( $i * $i * $i ) > $i)).
% 0.23/0.42 tff(tptp_fun_X_4_type, type, (
% 0.23/0.42 tptp_fun_X_4: ( $i * $i * $i ) > $i)).
% 0.23/0.42 tff(1,plain,
% 0.23/0.42 (^[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))))))))),
% 0.23/0.43 inference(bind,[status(th)],[])).
% 0.23/0.43 tff(2,plain,
% 0.23/0.43 (![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))))))) <=> ![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)))))))),
% 0.23/0.43 inference(quant_intro,[status(thm)],[1])).
% 0.23/0.43 tff(3,plain,
% 0.23/0.43 (^[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))))))))),
% 0.23/0.43 inference(bind,[status(th)],[])).
% 0.23/0.43 tff(4,plain,
% 0.23/0.43 (![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))))))) <=> ![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)))))))),
% 0.23/0.43 inference(quant_intro,[status(thm)],[3])).
% 0.23/0.43 tff(5,plain,
% 0.23/0.43 (![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))))))) <=> ![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)))))))),
% 0.23/0.43 inference(transitivity,[status(thm)],[4, 2])).
% 0.23/0.43 tff(6,plain,
% 0.23/0.43 (^[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)))))))))),
% 0.23/0.43 inference(bind,[status(th)],[])).
% 0.23/0.43 tff(7,plain,
% 0.23/0.43 (![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))))) <=> ![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)))))))),
% 0.23/0.43 inference(quant_intro,[status(thm)],[6])).
% 0.23/0.43 tff(8,plain,
% 0.23/0.43 (^[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))))))),
% 0.23/0.43 inference(bind,[status(th)],[])).
% 0.23/0.43 tff(9,plain,
% 0.23/0.43 (![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)))))) <=> ![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)))))),
% 0.23/0.43 inference(quant_intro,[status(thm)],[8])).
% 0.23/0.43 tff(10,plain,
% 0.23/0.43 (![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))))),
% 0.23/0.43 inference(rewrite,[status(thm)],[])).
% 0.23/0.43 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/sandbox2/benchmark/Axioms/SET006+1.ax','image3')).
% 0.23/0.43 tff(12,plain,
% 0.23/0.43 (![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))))),
% 0.23/0.43 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.23/0.43 tff(13,plain,(
% 0.23/0.43 ![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))))))),
% 0.23/0.43 inference(skolemize,[status(sab)],[12])).
% 0.23/0.43 tff(14,plain,
% 0.23/0.43 (![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)))))),
% 0.23/0.43 inference(modus_ponens,[status(thm)],[13, 9])).
% 0.23/0.43 tff(15,plain,
% 0.23/0.43 (![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)))))))),
% 0.23/0.43 inference(modus_ponens,[status(thm)],[14, 7])).
% 0.23/0.43 tff(16,plain,
% 0.23/0.43 (![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)))))))),
% 0.23/0.43 inference(modus_ponens,[status(thm)],[15, 5])).
% 0.23/0.43 tff(17,plain,
% 0.23/0.43 (((~![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_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), image3(F!42, X!39, B!40))) | (~((~member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), B!40)) | (~member(tptp_fun_X_24(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), X!39, F!42), X!39)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), X!39, F!42), tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42))))))) | (~((~member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), B!40)) | member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), image3(F!42, X!39, B!40)) | ![X: $i] : ((~member(X, X!39)) | (~apply(F!42, X, tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!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_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), image3(F!42, X!39, B!40))) | (~((~member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), B!40)) | (~member(tptp_fun_X_24(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), X!39, F!42), X!39)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), X!39, F!42), tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42))))))) | (~((~member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), B!40)) | member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), image3(F!42, X!39, B!40)) | ![X: $i] : ((~member(X, X!39)) | (~apply(F!42, X, tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42)))))))))),
% 0.23/0.43 inference(rewrite,[status(thm)],[])).
% 0.23/0.43 tff(18,plain,
% 0.23/0.43 ((~((~((~member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), image3(F!42, X!39, B!40))) | (~((~member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), B!40)) | (~member(tptp_fun_X_24(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), X!39, F!42), X!39)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), X!39, F!42), tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42))))))) | (~(member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), image3(F!42, X!39, B!40)) | (~member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), B!40)) | ![X: $i] : ((~member(X, X!39)) | (~apply(F!42, X, tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42)))))))) <=> (~((~((~member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), image3(F!42, X!39, B!40))) | (~((~member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), B!40)) | (~member(tptp_fun_X_24(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), X!39, F!42), X!39)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), X!39, F!42), tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42))))))) | (~((~member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), B!40)) | member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), image3(F!42, X!39, B!40)) | ![X: $i] : ((~member(X, X!39)) | (~apply(F!42, X, tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42))))))))),
% 0.23/0.43 inference(rewrite,[status(thm)],[])).
% 0.23/0.44 tff(19,plain,
% 0.23/0.44 (((~![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_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), image3(F!42, X!39, B!40))) | (~((~member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), B!40)) | (~member(tptp_fun_X_24(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), X!39, F!42), X!39)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), X!39, F!42), tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42))))))) | (~(member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), image3(F!42, X!39, B!40)) | (~member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), B!40)) | ![X: $i] : ((~member(X, X!39)) | (~apply(F!42, X, tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!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_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), image3(F!42, X!39, B!40))) | (~((~member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), B!40)) | (~member(tptp_fun_X_24(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), X!39, F!42), X!39)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), X!39, F!42), tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42))))))) | (~((~member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), B!40)) | member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), image3(F!42, X!39, B!40)) | ![X: $i] : ((~member(X, X!39)) | (~apply(F!42, X, tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42)))))))))),
% 0.23/0.44 inference(monotonicity,[status(thm)],[18])).
% 0.23/0.44 tff(20,plain,
% 0.23/0.44 (((~![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_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), image3(F!42, X!39, B!40))) | (~((~member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), B!40)) | (~member(tptp_fun_X_24(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), X!39, F!42), X!39)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), X!39, F!42), tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42))))))) | (~(member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), image3(F!42, X!39, B!40)) | (~member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), B!40)) | ![X: $i] : ((~member(X, X!39)) | (~apply(F!42, X, tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!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_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), image3(F!42, X!39, B!40))) | (~((~member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), B!40)) | (~member(tptp_fun_X_24(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), X!39, F!42), X!39)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), X!39, F!42), tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42))))))) | (~((~member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), B!40)) | member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), image3(F!42, X!39, B!40)) | ![X: $i] : ((~member(X, X!39)) | (~apply(F!42, X, tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42)))))))))),
% 0.23/0.44 inference(transitivity,[status(thm)],[19, 17])).
% 0.23/0.44 tff(21,plain,
% 0.23/0.44 ((~![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_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), image3(F!42, X!39, B!40))) | (~((~member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), B!40)) | (~member(tptp_fun_X_24(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), X!39, F!42), X!39)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), X!39, F!42), tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42))))))) | (~(member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), image3(F!42, X!39, B!40)) | (~member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), B!40)) | ![X: $i] : ((~member(X, X!39)) | (~apply(F!42, X, tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42))))))))),
% 0.23/0.44 inference(quant_inst,[status(thm)],[])).
% 0.23/0.44 tff(22,plain,
% 0.23/0.44 ((~![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_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), image3(F!42, X!39, B!40))) | (~((~member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), B!40)) | (~member(tptp_fun_X_24(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), X!39, F!42), X!39)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), X!39, F!42), tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42))))))) | (~((~member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), B!40)) | member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), image3(F!42, X!39, B!40)) | ![X: $i] : ((~member(X, X!39)) | (~apply(F!42, X, tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42))))))))),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.23/0.45 tff(23,plain,
% 0.23/0.45 (~((~((~member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), image3(F!42, X!39, B!40))) | (~((~member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), B!40)) | (~member(tptp_fun_X_24(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), X!39, F!42), X!39)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), X!39, F!42), tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42))))))) | (~((~member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), B!40)) | member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), image3(F!42, X!39, B!40)) | ![X: $i] : ((~member(X, X!39)) | (~apply(F!42, X, tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42)))))))),
% 0.23/0.45 inference(unit_resolution,[status(thm)],[22, 16])).
% 0.23/0.45 tff(24,plain,
% 0.23/0.45 (((~((~member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), image3(F!42, X!39, B!40))) | (~((~member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), B!40)) | (~member(tptp_fun_X_24(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), X!39, F!42), X!39)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), X!39, F!42), tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42))))))) | (~((~member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), B!40)) | member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), image3(F!42, X!39, B!40)) | ![X: $i] : ((~member(X, X!39)) | (~apply(F!42, X, tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42))))))) | ((~member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), B!40)) | member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), image3(F!42, X!39, B!40)) | ![X: $i] : ((~member(X, X!39)) | (~apply(F!42, X, tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42)))))),
% 0.23/0.45 inference(tautology,[status(thm)],[])).
% 0.23/0.45 tff(25,plain,
% 0.23/0.45 ((~member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), B!40)) | member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), image3(F!42, X!39, B!40)) | ![X: $i] : ((~member(X, X!39)) | (~apply(F!42, X, tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42))))),
% 0.23/0.45 inference(unit_resolution,[status(thm)],[24, 23])).
% 0.23/0.45 tff(26,plain,
% 0.23/0.45 (^[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))))))))),
% 0.23/0.45 inference(bind,[status(th)],[])).
% 0.23/0.45 tff(27,plain,
% 0.23/0.45 (![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)))))))),
% 0.23/0.45 inference(quant_intro,[status(thm)],[26])).
% 0.23/0.45 tff(28,plain,
% 0.23/0.45 (^[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))))))))),
% 0.23/0.45 inference(bind,[status(th)],[])).
% 0.23/0.45 tff(29,plain,
% 0.23/0.45 (![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)))))))),
% 0.23/0.45 inference(quant_intro,[status(thm)],[28])).
% 0.23/0.45 tff(30,plain,
% 0.23/0.45 (![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)))))))),
% 0.23/0.45 inference(transitivity,[status(thm)],[29, 27])).
% 0.23/0.45 tff(31,plain,
% 0.23/0.45 (^[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)))))))))),
% 0.23/0.45 inference(bind,[status(th)],[])).
% 0.23/0.45 tff(32,plain,
% 0.23/0.45 (![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)))))))),
% 0.23/0.45 inference(quant_intro,[status(thm)],[31])).
% 0.23/0.45 tff(33,plain,
% 0.23/0.45 (![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)))),
% 0.23/0.45 inference(rewrite,[status(thm)],[])).
% 0.23/0.45 tff(34,plain,
% 0.23/0.45 (^[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))))),
% 0.23/0.45 inference(bind,[status(th)],[])).
% 0.23/0.45 tff(35,plain,
% 0.23/0.45 (![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)))),
% 0.23/0.45 inference(quant_intro,[status(thm)],[34])).
% 0.23/0.45 tff(36,axiom,(![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : (member(X, A) => member(X, B)))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax','subset')).
% 0.23/0.45 tff(37,plain,
% 0.23/0.45 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.23/0.45 tff(38,plain,
% 0.23/0.45 (![A: $i, B: $i] : (subset(A, B) <=> ![X: $i] : ((~member(X, A)) | member(X, B)))),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[37, 33])).
% 0.23/0.45 tff(39,plain,(
% 0.23/0.45 ![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)))))),
% 0.23/0.45 inference(skolemize,[status(sab)],[38])).
% 0.23/0.45 tff(40,plain,
% 0.23/0.45 (![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)))))))),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[39, 32])).
% 0.23/0.45 tff(41,plain,
% 0.23/0.45 (![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)))))))),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[40, 30])).
% 0.23/0.45 tff(42,plain,
% 0.23/0.45 ((~![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(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))) | ![X: $i] : ((~member(X, X!39)) | member(X, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))))) | (~(subset(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)) | (~((~member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), X!39)) | member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))))))))),
% 0.23/0.45 inference(quant_inst,[status(thm)],[])).
% 0.23/0.45 tff(43,plain,
% 0.23/0.45 (~((~((~subset(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))) | ![X: $i] : ((~member(X, X!39)) | member(X, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))))) | (~(subset(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)) | (~((~member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), X!39)) | member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)))))))),
% 0.23/0.45 inference(unit_resolution,[status(thm)],[42, 41])).
% 0.23/0.45 tff(44,plain,
% 0.23/0.45 (((~((~subset(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))) | ![X: $i] : ((~member(X, X!39)) | member(X, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))))) | (~(subset(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)) | (~((~member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), X!39)) | member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))))))) | (subset(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)) | (~((~member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), X!39)) | member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)))))),
% 0.23/0.45 inference(tautology,[status(thm)],[])).
% 0.23/0.45 tff(45,plain,
% 0.23/0.45 (subset(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)) | (~((~member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), X!39)) | member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))))),
% 0.23/0.45 inference(unit_resolution,[status(thm)],[44, 43])).
% 0.23/0.45 tff(46,assumption,((~((~subset(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39)) | ![X: $i] : ((~member(X, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))) | member(X, X!39)))) | (~(subset(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39) | (~((~member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))) | member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), X!39)))))), introduced(assumption)).
% 0.23/0.46 tff(47,plain,
% 0.23/0.46 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![X: $i] : ((~member(X, A)) | member(X, B)))) | (~(subset(A, B) | (~((~member(tptp_fun_X_0(B, A), A)) | member(tptp_fun_X_0(B, A), B)))))))) | (~((~((~subset(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39)) | ![X: $i] : ((~member(X, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))) | member(X, X!39)))) | (~(subset(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39) | (~((~member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))) | member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), X!39)))))))),
% 0.23/0.46 inference(quant_inst,[status(thm)],[])).
% 0.23/0.46 tff(48,plain,
% 0.23/0.46 ($false),
% 0.23/0.46 inference(unit_resolution,[status(thm)],[47, 41, 46])).
% 0.23/0.46 tff(49,plain,(~((~((~subset(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39)) | ![X: $i] : ((~member(X, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))) | member(X, X!39)))) | (~(subset(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39) | (~((~member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))) | member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), X!39))))))), inference(lemma,lemma(discharge,[]))).
% 0.23/0.46 tff(50,plain,
% 0.23/0.46 (((~((~subset(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39)) | ![X: $i] : ((~member(X, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))) | member(X, X!39)))) | (~(subset(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39) | (~((~member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))) | member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), X!39)))))) | (subset(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39) | (~((~member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))) | member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), X!39))))),
% 0.23/0.46 inference(tautology,[status(thm)],[])).
% 0.23/0.46 tff(51,plain,
% 0.23/0.46 (subset(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39) | (~((~member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))) | member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), X!39)))),
% 0.23/0.46 inference(unit_resolution,[status(thm)],[50, 49])).
% 0.23/0.46 tff(52,plain,
% 0.23/0.46 (((~![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_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), image3(F!42, X!39, B!40))) | (~((~member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), B!40)) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), X!39)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42))))))) | (~(member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), image3(F!42, X!39, B!40)) | ![X: $i] : ((~member(X, X!39)) | (~apply(F!42, X, tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42)))) | (~member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), B!40))))))) <=> ((~![F: $i, A: $i, B: $i, Y: $i] : (~((~((~member(Y, image3(F, A, B))) | (~((~member(Y, B)) | (~member(tptp_fun_X_24(Y, A, F), A)) | (~apply(F, tptp_fun_X_24(Y, A, F), Y)))))) | (~(member(Y, image3(F, A, B)) | (~member(Y, B)) | ![X: $i] : ((~member(X, A)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), image3(F!42, X!39, B!40))) | (~((~member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), B!40)) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), X!39)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42))))))) | (~(member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), image3(F!42, X!39, B!40)) | ![X: $i] : ((~member(X, X!39)) | (~apply(F!42, X, tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42)))) | (~member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), B!40)))))))),
% 0.23/0.46 inference(rewrite,[status(thm)],[])).
% 0.23/0.46 tff(53,plain,
% 0.23/0.46 ((~((~((~member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), image3(F!42, X!39, B!40))) | (~((~member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), B!40)) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), X!39)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42))))))) | (~(member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), image3(F!42, X!39, B!40)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), B!40)) | ![X: $i] : ((~member(X, X!39)) | (~apply(F!42, X, tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42)))))))) <=> (~((~((~member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), image3(F!42, X!39, B!40))) | (~((~member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), B!40)) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), X!39)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42))))))) | (~(member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), image3(F!42, X!39, B!40)) | ![X: $i] : ((~member(X, X!39)) | (~apply(F!42, X, tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42)))) | (~member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), B!40))))))),
% 0.23/0.47 inference(rewrite,[status(thm)],[])).
% 0.23/0.47 tff(54,plain,
% 0.23/0.47 (((~![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_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), image3(F!42, X!39, B!40))) | (~((~member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), B!40)) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), X!39)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42))))))) | (~(member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), image3(F!42, X!39, B!40)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), B!40)) | ![X: $i] : ((~member(X, X!39)) | (~apply(F!42, X, tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!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_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), image3(F!42, X!39, B!40))) | (~((~member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), B!40)) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), X!39)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42))))))) | (~(member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), image3(F!42, X!39, B!40)) | ![X: $i] : ((~member(X, X!39)) | (~apply(F!42, X, tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42)))) | (~member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), B!40)))))))),
% 0.23/0.47 inference(monotonicity,[status(thm)],[53])).
% 0.23/0.47 tff(55,plain,
% 0.23/0.47 (((~![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_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), image3(F!42, X!39, B!40))) | (~((~member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), B!40)) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), X!39)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42))))))) | (~(member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), image3(F!42, X!39, B!40)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), B!40)) | ![X: $i] : ((~member(X, X!39)) | (~apply(F!42, X, tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!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_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), image3(F!42, X!39, B!40))) | (~((~member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), B!40)) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), X!39)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42))))))) | (~(member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), image3(F!42, X!39, B!40)) | ![X: $i] : ((~member(X, X!39)) | (~apply(F!42, X, tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42)))) | (~member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), B!40)))))))),
% 0.23/0.47 inference(transitivity,[status(thm)],[54, 52])).
% 0.23/0.47 tff(56,plain,
% 0.23/0.47 ((~![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_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), image3(F!42, X!39, B!40))) | (~((~member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), B!40)) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), X!39)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42))))))) | (~(member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), image3(F!42, X!39, B!40)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), B!40)) | ![X: $i] : ((~member(X, X!39)) | (~apply(F!42, X, tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42))))))))),
% 0.23/0.47 inference(quant_inst,[status(thm)],[])).
% 0.23/0.47 tff(57,plain,
% 0.23/0.47 ((~![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_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), image3(F!42, X!39, B!40))) | (~((~member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), B!40)) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), X!39)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42))))))) | (~(member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), image3(F!42, X!39, B!40)) | ![X: $i] : ((~member(X, X!39)) | (~apply(F!42, X, tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42)))) | (~member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), B!40))))))),
% 0.23/0.48 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.23/0.48 tff(58,plain,
% 0.23/0.48 (~((~((~member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), image3(F!42, X!39, B!40))) | (~((~member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), B!40)) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), X!39)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42))))))) | (~(member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), image3(F!42, X!39, B!40)) | ![X: $i] : ((~member(X, X!39)) | (~apply(F!42, X, tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42)))) | (~member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), B!40)))))),
% 0.23/0.48 inference(unit_resolution,[status(thm)],[57, 16])).
% 0.23/0.48 tff(59,plain,
% 0.23/0.48 (((~((~member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), image3(F!42, X!39, B!40))) | (~((~member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), B!40)) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), X!39)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42))))))) | (~(member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), image3(F!42, X!39, B!40)) | ![X: $i] : ((~member(X, X!39)) | (~apply(F!42, X, tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42)))) | (~member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), B!40))))) | ((~member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), image3(F!42, X!39, B!40))) | (~((~member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), B!40)) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), X!39)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42))))))),
% 0.23/0.48 inference(tautology,[status(thm)],[])).
% 0.23/0.48 tff(60,plain,
% 0.23/0.48 ((~member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), image3(F!42, X!39, B!40))) | (~((~member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), B!40)) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), X!39)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42)))))),
% 0.23/0.48 inference(unit_resolution,[status(thm)],[59, 58])).
% 0.23/0.48 tff(61,plain,
% 0.23/0.48 (^[F: $i, B: $i, A: $i, X: $i] : refl((~((~((~member(X, inverse_image3(F, B, A))) | (~((~member(X, A)) | (~member(tptp_fun_Y_26(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_26(X, B, F))))))) | (~(member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y))))))) <=> (~((~((~member(X, inverse_image3(F, B, A))) | (~((~member(X, A)) | (~member(tptp_fun_Y_26(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_26(X, B, F))))))) | (~(member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y))))))))),
% 0.23/0.48 inference(bind,[status(th)],[])).
% 0.23/0.48 tff(62,plain,
% 0.23/0.48 (![F: $i, B: $i, A: $i, X: $i] : (~((~((~member(X, inverse_image3(F, B, A))) | (~((~member(X, A)) | (~member(tptp_fun_Y_26(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_26(X, B, F))))))) | (~(member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y))))))) <=> ![F: $i, B: $i, A: $i, X: $i] : (~((~((~member(X, inverse_image3(F, B, A))) | (~((~member(X, A)) | (~member(tptp_fun_Y_26(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_26(X, B, F))))))) | (~(member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))),
% 0.23/0.48 inference(quant_intro,[status(thm)],[61])).
% 0.23/0.48 tff(63,plain,
% 0.23/0.48 (^[F: $i, B: $i, A: $i, X: $i] : rewrite((~((~((~member(X, inverse_image3(F, B, A))) | (~((~member(X, A)) | (~member(tptp_fun_Y_26(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_26(X, B, F))))))) | (~(member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y))))))) <=> (~((~((~member(X, inverse_image3(F, B, A))) | (~((~member(X, A)) | (~member(tptp_fun_Y_26(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_26(X, B, F))))))) | (~(member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y))))))))),
% 0.23/0.48 inference(bind,[status(th)],[])).
% 0.23/0.48 tff(64,plain,
% 0.23/0.48 (![F: $i, B: $i, A: $i, X: $i] : (~((~((~member(X, inverse_image3(F, B, A))) | (~((~member(X, A)) | (~member(tptp_fun_Y_26(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_26(X, B, F))))))) | (~(member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y))))))) <=> ![F: $i, B: $i, A: $i, X: $i] : (~((~((~member(X, inverse_image3(F, B, A))) | (~((~member(X, A)) | (~member(tptp_fun_Y_26(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_26(X, B, F))))))) | (~(member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))),
% 0.23/0.48 inference(quant_intro,[status(thm)],[63])).
% 0.23/0.48 tff(65,plain,
% 0.23/0.48 (![F: $i, B: $i, A: $i, X: $i] : (~((~((~member(X, inverse_image3(F, B, A))) | (~((~member(X, A)) | (~member(tptp_fun_Y_26(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_26(X, B, F))))))) | (~(member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y))))))) <=> ![F: $i, B: $i, A: $i, X: $i] : (~((~((~member(X, inverse_image3(F, B, A))) | (~((~member(X, A)) | (~member(tptp_fun_Y_26(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_26(X, B, F))))))) | (~(member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))),
% 0.23/0.48 inference(transitivity,[status(thm)],[64, 62])).
% 0.23/0.48 tff(66,plain,
% 0.23/0.48 (^[F: $i, B: $i, A: $i, X: $i] : trans(monotonicity(rewrite(((~member(X, inverse_image3(F, B, A))) | (member(X, A) & member(tptp_fun_Y_26(X, B, F), B) & apply(F, X, tptp_fun_Y_26(X, B, F)))) <=> ((~member(X, inverse_image3(F, B, A))) | (~((~member(X, A)) | (~member(tptp_fun_Y_26(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_26(X, B, F))))))), trans(monotonicity(quant_intro(proof_bind(^[Y: $i] : trans(monotonicity(rewrite((member(Y, B) & apply(F, X, Y)) <=> (~((~member(Y, B)) | (~apply(F, X, Y))))), ((~(member(Y, B) & apply(F, X, Y))) <=> (~(~((~member(Y, B)) | (~apply(F, X, Y))))))), rewrite((~(~((~member(Y, B)) | (~apply(F, X, Y))))) <=> ((~member(Y, B)) | (~apply(F, X, Y)))), ((~(member(Y, B) & apply(F, X, Y))) <=> ((~member(Y, B)) | (~apply(F, X, Y)))))), (![Y: $i] : (~(member(Y, B) & apply(F, X, Y))) <=> ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y))))), ((member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y)))) <=> (member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))), rewrite((member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))) <=> (member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y))))), ((member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y)))) <=> (member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))), ((((~member(X, inverse_image3(F, B, A))) | (member(X, A) & member(tptp_fun_Y_26(X, B, F), B) & apply(F, X, tptp_fun_Y_26(X, B, F)))) & (member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y))))) <=> (((~member(X, inverse_image3(F, B, A))) | (~((~member(X, A)) | (~member(tptp_fun_Y_26(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_26(X, B, F)))))) & (member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y))))))), rewrite((((~member(X, inverse_image3(F, B, A))) | (~((~member(X, A)) | (~member(tptp_fun_Y_26(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_26(X, B, F)))))) & (member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y))))) <=> (~((~((~member(X, inverse_image3(F, B, A))) | (~((~member(X, A)) | (~member(tptp_fun_Y_26(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_26(X, B, F))))))) | (~(member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))), ((((~member(X, inverse_image3(F, B, A))) | (member(X, A) & member(tptp_fun_Y_26(X, B, F), B) & apply(F, X, tptp_fun_Y_26(X, B, F)))) & (member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y))))) <=> (~((~((~member(X, inverse_image3(F, B, A))) | (~((~member(X, A)) | (~member(tptp_fun_Y_26(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_26(X, B, F))))))) | (~(member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))))),
% 0.23/0.48 inference(bind,[status(th)],[])).
% 0.23/0.48 tff(67,plain,
% 0.23/0.48 (![F: $i, B: $i, A: $i, X: $i] : (((~member(X, inverse_image3(F, B, A))) | (member(X, A) & member(tptp_fun_Y_26(X, B, F), B) & apply(F, X, tptp_fun_Y_26(X, B, F)))) & (member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y))))) <=> ![F: $i, B: $i, A: $i, X: $i] : (~((~((~member(X, inverse_image3(F, B, A))) | (~((~member(X, A)) | (~member(tptp_fun_Y_26(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_26(X, B, F))))))) | (~(member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))),
% 0.23/0.48 inference(quant_intro,[status(thm)],[66])).
% 0.23/0.48 tff(68,plain,
% 0.23/0.48 (^[F: $i, B: $i, A: $i, X: $i] : rewrite((((~member(X, inverse_image3(F, B, A))) | (member(X, A) & (member(tptp_fun_Y_26(X, B, F), B) & apply(F, X, tptp_fun_Y_26(X, B, F))))) & (member(X, inverse_image3(F, B, A)) | ((~member(X, A)) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y)))))) <=> (((~member(X, inverse_image3(F, B, A))) | (member(X, A) & member(tptp_fun_Y_26(X, B, F), B) & apply(F, X, tptp_fun_Y_26(X, B, F)))) & (member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y))))))),
% 0.23/0.48 inference(bind,[status(th)],[])).
% 0.23/0.48 tff(69,plain,
% 0.23/0.48 (![F: $i, B: $i, A: $i, X: $i] : (((~member(X, inverse_image3(F, B, A))) | (member(X, A) & (member(tptp_fun_Y_26(X, B, F), B) & apply(F, X, tptp_fun_Y_26(X, B, F))))) & (member(X, inverse_image3(F, B, A)) | ((~member(X, A)) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y)))))) <=> ![F: $i, B: $i, A: $i, X: $i] : (((~member(X, inverse_image3(F, B, A))) | (member(X, A) & member(tptp_fun_Y_26(X, B, F), B) & apply(F, X, tptp_fun_Y_26(X, B, F)))) & (member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y)))))),
% 0.23/0.48 inference(quant_intro,[status(thm)],[68])).
% 0.23/0.48 tff(70,plain,
% 0.23/0.48 (![F: $i, B: $i, A: $i, X: $i] : (member(X, inverse_image3(F, B, A)) <=> (member(X, A) & ?[Y: $i] : (member(Y, B) & apply(F, X, Y)))) <=> ![F: $i, B: $i, A: $i, X: $i] : (member(X, inverse_image3(F, B, A)) <=> (member(X, A) & ?[Y: $i] : (member(Y, B) & apply(F, X, Y))))),
% 0.23/0.48 inference(rewrite,[status(thm)],[])).
% 0.23/0.48 tff(71,axiom,(![F: $i, B: $i, A: $i, X: $i] : (member(X, inverse_image3(F, B, A)) <=> (member(X, A) & ?[Y: $i] : (member(Y, B) & apply(F, X, Y))))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+1.ax','inverse_image3')).
% 0.23/0.48 tff(72,plain,
% 0.23/0.48 (![F: $i, B: $i, A: $i, X: $i] : (member(X, inverse_image3(F, B, A)) <=> (member(X, A) & ?[Y: $i] : (member(Y, B) & apply(F, X, Y))))),
% 0.23/0.48 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.23/0.48 tff(73,plain,(
% 0.23/0.48 ![F: $i, B: $i, A: $i, X: $i] : (((~member(X, inverse_image3(F, B, A))) | (member(X, A) & (member(tptp_fun_Y_26(X, B, F), B) & apply(F, X, tptp_fun_Y_26(X, B, F))))) & (member(X, inverse_image3(F, B, A)) | ((~member(X, A)) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y))))))),
% 0.23/0.48 inference(skolemize,[status(sab)],[72])).
% 0.23/0.48 tff(74,plain,
% 0.23/0.48 (![F: $i, B: $i, A: $i, X: $i] : (((~member(X, inverse_image3(F, B, A))) | (member(X, A) & member(tptp_fun_Y_26(X, B, F), B) & apply(F, X, tptp_fun_Y_26(X, B, F)))) & (member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y)))))),
% 0.23/0.48 inference(modus_ponens,[status(thm)],[73, 69])).
% 0.23/0.48 tff(75,plain,
% 0.23/0.48 (![F: $i, B: $i, A: $i, X: $i] : (~((~((~member(X, inverse_image3(F, B, A))) | (~((~member(X, A)) | (~member(tptp_fun_Y_26(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_26(X, B, F))))))) | (~(member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))),
% 0.23/0.48 inference(modus_ponens,[status(thm)],[74, 67])).
% 0.23/0.48 tff(76,plain,
% 0.23/0.48 (![F: $i, B: $i, A: $i, X: $i] : (~((~((~member(X, inverse_image3(F, B, A))) | (~((~member(X, A)) | (~member(tptp_fun_Y_26(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_26(X, B, F))))))) | (~(member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))),
% 0.23/0.48 inference(modus_ponens,[status(thm)],[75, 65])).
% 0.23/0.48 tff(77,plain,
% 0.23/0.48 (((~![F: $i, B: $i, A: $i, X: $i] : (~((~((~member(X, inverse_image3(F, B, A))) | (~((~member(X, A)) | (~member(tptp_fun_Y_26(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_26(X, B, F))))))) | (~(member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))) | (~((~member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), A!41)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), image3(F!42, X!39, B!40))) | (~apply(F!42, tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42))))))) | (~(member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)) | ![Y: $i] : ((~member(Y, image3(F!42, X!39, B!40))) | (~apply(F!42, tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), Y))) | (~member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), A!41))))))) <=> ((~![F: $i, B: $i, A: $i, X: $i] : (~((~((~member(X, inverse_image3(F, B, A))) | (~((~member(X, A)) | (~member(tptp_fun_Y_26(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_26(X, B, F))))))) | (~(member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))) | (~((~member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), A!41)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), image3(F!42, X!39, B!40))) | (~apply(F!42, tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42))))))) | (~(member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)) | ![Y: $i] : ((~member(Y, image3(F!42, X!39, B!40))) | (~apply(F!42, tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), Y))) | (~member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), A!41)))))))),
% 0.23/0.49 inference(rewrite,[status(thm)],[])).
% 0.23/0.49 tff(78,plain,
% 0.23/0.49 ((~((~((~member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))) | (~((~member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), A!41)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), image3(F!42, X!39, B!40))) | (~apply(F!42, tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42))))))) | (~(member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)) | (~member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), A!41)) | ![Y: $i] : ((~member(Y, image3(F!42, X!39, B!40))) | (~apply(F!42, tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), Y))))))) <=> (~((~((~member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))) | (~((~member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), A!41)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), image3(F!42, X!39, B!40))) | (~apply(F!42, tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42))))))) | (~(member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)) | ![Y: $i] : ((~member(Y, image3(F!42, X!39, B!40))) | (~apply(F!42, tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), Y))) | (~member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), A!41))))))),
% 0.23/0.49 inference(rewrite,[status(thm)],[])).
% 0.23/0.49 tff(79,plain,
% 0.23/0.49 (((~![F: $i, B: $i, A: $i, X: $i] : (~((~((~member(X, inverse_image3(F, B, A))) | (~((~member(X, A)) | (~member(tptp_fun_Y_26(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_26(X, B, F))))))) | (~(member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))) | (~((~member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), A!41)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), image3(F!42, X!39, B!40))) | (~apply(F!42, tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42))))))) | (~(member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)) | (~member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), A!41)) | ![Y: $i] : ((~member(Y, image3(F!42, X!39, B!40))) | (~apply(F!42, tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), Y)))))))) <=> ((~![F: $i, B: $i, A: $i, X: $i] : (~((~((~member(X, inverse_image3(F, B, A))) | (~((~member(X, A)) | (~member(tptp_fun_Y_26(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_26(X, B, F))))))) | (~(member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))) | (~((~member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), A!41)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), image3(F!42, X!39, B!40))) | (~apply(F!42, tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42))))))) | (~(member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)) | ![Y: $i] : ((~member(Y, image3(F!42, X!39, B!40))) | (~apply(F!42, tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), Y))) | (~member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), A!41)))))))),
% 0.23/0.49 inference(monotonicity,[status(thm)],[78])).
% 0.23/0.49 tff(80,plain,
% 0.23/0.49 (((~![F: $i, B: $i, A: $i, X: $i] : (~((~((~member(X, inverse_image3(F, B, A))) | (~((~member(X, A)) | (~member(tptp_fun_Y_26(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_26(X, B, F))))))) | (~(member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))) | (~((~member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), A!41)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), image3(F!42, X!39, B!40))) | (~apply(F!42, tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42))))))) | (~(member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)) | (~member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), A!41)) | ![Y: $i] : ((~member(Y, image3(F!42, X!39, B!40))) | (~apply(F!42, tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), Y)))))))) <=> ((~![F: $i, B: $i, A: $i, X: $i] : (~((~((~member(X, inverse_image3(F, B, A))) | (~((~member(X, A)) | (~member(tptp_fun_Y_26(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_26(X, B, F))))))) | (~(member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))) | (~((~member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), A!41)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), image3(F!42, X!39, B!40))) | (~apply(F!42, tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42))))))) | (~(member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)) | ![Y: $i] : ((~member(Y, image3(F!42, X!39, B!40))) | (~apply(F!42, tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), Y))) | (~member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), A!41)))))))),
% 0.23/0.49 inference(transitivity,[status(thm)],[79, 77])).
% 0.23/0.49 tff(81,plain,
% 0.23/0.49 ((~![F: $i, B: $i, A: $i, X: $i] : (~((~((~member(X, inverse_image3(F, B, A))) | (~((~member(X, A)) | (~member(tptp_fun_Y_26(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_26(X, B, F))))))) | (~(member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))) | (~((~member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), A!41)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), image3(F!42, X!39, B!40))) | (~apply(F!42, tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42))))))) | (~(member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)) | (~member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), A!41)) | ![Y: $i] : ((~member(Y, image3(F!42, X!39, B!40))) | (~apply(F!42, tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), Y)))))))),
% 0.23/0.49 inference(quant_inst,[status(thm)],[])).
% 0.23/0.49 tff(82,plain,
% 0.23/0.49 ((~![F: $i, B: $i, A: $i, X: $i] : (~((~((~member(X, inverse_image3(F, B, A))) | (~((~member(X, A)) | (~member(tptp_fun_Y_26(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_26(X, B, F))))))) | (~(member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))) | (~((~member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), A!41)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), image3(F!42, X!39, B!40))) | (~apply(F!42, tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42))))))) | (~(member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)) | ![Y: $i] : ((~member(Y, image3(F!42, X!39, B!40))) | (~apply(F!42, tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), Y))) | (~member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), A!41))))))),
% 0.23/0.49 inference(modus_ponens,[status(thm)],[81, 80])).
% 0.23/0.49 tff(83,plain,
% 0.23/0.49 (~((~((~member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))) | (~((~member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), A!41)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), image3(F!42, X!39, B!40))) | (~apply(F!42, tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42))))))) | (~(member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)) | ![Y: $i] : ((~member(Y, image3(F!42, X!39, B!40))) | (~apply(F!42, tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), Y))) | (~member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), A!41)))))),
% 0.23/0.49 inference(unit_resolution,[status(thm)],[82, 76])).
% 0.23/0.49 tff(84,plain,
% 0.23/0.49 (((~((~member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))) | (~((~member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), A!41)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), image3(F!42, X!39, B!40))) | (~apply(F!42, tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42))))))) | (~(member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)) | ![Y: $i] : ((~member(Y, image3(F!42, X!39, B!40))) | (~apply(F!42, tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), Y))) | (~member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), A!41))))) | ((~member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))) | (~((~member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), A!41)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), image3(F!42, X!39, B!40))) | (~apply(F!42, tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42))))))),
% 0.23/0.49 inference(tautology,[status(thm)],[])).
% 0.23/0.49 tff(85,plain,
% 0.23/0.49 ((~member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))) | (~((~member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), A!41)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), image3(F!42, X!39, B!40))) | (~apply(F!42, tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42)))))),
% 0.23/0.49 inference(unit_resolution,[status(thm)],[84, 83])).
% 0.23/0.49 tff(86,assumption,(~((~member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))) | member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), X!39))), introduced(assumption)).
% 0.23/0.49 tff(87,plain,
% 0.23/0.49 (((~member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))) | member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), X!39)) | member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))),
% 0.23/0.50 inference(tautology,[status(thm)],[])).
% 0.23/0.50 tff(88,plain,
% 0.23/0.50 (member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))),
% 0.23/0.50 inference(unit_resolution,[status(thm)],[87, 86])).
% 0.23/0.50 tff(89,plain,
% 0.23/0.50 ((~((~member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))) | (~((~member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), A!41)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), image3(F!42, X!39, B!40))) | (~apply(F!42, tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42))))))) | (~member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))) | (~((~member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), A!41)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), image3(F!42, X!39, B!40))) | (~apply(F!42, tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42)))))),
% 0.23/0.50 inference(tautology,[status(thm)],[])).
% 0.23/0.50 tff(90,plain,
% 0.23/0.50 ((~((~member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))) | (~((~member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), A!41)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), image3(F!42, X!39, B!40))) | (~apply(F!42, tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42))))))) | (~((~member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), A!41)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), image3(F!42, X!39, B!40))) | (~apply(F!42, tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42)))))),
% 0.23/0.50 inference(unit_resolution,[status(thm)],[89, 88])).
% 0.23/0.50 tff(91,plain,
% 0.23/0.50 (~((~member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), A!41)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), image3(F!42, X!39, B!40))) | (~apply(F!42, tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42))))),
% 0.23/0.50 inference(unit_resolution,[status(thm)],[90, 85])).
% 0.23/0.50 tff(92,plain,
% 0.23/0.50 (((~member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), A!41)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), image3(F!42, X!39, B!40))) | (~apply(F!42, tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42)))) | member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), image3(F!42, X!39, B!40))),
% 0.23/0.50 inference(tautology,[status(thm)],[])).
% 0.23/0.50 tff(93,plain,
% 0.23/0.50 (member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), image3(F!42, X!39, B!40))),
% 0.23/0.50 inference(unit_resolution,[status(thm)],[92, 91])).
% 0.23/0.50 tff(94,plain,
% 0.23/0.50 ((~((~member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), image3(F!42, X!39, B!40))) | (~((~member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), B!40)) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), X!39)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42))))))) | (~member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), image3(F!42, X!39, B!40))) | (~((~member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), B!40)) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), X!39)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42)))))),
% 0.23/0.50 inference(tautology,[status(thm)],[])).
% 0.23/0.50 tff(95,plain,
% 0.23/0.50 ((~((~member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), image3(F!42, X!39, B!40))) | (~((~member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), B!40)) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), X!39)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42))))))) | (~((~member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), B!40)) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), X!39)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42)))))),
% 0.23/0.50 inference(unit_resolution,[status(thm)],[94, 93])).
% 0.23/0.50 tff(96,plain,
% 0.23/0.50 (~((~member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), B!40)) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), X!39)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42))))),
% 0.23/0.50 inference(unit_resolution,[status(thm)],[95, 60])).
% 0.23/0.50 tff(97,plain,
% 0.23/0.50 (((~member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), B!40)) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), X!39)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42)))) | member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), X!39)),
% 0.23/0.50 inference(tautology,[status(thm)],[])).
% 0.23/0.50 tff(98,plain,
% 0.23/0.50 (member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), X!39)),
% 0.23/0.50 inference(unit_resolution,[status(thm)],[97, 96])).
% 0.23/0.50 tff(99,plain,
% 0.23/0.50 ((~![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(X!39, A!41)) | ![X: $i] : ((~member(X, X!39)) | member(X, A!41)))) | (~(subset(X!39, A!41) | (~((~member(tptp_fun_X_0(A!41, X!39), X!39)) | member(tptp_fun_X_0(A!41, X!39), A!41)))))))),
% 0.23/0.50 inference(quant_inst,[status(thm)],[])).
% 0.23/0.50 tff(100,plain,
% 0.23/0.50 (~((~((~subset(X!39, A!41)) | ![X: $i] : ((~member(X, X!39)) | member(X, A!41)))) | (~(subset(X!39, A!41) | (~((~member(tptp_fun_X_0(A!41, X!39), X!39)) | member(tptp_fun_X_0(A!41, X!39), A!41))))))),
% 0.23/0.50 inference(unit_resolution,[status(thm)],[99, 41])).
% 0.23/0.50 tff(101,plain,
% 0.23/0.50 (((~((~subset(X!39, A!41)) | ![X: $i] : ((~member(X, X!39)) | member(X, A!41)))) | (~(subset(X!39, A!41) | (~((~member(tptp_fun_X_0(A!41, X!39), X!39)) | member(tptp_fun_X_0(A!41, X!39), A!41)))))) | ((~subset(X!39, A!41)) | ![X: $i] : ((~member(X, X!39)) | member(X, A!41)))),
% 0.23/0.50 inference(tautology,[status(thm)],[])).
% 0.23/0.50 tff(102,plain,
% 0.23/0.50 ((~subset(X!39, A!41)) | ![X: $i] : ((~member(X, X!39)) | member(X, A!41))),
% 0.23/0.50 inference(unit_resolution,[status(thm)],[101, 100])).
% 0.23/0.50 tff(103,plain,
% 0.23/0.50 ((~![F: $i, A: $i, B: $i, X: $i] : ((~(maps(F, A, B) & injective(F, A, B) & subset(X, A))) | equal_set(inverse_image3(F, image3(F, X, B), A), X))) <=> (~![F: $i, A: $i, B: $i, X: $i] : ((~(maps(F, A, B) & injective(F, A, B) & subset(X, A))) | equal_set(inverse_image3(F, image3(F, X, B), A), X)))),
% 0.23/0.50 inference(rewrite,[status(thm)],[])).
% 0.23/0.50 tff(104,plain,
% 0.23/0.50 ((~![F: $i, A: $i, B: $i, X: $i] : (((maps(F, A, B) & injective(F, A, B)) & subset(X, A)) => equal_set(inverse_image3(F, image3(F, X, B), A), X))) <=> (~![F: $i, A: $i, B: $i, X: $i] : ((~(maps(F, A, B) & injective(F, A, B) & subset(X, A))) | equal_set(inverse_image3(F, image3(F, X, B), A), X)))),
% 0.23/0.50 inference(rewrite,[status(thm)],[])).
% 0.23/0.50 tff(105,axiom,(~![F: $i, A: $i, B: $i, X: $i] : (((maps(F, A, B) & injective(F, A, B)) & subset(X, A)) => equal_set(inverse_image3(F, image3(F, X, B), A), X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thIIa09')).
% 0.23/0.50 tff(106,plain,
% 0.23/0.50 (~![F: $i, A: $i, B: $i, X: $i] : ((~(maps(F, A, B) & injective(F, A, B) & subset(X, A))) | equal_set(inverse_image3(F, image3(F, X, B), A), X))),
% 0.23/0.50 inference(modus_ponens,[status(thm)],[105, 104])).
% 0.23/0.50 tff(107,plain,
% 0.23/0.50 (~![F: $i, A: $i, B: $i, X: $i] : ((~(maps(F, A, B) & injective(F, A, B) & subset(X, A))) | equal_set(inverse_image3(F, image3(F, X, B), A), X))),
% 0.23/0.50 inference(modus_ponens,[status(thm)],[106, 103])).
% 0.23/0.50 tff(108,plain,
% 0.23/0.50 (~![F: $i, A: $i, B: $i, X: $i] : ((~(maps(F, A, B) & injective(F, A, B) & subset(X, A))) | equal_set(inverse_image3(F, image3(F, X, B), A), X))),
% 0.23/0.50 inference(modus_ponens,[status(thm)],[107, 103])).
% 0.23/0.50 tff(109,plain,
% 0.23/0.50 (~![F: $i, A: $i, B: $i, X: $i] : ((~(maps(F, A, B) & injective(F, A, B) & subset(X, A))) | equal_set(inverse_image3(F, image3(F, X, B), A), X))),
% 0.23/0.50 inference(modus_ponens,[status(thm)],[108, 103])).
% 0.23/0.50 tff(110,plain,(
% 0.23/0.50 ~((~(maps(F!42, A!41, B!40) & injective(F!42, A!41, B!40) & subset(X!39, A!41))) | equal_set(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39))),
% 0.23/0.50 inference(skolemize,[status(sab)],[109])).
% 0.23/0.50 tff(111,plain,
% 0.23/0.50 (maps(F!42, A!41, B!40) & injective(F!42, A!41, B!40) & subset(X!39, A!41)),
% 0.23/0.50 inference(or_elim,[status(thm)],[110])).
% 0.23/0.50 tff(112,plain,
% 0.23/0.50 (subset(X!39, A!41)),
% 0.23/0.50 inference(and_elim,[status(thm)],[111])).
% 0.23/0.50 tff(113,plain,
% 0.23/0.50 ((~((~subset(X!39, A!41)) | ![X: $i] : ((~member(X, X!39)) | member(X, A!41)))) | (~subset(X!39, A!41)) | ![X: $i] : ((~member(X, X!39)) | member(X, A!41))),
% 0.23/0.50 inference(tautology,[status(thm)],[])).
% 0.23/0.50 tff(114,plain,
% 0.23/0.50 ((~((~subset(X!39, A!41)) | ![X: $i] : ((~member(X, X!39)) | member(X, A!41)))) | ![X: $i] : ((~member(X, X!39)) | member(X, A!41))),
% 0.23/0.50 inference(unit_resolution,[status(thm)],[113, 112])).
% 0.23/0.50 tff(115,plain,
% 0.23/0.50 (![X: $i] : ((~member(X, X!39)) | member(X, A!41))),
% 0.23/0.50 inference(unit_resolution,[status(thm)],[114, 102])).
% 0.23/0.50 tff(116,plain,
% 0.23/0.50 (((~![X: $i] : ((~member(X, X!39)) | member(X, A!41))) | ((~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), X!39)) | member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), A!41))) <=> ((~![X: $i] : ((~member(X, X!39)) | member(X, A!41))) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), X!39)) | member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), A!41))),
% 0.23/0.50 inference(rewrite,[status(thm)],[])).
% 0.23/0.50 tff(117,plain,
% 0.23/0.50 ((~![X: $i] : ((~member(X, X!39)) | member(X, A!41))) | ((~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), X!39)) | member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), A!41))),
% 0.23/0.50 inference(quant_inst,[status(thm)],[])).
% 0.23/0.50 tff(118,plain,
% 0.23/0.50 ((~![X: $i] : ((~member(X, X!39)) | member(X, A!41))) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), X!39)) | member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), A!41)),
% 0.23/0.50 inference(modus_ponens,[status(thm)],[117, 116])).
% 0.23/0.50 tff(119,plain,
% 0.23/0.50 (member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), A!41)),
% 0.23/0.50 inference(unit_resolution,[status(thm)],[118, 115, 98])).
% 0.23/0.50 tff(120,plain,
% 0.23/0.50 (((~member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), B!40)) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), X!39)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42)))) | apply(F!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42))),
% 0.23/0.50 inference(tautology,[status(thm)],[])).
% 0.23/0.50 tff(121,plain,
% 0.23/0.50 (apply(F!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42))),
% 0.23/0.50 inference(unit_resolution,[status(thm)],[120, 96])).
% 0.23/0.50 tff(122,plain,
% 0.23/0.51 (((~member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), B!40)) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), X!39)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42)))) | member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), B!40)),
% 0.23/0.51 inference(tautology,[status(thm)],[])).
% 0.23/0.51 tff(123,plain,
% 0.23/0.51 (member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), B!40)),
% 0.23/0.51 inference(unit_resolution,[status(thm)],[122, 96])).
% 0.23/0.51 tff(124,plain,
% 0.23/0.51 (((~member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), A!41)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), image3(F!42, X!39, B!40))) | (~apply(F!42, tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42)))) | apply(F!42, tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42))),
% 0.23/0.51 inference(tautology,[status(thm)],[])).
% 0.23/0.51 tff(125,plain,
% 0.23/0.51 (apply(F!42, tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42))),
% 0.23/0.51 inference(unit_resolution,[status(thm)],[124, 91])).
% 0.23/0.51 tff(126,plain,
% 0.23/0.51 (((~member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), A!41)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), image3(F!42, X!39, B!40))) | (~apply(F!42, tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42)))) | member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), A!41)),
% 0.23/0.51 inference(tautology,[status(thm)],[])).
% 0.23/0.51 tff(127,plain,
% 0.23/0.51 (member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), A!41)),
% 0.23/0.51 inference(unit_resolution,[status(thm)],[126, 91])).
% 0.23/0.51 tff(128,plain,
% 0.23/0.51 (^[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)))))))))),
% 0.23/0.51 inference(bind,[status(th)],[])).
% 0.23/0.51 tff(129,plain,
% 0.23/0.51 (![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))))))))),
% 0.23/0.51 inference(quant_intro,[status(thm)],[128])).
% 0.23/0.51 tff(130,plain,
% 0.23/0.51 (^[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)))))))))),
% 0.23/0.51 inference(bind,[status(th)],[])).
% 0.23/0.51 tff(131,plain,
% 0.23/0.51 (![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))))))))),
% 0.23/0.51 inference(quant_intro,[status(thm)],[130])).
% 0.23/0.51 tff(132,plain,
% 0.23/0.51 (![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))))))))),
% 0.23/0.51 inference(transitivity,[status(thm)],[131, 129])).
% 0.23/0.51 tff(133,plain,
% 0.23/0.51 (^[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))))))))))),
% 0.23/0.51 inference(bind,[status(th)],[])).
% 0.23/0.51 tff(134,plain,
% 0.23/0.51 (![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))))))))),
% 0.23/0.51 inference(quant_intro,[status(thm)],[133])).
% 0.23/0.51 tff(135,plain,
% 0.23/0.51 (![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)))))),
% 0.23/0.51 inference(rewrite,[status(thm)],[])).
% 0.23/0.51 tff(136,plain,
% 0.23/0.51 (^[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))))))),
% 0.23/0.51 inference(bind,[status(th)],[])).
% 0.23/0.51 tff(137,plain,
% 0.23/0.51 (![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)))))),
% 0.23/0.51 inference(quant_intro,[status(thm)],[136])).
% 0.23/0.51 tff(138,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/sandbox2/benchmark/Axioms/SET006+1.ax','injective')).
% 0.23/0.51 tff(139,plain,
% 0.23/0.51 (![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)))))),
% 0.23/0.51 inference(modus_ponens,[status(thm)],[138, 137])).
% 0.23/0.51 tff(140,plain,
% 0.23/0.51 (![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)))))),
% 0.23/0.51 inference(modus_ponens,[status(thm)],[139, 135])).
% 0.23/0.51 tff(141,plain,(
% 0.23/0.51 ![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)))))))),
% 0.23/0.51 inference(skolemize,[status(sab)],[140])).
% 0.23/0.51 tff(142,plain,
% 0.23/0.51 (![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))))))))),
% 0.23/0.51 inference(modus_ponens,[status(thm)],[141, 134])).
% 0.23/0.51 tff(143,plain,
% 0.23/0.51 (![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))))))))),
% 0.23/0.51 inference(modus_ponens,[status(thm)],[142, 132])).
% 0.23/0.51 tff(144,plain,
% 0.23/0.51 (((~![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!42, A!41, B!40)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!40)) | (~apply(F!42, X1, Y)) | (~member(X1, A!41)) | (~member(X2, A!41)) | (~apply(F!42, X2, Y))))) | (~(injective(F!42, A!41, B!40) | (~((~member(tptp_fun_Y_16(B!40, A!41, F!42), B!40)) | (~member(tptp_fun_X2_17(B!40, A!41, F!42), A!41)) | (~member(tptp_fun_X1_18(B!40, A!41, F!42), A!41)) | (~apply(F!42, tptp_fun_X2_17(B!40, A!41, F!42), tptp_fun_Y_16(B!40, A!41, F!42))) | (~apply(F!42, tptp_fun_X1_18(B!40, A!41, F!42), tptp_fun_Y_16(B!40, A!41, F!42))) | (tptp_fun_X1_18(B!40, A!41, F!42) = tptp_fun_X2_17(B!40, A!41, F!42))))))))) <=> ((~![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!42, A!41, B!40)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!40)) | (~apply(F!42, X1, Y)) | (~member(X1, A!41)) | (~member(X2, A!41)) | (~apply(F!42, X2, Y))))) | (~(injective(F!42, A!41, B!40) | (~((~member(tptp_fun_Y_16(B!40, A!41, F!42), B!40)) | (~member(tptp_fun_X2_17(B!40, A!41, F!42), A!41)) | (~member(tptp_fun_X1_18(B!40, A!41, F!42), A!41)) | (~apply(F!42, tptp_fun_X2_17(B!40, A!41, F!42), tptp_fun_Y_16(B!40, A!41, F!42))) | (~apply(F!42, tptp_fun_X1_18(B!40, A!41, F!42), tptp_fun_Y_16(B!40, A!41, F!42))) | (tptp_fun_X1_18(B!40, A!41, F!42) = tptp_fun_X2_17(B!40, A!41, F!42)))))))))),
% 0.23/0.51 inference(rewrite,[status(thm)],[])).
% 0.23/0.51 tff(145,plain,
% 0.23/0.51 ((~((~((~injective(F!42, A!41, B!40)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!42, X1, Y)) | (~member(X2, A!41)) | (~member(X1, A!41)) | (~member(Y, B!40)) | (~apply(F!42, X2, Y))))) | (~(injective(F!42, A!41, B!40) | (~((tptp_fun_X1_18(B!40, A!41, F!42) = tptp_fun_X2_17(B!40, A!41, F!42)) | (~apply(F!42, tptp_fun_X1_18(B!40, A!41, F!42), tptp_fun_Y_16(B!40, A!41, F!42))) | (~apply(F!42, tptp_fun_X2_17(B!40, A!41, F!42), tptp_fun_Y_16(B!40, A!41, F!42))) | (~member(tptp_fun_X1_18(B!40, A!41, F!42), A!41)) | (~member(tptp_fun_X2_17(B!40, A!41, F!42), A!41)) | (~member(tptp_fun_Y_16(B!40, A!41, F!42), B!40)))))))) <=> (~((~((~injective(F!42, A!41, B!40)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!40)) | (~apply(F!42, X1, Y)) | (~member(X1, A!41)) | (~member(X2, A!41)) | (~apply(F!42, X2, Y))))) | (~(injective(F!42, A!41, B!40) | (~((~member(tptp_fun_Y_16(B!40, A!41, F!42), B!40)) | (~member(tptp_fun_X2_17(B!40, A!41, F!42), A!41)) | (~member(tptp_fun_X1_18(B!40, A!41, F!42), A!41)) | (~apply(F!42, tptp_fun_X2_17(B!40, A!41, F!42), tptp_fun_Y_16(B!40, A!41, F!42))) | (~apply(F!42, tptp_fun_X1_18(B!40, A!41, F!42), tptp_fun_Y_16(B!40, A!41, F!42))) | (tptp_fun_X1_18(B!40, A!41, F!42) = tptp_fun_X2_17(B!40, A!41, F!42))))))))),
% 0.23/0.51 inference(rewrite,[status(thm)],[])).
% 0.23/0.51 tff(146,plain,
% 0.23/0.51 (((~![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!42, A!41, B!40)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!42, X1, Y)) | (~member(X2, A!41)) | (~member(X1, A!41)) | (~member(Y, B!40)) | (~apply(F!42, X2, Y))))) | (~(injective(F!42, A!41, B!40) | (~((tptp_fun_X1_18(B!40, A!41, F!42) = tptp_fun_X2_17(B!40, A!41, F!42)) | (~apply(F!42, tptp_fun_X1_18(B!40, A!41, F!42), tptp_fun_Y_16(B!40, A!41, F!42))) | (~apply(F!42, tptp_fun_X2_17(B!40, A!41, F!42), tptp_fun_Y_16(B!40, A!41, F!42))) | (~member(tptp_fun_X1_18(B!40, A!41, F!42), A!41)) | (~member(tptp_fun_X2_17(B!40, A!41, F!42), A!41)) | (~member(tptp_fun_Y_16(B!40, A!41, F!42), B!40))))))))) <=> ((~![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!42, A!41, B!40)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!40)) | (~apply(F!42, X1, Y)) | (~member(X1, A!41)) | (~member(X2, A!41)) | (~apply(F!42, X2, Y))))) | (~(injective(F!42, A!41, B!40) | (~((~member(tptp_fun_Y_16(B!40, A!41, F!42), B!40)) | (~member(tptp_fun_X2_17(B!40, A!41, F!42), A!41)) | (~member(tptp_fun_X1_18(B!40, A!41, F!42), A!41)) | (~apply(F!42, tptp_fun_X2_17(B!40, A!41, F!42), tptp_fun_Y_16(B!40, A!41, F!42))) | (~apply(F!42, tptp_fun_X1_18(B!40, A!41, F!42), tptp_fun_Y_16(B!40, A!41, F!42))) | (tptp_fun_X1_18(B!40, A!41, F!42) = tptp_fun_X2_17(B!40, A!41, F!42)))))))))),
% 0.23/0.52 inference(monotonicity,[status(thm)],[145])).
% 0.23/0.52 tff(147,plain,
% 0.23/0.52 (((~![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!42, A!41, B!40)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!42, X1, Y)) | (~member(X2, A!41)) | (~member(X1, A!41)) | (~member(Y, B!40)) | (~apply(F!42, X2, Y))))) | (~(injective(F!42, A!41, B!40) | (~((tptp_fun_X1_18(B!40, A!41, F!42) = tptp_fun_X2_17(B!40, A!41, F!42)) | (~apply(F!42, tptp_fun_X1_18(B!40, A!41, F!42), tptp_fun_Y_16(B!40, A!41, F!42))) | (~apply(F!42, tptp_fun_X2_17(B!40, A!41, F!42), tptp_fun_Y_16(B!40, A!41, F!42))) | (~member(tptp_fun_X1_18(B!40, A!41, F!42), A!41)) | (~member(tptp_fun_X2_17(B!40, A!41, F!42), A!41)) | (~member(tptp_fun_Y_16(B!40, A!41, F!42), B!40))))))))) <=> ((~![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!42, A!41, B!40)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!40)) | (~apply(F!42, X1, Y)) | (~member(X1, A!41)) | (~member(X2, A!41)) | (~apply(F!42, X2, Y))))) | (~(injective(F!42, A!41, B!40) | (~((~member(tptp_fun_Y_16(B!40, A!41, F!42), B!40)) | (~member(tptp_fun_X2_17(B!40, A!41, F!42), A!41)) | (~member(tptp_fun_X1_18(B!40, A!41, F!42), A!41)) | (~apply(F!42, tptp_fun_X2_17(B!40, A!41, F!42), tptp_fun_Y_16(B!40, A!41, F!42))) | (~apply(F!42, tptp_fun_X1_18(B!40, A!41, F!42), tptp_fun_Y_16(B!40, A!41, F!42))) | (tptp_fun_X1_18(B!40, A!41, F!42) = tptp_fun_X2_17(B!40, A!41, F!42)))))))))),
% 0.23/0.52 inference(transitivity,[status(thm)],[146, 144])).
% 0.23/0.52 tff(148,plain,
% 0.23/0.52 ((~![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!42, A!41, B!40)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!42, X1, Y)) | (~member(X2, A!41)) | (~member(X1, A!41)) | (~member(Y, B!40)) | (~apply(F!42, X2, Y))))) | (~(injective(F!42, A!41, B!40) | (~((tptp_fun_X1_18(B!40, A!41, F!42) = tptp_fun_X2_17(B!40, A!41, F!42)) | (~apply(F!42, tptp_fun_X1_18(B!40, A!41, F!42), tptp_fun_Y_16(B!40, A!41, F!42))) | (~apply(F!42, tptp_fun_X2_17(B!40, A!41, F!42), tptp_fun_Y_16(B!40, A!41, F!42))) | (~member(tptp_fun_X1_18(B!40, A!41, F!42), A!41)) | (~member(tptp_fun_X2_17(B!40, A!41, F!42), A!41)) | (~member(tptp_fun_Y_16(B!40, A!41, F!42), B!40))))))))),
% 0.23/0.52 inference(quant_inst,[status(thm)],[])).
% 0.23/0.52 tff(149,plain,
% 0.23/0.52 ((~![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!42, A!41, B!40)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!40)) | (~apply(F!42, X1, Y)) | (~member(X1, A!41)) | (~member(X2, A!41)) | (~apply(F!42, X2, Y))))) | (~(injective(F!42, A!41, B!40) | (~((~member(tptp_fun_Y_16(B!40, A!41, F!42), B!40)) | (~member(tptp_fun_X2_17(B!40, A!41, F!42), A!41)) | (~member(tptp_fun_X1_18(B!40, A!41, F!42), A!41)) | (~apply(F!42, tptp_fun_X2_17(B!40, A!41, F!42), tptp_fun_Y_16(B!40, A!41, F!42))) | (~apply(F!42, tptp_fun_X1_18(B!40, A!41, F!42), tptp_fun_Y_16(B!40, A!41, F!42))) | (tptp_fun_X1_18(B!40, A!41, F!42) = tptp_fun_X2_17(B!40, A!41, F!42))))))))),
% 0.23/0.52 inference(modus_ponens,[status(thm)],[148, 147])).
% 0.23/0.52 tff(150,plain,
% 0.23/0.52 (~((~((~injective(F!42, A!41, B!40)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!40)) | (~apply(F!42, X1, Y)) | (~member(X1, A!41)) | (~member(X2, A!41)) | (~apply(F!42, X2, Y))))) | (~(injective(F!42, A!41, B!40) | (~((~member(tptp_fun_Y_16(B!40, A!41, F!42), B!40)) | (~member(tptp_fun_X2_17(B!40, A!41, F!42), A!41)) | (~member(tptp_fun_X1_18(B!40, A!41, F!42), A!41)) | (~apply(F!42, tptp_fun_X2_17(B!40, A!41, F!42), tptp_fun_Y_16(B!40, A!41, F!42))) | (~apply(F!42, tptp_fun_X1_18(B!40, A!41, F!42), tptp_fun_Y_16(B!40, A!41, F!42))) | (tptp_fun_X1_18(B!40, A!41, F!42) = tptp_fun_X2_17(B!40, A!41, F!42)))))))),
% 0.23/0.52 inference(unit_resolution,[status(thm)],[149, 143])).
% 0.23/0.52 tff(151,plain,
% 0.23/0.52 (((~((~injective(F!42, A!41, B!40)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!40)) | (~apply(F!42, X1, Y)) | (~member(X1, A!41)) | (~member(X2, A!41)) | (~apply(F!42, X2, Y))))) | (~(injective(F!42, A!41, B!40) | (~((~member(tptp_fun_Y_16(B!40, A!41, F!42), B!40)) | (~member(tptp_fun_X2_17(B!40, A!41, F!42), A!41)) | (~member(tptp_fun_X1_18(B!40, A!41, F!42), A!41)) | (~apply(F!42, tptp_fun_X2_17(B!40, A!41, F!42), tptp_fun_Y_16(B!40, A!41, F!42))) | (~apply(F!42, tptp_fun_X1_18(B!40, A!41, F!42), tptp_fun_Y_16(B!40, A!41, F!42))) | (tptp_fun_X1_18(B!40, A!41, F!42) = tptp_fun_X2_17(B!40, A!41, F!42))))))) | ((~injective(F!42, A!41, B!40)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!40)) | (~apply(F!42, X1, Y)) | (~member(X1, A!41)) | (~member(X2, A!41)) | (~apply(F!42, X2, Y))))),
% 0.23/0.52 inference(tautology,[status(thm)],[])).
% 0.23/0.52 tff(152,plain,
% 0.23/0.52 ((~injective(F!42, A!41, B!40)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!40)) | (~apply(F!42, X1, Y)) | (~member(X1, A!41)) | (~member(X2, A!41)) | (~apply(F!42, X2, Y)))),
% 0.23/0.52 inference(unit_resolution,[status(thm)],[151, 150])).
% 0.23/0.52 tff(153,plain,
% 0.23/0.52 (injective(F!42, A!41, B!40)),
% 0.23/0.52 inference(and_elim,[status(thm)],[111])).
% 0.23/0.52 tff(154,plain,
% 0.23/0.52 ((~((~injective(F!42, A!41, B!40)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!40)) | (~apply(F!42, X1, Y)) | (~member(X1, A!41)) | (~member(X2, A!41)) | (~apply(F!42, X2, Y))))) | (~injective(F!42, A!41, B!40)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!40)) | (~apply(F!42, X1, Y)) | (~member(X1, A!41)) | (~member(X2, A!41)) | (~apply(F!42, X2, Y)))),
% 0.23/0.52 inference(tautology,[status(thm)],[])).
% 0.23/0.52 tff(155,plain,
% 0.23/0.52 ((~((~injective(F!42, A!41, B!40)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!40)) | (~apply(F!42, X1, Y)) | (~member(X1, A!41)) | (~member(X2, A!41)) | (~apply(F!42, X2, Y))))) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!40)) | (~apply(F!42, X1, Y)) | (~member(X1, A!41)) | (~member(X2, A!41)) | (~apply(F!42, X2, Y)))),
% 0.23/0.52 inference(unit_resolution,[status(thm)],[154, 153])).
% 0.23/0.52 tff(156,plain,
% 0.23/0.52 (![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!40)) | (~apply(F!42, X1, Y)) | (~member(X1, A!41)) | (~member(X2, A!41)) | (~apply(F!42, X2, Y)))),
% 0.23/0.52 inference(unit_resolution,[status(thm)],[155, 152])).
% 0.23/0.52 tff(157,plain,
% 0.23/0.52 (((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!40)) | (~apply(F!42, X1, Y)) | (~member(X1, A!41)) | (~member(X2, A!41)) | (~apply(F!42, X2, Y)))) | ((~member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), A!41)) | (~apply(F!42, tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42))) | (~member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), B!40)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42))) | (tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42) = tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), A!41)))) <=> ((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!40)) | (~apply(F!42, X1, Y)) | (~member(X1, A!41)) | (~member(X2, A!41)) | (~apply(F!42, X2, Y)))) | (~member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), A!41)) | (~apply(F!42, tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42))) | (~member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), B!40)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42))) | (tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42) = tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), A!41)))),
% 0.23/0.52 inference(rewrite,[status(thm)],[])).
% 0.23/0.52 tff(158,plain,
% 0.23/0.52 (((tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42) = tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))) | (~member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), B!40)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42))) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), A!41)) | (~member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), A!41)) | (~apply(F!42, tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42)))) <=> ((~member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), A!41)) | (~apply(F!42, tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42))) | (~member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), B!40)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42))) | (tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42) = tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), A!41)))),
% 0.23/0.52 inference(rewrite,[status(thm)],[])).
% 0.23/0.52 tff(159,plain,
% 0.23/0.52 (((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!40)) | (~apply(F!42, X1, Y)) | (~member(X1, A!41)) | (~member(X2, A!41)) | (~apply(F!42, X2, Y)))) | ((tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42) = tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))) | (~member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), B!40)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42))) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), A!41)) | (~member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), A!41)) | (~apply(F!42, tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42))))) <=> ((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!40)) | (~apply(F!42, X1, Y)) | (~member(X1, A!41)) | (~member(X2, A!41)) | (~apply(F!42, X2, Y)))) | ((~member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), A!41)) | (~apply(F!42, tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42))) | (~member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), B!40)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42))) | (tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42) = tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), A!41))))),
% 0.23/0.52 inference(monotonicity,[status(thm)],[158])).
% 0.23/0.53 tff(160,plain,
% 0.23/0.53 (((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!40)) | (~apply(F!42, X1, Y)) | (~member(X1, A!41)) | (~member(X2, A!41)) | (~apply(F!42, X2, Y)))) | ((tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42) = tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))) | (~member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), B!40)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42))) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), A!41)) | (~member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), A!41)) | (~apply(F!42, tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42))))) <=> ((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!40)) | (~apply(F!42, X1, Y)) | (~member(X1, A!41)) | (~member(X2, A!41)) | (~apply(F!42, X2, Y)))) | (~member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), A!41)) | (~apply(F!42, tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42))) | (~member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), B!40)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42))) | (tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42) = tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), A!41)))),
% 0.23/0.53 inference(transitivity,[status(thm)],[159, 157])).
% 0.23/0.53 tff(161,plain,
% 0.23/0.53 ((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!40)) | (~apply(F!42, X1, Y)) | (~member(X1, A!41)) | (~member(X2, A!41)) | (~apply(F!42, X2, Y)))) | ((tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42) = tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))) | (~member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), B!40)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42))) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), A!41)) | (~member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), A!41)) | (~apply(F!42, tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42))))),
% 0.23/0.53 inference(quant_inst,[status(thm)],[])).
% 0.23/0.53 tff(162,plain,
% 0.23/0.53 ((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!40)) | (~apply(F!42, X1, Y)) | (~member(X1, A!41)) | (~member(X2, A!41)) | (~apply(F!42, X2, Y)))) | (~member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), A!41)) | (~apply(F!42, tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42))) | (~member(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), B!40)) | (~apply(F!42, tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42))) | (tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42) = tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), A!41))),
% 0.23/0.53 inference(modus_ponens,[status(thm)],[161, 160])).
% 0.23/0.53 tff(163,plain,
% 0.23/0.53 ((tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42) = tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))) | (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), A!41))),
% 0.23/0.53 inference(unit_resolution,[status(thm)],[162, 156, 127, 125, 123, 121])).
% 0.23/0.53 tff(164,plain,
% 0.23/0.53 (tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42) = tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))),
% 0.23/0.53 inference(unit_resolution,[status(thm)],[163, 119])).
% 0.23/0.53 tff(165,plain,
% 0.23/0.53 (member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), X!39) <=> member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), X!39)),
% 0.23/0.53 inference(monotonicity,[status(thm)],[164])).
% 0.23/0.53 tff(166,plain,
% 0.23/0.53 (member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), X!39) <=> member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), X!39)),
% 0.23/0.53 inference(symmetry,[status(thm)],[165])).
% 0.23/0.53 tff(167,plain,
% 0.23/0.53 ((~member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), X!39)) <=> (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), X!39))),
% 0.23/0.53 inference(monotonicity,[status(thm)],[166])).
% 0.23/0.53 tff(168,plain,
% 0.23/0.53 (((~member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))) | member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), X!39)) | (~member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), X!39))),
% 0.23/0.53 inference(tautology,[status(thm)],[])).
% 0.23/0.53 tff(169,plain,
% 0.23/0.53 (~member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), X!39)),
% 0.23/0.53 inference(unit_resolution,[status(thm)],[168, 86])).
% 0.23/0.53 tff(170,plain,
% 0.23/0.53 (~member(tptp_fun_X_24(tptp_fun_Y_26(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), image3(F!42, X!39, B!40), F!42), X!39, F!42), X!39)),
% 0.23/0.53 inference(modus_ponens,[status(thm)],[169, 167])).
% 0.23/0.53 tff(171,plain,
% 0.23/0.53 ($false),
% 0.23/0.53 inference(unit_resolution,[status(thm)],[98, 170])).
% 0.23/0.53 tff(172,plain,((~member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))) | member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), X!39)), inference(lemma,lemma(discharge,[]))).
% 0.23/0.53 tff(173,plain,
% 0.23/0.53 ((~(subset(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39) | (~((~member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))) | member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), X!39))))) | subset(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39) | (~((~member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))) | member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), X!39)))),
% 0.23/0.53 inference(tautology,[status(thm)],[])).
% 0.23/0.53 tff(174,plain,
% 0.23/0.53 ((~(subset(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39) | (~((~member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))) | member(tptp_fun_X_0(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)), X!39))))) | subset(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39)),
% 0.23/0.53 inference(unit_resolution,[status(thm)],[173, 172])).
% 0.23/0.53 tff(175,plain,
% 0.23/0.53 (subset(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39)),
% 0.23/0.53 inference(unit_resolution,[status(thm)],[174, 51])).
% 0.23/0.53 tff(176,plain,
% 0.23/0.53 (^[A: $i, B: $i] : refl((~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B))) <=> (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B))))),
% 0.23/0.53 inference(bind,[status(th)],[])).
% 0.23/0.53 tff(177,plain,
% 0.23/0.53 (![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B))) <=> ![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))),
% 0.23/0.53 inference(quant_intro,[status(thm)],[176])).
% 0.23/0.53 tff(178,plain,
% 0.23/0.53 (^[A: $i, B: $i] : trans(trans(monotonicity(rewrite((subset(A, B) & subset(B, A)) <=> (~((~subset(A, B)) | (~subset(B, A))))), ((equal_set(A, B) <=> (subset(A, B) & subset(B, A))) <=> (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A))))))), rewrite((equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A))))) <=> (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))), ((equal_set(A, B) <=> (subset(A, B) & subset(B, A))) <=> (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B))))), rewrite((~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B))) <=> (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))), ((equal_set(A, B) <=> (subset(A, B) & subset(B, A))) <=> (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))))),
% 0.23/0.53 inference(bind,[status(th)],[])).
% 0.23/0.53 tff(179,plain,
% 0.23/0.53 (![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A))) <=> ![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))),
% 0.23/0.53 inference(quant_intro,[status(thm)],[178])).
% 0.23/0.53 tff(180,plain,
% 0.23/0.53 (![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A))) <=> ![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 0.23/0.53 inference(rewrite,[status(thm)],[])).
% 0.23/0.53 tff(181,axiom,(![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax','equal_set')).
% 0.23/0.53 tff(182,plain,
% 0.23/0.53 (![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 0.23/0.53 inference(modus_ponens,[status(thm)],[181, 180])).
% 0.23/0.53 tff(183,plain,(
% 0.23/0.53 ![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 0.23/0.53 inference(skolemize,[status(sab)],[182])).
% 0.23/0.53 tff(184,plain,
% 0.23/0.53 (![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))),
% 0.23/0.53 inference(modus_ponens,[status(thm)],[183, 179])).
% 0.23/0.53 tff(185,plain,
% 0.23/0.53 (![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))),
% 0.23/0.53 inference(modus_ponens,[status(thm)],[184, 177])).
% 0.23/0.53 tff(186,plain,
% 0.23/0.53 ((~![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> equal_set(A, B)))) | (~(((~subset(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39)) | (~subset(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)))) <=> equal_set(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39)))),
% 0.23/0.53 inference(quant_inst,[status(thm)],[])).
% 0.23/0.53 tff(187,plain,
% 0.23/0.53 (~(((~subset(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39)) | (~subset(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)))) <=> equal_set(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39))),
% 0.23/0.53 inference(unit_resolution,[status(thm)],[186, 185])).
% 0.23/0.53 tff(188,plain,
% 0.23/0.53 (~equal_set(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39)),
% 0.23/0.53 inference(or_elim,[status(thm)],[110])).
% 0.23/0.53 tff(189,plain,
% 0.23/0.53 ((((~subset(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39)) | (~subset(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)))) <=> equal_set(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39)) | ((~subset(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39)) | (~subset(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)))) | equal_set(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39)),
% 0.23/0.53 inference(tautology,[status(thm)],[])).
% 0.23/0.53 tff(190,plain,
% 0.23/0.53 ((((~subset(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39)) | (~subset(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)))) <=> equal_set(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39)) | ((~subset(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39)) | (~subset(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))))),
% 0.23/0.53 inference(unit_resolution,[status(thm)],[189, 188])).
% 0.23/0.53 tff(191,plain,
% 0.23/0.53 ((~subset(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39)) | (~subset(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)))),
% 0.23/0.53 inference(unit_resolution,[status(thm)],[190, 187])).
% 0.23/0.53 tff(192,plain,
% 0.23/0.53 ((~((~subset(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39)) | (~subset(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))))) | (~subset(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39)) | (~subset(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)))),
% 0.23/0.53 inference(tautology,[status(thm)],[])).
% 0.23/0.53 tff(193,plain,
% 0.23/0.53 ((~subset(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39)) | (~subset(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)))),
% 0.23/0.53 inference(unit_resolution,[status(thm)],[192, 191])).
% 0.23/0.53 tff(194,plain,
% 0.23/0.53 (~subset(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))),
% 0.23/0.53 inference(unit_resolution,[status(thm)],[193, 175])).
% 0.23/0.53 tff(195,plain,
% 0.23/0.53 ((~(subset(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)) | (~((~member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), X!39)) | member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)))))) | subset(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)) | (~((~member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), X!39)) | member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))))),
% 0.23/0.53 inference(tautology,[status(thm)],[])).
% 0.23/0.53 tff(196,plain,
% 0.23/0.53 ((~(subset(X!39, inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)) | (~((~member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), X!39)) | member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)))))) | (~((~member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), X!39)) | member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))))),
% 0.23/0.53 inference(unit_resolution,[status(thm)],[195, 194])).
% 0.23/0.53 tff(197,plain,
% 0.23/0.53 (~((~member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), X!39)) | member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)))),
% 0.23/0.53 inference(unit_resolution,[status(thm)],[196, 45])).
% 0.23/0.53 tff(198,plain,
% 0.23/0.53 (((~member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), X!39)) | member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))) | member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), X!39)),
% 0.23/0.53 inference(tautology,[status(thm)],[])).
% 0.23/0.53 tff(199,plain,
% 0.23/0.53 (member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), X!39)),
% 0.23/0.53 inference(unit_resolution,[status(thm)],[198, 197])).
% 0.23/0.53 tff(200,plain,
% 0.23/0.53 (((~![X: $i] : ((~member(X, X!39)) | member(X, A!41))) | ((~member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), X!39)) | member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), A!41))) <=> ((~![X: $i] : ((~member(X, X!39)) | member(X, A!41))) | (~member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), X!39)) | member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), A!41))),
% 0.23/0.53 inference(rewrite,[status(thm)],[])).
% 0.23/0.53 tff(201,plain,
% 0.23/0.53 ((~![X: $i] : ((~member(X, X!39)) | member(X, A!41))) | ((~member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), X!39)) | member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), A!41))),
% 0.23/0.53 inference(quant_inst,[status(thm)],[])).
% 0.23/0.53 tff(202,plain,
% 0.23/0.53 ((~![X: $i] : ((~member(X, X!39)) | member(X, A!41))) | (~member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), X!39)) | member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), A!41)),
% 0.23/0.53 inference(modus_ponens,[status(thm)],[201, 200])).
% 0.23/0.53 tff(203,plain,
% 0.23/0.53 (member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), A!41)),
% 0.23/0.53 inference(unit_resolution,[status(thm)],[202, 115, 199])).
% 0.23/0.53 tff(204,plain,
% 0.23/0.53 (^[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)))))))))))),
% 0.23/0.53 inference(bind,[status(th)],[])).
% 0.23/0.53 tff(205,plain,
% 0.23/0.53 (![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))))))))))),
% 0.23/0.54 inference(quant_intro,[status(thm)],[204])).
% 0.23/0.54 tff(206,plain,
% 0.23/0.54 (^[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)))))))))),
% 0.23/0.54 inference(bind,[status(th)],[])).
% 0.23/0.54 tff(207,plain,
% 0.23/0.54 (![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))))))))),
% 0.23/0.54 inference(quant_intro,[status(thm)],[206])).
% 0.23/0.54 tff(208,plain,
% 0.23/0.54 (^[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)))))))))),
% 0.23/0.54 inference(bind,[status(th)],[])).
% 0.23/0.54 tff(209,plain,
% 0.23/0.54 (![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))))))))),
% 0.23/0.54 inference(quant_intro,[status(thm)],[208])).
% 0.23/0.54 tff(210,plain,
% 0.23/0.54 (![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))))))))),
% 0.23/0.54 inference(transitivity,[status(thm)],[209, 207])).
% 0.23/0.54 tff(211,plain,
% 0.23/0.54 (^[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))))))))))),
% 0.23/0.54 inference(bind,[status(th)],[])).
% 0.23/0.54 tff(212,plain,
% 0.23/0.54 (![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))))))))),
% 0.23/0.54 inference(quant_intro,[status(thm)],[211])).
% 0.23/0.54 tff(213,plain,
% 0.23/0.54 (^[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))))))))),
% 0.23/0.54 inference(bind,[status(th)],[])).
% 0.23/0.54 tff(214,plain,
% 0.23/0.54 (![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)))))))),
% 0.23/0.54 inference(quant_intro,[status(thm)],[213])).
% 0.23/0.54 tff(215,plain,
% 0.23/0.54 (![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))))))),
% 0.23/0.54 inference(rewrite,[status(thm)],[])).
% 0.23/0.54 tff(216,plain,
% 0.23/0.54 (^[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)))))))),
% 0.23/0.54 inference(bind,[status(th)],[])).
% 0.23/0.54 tff(217,plain,
% 0.23/0.54 (![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))))))),
% 0.23/0.54 inference(quant_intro,[status(thm)],[216])).
% 0.23/0.54 tff(218,axiom,(![F: $i, A: $i, B: $i] : (maps(F, A, B) <=> (![X: $i] : (member(X, A) => ?[Y: $i] : (member(Y, B) & apply(F, X, Y))) & ![X: $i, Y1: $i, Y2: $i] : (((member(X, A) & member(Y1, B)) & member(Y2, B)) => ((apply(F, X, Y1) & apply(F, X, Y2)) => (Y1 = Y2)))))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+1.ax','maps')).
% 0.23/0.54 tff(219,plain,
% 0.23/0.54 (![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))))))),
% 0.23/0.54 inference(modus_ponens,[status(thm)],[218, 217])).
% 0.23/0.54 tff(220,plain,
% 0.23/0.54 (![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))))))),
% 0.23/0.54 inference(modus_ponens,[status(thm)],[219, 215])).
% 0.23/0.54 tff(221,plain,(
% 0.23/0.54 ![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))))))))),
% 0.23/0.54 inference(skolemize,[status(sab)],[220])).
% 0.23/0.54 tff(222,plain,
% 0.23/0.54 (![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)))))))),
% 0.23/0.54 inference(modus_ponens,[status(thm)],[221, 214])).
% 0.23/0.54 tff(223,plain,
% 0.23/0.54 (![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))))))))),
% 0.23/0.54 inference(modus_ponens,[status(thm)],[222, 212])).
% 0.23/0.54 tff(224,plain,
% 0.23/0.54 (![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))))))))),
% 0.23/0.54 inference(modus_ponens,[status(thm)],[223, 210])).
% 0.23/0.54 tff(225,plain,
% 0.23/0.54 (![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))))))))))),
% 0.23/0.54 inference(modus_ponens,[status(thm)],[224, 205])).
% 0.23/0.54 tff(226,plain,
% 0.23/0.54 (((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(F!42, A!41, B!40)) | (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!42), B!40)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!40, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)))))))) | (~(maps(F!42, A!41, B!40) | (~((~member(tptp_fun_X_4(B!40, A!41, F!42), A!41)) | (~![Y: $i] : ((~member(Y, B!40)) | (~apply(F!42, tptp_fun_X_4(B!40, A!41, F!42), Y)))))) | (~((~member(tptp_fun_Y2_5(B!40, A!41, F!42), B!40)) | (~member(tptp_fun_Y1_6(B!40, A!41, F!42), B!40)) | (~member(tptp_fun_X_7(B!40, A!41, F!42), A!41)) | (~apply(F!42, tptp_fun_X_7(B!40, A!41, F!42), tptp_fun_Y2_5(B!40, A!41, F!42))) | (~apply(F!42, tptp_fun_X_7(B!40, A!41, F!42), tptp_fun_Y1_6(B!40, A!41, F!42))) | (tptp_fun_Y1_6(B!40, A!41, F!42) = tptp_fun_Y2_5(B!40, A!41, F!42))))))))) <=> ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(F!42, A!41, B!40)) | (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!42), B!40)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!40, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)))))))) | (~(maps(F!42, A!41, B!40) | (~((~member(tptp_fun_X_4(B!40, A!41, F!42), A!41)) | (~![Y: $i] : ((~member(Y, B!40)) | (~apply(F!42, tptp_fun_X_4(B!40, A!41, F!42), Y)))))) | (~((~member(tptp_fun_Y2_5(B!40, A!41, F!42), B!40)) | (~member(tptp_fun_Y1_6(B!40, A!41, F!42), B!40)) | (~member(tptp_fun_X_7(B!40, A!41, F!42), A!41)) | (~apply(F!42, tptp_fun_X_7(B!40, A!41, F!42), tptp_fun_Y2_5(B!40, A!41, F!42))) | (~apply(F!42, tptp_fun_X_7(B!40, A!41, F!42), tptp_fun_Y1_6(B!40, A!41, F!42))) | (tptp_fun_Y1_6(B!40, A!41, F!42) = tptp_fun_Y2_5(B!40, A!41, F!42)))))))))),
% 0.23/0.54 inference(rewrite,[status(thm)],[])).
% 0.23/0.54 tff(227,plain,
% 0.23/0.55 ((~((~((~maps(F!42, A!41, B!40)) | (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!42), B!40)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!40, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)) | (~member(Y2, B!40)))))))) | (~(maps(F!42, A!41, B!40) | (~((tptp_fun_Y1_6(B!40, A!41, F!42) = tptp_fun_Y2_5(B!40, A!41, F!42)) | (~apply(F!42, tptp_fun_X_7(B!40, A!41, F!42), tptp_fun_Y1_6(B!40, A!41, F!42))) | (~apply(F!42, tptp_fun_X_7(B!40, A!41, F!42), tptp_fun_Y2_5(B!40, A!41, F!42))) | (~member(tptp_fun_X_7(B!40, A!41, F!42), A!41)) | (~member(tptp_fun_Y1_6(B!40, A!41, F!42), B!40)) | (~member(tptp_fun_Y2_5(B!40, A!41, F!42), B!40)))) | (~((~member(tptp_fun_X_4(B!40, A!41, F!42), A!41)) | (~![Y: $i] : ((~member(Y, B!40)) | (~apply(F!42, tptp_fun_X_4(B!40, A!41, F!42), Y)))))))))) <=> (~((~((~maps(F!42, A!41, B!40)) | (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!42), B!40)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!40, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)))))))) | (~(maps(F!42, A!41, B!40) | (~((~member(tptp_fun_X_4(B!40, A!41, F!42), A!41)) | (~![Y: $i] : ((~member(Y, B!40)) | (~apply(F!42, tptp_fun_X_4(B!40, A!41, F!42), Y)))))) | (~((~member(tptp_fun_Y2_5(B!40, A!41, F!42), B!40)) | (~member(tptp_fun_Y1_6(B!40, A!41, F!42), B!40)) | (~member(tptp_fun_X_7(B!40, A!41, F!42), A!41)) | (~apply(F!42, tptp_fun_X_7(B!40, A!41, F!42), tptp_fun_Y2_5(B!40, A!41, F!42))) | (~apply(F!42, tptp_fun_X_7(B!40, A!41, F!42), tptp_fun_Y1_6(B!40, A!41, F!42))) | (tptp_fun_Y1_6(B!40, A!41, F!42) = tptp_fun_Y2_5(B!40, A!41, F!42))))))))),
% 0.23/0.55 inference(rewrite,[status(thm)],[])).
% 0.23/0.55 tff(228,plain,
% 0.23/0.55 (((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(F!42, A!41, B!40)) | (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!42), B!40)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!40, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)) | (~member(Y2, B!40)))))))) | (~(maps(F!42, A!41, B!40) | (~((tptp_fun_Y1_6(B!40, A!41, F!42) = tptp_fun_Y2_5(B!40, A!41, F!42)) | (~apply(F!42, tptp_fun_X_7(B!40, A!41, F!42), tptp_fun_Y1_6(B!40, A!41, F!42))) | (~apply(F!42, tptp_fun_X_7(B!40, A!41, F!42), tptp_fun_Y2_5(B!40, A!41, F!42))) | (~member(tptp_fun_X_7(B!40, A!41, F!42), A!41)) | (~member(tptp_fun_Y1_6(B!40, A!41, F!42), B!40)) | (~member(tptp_fun_Y2_5(B!40, A!41, F!42), B!40)))) | (~((~member(tptp_fun_X_4(B!40, A!41, F!42), A!41)) | (~![Y: $i] : ((~member(Y, B!40)) | (~apply(F!42, tptp_fun_X_4(B!40, A!41, F!42), Y))))))))))) <=> ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(F!42, A!41, B!40)) | (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!42), B!40)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!40, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)))))))) | (~(maps(F!42, A!41, B!40) | (~((~member(tptp_fun_X_4(B!40, A!41, F!42), A!41)) | (~![Y: $i] : ((~member(Y, B!40)) | (~apply(F!42, tptp_fun_X_4(B!40, A!41, F!42), Y)))))) | (~((~member(tptp_fun_Y2_5(B!40, A!41, F!42), B!40)) | (~member(tptp_fun_Y1_6(B!40, A!41, F!42), B!40)) | (~member(tptp_fun_X_7(B!40, A!41, F!42), A!41)) | (~apply(F!42, tptp_fun_X_7(B!40, A!41, F!42), tptp_fun_Y2_5(B!40, A!41, F!42))) | (~apply(F!42, tptp_fun_X_7(B!40, A!41, F!42), tptp_fun_Y1_6(B!40, A!41, F!42))) | (tptp_fun_Y1_6(B!40, A!41, F!42) = tptp_fun_Y2_5(B!40, A!41, F!42)))))))))),
% 0.23/0.55 inference(monotonicity,[status(thm)],[227])).
% 0.23/0.55 tff(229,plain,
% 0.23/0.55 (((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(F!42, A!41, B!40)) | (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!42), B!40)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!40, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)) | (~member(Y2, B!40)))))))) | (~(maps(F!42, A!41, B!40) | (~((tptp_fun_Y1_6(B!40, A!41, F!42) = tptp_fun_Y2_5(B!40, A!41, F!42)) | (~apply(F!42, tptp_fun_X_7(B!40, A!41, F!42), tptp_fun_Y1_6(B!40, A!41, F!42))) | (~apply(F!42, tptp_fun_X_7(B!40, A!41, F!42), tptp_fun_Y2_5(B!40, A!41, F!42))) | (~member(tptp_fun_X_7(B!40, A!41, F!42), A!41)) | (~member(tptp_fun_Y1_6(B!40, A!41, F!42), B!40)) | (~member(tptp_fun_Y2_5(B!40, A!41, F!42), B!40)))) | (~((~member(tptp_fun_X_4(B!40, A!41, F!42), A!41)) | (~![Y: $i] : ((~member(Y, B!40)) | (~apply(F!42, tptp_fun_X_4(B!40, A!41, F!42), Y))))))))))) <=> ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(F!42, A!41, B!40)) | (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!42), B!40)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!40, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)))))))) | (~(maps(F!42, A!41, B!40) | (~((~member(tptp_fun_X_4(B!40, A!41, F!42), A!41)) | (~![Y: $i] : ((~member(Y, B!40)) | (~apply(F!42, tptp_fun_X_4(B!40, A!41, F!42), Y)))))) | (~((~member(tptp_fun_Y2_5(B!40, A!41, F!42), B!40)) | (~member(tptp_fun_Y1_6(B!40, A!41, F!42), B!40)) | (~member(tptp_fun_X_7(B!40, A!41, F!42), A!41)) | (~apply(F!42, tptp_fun_X_7(B!40, A!41, F!42), tptp_fun_Y2_5(B!40, A!41, F!42))) | (~apply(F!42, tptp_fun_X_7(B!40, A!41, F!42), tptp_fun_Y1_6(B!40, A!41, F!42))) | (tptp_fun_Y1_6(B!40, A!41, F!42) = tptp_fun_Y2_5(B!40, A!41, F!42)))))))))),
% 0.23/0.55 inference(transitivity,[status(thm)],[228, 226])).
% 0.23/0.55 tff(230,plain,
% 0.23/0.55 ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(F!42, A!41, B!40)) | (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!42), B!40)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!40, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)) | (~member(Y2, B!40)))))))) | (~(maps(F!42, A!41, B!40) | (~((tptp_fun_Y1_6(B!40, A!41, F!42) = tptp_fun_Y2_5(B!40, A!41, F!42)) | (~apply(F!42, tptp_fun_X_7(B!40, A!41, F!42), tptp_fun_Y1_6(B!40, A!41, F!42))) | (~apply(F!42, tptp_fun_X_7(B!40, A!41, F!42), tptp_fun_Y2_5(B!40, A!41, F!42))) | (~member(tptp_fun_X_7(B!40, A!41, F!42), A!41)) | (~member(tptp_fun_Y1_6(B!40, A!41, F!42), B!40)) | (~member(tptp_fun_Y2_5(B!40, A!41, F!42), B!40)))) | (~((~member(tptp_fun_X_4(B!40, A!41, F!42), A!41)) | (~![Y: $i] : ((~member(Y, B!40)) | (~apply(F!42, tptp_fun_X_4(B!40, A!41, F!42), Y))))))))))),
% 0.23/0.55 inference(quant_inst,[status(thm)],[])).
% 0.23/0.55 tff(231,plain,
% 0.23/0.55 ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(F!42, A!41, B!40)) | (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!42), B!40)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!40, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)))))))) | (~(maps(F!42, A!41, B!40) | (~((~member(tptp_fun_X_4(B!40, A!41, F!42), A!41)) | (~![Y: $i] : ((~member(Y, B!40)) | (~apply(F!42, tptp_fun_X_4(B!40, A!41, F!42), Y)))))) | (~((~member(tptp_fun_Y2_5(B!40, A!41, F!42), B!40)) | (~member(tptp_fun_Y1_6(B!40, A!41, F!42), B!40)) | (~member(tptp_fun_X_7(B!40, A!41, F!42), A!41)) | (~apply(F!42, tptp_fun_X_7(B!40, A!41, F!42), tptp_fun_Y2_5(B!40, A!41, F!42))) | (~apply(F!42, tptp_fun_X_7(B!40, A!41, F!42), tptp_fun_Y1_6(B!40, A!41, F!42))) | (tptp_fun_Y1_6(B!40, A!41, F!42) = tptp_fun_Y2_5(B!40, A!41, F!42))))))))),
% 0.23/0.55 inference(modus_ponens,[status(thm)],[230, 229])).
% 0.23/0.55 tff(232,plain,
% 0.23/0.55 (~((~((~maps(F!42, A!41, B!40)) | (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!42), B!40)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!40, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)))))))) | (~(maps(F!42, A!41, B!40) | (~((~member(tptp_fun_X_4(B!40, A!41, F!42), A!41)) | (~![Y: $i] : ((~member(Y, B!40)) | (~apply(F!42, tptp_fun_X_4(B!40, A!41, F!42), Y)))))) | (~((~member(tptp_fun_Y2_5(B!40, A!41, F!42), B!40)) | (~member(tptp_fun_Y1_6(B!40, A!41, F!42), B!40)) | (~member(tptp_fun_X_7(B!40, A!41, F!42), A!41)) | (~apply(F!42, tptp_fun_X_7(B!40, A!41, F!42), tptp_fun_Y2_5(B!40, A!41, F!42))) | (~apply(F!42, tptp_fun_X_7(B!40, A!41, F!42), tptp_fun_Y1_6(B!40, A!41, F!42))) | (tptp_fun_Y1_6(B!40, A!41, F!42) = tptp_fun_Y2_5(B!40, A!41, F!42)))))))),
% 0.23/0.55 inference(unit_resolution,[status(thm)],[231, 225])).
% 0.23/0.55 tff(233,plain,
% 0.23/0.55 (((~((~maps(F!42, A!41, B!40)) | (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!42), B!40)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!40, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)))))))) | (~(maps(F!42, A!41, B!40) | (~((~member(tptp_fun_X_4(B!40, A!41, F!42), A!41)) | (~![Y: $i] : ((~member(Y, B!40)) | (~apply(F!42, tptp_fun_X_4(B!40, A!41, F!42), Y)))))) | (~((~member(tptp_fun_Y2_5(B!40, A!41, F!42), B!40)) | (~member(tptp_fun_Y1_6(B!40, A!41, F!42), B!40)) | (~member(tptp_fun_X_7(B!40, A!41, F!42), A!41)) | (~apply(F!42, tptp_fun_X_7(B!40, A!41, F!42), tptp_fun_Y2_5(B!40, A!41, F!42))) | (~apply(F!42, tptp_fun_X_7(B!40, A!41, F!42), tptp_fun_Y1_6(B!40, A!41, F!42))) | (tptp_fun_Y1_6(B!40, A!41, F!42) = tptp_fun_Y2_5(B!40, A!41, F!42))))))) | ((~maps(F!42, A!41, B!40)) | (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!42), B!40)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!40, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)))))))),
% 0.23/0.55 inference(tautology,[status(thm)],[])).
% 0.23/0.55 tff(234,plain,
% 0.23/0.55 ((~maps(F!42, A!41, B!40)) | (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!42), B!40)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!40, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40))))))),
% 0.23/0.55 inference(unit_resolution,[status(thm)],[233, 232])).
% 0.23/0.55 tff(235,plain,
% 0.23/0.55 (maps(F!42, A!41, B!40)),
% 0.23/0.55 inference(and_elim,[status(thm)],[111])).
% 0.23/0.55 tff(236,plain,
% 0.23/0.55 ((~((~maps(F!42, A!41, B!40)) | (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!42), B!40)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!40, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)))))))) | (~maps(F!42, A!41, B!40)) | (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!42), B!40)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!40, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40))))))),
% 0.23/0.55 inference(tautology,[status(thm)],[])).
% 0.23/0.55 tff(237,plain,
% 0.23/0.55 ((~((~maps(F!42, A!41, B!40)) | (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!42), B!40)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!40, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)))))))) | (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!42), B!40)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!40, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40))))))),
% 0.23/0.55 inference(unit_resolution,[status(thm)],[236, 235])).
% 0.23/0.55 tff(238,plain,
% 0.23/0.55 (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!42), B!40)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!40, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)))))),
% 0.23/0.56 inference(unit_resolution,[status(thm)],[237, 234])).
% 0.23/0.56 tff(239,plain,
% 0.23/0.56 (((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!42), B!40)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!40, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40))))) | ![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!42), B!40)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!40, F!42))))))),
% 0.23/0.56 inference(tautology,[status(thm)],[])).
% 0.23/0.56 tff(240,plain,
% 0.23/0.56 (![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!42), B!40)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!40, F!42))))))),
% 0.23/0.56 inference(unit_resolution,[status(thm)],[239, 238])).
% 0.23/0.56 tff(241,plain,
% 0.23/0.56 (((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!42), B!40)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!40, F!42))))))) | ((~member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), A!41)) | (~((~member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), B!40)) | (~apply(F!42, tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42))))))) <=> ((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!42), B!40)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!40, F!42))))))) | (~member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), A!41)) | (~((~member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), B!40)) | (~apply(F!42, tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42))))))),
% 0.23/0.56 inference(rewrite,[status(thm)],[])).
% 0.23/0.56 tff(242,plain,
% 0.23/0.56 ((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!42), B!40)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!40, F!42))))))) | ((~member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), A!41)) | (~((~member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), B!40)) | (~apply(F!42, tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42))))))),
% 0.23/0.56 inference(quant_inst,[status(thm)],[])).
% 0.23/0.56 tff(243,plain,
% 0.23/0.56 ((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!42), B!40)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!40, F!42))))))) | (~member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), A!41)) | (~((~member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), B!40)) | (~apply(F!42, tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42)))))),
% 0.23/0.56 inference(modus_ponens,[status(thm)],[242, 241])).
% 0.23/0.56 tff(244,plain,
% 0.23/0.56 (~((~member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), B!40)) | (~apply(F!42, tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42))))),
% 0.23/0.56 inference(unit_resolution,[status(thm)],[243, 240, 203])).
% 0.23/0.56 tff(245,plain,
% 0.23/0.56 (((~member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), B!40)) | (~apply(F!42, tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42)))) | apply(F!42, tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42))),
% 0.23/0.56 inference(tautology,[status(thm)],[])).
% 0.23/0.56 tff(246,plain,
% 0.23/0.56 (apply(F!42, tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42))),
% 0.23/0.56 inference(unit_resolution,[status(thm)],[245, 244])).
% 0.23/0.56 tff(247,plain,
% 0.23/0.56 (((~![F: $i, B: $i, A: $i, X: $i] : (~((~((~member(X, inverse_image3(F, B, A))) | (~((~member(X, A)) | (~member(tptp_fun_Y_26(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_26(X, B, F))))))) | (~(member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))) | (~((~(member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)) | (~member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), A!41)) | ![Y: $i] : ((~member(Y, image3(F!42, X!39, B!40))) | (~apply(F!42, tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), Y))))) | (~((~member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))) | (~((~member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), A!41)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), image3(F!42, X!39, B!40), F!42), image3(F!42, X!39, B!40))) | (~apply(F!42, tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), image3(F!42, X!39, B!40), F!42)))))))))) <=> ((~![F: $i, B: $i, A: $i, X: $i] : (~((~((~member(X, inverse_image3(F, B, A))) | (~((~member(X, A)) | (~member(tptp_fun_Y_26(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_26(X, B, F))))))) | (~(member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))) | (~((~(member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)) | (~member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), A!41)) | ![Y: $i] : ((~member(Y, image3(F!42, X!39, B!40))) | (~apply(F!42, tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), Y))))) | (~((~member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))) | (~((~member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), A!41)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), image3(F!42, X!39, B!40), F!42), image3(F!42, X!39, B!40))) | (~apply(F!42, tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), image3(F!42, X!39, B!40), F!42))))))))))),
% 0.23/0.56 inference(rewrite,[status(thm)],[])).
% 0.23/0.56 tff(248,plain,
% 0.23/0.56 ((~((~((~member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))) | (~((~member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), A!41)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), image3(F!42, X!39, B!40), F!42), image3(F!42, X!39, B!40))) | (~apply(F!42, tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), image3(F!42, X!39, B!40), F!42))))))) | (~(member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)) | (~member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), A!41)) | ![Y: $i] : ((~member(Y, image3(F!42, X!39, B!40))) | (~apply(F!42, tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), Y))))))) <=> (~((~(member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)) | (~member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), A!41)) | ![Y: $i] : ((~member(Y, image3(F!42, X!39, B!40))) | (~apply(F!42, tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), Y))))) | (~((~member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))) | (~((~member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), A!41)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), image3(F!42, X!39, B!40), F!42), image3(F!42, X!39, B!40))) | (~apply(F!42, tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), image3(F!42, X!39, B!40), F!42)))))))))),
% 0.23/0.56 inference(rewrite,[status(thm)],[])).
% 0.23/0.56 tff(249,plain,
% 0.23/0.56 (((~![F: $i, B: $i, A: $i, X: $i] : (~((~((~member(X, inverse_image3(F, B, A))) | (~((~member(X, A)) | (~member(tptp_fun_Y_26(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_26(X, B, F))))))) | (~(member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))) | (~((~member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), A!41)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), image3(F!42, X!39, B!40), F!42), image3(F!42, X!39, B!40))) | (~apply(F!42, tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), image3(F!42, X!39, B!40), F!42))))))) | (~(member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)) | (~member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), A!41)) | ![Y: $i] : ((~member(Y, image3(F!42, X!39, B!40))) | (~apply(F!42, tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), Y)))))))) <=> ((~![F: $i, B: $i, A: $i, X: $i] : (~((~((~member(X, inverse_image3(F, B, A))) | (~((~member(X, A)) | (~member(tptp_fun_Y_26(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_26(X, B, F))))))) | (~(member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))) | (~((~(member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)) | (~member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), A!41)) | ![Y: $i] : ((~member(Y, image3(F!42, X!39, B!40))) | (~apply(F!42, tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), Y))))) | (~((~member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))) | (~((~member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), A!41)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), image3(F!42, X!39, B!40), F!42), image3(F!42, X!39, B!40))) | (~apply(F!42, tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), image3(F!42, X!39, B!40), F!42))))))))))),
% 0.23/0.56 inference(monotonicity,[status(thm)],[248])).
% 0.23/0.56 tff(250,plain,
% 0.23/0.56 (((~![F: $i, B: $i, A: $i, X: $i] : (~((~((~member(X, inverse_image3(F, B, A))) | (~((~member(X, A)) | (~member(tptp_fun_Y_26(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_26(X, B, F))))))) | (~(member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))) | (~((~member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), A!41)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), image3(F!42, X!39, B!40), F!42), image3(F!42, X!39, B!40))) | (~apply(F!42, tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), image3(F!42, X!39, B!40), F!42))))))) | (~(member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)) | (~member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), A!41)) | ![Y: $i] : ((~member(Y, image3(F!42, X!39, B!40))) | (~apply(F!42, tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), Y)))))))) <=> ((~![F: $i, B: $i, A: $i, X: $i] : (~((~((~member(X, inverse_image3(F, B, A))) | (~((~member(X, A)) | (~member(tptp_fun_Y_26(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_26(X, B, F))))))) | (~(member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))) | (~((~(member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)) | (~member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), A!41)) | ![Y: $i] : ((~member(Y, image3(F!42, X!39, B!40))) | (~apply(F!42, tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), Y))))) | (~((~member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))) | (~((~member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), A!41)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), image3(F!42, X!39, B!40), F!42), image3(F!42, X!39, B!40))) | (~apply(F!42, tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), image3(F!42, X!39, B!40), F!42))))))))))),
% 0.23/0.56 inference(transitivity,[status(thm)],[249, 247])).
% 0.23/0.56 tff(251,plain,
% 0.23/0.56 ((~![F: $i, B: $i, A: $i, X: $i] : (~((~((~member(X, inverse_image3(F, B, A))) | (~((~member(X, A)) | (~member(tptp_fun_Y_26(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_26(X, B, F))))))) | (~(member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))) | (~((~((~member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))) | (~((~member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), A!41)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), image3(F!42, X!39, B!40), F!42), image3(F!42, X!39, B!40))) | (~apply(F!42, tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), image3(F!42, X!39, B!40), F!42))))))) | (~(member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)) | (~member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), A!41)) | ![Y: $i] : ((~member(Y, image3(F!42, X!39, B!40))) | (~apply(F!42, tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), Y)))))))),
% 0.23/0.56 inference(quant_inst,[status(thm)],[])).
% 0.23/0.56 tff(252,plain,
% 0.23/0.56 ((~![F: $i, B: $i, A: $i, X: $i] : (~((~((~member(X, inverse_image3(F, B, A))) | (~((~member(X, A)) | (~member(tptp_fun_Y_26(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_26(X, B, F))))))) | (~(member(X, inverse_image3(F, B, A)) | (~member(X, A)) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)))))))) | (~((~(member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)) | (~member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), A!41)) | ![Y: $i] : ((~member(Y, image3(F!42, X!39, B!40))) | (~apply(F!42, tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), Y))))) | (~((~member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))) | (~((~member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), A!41)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), image3(F!42, X!39, B!40), F!42), image3(F!42, X!39, B!40))) | (~apply(F!42, tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), image3(F!42, X!39, B!40), F!42)))))))))),
% 0.23/0.57 inference(modus_ponens,[status(thm)],[251, 250])).
% 0.23/0.57 tff(253,plain,
% 0.23/0.57 (~((~(member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)) | (~member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), A!41)) | ![Y: $i] : ((~member(Y, image3(F!42, X!39, B!40))) | (~apply(F!42, tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), Y))))) | (~((~member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))) | (~((~member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), A!41)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), image3(F!42, X!39, B!40), F!42), image3(F!42, X!39, B!40))) | (~apply(F!42, tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), image3(F!42, X!39, B!40), F!42))))))))),
% 0.23/0.57 inference(unit_resolution,[status(thm)],[252, 76])).
% 0.23/0.57 tff(254,plain,
% 0.23/0.57 (((~(member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)) | (~member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), A!41)) | ![Y: $i] : ((~member(Y, image3(F!42, X!39, B!40))) | (~apply(F!42, tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), Y))))) | (~((~member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))) | (~((~member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), A!41)) | (~member(tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), image3(F!42, X!39, B!40), F!42), image3(F!42, X!39, B!40))) | (~apply(F!42, tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), tptp_fun_Y_26(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), image3(F!42, X!39, B!40), F!42)))))))) | (member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)) | (~member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), A!41)) | ![Y: $i] : ((~member(Y, image3(F!42, X!39, B!40))) | (~apply(F!42, tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), Y))))),
% 0.23/0.57 inference(tautology,[status(thm)],[])).
% 0.23/0.57 tff(255,plain,
% 0.23/0.57 (member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)) | (~member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), A!41)) | ![Y: $i] : ((~member(Y, image3(F!42, X!39, B!40))) | (~apply(F!42, tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), Y)))),
% 0.23/0.57 inference(unit_resolution,[status(thm)],[254, 253])).
% 0.23/0.57 tff(256,plain,
% 0.23/0.57 (((~member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), X!39)) | member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))) | (~member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)))),
% 0.23/0.57 inference(tautology,[status(thm)],[])).
% 0.23/0.57 tff(257,plain,
% 0.23/0.57 (~member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), inverse_image3(F!42, image3(F!42, X!39, B!40), A!41))),
% 0.23/0.57 inference(unit_resolution,[status(thm)],[256, 197])).
% 0.23/0.57 tff(258,plain,
% 0.23/0.57 ((~(member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)) | (~member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), A!41)) | ![Y: $i] : ((~member(Y, image3(F!42, X!39, B!40))) | (~apply(F!42, tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), Y))))) | member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)) | (~member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), A!41)) | ![Y: $i] : ((~member(Y, image3(F!42, X!39, B!40))) | (~apply(F!42, tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), Y)))),
% 0.23/0.57 inference(tautology,[status(thm)],[])).
% 0.23/0.57 tff(259,plain,
% 0.23/0.57 ((~(member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), inverse_image3(F!42, image3(F!42, X!39, B!40), A!41)) | (~member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), A!41)) | ![Y: $i] : ((~member(Y, image3(F!42, X!39, B!40))) | (~apply(F!42, tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), Y))))) | (~member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), A!41)) | ![Y: $i] : ((~member(Y, image3(F!42, X!39, B!40))) | (~apply(F!42, tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), Y)))),
% 0.23/0.57 inference(unit_resolution,[status(thm)],[258, 257])).
% 0.23/0.57 tff(260,plain,
% 0.23/0.57 (![Y: $i] : ((~member(Y, image3(F!42, X!39, B!40))) | (~apply(F!42, tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), Y)))),
% 0.23/0.57 inference(unit_resolution,[status(thm)],[259, 203, 255])).
% 0.23/0.57 tff(261,plain,
% 0.23/0.57 (((~![Y: $i] : ((~member(Y, image3(F!42, X!39, B!40))) | (~apply(F!42, tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), Y)))) | ((~member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), image3(F!42, X!39, B!40))) | (~apply(F!42, tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42))))) <=> ((~![Y: $i] : ((~member(Y, image3(F!42, X!39, B!40))) | (~apply(F!42, tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), Y)))) | (~member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), image3(F!42, X!39, B!40))) | (~apply(F!42, tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42))))),
% 0.23/0.57 inference(rewrite,[status(thm)],[])).
% 0.23/0.57 tff(262,plain,
% 0.23/0.57 ((~![Y: $i] : ((~member(Y, image3(F!42, X!39, B!40))) | (~apply(F!42, tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), Y)))) | ((~member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), image3(F!42, X!39, B!40))) | (~apply(F!42, tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42))))),
% 0.23/0.57 inference(quant_inst,[status(thm)],[])).
% 0.23/0.57 tff(263,plain,
% 0.23/0.57 ((~![Y: $i] : ((~member(Y, image3(F!42, X!39, B!40))) | (~apply(F!42, tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), Y)))) | (~member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), image3(F!42, X!39, B!40))) | (~apply(F!42, tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42)))),
% 0.23/0.57 inference(modus_ponens,[status(thm)],[262, 261])).
% 0.23/0.57 tff(264,plain,
% 0.23/0.57 (~member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), image3(F!42, X!39, B!40))),
% 0.23/0.57 inference(unit_resolution,[status(thm)],[263, 260, 246])).
% 0.23/0.57 tff(265,plain,
% 0.23/0.57 (((~member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), B!40)) | (~apply(F!42, tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42)))) | member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), B!40)),
% 0.23/0.57 inference(tautology,[status(thm)],[])).
% 0.23/0.57 tff(266,plain,
% 0.23/0.57 (member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), B!40)),
% 0.23/0.57 inference(unit_resolution,[status(thm)],[265, 244])).
% 0.23/0.57 tff(267,plain,
% 0.23/0.57 ((~((~member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), B!40)) | member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), image3(F!42, X!39, B!40)) | ![X: $i] : ((~member(X, X!39)) | (~apply(F!42, X, tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42)))))) | (~member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), B!40)) | member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), image3(F!42, X!39, B!40)) | ![X: $i] : ((~member(X, X!39)) | (~apply(F!42, X, tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42))))),
% 0.23/0.57 inference(tautology,[status(thm)],[])).
% 0.23/0.57 tff(268,plain,
% 0.23/0.57 ((~((~member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), B!40)) | member(tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42), image3(F!42, X!39, B!40)) | ![X: $i] : ((~member(X, X!39)) | (~apply(F!42, X, tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42)))))) | ![X: $i] : ((~member(X, X!39)) | (~apply(F!42, X, tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42))))),
% 0.23/0.57 inference(unit_resolution,[status(thm)],[267, 266, 264])).
% 0.23/0.57 tff(269,plain,
% 0.23/0.57 (![X: $i] : ((~member(X, X!39)) | (~apply(F!42, X, tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42))))),
% 0.23/0.57 inference(unit_resolution,[status(thm)],[268, 25])).
% 0.23/0.57 tff(270,plain,
% 0.23/0.57 (((~![X: $i] : ((~member(X, X!39)) | (~apply(F!42, X, tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42))))) | ((~member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), X!39)) | (~apply(F!42, tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42))))) <=> ((~![X: $i] : ((~member(X, X!39)) | (~apply(F!42, X, tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42))))) | (~member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), X!39)) | (~apply(F!42, tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42))))),
% 0.23/0.57 inference(rewrite,[status(thm)],[])).
% 0.23/0.57 tff(271,plain,
% 0.23/0.57 ((~![X: $i] : ((~member(X, X!39)) | (~apply(F!42, X, tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42))))) | ((~member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), X!39)) | (~apply(F!42, tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42))))),
% 0.23/0.57 inference(quant_inst,[status(thm)],[])).
% 0.23/0.57 tff(272,plain,
% 0.23/0.57 ((~![X: $i] : ((~member(X, X!39)) | (~apply(F!42, X, tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42))))) | (~member(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), X!39)) | (~apply(F!42, tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), tptp_fun_Y_3(tptp_fun_X_0(inverse_image3(F!42, image3(F!42, X!39, B!40), A!41), X!39), B!40, F!42)))),
% 0.23/0.57 inference(modus_ponens,[status(thm)],[271, 270])).
% 0.23/0.57 tff(273,plain,
% 0.23/0.57 ($false),
% 0.23/0.57 inference(unit_resolution,[status(thm)],[272, 199, 246, 269])).
% 0.23/0.57 % SZS output end Proof
% 0.23/0.58 % E exiting
%------------------------------------------------------------------------------