%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET727+4 : TPTP v9.0.0. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n013.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 05:26:13 AM UTC 2025
% Result : Theorem 0.21s 0.42s
% Output : Proof 0.48s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SET727+4 : TPTP v9.0.0. Bugfixed v2.2.1.
% 0.08/0.13 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n013.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Jun 20 05:39:08 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.21/0.42 % SZS status Theorem
% 0.21/0.42 % SZS output start Proof
% 0.21/0.42 tff(tptp_fun_Y2_12_type, type, (
% 0.21/0.42 tptp_fun_Y2_12: ( $i * $i * $i * $i ) > $i)).
% 0.21/0.42 tff(inverse_function_type, type, (
% 0.21/0.42 inverse_function: ( $i * $i * $i ) > $i)).
% 0.21/0.42 tff(tptp_fun_B_39_type, type, (
% 0.21/0.42 tptp_fun_B_39: $i)).
% 0.21/0.42 tff(tptp_fun_A_40_type, type, (
% 0.21/0.42 tptp_fun_A_40: $i)).
% 0.21/0.42 tff(tptp_fun_F_43_type, type, (
% 0.21/0.42 tptp_fun_F_43: $i)).
% 0.21/0.42 tff(tptp_fun_H_41_type, type, (
% 0.21/0.42 tptp_fun_H_41: $i)).
% 0.21/0.42 tff(tptp_fun_Y1_13_type, type, (
% 0.21/0.42 tptp_fun_Y1_13: ( $i * $i * $i * $i ) > $i)).
% 0.21/0.42 tff(tptp_fun_Y_3_type, type, (
% 0.21/0.42 tptp_fun_Y_3: ( $i * $i * $i ) > $i)).
% 0.21/0.42 tff(tptp_fun_G_42_type, type, (
% 0.21/0.42 tptp_fun_G_42: $i)).
% 0.21/0.42 tff(apply_type, type, (
% 0.21/0.42 apply: ( $i * $i * $i ) > $o)).
% 0.21/0.42 tff(tptp_fun_Y_8_type, type, (
% 0.21/0.42 tptp_fun_Y_8: ( $i * $i * $i * $i * $i ) > $i)).
% 0.21/0.42 tff(member_type, type, (
% 0.21/0.42 member: ( $i * $i ) > $o)).
% 0.21/0.42 tff(compose_function_type, type, (
% 0.21/0.42 compose_function: ( $i * $i * $i * $i * $i ) > $i)).
% 0.21/0.42 tff(tptp_fun_X_14_type, type, (
% 0.21/0.42 tptp_fun_X_14: ( $i * $i * $i * $i ) > $i)).
% 0.21/0.42 tff(equal_maps_type, type, (
% 0.21/0.42 equal_maps: ( $i * $i * $i * $i ) > $o)).
% 0.21/0.42 tff(identity_type, type, (
% 0.21/0.42 identity: ( $i * $i ) > $o)).
% 0.21/0.42 tff(maps_type, type, (
% 0.21/0.42 maps: ( $i * $i * $i ) > $o)).
% 0.21/0.42 tff(tptp_fun_X_15_type, type, (
% 0.21/0.42 tptp_fun_X_15: ( $i * $i ) > $i)).
% 0.21/0.42 tff(tptp_fun_Y2_5_type, type, (
% 0.21/0.42 tptp_fun_Y2_5: ( $i * $i * $i ) > $i)).
% 0.21/0.42 tff(tptp_fun_Y1_6_type, type, (
% 0.21/0.42 tptp_fun_Y1_6: ( $i * $i * $i ) > $i)).
% 0.21/0.42 tff(tptp_fun_X_7_type, type, (
% 0.21/0.42 tptp_fun_X_7: ( $i * $i * $i ) > $i)).
% 0.21/0.42 tff(tptp_fun_X_4_type, type, (
% 0.21/0.42 tptp_fun_X_4: ( $i * $i * $i ) > $i)).
% 0.21/0.42 tff(1,plain,
% 0.21/0.42 (^[F: $i, G: $i, A: $i, B: $i] : refl((~((~((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1))))) | (~(equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F))))))))) <=> (~((~((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1))))) | (~(equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F))))))))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(2,plain,
% 0.21/0.42 (![F: $i, G: $i, A: $i, B: $i] : (~((~((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1))))) | (~(equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F))))))))) <=> ![F: $i, G: $i, A: $i, B: $i] : (~((~((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1))))) | (~(equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F)))))))))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[1])).
% 0.21/0.42 tff(3,plain,
% 0.21/0.42 (^[F: $i, G: $i, A: $i, B: $i] : rewrite((~((~((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1))))) | (~(equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F))))))))) <=> (~((~((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1))))) | (~(equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F))))))))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(4,plain,
% 0.21/0.42 (![F: $i, G: $i, A: $i, B: $i] : (~((~((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1))))) | (~(equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F))))))))) <=> ![F: $i, G: $i, A: $i, B: $i] : (~((~((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1))))) | (~(equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F)))))))))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[3])).
% 0.21/0.42 tff(5,plain,
% 0.21/0.42 (![F: $i, G: $i, A: $i, B: $i] : (~((~((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1))))) | (~(equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F))))))))) <=> ![F: $i, G: $i, A: $i, B: $i] : (~((~((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1))))) | (~(equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F)))))))))),
% 0.21/0.42 inference(transitivity,[status(thm)],[4, 2])).
% 0.21/0.42 tff(6,plain,
% 0.21/0.42 (^[F: $i, G: $i, A: $i, B: $i] : trans(monotonicity(rewrite(((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(member(X, A) & member(Y1, B) & member(Y2, B))) | (~(apply(F, X, Y1) & apply(G, X, Y2))))) <=> ((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1))))), trans(monotonicity(rewrite((~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~(member(tptp_fun_X_14(B, A, G, F), A) & member(tptp_fun_Y1_13(B, A, G, F), B) & member(tptp_fun_Y2_12(B, A, G, F), B))) | (~(apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F)) & apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F)))))) <=> (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F)))))), ((equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~(member(tptp_fun_X_14(B, A, G, F), A) & member(tptp_fun_Y1_13(B, A, G, F), B) & member(tptp_fun_Y2_12(B, A, G, F), B))) | (~(apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F)) & apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F))))))) <=> (equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F)))))))), rewrite((equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F)))))) <=> (equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F))))))), ((equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~(member(tptp_fun_X_14(B, A, G, F), A) & member(tptp_fun_Y1_13(B, A, G, F), B) & member(tptp_fun_Y2_12(B, A, G, F), B))) | (~(apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F)) & apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F))))))) <=> (equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F)))))))), ((((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(member(X, A) & member(Y1, B) & member(Y2, B))) | (~(apply(F, X, Y1) & apply(G, X, Y2))))) & (equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~(member(tptp_fun_X_14(B, A, G, F), A) & member(tptp_fun_Y1_13(B, A, G, F), B) & member(tptp_fun_Y2_12(B, A, G, F), B))) | (~(apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F)) & apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F)))))))) <=> (((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1)))) & (equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F))))))))), rewrite((((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1)))) & (equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F))))))) <=> (~((~((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1))))) | (~(equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F)))))))))), ((((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(member(X, A) & member(Y1, B) & member(Y2, B))) | (~(apply(F, X, Y1) & apply(G, X, Y2))))) & (equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~(member(tptp_fun_X_14(B, A, G, F), A) & member(tptp_fun_Y1_13(B, A, G, F), B) & member(tptp_fun_Y2_12(B, A, G, F), B))) | (~(apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F)) & apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F)))))))) <=> (~((~((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1))))) | (~(equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F)))))))))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(7,plain,
% 0.21/0.42 (![F: $i, G: $i, A: $i, B: $i] : (((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(member(X, A) & member(Y1, B) & member(Y2, B))) | (~(apply(F, X, Y1) & apply(G, X, Y2))))) & (equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~(member(tptp_fun_X_14(B, A, G, F), A) & member(tptp_fun_Y1_13(B, A, G, F), B) & member(tptp_fun_Y2_12(B, A, G, F), B))) | (~(apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F)) & apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F)))))))) <=> ![F: $i, G: $i, A: $i, B: $i] : (~((~((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1))))) | (~(equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F)))))))))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[6])).
% 0.21/0.42 tff(8,plain,
% 0.21/0.42 (![F: $i, G: $i, A: $i, B: $i] : (equal_maps(F, G, A, B) <=> ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(member(X, A) & member(Y1, B) & member(Y2, B))) | (~(apply(F, X, Y1) & apply(G, X, Y2))))) <=> ![F: $i, G: $i, A: $i, B: $i] : (equal_maps(F, G, A, B) <=> ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(member(X, A) & member(Y1, B) & member(Y2, B))) | (~(apply(F, X, Y1) & apply(G, X, Y2)))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(9,plain,
% 0.21/0.42 (^[F: $i, G: $i, A: $i, B: $i] : rewrite((equal_maps(F, G, A, B) <=> ![X: $i, Y1: $i, Y2: $i] : (((member(X, A) & member(Y1, B)) & member(Y2, B)) => ((apply(F, X, Y1) & apply(G, X, Y2)) => (Y1 = Y2)))) <=> (equal_maps(F, G, A, B) <=> ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(member(X, A) & member(Y1, B) & member(Y2, B))) | (~(apply(F, X, Y1) & apply(G, X, Y2))))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(10,plain,
% 0.21/0.42 (![F: $i, G: $i, A: $i, B: $i] : (equal_maps(F, G, A, B) <=> ![X: $i, Y1: $i, Y2: $i] : (((member(X, A) & member(Y1, B)) & member(Y2, B)) => ((apply(F, X, Y1) & apply(G, X, Y2)) => (Y1 = Y2)))) <=> ![F: $i, G: $i, A: $i, B: $i] : (equal_maps(F, G, A, B) <=> ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(member(X, A) & member(Y1, B) & member(Y2, B))) | (~(apply(F, X, Y1) & apply(G, X, Y2)))))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[9])).
% 0.21/0.42 tff(11,axiom,(![F: $i, G: $i, A: $i, B: $i] : (equal_maps(F, G, A, B) <=> ![X: $i, Y1: $i, Y2: $i] : (((member(X, A) & member(Y1, B)) & member(Y2, B)) => ((apply(F, X, Y1) & apply(G, X, Y2)) => (Y1 = Y2))))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+1.ax','equal_maps')).
% 0.21/0.42 tff(12,plain,
% 0.21/0.42 (![F: $i, G: $i, A: $i, B: $i] : (equal_maps(F, G, A, B) <=> ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(member(X, A) & member(Y1, B) & member(Y2, B))) | (~(apply(F, X, Y1) & apply(G, X, Y2)))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.21/0.42 tff(13,plain,
% 0.21/0.42 (![F: $i, G: $i, A: $i, B: $i] : (equal_maps(F, G, A, B) <=> ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(member(X, A) & member(Y1, B) & member(Y2, B))) | (~(apply(F, X, Y1) & apply(G, X, Y2)))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[12, 8])).
% 0.21/0.42 tff(14,plain,(
% 0.21/0.42 ![F: $i, G: $i, A: $i, B: $i] : (((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(member(X, A) & member(Y1, B) & member(Y2, B))) | (~(apply(F, X, Y1) & apply(G, X, Y2))))) & (equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~(member(tptp_fun_X_14(B, A, G, F), A) & member(tptp_fun_Y1_13(B, A, G, F), B) & member(tptp_fun_Y2_12(B, A, G, F), B))) | (~(apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F)) & apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F))))))))),
% 0.21/0.42 inference(skolemize,[status(sab)],[13])).
% 0.21/0.42 tff(15,plain,
% 0.21/0.42 (![F: $i, G: $i, A: $i, B: $i] : (~((~((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1))))) | (~(equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F)))))))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[14, 7])).
% 0.21/0.42 tff(16,plain,
% 0.21/0.42 (![F: $i, G: $i, A: $i, B: $i] : (~((~((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1))))) | (~(equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F)))))))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[15, 5])).
% 0.21/0.42 tff(17,plain,
% 0.21/0.42 (((~![F: $i, G: $i, A: $i, B: $i] : (~((~((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1))))) | (~(equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F)))))))))) | (~((~((~equal_maps(inverse_function(F!43, A!40, B!39), H!41, B!39, A!40)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~member(X, B!39)) | (~member(Y1, A!40)) | (~apply(H!41, X, Y2)) | (~apply(inverse_function(F!43, A!40, B!39), X, Y1))))) | (~(equal_maps(inverse_function(F!43, A!40, B!39), H!41, B!39, A!40) | (~((~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~apply(inverse_function(F!43, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))))))) <=> ((~![F: $i, G: $i, A: $i, B: $i] : (~((~((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1))))) | (~(equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F)))))))))) | (~((~((~equal_maps(inverse_function(F!43, A!40, B!39), H!41, B!39, A!40)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~member(X, B!39)) | (~member(Y1, A!40)) | (~apply(H!41, X, Y2)) | (~apply(inverse_function(F!43, A!40, B!39), X, Y1))))) | (~(equal_maps(inverse_function(F!43, A!40, B!39), H!41, B!39, A!40) | (~((~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~apply(inverse_function(F!43, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))))))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(18,plain,
% 0.21/0.43 ((~((~((~equal_maps(inverse_function(F!43, A!40, B!39), H!41, B!39, A!40)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(H!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)) | (~member(Y2, A!40)) | (~apply(inverse_function(F!43, A!40, B!39), X, Y1))))) | (~(equal_maps(inverse_function(F!43, A!40, B!39), H!41, B!39, A!40) | (~((tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | (~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~apply(inverse_function(F!43, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))))))) <=> (~((~((~equal_maps(inverse_function(F!43, A!40, B!39), H!41, B!39, A!40)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~member(X, B!39)) | (~member(Y1, A!40)) | (~apply(H!41, X, Y2)) | (~apply(inverse_function(F!43, A!40, B!39), X, Y1))))) | (~(equal_maps(inverse_function(F!43, A!40, B!39), H!41, B!39, A!40) | (~((~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~apply(inverse_function(F!43, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(19,plain,
% 0.21/0.43 (((~![F: $i, G: $i, A: $i, B: $i] : (~((~((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1))))) | (~(equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F)))))))))) | (~((~((~equal_maps(inverse_function(F!43, A!40, B!39), H!41, B!39, A!40)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(H!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)) | (~member(Y2, A!40)) | (~apply(inverse_function(F!43, A!40, B!39), X, Y1))))) | (~(equal_maps(inverse_function(F!43, A!40, B!39), H!41, B!39, A!40) | (~((tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | (~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~apply(inverse_function(F!43, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))))))))) <=> ((~![F: $i, G: $i, A: $i, B: $i] : (~((~((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1))))) | (~(equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F)))))))))) | (~((~((~equal_maps(inverse_function(F!43, A!40, B!39), H!41, B!39, A!40)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~member(X, B!39)) | (~member(Y1, A!40)) | (~apply(H!41, X, Y2)) | (~apply(inverse_function(F!43, A!40, B!39), X, Y1))))) | (~(equal_maps(inverse_function(F!43, A!40, B!39), H!41, B!39, A!40) | (~((~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~apply(inverse_function(F!43, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))))))))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[18])).
% 0.21/0.43 tff(20,plain,
% 0.21/0.43 (((~![F: $i, G: $i, A: $i, B: $i] : (~((~((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1))))) | (~(equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F)))))))))) | (~((~((~equal_maps(inverse_function(F!43, A!40, B!39), H!41, B!39, A!40)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(H!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)) | (~member(Y2, A!40)) | (~apply(inverse_function(F!43, A!40, B!39), X, Y1))))) | (~(equal_maps(inverse_function(F!43, A!40, B!39), H!41, B!39, A!40) | (~((tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | (~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~apply(inverse_function(F!43, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))))))))) <=> ((~![F: $i, G: $i, A: $i, B: $i] : (~((~((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1))))) | (~(equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F)))))))))) | (~((~((~equal_maps(inverse_function(F!43, A!40, B!39), H!41, B!39, A!40)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~member(X, B!39)) | (~member(Y1, A!40)) | (~apply(H!41, X, Y2)) | (~apply(inverse_function(F!43, A!40, B!39), X, Y1))))) | (~(equal_maps(inverse_function(F!43, A!40, B!39), H!41, B!39, A!40) | (~((~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~apply(inverse_function(F!43, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))))))))),
% 0.21/0.44 inference(transitivity,[status(thm)],[19, 17])).
% 0.21/0.44 tff(21,plain,
% 0.21/0.44 ((~![F: $i, G: $i, A: $i, B: $i] : (~((~((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1))))) | (~(equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F)))))))))) | (~((~((~equal_maps(inverse_function(F!43, A!40, B!39), H!41, B!39, A!40)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(H!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)) | (~member(Y2, A!40)) | (~apply(inverse_function(F!43, A!40, B!39), X, Y1))))) | (~(equal_maps(inverse_function(F!43, A!40, B!39), H!41, B!39, A!40) | (~((tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | (~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~apply(inverse_function(F!43, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))))))))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(22,plain,
% 0.21/0.44 ((~![F: $i, G: $i, A: $i, B: $i] : (~((~((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1))))) | (~(equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F)))))))))) | (~((~((~equal_maps(inverse_function(F!43, A!40, B!39), H!41, B!39, A!40)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~member(X, B!39)) | (~member(Y1, A!40)) | (~apply(H!41, X, Y2)) | (~apply(inverse_function(F!43, A!40, B!39), X, Y1))))) | (~(equal_maps(inverse_function(F!43, A!40, B!39), H!41, B!39, A!40) | (~((~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~apply(inverse_function(F!43, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.21/0.44 tff(23,plain,
% 0.21/0.44 (~((~((~equal_maps(inverse_function(F!43, A!40, B!39), H!41, B!39, A!40)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~member(X, B!39)) | (~member(Y1, A!40)) | (~apply(H!41, X, Y2)) | (~apply(inverse_function(F!43, A!40, B!39), X, Y1))))) | (~(equal_maps(inverse_function(F!43, A!40, B!39), H!41, B!39, A!40) | (~((~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~apply(inverse_function(F!43, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))))))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[22, 16])).
% 0.21/0.44 tff(24,plain,
% 0.21/0.44 (((~((~equal_maps(inverse_function(F!43, A!40, B!39), H!41, B!39, A!40)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~member(X, B!39)) | (~member(Y1, A!40)) | (~apply(H!41, X, Y2)) | (~apply(inverse_function(F!43, A!40, B!39), X, Y1))))) | (~(equal_maps(inverse_function(F!43, A!40, B!39), H!41, B!39, A!40) | (~((~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~apply(inverse_function(F!43, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))))) | (equal_maps(inverse_function(F!43, A!40, B!39), H!41, B!39, A!40) | (~((~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~apply(inverse_function(F!43, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))))),
% 0.21/0.44 inference(tautology,[status(thm)],[])).
% 0.21/0.44 tff(25,plain,
% 0.21/0.44 (equal_maps(inverse_function(F!43, A!40, B!39), H!41, B!39, A!40) | (~((~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~apply(inverse_function(F!43, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[24, 23])).
% 0.21/0.44 tff(26,plain,
% 0.21/0.44 ((~![F: $i, G: $i, H: $i, A: $i, B: $i] : ((~(maps(F, A, B) & maps(G, B, A) & maps(H, B, A) & identity(compose_function(G, F, A, B, A), A) & identity(compose_function(F, H, B, A, B), B))) | equal_maps(inverse_function(F, A, B), H, B, A))) <=> (~![F: $i, G: $i, H: $i, A: $i, B: $i] : ((~(maps(F, A, B) & maps(G, B, A) & maps(H, B, A) & identity(compose_function(G, F, A, B, A), A) & identity(compose_function(F, H, B, A, B), B))) | equal_maps(inverse_function(F, A, B), H, B, A)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(27,plain,
% 0.21/0.44 ((~![F: $i, G: $i, H: $i, A: $i, B: $i] : (((((maps(F, A, B) & maps(G, B, A)) & maps(H, B, A)) & identity(compose_function(G, F, A, B, A), A)) & identity(compose_function(F, H, B, A, B), B)) => equal_maps(inverse_function(F, A, B), H, B, A))) <=> (~![F: $i, G: $i, H: $i, A: $i, B: $i] : ((~(maps(F, A, B) & maps(G, B, A) & maps(H, B, A) & identity(compose_function(G, F, A, B, A), A) & identity(compose_function(F, H, B, A, B), B))) | equal_maps(inverse_function(F, A, B), H, B, A)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(28,axiom,(~![F: $i, G: $i, H: $i, A: $i, B: $i] : (((((maps(F, A, B) & maps(G, B, A)) & maps(H, B, A)) & identity(compose_function(G, F, A, B, A), A)) & identity(compose_function(F, H, B, A, B), B)) => equal_maps(inverse_function(F, A, B), H, B, A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','thII18')).
% 0.21/0.44 tff(29,plain,
% 0.21/0.44 (~![F: $i, G: $i, H: $i, A: $i, B: $i] : ((~(maps(F, A, B) & maps(G, B, A) & maps(H, B, A) & identity(compose_function(G, F, A, B, A), A) & identity(compose_function(F, H, B, A, B), B))) | equal_maps(inverse_function(F, A, B), H, B, A))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.21/0.44 tff(30,plain,
% 0.21/0.44 (~![F: $i, G: $i, H: $i, A: $i, B: $i] : ((~(maps(F, A, B) & maps(G, B, A) & maps(H, B, A) & identity(compose_function(G, F, A, B, A), A) & identity(compose_function(F, H, B, A, B), B))) | equal_maps(inverse_function(F, A, B), H, B, A))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[29, 26])).
% 0.21/0.45 tff(31,plain,
% 0.21/0.45 (~![F: $i, G: $i, H: $i, A: $i, B: $i] : ((~(maps(F, A, B) & maps(G, B, A) & maps(H, B, A) & identity(compose_function(G, F, A, B, A), A) & identity(compose_function(F, H, B, A, B), B))) | equal_maps(inverse_function(F, A, B), H, B, A))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[30, 26])).
% 0.21/0.45 tff(32,plain,
% 0.21/0.45 (~![F: $i, G: $i, H: $i, A: $i, B: $i] : ((~(maps(F, A, B) & maps(G, B, A) & maps(H, B, A) & identity(compose_function(G, F, A, B, A), A) & identity(compose_function(F, H, B, A, B), B))) | equal_maps(inverse_function(F, A, B), H, B, A))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[31, 26])).
% 0.21/0.45 tff(33,plain,(
% 0.21/0.45 ~((~(maps(F!43, A!40, B!39) & maps(G!42, B!39, A!40) & maps(H!41, B!39, A!40) & identity(compose_function(G!42, F!43, A!40, B!39, A!40), A!40) & identity(compose_function(F!43, H!41, B!39, A!40, B!39), B!39))) | equal_maps(inverse_function(F!43, A!40, B!39), H!41, B!39, A!40))),
% 0.21/0.45 inference(skolemize,[status(sab)],[32])).
% 0.21/0.45 tff(34,plain,
% 0.21/0.45 (~equal_maps(inverse_function(F!43, A!40, B!39), H!41, B!39, A!40)),
% 0.21/0.45 inference(or_elim,[status(thm)],[33])).
% 0.21/0.45 tff(35,plain,
% 0.21/0.45 ((~(equal_maps(inverse_function(F!43, A!40, B!39), H!41, B!39, A!40) | (~((~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~apply(inverse_function(F!43, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))))) | equal_maps(inverse_function(F!43, A!40, B!39), H!41, B!39, A!40) | (~((~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~apply(inverse_function(F!43, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))),
% 0.21/0.45 inference(tautology,[status(thm)],[])).
% 0.21/0.45 tff(36,plain,
% 0.21/0.45 ((~(equal_maps(inverse_function(F!43, A!40, B!39), H!41, B!39, A!40) | (~((~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~apply(inverse_function(F!43, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))))) | (~((~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~apply(inverse_function(F!43, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[35, 34])).
% 0.21/0.45 tff(37,plain,
% 0.21/0.45 (~((~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~apply(inverse_function(F!43, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[36, 25])).
% 0.21/0.45 tff(38,plain,
% 0.21/0.45 (((~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~apply(inverse_function(F!43, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)),
% 0.21/0.45 inference(tautology,[status(thm)],[])).
% 0.21/0.45 tff(39,plain,
% 0.21/0.45 (member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[38, 37])).
% 0.21/0.45 tff(40,plain,
% 0.21/0.45 (^[G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : refl(((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z)))))))) <=> ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z)))))))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(41,plain,
% 0.21/0.45 (![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z)))))))) <=> ![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[40])).
% 0.21/0.45 tff(42,plain,
% 0.21/0.45 (^[G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : rewrite(((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z)))))))) <=> ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z)))))))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(43,plain,
% 0.21/0.45 (![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z)))))))) <=> ![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[42])).
% 0.21/0.45 tff(44,plain,
% 0.21/0.45 (![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z)))))))) <=> ![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))),
% 0.21/0.45 inference(transitivity,[status(thm)],[43, 41])).
% 0.21/0.45 tff(45,plain,
% 0.21/0.45 (^[G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : trans(monotonicity(trans(monotonicity(rewrite((member(X, A) & member(Z, C)) <=> (~((~member(Z, C)) | (~member(X, A))))), ((~(member(X, A) & member(Z, C))) <=> (~(~((~member(Z, C)) | (~member(X, A))))))), rewrite((~(~((~member(Z, C)) | (~member(X, A))))) <=> ((~member(Z, C)) | (~member(X, A)))), ((~(member(X, A) & member(Z, C))) <=> ((~member(Z, C)) | (~member(X, A))))), trans(monotonicity(rewrite(((~apply(compose_function(G, F, A, B, C), X, Z)) | (member(tptp_fun_Y_8(Z, X, B, F, G), B) & apply(F, X, tptp_fun_Y_8(Z, X, B, F, G)) & apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z))) <=> ((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))), rewrite((apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y) & apply(G, Y, Z)))) <=> (apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))), ((((~apply(compose_function(G, F, A, B, C), X, Z)) | (member(tptp_fun_Y_8(Z, X, B, F, G), B) & apply(F, X, tptp_fun_Y_8(Z, X, B, F, G)) & apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z))) & (apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y) & apply(G, Y, Z))))) <=> (((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z))))) & (apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))), rewrite((((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z))))) & (apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))) <=> (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z)))))))), ((((~apply(compose_function(G, F, A, B, C), X, Z)) | (member(tptp_fun_Y_8(Z, X, B, F, G), B) & apply(F, X, tptp_fun_Y_8(Z, X, B, F, G)) & apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z))) & (apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y) & apply(G, Y, Z))))) <=> (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))), (((~(member(X, A) & member(Z, C))) | (((~apply(compose_function(G, F, A, B, C), X, Z)) | (member(tptp_fun_Y_8(Z, X, B, F, G), B) & apply(F, X, tptp_fun_Y_8(Z, X, B, F, G)) & apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z))) & (apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y) & apply(G, Y, Z)))))) <=> (((~member(Z, C)) | (~member(X, A))) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z)))))))))), rewrite((((~member(Z, C)) | (~member(X, A))) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z)))))))) <=> ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))), (((~(member(X, A) & member(Z, C))) | (((~apply(compose_function(G, F, A, B, C), X, Z)) | (member(tptp_fun_Y_8(Z, X, B, F, G), B) & apply(F, X, tptp_fun_Y_8(Z, X, B, F, G)) & apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z))) & (apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y) & apply(G, Y, Z)))))) <=> ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(46,plain,
% 0.21/0.46 (![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~(member(X, A) & member(Z, C))) | (((~apply(compose_function(G, F, A, B, C), X, Z)) | (member(tptp_fun_Y_8(Z, X, B, F, G), B) & apply(F, X, tptp_fun_Y_8(Z, X, B, F, G)) & apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z))) & (apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y) & apply(G, Y, Z)))))) <=> ![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[45])).
% 0.21/0.46 tff(47,plain,
% 0.21/0.46 (![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~(member(X, A) & member(Z, C))) | (apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : (member(Y, B) & apply(F, X, Y) & apply(G, Y, Z)))) <=> ![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~(member(X, A) & member(Z, C))) | (apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : (member(Y, B) & apply(F, X, Y) & apply(G, Y, Z))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(48,plain,
% 0.21/0.46 (^[G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : trans(monotonicity(rewrite((apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : ((member(Y, B) & apply(F, X, Y)) & apply(G, Y, Z))) <=> (apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : (member(Y, B) & apply(F, X, Y) & apply(G, Y, Z)))), (((member(X, A) & member(Z, C)) => (apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : ((member(Y, B) & apply(F, X, Y)) & apply(G, Y, Z)))) <=> ((member(X, A) & member(Z, C)) => (apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : (member(Y, B) & apply(F, X, Y) & apply(G, Y, Z)))))), rewrite(((member(X, A) & member(Z, C)) => (apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : (member(Y, B) & apply(F, X, Y) & apply(G, Y, Z)))) <=> ((~(member(X, A) & member(Z, C))) | (apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : (member(Y, B) & apply(F, X, Y) & apply(G, Y, Z))))), (((member(X, A) & member(Z, C)) => (apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : ((member(Y, B) & apply(F, X, Y)) & apply(G, Y, Z)))) <=> ((~(member(X, A) & member(Z, C))) | (apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : (member(Y, B) & apply(F, X, Y) & apply(G, Y, Z))))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(49,plain,
% 0.21/0.46 (![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((member(X, A) & member(Z, C)) => (apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : ((member(Y, B) & apply(F, X, Y)) & apply(G, Y, Z)))) <=> ![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~(member(X, A) & member(Z, C))) | (apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : (member(Y, B) & apply(F, X, Y) & apply(G, Y, Z))))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[48])).
% 0.21/0.46 tff(50,axiom,(![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((member(X, A) & member(Z, C)) => (apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : ((member(Y, B) & apply(F, X, Y)) & apply(G, Y, Z))))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+1.ax','compose_function')).
% 0.21/0.46 tff(51,plain,
% 0.21/0.46 (![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~(member(X, A) & member(Z, C))) | (apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : (member(Y, B) & apply(F, X, Y) & apply(G, Y, Z))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.21/0.46 tff(52,plain,
% 0.21/0.46 (![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~(member(X, A) & member(Z, C))) | (apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : (member(Y, B) & apply(F, X, Y) & apply(G, Y, Z))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[51, 47])).
% 0.21/0.46 tff(53,plain,(
% 0.21/0.46 ![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~(member(X, A) & member(Z, C))) | (((~apply(compose_function(G, F, A, B, C), X, Z)) | (member(tptp_fun_Y_8(Z, X, B, F, G), B) & apply(F, X, tptp_fun_Y_8(Z, X, B, F, G)) & apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z))) & (apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y) & apply(G, Y, Z))))))),
% 0.21/0.46 inference(skolemize,[status(sab)],[52])).
% 0.21/0.46 tff(54,plain,
% 0.21/0.46 (![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[53, 46])).
% 0.21/0.46 tff(55,plain,
% 0.21/0.46 (![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[54, 44])).
% 0.21/0.46 tff(56,plain,
% 0.21/0.46 (((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~((~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))))) | (~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))))))))) <=> ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~((~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))))) | (~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))))))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(57,plain,
% 0.21/0.47 (((~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~((~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))))) | (~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))))))))) <=> ((~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~((~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))))) | (~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))))))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(58,plain,
% 0.21/0.47 ((~((~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))))) | (~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))))))) <=> (~((~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))))) | (~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))))))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(59,plain,
% 0.21/0.47 (((~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~((~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))))) | (~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))))))) <=> ((~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~((~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))))) | (~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))))))))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[58])).
% 0.21/0.48 tff(60,plain,
% 0.21/0.48 (((~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~((~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))))) | (~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))))))) <=> ((~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~((~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))))) | (~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))))))))),
% 0.21/0.48 inference(transitivity,[status(thm)],[59, 57])).
% 0.21/0.48 tff(61,plain,
% 0.21/0.48 (((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~((~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))))) | (~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))))))))) <=> ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~((~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))))) | (~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))))))))))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[60])).
% 0.21/0.49 tff(62,plain,
% 0.21/0.49 (((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~((~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))))) | (~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))))))))) <=> ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~((~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))))) | (~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))))))))),
% 0.21/0.49 inference(transitivity,[status(thm)],[61, 56])).
% 0.21/0.49 tff(63,plain,
% 0.21/0.49 ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~((~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))))) | (~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))))))))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(64,plain,
% 0.21/0.49 ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~((~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))))) | (~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))))))))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.21/0.49 tff(65,plain,
% 0.21/0.49 (~((~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))))) | (~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))))))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[64, 55, 39])).
% 0.21/0.49 tff(66,plain,
% 0.21/0.49 (((~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))))) | (~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))))))) | ((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))))),
% 0.21/0.49 inference(tautology,[status(thm)],[])).
% 0.21/0.49 tff(67,plain,
% 0.21/0.49 ((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[66, 65])).
% 0.21/0.49 tff(68,plain,
% 0.21/0.49 (^[F: $i, A: $i] : refl((~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F)))))))) <=> (~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F)))))))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(69,plain,
% 0.21/0.49 (![F: $i, A: $i] : (~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F)))))))) <=> ![F: $i, A: $i] : (~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F))))))))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[68])).
% 0.21/0.49 tff(70,plain,
% 0.21/0.49 (^[F: $i, A: $i] : rewrite((~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F)))))))) <=> (~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F)))))))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(71,plain,
% 0.21/0.49 (![F: $i, A: $i] : (~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F)))))))) <=> ![F: $i, A: $i] : (~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F))))))))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[70])).
% 0.21/0.49 tff(72,plain,
% 0.21/0.49 (![F: $i, A: $i] : (~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F)))))))) <=> ![F: $i, A: $i] : (~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F))))))))),
% 0.21/0.49 inference(transitivity,[status(thm)],[71, 69])).
% 0.21/0.49 tff(73,plain,
% 0.21/0.49 (^[F: $i, A: $i] : trans(monotonicity(rewrite(((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X))) <=> ((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))), rewrite((identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F))))) <=> (identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F)))))), ((((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X))) & (identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F)))))) <=> (((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X))) & (identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F)))))))), rewrite((((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X))) & (identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F)))))) <=> (~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F))))))))), ((((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X))) & (identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F)))))) <=> (~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F))))))))))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(74,plain,
% 0.21/0.50 (![F: $i, A: $i] : (((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X))) & (identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F)))))) <=> ![F: $i, A: $i] : (~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F))))))))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[73])).
% 0.21/0.50 tff(75,plain,
% 0.21/0.50 (![F: $i, A: $i] : (identity(F, A) <=> ![X: $i] : ((~member(X, A)) | apply(F, X, X))) <=> ![F: $i, A: $i] : (identity(F, A) <=> ![X: $i] : ((~member(X, A)) | apply(F, X, X)))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(76,plain,
% 0.21/0.50 (^[F: $i, A: $i] : rewrite((identity(F, A) <=> ![X: $i] : (member(X, A) => apply(F, X, X))) <=> (identity(F, A) <=> ![X: $i] : ((~member(X, A)) | apply(F, X, X))))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(77,plain,
% 0.21/0.50 (![F: $i, A: $i] : (identity(F, A) <=> ![X: $i] : (member(X, A) => apply(F, X, X))) <=> ![F: $i, A: $i] : (identity(F, A) <=> ![X: $i] : ((~member(X, A)) | apply(F, X, X)))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[76])).
% 0.21/0.50 tff(78,axiom,(![F: $i, A: $i] : (identity(F, A) <=> ![X: $i] : (member(X, A) => apply(F, X, X)))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+1.ax','identity')).
% 0.21/0.50 tff(79,plain,
% 0.21/0.50 (![F: $i, A: $i] : (identity(F, A) <=> ![X: $i] : ((~member(X, A)) | apply(F, X, X)))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.21/0.50 tff(80,plain,
% 0.21/0.50 (![F: $i, A: $i] : (identity(F, A) <=> ![X: $i] : ((~member(X, A)) | apply(F, X, X)))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[79, 75])).
% 0.21/0.50 tff(81,plain,(
% 0.21/0.50 ![F: $i, A: $i] : (((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X))) & (identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F))))))),
% 0.21/0.50 inference(skolemize,[status(sab)],[80])).
% 0.21/0.50 tff(82,plain,
% 0.21/0.50 (![F: $i, A: $i] : (~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F))))))))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[81, 74])).
% 0.21/0.50 tff(83,plain,
% 0.21/0.50 (![F: $i, A: $i] : (~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F))))))))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[82, 72])).
% 0.21/0.50 tff(84,plain,
% 0.21/0.50 ((~![F: $i, A: $i] : (~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F))))))))) | (~((~((~identity(compose_function(G!42, F!43, A!40, B!39, A!40), A!40)) | ![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!42, F!43, A!40, B!39, A!40), X, X)))) | (~(identity(compose_function(G!42, F!43, A!40, B!39, A!40), A!40) | (~((~member(tptp_fun_X_15(A!40, compose_function(G!42, F!43, A!40, B!39, A!40)), A!40)) | apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X_15(A!40, compose_function(G!42, F!43, A!40, B!39, A!40)), tptp_fun_X_15(A!40, compose_function(G!42, F!43, A!40, B!39, A!40)))))))))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(85,plain,
% 0.21/0.50 (~((~((~identity(compose_function(G!42, F!43, A!40, B!39, A!40), A!40)) | ![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!42, F!43, A!40, B!39, A!40), X, X)))) | (~(identity(compose_function(G!42, F!43, A!40, B!39, A!40), A!40) | (~((~member(tptp_fun_X_15(A!40, compose_function(G!42, F!43, A!40, B!39, A!40)), A!40)) | apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X_15(A!40, compose_function(G!42, F!43, A!40, B!39, A!40)), tptp_fun_X_15(A!40, compose_function(G!42, F!43, A!40, B!39, A!40))))))))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[84, 83])).
% 0.21/0.50 tff(86,plain,
% 0.21/0.50 (((~((~identity(compose_function(G!42, F!43, A!40, B!39, A!40), A!40)) | ![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!42, F!43, A!40, B!39, A!40), X, X)))) | (~(identity(compose_function(G!42, F!43, A!40, B!39, A!40), A!40) | (~((~member(tptp_fun_X_15(A!40, compose_function(G!42, F!43, A!40, B!39, A!40)), A!40)) | apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X_15(A!40, compose_function(G!42, F!43, A!40, B!39, A!40)), tptp_fun_X_15(A!40, compose_function(G!42, F!43, A!40, B!39, A!40)))))))) | ((~identity(compose_function(G!42, F!43, A!40, B!39, A!40), A!40)) | ![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!42, F!43, A!40, B!39, A!40), X, X)))),
% 0.21/0.50 inference(tautology,[status(thm)],[])).
% 0.21/0.50 tff(87,plain,
% 0.21/0.50 ((~identity(compose_function(G!42, F!43, A!40, B!39, A!40), A!40)) | ![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!42, F!43, A!40, B!39, A!40), X, X))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[86, 85])).
% 0.21/0.50 tff(88,plain,
% 0.21/0.50 (maps(F!43, A!40, B!39) & maps(G!42, B!39, A!40) & maps(H!41, B!39, A!40) & identity(compose_function(G!42, F!43, A!40, B!39, A!40), A!40) & identity(compose_function(F!43, H!41, B!39, A!40, B!39), B!39)),
% 0.21/0.50 inference(or_elim,[status(thm)],[33])).
% 0.21/0.50 tff(89,plain,
% 0.21/0.50 (identity(compose_function(G!42, F!43, A!40, B!39, A!40), A!40)),
% 0.21/0.50 inference(and_elim,[status(thm)],[88])).
% 0.21/0.50 tff(90,plain,
% 0.21/0.50 ((~((~identity(compose_function(G!42, F!43, A!40, B!39, A!40), A!40)) | ![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!42, F!43, A!40, B!39, A!40), X, X)))) | (~identity(compose_function(G!42, F!43, A!40, B!39, A!40), A!40)) | ![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!42, F!43, A!40, B!39, A!40), X, X))),
% 0.21/0.50 inference(tautology,[status(thm)],[])).
% 0.21/0.50 tff(91,plain,
% 0.21/0.50 ((~((~identity(compose_function(G!42, F!43, A!40, B!39, A!40), A!40)) | ![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!42, F!43, A!40, B!39, A!40), X, X)))) | ![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!42, F!43, A!40, B!39, A!40), X, X))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[90, 89])).
% 0.21/0.50 tff(92,plain,
% 0.21/0.50 (![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!42, F!43, A!40, B!39, A!40), X, X))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[91, 87])).
% 0.21/0.50 tff(93,plain,
% 0.21/0.50 (((~![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!42, F!43, A!40, B!39, A!40), X, X))) | ((~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))) <=> ((~![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!42, F!43, A!40, B!39, A!40), X, X))) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(94,plain,
% 0.21/0.50 ((~![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!42, F!43, A!40, B!39, A!40), X, X))) | ((~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(95,plain,
% 0.21/0.50 ((~![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!42, F!43, A!40, B!39, A!40), X, X))) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.21/0.50 tff(96,plain,
% 0.21/0.50 (apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[95, 39, 92])).
% 0.21/0.50 tff(97,plain,
% 0.21/0.50 ((~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))))) | (~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))))),
% 0.21/0.50 inference(tautology,[status(thm)],[])).
% 0.21/0.50 tff(98,plain,
% 0.21/0.50 ((~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[97, 96])).
% 0.21/0.50 tff(99,plain,
% 0.21/0.50 (~((~member(tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[98, 67])).
% 0.21/0.50 tff(100,plain,
% 0.21/0.50 (((~member(tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))) | apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))),
% 0.21/0.50 inference(tautology,[status(thm)],[])).
% 0.21/0.50 tff(101,plain,
% 0.21/0.50 (apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[100, 99])).
% 0.21/0.50 tff(102,plain,
% 0.21/0.50 (((~member(tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))) | member(tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)),
% 0.21/0.50 inference(tautology,[status(thm)],[])).
% 0.21/0.50 tff(103,plain,
% 0.21/0.50 (member(tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[102, 99])).
% 0.21/0.50 tff(104,plain,
% 0.21/0.50 (^[F: $i, A: $i, B: $i] : rewrite((~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))) <=> (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))))))))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(105,plain,
% 0.21/0.50 (![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[104])).
% 0.21/0.50 tff(106,plain,
% 0.21/0.50 (^[F: $i, A: $i, B: $i] : refl((~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))) <=> (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(107,plain,
% 0.21/0.50 (![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))))))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[106])).
% 0.21/0.51 tff(108,plain,
% 0.21/0.51 (^[F: $i, A: $i, B: $i] : rewrite((~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))) <=> (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))))),
% 0.21/0.51 inference(bind,[status(th)],[])).
% 0.21/0.51 tff(109,plain,
% 0.21/0.51 (![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))))))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[108])).
% 0.21/0.51 tff(110,plain,
% 0.21/0.51 (![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))))))),
% 0.21/0.51 inference(transitivity,[status(thm)],[109, 107])).
% 0.21/0.51 tff(111,plain,
% 0.21/0.51 (^[F: $i, A: $i, B: $i] : trans(monotonicity(rewrite(((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) <=> ((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))), trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[Y: $i] : trans(monotonicity(rewrite((member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)) <=> (~((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))), ((~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y))) <=> (~(~((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))), rewrite((~(~((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))) <=> ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))), ((~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y))) <=> ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))), (![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y))) <=> ![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))), ((member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) <=> (member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))), rewrite((member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))) <=> (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))), ((member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) <=> (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))))), rewrite((~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B))))) <=> (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))), ((maps(F, A, B) | (member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B)))))) <=> (maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))))), rewrite((maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))) <=> (maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))), ((maps(F, A, B) | (member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B)))))) <=> (maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))))), ((((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) & (maps(F, A, B) | (member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B))))))) <=> (((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B))))))) & (maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))), rewrite((((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B))))))) & (maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))) <=> (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))))))), ((((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) & (maps(F, A, B) | (member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B))))))) <=> (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))))))))),
% 0.21/0.51 inference(bind,[status(th)],[])).
% 0.21/0.51 tff(112,plain,
% 0.21/0.51 (![F: $i, A: $i, B: $i] : (((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) & (maps(F, A, B) | (member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))))))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[111])).
% 0.21/0.51 tff(113,plain,
% 0.21/0.51 (^[F: $i, A: $i, B: $i] : rewrite((((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) & (maps(F, A, B) | ((member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B)))))))) <=> (((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) & (maps(F, A, B) | (member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B))))))))),
% 0.21/0.51 inference(bind,[status(th)],[])).
% 0.21/0.51 tff(114,plain,
% 0.21/0.51 (![F: $i, A: $i, B: $i] : (((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) & (maps(F, A, B) | ((member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B)))))))) <=> ![F: $i, A: $i, B: $i] : (((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) & (maps(F, A, B) | (member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B)))))))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[113])).
% 0.21/0.51 tff(115,plain,
% 0.21/0.51 (![F: $i, A: $i, B: $i] : (maps(F, A, B) <=> (![X: $i] : ((~member(X, A)) | ?[Y: $i] : (member(Y, B) & apply(F, X, Y))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) <=> ![F: $i, A: $i, B: $i] : (maps(F, A, B) <=> (![X: $i] : ((~member(X, A)) | ?[Y: $i] : (member(Y, B) & apply(F, X, Y))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B))))))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(116,plain,
% 0.21/0.51 (^[F: $i, A: $i, B: $i] : rewrite((maps(F, A, B) <=> (![X: $i] : (member(X, A) => ?[Y: $i] : (member(Y, B) & apply(F, X, Y))) & ![X: $i, Y1: $i, Y2: $i] : (((member(X, A) & member(Y1, B)) & member(Y2, B)) => ((apply(F, X, Y1) & apply(F, X, Y2)) => (Y1 = Y2))))) <=> (maps(F, A, B) <=> (![X: $i] : ((~member(X, A)) | ?[Y: $i] : (member(Y, B) & apply(F, X, Y))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))))),
% 0.21/0.51 inference(bind,[status(th)],[])).
% 0.21/0.51 tff(117,plain,
% 0.21/0.51 (![F: $i, A: $i, B: $i] : (maps(F, A, B) <=> (![X: $i] : (member(X, A) => ?[Y: $i] : (member(Y, B) & apply(F, X, Y))) & ![X: $i, Y1: $i, Y2: $i] : (((member(X, A) & member(Y1, B)) & member(Y2, B)) => ((apply(F, X, Y1) & apply(F, X, Y2)) => (Y1 = Y2))))) <=> ![F: $i, A: $i, B: $i] : (maps(F, A, B) <=> (![X: $i] : ((~member(X, A)) | ?[Y: $i] : (member(Y, B) & apply(F, X, Y))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B))))))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[116])).
% 0.21/0.51 tff(118,axiom,(![F: $i, A: $i, B: $i] : (maps(F, A, B) <=> (![X: $i] : (member(X, A) => ?[Y: $i] : (member(Y, B) & apply(F, X, Y))) & ![X: $i, Y1: $i, Y2: $i] : (((member(X, A) & member(Y1, B)) & member(Y2, B)) => ((apply(F, X, Y1) & apply(F, X, Y2)) => (Y1 = Y2)))))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+1.ax','maps')).
% 0.21/0.51 tff(119,plain,
% 0.21/0.51 (![F: $i, A: $i, B: $i] : (maps(F, A, B) <=> (![X: $i] : ((~member(X, A)) | ?[Y: $i] : (member(Y, B) & apply(F, X, Y))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B))))))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[118, 117])).
% 0.21/0.51 tff(120,plain,
% 0.21/0.51 (![F: $i, A: $i, B: $i] : (maps(F, A, B) <=> (![X: $i] : ((~member(X, A)) | ?[Y: $i] : (member(Y, B) & apply(F, X, Y))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B))))))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[119, 115])).
% 0.21/0.51 tff(121,plain,(
% 0.21/0.51 ![F: $i, A: $i, B: $i] : (((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) & (maps(F, A, B) | ((member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B))))))))),
% 0.21/0.51 inference(skolemize,[status(sab)],[120])).
% 0.21/0.51 tff(122,plain,
% 0.21/0.51 (![F: $i, A: $i, B: $i] : (((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) & (maps(F, A, B) | (member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B)))))))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[121, 114])).
% 0.21/0.51 tff(123,plain,
% 0.21/0.51 (![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))))))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[122, 112])).
% 0.21/0.51 tff(124,plain,
% 0.21/0.51 (![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))))))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[123, 110])).
% 0.21/0.51 tff(125,plain,
% 0.21/0.51 (![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[124, 105])).
% 0.21/0.51 tff(126,plain,
% 0.21/0.51 (((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(F!43, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!43), B!39)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!39, F!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))))))) | (~(maps(F!43, A!40, B!39) | (~((~member(tptp_fun_X_4(B!39, A!40, F!43), A!40)) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_X_4(B!39, A!40, F!43), Y)))))) | (~((~member(tptp_fun_Y2_5(B!39, A!40, F!43), B!39)) | (~member(tptp_fun_Y1_6(B!39, A!40, F!43), B!39)) | (~member(tptp_fun_X_7(B!39, A!40, F!43), A!40)) | (~apply(F!43, tptp_fun_X_7(B!39, A!40, F!43), tptp_fun_Y2_5(B!39, A!40, F!43))) | (~apply(F!43, tptp_fun_X_7(B!39, A!40, F!43), tptp_fun_Y1_6(B!39, A!40, F!43))) | (tptp_fun_Y1_6(B!39, A!40, F!43) = tptp_fun_Y2_5(B!39, A!40, F!43))))))))) <=> ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(F!43, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!43), B!39)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!39, F!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))))))) | (~(maps(F!43, A!40, B!39) | (~((~member(tptp_fun_X_4(B!39, A!40, F!43), A!40)) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_X_4(B!39, A!40, F!43), Y)))))) | (~((~member(tptp_fun_Y2_5(B!39, A!40, F!43), B!39)) | (~member(tptp_fun_Y1_6(B!39, A!40, F!43), B!39)) | (~member(tptp_fun_X_7(B!39, A!40, F!43), A!40)) | (~apply(F!43, tptp_fun_X_7(B!39, A!40, F!43), tptp_fun_Y2_5(B!39, A!40, F!43))) | (~apply(F!43, tptp_fun_X_7(B!39, A!40, F!43), tptp_fun_Y1_6(B!39, A!40, F!43))) | (tptp_fun_Y1_6(B!39, A!40, F!43) = tptp_fun_Y2_5(B!39, A!40, F!43)))))))))),
% 0.36/0.51 inference(rewrite,[status(thm)],[])).
% 0.36/0.51 tff(127,plain,
% 0.36/0.51 ((~((~((~maps(F!43, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!43), B!39)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!39, F!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))))))) | (~(maps(F!43, A!40, B!39) | (~((tptp_fun_Y1_6(B!39, A!40, F!43) = tptp_fun_Y2_5(B!39, A!40, F!43)) | (~apply(F!43, tptp_fun_X_7(B!39, A!40, F!43), tptp_fun_Y1_6(B!39, A!40, F!43))) | (~apply(F!43, tptp_fun_X_7(B!39, A!40, F!43), tptp_fun_Y2_5(B!39, A!40, F!43))) | (~member(tptp_fun_X_7(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_Y1_6(B!39, A!40, F!43), B!39)) | (~member(tptp_fun_Y2_5(B!39, A!40, F!43), B!39)))) | (~((~member(tptp_fun_X_4(B!39, A!40, F!43), A!40)) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_X_4(B!39, A!40, F!43), Y)))))))))) <=> (~((~((~maps(F!43, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!43), B!39)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!39, F!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))))))) | (~(maps(F!43, A!40, B!39) | (~((~member(tptp_fun_X_4(B!39, A!40, F!43), A!40)) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_X_4(B!39, A!40, F!43), Y)))))) | (~((~member(tptp_fun_Y2_5(B!39, A!40, F!43), B!39)) | (~member(tptp_fun_Y1_6(B!39, A!40, F!43), B!39)) | (~member(tptp_fun_X_7(B!39, A!40, F!43), A!40)) | (~apply(F!43, tptp_fun_X_7(B!39, A!40, F!43), tptp_fun_Y2_5(B!39, A!40, F!43))) | (~apply(F!43, tptp_fun_X_7(B!39, A!40, F!43), tptp_fun_Y1_6(B!39, A!40, F!43))) | (tptp_fun_Y1_6(B!39, A!40, F!43) = tptp_fun_Y2_5(B!39, A!40, F!43))))))))),
% 0.36/0.51 inference(rewrite,[status(thm)],[])).
% 0.36/0.51 tff(128,plain,
% 0.36/0.51 (((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(F!43, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!43), B!39)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!39, F!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))))))) | (~(maps(F!43, A!40, B!39) | (~((tptp_fun_Y1_6(B!39, A!40, F!43) = tptp_fun_Y2_5(B!39, A!40, F!43)) | (~apply(F!43, tptp_fun_X_7(B!39, A!40, F!43), tptp_fun_Y1_6(B!39, A!40, F!43))) | (~apply(F!43, tptp_fun_X_7(B!39, A!40, F!43), tptp_fun_Y2_5(B!39, A!40, F!43))) | (~member(tptp_fun_X_7(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_Y1_6(B!39, A!40, F!43), B!39)) | (~member(tptp_fun_Y2_5(B!39, A!40, F!43), B!39)))) | (~((~member(tptp_fun_X_4(B!39, A!40, F!43), A!40)) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_X_4(B!39, A!40, F!43), Y))))))))))) <=> ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(F!43, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!43), B!39)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!39, F!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))))))) | (~(maps(F!43, A!40, B!39) | (~((~member(tptp_fun_X_4(B!39, A!40, F!43), A!40)) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_X_4(B!39, A!40, F!43), Y)))))) | (~((~member(tptp_fun_Y2_5(B!39, A!40, F!43), B!39)) | (~member(tptp_fun_Y1_6(B!39, A!40, F!43), B!39)) | (~member(tptp_fun_X_7(B!39, A!40, F!43), A!40)) | (~apply(F!43, tptp_fun_X_7(B!39, A!40, F!43), tptp_fun_Y2_5(B!39, A!40, F!43))) | (~apply(F!43, tptp_fun_X_7(B!39, A!40, F!43), tptp_fun_Y1_6(B!39, A!40, F!43))) | (tptp_fun_Y1_6(B!39, A!40, F!43) = tptp_fun_Y2_5(B!39, A!40, F!43)))))))))),
% 0.36/0.52 inference(monotonicity,[status(thm)],[127])).
% 0.36/0.52 tff(129,plain,
% 0.36/0.52 (((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(F!43, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!43), B!39)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!39, F!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))))))) | (~(maps(F!43, A!40, B!39) | (~((tptp_fun_Y1_6(B!39, A!40, F!43) = tptp_fun_Y2_5(B!39, A!40, F!43)) | (~apply(F!43, tptp_fun_X_7(B!39, A!40, F!43), tptp_fun_Y1_6(B!39, A!40, F!43))) | (~apply(F!43, tptp_fun_X_7(B!39, A!40, F!43), tptp_fun_Y2_5(B!39, A!40, F!43))) | (~member(tptp_fun_X_7(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_Y1_6(B!39, A!40, F!43), B!39)) | (~member(tptp_fun_Y2_5(B!39, A!40, F!43), B!39)))) | (~((~member(tptp_fun_X_4(B!39, A!40, F!43), A!40)) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_X_4(B!39, A!40, F!43), Y))))))))))) <=> ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(F!43, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!43), B!39)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!39, F!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))))))) | (~(maps(F!43, A!40, B!39) | (~((~member(tptp_fun_X_4(B!39, A!40, F!43), A!40)) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_X_4(B!39, A!40, F!43), Y)))))) | (~((~member(tptp_fun_Y2_5(B!39, A!40, F!43), B!39)) | (~member(tptp_fun_Y1_6(B!39, A!40, F!43), B!39)) | (~member(tptp_fun_X_7(B!39, A!40, F!43), A!40)) | (~apply(F!43, tptp_fun_X_7(B!39, A!40, F!43), tptp_fun_Y2_5(B!39, A!40, F!43))) | (~apply(F!43, tptp_fun_X_7(B!39, A!40, F!43), tptp_fun_Y1_6(B!39, A!40, F!43))) | (tptp_fun_Y1_6(B!39, A!40, F!43) = tptp_fun_Y2_5(B!39, A!40, F!43)))))))))),
% 0.36/0.52 inference(transitivity,[status(thm)],[128, 126])).
% 0.36/0.52 tff(130,plain,
% 0.36/0.52 ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(F!43, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!43), B!39)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!39, F!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))))))) | (~(maps(F!43, A!40, B!39) | (~((tptp_fun_Y1_6(B!39, A!40, F!43) = tptp_fun_Y2_5(B!39, A!40, F!43)) | (~apply(F!43, tptp_fun_X_7(B!39, A!40, F!43), tptp_fun_Y1_6(B!39, A!40, F!43))) | (~apply(F!43, tptp_fun_X_7(B!39, A!40, F!43), tptp_fun_Y2_5(B!39, A!40, F!43))) | (~member(tptp_fun_X_7(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_Y1_6(B!39, A!40, F!43), B!39)) | (~member(tptp_fun_Y2_5(B!39, A!40, F!43), B!39)))) | (~((~member(tptp_fun_X_4(B!39, A!40, F!43), A!40)) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_X_4(B!39, A!40, F!43), Y))))))))))),
% 0.36/0.52 inference(quant_inst,[status(thm)],[])).
% 0.36/0.52 tff(131,plain,
% 0.36/0.52 ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(F!43, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!43), B!39)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!39, F!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))))))) | (~(maps(F!43, A!40, B!39) | (~((~member(tptp_fun_X_4(B!39, A!40, F!43), A!40)) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_X_4(B!39, A!40, F!43), Y)))))) | (~((~member(tptp_fun_Y2_5(B!39, A!40, F!43), B!39)) | (~member(tptp_fun_Y1_6(B!39, A!40, F!43), B!39)) | (~member(tptp_fun_X_7(B!39, A!40, F!43), A!40)) | (~apply(F!43, tptp_fun_X_7(B!39, A!40, F!43), tptp_fun_Y2_5(B!39, A!40, F!43))) | (~apply(F!43, tptp_fun_X_7(B!39, A!40, F!43), tptp_fun_Y1_6(B!39, A!40, F!43))) | (tptp_fun_Y1_6(B!39, A!40, F!43) = tptp_fun_Y2_5(B!39, A!40, F!43))))))))),
% 0.36/0.52 inference(modus_ponens,[status(thm)],[130, 129])).
% 0.36/0.52 tff(132,plain,
% 0.36/0.52 (~((~((~maps(F!43, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!43), B!39)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!39, F!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))))))) | (~(maps(F!43, A!40, B!39) | (~((~member(tptp_fun_X_4(B!39, A!40, F!43), A!40)) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_X_4(B!39, A!40, F!43), Y)))))) | (~((~member(tptp_fun_Y2_5(B!39, A!40, F!43), B!39)) | (~member(tptp_fun_Y1_6(B!39, A!40, F!43), B!39)) | (~member(tptp_fun_X_7(B!39, A!40, F!43), A!40)) | (~apply(F!43, tptp_fun_X_7(B!39, A!40, F!43), tptp_fun_Y2_5(B!39, A!40, F!43))) | (~apply(F!43, tptp_fun_X_7(B!39, A!40, F!43), tptp_fun_Y1_6(B!39, A!40, F!43))) | (tptp_fun_Y1_6(B!39, A!40, F!43) = tptp_fun_Y2_5(B!39, A!40, F!43)))))))),
% 0.36/0.52 inference(unit_resolution,[status(thm)],[131, 125])).
% 0.36/0.52 tff(133,plain,
% 0.36/0.52 (((~((~maps(F!43, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!43), B!39)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!39, F!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))))))) | (~(maps(F!43, A!40, B!39) | (~((~member(tptp_fun_X_4(B!39, A!40, F!43), A!40)) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_X_4(B!39, A!40, F!43), Y)))))) | (~((~member(tptp_fun_Y2_5(B!39, A!40, F!43), B!39)) | (~member(tptp_fun_Y1_6(B!39, A!40, F!43), B!39)) | (~member(tptp_fun_X_7(B!39, A!40, F!43), A!40)) | (~apply(F!43, tptp_fun_X_7(B!39, A!40, F!43), tptp_fun_Y2_5(B!39, A!40, F!43))) | (~apply(F!43, tptp_fun_X_7(B!39, A!40, F!43), tptp_fun_Y1_6(B!39, A!40, F!43))) | (tptp_fun_Y1_6(B!39, A!40, F!43) = tptp_fun_Y2_5(B!39, A!40, F!43))))))) | ((~maps(F!43, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!43), B!39)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!39, F!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))))))),
% 0.36/0.52 inference(tautology,[status(thm)],[])).
% 0.36/0.52 tff(134,plain,
% 0.36/0.52 ((~maps(F!43, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!43), B!39)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!39, F!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39))))))),
% 0.36/0.52 inference(unit_resolution,[status(thm)],[133, 132])).
% 0.36/0.52 tff(135,plain,
% 0.36/0.52 (maps(F!43, A!40, B!39)),
% 0.36/0.52 inference(and_elim,[status(thm)],[88])).
% 0.36/0.52 tff(136,plain,
% 0.36/0.52 ((~((~maps(F!43, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!43), B!39)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!39, F!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))))))) | (~maps(F!43, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!43), B!39)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!39, F!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39))))))),
% 0.36/0.52 inference(tautology,[status(thm)],[])).
% 0.36/0.52 tff(137,plain,
% 0.36/0.52 ((~((~maps(F!43, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!43), B!39)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!39, F!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))))))) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!43), B!39)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!39, F!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39))))))),
% 0.36/0.52 inference(unit_resolution,[status(thm)],[136, 135])).
% 0.36/0.52 tff(138,plain,
% 0.36/0.52 (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!43), B!39)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!39, F!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))))),
% 0.36/0.52 inference(unit_resolution,[status(thm)],[137, 134])).
% 0.36/0.52 tff(139,plain,
% 0.36/0.52 (((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!43), B!39)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!39, F!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39))))) | ![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!43), B!39)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!39, F!43))))))),
% 0.36/0.52 inference(tautology,[status(thm)],[])).
% 0.36/0.52 tff(140,plain,
% 0.36/0.52 (![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!43), B!39)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!39, F!43))))))),
% 0.36/0.52 inference(unit_resolution,[status(thm)],[139, 138])).
% 0.36/0.52 tff(141,plain,
% 0.36/0.52 (((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!43), B!39)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!39, F!43))))))) | ((~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~((~member(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43))))))) <=> ((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!43), B!39)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!39, F!43))))))) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~((~member(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43))))))),
% 0.36/0.52 inference(rewrite,[status(thm)],[])).
% 0.36/0.52 tff(142,plain,
% 0.36/0.52 ((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!43), B!39)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!39, F!43))))))) | ((~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~((~member(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43))))))),
% 0.36/0.52 inference(quant_inst,[status(thm)],[])).
% 0.36/0.52 tff(143,plain,
% 0.36/0.52 ((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!43), B!39)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!39, F!43))))))) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~((~member(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43)))))),
% 0.36/0.53 inference(modus_ponens,[status(thm)],[142, 141])).
% 0.36/0.53 tff(144,plain,
% 0.36/0.53 (~((~member(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43))))),
% 0.36/0.53 inference(unit_resolution,[status(thm)],[143, 140, 39])).
% 0.36/0.53 tff(145,plain,
% 0.36/0.53 (((~member(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43)))) | apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43))),
% 0.36/0.53 inference(tautology,[status(thm)],[])).
% 0.36/0.53 tff(146,plain,
% 0.36/0.53 (apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43))),
% 0.36/0.53 inference(unit_resolution,[status(thm)],[145, 144])).
% 0.36/0.53 tff(147,plain,
% 0.36/0.53 (((~member(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43)))) | member(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)),
% 0.36/0.53 inference(tautology,[status(thm)],[])).
% 0.36/0.53 tff(148,plain,
% 0.36/0.53 (member(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)),
% 0.36/0.53 inference(unit_resolution,[status(thm)],[147, 144])).
% 0.36/0.53 tff(149,plain,
% 0.36/0.53 (((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!43), B!39)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!39, F!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39))))) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))),
% 0.36/0.53 inference(tautology,[status(thm)],[])).
% 0.36/0.53 tff(150,plain,
% 0.36/0.53 (![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))),
% 0.36/0.53 inference(unit_resolution,[status(thm)],[149, 138])).
% 0.36/0.53 tff(151,plain,
% 0.36/0.53 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))) | ((~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43))) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~member(tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42) = tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43))) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~member(tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42) = tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43)))),
% 0.36/0.53 inference(rewrite,[status(thm)],[])).
% 0.36/0.53 tff(152,plain,
% 0.36/0.53 (((tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42) = tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43)) | (~member(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43))) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39))) <=> ((~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43))) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~member(tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42) = tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43)))),
% 0.36/0.53 inference(rewrite,[status(thm)],[])).
% 0.36/0.53 tff(153,plain,
% 0.36/0.53 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))) | ((tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42) = tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43)) | (~member(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43))) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))) | ((~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43))) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~member(tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42) = tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43))))),
% 0.36/0.53 inference(monotonicity,[status(thm)],[152])).
% 0.36/0.53 tff(154,plain,
% 0.36/0.53 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))) | ((tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42) = tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43)) | (~member(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43))) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43))) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~member(tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42) = tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43)))),
% 0.38/0.53 inference(transitivity,[status(thm)],[153, 151])).
% 0.38/0.53 tff(155,plain,
% 0.38/0.53 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))) | ((tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42) = tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43)) | (~member(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43))) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)))),
% 0.38/0.53 inference(quant_inst,[status(thm)],[])).
% 0.38/0.53 tff(156,plain,
% 0.38/0.53 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43))) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~member(tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42) = tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43))),
% 0.38/0.53 inference(modus_ponens,[status(thm)],[155, 154])).
% 0.38/0.53 tff(157,plain,
% 0.38/0.53 (tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42) = tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43)),
% 0.38/0.53 inference(unit_resolution,[status(thm)],[156, 150, 39, 148, 146, 103, 101])).
% 0.38/0.53 tff(158,plain,
% 0.38/0.53 (tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43) = tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42)),
% 0.38/0.54 inference(symmetry,[status(thm)],[157])).
% 0.38/0.54 tff(159,plain,
% 0.38/0.54 (apply(G!42, tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) <=> apply(G!42, tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))),
% 0.38/0.54 inference(monotonicity,[status(thm)],[158])).
% 0.38/0.54 tff(160,plain,
% 0.38/0.54 (apply(G!42, tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) <=> apply(G!42, tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))),
% 0.38/0.54 inference(symmetry,[status(thm)],[159])).
% 0.38/0.54 tff(161,plain,
% 0.38/0.54 (((~member(tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))) | apply(G!42, tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))),
% 0.38/0.54 inference(tautology,[status(thm)],[])).
% 0.38/0.54 tff(162,plain,
% 0.38/0.54 (apply(G!42, tptp_fun_Y_8(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))),
% 0.38/0.54 inference(unit_resolution,[status(thm)],[161, 99])).
% 0.38/0.54 tff(163,plain,
% 0.38/0.54 (apply(G!42, tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))),
% 0.38/0.54 inference(modus_ponens,[status(thm)],[162, 160])).
% 0.38/0.54 tff(164,plain,
% 0.38/0.54 (((~![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(G!42, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!42), A!40)) | (~apply(G!42, X, tptp_fun_Y_3(X, A!40, G!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))))))) | (~(maps(G!42, B!39, A!40) | (~((~member(tptp_fun_X_4(A!40, B!39, G!42), B!39)) | (~![Y: $i] : ((~member(Y, A!40)) | (~apply(G!42, tptp_fun_X_4(A!40, B!39, G!42), Y)))))) | (~((~member(tptp_fun_Y2_5(A!40, B!39, G!42), A!40)) | (~member(tptp_fun_Y1_6(A!40, B!39, G!42), A!40)) | (~member(tptp_fun_X_7(A!40, B!39, G!42), B!39)) | (~apply(G!42, tptp_fun_X_7(A!40, B!39, G!42), tptp_fun_Y2_5(A!40, B!39, G!42))) | (~apply(G!42, tptp_fun_X_7(A!40, B!39, G!42), tptp_fun_Y1_6(A!40, B!39, G!42))) | (tptp_fun_Y1_6(A!40, B!39, G!42) = tptp_fun_Y2_5(A!40, B!39, G!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(G!42, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!42), A!40)) | (~apply(G!42, X, tptp_fun_Y_3(X, A!40, G!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))))))) | (~(maps(G!42, B!39, A!40) | (~((~member(tptp_fun_X_4(A!40, B!39, G!42), B!39)) | (~![Y: $i] : ((~member(Y, A!40)) | (~apply(G!42, tptp_fun_X_4(A!40, B!39, G!42), Y)))))) | (~((~member(tptp_fun_Y2_5(A!40, B!39, G!42), A!40)) | (~member(tptp_fun_Y1_6(A!40, B!39, G!42), A!40)) | (~member(tptp_fun_X_7(A!40, B!39, G!42), B!39)) | (~apply(G!42, tptp_fun_X_7(A!40, B!39, G!42), tptp_fun_Y2_5(A!40, B!39, G!42))) | (~apply(G!42, tptp_fun_X_7(A!40, B!39, G!42), tptp_fun_Y1_6(A!40, B!39, G!42))) | (tptp_fun_Y1_6(A!40, B!39, G!42) = tptp_fun_Y2_5(A!40, B!39, G!42)))))))))),
% 0.38/0.54 inference(rewrite,[status(thm)],[])).
% 0.38/0.54 tff(165,plain,
% 0.38/0.54 ((~((~((~maps(G!42, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!42), A!40)) | (~apply(G!42, X, tptp_fun_Y_3(X, A!40, G!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)) | (~member(Y2, A!40)))))))) | (~(maps(G!42, B!39, A!40) | (~((tptp_fun_Y1_6(A!40, B!39, G!42) = tptp_fun_Y2_5(A!40, B!39, G!42)) | (~apply(G!42, tptp_fun_X_7(A!40, B!39, G!42), tptp_fun_Y1_6(A!40, B!39, G!42))) | (~apply(G!42, tptp_fun_X_7(A!40, B!39, G!42), tptp_fun_Y2_5(A!40, B!39, G!42))) | (~member(tptp_fun_X_7(A!40, B!39, G!42), B!39)) | (~member(tptp_fun_Y1_6(A!40, B!39, G!42), A!40)) | (~member(tptp_fun_Y2_5(A!40, B!39, G!42), A!40)))) | (~((~member(tptp_fun_X_4(A!40, B!39, G!42), B!39)) | (~![Y: $i] : ((~member(Y, A!40)) | (~apply(G!42, tptp_fun_X_4(A!40, B!39, G!42), Y)))))))))) <=> (~((~((~maps(G!42, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!42), A!40)) | (~apply(G!42, X, tptp_fun_Y_3(X, A!40, G!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))))))) | (~(maps(G!42, B!39, A!40) | (~((~member(tptp_fun_X_4(A!40, B!39, G!42), B!39)) | (~![Y: $i] : ((~member(Y, A!40)) | (~apply(G!42, tptp_fun_X_4(A!40, B!39, G!42), Y)))))) | (~((~member(tptp_fun_Y2_5(A!40, B!39, G!42), A!40)) | (~member(tptp_fun_Y1_6(A!40, B!39, G!42), A!40)) | (~member(tptp_fun_X_7(A!40, B!39, G!42), B!39)) | (~apply(G!42, tptp_fun_X_7(A!40, B!39, G!42), tptp_fun_Y2_5(A!40, B!39, G!42))) | (~apply(G!42, tptp_fun_X_7(A!40, B!39, G!42), tptp_fun_Y1_6(A!40, B!39, G!42))) | (tptp_fun_Y1_6(A!40, B!39, G!42) = tptp_fun_Y2_5(A!40, B!39, G!42))))))))),
% 0.38/0.54 inference(rewrite,[status(thm)],[])).
% 0.38/0.54 tff(166,plain,
% 0.38/0.54 (((~![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(G!42, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!42), A!40)) | (~apply(G!42, X, tptp_fun_Y_3(X, A!40, G!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)) | (~member(Y2, A!40)))))))) | (~(maps(G!42, B!39, A!40) | (~((tptp_fun_Y1_6(A!40, B!39, G!42) = tptp_fun_Y2_5(A!40, B!39, G!42)) | (~apply(G!42, tptp_fun_X_7(A!40, B!39, G!42), tptp_fun_Y1_6(A!40, B!39, G!42))) | (~apply(G!42, tptp_fun_X_7(A!40, B!39, G!42), tptp_fun_Y2_5(A!40, B!39, G!42))) | (~member(tptp_fun_X_7(A!40, B!39, G!42), B!39)) | (~member(tptp_fun_Y1_6(A!40, B!39, G!42), A!40)) | (~member(tptp_fun_Y2_5(A!40, B!39, G!42), A!40)))) | (~((~member(tptp_fun_X_4(A!40, B!39, G!42), B!39)) | (~![Y: $i] : ((~member(Y, A!40)) | (~apply(G!42, tptp_fun_X_4(A!40, B!39, G!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(G!42, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!42), A!40)) | (~apply(G!42, X, tptp_fun_Y_3(X, A!40, G!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))))))) | (~(maps(G!42, B!39, A!40) | (~((~member(tptp_fun_X_4(A!40, B!39, G!42), B!39)) | (~![Y: $i] : ((~member(Y, A!40)) | (~apply(G!42, tptp_fun_X_4(A!40, B!39, G!42), Y)))))) | (~((~member(tptp_fun_Y2_5(A!40, B!39, G!42), A!40)) | (~member(tptp_fun_Y1_6(A!40, B!39, G!42), A!40)) | (~member(tptp_fun_X_7(A!40, B!39, G!42), B!39)) | (~apply(G!42, tptp_fun_X_7(A!40, B!39, G!42), tptp_fun_Y2_5(A!40, B!39, G!42))) | (~apply(G!42, tptp_fun_X_7(A!40, B!39, G!42), tptp_fun_Y1_6(A!40, B!39, G!42))) | (tptp_fun_Y1_6(A!40, B!39, G!42) = tptp_fun_Y2_5(A!40, B!39, G!42)))))))))),
% 0.38/0.54 inference(monotonicity,[status(thm)],[165])).
% 0.38/0.54 tff(167,plain,
% 0.38/0.54 (((~![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(G!42, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!42), A!40)) | (~apply(G!42, X, tptp_fun_Y_3(X, A!40, G!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)) | (~member(Y2, A!40)))))))) | (~(maps(G!42, B!39, A!40) | (~((tptp_fun_Y1_6(A!40, B!39, G!42) = tptp_fun_Y2_5(A!40, B!39, G!42)) | (~apply(G!42, tptp_fun_X_7(A!40, B!39, G!42), tptp_fun_Y1_6(A!40, B!39, G!42))) | (~apply(G!42, tptp_fun_X_7(A!40, B!39, G!42), tptp_fun_Y2_5(A!40, B!39, G!42))) | (~member(tptp_fun_X_7(A!40, B!39, G!42), B!39)) | (~member(tptp_fun_Y1_6(A!40, B!39, G!42), A!40)) | (~member(tptp_fun_Y2_5(A!40, B!39, G!42), A!40)))) | (~((~member(tptp_fun_X_4(A!40, B!39, G!42), B!39)) | (~![Y: $i] : ((~member(Y, A!40)) | (~apply(G!42, tptp_fun_X_4(A!40, B!39, G!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(G!42, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!42), A!40)) | (~apply(G!42, X, tptp_fun_Y_3(X, A!40, G!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))))))) | (~(maps(G!42, B!39, A!40) | (~((~member(tptp_fun_X_4(A!40, B!39, G!42), B!39)) | (~![Y: $i] : ((~member(Y, A!40)) | (~apply(G!42, tptp_fun_X_4(A!40, B!39, G!42), Y)))))) | (~((~member(tptp_fun_Y2_5(A!40, B!39, G!42), A!40)) | (~member(tptp_fun_Y1_6(A!40, B!39, G!42), A!40)) | (~member(tptp_fun_X_7(A!40, B!39, G!42), B!39)) | (~apply(G!42, tptp_fun_X_7(A!40, B!39, G!42), tptp_fun_Y2_5(A!40, B!39, G!42))) | (~apply(G!42, tptp_fun_X_7(A!40, B!39, G!42), tptp_fun_Y1_6(A!40, B!39, G!42))) | (tptp_fun_Y1_6(A!40, B!39, G!42) = tptp_fun_Y2_5(A!40, B!39, G!42)))))))))),
% 0.38/0.54 inference(transitivity,[status(thm)],[166, 164])).
% 0.38/0.54 tff(168,plain,
% 0.38/0.54 ((~![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(G!42, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!42), A!40)) | (~apply(G!42, X, tptp_fun_Y_3(X, A!40, G!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)) | (~member(Y2, A!40)))))))) | (~(maps(G!42, B!39, A!40) | (~((tptp_fun_Y1_6(A!40, B!39, G!42) = tptp_fun_Y2_5(A!40, B!39, G!42)) | (~apply(G!42, tptp_fun_X_7(A!40, B!39, G!42), tptp_fun_Y1_6(A!40, B!39, G!42))) | (~apply(G!42, tptp_fun_X_7(A!40, B!39, G!42), tptp_fun_Y2_5(A!40, B!39, G!42))) | (~member(tptp_fun_X_7(A!40, B!39, G!42), B!39)) | (~member(tptp_fun_Y1_6(A!40, B!39, G!42), A!40)) | (~member(tptp_fun_Y2_5(A!40, B!39, G!42), A!40)))) | (~((~member(tptp_fun_X_4(A!40, B!39, G!42), B!39)) | (~![Y: $i] : ((~member(Y, A!40)) | (~apply(G!42, tptp_fun_X_4(A!40, B!39, G!42), Y))))))))))),
% 0.38/0.55 inference(quant_inst,[status(thm)],[])).
% 0.38/0.55 tff(169,plain,
% 0.38/0.55 ((~![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(G!42, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!42), A!40)) | (~apply(G!42, X, tptp_fun_Y_3(X, A!40, G!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))))))) | (~(maps(G!42, B!39, A!40) | (~((~member(tptp_fun_X_4(A!40, B!39, G!42), B!39)) | (~![Y: $i] : ((~member(Y, A!40)) | (~apply(G!42, tptp_fun_X_4(A!40, B!39, G!42), Y)))))) | (~((~member(tptp_fun_Y2_5(A!40, B!39, G!42), A!40)) | (~member(tptp_fun_Y1_6(A!40, B!39, G!42), A!40)) | (~member(tptp_fun_X_7(A!40, B!39, G!42), B!39)) | (~apply(G!42, tptp_fun_X_7(A!40, B!39, G!42), tptp_fun_Y2_5(A!40, B!39, G!42))) | (~apply(G!42, tptp_fun_X_7(A!40, B!39, G!42), tptp_fun_Y1_6(A!40, B!39, G!42))) | (tptp_fun_Y1_6(A!40, B!39, G!42) = tptp_fun_Y2_5(A!40, B!39, G!42))))))))),
% 0.38/0.55 inference(modus_ponens,[status(thm)],[168, 167])).
% 0.38/0.55 tff(170,plain,
% 0.38/0.55 (~((~((~maps(G!42, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!42), A!40)) | (~apply(G!42, X, tptp_fun_Y_3(X, A!40, G!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))))))) | (~(maps(G!42, B!39, A!40) | (~((~member(tptp_fun_X_4(A!40, B!39, G!42), B!39)) | (~![Y: $i] : ((~member(Y, A!40)) | (~apply(G!42, tptp_fun_X_4(A!40, B!39, G!42), Y)))))) | (~((~member(tptp_fun_Y2_5(A!40, B!39, G!42), A!40)) | (~member(tptp_fun_Y1_6(A!40, B!39, G!42), A!40)) | (~member(tptp_fun_X_7(A!40, B!39, G!42), B!39)) | (~apply(G!42, tptp_fun_X_7(A!40, B!39, G!42), tptp_fun_Y2_5(A!40, B!39, G!42))) | (~apply(G!42, tptp_fun_X_7(A!40, B!39, G!42), tptp_fun_Y1_6(A!40, B!39, G!42))) | (tptp_fun_Y1_6(A!40, B!39, G!42) = tptp_fun_Y2_5(A!40, B!39, G!42)))))))),
% 0.38/0.55 inference(unit_resolution,[status(thm)],[169, 125])).
% 0.38/0.55 tff(171,plain,
% 0.38/0.55 (((~((~maps(G!42, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!42), A!40)) | (~apply(G!42, X, tptp_fun_Y_3(X, A!40, G!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))))))) | (~(maps(G!42, B!39, A!40) | (~((~member(tptp_fun_X_4(A!40, B!39, G!42), B!39)) | (~![Y: $i] : ((~member(Y, A!40)) | (~apply(G!42, tptp_fun_X_4(A!40, B!39, G!42), Y)))))) | (~((~member(tptp_fun_Y2_5(A!40, B!39, G!42), A!40)) | (~member(tptp_fun_Y1_6(A!40, B!39, G!42), A!40)) | (~member(tptp_fun_X_7(A!40, B!39, G!42), B!39)) | (~apply(G!42, tptp_fun_X_7(A!40, B!39, G!42), tptp_fun_Y2_5(A!40, B!39, G!42))) | (~apply(G!42, tptp_fun_X_7(A!40, B!39, G!42), tptp_fun_Y1_6(A!40, B!39, G!42))) | (tptp_fun_Y1_6(A!40, B!39, G!42) = tptp_fun_Y2_5(A!40, B!39, G!42))))))) | ((~maps(G!42, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!42), A!40)) | (~apply(G!42, X, tptp_fun_Y_3(X, A!40, G!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))))))),
% 0.38/0.55 inference(tautology,[status(thm)],[])).
% 0.38/0.55 tff(172,plain,
% 0.38/0.55 ((~maps(G!42, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!42), A!40)) | (~apply(G!42, X, tptp_fun_Y_3(X, A!40, G!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40))))))),
% 0.38/0.55 inference(unit_resolution,[status(thm)],[171, 170])).
% 0.38/0.55 tff(173,plain,
% 0.38/0.55 (maps(G!42, B!39, A!40)),
% 0.38/0.55 inference(and_elim,[status(thm)],[88])).
% 0.38/0.55 tff(174,plain,
% 0.38/0.55 ((~((~maps(G!42, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!42), A!40)) | (~apply(G!42, X, tptp_fun_Y_3(X, A!40, G!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))))))) | (~maps(G!42, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!42), A!40)) | (~apply(G!42, X, tptp_fun_Y_3(X, A!40, G!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40))))))),
% 0.38/0.55 inference(tautology,[status(thm)],[])).
% 0.38/0.55 tff(175,plain,
% 0.38/0.55 ((~((~maps(G!42, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!42), A!40)) | (~apply(G!42, X, tptp_fun_Y_3(X, A!40, G!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))))))) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!42), A!40)) | (~apply(G!42, X, tptp_fun_Y_3(X, A!40, G!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40))))))),
% 0.38/0.55 inference(unit_resolution,[status(thm)],[174, 173])).
% 0.38/0.55 tff(176,plain,
% 0.38/0.55 (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!42), A!40)) | (~apply(G!42, X, tptp_fun_Y_3(X, A!40, G!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))))),
% 0.38/0.55 inference(unit_resolution,[status(thm)],[175, 172])).
% 0.38/0.55 tff(177,plain,
% 0.38/0.55 (((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!42), A!40)) | (~apply(G!42, X, tptp_fun_Y_3(X, A!40, G!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40))))) | ![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!42), A!40)) | (~apply(G!42, X, tptp_fun_Y_3(X, A!40, G!42))))))),
% 0.38/0.55 inference(tautology,[status(thm)],[])).
% 0.38/0.55 tff(178,plain,
% 0.38/0.55 (![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!42), A!40)) | (~apply(G!42, X, tptp_fun_Y_3(X, A!40, G!42))))))),
% 0.38/0.55 inference(unit_resolution,[status(thm)],[177, 176])).
% 0.38/0.55 tff(179,plain,
% 0.38/0.55 (((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!42), A!40)) | (~apply(G!42, X, tptp_fun_Y_3(X, A!40, G!42))))))) | ((~member(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42), A!40)) | (~apply(G!42, tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42))))))) <=> ((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!42), A!40)) | (~apply(G!42, X, tptp_fun_Y_3(X, A!40, G!42))))))) | (~member(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42), A!40)) | (~apply(G!42, tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42))))))),
% 0.38/0.55 inference(rewrite,[status(thm)],[])).
% 0.38/0.55 tff(180,plain,
% 0.38/0.55 ((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!42), A!40)) | (~apply(G!42, X, tptp_fun_Y_3(X, A!40, G!42))))))) | ((~member(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42), A!40)) | (~apply(G!42, tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42))))))),
% 0.38/0.55 inference(quant_inst,[status(thm)],[])).
% 0.38/0.55 tff(181,plain,
% 0.38/0.55 ((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!42), A!40)) | (~apply(G!42, X, tptp_fun_Y_3(X, A!40, G!42))))))) | (~member(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42), A!40)) | (~apply(G!42, tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42)))))),
% 0.38/0.55 inference(modus_ponens,[status(thm)],[180, 179])).
% 0.38/0.55 tff(182,plain,
% 0.38/0.55 (~((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42), A!40)) | (~apply(G!42, tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42))))),
% 0.38/0.55 inference(unit_resolution,[status(thm)],[181, 178, 148])).
% 0.38/0.55 tff(183,plain,
% 0.38/0.55 (((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42), A!40)) | (~apply(G!42, tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42)))) | apply(G!42, tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42))),
% 0.38/0.55 inference(tautology,[status(thm)],[])).
% 0.38/0.55 tff(184,plain,
% 0.38/0.55 (apply(G!42, tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42))),
% 0.38/0.55 inference(unit_resolution,[status(thm)],[183, 182])).
% 0.38/0.55 tff(185,plain,
% 0.38/0.55 (((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42), A!40)) | (~apply(G!42, tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42)))) | member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42), A!40)),
% 0.38/0.55 inference(tautology,[status(thm)],[])).
% 0.38/0.55 tff(186,plain,
% 0.38/0.55 (member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42), A!40)),
% 0.38/0.55 inference(unit_resolution,[status(thm)],[185, 182])).
% 0.38/0.55 tff(187,plain,
% 0.38/0.55 (((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!42), A!40)) | (~apply(G!42, X, tptp_fun_Y_3(X, A!40, G!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40))))) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))),
% 0.38/0.55 inference(tautology,[status(thm)],[])).
% 0.38/0.55 tff(188,plain,
% 0.38/0.55 (![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))),
% 0.38/0.55 inference(unit_resolution,[status(thm)],[187, 176])).
% 0.38/0.55 tff(189,plain,
% 0.38/0.55 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))) | ((~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42), A!40)) | (~apply(G!42, tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42))) | (tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42)) | (~apply(G!42, tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42), A!40)) | (~apply(G!42, tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42))) | (tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42)) | (~apply(G!42, tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))),
% 0.38/0.55 inference(rewrite,[status(thm)],[])).
% 0.38/0.55 tff(190,plain,
% 0.38/0.55 (((tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42), A!40)) | (~apply(G!42, tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~apply(G!42, tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42))) | (~member(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40))) <=> ((~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42), A!40)) | (~apply(G!42, tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42))) | (tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42)) | (~apply(G!42, tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))),
% 0.38/0.56 inference(rewrite,[status(thm)],[])).
% 0.38/0.56 tff(191,plain,
% 0.38/0.56 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))) | ((tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42), A!40)) | (~apply(G!42, tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~apply(G!42, tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42))) | (~member(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))) | ((~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42), A!40)) | (~apply(G!42, tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42))) | (tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42)) | (~apply(G!42, tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))))),
% 0.38/0.56 inference(monotonicity,[status(thm)],[190])).
% 0.38/0.56 tff(192,plain,
% 0.38/0.56 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))) | ((tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42), A!40)) | (~apply(G!42, tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~apply(G!42, tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42))) | (~member(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42), A!40)) | (~apply(G!42, tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42))) | (tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42)) | (~apply(G!42, tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))),
% 0.38/0.56 inference(transitivity,[status(thm)],[191, 189])).
% 0.38/0.56 tff(193,plain,
% 0.38/0.56 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))) | ((tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42), A!40)) | (~apply(G!42, tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~apply(G!42, tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42))) | (~member(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)))),
% 0.38/0.56 inference(quant_inst,[status(thm)],[])).
% 0.38/0.56 tff(194,plain,
% 0.38/0.56 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42), A!40)) | (~apply(G!42, tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42))) | (tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42)) | (~apply(G!42, tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))),
% 0.38/0.56 inference(modus_ponens,[status(thm)],[193, 192])).
% 0.38/0.56 tff(195,plain,
% 0.38/0.56 ((tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42)) | (~apply(G!42, tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))),
% 0.38/0.56 inference(unit_resolution,[status(thm)],[194, 188, 39, 148, 186, 184])).
% 0.38/0.56 tff(196,plain,
% 0.38/0.56 (tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42)),
% 0.38/0.56 inference(unit_resolution,[status(thm)],[195, 163])).
% 0.38/0.56 tff(197,plain,
% 0.38/0.56 (tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42) = tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))),
% 0.38/0.56 inference(symmetry,[status(thm)],[196])).
% 0.38/0.56 tff(198,plain,
% 0.38/0.56 (((~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~apply(inverse_function(F!43, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)),
% 0.38/0.56 inference(tautology,[status(thm)],[])).
% 0.38/0.56 tff(199,plain,
% 0.38/0.56 (member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)),
% 0.38/0.56 inference(unit_resolution,[status(thm)],[198, 37])).
% 0.38/0.56 tff(200,plain,
% 0.38/0.56 (((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (~((~(apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | ![Y: $i] : ((~member(Y, A!40)) | (~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), Y)) | (~apply(F!43, Y, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))))) | (~((~apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~((~apply(F!43, tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43))) | (~member(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), A!40)))))))))) <=> ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | (~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (~((~(apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | ![Y: $i] : ((~member(Y, A!40)) | (~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), Y)) | (~apply(F!43, Y, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))))) | (~((~apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~((~apply(F!43, tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43))) | (~member(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), A!40)))))))))),
% 0.38/0.56 inference(rewrite,[status(thm)],[])).
% 0.38/0.56 tff(201,plain,
% 0.38/0.56 (((~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (~((~(apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | ![Y: $i] : ((~member(Y, A!40)) | (~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), Y)) | (~apply(F!43, Y, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))))) | (~((~apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~((~apply(F!43, tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43))) | (~member(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), A!40))))))))) <=> ((~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (~((~(apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | ![Y: $i] : ((~member(Y, A!40)) | (~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), Y)) | (~apply(F!43, Y, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))))) | (~((~apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~((~apply(F!43, tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43))) | (~member(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), A!40)))))))))),
% 0.38/0.57 inference(rewrite,[status(thm)],[])).
% 0.38/0.57 tff(202,plain,
% 0.38/0.57 ((~((~((~apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), A!40)) | (~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43))) | (~apply(F!43, tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))))) | (~(apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | ![Y: $i] : ((~member(Y, A!40)) | (~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), Y)) | (~apply(F!43, Y, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))))))) <=> (~((~(apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | ![Y: $i] : ((~member(Y, A!40)) | (~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), Y)) | (~apply(F!43, Y, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))))) | (~((~apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~((~apply(F!43, tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43))) | (~member(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), A!40))))))))),
% 0.38/0.57 inference(rewrite,[status(thm)],[])).
% 0.38/0.57 tff(203,plain,
% 0.38/0.57 (((~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (~((~((~apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), A!40)) | (~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43))) | (~apply(F!43, tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))))) | (~(apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | ![Y: $i] : ((~member(Y, A!40)) | (~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), Y)) | (~apply(F!43, Y, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))))))) <=> ((~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (~((~(apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | ![Y: $i] : ((~member(Y, A!40)) | (~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), Y)) | (~apply(F!43, Y, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))))) | (~((~apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~((~apply(F!43, tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43))) | (~member(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), A!40)))))))))),
% 0.38/0.57 inference(monotonicity,[status(thm)],[202])).
% 0.38/0.57 tff(204,plain,
% 0.38/0.57 (((~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (~((~((~apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), A!40)) | (~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43))) | (~apply(F!43, tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))))) | (~(apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | ![Y: $i] : ((~member(Y, A!40)) | (~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), Y)) | (~apply(F!43, Y, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))))))) <=> ((~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (~((~(apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | ![Y: $i] : ((~member(Y, A!40)) | (~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), Y)) | (~apply(F!43, Y, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))))) | (~((~apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~((~apply(F!43, tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43))) | (~member(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), A!40)))))))))),
% 0.38/0.57 inference(transitivity,[status(thm)],[203, 201])).
% 0.38/0.57 tff(205,plain,
% 0.38/0.57 (((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (~((~((~apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), A!40)) | (~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43))) | (~apply(F!43, tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))))) | (~(apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | ![Y: $i] : ((~member(Y, A!40)) | (~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), Y)) | (~apply(F!43, Y, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))))))))) <=> ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (~((~(apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | ![Y: $i] : ((~member(Y, A!40)) | (~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), Y)) | (~apply(F!43, Y, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))))) | (~((~apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~((~apply(F!43, tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43))) | (~member(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), A!40))))))))))),
% 0.38/0.58 inference(monotonicity,[status(thm)],[204])).
% 0.38/0.58 tff(206,plain,
% 0.38/0.58 (((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (~((~((~apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), A!40)) | (~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43))) | (~apply(F!43, tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))))) | (~(apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | ![Y: $i] : ((~member(Y, A!40)) | (~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), Y)) | (~apply(F!43, Y, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))))))))) <=> ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | (~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (~((~(apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | ![Y: $i] : ((~member(Y, A!40)) | (~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), Y)) | (~apply(F!43, Y, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))))) | (~((~apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~((~apply(F!43, tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43))) | (~member(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), A!40)))))))))),
% 0.38/0.58 inference(transitivity,[status(thm)],[205, 200])).
% 0.38/0.58 tff(207,plain,
% 0.38/0.58 ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (~((~((~apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), A!40)) | (~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43))) | (~apply(F!43, tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))))) | (~(apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | ![Y: $i] : ((~member(Y, A!40)) | (~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), Y)) | (~apply(F!43, Y, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))))))))),
% 0.38/0.58 inference(quant_inst,[status(thm)],[])).
% 0.38/0.58 tff(208,plain,
% 0.38/0.58 ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | (~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (~((~(apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | ![Y: $i] : ((~member(Y, A!40)) | (~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), Y)) | (~apply(F!43, Y, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))))) | (~((~apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~((~apply(F!43, tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43))) | (~member(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), A!40))))))))),
% 0.38/0.58 inference(modus_ponens,[status(thm)],[207, 206])).
% 0.38/0.58 tff(209,plain,
% 0.38/0.58 (~((~(apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | ![Y: $i] : ((~member(Y, A!40)) | (~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), Y)) | (~apply(F!43, Y, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))))) | (~((~apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~((~apply(F!43, tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43))) | (~member(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), A!40)))))))),
% 0.38/0.58 inference(unit_resolution,[status(thm)],[208, 55, 199])).
% 0.38/0.58 tff(210,plain,
% 0.38/0.58 (((~(apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | ![Y: $i] : ((~member(Y, A!40)) | (~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), Y)) | (~apply(F!43, Y, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))))) | (~((~apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~((~apply(F!43, tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43))) | (~member(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), A!40))))))) | ((~apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~((~apply(F!43, tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43))) | (~member(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), A!40)))))),
% 0.38/0.58 inference(tautology,[status(thm)],[])).
% 0.38/0.58 tff(211,plain,
% 0.38/0.58 ((~apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~((~apply(F!43, tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43))) | (~member(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), A!40))))),
% 0.38/0.58 inference(unit_resolution,[status(thm)],[210, 209])).
% 0.38/0.58 tff(212,plain,
% 0.38/0.58 ((~![F: $i, A: $i] : (~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F))))))))) | (~((~((~identity(compose_function(F!43, H!41, B!39, A!40, B!39), B!39)) | ![X: $i] : ((~member(X, B!39)) | apply(compose_function(F!43, H!41, B!39, A!40, B!39), X, X)))) | (~(identity(compose_function(F!43, H!41, B!39, A!40, B!39), B!39) | (~((~member(tptp_fun_X_15(B!39, compose_function(F!43, H!41, B!39, A!40, B!39)), B!39)) | apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!43, H!41, B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!43, H!41, B!39, A!40, B!39)))))))))),
% 0.38/0.58 inference(quant_inst,[status(thm)],[])).
% 0.38/0.58 tff(213,plain,
% 0.38/0.58 (~((~((~identity(compose_function(F!43, H!41, B!39, A!40, B!39), B!39)) | ![X: $i] : ((~member(X, B!39)) | apply(compose_function(F!43, H!41, B!39, A!40, B!39), X, X)))) | (~(identity(compose_function(F!43, H!41, B!39, A!40, B!39), B!39) | (~((~member(tptp_fun_X_15(B!39, compose_function(F!43, H!41, B!39, A!40, B!39)), B!39)) | apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!43, H!41, B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!43, H!41, B!39, A!40, B!39))))))))),
% 0.38/0.58 inference(unit_resolution,[status(thm)],[212, 83])).
% 0.38/0.58 tff(214,plain,
% 0.38/0.58 (((~((~identity(compose_function(F!43, H!41, B!39, A!40, B!39), B!39)) | ![X: $i] : ((~member(X, B!39)) | apply(compose_function(F!43, H!41, B!39, A!40, B!39), X, X)))) | (~(identity(compose_function(F!43, H!41, B!39, A!40, B!39), B!39) | (~((~member(tptp_fun_X_15(B!39, compose_function(F!43, H!41, B!39, A!40, B!39)), B!39)) | apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!43, H!41, B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!43, H!41, B!39, A!40, B!39)))))))) | ((~identity(compose_function(F!43, H!41, B!39, A!40, B!39), B!39)) | ![X: $i] : ((~member(X, B!39)) | apply(compose_function(F!43, H!41, B!39, A!40, B!39), X, X)))),
% 0.38/0.58 inference(tautology,[status(thm)],[])).
% 0.38/0.58 tff(215,plain,
% 0.38/0.58 ((~identity(compose_function(F!43, H!41, B!39, A!40, B!39), B!39)) | ![X: $i] : ((~member(X, B!39)) | apply(compose_function(F!43, H!41, B!39, A!40, B!39), X, X))),
% 0.38/0.58 inference(unit_resolution,[status(thm)],[214, 213])).
% 0.38/0.58 tff(216,plain,
% 0.38/0.58 (identity(compose_function(F!43, H!41, B!39, A!40, B!39), B!39)),
% 0.38/0.58 inference(and_elim,[status(thm)],[88])).
% 0.38/0.58 tff(217,plain,
% 0.38/0.58 ((~((~identity(compose_function(F!43, H!41, B!39, A!40, B!39), B!39)) | ![X: $i] : ((~member(X, B!39)) | apply(compose_function(F!43, H!41, B!39, A!40, B!39), X, X)))) | (~identity(compose_function(F!43, H!41, B!39, A!40, B!39), B!39)) | ![X: $i] : ((~member(X, B!39)) | apply(compose_function(F!43, H!41, B!39, A!40, B!39), X, X))),
% 0.38/0.58 inference(tautology,[status(thm)],[])).
% 0.38/0.58 tff(218,plain,
% 0.38/0.58 ((~((~identity(compose_function(F!43, H!41, B!39, A!40, B!39), B!39)) | ![X: $i] : ((~member(X, B!39)) | apply(compose_function(F!43, H!41, B!39, A!40, B!39), X, X)))) | ![X: $i] : ((~member(X, B!39)) | apply(compose_function(F!43, H!41, B!39, A!40, B!39), X, X))),
% 0.38/0.58 inference(unit_resolution,[status(thm)],[217, 216])).
% 0.38/0.58 tff(219,plain,
% 0.38/0.58 (![X: $i] : ((~member(X, B!39)) | apply(compose_function(F!43, H!41, B!39, A!40, B!39), X, X))),
% 0.38/0.58 inference(unit_resolution,[status(thm)],[218, 215])).
% 0.38/0.58 tff(220,plain,
% 0.38/0.58 (((~![X: $i] : ((~member(X, B!39)) | apply(compose_function(F!43, H!41, B!39, A!40, B!39), X, X))) | ((~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))) <=> ((~![X: $i] : ((~member(X, B!39)) | apply(compose_function(F!43, H!41, B!39, A!40, B!39), X, X))) | (~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))),
% 0.38/0.59 inference(rewrite,[status(thm)],[])).
% 0.38/0.59 tff(221,plain,
% 0.38/0.59 ((~![X: $i] : ((~member(X, B!39)) | apply(compose_function(F!43, H!41, B!39, A!40, B!39), X, X))) | ((~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))),
% 0.38/0.59 inference(quant_inst,[status(thm)],[])).
% 0.38/0.59 tff(222,plain,
% 0.38/0.59 ((~![X: $i] : ((~member(X, B!39)) | apply(compose_function(F!43, H!41, B!39, A!40, B!39), X, X))) | (~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))),
% 0.38/0.59 inference(modus_ponens,[status(thm)],[221, 220])).
% 0.38/0.59 tff(223,plain,
% 0.38/0.59 (apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))),
% 0.38/0.59 inference(unit_resolution,[status(thm)],[222, 199, 219])).
% 0.38/0.59 tff(224,plain,
% 0.38/0.59 ((~((~apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~((~apply(F!43, tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43))) | (~member(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), A!40)))))) | (~apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~((~apply(F!43, tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43))) | (~member(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), A!40))))),
% 0.38/0.59 inference(tautology,[status(thm)],[])).
% 0.38/0.59 tff(225,plain,
% 0.38/0.59 ((~((~apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~((~apply(F!43, tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43))) | (~member(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), A!40)))))) | (~((~apply(F!43, tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43))) | (~member(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), A!40))))),
% 0.38/0.59 inference(unit_resolution,[status(thm)],[224, 223])).
% 0.38/0.59 tff(226,plain,
% 0.38/0.59 (~((~apply(F!43, tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43))) | (~member(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), A!40)))),
% 0.38/0.59 inference(unit_resolution,[status(thm)],[225, 211])).
% 0.38/0.59 tff(227,plain,
% 0.38/0.59 (((~apply(F!43, tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43))) | (~member(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), A!40))) | member(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), A!40)),
% 0.38/0.59 inference(tautology,[status(thm)],[])).
% 0.38/0.59 tff(228,plain,
% 0.38/0.59 (member(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), A!40)),
% 0.38/0.59 inference(unit_resolution,[status(thm)],[227, 226])).
% 0.38/0.59 tff(229,plain,
% 0.38/0.59 (((~apply(F!43, tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43))) | (~member(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), A!40))) | apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43))),
% 0.38/0.59 inference(tautology,[status(thm)],[])).
% 0.38/0.59 tff(230,plain,
% 0.38/0.59 (apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43))),
% 0.38/0.59 inference(unit_resolution,[status(thm)],[229, 226])).
% 0.38/0.59 tff(231,plain,
% 0.38/0.59 (((~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~apply(inverse_function(F!43, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))),
% 0.38/0.59 inference(tautology,[status(thm)],[])).
% 0.38/0.59 tff(232,plain,
% 0.38/0.59 (apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))),
% 0.38/0.59 inference(unit_resolution,[status(thm)],[231, 37])).
% 0.38/0.59 tff(233,plain,
% 0.38/0.59 (((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(H!41, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, H!41), A!40)) | (~apply(H!41, X, tptp_fun_Y_3(X, A!40, H!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~member(X, B!39)) | (~member(Y1, A!40)) | (~apply(H!41, X, Y1)) | (~apply(H!41, X, Y2)))))))) | (~(maps(H!41, B!39, A!40) | (~((~member(tptp_fun_X_4(A!40, B!39, H!41), B!39)) | (~![Y: $i] : ((~member(Y, A!40)) | (~apply(H!41, tptp_fun_X_4(A!40, B!39, H!41), Y)))))) | (~((~member(tptp_fun_Y2_5(A!40, B!39, H!41), A!40)) | (~member(tptp_fun_Y1_6(A!40, B!39, H!41), A!40)) | (~member(tptp_fun_X_7(A!40, B!39, H!41), B!39)) | (~apply(H!41, tptp_fun_X_7(A!40, B!39, H!41), tptp_fun_Y2_5(A!40, B!39, H!41))) | (~apply(H!41, tptp_fun_X_7(A!40, B!39, H!41), tptp_fun_Y1_6(A!40, B!39, H!41))) | (tptp_fun_Y1_6(A!40, B!39, H!41) = tptp_fun_Y2_5(A!40, B!39, H!41))))))))) <=> ((~![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(H!41, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, H!41), A!40)) | (~apply(H!41, X, tptp_fun_Y_3(X, A!40, H!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~member(X, B!39)) | (~member(Y1, A!40)) | (~apply(H!41, X, Y1)) | (~apply(H!41, X, Y2)))))))) | (~(maps(H!41, B!39, A!40) | (~((~member(tptp_fun_X_4(A!40, B!39, H!41), B!39)) | (~![Y: $i] : ((~member(Y, A!40)) | (~apply(H!41, tptp_fun_X_4(A!40, B!39, H!41), Y)))))) | (~((~member(tptp_fun_Y2_5(A!40, B!39, H!41), A!40)) | (~member(tptp_fun_Y1_6(A!40, B!39, H!41), A!40)) | (~member(tptp_fun_X_7(A!40, B!39, H!41), B!39)) | (~apply(H!41, tptp_fun_X_7(A!40, B!39, H!41), tptp_fun_Y2_5(A!40, B!39, H!41))) | (~apply(H!41, tptp_fun_X_7(A!40, B!39, H!41), tptp_fun_Y1_6(A!40, B!39, H!41))) | (tptp_fun_Y1_6(A!40, B!39, H!41) = tptp_fun_Y2_5(A!40, B!39, H!41)))))))))),
% 0.38/0.60 inference(rewrite,[status(thm)],[])).
% 0.38/0.60 tff(234,plain,
% 0.38/0.60 ((~((~((~maps(H!41, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, H!41), A!40)) | (~apply(H!41, X, tptp_fun_Y_3(X, A!40, H!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(H!41, X, Y1)) | (~apply(H!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)) | (~member(Y2, A!40)))))))) | (~(maps(H!41, B!39, A!40) | (~((tptp_fun_Y1_6(A!40, B!39, H!41) = tptp_fun_Y2_5(A!40, B!39, H!41)) | (~apply(H!41, tptp_fun_X_7(A!40, B!39, H!41), tptp_fun_Y1_6(A!40, B!39, H!41))) | (~apply(H!41, tptp_fun_X_7(A!40, B!39, H!41), tptp_fun_Y2_5(A!40, B!39, H!41))) | (~member(tptp_fun_X_7(A!40, B!39, H!41), B!39)) | (~member(tptp_fun_Y1_6(A!40, B!39, H!41), A!40)) | (~member(tptp_fun_Y2_5(A!40, B!39, H!41), A!40)))) | (~((~member(tptp_fun_X_4(A!40, B!39, H!41), B!39)) | (~![Y: $i] : ((~member(Y, A!40)) | (~apply(H!41, tptp_fun_X_4(A!40, B!39, H!41), Y)))))))))) <=> (~((~((~maps(H!41, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, H!41), A!40)) | (~apply(H!41, X, tptp_fun_Y_3(X, A!40, H!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~member(X, B!39)) | (~member(Y1, A!40)) | (~apply(H!41, X, Y1)) | (~apply(H!41, X, Y2)))))))) | (~(maps(H!41, B!39, A!40) | (~((~member(tptp_fun_X_4(A!40, B!39, H!41), B!39)) | (~![Y: $i] : ((~member(Y, A!40)) | (~apply(H!41, tptp_fun_X_4(A!40, B!39, H!41), Y)))))) | (~((~member(tptp_fun_Y2_5(A!40, B!39, H!41), A!40)) | (~member(tptp_fun_Y1_6(A!40, B!39, H!41), A!40)) | (~member(tptp_fun_X_7(A!40, B!39, H!41), B!39)) | (~apply(H!41, tptp_fun_X_7(A!40, B!39, H!41), tptp_fun_Y2_5(A!40, B!39, H!41))) | (~apply(H!41, tptp_fun_X_7(A!40, B!39, H!41), tptp_fun_Y1_6(A!40, B!39, H!41))) | (tptp_fun_Y1_6(A!40, B!39, H!41) = tptp_fun_Y2_5(A!40, B!39, H!41))))))))),
% 0.38/0.60 inference(rewrite,[status(thm)],[])).
% 0.38/0.60 tff(235,plain,
% 0.38/0.60 (((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(H!41, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, H!41), A!40)) | (~apply(H!41, X, tptp_fun_Y_3(X, A!40, H!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(H!41, X, Y1)) | (~apply(H!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)) | (~member(Y2, A!40)))))))) | (~(maps(H!41, B!39, A!40) | (~((tptp_fun_Y1_6(A!40, B!39, H!41) = tptp_fun_Y2_5(A!40, B!39, H!41)) | (~apply(H!41, tptp_fun_X_7(A!40, B!39, H!41), tptp_fun_Y1_6(A!40, B!39, H!41))) | (~apply(H!41, tptp_fun_X_7(A!40, B!39, H!41), tptp_fun_Y2_5(A!40, B!39, H!41))) | (~member(tptp_fun_X_7(A!40, B!39, H!41), B!39)) | (~member(tptp_fun_Y1_6(A!40, B!39, H!41), A!40)) | (~member(tptp_fun_Y2_5(A!40, B!39, H!41), A!40)))) | (~((~member(tptp_fun_X_4(A!40, B!39, H!41), B!39)) | (~![Y: $i] : ((~member(Y, A!40)) | (~apply(H!41, tptp_fun_X_4(A!40, B!39, H!41), 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(H!41, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, H!41), A!40)) | (~apply(H!41, X, tptp_fun_Y_3(X, A!40, H!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~member(X, B!39)) | (~member(Y1, A!40)) | (~apply(H!41, X, Y1)) | (~apply(H!41, X, Y2)))))))) | (~(maps(H!41, B!39, A!40) | (~((~member(tptp_fun_X_4(A!40, B!39, H!41), B!39)) | (~![Y: $i] : ((~member(Y, A!40)) | (~apply(H!41, tptp_fun_X_4(A!40, B!39, H!41), Y)))))) | (~((~member(tptp_fun_Y2_5(A!40, B!39, H!41), A!40)) | (~member(tptp_fun_Y1_6(A!40, B!39, H!41), A!40)) | (~member(tptp_fun_X_7(A!40, B!39, H!41), B!39)) | (~apply(H!41, tptp_fun_X_7(A!40, B!39, H!41), tptp_fun_Y2_5(A!40, B!39, H!41))) | (~apply(H!41, tptp_fun_X_7(A!40, B!39, H!41), tptp_fun_Y1_6(A!40, B!39, H!41))) | (tptp_fun_Y1_6(A!40, B!39, H!41) = tptp_fun_Y2_5(A!40, B!39, H!41)))))))))),
% 0.38/0.60 inference(monotonicity,[status(thm)],[234])).
% 0.38/0.60 tff(236,plain,
% 0.38/0.60 (((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(H!41, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, H!41), A!40)) | (~apply(H!41, X, tptp_fun_Y_3(X, A!40, H!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(H!41, X, Y1)) | (~apply(H!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)) | (~member(Y2, A!40)))))))) | (~(maps(H!41, B!39, A!40) | (~((tptp_fun_Y1_6(A!40, B!39, H!41) = tptp_fun_Y2_5(A!40, B!39, H!41)) | (~apply(H!41, tptp_fun_X_7(A!40, B!39, H!41), tptp_fun_Y1_6(A!40, B!39, H!41))) | (~apply(H!41, tptp_fun_X_7(A!40, B!39, H!41), tptp_fun_Y2_5(A!40, B!39, H!41))) | (~member(tptp_fun_X_7(A!40, B!39, H!41), B!39)) | (~member(tptp_fun_Y1_6(A!40, B!39, H!41), A!40)) | (~member(tptp_fun_Y2_5(A!40, B!39, H!41), A!40)))) | (~((~member(tptp_fun_X_4(A!40, B!39, H!41), B!39)) | (~![Y: $i] : ((~member(Y, A!40)) | (~apply(H!41, tptp_fun_X_4(A!40, B!39, H!41), 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(H!41, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, H!41), A!40)) | (~apply(H!41, X, tptp_fun_Y_3(X, A!40, H!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~member(X, B!39)) | (~member(Y1, A!40)) | (~apply(H!41, X, Y1)) | (~apply(H!41, X, Y2)))))))) | (~(maps(H!41, B!39, A!40) | (~((~member(tptp_fun_X_4(A!40, B!39, H!41), B!39)) | (~![Y: $i] : ((~member(Y, A!40)) | (~apply(H!41, tptp_fun_X_4(A!40, B!39, H!41), Y)))))) | (~((~member(tptp_fun_Y2_5(A!40, B!39, H!41), A!40)) | (~member(tptp_fun_Y1_6(A!40, B!39, H!41), A!40)) | (~member(tptp_fun_X_7(A!40, B!39, H!41), B!39)) | (~apply(H!41, tptp_fun_X_7(A!40, B!39, H!41), tptp_fun_Y2_5(A!40, B!39, H!41))) | (~apply(H!41, tptp_fun_X_7(A!40, B!39, H!41), tptp_fun_Y1_6(A!40, B!39, H!41))) | (tptp_fun_Y1_6(A!40, B!39, H!41) = tptp_fun_Y2_5(A!40, B!39, H!41)))))))))),
% 0.38/0.60 inference(transitivity,[status(thm)],[235, 233])).
% 0.38/0.60 tff(237,plain,
% 0.38/0.60 ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(H!41, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, H!41), A!40)) | (~apply(H!41, X, tptp_fun_Y_3(X, A!40, H!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(H!41, X, Y1)) | (~apply(H!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)) | (~member(Y2, A!40)))))))) | (~(maps(H!41, B!39, A!40) | (~((tptp_fun_Y1_6(A!40, B!39, H!41) = tptp_fun_Y2_5(A!40, B!39, H!41)) | (~apply(H!41, tptp_fun_X_7(A!40, B!39, H!41), tptp_fun_Y1_6(A!40, B!39, H!41))) | (~apply(H!41, tptp_fun_X_7(A!40, B!39, H!41), tptp_fun_Y2_5(A!40, B!39, H!41))) | (~member(tptp_fun_X_7(A!40, B!39, H!41), B!39)) | (~member(tptp_fun_Y1_6(A!40, B!39, H!41), A!40)) | (~member(tptp_fun_Y2_5(A!40, B!39, H!41), A!40)))) | (~((~member(tptp_fun_X_4(A!40, B!39, H!41), B!39)) | (~![Y: $i] : ((~member(Y, A!40)) | (~apply(H!41, tptp_fun_X_4(A!40, B!39, H!41), Y))))))))))),
% 0.38/0.60 inference(quant_inst,[status(thm)],[])).
% 0.38/0.60 tff(238,plain,
% 0.38/0.60 ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(H!41, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, H!41), A!40)) | (~apply(H!41, X, tptp_fun_Y_3(X, A!40, H!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~member(X, B!39)) | (~member(Y1, A!40)) | (~apply(H!41, X, Y1)) | (~apply(H!41, X, Y2)))))))) | (~(maps(H!41, B!39, A!40) | (~((~member(tptp_fun_X_4(A!40, B!39, H!41), B!39)) | (~![Y: $i] : ((~member(Y, A!40)) | (~apply(H!41, tptp_fun_X_4(A!40, B!39, H!41), Y)))))) | (~((~member(tptp_fun_Y2_5(A!40, B!39, H!41), A!40)) | (~member(tptp_fun_Y1_6(A!40, B!39, H!41), A!40)) | (~member(tptp_fun_X_7(A!40, B!39, H!41), B!39)) | (~apply(H!41, tptp_fun_X_7(A!40, B!39, H!41), tptp_fun_Y2_5(A!40, B!39, H!41))) | (~apply(H!41, tptp_fun_X_7(A!40, B!39, H!41), tptp_fun_Y1_6(A!40, B!39, H!41))) | (tptp_fun_Y1_6(A!40, B!39, H!41) = tptp_fun_Y2_5(A!40, B!39, H!41))))))))),
% 0.38/0.60 inference(modus_ponens,[status(thm)],[237, 236])).
% 0.38/0.60 tff(239,plain,
% 0.38/0.60 (~((~((~maps(H!41, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, H!41), A!40)) | (~apply(H!41, X, tptp_fun_Y_3(X, A!40, H!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~member(X, B!39)) | (~member(Y1, A!40)) | (~apply(H!41, X, Y1)) | (~apply(H!41, X, Y2)))))))) | (~(maps(H!41, B!39, A!40) | (~((~member(tptp_fun_X_4(A!40, B!39, H!41), B!39)) | (~![Y: $i] : ((~member(Y, A!40)) | (~apply(H!41, tptp_fun_X_4(A!40, B!39, H!41), Y)))))) | (~((~member(tptp_fun_Y2_5(A!40, B!39, H!41), A!40)) | (~member(tptp_fun_Y1_6(A!40, B!39, H!41), A!40)) | (~member(tptp_fun_X_7(A!40, B!39, H!41), B!39)) | (~apply(H!41, tptp_fun_X_7(A!40, B!39, H!41), tptp_fun_Y2_5(A!40, B!39, H!41))) | (~apply(H!41, tptp_fun_X_7(A!40, B!39, H!41), tptp_fun_Y1_6(A!40, B!39, H!41))) | (tptp_fun_Y1_6(A!40, B!39, H!41) = tptp_fun_Y2_5(A!40, B!39, H!41)))))))),
% 0.38/0.60 inference(unit_resolution,[status(thm)],[238, 125])).
% 0.38/0.60 tff(240,plain,
% 0.38/0.60 (((~((~maps(H!41, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, H!41), A!40)) | (~apply(H!41, X, tptp_fun_Y_3(X, A!40, H!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~member(X, B!39)) | (~member(Y1, A!40)) | (~apply(H!41, X, Y1)) | (~apply(H!41, X, Y2)))))))) | (~(maps(H!41, B!39, A!40) | (~((~member(tptp_fun_X_4(A!40, B!39, H!41), B!39)) | (~![Y: $i] : ((~member(Y, A!40)) | (~apply(H!41, tptp_fun_X_4(A!40, B!39, H!41), Y)))))) | (~((~member(tptp_fun_Y2_5(A!40, B!39, H!41), A!40)) | (~member(tptp_fun_Y1_6(A!40, B!39, H!41), A!40)) | (~member(tptp_fun_X_7(A!40, B!39, H!41), B!39)) | (~apply(H!41, tptp_fun_X_7(A!40, B!39, H!41), tptp_fun_Y2_5(A!40, B!39, H!41))) | (~apply(H!41, tptp_fun_X_7(A!40, B!39, H!41), tptp_fun_Y1_6(A!40, B!39, H!41))) | (tptp_fun_Y1_6(A!40, B!39, H!41) = tptp_fun_Y2_5(A!40, B!39, H!41))))))) | ((~maps(H!41, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, H!41), A!40)) | (~apply(H!41, X, tptp_fun_Y_3(X, A!40, H!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~member(X, B!39)) | (~member(Y1, A!40)) | (~apply(H!41, X, Y1)) | (~apply(H!41, X, Y2)))))))),
% 0.38/0.60 inference(tautology,[status(thm)],[])).
% 0.38/0.60 tff(241,plain,
% 0.38/0.60 ((~maps(H!41, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, H!41), A!40)) | (~apply(H!41, X, tptp_fun_Y_3(X, A!40, H!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~member(X, B!39)) | (~member(Y1, A!40)) | (~apply(H!41, X, Y1)) | (~apply(H!41, X, Y2))))))),
% 0.38/0.60 inference(unit_resolution,[status(thm)],[240, 239])).
% 0.38/0.60 tff(242,plain,
% 0.38/0.60 (maps(H!41, B!39, A!40)),
% 0.38/0.60 inference(and_elim,[status(thm)],[88])).
% 0.38/0.60 tff(243,plain,
% 0.38/0.60 ((~((~maps(H!41, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, H!41), A!40)) | (~apply(H!41, X, tptp_fun_Y_3(X, A!40, H!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~member(X, B!39)) | (~member(Y1, A!40)) | (~apply(H!41, X, Y1)) | (~apply(H!41, X, Y2)))))))) | (~maps(H!41, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, H!41), A!40)) | (~apply(H!41, X, tptp_fun_Y_3(X, A!40, H!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~member(X, B!39)) | (~member(Y1, A!40)) | (~apply(H!41, X, Y1)) | (~apply(H!41, X, Y2))))))),
% 0.38/0.60 inference(tautology,[status(thm)],[])).
% 0.38/0.60 tff(244,plain,
% 0.38/0.60 ((~((~maps(H!41, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, H!41), A!40)) | (~apply(H!41, X, tptp_fun_Y_3(X, A!40, H!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~member(X, B!39)) | (~member(Y1, A!40)) | (~apply(H!41, X, Y1)) | (~apply(H!41, X, Y2)))))))) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, H!41), A!40)) | (~apply(H!41, X, tptp_fun_Y_3(X, A!40, H!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~member(X, B!39)) | (~member(Y1, A!40)) | (~apply(H!41, X, Y1)) | (~apply(H!41, X, Y2))))))),
% 0.38/0.60 inference(unit_resolution,[status(thm)],[243, 242])).
% 0.38/0.60 tff(245,plain,
% 0.38/0.60 (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, H!41), A!40)) | (~apply(H!41, X, tptp_fun_Y_3(X, A!40, H!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~member(X, B!39)) | (~member(Y1, A!40)) | (~apply(H!41, X, Y1)) | (~apply(H!41, X, Y2)))))),
% 0.38/0.60 inference(unit_resolution,[status(thm)],[244, 241])).
% 0.38/0.60 tff(246,plain,
% 0.38/0.60 (((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, H!41), A!40)) | (~apply(H!41, X, tptp_fun_Y_3(X, A!40, H!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~member(X, B!39)) | (~member(Y1, A!40)) | (~apply(H!41, X, Y1)) | (~apply(H!41, X, Y2))))) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~member(X, B!39)) | (~member(Y1, A!40)) | (~apply(H!41, X, Y1)) | (~apply(H!41, X, Y2)))),
% 0.38/0.60 inference(tautology,[status(thm)],[])).
% 0.38/0.60 tff(247,plain,
% 0.38/0.60 (![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~member(X, B!39)) | (~member(Y1, A!40)) | (~apply(H!41, X, Y1)) | (~apply(H!41, X, Y2)))),
% 0.38/0.60 inference(unit_resolution,[status(thm)],[246, 245])).
% 0.38/0.60 tff(248,plain,
% 0.38/0.60 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~member(X, B!39)) | (~member(Y1, A!40)) | (~apply(H!41, X, Y1)) | (~apply(H!41, X, Y2)))) | ((~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43))) | (~member(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), A!40)) | (tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43) = tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~member(X, B!39)) | (~member(Y1, A!40)) | (~apply(H!41, X, Y1)) | (~apply(H!41, X, Y2)))) | (~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43))) | (~member(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), A!40)) | (tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43) = tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))),
% 0.38/0.61 inference(rewrite,[status(thm)],[])).
% 0.38/0.61 tff(249,plain,
% 0.38/0.61 (((tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43) = tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (~member(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), A!40)) | (~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43))) | (~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))) <=> ((~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43))) | (~member(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), A!40)) | (tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43) = tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))),
% 0.38/0.61 inference(rewrite,[status(thm)],[])).
% 0.38/0.61 tff(250,plain,
% 0.38/0.61 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~member(X, B!39)) | (~member(Y1, A!40)) | (~apply(H!41, X, Y1)) | (~apply(H!41, X, Y2)))) | ((tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43) = tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (~member(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), A!40)) | (~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43))) | (~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~member(X, B!39)) | (~member(Y1, A!40)) | (~apply(H!41, X, Y1)) | (~apply(H!41, X, Y2)))) | ((~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43))) | (~member(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), A!40)) | (tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43) = tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))),
% 0.38/0.61 inference(monotonicity,[status(thm)],[249])).
% 0.38/0.61 tff(251,plain,
% 0.38/0.61 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~member(X, B!39)) | (~member(Y1, A!40)) | (~apply(H!41, X, Y1)) | (~apply(H!41, X, Y2)))) | ((tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43) = tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (~member(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), A!40)) | (~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43))) | (~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~member(X, B!39)) | (~member(Y1, A!40)) | (~apply(H!41, X, Y1)) | (~apply(H!41, X, Y2)))) | (~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43))) | (~member(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), A!40)) | (tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43) = tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))),
% 0.38/0.61 inference(transitivity,[status(thm)],[250, 248])).
% 0.38/0.61 tff(252,plain,
% 0.38/0.61 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~member(X, B!39)) | (~member(Y1, A!40)) | (~apply(H!41, X, Y1)) | (~apply(H!41, X, Y2)))) | ((tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43) = tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (~member(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), A!40)) | (~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43))) | (~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))),
% 0.38/0.61 inference(quant_inst,[status(thm)],[])).
% 0.38/0.61 tff(253,plain,
% 0.38/0.61 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~member(X, B!39)) | (~member(Y1, A!40)) | (~apply(H!41, X, Y1)) | (~apply(H!41, X, Y2)))) | (~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43))) | (~member(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), A!40)) | (tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43) = tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))),
% 0.38/0.61 inference(modus_ponens,[status(thm)],[252, 251])).
% 0.38/0.61 tff(254,plain,
% 0.38/0.61 (tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43) = tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))),
% 0.38/0.61 inference(unit_resolution,[status(thm)],[253, 247, 232, 39, 199, 230, 228])).
% 0.38/0.61 tff(255,plain,
% 0.38/0.61 (tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43)),
% 0.38/0.61 inference(symmetry,[status(thm)],[254])).
% 0.38/0.61 tff(256,plain,
% 0.38/0.61 (apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) <=> apply(F!43, tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))),
% 0.38/0.61 inference(monotonicity,[status(thm)],[255])).
% 0.38/0.61 tff(257,plain,
% 0.38/0.61 (apply(F!43, tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) <=> apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))),
% 0.38/0.61 inference(symmetry,[status(thm)],[256])).
% 0.38/0.61 tff(258,plain,
% 0.38/0.61 (((~apply(F!43, tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43))) | (~member(tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), A!40))) | apply(F!43, tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))),
% 0.38/0.62 inference(tautology,[status(thm)],[])).
% 0.38/0.62 tff(259,plain,
% 0.38/0.62 (apply(F!43, tptp_fun_Y_8(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, H!41, F!43), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))),
% 0.38/0.62 inference(unit_resolution,[status(thm)],[258, 226])).
% 0.38/0.62 tff(260,plain,
% 0.38/0.62 (apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))),
% 0.38/0.62 inference(modus_ponens,[status(thm)],[259, 257])).
% 0.38/0.62 tff(261,plain,
% 0.38/0.62 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))) | ((~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43))) | (tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43))) | (tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))),
% 0.38/0.62 inference(rewrite,[status(thm)],[])).
% 0.38/0.62 tff(262,plain,
% 0.38/0.62 (((tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43)) | (~member(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43))) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39))) <=> ((~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43))) | (tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))),
% 0.38/0.62 inference(rewrite,[status(thm)],[])).
% 0.38/0.62 tff(263,plain,
% 0.38/0.62 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))) | ((tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43)) | (~member(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43))) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))) | ((~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43))) | (tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))))),
% 0.38/0.62 inference(monotonicity,[status(thm)],[262])).
% 0.38/0.62 tff(264,plain,
% 0.38/0.62 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))) | ((tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43)) | (~member(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43))) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43))) | (tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))),
% 0.38/0.62 inference(transitivity,[status(thm)],[263, 261])).
% 0.38/0.62 tff(265,plain,
% 0.38/0.62 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))) | ((tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43)) | (~member(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43))) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)))),
% 0.38/0.62 inference(quant_inst,[status(thm)],[])).
% 0.38/0.62 tff(266,plain,
% 0.38/0.62 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), B!39)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43))) | (tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))),
% 0.38/0.62 inference(modus_ponens,[status(thm)],[265, 264])).
% 0.38/0.62 tff(267,plain,
% 0.38/0.62 ((tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43)) | (~apply(F!43, tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))),
% 0.38/0.62 inference(unit_resolution,[status(thm)],[266, 150, 39, 199, 148, 146])).
% 0.38/0.62 tff(268,plain,
% 0.38/0.62 (tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43)),
% 0.38/0.62 inference(unit_resolution,[status(thm)],[267, 260])).
% 0.38/0.62 tff(269,plain,
% 0.38/0.62 (tptp_fun_Y_3(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, G!42) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43), A!40, G!42)),
% 0.38/0.62 inference(monotonicity,[status(thm)],[268])).
% 0.38/0.62 tff(270,plain,
% 0.38/0.62 (((~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~apply(inverse_function(F!43, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)),
% 0.38/0.62 inference(tautology,[status(thm)],[])).
% 0.38/0.62 tff(271,plain,
% 0.38/0.62 (member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)),
% 0.38/0.62 inference(unit_resolution,[status(thm)],[270, 37])).
% 0.38/0.62 tff(272,plain,
% 0.38/0.62 (((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~((~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))))) | (~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))))))))) <=> ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~((~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))))) | (~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))))))))),
% 0.38/0.62 inference(rewrite,[status(thm)],[])).
% 0.38/0.62 tff(273,plain,
% 0.38/0.62 (((~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~((~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))))) | (~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))))))))) <=> ((~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~((~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))))) | (~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))))))))),
% 0.38/0.63 inference(rewrite,[status(thm)],[])).
% 0.38/0.63 tff(274,plain,
% 0.38/0.63 ((~((~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))))) | (~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))))))) <=> (~((~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))))) | (~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))))))))),
% 0.38/0.63 inference(rewrite,[status(thm)],[])).
% 0.38/0.63 tff(275,plain,
% 0.38/0.63 (((~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~((~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))))) | (~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))))))) <=> ((~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~((~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))))) | (~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))))))))),
% 0.38/0.63 inference(monotonicity,[status(thm)],[274])).
% 0.38/0.63 tff(276,plain,
% 0.38/0.63 (((~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~((~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))))) | (~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))))))) <=> ((~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~((~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))))) | (~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))))))))),
% 0.38/0.63 inference(transitivity,[status(thm)],[275, 273])).
% 0.38/0.63 tff(277,plain,
% 0.38/0.63 (((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~((~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))))) | (~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))))))))) <=> ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~((~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))))) | (~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))))))))))),
% 0.48/0.64 inference(monotonicity,[status(thm)],[276])).
% 0.48/0.64 tff(278,plain,
% 0.48/0.64 (((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~((~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))))) | (~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))))))))) <=> ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~((~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))))) | (~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))))))))),
% 0.48/0.64 inference(transitivity,[status(thm)],[277, 272])).
% 0.48/0.64 tff(279,plain,
% 0.48/0.64 ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~((~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))))) | (~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))))))))),
% 0.48/0.64 inference(quant_inst,[status(thm)],[])).
% 0.48/0.64 tff(280,plain,
% 0.48/0.64 ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~((~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))))) | (~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))))))))),
% 0.48/0.64 inference(modus_ponens,[status(thm)],[279, 278])).
% 0.48/0.64 tff(281,plain,
% 0.48/0.64 (~((~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))))) | (~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))))))),
% 0.48/0.64 inference(unit_resolution,[status(thm)],[280, 55, 271])).
% 0.48/0.64 tff(282,plain,
% 0.48/0.64 (((~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))))) | (~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))))))) | ((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))))),
% 0.48/0.64 inference(tautology,[status(thm)],[])).
% 0.48/0.64 tff(283,plain,
% 0.48/0.64 ((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))))),
% 0.48/0.64 inference(unit_resolution,[status(thm)],[282, 281])).
% 0.48/0.64 tff(284,plain,
% 0.48/0.64 (((~![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!42, F!43, A!40, B!39, A!40), X, X))) | ((~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))) <=> ((~![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!42, F!43, A!40, B!39, A!40), X, X))) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))),
% 0.48/0.65 inference(rewrite,[status(thm)],[])).
% 0.48/0.65 tff(285,plain,
% 0.48/0.65 ((~![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!42, F!43, A!40, B!39, A!40), X, X))) | ((~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))),
% 0.48/0.65 inference(quant_inst,[status(thm)],[])).
% 0.48/0.65 tff(286,plain,
% 0.48/0.65 ((~![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!42, F!43, A!40, B!39, A!40), X, X))) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))),
% 0.48/0.65 inference(modus_ponens,[status(thm)],[285, 284])).
% 0.48/0.65 tff(287,plain,
% 0.48/0.65 (apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))),
% 0.48/0.65 inference(unit_resolution,[status(thm)],[286, 271, 92])).
% 0.48/0.65 tff(288,plain,
% 0.48/0.65 ((~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))))) | (~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))))),
% 0.48/0.65 inference(tautology,[status(thm)],[])).
% 0.48/0.65 tff(289,plain,
% 0.48/0.65 ((~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))))),
% 0.48/0.65 inference(unit_resolution,[status(thm)],[288, 287])).
% 0.48/0.65 tff(290,plain,
% 0.48/0.65 (~((~member(tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))),
% 0.48/0.65 inference(unit_resolution,[status(thm)],[289, 283])).
% 0.48/0.65 tff(291,plain,
% 0.48/0.65 (((~member(tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))) | apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))),
% 0.48/0.65 inference(tautology,[status(thm)],[])).
% 0.48/0.65 tff(292,plain,
% 0.48/0.65 (apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))),
% 0.48/0.65 inference(unit_resolution,[status(thm)],[291, 290])).
% 0.48/0.65 tff(293,plain,
% 0.48/0.65 (((~member(tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))) | member(tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)),
% 0.48/0.65 inference(tautology,[status(thm)],[])).
% 0.48/0.65 tff(294,plain,
% 0.48/0.65 (member(tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)),
% 0.48/0.65 inference(unit_resolution,[status(thm)],[293, 290])).
% 0.48/0.65 tff(295,plain,
% 0.48/0.65 (^[F: $i, A: $i, B: $i, X: $i, Y: $i] : refl(((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A))) <=> ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A))))),
% 0.48/0.65 inference(bind,[status(th)],[])).
% 0.48/0.65 tff(296,plain,
% 0.48/0.65 (![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A))) <=> ![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))),
% 0.48/0.65 inference(quant_intro,[status(thm)],[295])).
% 0.48/0.65 tff(297,plain,
% 0.48/0.65 (^[F: $i, A: $i, B: $i, X: $i, Y: $i] : trans(monotonicity(trans(monotonicity(rewrite((member(X, A) & member(Y, B)) <=> (~((~member(Y, B)) | (~member(X, A))))), ((~(member(X, A) & member(Y, B))) <=> (~(~((~member(Y, B)) | (~member(X, A))))))), rewrite((~(~((~member(Y, B)) | (~member(X, A))))) <=> ((~member(Y, B)) | (~member(X, A)))), ((~(member(X, A) & member(Y, B))) <=> ((~member(Y, B)) | (~member(X, A))))), (((~(member(X, A) & member(Y, B))) | (apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X))) <=> (((~member(Y, B)) | (~member(X, A))) | (apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X))))), rewrite((((~member(Y, B)) | (~member(X, A))) | (apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X))) <=> ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))), (((~(member(X, A) & member(Y, B))) | (apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X))) <=> ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))))),
% 0.48/0.65 inference(bind,[status(th)],[])).
% 0.48/0.65 tff(298,plain,
% 0.48/0.65 (![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((~(member(X, A) & member(Y, B))) | (apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X))) <=> ![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))),
% 0.48/0.65 inference(quant_intro,[status(thm)],[297])).
% 0.48/0.65 tff(299,plain,
% 0.48/0.65 (![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((~(member(X, A) & member(Y, B))) | (apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X))) <=> ![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((~(member(X, A) & member(Y, B))) | (apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)))),
% 0.48/0.65 inference(rewrite,[status(thm)],[])).
% 0.48/0.65 tff(300,plain,
% 0.48/0.65 (^[F: $i, A: $i, B: $i, X: $i, Y: $i] : rewrite(((member(X, A) & member(Y, B)) => (apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X))) <=> ((~(member(X, A) & member(Y, B))) | (apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X))))),
% 0.48/0.65 inference(bind,[status(th)],[])).
% 0.48/0.65 tff(301,plain,
% 0.48/0.65 (![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((member(X, A) & member(Y, B)) => (apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X))) <=> ![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((~(member(X, A) & member(Y, B))) | (apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)))),
% 0.48/0.65 inference(quant_intro,[status(thm)],[300])).
% 0.48/0.65 tff(302,axiom,(![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((member(X, A) & member(Y, B)) => (apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+1.ax','inverse_function')).
% 0.48/0.65 tff(303,plain,
% 0.48/0.65 (![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((~(member(X, A) & member(Y, B))) | (apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)))),
% 0.48/0.65 inference(modus_ponens,[status(thm)],[302, 301])).
% 0.48/0.65 tff(304,plain,
% 0.48/0.65 (![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((~(member(X, A) & member(Y, B))) | (apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)))),
% 0.48/0.65 inference(modus_ponens,[status(thm)],[303, 299])).
% 0.48/0.65 tff(305,plain,(
% 0.48/0.65 ![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((~(member(X, A) & member(Y, B))) | (apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)))),
% 0.48/0.65 inference(skolemize,[status(sab)],[304])).
% 0.48/0.65 tff(306,plain,
% 0.48/0.65 (![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))),
% 0.48/0.65 inference(modus_ponens,[status(thm)],[305, 298])).
% 0.48/0.65 tff(307,plain,
% 0.48/0.65 (![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))),
% 0.48/0.65 inference(modus_ponens,[status(thm)],[306, 296])).
% 0.48/0.65 tff(308,plain,
% 0.48/0.65 (((~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))) | ((~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) <=> apply(inverse_function(F!43, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))) <=> ((~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) <=> apply(inverse_function(F!43, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))),
% 0.48/0.65 inference(rewrite,[status(thm)],[])).
% 0.48/0.65 tff(309,plain,
% 0.48/0.65 (((apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) <=> apply(inverse_function(F!43, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40))) <=> ((~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) <=> apply(inverse_function(F!43, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))),
% 0.48/0.65 inference(rewrite,[status(thm)],[])).
% 0.48/0.65 tff(310,plain,
% 0.48/0.65 (((~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))) | ((apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) <=> apply(inverse_function(F!43, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)))) <=> ((~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))) | ((~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) <=> apply(inverse_function(F!43, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))))),
% 0.48/0.66 inference(monotonicity,[status(thm)],[309])).
% 0.48/0.66 tff(311,plain,
% 0.48/0.66 (((~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))) | ((apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) <=> apply(inverse_function(F!43, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)))) <=> ((~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) <=> apply(inverse_function(F!43, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))),
% 0.48/0.66 inference(transitivity,[status(thm)],[310, 308])).
% 0.48/0.66 tff(312,plain,
% 0.48/0.66 ((~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))) | ((apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) <=> apply(inverse_function(F!43, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)))),
% 0.48/0.66 inference(quant_inst,[status(thm)],[])).
% 0.48/0.66 tff(313,plain,
% 0.48/0.66 ((~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) <=> apply(inverse_function(F!43, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))),
% 0.48/0.66 inference(modus_ponens,[status(thm)],[312, 311])).
% 0.48/0.66 tff(314,plain,
% 0.48/0.66 (apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) <=> apply(inverse_function(F!43, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))),
% 0.48/0.66 inference(unit_resolution,[status(thm)],[313, 307, 271, 199])).
% 0.48/0.66 tff(315,plain,
% 0.48/0.66 (((~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~apply(inverse_function(F!43, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | apply(inverse_function(F!43, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))),
% 0.48/0.66 inference(tautology,[status(thm)],[])).
% 0.48/0.66 tff(316,plain,
% 0.48/0.66 (apply(inverse_function(F!43, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))),
% 0.48/0.66 inference(unit_resolution,[status(thm)],[315, 37])).
% 0.48/0.66 tff(317,plain,
% 0.48/0.66 ((~(apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) <=> apply(inverse_function(F!43, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))) | apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | (~apply(inverse_function(F!43, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))),
% 0.48/0.66 inference(tautology,[status(thm)],[])).
% 0.48/0.66 tff(318,plain,
% 0.48/0.66 ((~(apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) <=> apply(inverse_function(F!43, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))) | apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))),
% 0.48/0.66 inference(unit_resolution,[status(thm)],[317, 316])).
% 0.48/0.66 tff(319,plain,
% 0.48/0.66 (apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))),
% 0.48/0.66 inference(unit_resolution,[status(thm)],[318, 314])).
% 0.48/0.66 tff(320,plain,
% 0.48/0.66 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))) | ((~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~member(tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42) = tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~member(tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42) = tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))),
% 0.48/0.66 inference(rewrite,[status(thm)],[])).
% 0.48/0.66 tff(321,plain,
% 0.48/0.66 (((tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42) = tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | (~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39))) <=> ((~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~member(tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42) = tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))),
% 0.48/0.66 inference(rewrite,[status(thm)],[])).
% 0.48/0.66 tff(322,plain,
% 0.48/0.66 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))) | ((tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42) = tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | (~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))) | ((~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~member(tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42) = tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))),
% 0.48/0.67 inference(monotonicity,[status(thm)],[321])).
% 0.48/0.67 tff(323,plain,
% 0.48/0.67 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))) | ((tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42) = tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | (~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~member(tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42) = tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))),
% 0.48/0.67 inference(transitivity,[status(thm)],[322, 320])).
% 0.48/0.67 tff(324,plain,
% 0.48/0.67 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))) | ((tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42) = tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) | (~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)))),
% 0.48/0.67 inference(quant_inst,[status(thm)],[])).
% 0.48/0.67 tff(325,plain,
% 0.48/0.67 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~member(tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42) = tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))),
% 0.48/0.67 inference(modus_ponens,[status(thm)],[324, 323])).
% 0.48/0.67 tff(326,plain,
% 0.48/0.67 (tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42) = tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))),
% 0.48/0.67 inference(unit_resolution,[status(thm)],[325, 150, 271, 199, 319, 294, 292])).
% 0.48/0.67 tff(327,plain,
% 0.48/0.67 (tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42)),
% 0.48/0.67 inference(symmetry,[status(thm)],[326])).
% 0.48/0.67 tff(328,plain,
% 0.48/0.67 (apply(G!42, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) <=> apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))),
% 0.48/0.67 inference(monotonicity,[status(thm)],[327])).
% 0.48/0.67 tff(329,plain,
% 0.48/0.67 (apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))) <=> apply(G!42, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))),
% 0.48/0.67 inference(symmetry,[status(thm)],[328])).
% 0.48/0.67 tff(330,plain,
% 0.48/0.67 (((~member(tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))) | apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))),
% 0.48/0.67 inference(tautology,[status(thm)],[])).
% 0.48/0.67 tff(331,plain,
% 0.48/0.67 (apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39, F!43, G!42), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))),
% 0.48/0.67 inference(unit_resolution,[status(thm)],[330, 290])).
% 0.48/0.67 tff(332,plain,
% 0.48/0.67 (apply(G!42, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))),
% 0.48/0.67 inference(modus_ponens,[status(thm)],[331, 329])).
% 0.48/0.67 tff(333,plain,
% 0.48/0.67 (((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!42), A!40)) | (~apply(G!42, X, tptp_fun_Y_3(X, A!40, G!42))))))) | ((~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (~((~member(tptp_fun_Y_3(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, G!42), A!40)) | (~apply(G!42, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_3(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, G!42))))))) <=> ((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!42), A!40)) | (~apply(G!42, X, tptp_fun_Y_3(X, A!40, G!42))))))) | (~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (~((~member(tptp_fun_Y_3(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, G!42), A!40)) | (~apply(G!42, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_3(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, G!42))))))),
% 0.48/0.67 inference(rewrite,[status(thm)],[])).
% 0.48/0.67 tff(334,plain,
% 0.48/0.67 ((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!42), A!40)) | (~apply(G!42, X, tptp_fun_Y_3(X, A!40, G!42))))))) | ((~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (~((~member(tptp_fun_Y_3(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, G!42), A!40)) | (~apply(G!42, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_3(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, G!42))))))),
% 0.48/0.67 inference(quant_inst,[status(thm)],[])).
% 0.48/0.67 tff(335,plain,
% 0.48/0.67 ((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!42), A!40)) | (~apply(G!42, X, tptp_fun_Y_3(X, A!40, G!42))))))) | (~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (~((~member(tptp_fun_Y_3(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, G!42), A!40)) | (~apply(G!42, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_3(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, G!42)))))),
% 0.48/0.67 inference(modus_ponens,[status(thm)],[334, 333])).
% 0.48/0.67 tff(336,plain,
% 0.48/0.67 (~((~member(tptp_fun_Y_3(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, G!42), A!40)) | (~apply(G!42, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_3(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, G!42))))),
% 0.48/0.67 inference(unit_resolution,[status(thm)],[335, 178, 199])).
% 0.48/0.67 tff(337,plain,
% 0.48/0.67 (((~member(tptp_fun_Y_3(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, G!42), A!40)) | (~apply(G!42, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_3(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, G!42)))) | apply(G!42, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_3(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, G!42))),
% 0.48/0.67 inference(tautology,[status(thm)],[])).
% 0.48/0.67 tff(338,plain,
% 0.48/0.67 (apply(G!42, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_3(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, G!42))),
% 0.48/0.67 inference(unit_resolution,[status(thm)],[337, 336])).
% 0.48/0.67 tff(339,plain,
% 0.48/0.67 (((~member(tptp_fun_Y_3(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, G!42), A!40)) | (~apply(G!42, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_3(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, G!42)))) | member(tptp_fun_Y_3(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, G!42), A!40)),
% 0.48/0.67 inference(tautology,[status(thm)],[])).
% 0.48/0.67 tff(340,plain,
% 0.48/0.67 (member(tptp_fun_Y_3(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, G!42), A!40)),
% 0.48/0.67 inference(unit_resolution,[status(thm)],[339, 336])).
% 0.48/0.67 tff(341,plain,
% 0.48/0.67 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))) | ((~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (~member(tptp_fun_Y_3(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, G!42), A!40)) | (~apply(G!42, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_3(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, G!42))) | (tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y_3(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, G!42)) | (~apply(G!42, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (~member(tptp_fun_Y_3(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, G!42), A!40)) | (~apply(G!42, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_3(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, G!42))) | (tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y_3(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, G!42)) | (~apply(G!42, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))),
% 0.48/0.67 inference(rewrite,[status(thm)],[])).
% 0.48/0.67 tff(342,plain,
% 0.48/0.67 (((tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y_3(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, G!42)) | (~member(tptp_fun_Y_3(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, G!42), A!40)) | (~apply(G!42, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~apply(G!42, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_3(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, G!42))) | (~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40))) <=> ((~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (~member(tptp_fun_Y_3(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, G!42), A!40)) | (~apply(G!42, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_3(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, G!42))) | (tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y_3(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, G!42)) | (~apply(G!42, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))),
% 0.48/0.68 inference(rewrite,[status(thm)],[])).
% 0.48/0.68 tff(343,plain,
% 0.48/0.68 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))) | ((tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y_3(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, G!42)) | (~member(tptp_fun_Y_3(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, G!42), A!40)) | (~apply(G!42, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~apply(G!42, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_3(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, G!42))) | (~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))) | ((~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (~member(tptp_fun_Y_3(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, G!42), A!40)) | (~apply(G!42, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_3(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, G!42))) | (tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y_3(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, G!42)) | (~apply(G!42, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))))),
% 0.48/0.68 inference(monotonicity,[status(thm)],[342])).
% 0.48/0.68 tff(344,plain,
% 0.48/0.68 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))) | ((tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y_3(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, G!42)) | (~member(tptp_fun_Y_3(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, G!42), A!40)) | (~apply(G!42, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~apply(G!42, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_3(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, G!42))) | (~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (~member(tptp_fun_Y_3(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, G!42), A!40)) | (~apply(G!42, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_3(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, G!42))) | (tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y_3(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, G!42)) | (~apply(G!42, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))))),
% 0.48/0.68 inference(transitivity,[status(thm)],[343, 341])).
% 0.48/0.68 tff(345,plain,
% 0.48/0.68 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))) | ((tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y_3(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, G!42)) | (~member(tptp_fun_Y_3(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, G!42), A!40)) | (~apply(G!42, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~apply(G!42, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_3(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, G!42))) | (~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)))),
% 0.48/0.68 inference(quant_inst,[status(thm)],[])).
% 0.48/0.68 tff(346,plain,
% 0.48/0.68 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (~member(tptp_fun_Y_3(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, G!42), A!40)) | (~apply(G!42, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y_3(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, G!42))) | (tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y_3(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, G!42)) | (~apply(G!42, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))),
% 0.48/0.68 inference(modus_ponens,[status(thm)],[345, 344])).
% 0.48/0.68 tff(347,plain,
% 0.48/0.68 ((tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y_3(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, G!42)) | (~apply(G!42, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))),
% 0.48/0.68 inference(unit_resolution,[status(thm)],[346, 188, 271, 199, 340, 338])).
% 0.48/0.68 tff(348,plain,
% 0.48/0.68 (tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y_3(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40, G!42)),
% 0.48/0.68 inference(unit_resolution,[status(thm)],[347, 332])).
% 0.48/0.68 tff(349,plain,
% 0.48/0.68 (tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))),
% 0.48/0.68 inference(transitivity,[status(thm)],[348, 269, 197])).
% 0.48/0.68 tff(350,plain,
% 0.48/0.68 (((~apply(H!41, tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~apply(inverse_function(F!43, A!40, B!39), tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~member(tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), A!40)) | (~member(tptp_fun_X_14(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)), B!39)) | (tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))) | (~(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39))))),
% 0.48/0.68 inference(tautology,[status(thm)],[])).
% 0.48/0.68 tff(351,plain,
% 0.48/0.68 (~(tptp_fun_Y1_13(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)) = tptp_fun_Y2_12(A!40, B!39, H!41, inverse_function(F!43, A!40, B!39)))),
% 0.48/0.68 inference(unit_resolution,[status(thm)],[350, 37])).
% 0.48/0.68 tff(352,plain,
% 0.48/0.68 ($false),
% 0.48/0.68 inference(unit_resolution,[status(thm)],[351, 349])).
% 0.48/0.68 % SZS output end Proof
% 0.48/0.68 % E exiting
%------------------------------------------------------------------------------