%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET719+4 : TPTP v9.0.0. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:26:13 AM UTC 2025
% Result : Theorem 0.12s 0.40s
% Output : Proof 0.64s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET719+4 : TPTP v9.0.0. Bugfixed v2.2.1.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n003.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 05:39:09 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.12/0.40 % SZS status Theorem
% 0.12/0.40 % SZS output start Proof
% 0.12/0.40 tff(tptp_fun_Y2_12_type, type, (
% 0.12/0.40 tptp_fun_Y2_12: ( $i * $i * $i * $i ) > $i)).
% 0.12/0.40 tff(inverse_function_type, type, (
% 0.12/0.40 inverse_function: ( $i * $i * $i ) > $i)).
% 0.12/0.40 tff(tptp_fun_C_39_type, type, (
% 0.12/0.40 tptp_fun_C_39: $i)).
% 0.12/0.40 tff(tptp_fun_A_41_type, type, (
% 0.12/0.40 tptp_fun_A_41: $i)).
% 0.12/0.40 tff(compose_function_type, type, (
% 0.12/0.40 compose_function: ( $i * $i * $i * $i * $i ) > $i)).
% 0.12/0.40 tff(tptp_fun_B_40_type, type, (
% 0.12/0.40 tptp_fun_B_40: $i)).
% 0.12/0.40 tff(tptp_fun_F_43_type, type, (
% 0.12/0.40 tptp_fun_F_43: $i)).
% 0.12/0.40 tff(tptp_fun_G_42_type, type, (
% 0.12/0.40 tptp_fun_G_42: $i)).
% 0.12/0.40 tff(tptp_fun_Y1_13_type, type, (
% 0.12/0.40 tptp_fun_Y1_13: ( $i * $i * $i * $i ) > $i)).
% 0.12/0.40 tff(tptp_fun_E_19_type, type, (
% 0.12/0.40 tptp_fun_E_19: ( $i * $i * $i ) > $i)).
% 0.12/0.40 tff(tptp_fun_Y_8_type, type, (
% 0.12/0.40 tptp_fun_Y_8: ( $i * $i * $i * $i * $i ) > $i)).
% 0.12/0.40 tff(tptp_fun_X_14_type, type, (
% 0.12/0.40 tptp_fun_X_14: ( $i * $i * $i * $i ) > $i)).
% 0.12/0.40 tff(apply_type, type, (
% 0.12/0.40 apply: ( $i * $i * $i ) > $o)).
% 0.12/0.40 tff(member_type, type, (
% 0.12/0.40 member: ( $i * $i ) > $o)).
% 0.12/0.40 tff(equal_maps_type, type, (
% 0.12/0.40 equal_maps: ( $i * $i * $i * $i ) > $o)).
% 0.12/0.40 tff(one_to_one_type, type, (
% 0.12/0.40 one_to_one: ( $i * $i * $i ) > $o)).
% 0.12/0.40 tff(maps_type, type, (
% 0.12/0.40 maps: ( $i * $i * $i ) > $o)).
% 0.12/0.40 tff(surjective_type, type, (
% 0.12/0.40 surjective: ( $i * $i * $i ) > $o)).
% 0.12/0.40 tff(tptp_fun_Y_20_type, type, (
% 0.12/0.40 tptp_fun_Y_20: ( $i * $i * $i ) > $i)).
% 0.12/0.40 tff(injective_type, type, (
% 0.12/0.40 injective: ( $i * $i * $i ) > $o)).
% 0.12/0.40 tff(tptp_fun_X2_17_type, type, (
% 0.12/0.40 tptp_fun_X2_17: ( $i * $i * $i ) > $i)).
% 0.12/0.40 tff(tptp_fun_X1_18_type, type, (
% 0.12/0.40 tptp_fun_X1_18: ( $i * $i * $i ) > $i)).
% 0.12/0.40 tff(tptp_fun_Y_16_type, type, (
% 0.12/0.40 tptp_fun_Y_16: ( $i * $i * $i ) > $i)).
% 0.12/0.40 tff(tptp_fun_Y_3_type, type, (
% 0.12/0.40 tptp_fun_Y_3: ( $i * $i * $i ) > $i)).
% 0.12/0.40 tff(tptp_fun_Y2_5_type, type, (
% 0.12/0.40 tptp_fun_Y2_5: ( $i * $i * $i ) > $i)).
% 0.12/0.40 tff(tptp_fun_Y1_6_type, type, (
% 0.12/0.40 tptp_fun_Y1_6: ( $i * $i * $i ) > $i)).
% 0.12/0.40 tff(tptp_fun_X_7_type, type, (
% 0.12/0.40 tptp_fun_X_7: ( $i * $i * $i ) > $i)).
% 0.12/0.40 tff(tptp_fun_X_4_type, type, (
% 0.12/0.40 tptp_fun_X_4: ( $i * $i * $i ) > $i)).
% 0.12/0.40 tff(1,plain,
% 0.12/0.40 (^[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))))))))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(2,plain,
% 0.12/0.40 (![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)))))))))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[1])).
% 0.12/0.40 tff(3,plain,
% 0.12/0.40 (^[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))))))))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(4,plain,
% 0.12/0.40 (![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)))))))))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[3])).
% 0.12/0.40 tff(5,plain,
% 0.12/0.40 (![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)))))))))),
% 0.12/0.40 inference(transitivity,[status(thm)],[4, 2])).
% 0.12/0.40 tff(6,plain,
% 0.12/0.40 (^[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)))))))))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(7,plain,
% 0.12/0.40 (![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)))))))))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[6])).
% 0.12/0.40 tff(8,plain,
% 0.12/0.40 (![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)))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(9,plain,
% 0.12/0.40 (^[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))))))),
% 0.12/0.41 inference(bind,[status(th)],[])).
% 0.12/0.41 tff(10,plain,
% 0.12/0.41 (![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)))))),
% 0.12/0.41 inference(quant_intro,[status(thm)],[9])).
% 0.12/0.41 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/sandbox2/benchmark/Axioms/SET006+1.ax','equal_maps')).
% 0.12/0.41 tff(12,plain,
% 0.12/0.41 (![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)))))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.12/0.41 tff(13,plain,
% 0.12/0.41 (![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)))))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[12, 8])).
% 0.12/0.41 tff(14,plain,(
% 0.12/0.41 ![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))))))))),
% 0.12/0.41 inference(skolemize,[status(sab)],[13])).
% 0.12/0.41 tff(15,plain,
% 0.12/0.41 (![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)))))))))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[14, 7])).
% 0.12/0.41 tff(16,plain,
% 0.12/0.41 (![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)))))))))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[15, 5])).
% 0.12/0.41 tff(17,plain,
% 0.12/0.41 (((~![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(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39), compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), C!39, A!41)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!41)) | (~apply(compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), X, Y2)) | (~member(X, C!39)) | (~member(Y1, A!41)) | (~apply(inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39), X, Y1))))) | (~(equal_maps(inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39), compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), C!39, A!41) | (~((~apply(compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_Y2_12(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)))) | (~apply(inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39), tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)))) | (~member(tptp_fun_Y2_12(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), A!41)) | (~member(tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), A!41)) | (~member(tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), 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% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(18,plain,
% 0.20/0.42 ((~((~((~equal_maps(inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39), compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), C!39, A!41)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), X, Y2)) | (~member(X, C!39)) | (~member(Y1, A!41)) | (~member(Y2, A!41)) | (~apply(inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39), X, Y1))))) | (~(equal_maps(inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39), compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), C!39, A!41) | (~((tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)) = 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% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(19,plain,
% 0.20/0.43 (((~![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(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39), compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), C!39, A!41)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), X, Y2)) | (~member(X, C!39)) | 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% 0.20/0.43 inference(monotonicity,[status(thm)],[18])).
% 0.20/0.43 tff(20,plain,
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% 0.20/0.44 inference(transitivity,[status(thm)],[19, 17])).
% 0.20/0.44 tff(21,plain,
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% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(22,plain,
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% 0.20/0.45 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.20/0.45 tff(23,plain,
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% 0.20/0.45 inference(unit_resolution,[status(thm)],[22, 16])).
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% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(25,plain,
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% 0.20/0.46 inference(unit_resolution,[status(thm)],[24, 23])).
% 0.20/0.46 tff(26,plain,
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% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(27,plain,
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% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(28,axiom,(~![F: $i, G: $i, A: $i, B: $i, C: $i] : ((((maps(F, A, B) & maps(G, B, C)) & one_to_one(F, A, B)) & one_to_one(G, B, C)) => equal_maps(inverse_function(compose_function(G, F, A, B, C), A, C), compose_function(inverse_function(F, A, B), inverse_function(G, B, C), C, B, A), C, A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thII10')).
% 0.20/0.46 tff(29,plain,
% 0.20/0.46 (~![F: $i, G: $i, A: $i, B: $i, C: $i] : ((~(maps(F, A, B) & maps(G, B, C) & one_to_one(F, A, B) & one_to_one(G, B, C))) | equal_maps(inverse_function(compose_function(G, F, A, B, C), A, C), compose_function(inverse_function(F, A, B), inverse_function(G, B, C), C, B, A), C, A))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.20/0.46 tff(30,plain,
% 0.20/0.46 (~![F: $i, G: $i, A: $i, B: $i, C: $i] : ((~(maps(F, A, B) & maps(G, B, C) & one_to_one(F, A, B) & one_to_one(G, B, C))) | equal_maps(inverse_function(compose_function(G, F, A, B, C), A, C), compose_function(inverse_function(F, A, B), inverse_function(G, B, C), C, B, A), C, A))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[29, 26])).
% 0.20/0.46 tff(31,plain,
% 0.20/0.46 (~![F: $i, G: $i, A: $i, B: $i, C: $i] : ((~(maps(F, A, B) & maps(G, B, C) & one_to_one(F, A, B) & one_to_one(G, B, C))) | equal_maps(inverse_function(compose_function(G, F, A, B, C), A, C), compose_function(inverse_function(F, A, B), inverse_function(G, B, C), C, B, A), C, A))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[30, 26])).
% 0.20/0.46 tff(32,plain,
% 0.20/0.46 (~![F: $i, G: $i, A: $i, B: $i, C: $i] : ((~(maps(F, A, B) & maps(G, B, C) & one_to_one(F, A, B) & one_to_one(G, B, C))) | equal_maps(inverse_function(compose_function(G, F, A, B, C), A, C), compose_function(inverse_function(F, A, B), inverse_function(G, B, C), C, B, A), C, A))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[31, 26])).
% 0.20/0.46 tff(33,plain,(
% 0.20/0.46 ~((~(maps(F!43, A!41, B!40) & maps(G!42, B!40, C!39) & one_to_one(F!43, A!41, B!40) & one_to_one(G!42, B!40, C!39))) | equal_maps(inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39), compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), C!39, A!41))),
% 0.20/0.46 inference(skolemize,[status(sab)],[32])).
% 0.20/0.46 tff(34,plain,
% 0.20/0.46 (~equal_maps(inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39), compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), C!39, A!41)),
% 0.20/0.46 inference(or_elim,[status(thm)],[33])).
% 0.20/0.46 tff(35,plain,
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% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(36,plain,
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% 0.20/0.48 inference(unit_resolution,[status(thm)],[35, 34])).
% 0.20/0.48 tff(37,plain,
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% 0.20/0.48 inference(unit_resolution,[status(thm)],[36, 25])).
% 0.20/0.48 tff(38,plain,
% 0.20/0.48 (((~apply(compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_Y2_12(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)))) | (~apply(inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39), tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)))) | (~member(tptp_fun_Y2_12(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), A!41)) | (~member(tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), A!41)) | (~member(tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), C!39)) | (tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)) = tptp_fun_Y2_12(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)))) | member(tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), C!39)),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(39,plain,
% 0.20/0.48 (member(tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), C!39)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[38, 37])).
% 0.20/0.48 tff(40,plain,
% 0.20/0.48 (((~apply(compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_Y2_12(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)))) | (~apply(inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39), tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)))) | (~member(tptp_fun_Y2_12(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), A!41)) | (~member(tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), A!41)) | (~member(tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), C!39)) | (tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)) = tptp_fun_Y2_12(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)))) | member(tptp_fun_Y2_12(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), A!41)),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(41,plain,
% 0.20/0.48 (member(tptp_fun_Y2_12(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), A!41)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[40, 37])).
% 0.20/0.48 tff(42,plain,
% 0.20/0.48 (^[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)))))))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(43,plain,
% 0.20/0.48 (![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)))))))) <=> ![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))))))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[42])).
% 0.20/0.48 tff(44,plain,
% 0.20/0.48 (^[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)))))))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(45,plain,
% 0.20/0.48 (![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)))))))) <=> ![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))))))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[44])).
% 0.20/0.48 tff(46,plain,
% 0.20/0.48 (![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)))))))) <=> ![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))))))))),
% 0.20/0.48 inference(transitivity,[status(thm)],[45, 43])).
% 0.20/0.48 tff(47,plain,
% 0.20/0.48 (^[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))))))))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(48,plain,
% 0.20/0.48 (![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))))))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[47])).
% 0.20/0.48 tff(49,plain,
% 0.20/0.48 (![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))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(50,plain,
% 0.20/0.48 (^[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))))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(51,plain,
% 0.20/0.48 (![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))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[50])).
% 0.20/0.48 tff(52,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/sandbox2/benchmark/Axioms/SET006+1.ax','compose_function')).
% 0.20/0.48 tff(53,plain,
% 0.20/0.48 (![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))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.20/0.48 tff(54,plain,
% 0.20/0.48 (![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))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[53, 49])).
% 0.20/0.48 tff(55,plain,(
% 0.20/0.48 ![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))))))),
% 0.20/0.48 inference(skolemize,[status(sab)],[54])).
% 0.20/0.48 tff(56,plain,
% 0.20/0.48 (![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))))))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[55, 48])).
% 0.20/0.48 tff(57,plain,
% 0.20/0.48 (![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))))))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[56, 46])).
% 0.20/0.48 tff(58,plain,
% 0.20/0.48 (((~![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!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), A!41)) | (~member(tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), C!39)) | (~((~(apply(compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), 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% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(59,plain,
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% 0.20/0.53 inference(transitivity,[status(thm)],[63, 58])).
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% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
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% 0.20/0.53 inference(modus_ponens,[status(thm)],[65, 64])).
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% 0.20/0.54 inference(unit_resolution,[status(thm)],[66, 57, 41, 39])).
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% 0.20/0.55 inference(unit_resolution,[status(thm)],[72, 71])).
% 0.20/0.55 tff(74,plain,
% 0.20/0.55 (~((~apply(inverse_function(F!43, A!41, B!40), tptp_fun_Y_8(tptp_fun_Y2_12(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, inverse_function(G!42, B!40, C!39), inverse_function(F!43, A!41, B!40)), tptp_fun_Y2_12(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)))) | (~apply(inverse_function(G!42, B!40, C!39), tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_Y_8(tptp_fun_Y2_12(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, inverse_function(G!42, B!40, C!39), inverse_function(F!43, A!41, B!40)))) | (~member(tptp_fun_Y_8(tptp_fun_Y2_12(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, inverse_function(G!42, B!40, C!39), inverse_function(F!43, A!41, B!40)), B!40)))),
% 0.20/0.56 inference(unit_resolution,[status(thm)],[73, 69])).
% 0.20/0.56 tff(75,plain,
% 0.20/0.56 (((~apply(inverse_function(F!43, A!41, B!40), tptp_fun_Y_8(tptp_fun_Y2_12(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, inverse_function(G!42, B!40, C!39), inverse_function(F!43, A!41, B!40)), tptp_fun_Y2_12(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)))) | (~apply(inverse_function(G!42, B!40, C!39), tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_Y_8(tptp_fun_Y2_12(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, inverse_function(G!42, B!40, C!39), inverse_function(F!43, A!41, B!40)))) | (~member(tptp_fun_Y_8(tptp_fun_Y2_12(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, inverse_function(G!42, B!40, C!39), inverse_function(F!43, A!41, B!40)), B!40))) | member(tptp_fun_Y_8(tptp_fun_Y2_12(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, inverse_function(G!42, B!40, C!39), inverse_function(F!43, A!41, B!40)), B!40)),
% 0.20/0.56 inference(tautology,[status(thm)],[])).
% 0.20/0.56 tff(76,plain,
% 0.20/0.56 (member(tptp_fun_Y_8(tptp_fun_Y2_12(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, inverse_function(G!42, B!40, C!39), inverse_function(F!43, A!41, B!40)), B!40)),
% 0.20/0.56 inference(unit_resolution,[status(thm)],[75, 74])).
% 0.20/0.56 tff(77,plain,
% 0.20/0.56 (^[F: $i, A: $i, B: $i] : refl((~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))))))) <=> (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))))))))),
% 0.20/0.56 inference(bind,[status(th)],[])).
% 0.20/0.56 tff(78,plain,
% 0.20/0.56 (![F: $i, A: $i, B: $i] : (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))))))),
% 0.20/0.56 inference(quant_intro,[status(thm)],[77])).
% 0.20/0.56 tff(79,plain,
% 0.20/0.56 (^[F: $i, A: $i, B: $i] : rewrite((~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))))))) <=> (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))))))))),
% 0.20/0.56 inference(bind,[status(th)],[])).
% 0.20/0.56 tff(80,plain,
% 0.20/0.56 (![F: $i, A: $i, B: $i] : (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))))))),
% 0.20/0.56 inference(quant_intro,[status(thm)],[79])).
% 0.20/0.56 tff(81,plain,
% 0.20/0.56 (![F: $i, A: $i, B: $i] : (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))))))),
% 0.20/0.56 inference(transitivity,[status(thm)],[80, 78])).
% 0.20/0.56 tff(82,plain,
% 0.20/0.56 (^[F: $i, A: $i, B: $i] : trans(monotonicity(rewrite(((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (member(tptp_fun_E_19(Y, A, F), A) & apply(F, tptp_fun_E_19(Y, A, F), Y)))) <=> ((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))), trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[E: $i] : trans(monotonicity(rewrite((member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F))) <=> (~((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))), ((~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F)))) <=> (~(~((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))), rewrite((~(~((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))) <=> ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))), ((~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F)))) <=> ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))), (![E: $i] : (~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F)))) <=> ![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))), ((member(tptp_fun_Y_20(B, A, F), B) & ![E: $i] : (~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F))))) <=> (member(tptp_fun_Y_20(B, A, F), B) & ![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))), rewrite((member(tptp_fun_Y_20(B, A, F), B) & ![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))) <=> (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))), ((member(tptp_fun_Y_20(B, A, F), B) & ![E: $i] : (~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F))))) <=> (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))))), ((surjective(F, A, B) | (member(tptp_fun_Y_20(B, A, F), B) & ![E: $i] : (~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F)))))) <=> (surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))))), rewrite((surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))) <=> (surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))))), ((surjective(F, A, B) | (member(tptp_fun_Y_20(B, A, F), B) & ![E: $i] : (~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F)))))) <=> (surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))))), ((((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (member(tptp_fun_E_19(Y, A, F), A) & apply(F, tptp_fun_E_19(Y, A, F), Y)))) & (surjective(F, A, B) | (member(tptp_fun_Y_20(B, A, F), B) & ![E: $i] : (~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F))))))) <=> (((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y)))))) & (surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))))))), rewrite((((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y)))))) & (surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))))) <=> (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))))))), ((((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (member(tptp_fun_E_19(Y, A, F), A) & apply(F, tptp_fun_E_19(Y, A, F), Y)))) & (surjective(F, A, B) | (member(tptp_fun_Y_20(B, A, F), B) & ![E: $i] : (~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F))))))) <=> (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))))))))),
% 0.20/0.56 inference(bind,[status(th)],[])).
% 0.20/0.56 tff(83,plain,
% 0.20/0.56 (![F: $i, A: $i, B: $i] : (((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (member(tptp_fun_E_19(Y, A, F), A) & apply(F, tptp_fun_E_19(Y, A, F), Y)))) & (surjective(F, A, B) | (member(tptp_fun_Y_20(B, A, F), B) & ![E: $i] : (~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))))))),
% 0.20/0.56 inference(quant_intro,[status(thm)],[82])).
% 0.20/0.56 tff(84,plain,
% 0.20/0.56 (![F: $i, A: $i, B: $i] : (surjective(F, A, B) <=> ![Y: $i] : ((~member(Y, B)) | ?[E: $i] : (member(E, A) & apply(F, E, Y)))) <=> ![F: $i, A: $i, B: $i] : (surjective(F, A, B) <=> ![Y: $i] : ((~member(Y, B)) | ?[E: $i] : (member(E, A) & apply(F, E, Y))))),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(85,plain,
% 0.20/0.56 (^[F: $i, A: $i, B: $i] : rewrite((surjective(F, A, B) <=> ![Y: $i] : (member(Y, B) => ?[E: $i] : (member(E, A) & apply(F, E, Y)))) <=> (surjective(F, A, B) <=> ![Y: $i] : ((~member(Y, B)) | ?[E: $i] : (member(E, A) & apply(F, E, Y)))))),
% 0.20/0.56 inference(bind,[status(th)],[])).
% 0.20/0.56 tff(86,plain,
% 0.20/0.56 (![F: $i, A: $i, B: $i] : (surjective(F, A, B) <=> ![Y: $i] : (member(Y, B) => ?[E: $i] : (member(E, A) & apply(F, E, Y)))) <=> ![F: $i, A: $i, B: $i] : (surjective(F, A, B) <=> ![Y: $i] : ((~member(Y, B)) | ?[E: $i] : (member(E, A) & apply(F, E, Y))))),
% 0.20/0.56 inference(quant_intro,[status(thm)],[85])).
% 0.20/0.56 tff(87,axiom,(![F: $i, A: $i, B: $i] : (surjective(F, A, B) <=> ![Y: $i] : (member(Y, B) => ?[E: $i] : (member(E, A) & apply(F, E, Y))))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+1.ax','surjective')).
% 0.20/0.56 tff(88,plain,
% 0.20/0.56 (![F: $i, A: $i, B: $i] : (surjective(F, A, B) <=> ![Y: $i] : ((~member(Y, B)) | ?[E: $i] : (member(E, A) & apply(F, E, Y))))),
% 0.20/0.56 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.20/0.56 tff(89,plain,
% 0.20/0.56 (![F: $i, A: $i, B: $i] : (surjective(F, A, B) <=> ![Y: $i] : ((~member(Y, B)) | ?[E: $i] : (member(E, A) & apply(F, E, Y))))),
% 0.20/0.56 inference(modus_ponens,[status(thm)],[88, 84])).
% 0.20/0.56 tff(90,plain,(
% 0.20/0.56 ![F: $i, A: $i, B: $i] : (((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (member(tptp_fun_E_19(Y, A, F), A) & apply(F, tptp_fun_E_19(Y, A, F), Y)))) & (surjective(F, A, B) | (member(tptp_fun_Y_20(B, A, F), B) & ![E: $i] : (~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F)))))))),
% 0.20/0.56 inference(skolemize,[status(sab)],[89])).
% 0.20/0.56 tff(91,plain,
% 0.20/0.56 (![F: $i, A: $i, B: $i] : (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))))))),
% 0.20/0.56 inference(modus_ponens,[status(thm)],[90, 83])).
% 0.20/0.56 tff(92,plain,
% 0.20/0.56 (![F: $i, A: $i, B: $i] : (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))))))),
% 0.20/0.56 inference(modus_ponens,[status(thm)],[91, 81])).
% 0.20/0.56 tff(93,plain,
% 0.20/0.56 ((~![F: $i, A: $i, B: $i] : (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))))))) | (~((~((~surjective(F!43, A!41, B!40)) | ![Y: $i] : ((~member(Y, B!40)) | (~((~member(tptp_fun_E_19(Y, A!41, F!43), A!41)) | (~apply(F!43, tptp_fun_E_19(Y, A!41, F!43), Y))))))) | (~(surjective(F!43, A!41, B!40) | (~((~member(tptp_fun_Y_20(B!40, A!41, F!43), B!40)) | (~![E: $i] : ((~member(E, A!41)) | (~apply(F!43, E, tptp_fun_Y_20(B!40, A!41, F!43)))))))))))),
% 0.20/0.56 inference(quant_inst,[status(thm)],[])).
% 0.20/0.56 tff(94,plain,
% 0.20/0.56 (~((~((~surjective(F!43, A!41, B!40)) | ![Y: $i] : ((~member(Y, B!40)) | (~((~member(tptp_fun_E_19(Y, A!41, F!43), A!41)) | (~apply(F!43, tptp_fun_E_19(Y, A!41, F!43), Y))))))) | (~(surjective(F!43, A!41, B!40) | (~((~member(tptp_fun_Y_20(B!40, A!41, F!43), B!40)) | (~![E: $i] : ((~member(E, A!41)) | (~apply(F!43, E, tptp_fun_Y_20(B!40, A!41, F!43))))))))))),
% 0.20/0.56 inference(unit_resolution,[status(thm)],[93, 92])).
% 0.20/0.56 tff(95,plain,
% 0.20/0.56 (((~((~surjective(F!43, A!41, B!40)) | ![Y: $i] : ((~member(Y, B!40)) | (~((~member(tptp_fun_E_19(Y, A!41, F!43), A!41)) | (~apply(F!43, tptp_fun_E_19(Y, A!41, F!43), Y))))))) | (~(surjective(F!43, A!41, B!40) | (~((~member(tptp_fun_Y_20(B!40, A!41, F!43), B!40)) | (~![E: $i] : ((~member(E, A!41)) | (~apply(F!43, E, tptp_fun_Y_20(B!40, A!41, F!43)))))))))) | ((~surjective(F!43, A!41, B!40)) | ![Y: $i] : ((~member(Y, B!40)) | (~((~member(tptp_fun_E_19(Y, A!41, F!43), A!41)) | (~apply(F!43, tptp_fun_E_19(Y, A!41, F!43), Y))))))),
% 0.20/0.56 inference(tautology,[status(thm)],[])).
% 0.20/0.56 tff(96,plain,
% 0.20/0.56 ((~surjective(F!43, A!41, B!40)) | ![Y: $i] : ((~member(Y, B!40)) | (~((~member(tptp_fun_E_19(Y, A!41, F!43), A!41)) | (~apply(F!43, tptp_fun_E_19(Y, A!41, F!43), Y)))))),
% 0.20/0.56 inference(unit_resolution,[status(thm)],[95, 94])).
% 0.20/0.56 tff(97,plain,
% 0.20/0.56 (^[F: $i, A: $i, B: $i] : refl((~(((~injective(F, A, B)) | (~surjective(F, A, B))) <=> one_to_one(F, A, B))) <=> (~(((~injective(F, A, B)) | (~surjective(F, A, B))) <=> one_to_one(F, A, B))))),
% 0.20/0.56 inference(bind,[status(th)],[])).
% 0.20/0.56 tff(98,plain,
% 0.20/0.56 (![F: $i, A: $i, B: $i] : (~(((~injective(F, A, B)) | (~surjective(F, A, B))) <=> one_to_one(F, A, B))) <=> ![F: $i, A: $i, B: $i] : (~(((~injective(F, A, B)) | (~surjective(F, A, B))) <=> one_to_one(F, A, B)))),
% 0.20/0.56 inference(quant_intro,[status(thm)],[97])).
% 0.20/0.56 tff(99,plain,
% 0.20/0.56 (^[F: $i, A: $i, B: $i] : trans(trans(monotonicity(rewrite((injective(F, A, B) & surjective(F, A, B)) <=> (~((~injective(F, A, B)) | (~surjective(F, A, B))))), ((one_to_one(F, A, B) <=> (injective(F, A, B) & surjective(F, A, B))) <=> (one_to_one(F, A, B) <=> (~((~injective(F, A, B)) | (~surjective(F, A, B))))))), rewrite((one_to_one(F, A, B) <=> (~((~injective(F, A, B)) | (~surjective(F, A, B))))) <=> (~(((~injective(F, A, B)) | (~surjective(F, A, B))) <=> one_to_one(F, A, B)))), ((one_to_one(F, A, B) <=> (injective(F, A, B) & surjective(F, A, B))) <=> (~(((~injective(F, A, B)) | (~surjective(F, A, B))) <=> one_to_one(F, A, B))))), rewrite((~(((~injective(F, A, B)) | (~surjective(F, A, B))) <=> one_to_one(F, A, B))) <=> (~(((~injective(F, A, B)) | (~surjective(F, A, B))) <=> one_to_one(F, A, B)))), ((one_to_one(F, A, B) <=> (injective(F, A, B) & surjective(F, A, B))) <=> (~(((~injective(F, A, B)) | (~surjective(F, A, B))) <=> one_to_one(F, A, B)))))),
% 0.20/0.56 inference(bind,[status(th)],[])).
% 0.20/0.56 tff(100,plain,
% 0.20/0.56 (![F: $i, A: $i, B: $i] : (one_to_one(F, A, B) <=> (injective(F, A, B) & surjective(F, A, B))) <=> ![F: $i, A: $i, B: $i] : (~(((~injective(F, A, B)) | (~surjective(F, A, B))) <=> one_to_one(F, A, B)))),
% 0.20/0.56 inference(quant_intro,[status(thm)],[99])).
% 0.20/0.56 tff(101,plain,
% 0.20/0.56 (![F: $i, A: $i, B: $i] : (one_to_one(F, A, B) <=> (injective(F, A, B) & surjective(F, A, B))) <=> ![F: $i, A: $i, B: $i] : (one_to_one(F, A, B) <=> (injective(F, A, B) & surjective(F, A, B)))),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(102,axiom,(![F: $i, A: $i, B: $i] : (one_to_one(F, A, B) <=> (injective(F, A, B) & surjective(F, A, B)))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+1.ax','one_to_one')).
% 0.20/0.56 tff(103,plain,
% 0.20/0.56 (![F: $i, A: $i, B: $i] : (one_to_one(F, A, B) <=> (injective(F, A, B) & surjective(F, A, B)))),
% 0.20/0.56 inference(modus_ponens,[status(thm)],[102, 101])).
% 0.20/0.56 tff(104,plain,(
% 0.20/0.56 ![F: $i, A: $i, B: $i] : (one_to_one(F, A, B) <=> (injective(F, A, B) & surjective(F, A, B)))),
% 0.20/0.56 inference(skolemize,[status(sab)],[103])).
% 0.20/0.56 tff(105,plain,
% 0.20/0.56 (![F: $i, A: $i, B: $i] : (~(((~injective(F, A, B)) | (~surjective(F, A, B))) <=> one_to_one(F, A, B)))),
% 0.20/0.56 inference(modus_ponens,[status(thm)],[104, 100])).
% 0.20/0.56 tff(106,plain,
% 0.20/0.56 (![F: $i, A: $i, B: $i] : (~(((~injective(F, A, B)) | (~surjective(F, A, B))) <=> one_to_one(F, A, B)))),
% 0.20/0.56 inference(modus_ponens,[status(thm)],[105, 98])).
% 0.20/0.56 tff(107,plain,
% 0.20/0.56 ((~![F: $i, A: $i, B: $i] : (~(((~injective(F, A, B)) | (~surjective(F, A, B))) <=> one_to_one(F, A, B)))) | (~(((~injective(F!43, A!41, B!40)) | (~surjective(F!43, A!41, B!40))) <=> one_to_one(F!43, A!41, B!40)))),
% 0.20/0.56 inference(quant_inst,[status(thm)],[])).
% 0.20/0.56 tff(108,plain,
% 0.20/0.56 (~(((~injective(F!43, A!41, B!40)) | (~surjective(F!43, A!41, B!40))) <=> one_to_one(F!43, A!41, B!40))),
% 0.20/0.56 inference(unit_resolution,[status(thm)],[107, 106])).
% 0.20/0.56 tff(109,plain,
% 0.20/0.56 (maps(F!43, A!41, B!40) & maps(G!42, B!40, C!39) & one_to_one(F!43, A!41, B!40) & one_to_one(G!42, B!40, C!39)),
% 0.20/0.56 inference(or_elim,[status(thm)],[33])).
% 0.20/0.56 tff(110,plain,
% 0.20/0.56 (one_to_one(F!43, A!41, B!40)),
% 0.20/0.56 inference(and_elim,[status(thm)],[109])).
% 0.20/0.56 tff(111,plain,
% 0.20/0.56 ((((~injective(F!43, A!41, B!40)) | (~surjective(F!43, A!41, B!40))) <=> one_to_one(F!43, A!41, B!40)) | (~((~injective(F!43, A!41, B!40)) | (~surjective(F!43, A!41, B!40)))) | (~one_to_one(F!43, A!41, B!40))),
% 0.20/0.56 inference(tautology,[status(thm)],[])).
% 0.20/0.56 tff(112,plain,
% 0.20/0.56 ((((~injective(F!43, A!41, B!40)) | (~surjective(F!43, A!41, B!40))) <=> one_to_one(F!43, A!41, B!40)) | (~((~injective(F!43, A!41, B!40)) | (~surjective(F!43, A!41, B!40))))),
% 0.20/0.56 inference(unit_resolution,[status(thm)],[111, 110])).
% 0.20/0.56 tff(113,plain,
% 0.20/0.56 (~((~injective(F!43, A!41, B!40)) | (~surjective(F!43, A!41, B!40)))),
% 0.20/0.56 inference(unit_resolution,[status(thm)],[112, 108])).
% 0.20/0.56 tff(114,plain,
% 0.20/0.56 (((~injective(F!43, A!41, B!40)) | (~surjective(F!43, A!41, B!40))) | surjective(F!43, A!41, B!40)),
% 0.20/0.56 inference(tautology,[status(thm)],[])).
% 0.20/0.56 tff(115,plain,
% 0.20/0.56 (surjective(F!43, A!41, B!40)),
% 0.20/0.56 inference(unit_resolution,[status(thm)],[114, 113])).
% 0.20/0.56 tff(116,plain,
% 0.20/0.56 ((~((~surjective(F!43, A!41, B!40)) | ![Y: $i] : ((~member(Y, B!40)) | (~((~member(tptp_fun_E_19(Y, A!41, F!43), A!41)) | (~apply(F!43, tptp_fun_E_19(Y, A!41, F!43), Y))))))) | (~surjective(F!43, A!41, B!40)) | ![Y: $i] : ((~member(Y, B!40)) | (~((~member(tptp_fun_E_19(Y, A!41, F!43), A!41)) | (~apply(F!43, tptp_fun_E_19(Y, A!41, F!43), Y)))))),
% 0.20/0.56 inference(tautology,[status(thm)],[])).
% 0.20/0.56 tff(117,plain,
% 0.20/0.56 ((~((~surjective(F!43, A!41, B!40)) | ![Y: $i] : ((~member(Y, B!40)) | (~((~member(tptp_fun_E_19(Y, A!41, F!43), A!41)) | (~apply(F!43, tptp_fun_E_19(Y, A!41, F!43), Y))))))) | ![Y: $i] : ((~member(Y, B!40)) | (~((~member(tptp_fun_E_19(Y, A!41, F!43), A!41)) | (~apply(F!43, tptp_fun_E_19(Y, A!41, F!43), Y)))))),
% 0.20/0.56 inference(unit_resolution,[status(thm)],[116, 115])).
% 0.20/0.56 tff(118,plain,
% 0.20/0.56 (![Y: $i] : ((~member(Y, B!40)) | (~((~member(tptp_fun_E_19(Y, A!41, F!43), A!41)) | (~apply(F!43, tptp_fun_E_19(Y, A!41, F!43), Y)))))),
% 0.20/0.56 inference(unit_resolution,[status(thm)],[117, 96])).
% 0.20/0.56 tff(119,plain,
% 0.20/0.56 (((~![Y: $i] : ((~member(Y, B!40)) | (~((~member(tptp_fun_E_19(Y, A!41, F!43), A!41)) | (~apply(F!43, tptp_fun_E_19(Y, A!41, F!43), Y)))))) | ((~member(tptp_fun_Y_8(tptp_fun_Y2_12(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, inverse_function(G!42, B!40, C!39), inverse_function(F!43, A!41, B!40)), B!40)) | (~((~member(tptp_fun_E_19(tptp_fun_Y_8(tptp_fun_Y2_12(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, inverse_function(G!42, B!40, C!39), inverse_function(F!43, A!41, B!40)), A!41, F!43), A!41)) | (~apply(F!43, tptp_fun_E_19(tptp_fun_Y_8(tptp_fun_Y2_12(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, inverse_function(G!42, B!40, C!39), inverse_function(F!43, A!41, B!40)), A!41, F!43), tptp_fun_Y_8(tptp_fun_Y2_12(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, inverse_function(G!42, B!40, C!39), inverse_function(F!43, A!41, B!40)))))))) <=> ((~![Y: $i] : ((~member(Y, B!40)) | (~((~member(tptp_fun_E_19(Y, A!41, F!43), A!41)) | (~apply(F!43, tptp_fun_E_19(Y, A!41, F!43), Y)))))) | (~member(tptp_fun_Y_8(tptp_fun_Y2_12(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, inverse_function(G!42, B!40, C!39), inverse_function(F!43, A!41, B!40)), B!40)) | (~((~member(tptp_fun_E_19(tptp_fun_Y_8(tptp_fun_Y2_12(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, inverse_function(G!42, B!40, C!39), inverse_function(F!43, A!41, B!40)), A!41, F!43), A!41)) | (~apply(F!43, tptp_fun_E_19(tptp_fun_Y_8(tptp_fun_Y2_12(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, inverse_function(G!42, B!40, C!39), inverse_function(F!43, A!41, B!40)), A!41, F!43), tptp_fun_Y_8(tptp_fun_Y2_12(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, inverse_function(G!42, B!40, C!39), inverse_function(F!43, A!41, B!40)))))))),
% 0.20/0.57 inference(rewrite,[status(thm)],[])).
% 0.20/0.57 tff(120,plain,
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% 0.20/0.57 inference(quant_inst,[status(thm)],[])).
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% 0.20/0.57 inference(modus_ponens,[status(thm)],[120, 119])).
% 0.20/0.57 tff(122,plain,
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% 0.20/0.57 inference(unit_resolution,[status(thm)],[121, 118, 76])).
% 0.20/0.57 tff(123,plain,
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% 0.20/0.57 inference(tautology,[status(thm)],[])).
% 0.20/0.57 tff(124,plain,
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% 0.20/0.58 inference(unit_resolution,[status(thm)],[123, 122])).
% 0.20/0.58 tff(125,plain,
% 0.20/0.58 (((~member(tptp_fun_E_19(tptp_fun_Y_8(tptp_fun_Y2_12(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, inverse_function(G!42, B!40, C!39), inverse_function(F!43, A!41, B!40)), A!41, F!43), A!41)) | (~apply(F!43, tptp_fun_E_19(tptp_fun_Y_8(tptp_fun_Y2_12(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, inverse_function(G!42, B!40, C!39), inverse_function(F!43, A!41, B!40)), A!41, F!43), tptp_fun_Y_8(tptp_fun_Y2_12(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, inverse_function(G!42, B!40, C!39), inverse_function(F!43, A!41, B!40))))) | member(tptp_fun_E_19(tptp_fun_Y_8(tptp_fun_Y2_12(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, inverse_function(G!42, B!40, C!39), inverse_function(F!43, A!41, B!40)), A!41, F!43), A!41)),
% 0.20/0.58 inference(tautology,[status(thm)],[])).
% 0.20/0.58 tff(126,plain,
% 0.20/0.58 (member(tptp_fun_E_19(tptp_fun_Y_8(tptp_fun_Y2_12(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, inverse_function(G!42, B!40, C!39), inverse_function(F!43, A!41, B!40)), A!41, F!43), A!41)),
% 0.20/0.58 inference(unit_resolution,[status(thm)],[125, 122])).
% 0.20/0.58 tff(127,plain,
% 0.20/0.58 (^[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))))),
% 0.20/0.58 inference(bind,[status(th)],[])).
% 0.20/0.58 tff(128,plain,
% 0.20/0.58 (![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)))),
% 0.20/0.58 inference(quant_intro,[status(thm)],[127])).
% 0.20/0.58 tff(129,plain,
% 0.20/0.58 (^[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)))))),
% 0.20/0.58 inference(bind,[status(th)],[])).
% 0.20/0.58 tff(130,plain,
% 0.20/0.58 (![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)))),
% 0.20/0.58 inference(quant_intro,[status(thm)],[129])).
% 0.20/0.58 tff(131,plain,
% 0.20/0.58 (![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)))),
% 0.20/0.58 inference(rewrite,[status(thm)],[])).
% 0.20/0.58 tff(132,plain,
% 0.20/0.58 (^[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))))),
% 0.20/0.58 inference(bind,[status(th)],[])).
% 0.20/0.58 tff(133,plain,
% 0.20/0.58 (![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)))),
% 0.20/0.58 inference(quant_intro,[status(thm)],[132])).
% 0.20/0.58 tff(134,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/sandbox2/benchmark/Axioms/SET006+1.ax','inverse_function')).
% 0.20/0.58 tff(135,plain,
% 0.20/0.58 (![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)))),
% 0.20/0.58 inference(modus_ponens,[status(thm)],[134, 133])).
% 0.20/0.58 tff(136,plain,
% 0.20/0.58 (![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)))),
% 0.20/0.58 inference(modus_ponens,[status(thm)],[135, 131])).
% 0.20/0.58 tff(137,plain,(
% 0.20/0.58 ![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)))),
% 0.20/0.58 inference(skolemize,[status(sab)],[136])).
% 0.20/0.58 tff(138,plain,
% 0.20/0.58 (![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)))),
% 0.20/0.58 inference(modus_ponens,[status(thm)],[137, 130])).
% 0.20/0.58 tff(139,plain,
% 0.20/0.58 (![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)))),
% 0.20/0.58 inference(modus_ponens,[status(thm)],[138, 128])).
% 0.20/0.58 tff(140,plain,
% 0.20/0.58 (((~![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_Y2_12(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), A!41)) | (~member(tptp_fun_Y_8(tptp_fun_Y2_12(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, inverse_function(G!42, B!40, C!39), inverse_function(F!43, A!41, B!40)), B!40)) | (apply(F!43, tptp_fun_Y2_12(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_Y_8(tptp_fun_Y2_12(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, inverse_function(G!42, B!40, C!39), inverse_function(F!43, A!41, B!40))) <=> apply(inverse_function(F!43, A!41, B!40), tptp_fun_Y_8(tptp_fun_Y2_12(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, inverse_function(G!42, B!40, C!39), inverse_function(F!43, A!41, B!40)), tptp_fun_Y2_12(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!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_Y2_12(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), A!41)) | (~member(tptp_fun_Y_8(tptp_fun_Y2_12(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, inverse_function(G!42, B!40, C!39), inverse_function(F!43, A!41, B!40)), B!40)) | (apply(F!43, tptp_fun_Y2_12(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_Y_8(tptp_fun_Y2_12(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, inverse_function(G!42, B!40, C!39), inverse_function(F!43, A!41, B!40))) <=> apply(inverse_function(F!43, A!41, B!40), tptp_fun_Y_8(tptp_fun_Y2_12(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, inverse_function(G!42, B!40, C!39), inverse_function(F!43, A!41, B!40)), tptp_fun_Y2_12(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)))))),
% 0.42/0.58 inference(rewrite,[status(thm)],[])).
% 0.42/0.58 tff(141,plain,
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% 0.42/0.59 inference(rewrite,[status(thm)],[])).
% 0.42/0.59 tff(142,plain,
% 0.42/0.59 (((~![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_Y2_12(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_Y_8(tptp_fun_Y2_12(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, inverse_function(G!42, B!40, C!39), inverse_function(F!43, A!41, B!40))) <=> apply(inverse_function(F!43, A!41, B!40), tptp_fun_Y_8(tptp_fun_Y2_12(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, inverse_function(G!42, B!40, C!39), inverse_function(F!43, A!41, B!40)), tptp_fun_Y2_12(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)))) | (~member(tptp_fun_Y_8(tptp_fun_Y2_12(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, inverse_function(G!42, B!40, C!39), inverse_function(F!43, A!41, B!40)), B!40)) | (~member(tptp_fun_Y2_12(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), A!41)))) <=> ((~![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_Y2_12(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), A!41)) | (~member(tptp_fun_Y_8(tptp_fun_Y2_12(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, inverse_function(G!42, B!40, C!39), inverse_function(F!43, A!41, B!40)), B!40)) | (apply(F!43, tptp_fun_Y2_12(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_Y_8(tptp_fun_Y2_12(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, inverse_function(G!42, B!40, C!39), inverse_function(F!43, A!41, B!40))) <=> apply(inverse_function(F!43, A!41, B!40), tptp_fun_Y_8(tptp_fun_Y2_12(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, inverse_function(G!42, B!40, C!39), inverse_function(F!43, A!41, B!40)), tptp_fun_Y2_12(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39))))))),
% 0.42/0.59 inference(monotonicity,[status(thm)],[141])).
% 0.42/0.59 tff(143,plain,
% 0.42/0.59 (((~![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_Y2_12(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_Y_8(tptp_fun_Y2_12(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, inverse_function(G!42, B!40, C!39), inverse_function(F!43, A!41, B!40))) <=> apply(inverse_function(F!43, A!41, B!40), tptp_fun_Y_8(tptp_fun_Y2_12(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, inverse_function(G!42, B!40, C!39), inverse_function(F!43, A!41, B!40)), tptp_fun_Y2_12(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)))) | (~member(tptp_fun_Y_8(tptp_fun_Y2_12(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, inverse_function(G!42, B!40, C!39), inverse_function(F!43, A!41, B!40)), B!40)) | (~member(tptp_fun_Y2_12(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), A!41)))) <=> ((~![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_Y2_12(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), A!41)) | (~member(tptp_fun_Y_8(tptp_fun_Y2_12(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, inverse_function(G!42, B!40, C!39), inverse_function(F!43, A!41, B!40)), B!40)) | (apply(F!43, tptp_fun_Y2_12(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_Y_8(tptp_fun_Y2_12(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, inverse_function(G!42, B!40, C!39), inverse_function(F!43, A!41, B!40))) <=> apply(inverse_function(F!43, A!41, B!40), tptp_fun_Y_8(tptp_fun_Y2_12(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, inverse_function(G!42, B!40, C!39), inverse_function(F!43, A!41, B!40)), tptp_fun_Y2_12(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)))))),
% 0.42/0.59 inference(transitivity,[status(thm)],[142, 140])).
% 0.42/0.59 tff(144,plain,
% 0.42/0.59 ((~![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_Y2_12(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_Y_8(tptp_fun_Y2_12(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, inverse_function(G!42, B!40, C!39), inverse_function(F!43, A!41, B!40))) <=> apply(inverse_function(F!43, A!41, B!40), tptp_fun_Y_8(tptp_fun_Y2_12(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, inverse_function(G!42, B!40, C!39), inverse_function(F!43, A!41, B!40)), tptp_fun_Y2_12(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)))) | (~member(tptp_fun_Y_8(tptp_fun_Y2_12(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, inverse_function(G!42, B!40, C!39), inverse_function(F!43, A!41, B!40)), B!40)) | (~member(tptp_fun_Y2_12(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), A!41)))),
% 0.42/0.59 inference(quant_inst,[status(thm)],[])).
% 0.42/0.59 tff(145,plain,
% 0.42/0.59 ((~![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_Y2_12(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), A!41)) | (~member(tptp_fun_Y_8(tptp_fun_Y2_12(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, inverse_function(G!42, B!40, C!39), inverse_function(F!43, A!41, B!40)), B!40)) | (apply(F!43, tptp_fun_Y2_12(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_Y_8(tptp_fun_Y2_12(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, inverse_function(G!42, B!40, C!39), inverse_function(F!43, A!41, B!40))) <=> apply(inverse_function(F!43, A!41, B!40), tptp_fun_Y_8(tptp_fun_Y2_12(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, inverse_function(G!42, B!40, C!39), inverse_function(F!43, A!41, B!40)), tptp_fun_Y2_12(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39))))),
% 0.42/0.59 inference(modus_ponens,[status(thm)],[144, 143])).
% 0.42/0.59 tff(146,plain,
% 0.42/0.59 (apply(F!43, tptp_fun_Y2_12(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_Y_8(tptp_fun_Y2_12(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, inverse_function(G!42, B!40, C!39), inverse_function(F!43, A!41, B!40))) <=> apply(inverse_function(F!43, A!41, B!40), tptp_fun_Y_8(tptp_fun_Y2_12(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, inverse_function(G!42, B!40, C!39), inverse_function(F!43, A!41, B!40)), tptp_fun_Y2_12(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)))),
% 0.44/0.60 inference(unit_resolution,[status(thm)],[145, 139, 41, 76])).
% 0.44/0.60 tff(147,plain,
% 0.44/0.60 (((~apply(inverse_function(F!43, A!41, B!40), tptp_fun_Y_8(tptp_fun_Y2_12(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, inverse_function(G!42, B!40, C!39), inverse_function(F!43, A!41, B!40)), tptp_fun_Y2_12(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)))) | (~apply(inverse_function(G!42, B!40, C!39), tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_Y_8(tptp_fun_Y2_12(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, inverse_function(G!42, B!40, C!39), inverse_function(F!43, A!41, B!40)))) | (~member(tptp_fun_Y_8(tptp_fun_Y2_12(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, inverse_function(G!42, B!40, C!39), inverse_function(F!43, A!41, B!40)), B!40))) | apply(inverse_function(F!43, A!41, B!40), tptp_fun_Y_8(tptp_fun_Y2_12(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, inverse_function(G!42, B!40, C!39), inverse_function(F!43, A!41, B!40)), tptp_fun_Y2_12(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)))),
% 0.44/0.60 inference(tautology,[status(thm)],[])).
% 0.44/0.60 tff(148,plain,
% 0.44/0.60 (apply(inverse_function(F!43, A!41, B!40), tptp_fun_Y_8(tptp_fun_Y2_12(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, inverse_function(G!42, B!40, C!39), inverse_function(F!43, A!41, B!40)), tptp_fun_Y2_12(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)))),
% 0.44/0.60 inference(unit_resolution,[status(thm)],[147, 74])).
% 0.44/0.60 tff(149,plain,
% 0.44/0.60 ((~(apply(F!43, tptp_fun_Y2_12(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_Y_8(tptp_fun_Y2_12(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, inverse_function(G!42, B!40, C!39), inverse_function(F!43, A!41, B!40))) <=> apply(inverse_function(F!43, A!41, B!40), tptp_fun_Y_8(tptp_fun_Y2_12(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, inverse_function(G!42, B!40, C!39), inverse_function(F!43, A!41, B!40)), tptp_fun_Y2_12(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39))))) | apply(F!43, tptp_fun_Y2_12(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_Y_8(tptp_fun_Y2_12(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, inverse_function(G!42, B!40, C!39), inverse_function(F!43, A!41, B!40))) | (~apply(inverse_function(F!43, A!41, B!40), tptp_fun_Y_8(tptp_fun_Y2_12(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, inverse_function(G!42, B!40, C!39), inverse_function(F!43, A!41, B!40)), tptp_fun_Y2_12(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39))))),
% 0.44/0.60 inference(tautology,[status(thm)],[])).
% 0.44/0.60 tff(150,plain,
% 0.44/0.60 ((~(apply(F!43, tptp_fun_Y2_12(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_Y_8(tptp_fun_Y2_12(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, inverse_function(G!42, B!40, C!39), inverse_function(F!43, A!41, B!40))) <=> apply(inverse_function(F!43, A!41, B!40), tptp_fun_Y_8(tptp_fun_Y2_12(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, inverse_function(G!42, B!40, C!39), inverse_function(F!43, A!41, B!40)), tptp_fun_Y2_12(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39))))) | apply(F!43, tptp_fun_Y2_12(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_Y_8(tptp_fun_Y2_12(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, inverse_function(G!42, B!40, C!39), inverse_function(F!43, A!41, B!40)))),
% 0.44/0.60 inference(unit_resolution,[status(thm)],[149, 148])).
% 0.44/0.60 tff(151,plain,
% 0.44/0.60 (apply(F!43, tptp_fun_Y2_12(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_Y_8(tptp_fun_Y2_12(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, inverse_function(G!42, B!40, C!39), inverse_function(F!43, A!41, B!40)))),
% 0.44/0.60 inference(unit_resolution,[status(thm)],[150, 146])).
% 0.44/0.60 tff(152,plain,
% 0.44/0.60 (^[F: $i, A: $i, B: $i] : refl((~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B)))))))) <=> (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B)))))))))),
% 0.44/0.60 inference(bind,[status(th)],[])).
% 0.44/0.60 tff(153,plain,
% 0.44/0.60 (![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B)))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))),
% 0.44/0.60 inference(quant_intro,[status(thm)],[152])).
% 0.44/0.60 tff(154,plain,
% 0.44/0.60 (^[F: $i, A: $i, B: $i] : rewrite((~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B)))))))) <=> (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B)))))))))),
% 0.44/0.60 inference(bind,[status(th)],[])).
% 0.44/0.60 tff(155,plain,
% 0.44/0.60 (![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B)))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))),
% 0.44/0.60 inference(quant_intro,[status(thm)],[154])).
% 0.44/0.60 tff(156,plain,
% 0.44/0.60 (![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B)))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))),
% 0.44/0.60 inference(transitivity,[status(thm)],[155, 153])).
% 0.44/0.60 tff(157,plain,
% 0.44/0.60 (^[F: $i, A: $i, B: $i] : trans(monotonicity(rewrite(((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~(apply(F, X1, Y) & apply(F, X2, Y))) | (~(member(X1, A) & member(X2, A) & member(Y, B))))) <=> ((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))), trans(monotonicity(rewrite((~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~(apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F)) & apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F)))) | (~(member(tptp_fun_X1_18(B, A, F), A) & member(tptp_fun_X2_17(B, A, F), A) & member(tptp_fun_Y_16(B, A, F), B))))) <=> (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))), ((injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~(apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F)) & apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F)))) | (~(member(tptp_fun_X1_18(B, A, F), A) & member(tptp_fun_X2_17(B, A, F), A) & member(tptp_fun_Y_16(B, A, F), B)))))) <=> (injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))), rewrite((injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))) <=> (injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B)))))), ((injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~(apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F)) & apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F)))) | (~(member(tptp_fun_X1_18(B, A, F), A) & member(tptp_fun_X2_17(B, A, F), A) & member(tptp_fun_Y_16(B, A, F), B)))))) <=> (injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))), ((((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~(apply(F, X1, Y) & apply(F, X2, Y))) | (~(member(X1, A) & member(X2, A) & member(Y, B))))) & (injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~(apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F)) & apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F)))) | (~(member(tptp_fun_X1_18(B, A, F), A) & member(tptp_fun_X2_17(B, A, F), A) & member(tptp_fun_Y_16(B, A, F), B))))))) <=> (((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y)))) & (injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B)))))))), rewrite((((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y)))) & (injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B)))))) <=> (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))), ((((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~(apply(F, X1, Y) & apply(F, X2, Y))) | (~(member(X1, A) & member(X2, A) & member(Y, B))))) & (injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~(apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F)) & apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F)))) | (~(member(tptp_fun_X1_18(B, A, F), A) & member(tptp_fun_X2_17(B, A, F), A) & member(tptp_fun_Y_16(B, A, F), B))))))) <=> (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))))),
% 0.44/0.61 inference(bind,[status(th)],[])).
% 0.44/0.61 tff(158,plain,
% 0.44/0.61 (![F: $i, A: $i, B: $i] : (((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~(apply(F, X1, Y) & apply(F, X2, Y))) | (~(member(X1, A) & member(X2, A) & member(Y, B))))) & (injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~(apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F)) & apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F)))) | (~(member(tptp_fun_X1_18(B, A, F), A) & member(tptp_fun_X2_17(B, A, F), A) & member(tptp_fun_Y_16(B, A, F), B))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))),
% 0.44/0.61 inference(quant_intro,[status(thm)],[157])).
% 0.44/0.61 tff(159,plain,
% 0.44/0.61 (![F: $i, A: $i, B: $i] : (injective(F, A, B) <=> ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~(apply(F, X1, Y) & apply(F, X2, Y))) | (~(member(X1, A) & member(X2, A) & member(Y, B))))) <=> ![F: $i, A: $i, B: $i] : (injective(F, A, B) <=> ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~(apply(F, X1, Y) & apply(F, X2, Y))) | (~(member(X1, A) & member(X2, A) & member(Y, B)))))),
% 0.44/0.61 inference(rewrite,[status(thm)],[])).
% 0.44/0.61 tff(160,plain,
% 0.44/0.61 (^[F: $i, A: $i, B: $i] : rewrite((injective(F, A, B) <=> ![X1: $i, X2: $i, Y: $i] : (((member(X1, A) & member(X2, A)) & member(Y, B)) => ((apply(F, X1, Y) & apply(F, X2, Y)) => (X1 = X2)))) <=> (injective(F, A, B) <=> ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~(apply(F, X1, Y) & apply(F, X2, Y))) | (~(member(X1, A) & member(X2, A) & member(Y, B))))))),
% 0.44/0.61 inference(bind,[status(th)],[])).
% 0.44/0.61 tff(161,plain,
% 0.44/0.61 (![F: $i, A: $i, B: $i] : (injective(F, A, B) <=> ![X1: $i, X2: $i, Y: $i] : (((member(X1, A) & member(X2, A)) & member(Y, B)) => ((apply(F, X1, Y) & apply(F, X2, Y)) => (X1 = X2)))) <=> ![F: $i, A: $i, B: $i] : (injective(F, A, B) <=> ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~(apply(F, X1, Y) & apply(F, X2, Y))) | (~(member(X1, A) & member(X2, A) & member(Y, B)))))),
% 0.44/0.61 inference(quant_intro,[status(thm)],[160])).
% 0.44/0.61 tff(162,axiom,(![F: $i, A: $i, B: $i] : (injective(F, A, B) <=> ![X1: $i, X2: $i, Y: $i] : (((member(X1, A) & member(X2, A)) & member(Y, B)) => ((apply(F, X1, Y) & apply(F, X2, Y)) => (X1 = X2))))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+1.ax','injective')).
% 0.44/0.61 tff(163,plain,
% 0.44/0.61 (![F: $i, A: $i, B: $i] : (injective(F, A, B) <=> ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~(apply(F, X1, Y) & apply(F, X2, Y))) | (~(member(X1, A) & member(X2, A) & member(Y, B)))))),
% 0.44/0.61 inference(modus_ponens,[status(thm)],[162, 161])).
% 0.44/0.61 tff(164,plain,
% 0.44/0.61 (![F: $i, A: $i, B: $i] : (injective(F, A, B) <=> ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~(apply(F, X1, Y) & apply(F, X2, Y))) | (~(member(X1, A) & member(X2, A) & member(Y, B)))))),
% 0.44/0.61 inference(modus_ponens,[status(thm)],[163, 159])).
% 0.44/0.61 tff(165,plain,(
% 0.44/0.61 ![F: $i, A: $i, B: $i] : (((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~(apply(F, X1, Y) & apply(F, X2, Y))) | (~(member(X1, A) & member(X2, A) & member(Y, B))))) & (injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~(apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F)) & apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F)))) | (~(member(tptp_fun_X1_18(B, A, F), A) & member(tptp_fun_X2_17(B, A, F), A) & member(tptp_fun_Y_16(B, A, F), B)))))))),
% 0.44/0.61 inference(skolemize,[status(sab)],[164])).
% 0.44/0.61 tff(166,plain,
% 0.44/0.61 (![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))),
% 0.44/0.61 inference(modus_ponens,[status(thm)],[165, 158])).
% 0.44/0.61 tff(167,plain,
% 0.44/0.61 (![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))),
% 0.44/0.61 inference(modus_ponens,[status(thm)],[166, 156])).
% 0.44/0.61 tff(168,plain,
% 0.44/0.61 (((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(F!43, A!41, B!40)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!40)) | (~apply(F!43, X1, Y)) | (~member(X1, A!41)) | (~member(X2, A!41)) | (~apply(F!43, X2, Y))))) | (~(injective(F!43, A!41, B!40) | (~((~member(tptp_fun_Y_16(B!40, A!41, F!43), B!40)) | (~member(tptp_fun_X1_18(B!40, A!41, F!43), A!41)) | (~member(tptp_fun_X2_17(B!40, A!41, F!43), A!41)) | (~apply(F!43, tptp_fun_X2_17(B!40, A!41, F!43), tptp_fun_Y_16(B!40, A!41, F!43))) | (~apply(F!43, tptp_fun_X1_18(B!40, A!41, F!43), tptp_fun_Y_16(B!40, A!41, F!43))) | (tptp_fun_X1_18(B!40, A!41, F!43) = tptp_fun_X2_17(B!40, A!41, F!43))))))))) <=> ((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(F!43, A!41, B!40)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!40)) | (~apply(F!43, X1, Y)) | (~member(X1, A!41)) | (~member(X2, A!41)) | (~apply(F!43, X2, Y))))) | (~(injective(F!43, A!41, B!40) | (~((~member(tptp_fun_Y_16(B!40, A!41, F!43), B!40)) | (~member(tptp_fun_X1_18(B!40, A!41, F!43), A!41)) | (~member(tptp_fun_X2_17(B!40, A!41, F!43), A!41)) | (~apply(F!43, tptp_fun_X2_17(B!40, A!41, F!43), tptp_fun_Y_16(B!40, A!41, F!43))) | (~apply(F!43, tptp_fun_X1_18(B!40, A!41, F!43), tptp_fun_Y_16(B!40, A!41, F!43))) | (tptp_fun_X1_18(B!40, A!41, F!43) = tptp_fun_X2_17(B!40, A!41, F!43)))))))))),
% 0.44/0.61 inference(rewrite,[status(thm)],[])).
% 0.44/0.61 tff(169,plain,
% 0.44/0.61 ((~((~((~injective(F!43, A!41, B!40)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!43, X1, Y)) | (~member(X2, A!41)) | (~member(X1, A!41)) | (~member(Y, B!40)) | (~apply(F!43, X2, Y))))) | (~(injective(F!43, A!41, B!40) | (~((tptp_fun_X1_18(B!40, A!41, F!43) = tptp_fun_X2_17(B!40, A!41, F!43)) | (~apply(F!43, tptp_fun_X1_18(B!40, A!41, F!43), tptp_fun_Y_16(B!40, A!41, F!43))) | (~apply(F!43, tptp_fun_X2_17(B!40, A!41, F!43), tptp_fun_Y_16(B!40, A!41, F!43))) | (~member(tptp_fun_X1_18(B!40, A!41, F!43), A!41)) | (~member(tptp_fun_X2_17(B!40, A!41, F!43), A!41)) | (~member(tptp_fun_Y_16(B!40, A!41, F!43), B!40)))))))) <=> (~((~((~injective(F!43, A!41, B!40)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!40)) | (~apply(F!43, X1, Y)) | (~member(X1, A!41)) | (~member(X2, A!41)) | (~apply(F!43, X2, Y))))) | (~(injective(F!43, A!41, B!40) | (~((~member(tptp_fun_Y_16(B!40, A!41, F!43), B!40)) | (~member(tptp_fun_X1_18(B!40, A!41, F!43), A!41)) | (~member(tptp_fun_X2_17(B!40, A!41, F!43), A!41)) | (~apply(F!43, tptp_fun_X2_17(B!40, A!41, F!43), tptp_fun_Y_16(B!40, A!41, F!43))) | (~apply(F!43, tptp_fun_X1_18(B!40, A!41, F!43), tptp_fun_Y_16(B!40, A!41, F!43))) | (tptp_fun_X1_18(B!40, A!41, F!43) = tptp_fun_X2_17(B!40, A!41, F!43))))))))),
% 0.44/0.61 inference(rewrite,[status(thm)],[])).
% 0.44/0.61 tff(170,plain,
% 0.44/0.61 (((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(F!43, A!41, B!40)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!43, X1, Y)) | (~member(X2, A!41)) | (~member(X1, A!41)) | (~member(Y, B!40)) | (~apply(F!43, X2, Y))))) | (~(injective(F!43, A!41, B!40) | (~((tptp_fun_X1_18(B!40, A!41, F!43) = tptp_fun_X2_17(B!40, A!41, F!43)) | (~apply(F!43, tptp_fun_X1_18(B!40, A!41, F!43), tptp_fun_Y_16(B!40, A!41, F!43))) | (~apply(F!43, tptp_fun_X2_17(B!40, A!41, F!43), tptp_fun_Y_16(B!40, A!41, F!43))) | (~member(tptp_fun_X1_18(B!40, A!41, F!43), A!41)) | (~member(tptp_fun_X2_17(B!40, A!41, F!43), A!41)) | (~member(tptp_fun_Y_16(B!40, A!41, F!43), B!40))))))))) <=> ((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(F!43, A!41, B!40)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!40)) | (~apply(F!43, X1, Y)) | (~member(X1, A!41)) | (~member(X2, A!41)) | (~apply(F!43, X2, Y))))) | (~(injective(F!43, A!41, B!40) | (~((~member(tptp_fun_Y_16(B!40, A!41, F!43), B!40)) | (~member(tptp_fun_X1_18(B!40, A!41, F!43), A!41)) | (~member(tptp_fun_X2_17(B!40, A!41, F!43), A!41)) | (~apply(F!43, tptp_fun_X2_17(B!40, A!41, F!43), tptp_fun_Y_16(B!40, A!41, F!43))) | (~apply(F!43, tptp_fun_X1_18(B!40, A!41, F!43), tptp_fun_Y_16(B!40, A!41, F!43))) | (tptp_fun_X1_18(B!40, A!41, F!43) = tptp_fun_X2_17(B!40, A!41, F!43)))))))))),
% 0.44/0.61 inference(monotonicity,[status(thm)],[169])).
% 0.44/0.61 tff(171,plain,
% 0.44/0.61 (((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(F!43, A!41, B!40)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!43, X1, Y)) | (~member(X2, A!41)) | (~member(X1, A!41)) | (~member(Y, B!40)) | (~apply(F!43, X2, Y))))) | (~(injective(F!43, A!41, B!40) | (~((tptp_fun_X1_18(B!40, A!41, F!43) = tptp_fun_X2_17(B!40, A!41, F!43)) | (~apply(F!43, tptp_fun_X1_18(B!40, A!41, F!43), tptp_fun_Y_16(B!40, A!41, F!43))) | (~apply(F!43, tptp_fun_X2_17(B!40, A!41, F!43), tptp_fun_Y_16(B!40, A!41, F!43))) | (~member(tptp_fun_X1_18(B!40, A!41, F!43), A!41)) | (~member(tptp_fun_X2_17(B!40, A!41, F!43), A!41)) | (~member(tptp_fun_Y_16(B!40, A!41, F!43), B!40))))))))) <=> ((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(F!43, A!41, B!40)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!40)) | (~apply(F!43, X1, Y)) | (~member(X1, A!41)) | (~member(X2, A!41)) | (~apply(F!43, X2, Y))))) | (~(injective(F!43, A!41, B!40) | (~((~member(tptp_fun_Y_16(B!40, A!41, F!43), B!40)) | (~member(tptp_fun_X1_18(B!40, A!41, F!43), A!41)) | (~member(tptp_fun_X2_17(B!40, A!41, F!43), A!41)) | (~apply(F!43, tptp_fun_X2_17(B!40, A!41, F!43), tptp_fun_Y_16(B!40, A!41, F!43))) | (~apply(F!43, tptp_fun_X1_18(B!40, A!41, F!43), tptp_fun_Y_16(B!40, A!41, F!43))) | (tptp_fun_X1_18(B!40, A!41, F!43) = tptp_fun_X2_17(B!40, A!41, F!43)))))))))),
% 0.44/0.61 inference(transitivity,[status(thm)],[170, 168])).
% 0.44/0.61 tff(172,plain,
% 0.44/0.61 ((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(F!43, A!41, B!40)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!43, X1, Y)) | (~member(X2, A!41)) | (~member(X1, A!41)) | (~member(Y, B!40)) | (~apply(F!43, X2, Y))))) | (~(injective(F!43, A!41, B!40) | (~((tptp_fun_X1_18(B!40, A!41, F!43) = tptp_fun_X2_17(B!40, A!41, F!43)) | (~apply(F!43, tptp_fun_X1_18(B!40, A!41, F!43), tptp_fun_Y_16(B!40, A!41, F!43))) | (~apply(F!43, tptp_fun_X2_17(B!40, A!41, F!43), tptp_fun_Y_16(B!40, A!41, F!43))) | (~member(tptp_fun_X1_18(B!40, A!41, F!43), A!41)) | (~member(tptp_fun_X2_17(B!40, A!41, F!43), A!41)) | (~member(tptp_fun_Y_16(B!40, A!41, F!43), B!40))))))))),
% 0.44/0.61 inference(quant_inst,[status(thm)],[])).
% 0.44/0.61 tff(173,plain,
% 0.44/0.61 ((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(F!43, A!41, B!40)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!40)) | (~apply(F!43, X1, Y)) | (~member(X1, A!41)) | (~member(X2, A!41)) | (~apply(F!43, X2, Y))))) | (~(injective(F!43, A!41, B!40) | (~((~member(tptp_fun_Y_16(B!40, A!41, F!43), B!40)) | (~member(tptp_fun_X1_18(B!40, A!41, F!43), A!41)) | (~member(tptp_fun_X2_17(B!40, A!41, F!43), A!41)) | (~apply(F!43, tptp_fun_X2_17(B!40, A!41, F!43), tptp_fun_Y_16(B!40, A!41, F!43))) | (~apply(F!43, tptp_fun_X1_18(B!40, A!41, F!43), tptp_fun_Y_16(B!40, A!41, F!43))) | (tptp_fun_X1_18(B!40, A!41, F!43) = tptp_fun_X2_17(B!40, A!41, F!43))))))))),
% 0.44/0.61 inference(modus_ponens,[status(thm)],[172, 171])).
% 0.44/0.61 tff(174,plain,
% 0.44/0.61 (~((~((~injective(F!43, A!41, B!40)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!40)) | (~apply(F!43, X1, Y)) | (~member(X1, A!41)) | (~member(X2, A!41)) | (~apply(F!43, X2, Y))))) | (~(injective(F!43, A!41, B!40) | (~((~member(tptp_fun_Y_16(B!40, A!41, F!43), B!40)) | (~member(tptp_fun_X1_18(B!40, A!41, F!43), A!41)) | (~member(tptp_fun_X2_17(B!40, A!41, F!43), A!41)) | (~apply(F!43, tptp_fun_X2_17(B!40, A!41, F!43), tptp_fun_Y_16(B!40, A!41, F!43))) | (~apply(F!43, tptp_fun_X1_18(B!40, A!41, F!43), tptp_fun_Y_16(B!40, A!41, F!43))) | (tptp_fun_X1_18(B!40, A!41, F!43) = tptp_fun_X2_17(B!40, A!41, F!43)))))))),
% 0.44/0.61 inference(unit_resolution,[status(thm)],[173, 167])).
% 0.44/0.61 tff(175,plain,
% 0.44/0.61 (((~((~injective(F!43, A!41, B!40)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!40)) | (~apply(F!43, X1, Y)) | (~member(X1, A!41)) | (~member(X2, A!41)) | (~apply(F!43, X2, Y))))) | (~(injective(F!43, A!41, B!40) | (~((~member(tptp_fun_Y_16(B!40, A!41, F!43), B!40)) | (~member(tptp_fun_X1_18(B!40, A!41, F!43), A!41)) | (~member(tptp_fun_X2_17(B!40, A!41, F!43), A!41)) | (~apply(F!43, tptp_fun_X2_17(B!40, A!41, F!43), tptp_fun_Y_16(B!40, A!41, F!43))) | (~apply(F!43, tptp_fun_X1_18(B!40, A!41, F!43), tptp_fun_Y_16(B!40, A!41, F!43))) | (tptp_fun_X1_18(B!40, A!41, F!43) = tptp_fun_X2_17(B!40, A!41, F!43))))))) | ((~injective(F!43, A!41, B!40)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!40)) | (~apply(F!43, X1, Y)) | (~member(X1, A!41)) | (~member(X2, A!41)) | (~apply(F!43, X2, Y))))),
% 0.44/0.61 inference(tautology,[status(thm)],[])).
% 0.44/0.61 tff(176,plain,
% 0.44/0.61 ((~injective(F!43, A!41, B!40)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!40)) | (~apply(F!43, X1, Y)) | (~member(X1, A!41)) | (~member(X2, A!41)) | (~apply(F!43, X2, Y)))),
% 0.44/0.61 inference(unit_resolution,[status(thm)],[175, 174])).
% 0.44/0.62 tff(177,plain,
% 0.44/0.62 (((~injective(F!43, A!41, B!40)) | (~surjective(F!43, A!41, B!40))) | injective(F!43, A!41, B!40)),
% 0.44/0.62 inference(tautology,[status(thm)],[])).
% 0.44/0.62 tff(178,plain,
% 0.44/0.62 (injective(F!43, A!41, B!40)),
% 0.44/0.62 inference(unit_resolution,[status(thm)],[177, 113])).
% 0.44/0.62 tff(179,plain,
% 0.44/0.62 ((~((~injective(F!43, A!41, B!40)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!40)) | (~apply(F!43, X1, Y)) | (~member(X1, A!41)) | (~member(X2, A!41)) | (~apply(F!43, X2, Y))))) | (~injective(F!43, A!41, B!40)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!40)) | (~apply(F!43, X1, Y)) | (~member(X1, A!41)) | (~member(X2, A!41)) | (~apply(F!43, X2, Y)))),
% 0.44/0.62 inference(tautology,[status(thm)],[])).
% 0.44/0.62 tff(180,plain,
% 0.44/0.62 ((~((~injective(F!43, A!41, B!40)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!40)) | (~apply(F!43, X1, Y)) | (~member(X1, A!41)) | (~member(X2, A!41)) | (~apply(F!43, X2, Y))))) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!40)) | (~apply(F!43, X1, Y)) | (~member(X1, A!41)) | (~member(X2, A!41)) | (~apply(F!43, X2, Y)))),
% 0.44/0.62 inference(unit_resolution,[status(thm)],[179, 178])).
% 0.44/0.62 tff(181,plain,
% 0.44/0.62 (![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!40)) | (~apply(F!43, X1, Y)) | (~member(X1, A!41)) | (~member(X2, A!41)) | (~apply(F!43, X2, Y)))),
% 0.44/0.62 inference(unit_resolution,[status(thm)],[180, 176])).
% 0.44/0.62 tff(182,plain,
% 0.44/0.62 (((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!40)) | (~apply(F!43, X1, Y)) | (~member(X1, A!41)) | (~member(X2, A!41)) | (~apply(F!43, X2, Y)))) | ((~member(tptp_fun_Y2_12(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), A!41)) | (~member(tptp_fun_Y_8(tptp_fun_Y2_12(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, inverse_function(G!42, B!40, C!39), inverse_function(F!43, A!41, B!40)), B!40)) | (~apply(F!43, tptp_fun_Y2_12(A!41, C!39, 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% 0.44/0.62 inference(rewrite,[status(thm)],[])).
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% 0.47/0.63 inference(monotonicity,[status(thm)],[183])).
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% 0.47/0.64 inference(transitivity,[status(thm)],[184, 182])).
% 0.47/0.64 tff(186,plain,
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% 0.47/0.64 inference(quant_inst,[status(thm)],[])).
% 0.47/0.64 tff(187,plain,
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% 0.47/0.65 inference(modus_ponens,[status(thm)],[186, 185])).
% 0.47/0.65 tff(188,plain,
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% 0.47/0.65 inference(unit_resolution,[status(thm)],[187, 41, 181, 76, 151, 126, 124])).
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% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(190,plain,
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% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(191,plain,
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% 0.47/0.66 inference(monotonicity,[status(thm)],[190])).
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% 0.47/0.66 inference(transitivity,[status(thm)],[191, 189])).
% 0.47/0.66 tff(193,plain,
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% 0.47/0.66 inference(quant_inst,[status(thm)],[])).
% 0.47/0.66 tff(194,plain,
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% 0.47/0.66 inference(modus_ponens,[status(thm)],[193, 192])).
% 0.47/0.66 tff(195,plain,
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% 0.47/0.66 inference(unit_resolution,[status(thm)],[194, 139, 39, 76])).
% 0.47/0.66 tff(196,plain,
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% 0.47/0.67 inference(tautology,[status(thm)],[])).
% 0.47/0.67 tff(197,plain,
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% 0.47/0.67 inference(unit_resolution,[status(thm)],[196, 74])).
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% 0.47/0.67 inference(tautology,[status(thm)],[])).
% 0.47/0.67 tff(199,plain,
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% 0.47/0.67 inference(unit_resolution,[status(thm)],[198, 197])).
% 0.47/0.67 tff(200,plain,
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% 0.47/0.67 inference(unit_resolution,[status(thm)],[199, 195])).
% 0.47/0.67 tff(201,plain,
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% 0.47/0.67 inference(tautology,[status(thm)],[])).
% 0.47/0.67 tff(202,plain,
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% 0.47/0.67 inference(unit_resolution,[status(thm)],[201, 37])).
% 0.47/0.67 tff(203,plain,
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% 0.47/0.70 inference(transitivity,[status(thm)],[205, 203])).
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% 0.47/0.70 inference(quant_inst,[status(thm)],[])).
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% 0.47/0.70 inference(modus_ponens,[status(thm)],[207, 206])).
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% 0.47/0.71 inference(unit_resolution,[status(thm)],[208, 57, 202, 39])).
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% 0.47/0.71 inference(tautology,[status(thm)],[])).
% 0.47/0.71 tff(211,plain,
% 0.47/0.71 ((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_Y_8(tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, F!43, G!42), tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39))))))),
% 0.47/0.71 inference(unit_resolution,[status(thm)],[210, 209])).
% 0.47/0.71 tff(212,plain,
% 0.47/0.71 (((~![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!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), A!41)) | (~member(tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), C!39)) | (apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39))) <=> apply(inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39), tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!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!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), A!41)) | (~member(tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), C!39)) | (apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39))) <=> apply(inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39), tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)))))),
% 0.47/0.71 inference(rewrite,[status(thm)],[])).
% 0.47/0.71 tff(213,plain,
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% 0.47/0.72 inference(rewrite,[status(thm)],[])).
% 0.47/0.72 tff(214,plain,
% 0.47/0.72 (((~![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(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39))) <=> apply(inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39), tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)))) | (~member(tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), C!39)) | (~member(tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), A!41)))) <=> ((~![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!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), A!41)) | (~member(tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), C!39)) | (apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39))) <=> apply(inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39), tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39))))))),
% 0.47/0.72 inference(monotonicity,[status(thm)],[213])).
% 0.47/0.72 tff(215,plain,
% 0.47/0.72 (((~![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(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39))) <=> apply(inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39), tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)))) | (~member(tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), C!39)) | (~member(tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), A!41)))) <=> ((~![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!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), A!41)) | (~member(tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), C!39)) | (apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39))) <=> apply(inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39), tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)))))),
% 0.47/0.72 inference(transitivity,[status(thm)],[214, 212])).
% 0.47/0.72 tff(216,plain,
% 0.47/0.72 ((~![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(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39))) <=> apply(inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39), tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)))) | (~member(tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), C!39)) | (~member(tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), A!41)))),
% 0.47/0.72 inference(quant_inst,[status(thm)],[])).
% 0.47/0.72 tff(217,plain,
% 0.47/0.72 ((~![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!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), A!41)) | (~member(tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), C!39)) | (apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39))) <=> apply(inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39), tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39))))),
% 0.47/0.72 inference(modus_ponens,[status(thm)],[216, 215])).
% 0.47/0.72 tff(218,plain,
% 0.47/0.72 (apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39))) <=> apply(inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39), tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)))),
% 0.47/0.72 inference(unit_resolution,[status(thm)],[217, 139, 202, 39])).
% 0.47/0.72 tff(219,plain,
% 0.47/0.72 (((~apply(compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_Y2_12(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)))) | (~apply(inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39), tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)))) | (~member(tptp_fun_Y2_12(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), A!41)) | (~member(tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), A!41)) | (~member(tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), C!39)) | (tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)) = tptp_fun_Y2_12(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)))) | apply(inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39), tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)))),
% 0.47/0.73 inference(tautology,[status(thm)],[])).
% 0.47/0.73 tff(220,plain,
% 0.47/0.73 (apply(inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39), tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)))),
% 0.47/0.73 inference(unit_resolution,[status(thm)],[219, 37])).
% 0.47/0.73 tff(221,plain,
% 0.47/0.73 ((~(apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39))) <=> apply(inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39), tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39))))) | apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39))) | (~apply(inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39), tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39))))),
% 0.47/0.73 inference(tautology,[status(thm)],[])).
% 0.47/0.73 tff(222,plain,
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% 0.57/0.73 inference(unit_resolution,[status(thm)],[221, 220])).
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% 0.57/0.73 inference(unit_resolution,[status(thm)],[222, 218])).
% 0.57/0.73 tff(224,plain,
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% 0.57/0.73 inference(tautology,[status(thm)],[])).
% 0.57/0.73 tff(225,plain,
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% 0.57/0.74 inference(unit_resolution,[status(thm)],[224, 223])).
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% 0.57/0.74 inference(unit_resolution,[status(thm)],[225, 211])).
% 0.57/0.74 tff(227,plain,
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% 0.57/0.74 inference(tautology,[status(thm)],[])).
% 0.57/0.74 tff(228,plain,
% 0.57/0.74 (apply(G!42, tptp_fun_Y_8(tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, F!43, G!42), tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)))),
% 0.57/0.74 inference(unit_resolution,[status(thm)],[227, 226])).
% 0.57/0.74 tff(229,plain,
% 0.57/0.74 (((~member(tptp_fun_Y_8(tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_Y_8(tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, F!43, G!42), tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39))))) | member(tptp_fun_Y_8(tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, F!43, G!42), B!40)),
% 0.57/0.74 inference(tautology,[status(thm)],[])).
% 0.57/0.74 tff(230,plain,
% 0.57/0.74 (member(tptp_fun_Y_8(tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, F!43, G!42), B!40)),
% 0.57/0.74 inference(unit_resolution,[status(thm)],[229, 226])).
% 0.57/0.74 tff(231,plain,
% 0.57/0.74 (((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(G!42, B!40, C!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, B!40)) | (~member(Y, C!39)) | (~apply(G!42, X1, Y)) | (~member(X1, B!40)) | (~apply(G!42, X2, Y))))) | (~(injective(G!42, B!40, C!39) | (~((~member(tptp_fun_Y_16(C!39, B!40, G!42), C!39)) | (~member(tptp_fun_X2_17(C!39, B!40, G!42), B!40)) | (~member(tptp_fun_X1_18(C!39, B!40, G!42), B!40)) | (~apply(G!42, tptp_fun_X2_17(C!39, B!40, G!42), tptp_fun_Y_16(C!39, B!40, G!42))) | (~apply(G!42, tptp_fun_X1_18(C!39, B!40, G!42), tptp_fun_Y_16(C!39, B!40, G!42))) | (tptp_fun_X1_18(C!39, B!40, G!42) = tptp_fun_X2_17(C!39, B!40, G!42))))))))) <=> ((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(G!42, B!40, C!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, B!40)) | (~member(Y, C!39)) | (~apply(G!42, X1, Y)) | (~member(X1, B!40)) | (~apply(G!42, X2, Y))))) | (~(injective(G!42, B!40, C!39) | (~((~member(tptp_fun_Y_16(C!39, B!40, G!42), C!39)) | (~member(tptp_fun_X2_17(C!39, B!40, G!42), B!40)) | (~member(tptp_fun_X1_18(C!39, B!40, G!42), B!40)) | (~apply(G!42, tptp_fun_X2_17(C!39, B!40, G!42), tptp_fun_Y_16(C!39, B!40, G!42))) | (~apply(G!42, tptp_fun_X1_18(C!39, B!40, G!42), tptp_fun_Y_16(C!39, B!40, G!42))) | (tptp_fun_X1_18(C!39, B!40, G!42) = tptp_fun_X2_17(C!39, B!40, G!42)))))))))),
% 0.57/0.74 inference(rewrite,[status(thm)],[])).
% 0.57/0.74 tff(232,plain,
% 0.57/0.74 ((~((~((~injective(G!42, B!40, C!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(G!42, X1, Y)) | (~member(X2, B!40)) | (~member(X1, B!40)) | (~member(Y, C!39)) | (~apply(G!42, X2, Y))))) | (~(injective(G!42, B!40, C!39) | (~((tptp_fun_X1_18(C!39, B!40, G!42) = tptp_fun_X2_17(C!39, B!40, G!42)) | (~apply(G!42, tptp_fun_X1_18(C!39, B!40, G!42), tptp_fun_Y_16(C!39, B!40, G!42))) | (~apply(G!42, tptp_fun_X2_17(C!39, B!40, G!42), tptp_fun_Y_16(C!39, B!40, G!42))) | (~member(tptp_fun_X1_18(C!39, B!40, G!42), B!40)) | (~member(tptp_fun_X2_17(C!39, B!40, G!42), B!40)) | (~member(tptp_fun_Y_16(C!39, B!40, G!42), C!39)))))))) <=> (~((~((~injective(G!42, B!40, C!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, B!40)) | (~member(Y, C!39)) | (~apply(G!42, X1, Y)) | (~member(X1, B!40)) | (~apply(G!42, X2, Y))))) | (~(injective(G!42, B!40, C!39) | (~((~member(tptp_fun_Y_16(C!39, B!40, G!42), C!39)) | (~member(tptp_fun_X2_17(C!39, B!40, G!42), B!40)) | (~member(tptp_fun_X1_18(C!39, B!40, G!42), B!40)) | (~apply(G!42, tptp_fun_X2_17(C!39, B!40, G!42), tptp_fun_Y_16(C!39, B!40, G!42))) | (~apply(G!42, tptp_fun_X1_18(C!39, B!40, G!42), tptp_fun_Y_16(C!39, B!40, G!42))) | (tptp_fun_X1_18(C!39, B!40, G!42) = tptp_fun_X2_17(C!39, B!40, G!42))))))))),
% 0.57/0.74 inference(rewrite,[status(thm)],[])).
% 0.57/0.74 tff(233,plain,
% 0.57/0.74 (((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(G!42, B!40, C!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(G!42, X1, Y)) | (~member(X2, B!40)) | (~member(X1, B!40)) | (~member(Y, C!39)) | (~apply(G!42, X2, Y))))) | (~(injective(G!42, B!40, C!39) | (~((tptp_fun_X1_18(C!39, B!40, G!42) = tptp_fun_X2_17(C!39, B!40, G!42)) | (~apply(G!42, tptp_fun_X1_18(C!39, B!40, G!42), tptp_fun_Y_16(C!39, B!40, G!42))) | (~apply(G!42, tptp_fun_X2_17(C!39, B!40, G!42), tptp_fun_Y_16(C!39, B!40, G!42))) | (~member(tptp_fun_X1_18(C!39, B!40, G!42), B!40)) | (~member(tptp_fun_X2_17(C!39, B!40, G!42), B!40)) | (~member(tptp_fun_Y_16(C!39, B!40, G!42), C!39))))))))) <=> ((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(G!42, B!40, C!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, B!40)) | (~member(Y, C!39)) | (~apply(G!42, X1, Y)) | (~member(X1, B!40)) | (~apply(G!42, X2, Y))))) | (~(injective(G!42, B!40, C!39) | (~((~member(tptp_fun_Y_16(C!39, B!40, G!42), C!39)) | (~member(tptp_fun_X2_17(C!39, B!40, G!42), B!40)) | (~member(tptp_fun_X1_18(C!39, B!40, G!42), B!40)) | (~apply(G!42, tptp_fun_X2_17(C!39, B!40, G!42), tptp_fun_Y_16(C!39, B!40, G!42))) | (~apply(G!42, tptp_fun_X1_18(C!39, B!40, G!42), tptp_fun_Y_16(C!39, B!40, G!42))) | (tptp_fun_X1_18(C!39, B!40, G!42) = tptp_fun_X2_17(C!39, B!40, G!42)))))))))),
% 0.57/0.74 inference(monotonicity,[status(thm)],[232])).
% 0.57/0.74 tff(234,plain,
% 0.57/0.74 (((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(G!42, B!40, C!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(G!42, X1, Y)) | (~member(X2, B!40)) | (~member(X1, B!40)) | (~member(Y, C!39)) | (~apply(G!42, X2, Y))))) | (~(injective(G!42, B!40, C!39) | (~((tptp_fun_X1_18(C!39, B!40, G!42) = tptp_fun_X2_17(C!39, B!40, G!42)) | (~apply(G!42, tptp_fun_X1_18(C!39, B!40, G!42), tptp_fun_Y_16(C!39, B!40, G!42))) | (~apply(G!42, tptp_fun_X2_17(C!39, B!40, G!42), tptp_fun_Y_16(C!39, B!40, G!42))) | (~member(tptp_fun_X1_18(C!39, B!40, G!42), B!40)) | (~member(tptp_fun_X2_17(C!39, B!40, G!42), B!40)) | (~member(tptp_fun_Y_16(C!39, B!40, G!42), C!39))))))))) <=> ((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(G!42, B!40, C!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, B!40)) | (~member(Y, C!39)) | (~apply(G!42, X1, Y)) | (~member(X1, B!40)) | (~apply(G!42, X2, Y))))) | (~(injective(G!42, B!40, C!39) | (~((~member(tptp_fun_Y_16(C!39, B!40, G!42), C!39)) | (~member(tptp_fun_X2_17(C!39, B!40, G!42), B!40)) | (~member(tptp_fun_X1_18(C!39, B!40, G!42), B!40)) | (~apply(G!42, tptp_fun_X2_17(C!39, B!40, G!42), tptp_fun_Y_16(C!39, B!40, G!42))) | (~apply(G!42, tptp_fun_X1_18(C!39, B!40, G!42), tptp_fun_Y_16(C!39, B!40, G!42))) | (tptp_fun_X1_18(C!39, B!40, G!42) = tptp_fun_X2_17(C!39, B!40, G!42)))))))))),
% 0.57/0.75 inference(transitivity,[status(thm)],[233, 231])).
% 0.57/0.75 tff(235,plain,
% 0.57/0.75 ((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(G!42, B!40, C!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(G!42, X1, Y)) | (~member(X2, B!40)) | (~member(X1, B!40)) | (~member(Y, C!39)) | (~apply(G!42, X2, Y))))) | (~(injective(G!42, B!40, C!39) | (~((tptp_fun_X1_18(C!39, B!40, G!42) = tptp_fun_X2_17(C!39, B!40, G!42)) | (~apply(G!42, tptp_fun_X1_18(C!39, B!40, G!42), tptp_fun_Y_16(C!39, B!40, G!42))) | (~apply(G!42, tptp_fun_X2_17(C!39, B!40, G!42), tptp_fun_Y_16(C!39, B!40, G!42))) | (~member(tptp_fun_X1_18(C!39, B!40, G!42), B!40)) | (~member(tptp_fun_X2_17(C!39, B!40, G!42), B!40)) | (~member(tptp_fun_Y_16(C!39, B!40, G!42), C!39))))))))),
% 0.57/0.75 inference(quant_inst,[status(thm)],[])).
% 0.57/0.75 tff(236,plain,
% 0.57/0.75 ((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(G!42, B!40, C!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, B!40)) | (~member(Y, C!39)) | (~apply(G!42, X1, Y)) | (~member(X1, B!40)) | (~apply(G!42, X2, Y))))) | (~(injective(G!42, B!40, C!39) | (~((~member(tptp_fun_Y_16(C!39, B!40, G!42), C!39)) | (~member(tptp_fun_X2_17(C!39, B!40, G!42), B!40)) | (~member(tptp_fun_X1_18(C!39, B!40, G!42), B!40)) | (~apply(G!42, tptp_fun_X2_17(C!39, B!40, G!42), tptp_fun_Y_16(C!39, B!40, G!42))) | (~apply(G!42, tptp_fun_X1_18(C!39, B!40, G!42), tptp_fun_Y_16(C!39, B!40, G!42))) | (tptp_fun_X1_18(C!39, B!40, G!42) = tptp_fun_X2_17(C!39, B!40, G!42))))))))),
% 0.57/0.75 inference(modus_ponens,[status(thm)],[235, 234])).
% 0.57/0.75 tff(237,plain,
% 0.57/0.75 (~((~((~injective(G!42, B!40, C!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, B!40)) | (~member(Y, C!39)) | (~apply(G!42, X1, Y)) | (~member(X1, B!40)) | (~apply(G!42, X2, Y))))) | (~(injective(G!42, B!40, C!39) | (~((~member(tptp_fun_Y_16(C!39, B!40, G!42), C!39)) | (~member(tptp_fun_X2_17(C!39, B!40, G!42), B!40)) | (~member(tptp_fun_X1_18(C!39, B!40, G!42), B!40)) | (~apply(G!42, tptp_fun_X2_17(C!39, B!40, G!42), tptp_fun_Y_16(C!39, B!40, G!42))) | (~apply(G!42, tptp_fun_X1_18(C!39, B!40, G!42), tptp_fun_Y_16(C!39, B!40, G!42))) | (tptp_fun_X1_18(C!39, B!40, G!42) = tptp_fun_X2_17(C!39, B!40, G!42)))))))),
% 0.57/0.75 inference(unit_resolution,[status(thm)],[236, 167])).
% 0.57/0.75 tff(238,plain,
% 0.57/0.75 (((~((~injective(G!42, B!40, C!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, B!40)) | (~member(Y, C!39)) | (~apply(G!42, X1, Y)) | (~member(X1, B!40)) | (~apply(G!42, X2, Y))))) | (~(injective(G!42, B!40, C!39) | (~((~member(tptp_fun_Y_16(C!39, B!40, G!42), C!39)) | (~member(tptp_fun_X2_17(C!39, B!40, G!42), B!40)) | (~member(tptp_fun_X1_18(C!39, B!40, G!42), B!40)) | (~apply(G!42, tptp_fun_X2_17(C!39, B!40, G!42), tptp_fun_Y_16(C!39, B!40, G!42))) | (~apply(G!42, tptp_fun_X1_18(C!39, B!40, G!42), tptp_fun_Y_16(C!39, B!40, G!42))) | (tptp_fun_X1_18(C!39, B!40, G!42) = tptp_fun_X2_17(C!39, B!40, G!42))))))) | ((~injective(G!42, B!40, C!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, B!40)) | (~member(Y, C!39)) | (~apply(G!42, X1, Y)) | (~member(X1, B!40)) | (~apply(G!42, X2, Y))))),
% 0.57/0.75 inference(tautology,[status(thm)],[])).
% 0.57/0.75 tff(239,plain,
% 0.57/0.75 ((~injective(G!42, B!40, C!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, B!40)) | (~member(Y, C!39)) | (~apply(G!42, X1, Y)) | (~member(X1, B!40)) | (~apply(G!42, X2, Y)))),
% 0.57/0.75 inference(unit_resolution,[status(thm)],[238, 237])).
% 0.57/0.75 tff(240,plain,
% 0.57/0.75 ((~![F: $i, A: $i, B: $i] : (~(((~injective(F, A, B)) | (~surjective(F, A, B))) <=> one_to_one(F, A, B)))) | (~(((~injective(G!42, B!40, C!39)) | (~surjective(G!42, B!40, C!39))) <=> one_to_one(G!42, B!40, C!39)))),
% 0.57/0.75 inference(quant_inst,[status(thm)],[])).
% 0.57/0.75 tff(241,plain,
% 0.57/0.75 (~(((~injective(G!42, B!40, C!39)) | (~surjective(G!42, B!40, C!39))) <=> one_to_one(G!42, B!40, C!39))),
% 0.57/0.75 inference(unit_resolution,[status(thm)],[240, 106])).
% 0.57/0.75 tff(242,plain,
% 0.57/0.75 (one_to_one(G!42, B!40, C!39)),
% 0.57/0.75 inference(and_elim,[status(thm)],[109])).
% 0.57/0.75 tff(243,plain,
% 0.57/0.75 ((((~injective(G!42, B!40, C!39)) | (~surjective(G!42, B!40, C!39))) <=> one_to_one(G!42, B!40, C!39)) | (~((~injective(G!42, B!40, C!39)) | (~surjective(G!42, B!40, C!39)))) | (~one_to_one(G!42, B!40, C!39))),
% 0.57/0.75 inference(tautology,[status(thm)],[])).
% 0.57/0.75 tff(244,plain,
% 0.57/0.75 ((((~injective(G!42, B!40, C!39)) | (~surjective(G!42, B!40, C!39))) <=> one_to_one(G!42, B!40, C!39)) | (~((~injective(G!42, B!40, C!39)) | (~surjective(G!42, B!40, C!39))))),
% 0.57/0.75 inference(unit_resolution,[status(thm)],[243, 242])).
% 0.57/0.75 tff(245,plain,
% 0.57/0.75 (~((~injective(G!42, B!40, C!39)) | (~surjective(G!42, B!40, C!39)))),
% 0.57/0.75 inference(unit_resolution,[status(thm)],[244, 241])).
% 0.57/0.75 tff(246,plain,
% 0.57/0.75 (((~injective(G!42, B!40, C!39)) | (~surjective(G!42, B!40, C!39))) | injective(G!42, B!40, C!39)),
% 0.57/0.75 inference(tautology,[status(thm)],[])).
% 0.57/0.75 tff(247,plain,
% 0.57/0.75 (injective(G!42, B!40, C!39)),
% 0.57/0.75 inference(unit_resolution,[status(thm)],[246, 245])).
% 0.57/0.75 tff(248,plain,
% 0.57/0.75 ((~((~injective(G!42, B!40, C!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, B!40)) | (~member(Y, C!39)) | (~apply(G!42, X1, Y)) | (~member(X1, B!40)) | (~apply(G!42, X2, Y))))) | (~injective(G!42, B!40, C!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, B!40)) | (~member(Y, C!39)) | (~apply(G!42, X1, Y)) | (~member(X1, B!40)) | (~apply(G!42, X2, Y)))),
% 0.57/0.75 inference(tautology,[status(thm)],[])).
% 0.57/0.75 tff(249,plain,
% 0.57/0.75 ((~((~injective(G!42, B!40, C!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, B!40)) | (~member(Y, C!39)) | (~apply(G!42, X1, Y)) | (~member(X1, B!40)) | (~apply(G!42, X2, Y))))) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, B!40)) | (~member(Y, C!39)) | (~apply(G!42, X1, Y)) | (~member(X1, B!40)) | (~apply(G!42, X2, Y)))),
% 0.57/0.75 inference(unit_resolution,[status(thm)],[248, 247])).
% 0.57/0.75 tff(250,plain,
% 0.57/0.75 (![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, B!40)) | (~member(Y, C!39)) | (~apply(G!42, X1, Y)) | (~member(X1, B!40)) | (~apply(G!42, X2, Y)))),
% 0.57/0.75 inference(unit_resolution,[status(thm)],[249, 239])).
% 0.57/0.75 tff(251,plain,
% 0.57/0.75 (((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, B!40)) | (~member(Y, C!39)) | (~apply(G!42, X1, Y)) | (~member(X1, B!40)) | (~apply(G!42, X2, Y)))) | ((~member(tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), C!39)) | (~member(tptp_fun_Y_8(tptp_fun_Y2_12(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, inverse_function(G!42, B!40, C!39), inverse_function(F!43, A!41, B!40)), B!40)) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_X_14(A!41, C!39, 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A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, F!43, G!42), B!40)) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y2_12(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, inverse_function(G!42, B!40, C!39), inverse_function(F!43, A!41, B!40)), tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)))) | (tptp_fun_Y_8(tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, 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Y)))) | (~member(tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), C!39)) | (~member(tptp_fun_Y_8(tptp_fun_Y2_12(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, inverse_function(G!42, B!40, C!39), inverse_function(F!43, A!41, B!40)), B!40)) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, F!43, G!42), tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)))) | (~member(tptp_fun_Y_8(tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, F!43, G!42), B!40)) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y2_12(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, inverse_function(G!42, B!40, C!39), inverse_function(F!43, A!41, B!40)), tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)))) | (tptp_fun_Y_8(tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, F!43, G!42) = tptp_fun_Y_8(tptp_fun_Y2_12(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, inverse_function(G!42, B!40, C!39), inverse_function(F!43, A!41, B!40))))),
% 0.57/0.76 inference(rewrite,[status(thm)],[])).
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% 0.57/0.78 inference(modus_ponens,[status(thm)],[255, 254])).
% 0.57/0.78 tff(257,plain,
% 0.57/0.78 (tptp_fun_Y_8(tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, F!43, G!42) = tptp_fun_Y_8(tptp_fun_Y2_12(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, inverse_function(G!42, B!40, C!39), inverse_function(F!43, A!41, B!40))),
% 0.57/0.78 inference(unit_resolution,[status(thm)],[256, 39, 250, 76, 230, 228, 200])).
% 0.57/0.78 tff(258,plain,
% 0.57/0.78 (((~member(tptp_fun_Y_8(tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_Y_8(tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, F!43, G!42), tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39))))) | apply(F!43, tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_Y_8(tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, F!43, G!42))),
% 0.57/0.78 inference(tautology,[status(thm)],[])).
% 0.57/0.78 tff(259,plain,
% 0.57/0.78 (apply(F!43, tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_Y_8(tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, F!43, G!42))),
% 0.57/0.78 inference(unit_resolution,[status(thm)],[258, 226])).
% 0.57/0.78 tff(260,plain,
% 0.57/0.78 (^[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)))))))))))),
% 0.57/0.78 inference(bind,[status(th)],[])).
% 0.57/0.78 tff(261,plain,
% 0.57/0.78 (![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))))))))))),
% 0.57/0.78 inference(quant_intro,[status(thm)],[260])).
% 0.57/0.78 tff(262,plain,
% 0.57/0.78 (^[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)))))))))),
% 0.57/0.78 inference(bind,[status(th)],[])).
% 0.57/0.78 tff(263,plain,
% 0.57/0.78 (![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))))))))),
% 0.57/0.78 inference(quant_intro,[status(thm)],[262])).
% 0.57/0.78 tff(264,plain,
% 0.57/0.78 (^[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)))))))))),
% 0.57/0.78 inference(bind,[status(th)],[])).
% 0.57/0.78 tff(265,plain,
% 0.57/0.78 (![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))))))))),
% 0.57/0.78 inference(quant_intro,[status(thm)],[264])).
% 0.57/0.78 tff(266,plain,
% 0.57/0.78 (![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))))))))),
% 0.57/0.78 inference(transitivity,[status(thm)],[265, 263])).
% 0.57/0.78 tff(267,plain,
% 0.57/0.78 (^[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))))))))))),
% 0.57/0.79 inference(bind,[status(th)],[])).
% 0.57/0.79 tff(268,plain,
% 0.57/0.79 (![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))))))))),
% 0.57/0.79 inference(quant_intro,[status(thm)],[267])).
% 0.57/0.79 tff(269,plain,
% 0.57/0.79 (^[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))))))))),
% 0.57/0.79 inference(bind,[status(th)],[])).
% 0.57/0.79 tff(270,plain,
% 0.57/0.79 (![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)))))))),
% 0.57/0.79 inference(quant_intro,[status(thm)],[269])).
% 0.57/0.79 tff(271,plain,
% 0.57/0.79 (![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))))))),
% 0.57/0.79 inference(rewrite,[status(thm)],[])).
% 0.57/0.79 tff(272,plain,
% 0.57/0.79 (^[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)))))))),
% 0.57/0.79 inference(bind,[status(th)],[])).
% 0.57/0.79 tff(273,plain,
% 0.57/0.79 (![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))))))),
% 0.57/0.79 inference(quant_intro,[status(thm)],[272])).
% 0.57/0.79 tff(274,axiom,(![F: $i, A: $i, B: $i] : (maps(F, A, B) <=> (![X: $i] : (member(X, A) => ?[Y: $i] : (member(Y, B) & apply(F, X, Y))) & ![X: $i, Y1: $i, Y2: $i] : (((member(X, A) & member(Y1, B)) & member(Y2, B)) => ((apply(F, X, Y1) & apply(F, X, Y2)) => (Y1 = Y2)))))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+1.ax','maps')).
% 0.57/0.79 tff(275,plain,
% 0.57/0.79 (![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))))))),
% 0.57/0.79 inference(modus_ponens,[status(thm)],[274, 273])).
% 0.57/0.79 tff(276,plain,
% 0.57/0.79 (![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))))))),
% 0.57/0.79 inference(modus_ponens,[status(thm)],[275, 271])).
% 0.57/0.79 tff(277,plain,(
% 0.57/0.79 ![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))))))))),
% 0.57/0.79 inference(skolemize,[status(sab)],[276])).
% 0.57/0.79 tff(278,plain,
% 0.57/0.79 (![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)))))))),
% 0.57/0.79 inference(modus_ponens,[status(thm)],[277, 270])).
% 0.57/0.79 tff(279,plain,
% 0.57/0.79 (![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))))))))),
% 0.57/0.79 inference(modus_ponens,[status(thm)],[278, 268])).
% 0.57/0.79 tff(280,plain,
% 0.57/0.79 (![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))))))))),
% 0.57/0.79 inference(modus_ponens,[status(thm)],[279, 266])).
% 0.57/0.79 tff(281,plain,
% 0.57/0.79 (![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))))))))))),
% 0.57/0.79 inference(modus_ponens,[status(thm)],[280, 261])).
% 0.57/0.79 tff(282,plain,
% 0.57/0.79 (((~![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!41, B!40)) | (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!43), B!40)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!40, F!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)))))))) | (~(maps(F!43, A!41, B!40) | (~((~member(tptp_fun_X_4(B!40, A!41, F!43), A!41)) | (~![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X_4(B!40, A!41, F!43), Y)))))) | (~((~member(tptp_fun_Y2_5(B!40, A!41, F!43), B!40)) | (~member(tptp_fun_Y1_6(B!40, A!41, F!43), B!40)) | (~member(tptp_fun_X_7(B!40, A!41, F!43), A!41)) | (~apply(F!43, tptp_fun_X_7(B!40, A!41, F!43), tptp_fun_Y2_5(B!40, A!41, F!43))) | (~apply(F!43, tptp_fun_X_7(B!40, A!41, F!43), tptp_fun_Y1_6(B!40, A!41, F!43))) | (tptp_fun_Y1_6(B!40, A!41, F!43) = tptp_fun_Y2_5(B!40, A!41, 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!41, B!40)) | (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!43), B!40)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!40, F!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)))))))) | (~(maps(F!43, A!41, B!40) | (~((~member(tptp_fun_X_4(B!40, A!41, F!43), A!41)) | (~![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X_4(B!40, A!41, F!43), Y)))))) | (~((~member(tptp_fun_Y2_5(B!40, A!41, F!43), B!40)) | (~member(tptp_fun_Y1_6(B!40, A!41, F!43), B!40)) | (~member(tptp_fun_X_7(B!40, A!41, F!43), A!41)) | (~apply(F!43, tptp_fun_X_7(B!40, A!41, F!43), tptp_fun_Y2_5(B!40, A!41, F!43))) | (~apply(F!43, tptp_fun_X_7(B!40, A!41, F!43), tptp_fun_Y1_6(B!40, A!41, F!43))) | (tptp_fun_Y1_6(B!40, A!41, F!43) = tptp_fun_Y2_5(B!40, A!41, F!43)))))))))),
% 0.57/0.79 inference(rewrite,[status(thm)],[])).
% 0.57/0.79 tff(283,plain,
% 0.57/0.79 ((~((~((~maps(F!43, A!41, B!40)) | (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!43), B!40)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!40, F!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)) | (~member(Y2, B!40)))))))) | (~(maps(F!43, A!41, B!40) | (~((tptp_fun_Y1_6(B!40, A!41, F!43) = tptp_fun_Y2_5(B!40, A!41, F!43)) | (~apply(F!43, tptp_fun_X_7(B!40, A!41, F!43), tptp_fun_Y1_6(B!40, A!41, F!43))) | (~apply(F!43, tptp_fun_X_7(B!40, A!41, F!43), tptp_fun_Y2_5(B!40, A!41, F!43))) | (~member(tptp_fun_X_7(B!40, A!41, F!43), A!41)) | (~member(tptp_fun_Y1_6(B!40, A!41, F!43), B!40)) | (~member(tptp_fun_Y2_5(B!40, A!41, F!43), B!40)))) | (~((~member(tptp_fun_X_4(B!40, A!41, F!43), A!41)) | (~![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X_4(B!40, A!41, F!43), Y)))))))))) <=> (~((~((~maps(F!43, A!41, B!40)) | (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!43), B!40)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!40, F!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)))))))) | (~(maps(F!43, A!41, B!40) | (~((~member(tptp_fun_X_4(B!40, A!41, F!43), A!41)) | (~![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X_4(B!40, A!41, F!43), Y)))))) | (~((~member(tptp_fun_Y2_5(B!40, A!41, F!43), B!40)) | (~member(tptp_fun_Y1_6(B!40, A!41, F!43), B!40)) | (~member(tptp_fun_X_7(B!40, A!41, F!43), A!41)) | (~apply(F!43, tptp_fun_X_7(B!40, A!41, F!43), tptp_fun_Y2_5(B!40, A!41, F!43))) | (~apply(F!43, tptp_fun_X_7(B!40, A!41, F!43), tptp_fun_Y1_6(B!40, A!41, F!43))) | (tptp_fun_Y1_6(B!40, A!41, F!43) = tptp_fun_Y2_5(B!40, A!41, F!43))))))))),
% 0.57/0.79 inference(rewrite,[status(thm)],[])).
% 0.57/0.79 tff(284,plain,
% 0.57/0.79 (((~![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!41, B!40)) | (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!43), B!40)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!40, F!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)) | (~member(Y2, B!40)))))))) | (~(maps(F!43, A!41, B!40) | (~((tptp_fun_Y1_6(B!40, A!41, F!43) = tptp_fun_Y2_5(B!40, A!41, F!43)) | (~apply(F!43, tptp_fun_X_7(B!40, A!41, F!43), tptp_fun_Y1_6(B!40, A!41, F!43))) | (~apply(F!43, tptp_fun_X_7(B!40, A!41, F!43), tptp_fun_Y2_5(B!40, A!41, F!43))) | (~member(tptp_fun_X_7(B!40, A!41, F!43), A!41)) | (~member(tptp_fun_Y1_6(B!40, A!41, F!43), B!40)) | (~member(tptp_fun_Y2_5(B!40, A!41, F!43), B!40)))) | (~((~member(tptp_fun_X_4(B!40, A!41, F!43), A!41)) | (~![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X_4(B!40, A!41, 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!41, B!40)) | (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!43), B!40)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!40, F!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)))))))) | (~(maps(F!43, A!41, B!40) | (~((~member(tptp_fun_X_4(B!40, A!41, F!43), A!41)) | (~![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X_4(B!40, A!41, F!43), Y)))))) | (~((~member(tptp_fun_Y2_5(B!40, A!41, F!43), B!40)) | (~member(tptp_fun_Y1_6(B!40, A!41, F!43), B!40)) | (~member(tptp_fun_X_7(B!40, A!41, F!43), A!41)) | (~apply(F!43, tptp_fun_X_7(B!40, A!41, F!43), tptp_fun_Y2_5(B!40, A!41, F!43))) | (~apply(F!43, tptp_fun_X_7(B!40, A!41, F!43), tptp_fun_Y1_6(B!40, A!41, F!43))) | (tptp_fun_Y1_6(B!40, A!41, F!43) = tptp_fun_Y2_5(B!40, A!41, F!43)))))))))),
% 0.57/0.79 inference(monotonicity,[status(thm)],[283])).
% 0.57/0.79 tff(285,plain,
% 0.57/0.79 (((~![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!41, B!40)) | (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!43), B!40)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!40, F!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)) | (~member(Y2, B!40)))))))) | (~(maps(F!43, A!41, B!40) | (~((tptp_fun_Y1_6(B!40, A!41, F!43) = tptp_fun_Y2_5(B!40, A!41, F!43)) | (~apply(F!43, tptp_fun_X_7(B!40, A!41, F!43), tptp_fun_Y1_6(B!40, A!41, F!43))) | (~apply(F!43, tptp_fun_X_7(B!40, A!41, F!43), tptp_fun_Y2_5(B!40, A!41, F!43))) | (~member(tptp_fun_X_7(B!40, A!41, F!43), A!41)) | (~member(tptp_fun_Y1_6(B!40, A!41, F!43), B!40)) | (~member(tptp_fun_Y2_5(B!40, A!41, F!43), B!40)))) | (~((~member(tptp_fun_X_4(B!40, A!41, F!43), A!41)) | (~![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X_4(B!40, A!41, 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!41, B!40)) | (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!43), B!40)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!40, F!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)))))))) | (~(maps(F!43, A!41, B!40) | (~((~member(tptp_fun_X_4(B!40, A!41, F!43), A!41)) | (~![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X_4(B!40, A!41, F!43), Y)))))) | (~((~member(tptp_fun_Y2_5(B!40, A!41, F!43), B!40)) | (~member(tptp_fun_Y1_6(B!40, A!41, F!43), B!40)) | (~member(tptp_fun_X_7(B!40, A!41, F!43), A!41)) | (~apply(F!43, tptp_fun_X_7(B!40, A!41, F!43), tptp_fun_Y2_5(B!40, A!41, F!43))) | (~apply(F!43, tptp_fun_X_7(B!40, A!41, F!43), tptp_fun_Y1_6(B!40, A!41, F!43))) | (tptp_fun_Y1_6(B!40, A!41, F!43) = tptp_fun_Y2_5(B!40, A!41, F!43)))))))))),
% 0.64/0.80 inference(transitivity,[status(thm)],[284, 282])).
% 0.64/0.80 tff(286,plain,
% 0.64/0.80 ((~![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!41, B!40)) | (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!43), B!40)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!40, F!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)) | (~member(Y2, B!40)))))))) | (~(maps(F!43, A!41, B!40) | (~((tptp_fun_Y1_6(B!40, A!41, F!43) = tptp_fun_Y2_5(B!40, A!41, F!43)) | (~apply(F!43, tptp_fun_X_7(B!40, A!41, F!43), tptp_fun_Y1_6(B!40, A!41, F!43))) | (~apply(F!43, tptp_fun_X_7(B!40, A!41, F!43), tptp_fun_Y2_5(B!40, A!41, F!43))) | (~member(tptp_fun_X_7(B!40, A!41, F!43), A!41)) | (~member(tptp_fun_Y1_6(B!40, A!41, F!43), B!40)) | (~member(tptp_fun_Y2_5(B!40, A!41, F!43), B!40)))) | (~((~member(tptp_fun_X_4(B!40, A!41, F!43), A!41)) | (~![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X_4(B!40, A!41, F!43), Y))))))))))),
% 0.64/0.80 inference(quant_inst,[status(thm)],[])).
% 0.64/0.80 tff(287,plain,
% 0.64/0.80 ((~![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!41, B!40)) | (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!43), B!40)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!40, F!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)))))))) | (~(maps(F!43, A!41, B!40) | (~((~member(tptp_fun_X_4(B!40, A!41, F!43), A!41)) | (~![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X_4(B!40, A!41, F!43), Y)))))) | (~((~member(tptp_fun_Y2_5(B!40, A!41, F!43), B!40)) | (~member(tptp_fun_Y1_6(B!40, A!41, F!43), B!40)) | (~member(tptp_fun_X_7(B!40, A!41, F!43), A!41)) | (~apply(F!43, tptp_fun_X_7(B!40, A!41, F!43), tptp_fun_Y2_5(B!40, A!41, F!43))) | (~apply(F!43, tptp_fun_X_7(B!40, A!41, F!43), tptp_fun_Y1_6(B!40, A!41, F!43))) | (tptp_fun_Y1_6(B!40, A!41, F!43) = tptp_fun_Y2_5(B!40, A!41, F!43))))))))),
% 0.64/0.80 inference(modus_ponens,[status(thm)],[286, 285])).
% 0.64/0.80 tff(288,plain,
% 0.64/0.80 (~((~((~maps(F!43, A!41, B!40)) | (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!43), B!40)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!40, F!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)))))))) | (~(maps(F!43, A!41, B!40) | (~((~member(tptp_fun_X_4(B!40, A!41, F!43), A!41)) | (~![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X_4(B!40, A!41, F!43), Y)))))) | (~((~member(tptp_fun_Y2_5(B!40, A!41, F!43), B!40)) | (~member(tptp_fun_Y1_6(B!40, A!41, F!43), B!40)) | (~member(tptp_fun_X_7(B!40, A!41, F!43), A!41)) | (~apply(F!43, tptp_fun_X_7(B!40, A!41, F!43), tptp_fun_Y2_5(B!40, A!41, F!43))) | (~apply(F!43, tptp_fun_X_7(B!40, A!41, F!43), tptp_fun_Y1_6(B!40, A!41, F!43))) | (tptp_fun_Y1_6(B!40, A!41, F!43) = tptp_fun_Y2_5(B!40, A!41, F!43)))))))),
% 0.64/0.80 inference(unit_resolution,[status(thm)],[287, 281])).
% 0.64/0.80 tff(289,plain,
% 0.64/0.80 (((~((~maps(F!43, A!41, B!40)) | (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!43), B!40)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!40, F!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)))))))) | (~(maps(F!43, A!41, B!40) | (~((~member(tptp_fun_X_4(B!40, A!41, F!43), A!41)) | (~![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X_4(B!40, A!41, F!43), Y)))))) | (~((~member(tptp_fun_Y2_5(B!40, A!41, F!43), B!40)) | (~member(tptp_fun_Y1_6(B!40, A!41, F!43), B!40)) | (~member(tptp_fun_X_7(B!40, A!41, F!43), A!41)) | (~apply(F!43, tptp_fun_X_7(B!40, A!41, F!43), tptp_fun_Y2_5(B!40, A!41, F!43))) | (~apply(F!43, tptp_fun_X_7(B!40, A!41, F!43), tptp_fun_Y1_6(B!40, A!41, F!43))) | (tptp_fun_Y1_6(B!40, A!41, F!43) = tptp_fun_Y2_5(B!40, A!41, F!43))))))) | ((~maps(F!43, A!41, B!40)) | (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!43), B!40)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!40, F!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)))))))),
% 0.64/0.80 inference(tautology,[status(thm)],[])).
% 0.64/0.80 tff(290,plain,
% 0.64/0.80 ((~maps(F!43, A!41, B!40)) | (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!43), B!40)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!40, F!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40))))))),
% 0.64/0.80 inference(unit_resolution,[status(thm)],[289, 288])).
% 0.64/0.80 tff(291,plain,
% 0.64/0.80 (maps(F!43, A!41, B!40)),
% 0.64/0.80 inference(and_elim,[status(thm)],[109])).
% 0.64/0.80 tff(292,plain,
% 0.64/0.80 ((~((~maps(F!43, A!41, B!40)) | (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!43), B!40)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!40, F!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)))))))) | (~maps(F!43, A!41, B!40)) | (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!43), B!40)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!40, F!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40))))))),
% 0.64/0.80 inference(tautology,[status(thm)],[])).
% 0.64/0.80 tff(293,plain,
% 0.64/0.80 ((~((~maps(F!43, A!41, B!40)) | (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!43), B!40)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!40, F!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)))))))) | (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!43), B!40)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!40, F!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40))))))),
% 0.64/0.80 inference(unit_resolution,[status(thm)],[292, 291])).
% 0.64/0.80 tff(294,plain,
% 0.64/0.80 (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!43), B!40)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!40, F!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)))))),
% 0.64/0.80 inference(unit_resolution,[status(thm)],[293, 290])).
% 0.64/0.80 tff(295,plain,
% 0.64/0.80 (((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!43), B!40)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!40, F!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40))))) | ![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!43), B!40)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!40, F!43))))))),
% 0.64/0.80 inference(tautology,[status(thm)],[])).
% 0.64/0.80 tff(296,plain,
% 0.64/0.80 (![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!43), B!40)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!40, F!43))))))),
% 0.64/0.80 inference(unit_resolution,[status(thm)],[295, 294])).
% 0.64/0.80 tff(297,plain,
% 0.64/0.80 (((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!43), B!40)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!40, F!43))))))) | ((~member(tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), A!41)) | (~((~member(tptp_fun_Y_3(tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, F!43), B!40)) | (~apply(F!43, tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_Y_3(tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, F!43))))))) <=> ((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!43), B!40)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!40, F!43))))))) | (~member(tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), A!41)) | (~((~member(tptp_fun_Y_3(tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, F!43), B!40)) | (~apply(F!43, tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_Y_3(tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, F!43))))))),
% 0.64/0.80 inference(rewrite,[status(thm)],[])).
% 0.64/0.80 tff(298,plain,
% 0.64/0.80 ((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!43), B!40)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!40, F!43))))))) | ((~member(tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), A!41)) | (~((~member(tptp_fun_Y_3(tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, F!43), B!40)) | (~apply(F!43, tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_Y_3(tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, F!43))))))),
% 0.64/0.80 inference(quant_inst,[status(thm)],[])).
% 0.64/0.80 tff(299,plain,
% 0.64/0.80 ((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!43), B!40)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!40, F!43))))))) | (~member(tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), A!41)) | (~((~member(tptp_fun_Y_3(tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, F!43), B!40)) | (~apply(F!43, tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_Y_3(tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, F!43)))))),
% 0.64/0.80 inference(modus_ponens,[status(thm)],[298, 297])).
% 0.64/0.80 tff(300,plain,
% 0.64/0.80 (~((~member(tptp_fun_Y_3(tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, F!43), B!40)) | (~apply(F!43, tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_Y_3(tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, F!43))))),
% 0.64/0.80 inference(unit_resolution,[status(thm)],[299, 296, 202])).
% 0.64/0.80 tff(301,plain,
% 0.64/0.80 (((~member(tptp_fun_Y_3(tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, F!43), B!40)) | (~apply(F!43, tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_Y_3(tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, F!43)))) | apply(F!43, tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_Y_3(tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, F!43))),
% 0.64/0.81 inference(tautology,[status(thm)],[])).
% 0.64/0.81 tff(302,plain,
% 0.64/0.81 (apply(F!43, tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_Y_3(tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, F!43))),
% 0.64/0.81 inference(unit_resolution,[status(thm)],[301, 300])).
% 0.64/0.81 tff(303,plain,
% 0.64/0.81 (((~member(tptp_fun_Y_3(tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, F!43), B!40)) | (~apply(F!43, tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_Y_3(tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, F!43)))) | member(tptp_fun_Y_3(tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, F!43), B!40)),
% 0.64/0.81 inference(tautology,[status(thm)],[])).
% 0.64/0.81 tff(304,plain,
% 0.64/0.81 (member(tptp_fun_Y_3(tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, F!43), B!40)),
% 0.64/0.81 inference(unit_resolution,[status(thm)],[303, 300])).
% 0.64/0.81 tff(305,plain,
% 0.64/0.81 (((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!43), B!40)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!40, F!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40))))) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)))),
% 0.64/0.81 inference(tautology,[status(thm)],[])).
% 0.64/0.81 tff(306,plain,
% 0.64/0.81 (![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)))),
% 0.64/0.81 inference(unit_resolution,[status(thm)],[305, 294])).
% 0.64/0.81 tff(307,plain,
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% 0.64/0.82 inference(monotonicity,[status(thm)],[308])).
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% 0.64/0.82 inference(transitivity,[status(thm)],[309, 307])).
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% 0.64/0.83 inference(quant_inst,[status(thm)],[])).
% 0.64/0.83 tff(312,plain,
% 0.64/0.83 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)))) | (~member(tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), A!41)) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, F!43), B!40)) | (~apply(F!43, tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_Y_3(tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, F!43))) | (~apply(F!43, tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_Y_8(tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, F!43, G!42))) | (~member(tptp_fun_Y_8(tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, F!43, G!42), B!40)) | (tptp_fun_Y_8(tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, F!43, G!42) = tptp_fun_Y_3(tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, F!43))),
% 0.64/0.83 inference(modus_ponens,[status(thm)],[311, 310])).
% 0.64/0.83 tff(313,plain,
% 0.64/0.83 (tptp_fun_Y_8(tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, F!43, G!42) = tptp_fun_Y_3(tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, F!43)),
% 0.64/0.83 inference(unit_resolution,[status(thm)],[312, 306, 202, 304, 302, 230, 259])).
% 0.64/0.83 tff(314,plain,
% 0.64/0.83 (tptp_fun_Y_3(tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, F!43) = tptp_fun_Y_8(tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, F!43, G!42)),
% 0.64/0.83 inference(symmetry,[status(thm)],[313])).
% 0.64/0.83 tff(315,plain,
% 0.64/0.83 (tptp_fun_Y_3(tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, F!43) = tptp_fun_Y_8(tptp_fun_Y2_12(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, inverse_function(G!42, B!40, C!39), inverse_function(F!43, A!41, B!40))),
% 0.64/0.83 inference(transitivity,[status(thm)],[314, 257])).
% 0.64/0.83 tff(316,plain,
% 0.64/0.83 (tptp_fun_E_19(tptp_fun_Y_3(tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, F!43), A!41, F!43) = tptp_fun_E_19(tptp_fun_Y_8(tptp_fun_Y2_12(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, inverse_function(G!42, B!40, C!39), inverse_function(F!43, A!41, B!40)), A!41, F!43)),
% 0.64/0.83 inference(monotonicity,[status(thm)],[315])).
% 0.64/0.83 tff(317,plain,
% 0.64/0.83 (((~![Y: $i] : ((~member(Y, B!40)) | (~((~member(tptp_fun_E_19(Y, A!41, F!43), A!41)) | (~apply(F!43, tptp_fun_E_19(Y, A!41, F!43), Y)))))) | ((~member(tptp_fun_Y_3(tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, F!43), B!40)) | (~((~member(tptp_fun_E_19(tptp_fun_Y_3(tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, F!43), A!41, F!43), A!41)) | (~apply(F!43, tptp_fun_E_19(tptp_fun_Y_3(tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, F!43), A!41, F!43), tptp_fun_Y_3(tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, F!43))))))) <=> ((~![Y: $i] : ((~member(Y, B!40)) | (~((~member(tptp_fun_E_19(Y, A!41, F!43), A!41)) | (~apply(F!43, tptp_fun_E_19(Y, A!41, F!43), Y)))))) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, F!43), B!40)) | (~((~member(tptp_fun_E_19(tptp_fun_Y_3(tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, F!43), A!41, F!43), A!41)) | (~apply(F!43, tptp_fun_E_19(tptp_fun_Y_3(tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, F!43), A!41, F!43), tptp_fun_Y_3(tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, F!43))))))),
% 0.64/0.83 inference(rewrite,[status(thm)],[])).
% 0.64/0.83 tff(318,plain,
% 0.64/0.83 ((~![Y: $i] : ((~member(Y, B!40)) | (~((~member(tptp_fun_E_19(Y, A!41, F!43), A!41)) | (~apply(F!43, tptp_fun_E_19(Y, A!41, F!43), Y)))))) | ((~member(tptp_fun_Y_3(tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, F!43), B!40)) | (~((~member(tptp_fun_E_19(tptp_fun_Y_3(tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, F!43), A!41, F!43), A!41)) | (~apply(F!43, tptp_fun_E_19(tptp_fun_Y_3(tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, F!43), A!41, F!43), tptp_fun_Y_3(tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, F!43))))))),
% 0.64/0.83 inference(quant_inst,[status(thm)],[])).
% 0.64/0.83 tff(319,plain,
% 0.64/0.83 ((~![Y: $i] : ((~member(Y, B!40)) | (~((~member(tptp_fun_E_19(Y, A!41, F!43), A!41)) | (~apply(F!43, tptp_fun_E_19(Y, A!41, F!43), Y)))))) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, F!43), B!40)) | (~((~member(tptp_fun_E_19(tptp_fun_Y_3(tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, F!43), A!41, F!43), A!41)) | (~apply(F!43, tptp_fun_E_19(tptp_fun_Y_3(tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, F!43), A!41, F!43), tptp_fun_Y_3(tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, F!43)))))),
% 0.64/0.84 inference(modus_ponens,[status(thm)],[318, 317])).
% 0.64/0.84 tff(320,plain,
% 0.64/0.84 (~((~member(tptp_fun_E_19(tptp_fun_Y_3(tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, F!43), A!41, F!43), A!41)) | (~apply(F!43, tptp_fun_E_19(tptp_fun_Y_3(tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, F!43), A!41, F!43), tptp_fun_Y_3(tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, F!43))))),
% 0.64/0.84 inference(unit_resolution,[status(thm)],[319, 118, 304])).
% 0.64/0.84 tff(321,plain,
% 0.64/0.84 (((~member(tptp_fun_E_19(tptp_fun_Y_3(tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, F!43), A!41, F!43), A!41)) | (~apply(F!43, tptp_fun_E_19(tptp_fun_Y_3(tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, F!43), A!41, F!43), tptp_fun_Y_3(tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, F!43)))) | apply(F!43, tptp_fun_E_19(tptp_fun_Y_3(tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, F!43), A!41, F!43), tptp_fun_Y_3(tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, F!43))),
% 0.64/0.84 inference(tautology,[status(thm)],[])).
% 0.64/0.84 tff(322,plain,
% 0.64/0.84 (apply(F!43, tptp_fun_E_19(tptp_fun_Y_3(tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, F!43), A!41, F!43), tptp_fun_Y_3(tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, F!43))),
% 0.64/0.84 inference(unit_resolution,[status(thm)],[321, 320])).
% 0.64/0.84 tff(323,plain,
% 0.64/0.84 (((~member(tptp_fun_E_19(tptp_fun_Y_3(tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, F!43), A!41, F!43), A!41)) | (~apply(F!43, tptp_fun_E_19(tptp_fun_Y_3(tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, F!43), A!41, F!43), tptp_fun_Y_3(tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, F!43)))) | member(tptp_fun_E_19(tptp_fun_Y_3(tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, F!43), A!41, F!43), A!41)),
% 0.64/0.84 inference(tautology,[status(thm)],[])).
% 0.64/0.84 tff(324,plain,
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% 0.64/0.84 inference(unit_resolution,[status(thm)],[323, 320])).
% 0.64/0.84 tff(325,plain,
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% 0.64/0.84 inference(rewrite,[status(thm)],[])).
% 0.64/0.84 tff(326,plain,
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% 0.64/0.84 inference(rewrite,[status(thm)],[])).
% 0.64/0.84 tff(327,plain,
% 0.64/0.84 (((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!40)) | (~apply(F!43, X1, Y)) | (~member(X1, A!41)) | (~member(X2, A!41)) | (~apply(F!43, X2, Y)))) | ((tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)) = tptp_fun_E_19(tptp_fun_Y_3(tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, F!43), A!41, F!43)) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, F!43), B!40)) | (~apply(F!43, tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_Y_3(tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, F!43))) | (~member(tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), A!41)) | (~member(tptp_fun_E_19(tptp_fun_Y_3(tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, F!43), A!41, F!43), A!41)) | (~apply(F!43, tptp_fun_E_19(tptp_fun_Y_3(tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, F!43), A!41, F!43), tptp_fun_Y_3(tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, F!43))))) <=> ((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!40)) | (~apply(F!43, X1, Y)) | (~member(X1, A!41)) | (~member(X2, A!41)) | (~apply(F!43, X2, Y)))) | ((~member(tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), A!41)) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, F!43), B!40)) | (~apply(F!43, tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_Y_3(tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, F!43))) | (~member(tptp_fun_E_19(tptp_fun_Y_3(tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, F!43), A!41, F!43), A!41)) | (~apply(F!43, tptp_fun_E_19(tptp_fun_Y_3(tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, F!43), A!41, F!43), tptp_fun_Y_3(tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, F!43))) | (tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)) = tptp_fun_E_19(tptp_fun_Y_3(tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, F!43), A!41, F!43))))),
% 0.64/0.85 inference(monotonicity,[status(thm)],[326])).
% 0.64/0.85 tff(328,plain,
% 0.64/0.85 (((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!40)) | (~apply(F!43, X1, Y)) | (~member(X1, A!41)) | (~member(X2, A!41)) | (~apply(F!43, X2, Y)))) | ((tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)) = tptp_fun_E_19(tptp_fun_Y_3(tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, F!43), A!41, F!43)) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, F!43), B!40)) | (~apply(F!43, tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_Y_3(tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, F!43))) | (~member(tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), A!41)) | (~member(tptp_fun_E_19(tptp_fun_Y_3(tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, F!43), A!41, F!43), A!41)) | (~apply(F!43, tptp_fun_E_19(tptp_fun_Y_3(tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, F!43), A!41, F!43), tptp_fun_Y_3(tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, F!43))))) <=> ((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!40)) | (~apply(F!43, X1, Y)) | (~member(X1, A!41)) | (~member(X2, A!41)) | (~apply(F!43, X2, Y)))) | (~member(tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), A!41)) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, F!43), B!40)) | (~apply(F!43, tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_Y_3(tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, F!43))) | (~member(tptp_fun_E_19(tptp_fun_Y_3(tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, F!43), A!41, F!43), A!41)) | (~apply(F!43, tptp_fun_E_19(tptp_fun_Y_3(tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, F!43), A!41, F!43), tptp_fun_Y_3(tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, F!43))) | (tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)) = tptp_fun_E_19(tptp_fun_Y_3(tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, F!43), A!41, F!43)))),
% 0.64/0.85 inference(transitivity,[status(thm)],[327, 325])).
% 0.64/0.85 tff(329,plain,
% 0.64/0.85 ((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!40)) | (~apply(F!43, X1, Y)) | (~member(X1, A!41)) | (~member(X2, A!41)) | (~apply(F!43, X2, Y)))) | ((tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)) = tptp_fun_E_19(tptp_fun_Y_3(tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, F!43), A!41, F!43)) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, F!43), B!40)) | (~apply(F!43, tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_Y_3(tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, F!43))) | (~member(tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), A!41)) | (~member(tptp_fun_E_19(tptp_fun_Y_3(tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, F!43), A!41, F!43), A!41)) | (~apply(F!43, tptp_fun_E_19(tptp_fun_Y_3(tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, F!43), A!41, F!43), tptp_fun_Y_3(tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, F!43))))),
% 0.64/0.85 inference(quant_inst,[status(thm)],[])).
% 0.64/0.85 tff(330,plain,
% 0.64/0.85 ((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!40)) | (~apply(F!43, X1, Y)) | (~member(X1, A!41)) | (~member(X2, A!41)) | (~apply(F!43, X2, Y)))) | (~member(tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), A!41)) | (~member(tptp_fun_Y_3(tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, F!43), B!40)) | (~apply(F!43, tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_Y_3(tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, F!43))) | (~member(tptp_fun_E_19(tptp_fun_Y_3(tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, F!43), A!41, F!43), A!41)) | (~apply(F!43, tptp_fun_E_19(tptp_fun_Y_3(tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, F!43), A!41, F!43), tptp_fun_Y_3(tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, F!43))) | (tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)) = tptp_fun_E_19(tptp_fun_Y_3(tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, F!43), A!41, F!43))),
% 0.64/0.85 inference(modus_ponens,[status(thm)],[329, 328])).
% 0.64/0.85 tff(331,plain,
% 0.64/0.85 (tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)) = tptp_fun_E_19(tptp_fun_Y_3(tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), B!40, F!43), A!41, F!43)),
% 0.64/0.85 inference(unit_resolution,[status(thm)],[330, 202, 181, 304, 302, 324, 322])).
% 0.64/0.85 tff(332,plain,
% 0.64/0.85 (tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)) = tptp_fun_Y2_12(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39))),
% 0.64/0.85 inference(transitivity,[status(thm)],[331, 316, 188])).
% 0.64/0.85 tff(333,plain,
% 0.64/0.85 (((~apply(compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_Y2_12(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)))) | (~apply(inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39), tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)))) | (~member(tptp_fun_Y2_12(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), A!41)) | (~member(tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), A!41)) | (~member(tptp_fun_X_14(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)), C!39)) | (tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)) = tptp_fun_Y2_12(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)))) | (~(tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)) = tptp_fun_Y2_12(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39))))),
% 0.64/0.86 inference(tautology,[status(thm)],[])).
% 0.64/0.86 tff(334,plain,
% 0.64/0.86 (~(tptp_fun_Y1_13(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)) = tptp_fun_Y2_12(A!41, C!39, compose_function(inverse_function(F!43, A!41, B!40), inverse_function(G!42, B!40, C!39), C!39, B!40, A!41), inverse_function(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)))),
% 0.64/0.86 inference(unit_resolution,[status(thm)],[333, 37])).
% 0.64/0.86 tff(335,plain,
% 0.64/0.86 ($false),
% 0.64/0.86 inference(unit_resolution,[status(thm)],[334, 332])).
% 0.64/0.86 % SZS output end Proof
% 0.64/0.86 % E exiting
%------------------------------------------------------------------------------