%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET716+4 : TPTP v9.0.0. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n014.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 05:26:12 AM UTC 2025
% Result : Theorem 0.19s 0.39s
% Output : Proof 0.42s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET716+4 : TPTP v9.0.0. Bugfixed v2.2.1.
% 0.00/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n014.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 05:38:55 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.19/0.39 % SZS status Theorem
% 0.19/0.39 % SZS output start Proof
% 0.19/0.39 tff(apply_type, type, (
% 0.19/0.39 apply: ( $i * $i * $i ) > $o)).
% 0.19/0.39 tff(tptp_fun_Y_3_type, type, (
% 0.19/0.39 tptp_fun_Y_3: ( $i * $i * $i ) > $i)).
% 0.19/0.39 tff(tptp_fun_F_43_type, type, (
% 0.19/0.39 tptp_fun_F_43: $i)).
% 0.19/0.39 tff(tptp_fun_B_40_type, type, (
% 0.19/0.39 tptp_fun_B_40: $i)).
% 0.19/0.39 tff(tptp_fun_X2_17_type, type, (
% 0.19/0.39 tptp_fun_X2_17: ( $i * $i * $i ) > $i)).
% 0.19/0.39 tff(compose_function_type, type, (
% 0.19/0.39 compose_function: ( $i * $i * $i * $i * $i ) > $i)).
% 0.19/0.39 tff(tptp_fun_C_39_type, type, (
% 0.19/0.39 tptp_fun_C_39: $i)).
% 0.19/0.39 tff(tptp_fun_A_41_type, type, (
% 0.19/0.39 tptp_fun_A_41: $i)).
% 0.19/0.39 tff(tptp_fun_G_42_type, type, (
% 0.19/0.39 tptp_fun_G_42: $i)).
% 0.19/0.39 tff(tptp_fun_X1_18_type, type, (
% 0.19/0.39 tptp_fun_X1_18: ( $i * $i * $i ) > $i)).
% 0.19/0.39 tff(tptp_fun_Y_8_type, type, (
% 0.19/0.39 tptp_fun_Y_8: ( $i * $i * $i * $i * $i ) > $i)).
% 0.19/0.39 tff(tptp_fun_Y_16_type, type, (
% 0.19/0.39 tptp_fun_Y_16: ( $i * $i * $i ) > $i)).
% 0.19/0.39 tff(member_type, type, (
% 0.19/0.39 member: ( $i * $i ) > $o)).
% 0.19/0.39 tff(injective_type, type, (
% 0.19/0.39 injective: ( $i * $i * $i ) > $o)).
% 0.19/0.39 tff(maps_type, type, (
% 0.19/0.39 maps: ( $i * $i * $i ) > $o)).
% 0.19/0.39 tff(tptp_fun_Y2_5_type, type, (
% 0.19/0.39 tptp_fun_Y2_5: ( $i * $i * $i ) > $i)).
% 0.19/0.39 tff(tptp_fun_Y1_6_type, type, (
% 0.19/0.39 tptp_fun_Y1_6: ( $i * $i * $i ) > $i)).
% 0.19/0.39 tff(tptp_fun_X_7_type, type, (
% 0.19/0.39 tptp_fun_X_7: ( $i * $i * $i ) > $i)).
% 0.19/0.39 tff(tptp_fun_X_4_type, type, (
% 0.19/0.39 tptp_fun_X_4: ( $i * $i * $i ) > $i)).
% 0.19/0.39 tff(1,plain,
% 0.19/0.39 (^[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)))))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(2,plain,
% 0.19/0.39 (![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)))))))) <=> ![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))))))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.39 tff(3,plain,
% 0.19/0.39 (^[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)))))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(4,plain,
% 0.19/0.39 (![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)))))))) <=> ![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))))))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[3])).
% 0.19/0.39 tff(5,plain,
% 0.19/0.39 (![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)))))))) <=> ![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))))))))),
% 0.19/0.39 inference(transitivity,[status(thm)],[4, 2])).
% 0.19/0.39 tff(6,plain,
% 0.19/0.39 (^[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))))))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(7,plain,
% 0.19/0.39 (![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))))))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[6])).
% 0.19/0.39 tff(8,plain,
% 0.19/0.39 (![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)))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(9,plain,
% 0.19/0.39 (^[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))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(10,plain,
% 0.19/0.39 (![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)))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[9])).
% 0.19/0.39 tff(11,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')).
% 0.19/0.39 tff(12,plain,
% 0.19/0.39 (![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)))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.19/0.39 tff(13,plain,
% 0.19/0.39 (![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)))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[12, 8])).
% 0.19/0.39 tff(14,plain,(
% 0.19/0.39 ![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)))))))),
% 0.19/0.40 inference(skolemize,[status(sab)],[13])).
% 0.19/0.40 tff(15,plain,
% 0.19/0.40 (![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))))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[14, 7])).
% 0.19/0.40 tff(16,plain,
% 0.19/0.40 (![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))))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[15, 5])).
% 0.19/0.40 tff(17,plain,
% 0.19/0.40 (((~![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(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X1, A!41)) | (~member(Y, C!39)) | (~member(X2, A!41)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), X1, Y)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), X2, Y))))) | (~(injective(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39) | (~((~member(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)) = tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, 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(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X1, A!41)) | (~member(Y, C!39)) | (~member(X2, A!41)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), X1, Y)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), X2, Y))))) | (~(injective(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39) | (~((~member(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)) = tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(18,plain,
% 0.19/0.40 ((~((~((~injective(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), X1, Y)) | (~member(X2, A!41)) | (~member(X1, A!41)) | (~member(Y, C!39)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), X2, Y))))) | (~(injective(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39) | (~((tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)) = tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~member(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)))))))) <=> (~((~((~injective(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X1, A!41)) | (~member(Y, C!39)) | (~member(X2, A!41)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), X1, Y)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), X2, Y))))) | (~(injective(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39) | (~((~member(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)) = tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(19,plain,
% 0.19/0.40 (((~![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(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), X1, Y)) | (~member(X2, A!41)) | (~member(X1, A!41)) | (~member(Y, C!39)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), X2, Y))))) | (~(injective(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39) | (~((tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)) = tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~member(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), 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(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X1, A!41)) | (~member(Y, C!39)) | (~member(X2, A!41)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), X1, Y)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), X2, Y))))) | (~(injective(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39) | (~((~member(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)) = tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))))))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[18])).
% 0.19/0.41 tff(20,plain,
% 0.19/0.41 (((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), X1, Y)) | (~member(X2, A!41)) | (~member(X1, A!41)) | (~member(Y, C!39)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), X2, Y))))) | (~(injective(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39) | (~((tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)) = tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~member(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), 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(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X1, A!41)) | (~member(Y, C!39)) | (~member(X2, A!41)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), X1, Y)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), X2, Y))))) | (~(injective(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39) | (~((~member(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)) = tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))))))),
% 0.19/0.41 inference(transitivity,[status(thm)],[19, 17])).
% 0.19/0.41 tff(21,plain,
% 0.19/0.41 ((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), X1, Y)) | (~member(X2, A!41)) | (~member(X1, A!41)) | (~member(Y, C!39)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), X2, Y))))) | (~(injective(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39) | (~((tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)) = tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~member(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39))))))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(22,plain,
% 0.19/0.42 ((~![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(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X1, A!41)) | (~member(Y, C!39)) | (~member(X2, A!41)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), X1, Y)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), X2, Y))))) | (~(injective(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39) | (~((~member(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)) = tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.19/0.42 tff(23,plain,
% 0.19/0.42 (~((~((~injective(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X1, A!41)) | (~member(Y, C!39)) | (~member(X2, A!41)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), X1, Y)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), X2, Y))))) | (~(injective(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39) | (~((~member(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)) = tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[22, 16])).
% 0.19/0.42 tff(24,plain,
% 0.19/0.42 (((~((~injective(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X1, A!41)) | (~member(Y, C!39)) | (~member(X2, A!41)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), X1, Y)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), X2, Y))))) | (~(injective(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39) | (~((~member(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)) = tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))) | (injective(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39) | (~((~member(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)) = tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(25,plain,
% 0.19/0.42 (injective(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39) | (~((~member(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)) = tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[24, 23])).
% 0.19/0.42 tff(26,plain,
% 0.19/0.42 ((~![F: $i, G: $i, A: $i, B: $i, C: $i] : ((~(maps(F, A, B) & maps(G, B, C) & injective(F, A, B) & injective(G, B, C))) | injective(compose_function(G, F, A, B, C), A, C))) <=> (~![F: $i, G: $i, A: $i, B: $i, C: $i] : ((~(maps(F, A, B) & maps(G, B, C) & injective(F, A, B) & injective(G, B, C))) | injective(compose_function(G, F, A, B, C), A, C)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(27,plain,
% 0.19/0.42 ((~![F: $i, G: $i, A: $i, B: $i, C: $i] : ((((maps(F, A, B) & maps(G, B, C)) & injective(F, A, B)) & injective(G, B, C)) => injective(compose_function(G, F, A, B, C), A, C))) <=> (~![F: $i, G: $i, A: $i, B: $i, C: $i] : ((~(maps(F, A, B) & maps(G, B, C) & injective(F, A, B) & injective(G, B, C))) | injective(compose_function(G, F, A, B, C), A, C)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(28,axiom,(~![F: $i, G: $i, A: $i, B: $i, C: $i] : ((((maps(F, A, B) & maps(G, B, C)) & injective(F, A, B)) & injective(G, B, C)) => injective(compose_function(G, F, A, B, C), A, C))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thII07')).
% 0.19/0.42 tff(29,plain,
% 0.19/0.42 (~![F: $i, G: $i, A: $i, B: $i, C: $i] : ((~(maps(F, A, B) & maps(G, B, C) & injective(F, A, B) & injective(G, B, C))) | injective(compose_function(G, F, A, B, C), A, C))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.19/0.43 tff(30,plain,
% 0.19/0.43 (~![F: $i, G: $i, A: $i, B: $i, C: $i] : ((~(maps(F, A, B) & maps(G, B, C) & injective(F, A, B) & injective(G, B, C))) | injective(compose_function(G, F, A, B, C), A, C))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[29, 26])).
% 0.19/0.43 tff(31,plain,
% 0.19/0.43 (~![F: $i, G: $i, A: $i, B: $i, C: $i] : ((~(maps(F, A, B) & maps(G, B, C) & injective(F, A, B) & injective(G, B, C))) | injective(compose_function(G, F, A, B, C), A, C))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[30, 26])).
% 0.19/0.43 tff(32,plain,
% 0.19/0.43 (~![F: $i, G: $i, A: $i, B: $i, C: $i] : ((~(maps(F, A, B) & maps(G, B, C) & injective(F, A, B) & injective(G, B, C))) | injective(compose_function(G, F, A, B, C), A, C))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[31, 26])).
% 0.19/0.43 tff(33,plain,(
% 0.19/0.43 ~((~(maps(F!43, A!41, B!40) & maps(G!42, B!40, C!39) & injective(F!43, A!41, B!40) & injective(G!42, B!40, C!39))) | injective(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39))),
% 0.19/0.43 inference(skolemize,[status(sab)],[32])).
% 0.19/0.43 tff(34,plain,
% 0.19/0.43 (~injective(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)),
% 0.19/0.43 inference(or_elim,[status(thm)],[33])).
% 0.19/0.43 tff(35,plain,
% 0.19/0.43 ((~(injective(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39) | (~((~member(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)) = tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))) | injective(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39) | (~((~member(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)) = tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(36,plain,
% 0.19/0.43 ((~(injective(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39) | (~((~member(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)) = tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))) | (~((~member(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)) = tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[35, 34])).
% 0.19/0.43 tff(37,plain,
% 0.19/0.43 (~((~member(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)) = tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[36, 25])).
% 0.19/0.43 tff(38,plain,
% 0.19/0.43 (((~member(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)) = tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | member(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(39,plain,
% 0.19/0.43 (member(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[38, 37])).
% 0.19/0.43 tff(40,plain,
% 0.19/0.43 (^[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)))))))))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(41,plain,
% 0.19/0.43 (![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) | (~((~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))))))))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[40])).
% 0.19/0.43 tff(42,plain,
% 0.19/0.43 (^[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)))))))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(43,plain,
% 0.19/0.43 (![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) | (~((~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))))))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[42])).
% 0.19/0.43 tff(44,plain,
% 0.19/0.43 (^[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)))))))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(45,plain,
% 0.19/0.43 (![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) | (~((~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))))))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[44])).
% 0.19/0.43 tff(46,plain,
% 0.19/0.43 (![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) | (~((~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))))))))),
% 0.19/0.43 inference(transitivity,[status(thm)],[45, 43])).
% 0.19/0.43 tff(47,plain,
% 0.19/0.43 (^[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))))))))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(48,plain,
% 0.19/0.44 (![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))))))))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[47])).
% 0.19/0.44 tff(49,plain,
% 0.19/0.44 (^[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))))))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(50,plain,
% 0.19/0.44 (![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)))))))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[49])).
% 0.19/0.44 tff(51,plain,
% 0.19/0.44 (![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))))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(52,plain,
% 0.19/0.44 (^[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)))))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(53,plain,
% 0.19/0.44 (![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))))))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[52])).
% 0.19/0.44 tff(54,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')).
% 0.19/0.44 tff(55,plain,
% 0.19/0.44 (![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))))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.19/0.44 tff(56,plain,
% 0.19/0.44 (![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))))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[55, 51])).
% 0.19/0.44 tff(57,plain,(
% 0.19/0.44 ![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))))))))),
% 0.19/0.44 inference(skolemize,[status(sab)],[56])).
% 0.19/0.44 tff(58,plain,
% 0.19/0.44 (![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)))))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[57, 50])).
% 0.19/0.44 tff(59,plain,
% 0.19/0.44 (![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))))))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[58, 48])).
% 0.19/0.44 tff(60,plain,
% 0.19/0.44 (![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))))))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[59, 46])).
% 0.19/0.44 tff(61,plain,
% 0.19/0.44 (![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))))))))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[60, 41])).
% 0.19/0.44 tff(62,plain,
% 0.19/0.44 (((~![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)))))))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(63,plain,
% 0.19/0.45 ((~((~((~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))))))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(64,plain,
% 0.19/0.45 (((~![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)))))))))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[63])).
% 0.19/0.45 tff(65,plain,
% 0.19/0.45 (((~![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)))))))))),
% 0.19/0.45 inference(transitivity,[status(thm)],[64, 62])).
% 0.19/0.45 tff(66,plain,
% 0.19/0.45 ((~![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))))))))))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(67,plain,
% 0.19/0.45 ((~![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))))))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.19/0.46 tff(68,plain,
% 0.19/0.46 (~((~((~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)))))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[67, 61])).
% 0.19/0.46 tff(69,plain,
% 0.19/0.46 (((~((~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)))))))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(70,plain,
% 0.19/0.46 ((~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))))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[69, 68])).
% 0.19/0.46 tff(71,plain,
% 0.19/0.46 (maps(F!43, A!41, B!40) & maps(G!42, B!40, C!39) & injective(F!43, A!41, B!40) & injective(G!42, B!40, C!39)),
% 0.19/0.46 inference(or_elim,[status(thm)],[33])).
% 0.19/0.46 tff(72,plain,
% 0.19/0.46 (maps(F!43, A!41, B!40)),
% 0.19/0.46 inference(and_elim,[status(thm)],[71])).
% 0.19/0.46 tff(73,plain,
% 0.19/0.46 ((~((~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))))))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(74,plain,
% 0.19/0.46 ((~((~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))))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[73, 72])).
% 0.19/0.46 tff(75,plain,
% 0.19/0.46 (~((~![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)))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[74, 70])).
% 0.19/0.46 tff(76,plain,
% 0.19/0.46 (((~![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))))))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(77,plain,
% 0.19/0.46 (![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))))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[76, 75])).
% 0.19/0.46 tff(78,plain,
% 0.19/0.46 (((~![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_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~((~member(tptp_fun_Y_3(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), B!40)) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, 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_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~((~member(tptp_fun_Y_3(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), B!40)) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43))))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(79,plain,
% 0.19/0.46 ((~![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_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~((~member(tptp_fun_Y_3(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), B!40)) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43))))))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(80,plain,
% 0.19/0.47 ((~![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_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~((~member(tptp_fun_Y_3(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), B!40)) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43)))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.19/0.47 tff(81,plain,
% 0.19/0.47 (~((~member(tptp_fun_Y_3(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), B!40)) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[80, 77, 39])).
% 0.19/0.47 tff(82,plain,
% 0.19/0.47 (((~member(tptp_fun_Y_3(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), B!40)) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43)))) | apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(83,plain,
% 0.19/0.47 (apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[82, 81])).
% 0.19/0.47 tff(84,plain,
% 0.19/0.47 (((~member(tptp_fun_Y_3(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), B!40)) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43)))) | member(tptp_fun_Y_3(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), B!40)),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(85,plain,
% 0.19/0.47 (member(tptp_fun_Y_3(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), B!40)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[84, 81])).
% 0.19/0.47 tff(86,plain,
% 0.19/0.47 (((~member(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)) = tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | member(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(87,plain,
% 0.19/0.47 (member(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[86, 37])).
% 0.19/0.47 tff(88,plain,
% 0.19/0.47 (^[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)))))))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(89,plain,
% 0.19/0.47 (![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))))))))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[88])).
% 0.19/0.47 tff(90,plain,
% 0.19/0.47 (^[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)))))))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(91,plain,
% 0.19/0.47 (![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))))))))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[90])).
% 0.19/0.47 tff(92,plain,
% 0.19/0.47 (![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))))))))),
% 0.19/0.47 inference(transitivity,[status(thm)],[91, 89])).
% 0.19/0.47 tff(93,plain,
% 0.19/0.47 (^[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))))))))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(94,plain,
% 0.19/0.47 (![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))))))))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[93])).
% 0.19/0.47 tff(95,plain,
% 0.19/0.47 (![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))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(96,plain,
% 0.19/0.47 (^[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))))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(97,plain,
% 0.19/0.47 (![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))))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[96])).
% 0.19/0.47 tff(98,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')).
% 0.19/0.47 tff(99,plain,
% 0.19/0.47 (![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))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[98, 97])).
% 0.19/0.47 tff(100,plain,
% 0.19/0.47 (![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))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[99, 95])).
% 0.19/0.47 tff(101,plain,(
% 0.19/0.47 ![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))))))),
% 0.19/0.47 inference(skolemize,[status(sab)],[100])).
% 0.19/0.47 tff(102,plain,
% 0.19/0.47 (![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))))))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[101, 94])).
% 0.19/0.47 tff(103,plain,
% 0.19/0.47 (![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))))))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[102, 92])).
% 0.19/0.47 tff(104,plain,
% 0.19/0.47 (((~![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_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~((~(apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))) | (~((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))))))) <=> ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | (~member(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~((~(apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))) | (~((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(105,plain,
% 0.19/0.48 (((~member(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~((~(apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))) | (~((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))))))) <=> ((~member(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~((~(apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))) | (~((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(106,plain,
% 0.19/0.48 ((~((~((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))) | (~(apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))))) <=> (~((~(apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))) | (~((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(107,plain,
% 0.19/0.48 (((~member(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~((~((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))) | (~(apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))))) <=> ((~member(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~((~(apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))) | (~((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))))))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[106])).
% 0.19/0.48 tff(108,plain,
% 0.19/0.48 (((~member(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~((~((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))) | (~(apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))))) <=> ((~member(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~((~(apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))) | (~((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))))))),
% 0.19/0.49 inference(transitivity,[status(thm)],[107, 105])).
% 0.19/0.49 tff(109,plain,
% 0.19/0.49 (((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~((~((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))) | (~(apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))))))) <=> ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~((~(apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))) | (~((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))))))))),
% 0.19/0.49 inference(monotonicity,[status(thm)],[108])).
% 0.19/0.49 tff(110,plain,
% 0.19/0.49 (((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~((~((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))) | (~(apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))))))) <=> ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | (~member(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~((~(apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))) | (~((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))))))),
% 0.19/0.49 inference(transitivity,[status(thm)],[109, 104])).
% 0.19/0.49 tff(111,plain,
% 0.19/0.49 ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~((~((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))) | (~(apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))))))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(112,plain,
% 0.19/0.49 ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | (~member(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~((~(apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))) | (~((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[111, 110])).
% 0.19/0.49 tff(113,plain,
% 0.19/0.49 (~((~(apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))) | (~((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[112, 103, 87, 39])).
% 0.19/0.50 tff(114,plain,
% 0.19/0.50 (((~(apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))) | (~((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))))) | ((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))),
% 0.19/0.50 inference(tautology,[status(thm)],[])).
% 0.19/0.50 tff(115,plain,
% 0.19/0.50 ((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[114, 113])).
% 0.19/0.50 tff(116,plain,
% 0.19/0.50 (((~member(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)) = tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))),
% 0.19/0.50 inference(tautology,[status(thm)],[])).
% 0.19/0.50 tff(117,plain,
% 0.19/0.50 (apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[116, 37])).
% 0.19/0.50 tff(118,plain,
% 0.19/0.50 ((~((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))),
% 0.19/0.50 inference(tautology,[status(thm)],[])).
% 0.19/0.50 tff(119,plain,
% 0.19/0.50 ((~((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[118, 117])).
% 0.19/0.50 tff(120,plain,
% 0.19/0.50 (~((~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[119, 115])).
% 0.19/0.50 tff(121,plain,
% 0.19/0.50 (((~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))) | apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))),
% 0.19/0.50 inference(tautology,[status(thm)],[])).
% 0.19/0.50 tff(122,plain,
% 0.19/0.50 (apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[121, 120])).
% 0.19/0.50 tff(123,plain,
% 0.19/0.50 (((~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))) | member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)),
% 0.19/0.50 inference(tautology,[status(thm)],[])).
% 0.19/0.50 tff(124,plain,
% 0.19/0.51 (member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[123, 120])).
% 0.19/0.51 tff(125,plain,
% 0.19/0.51 (((~![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)))),
% 0.19/0.51 inference(tautology,[status(thm)],[])).
% 0.19/0.51 tff(126,plain,
% 0.19/0.51 (![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)))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[125, 75])).
% 0.19/0.51 tff(127,plain,
% 0.19/0.51 (((~![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_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~member(tptp_fun_Y_3(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), B!40)) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43))) | (tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42) = tptp_fun_Y_3(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), 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)))) | (~member(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~member(tptp_fun_Y_3(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), B!40)) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43))) | (tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42) = tptp_fun_Y_3(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43)))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(128,plain,
% 0.19/0.51 (((tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42) = tptp_fun_Y_3(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43)) | (~member(tptp_fun_Y_3(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), B!40)) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43))) | (~member(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40))) <=> ((~member(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~member(tptp_fun_Y_3(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), B!40)) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43))) | (tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42) = tptp_fun_Y_3(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43)))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(129,plain,
% 0.19/0.51 (((~![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)))) | ((tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42) = tptp_fun_Y_3(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43)) | (~member(tptp_fun_Y_3(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), B!40)) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43))) | (~member(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), 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)))) | ((~member(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~member(tptp_fun_Y_3(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), B!40)) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43))) | (tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42) = tptp_fun_Y_3(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43))))),
% 0.19/0.51 inference(monotonicity,[status(thm)],[128])).
% 0.19/0.51 tff(130,plain,
% 0.19/0.51 (((~![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)))) | ((tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42) = tptp_fun_Y_3(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43)) | (~member(tptp_fun_Y_3(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), B!40)) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43))) | (~member(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), 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)))) | (~member(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~member(tptp_fun_Y_3(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), B!40)) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43))) | (tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42) = tptp_fun_Y_3(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43)))),
% 0.19/0.51 inference(transitivity,[status(thm)],[129, 127])).
% 0.19/0.51 tff(131,plain,
% 0.19/0.51 ((~![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)))) | ((tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42) = tptp_fun_Y_3(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43)) | (~member(tptp_fun_Y_3(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), B!40)) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43))) | (~member(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)))),
% 0.19/0.52 inference(quant_inst,[status(thm)],[])).
% 0.19/0.52 tff(132,plain,
% 0.19/0.52 ((~![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_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~member(tptp_fun_Y_3(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), B!40)) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43))) | (tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42) = tptp_fun_Y_3(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[131, 130])).
% 0.19/0.52 tff(133,plain,
% 0.19/0.52 (tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42) = tptp_fun_Y_3(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43)),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[132, 126, 39, 124, 122, 85, 83])).
% 0.19/0.52 tff(134,plain,
% 0.19/0.52 (((~member(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)) = tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | member(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)),
% 0.19/0.52 inference(tautology,[status(thm)],[])).
% 0.19/0.52 tff(135,plain,
% 0.19/0.52 (member(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[134, 37])).
% 0.19/0.52 tff(136,plain,
% 0.19/0.52 (((~![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_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~((~(apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))) | (~((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))))))) <=> ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | (~member(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~((~(apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))) | (~((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))))))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(137,plain,
% 0.19/0.52 (((~member(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~((~(apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))) | (~((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))))))) <=> ((~member(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~((~(apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))) | (~((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))))))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(138,plain,
% 0.19/0.52 ((~((~((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))) | (~(apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))))) <=> (~((~(apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))) | (~((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))))))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(139,plain,
% 0.19/0.52 (((~member(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~((~((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))) | (~(apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))))) <=> ((~member(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~((~(apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))) | (~((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))))))),
% 0.19/0.53 inference(monotonicity,[status(thm)],[138])).
% 0.19/0.53 tff(140,plain,
% 0.19/0.53 (((~member(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~((~((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))) | (~(apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))))) <=> ((~member(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~((~(apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))) | (~((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))))))),
% 0.19/0.53 inference(transitivity,[status(thm)],[139, 137])).
% 0.19/0.53 tff(141,plain,
% 0.19/0.53 (((~![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_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~((~((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))) | (~(apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))))))) <=> ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~((~(apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))) | (~((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))))))))),
% 0.19/0.53 inference(monotonicity,[status(thm)],[140])).
% 0.19/0.53 tff(142,plain,
% 0.19/0.53 (((~![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_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~((~((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))) | (~(apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))))))) <=> ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | (~member(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~((~(apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))) | (~((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))))))),
% 0.19/0.54 inference(transitivity,[status(thm)],[141, 136])).
% 0.19/0.54 tff(143,plain,
% 0.19/0.54 ((~![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_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~((~((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))) | (~(apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))))))),
% 0.19/0.54 inference(quant_inst,[status(thm)],[])).
% 0.19/0.54 tff(144,plain,
% 0.19/0.54 ((~![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_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~((~(apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))) | (~((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))))))),
% 0.19/0.54 inference(modus_ponens,[status(thm)],[143, 142])).
% 0.19/0.54 tff(145,plain,
% 0.19/0.54 (~((~(apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))) | (~((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))))),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[144, 103, 87, 135])).
% 0.19/0.54 tff(146,plain,
% 0.19/0.54 (((~(apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))) | (~((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))))) | ((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))),
% 0.19/0.54 inference(tautology,[status(thm)],[])).
% 0.19/0.54 tff(147,plain,
% 0.19/0.54 ((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[146, 145])).
% 0.19/0.54 tff(148,plain,
% 0.19/0.54 (((~member(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)) = tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))),
% 0.19/0.54 inference(tautology,[status(thm)],[])).
% 0.19/0.54 tff(149,plain,
% 0.19/0.54 (apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[148, 37])).
% 0.19/0.54 tff(150,plain,
% 0.19/0.54 ((~((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))),
% 0.19/0.54 inference(tautology,[status(thm)],[])).
% 0.19/0.54 tff(151,plain,
% 0.19/0.54 ((~((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[150, 149])).
% 0.19/0.54 tff(152,plain,
% 0.19/0.54 (~((~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[151, 147])).
% 0.19/0.54 tff(153,plain,
% 0.19/0.54 (((~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))) | apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))),
% 0.19/0.55 inference(tautology,[status(thm)],[])).
% 0.19/0.55 tff(154,plain,
% 0.19/0.55 (apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[153, 152])).
% 0.19/0.55 tff(155,plain,
% 0.19/0.55 (((~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))) | member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)),
% 0.19/0.55 inference(tautology,[status(thm)],[])).
% 0.19/0.55 tff(156,plain,
% 0.19/0.55 (member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[155, 152])).
% 0.19/0.55 tff(157,plain,
% 0.19/0.55 (((~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))) | apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))),
% 0.19/0.55 inference(tautology,[status(thm)],[])).
% 0.19/0.55 tff(158,plain,
% 0.19/0.55 (apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[157, 120])).
% 0.19/0.55 tff(159,plain,
% 0.19/0.55 (((~![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)))))))))),
% 0.19/0.55 inference(rewrite,[status(thm)],[])).
% 0.19/0.55 tff(160,plain,
% 0.19/0.55 ((~((~((~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))))))))),
% 0.19/0.55 inference(rewrite,[status(thm)],[])).
% 0.19/0.55 tff(161,plain,
% 0.19/0.55 (((~![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)))))))))),
% 0.19/0.55 inference(monotonicity,[status(thm)],[160])).
% 0.19/0.55 tff(162,plain,
% 0.19/0.55 (((~![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)))))))))),
% 0.19/0.55 inference(transitivity,[status(thm)],[161, 159])).
% 0.19/0.55 tff(163,plain,
% 0.19/0.55 ((~![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))))))))),
% 0.19/0.55 inference(quant_inst,[status(thm)],[])).
% 0.19/0.55 tff(164,plain,
% 0.19/0.55 ((~![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))))))))),
% 0.19/0.55 inference(modus_ponens,[status(thm)],[163, 162])).
% 0.19/0.55 tff(165,plain,
% 0.19/0.55 (~((~((~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)))))))),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[164, 16])).
% 0.19/0.55 tff(166,plain,
% 0.19/0.55 (((~((~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))))),
% 0.19/0.55 inference(tautology,[status(thm)],[])).
% 0.19/0.55 tff(167,plain,
% 0.19/0.55 ((~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)))),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[166, 165])).
% 0.19/0.55 tff(168,plain,
% 0.19/0.55 (injective(G!42, B!40, C!39)),
% 0.19/0.55 inference(and_elim,[status(thm)],[71])).
% 0.19/0.55 tff(169,plain,
% 0.19/0.55 ((~((~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)))),
% 0.19/0.56 inference(tautology,[status(thm)],[])).
% 0.19/0.56 tff(170,plain,
% 0.19/0.56 ((~((~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)))),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[169, 168])).
% 0.19/0.56 tff(171,plain,
% 0.19/0.56 (![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)))),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[170, 167])).
% 0.19/0.56 tff(172,plain,
% 0.19/0.56 (((~![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_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42) = tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42)))) <=> ((~![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_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42) = tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42)))),
% 0.19/0.56 inference(rewrite,[status(thm)],[])).
% 0.19/0.56 tff(173,plain,
% 0.19/0.56 (((tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42) = tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42)) | (~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~member(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))) <=> ((~member(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42) = tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42)))),
% 0.19/0.56 inference(rewrite,[status(thm)],[])).
% 0.19/0.56 tff(174,plain,
% 0.19/0.56 (((~![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)))) | ((tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42) = tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42)) | (~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~member(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, 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)))) | ((~member(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42) = tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))))),
% 0.19/0.56 inference(monotonicity,[status(thm)],[173])).
% 0.19/0.56 tff(175,plain,
% 0.19/0.56 (((~![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)))) | ((tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42) = tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42)) | (~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~member(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, 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)))) | (~member(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42) = tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42)))),
% 0.19/0.57 inference(transitivity,[status(thm)],[174, 172])).
% 0.19/0.57 tff(176,plain,
% 0.19/0.57 ((~![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)))) | ((tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42) = tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42)) | (~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~member(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))),
% 0.19/0.57 inference(quant_inst,[status(thm)],[])).
% 0.19/0.57 tff(177,plain,
% 0.19/0.57 ((~![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_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42) = tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))),
% 0.40/0.57 inference(modus_ponens,[status(thm)],[176, 175])).
% 0.40/0.57 tff(178,plain,
% 0.40/0.57 (tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42) = tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42)),
% 0.40/0.57 inference(unit_resolution,[status(thm)],[177, 171, 87, 124, 158, 156, 154])).
% 0.40/0.57 tff(179,plain,
% 0.40/0.57 (tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42) = tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42)),
% 0.40/0.57 inference(symmetry,[status(thm)],[178])).
% 0.40/0.57 tff(180,plain,
% 0.40/0.57 (((~![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_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~((~member(tptp_fun_Y_3(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), B!40)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, 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_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~((~member(tptp_fun_Y_3(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), B!40)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43))))))),
% 0.40/0.57 inference(rewrite,[status(thm)],[])).
% 0.40/0.57 tff(181,plain,
% 0.40/0.57 ((~![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_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~((~member(tptp_fun_Y_3(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), B!40)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43))))))),
% 0.40/0.57 inference(quant_inst,[status(thm)],[])).
% 0.40/0.57 tff(182,plain,
% 0.40/0.57 ((~![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_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~((~member(tptp_fun_Y_3(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), B!40)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43)))))),
% 0.40/0.57 inference(modus_ponens,[status(thm)],[181, 180])).
% 0.40/0.57 tff(183,plain,
% 0.40/0.57 (~((~member(tptp_fun_Y_3(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), B!40)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43))))),
% 0.40/0.57 inference(unit_resolution,[status(thm)],[182, 77, 135])).
% 0.40/0.57 tff(184,plain,
% 0.40/0.57 (((~member(tptp_fun_Y_3(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), B!40)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43)))) | apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43))),
% 0.40/0.57 inference(tautology,[status(thm)],[])).
% 0.40/0.57 tff(185,plain,
% 0.40/0.57 (apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43))),
% 0.40/0.57 inference(unit_resolution,[status(thm)],[184, 183])).
% 0.40/0.57 tff(186,plain,
% 0.40/0.57 (((~member(tptp_fun_Y_3(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), B!40)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43)))) | member(tptp_fun_Y_3(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), B!40)),
% 0.40/0.57 inference(tautology,[status(thm)],[])).
% 0.40/0.57 tff(187,plain,
% 0.40/0.57 (member(tptp_fun_Y_3(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), B!40)),
% 0.40/0.57 inference(unit_resolution,[status(thm)],[186, 183])).
% 0.40/0.57 tff(188,plain,
% 0.40/0.57 (((~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))) | apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))),
% 0.40/0.57 inference(tautology,[status(thm)],[])).
% 0.40/0.57 tff(189,plain,
% 0.40/0.57 (apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))),
% 0.40/0.57 inference(unit_resolution,[status(thm)],[188, 152])).
% 0.40/0.57 tff(190,plain,
% 0.40/0.57 (((~![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_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~member(tptp_fun_Y_3(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), B!40)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43))) | (tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42) = tptp_fun_Y_3(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), 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)))) | (~member(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~member(tptp_fun_Y_3(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), B!40)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43))) | (tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42) = tptp_fun_Y_3(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43)))),
% 0.40/0.57 inference(rewrite,[status(thm)],[])).
% 0.40/0.57 tff(191,plain,
% 0.40/0.57 (((tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42) = tptp_fun_Y_3(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43)) | (~member(tptp_fun_Y_3(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), B!40)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43))) | (~member(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40))) <=> ((~member(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~member(tptp_fun_Y_3(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), B!40)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43))) | (tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42) = tptp_fun_Y_3(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43)))),
% 0.40/0.57 inference(rewrite,[status(thm)],[])).
% 0.40/0.57 tff(192,plain,
% 0.40/0.57 (((~![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)))) | ((tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42) = tptp_fun_Y_3(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43)) | (~member(tptp_fun_Y_3(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), B!40)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43))) | (~member(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), 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)))) | ((~member(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~member(tptp_fun_Y_3(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), B!40)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43))) | (tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42) = tptp_fun_Y_3(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43))))),
% 0.40/0.58 inference(monotonicity,[status(thm)],[191])).
% 0.40/0.58 tff(193,plain,
% 0.40/0.58 (((~![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)))) | ((tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42) = tptp_fun_Y_3(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43)) | (~member(tptp_fun_Y_3(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), B!40)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43))) | (~member(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), 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)))) | (~member(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~member(tptp_fun_Y_3(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), B!40)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43))) | (tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42) = tptp_fun_Y_3(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43)))),
% 0.40/0.58 inference(transitivity,[status(thm)],[192, 190])).
% 0.40/0.58 tff(194,plain,
% 0.40/0.58 ((~![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)))) | ((tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42) = tptp_fun_Y_3(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43)) | (~member(tptp_fun_Y_3(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), B!40)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43))) | (~member(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)))),
% 0.40/0.58 inference(quant_inst,[status(thm)],[])).
% 0.40/0.58 tff(195,plain,
% 0.40/0.58 ((~![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_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~member(tptp_fun_Y_3(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), B!40)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43))) | (tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42) = tptp_fun_Y_3(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43))),
% 0.40/0.58 inference(modus_ponens,[status(thm)],[194, 193])).
% 0.40/0.58 tff(196,plain,
% 0.40/0.58 (tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42) = tptp_fun_Y_3(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43)),
% 0.42/0.58 inference(unit_resolution,[status(thm)],[195, 126, 135, 156, 189, 187, 185])).
% 0.42/0.58 tff(197,plain,
% 0.42/0.58 (tptp_fun_Y_3(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43) = tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42)),
% 0.42/0.58 inference(symmetry,[status(thm)],[196])).
% 0.42/0.58 tff(198,plain,
% 0.42/0.58 (tptp_fun_Y_3(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43) = tptp_fun_Y_3(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43)),
% 0.42/0.58 inference(transitivity,[status(thm)],[197, 179, 133])).
% 0.42/0.58 tff(199,plain,
% 0.42/0.58 (apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43)) <=> apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43))),
% 0.42/0.58 inference(monotonicity,[status(thm)],[198])).
% 0.42/0.58 tff(200,plain,
% 0.42/0.58 (apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43)) <=> apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43))),
% 0.42/0.58 inference(symmetry,[status(thm)],[199])).
% 0.42/0.58 tff(201,plain,
% 0.42/0.58 (apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43))),
% 0.42/0.58 inference(modus_ponens,[status(thm)],[83, 200])).
% 0.42/0.58 tff(202,plain,
% 0.42/0.58 (((~member(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)) = tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)) = tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))),
% 0.42/0.58 inference(tautology,[status(thm)],[])).
% 0.42/0.58 tff(203,plain,
% 0.42/0.58 (~(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)) = tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))),
% 0.42/0.58 inference(unit_resolution,[status(thm)],[202, 37])).
% 0.42/0.58 tff(204,plain,
% 0.42/0.58 (((~![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_X2_17(B!40, A!41, F!43), A!41)) | (~member(tptp_fun_X1_18(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_X2_17(B!40, A!41, F!43), A!41)) | (~member(tptp_fun_X1_18(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)))))))))),
% 0.42/0.59 inference(rewrite,[status(thm)],[])).
% 0.42/0.59 tff(205,plain,
% 0.42/0.59 ((~((~((~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_X2_17(B!40, A!41, F!43), A!41)) | (~member(tptp_fun_X1_18(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))))))))),
% 0.42/0.59 inference(rewrite,[status(thm)],[])).
% 0.42/0.59 tff(206,plain,
% 0.42/0.59 (((~![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_X2_17(B!40, A!41, F!43), A!41)) | (~member(tptp_fun_X1_18(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)))))))))),
% 0.42/0.59 inference(monotonicity,[status(thm)],[205])).
% 0.42/0.59 tff(207,plain,
% 0.42/0.59 (((~![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_X2_17(B!40, A!41, F!43), A!41)) | (~member(tptp_fun_X1_18(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)))))))))),
% 0.42/0.59 inference(transitivity,[status(thm)],[206, 204])).
% 0.42/0.59 tff(208,plain,
% 0.42/0.59 ((~![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))))))))),
% 0.42/0.59 inference(quant_inst,[status(thm)],[])).
% 0.42/0.59 tff(209,plain,
% 0.42/0.59 ((~![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_X2_17(B!40, A!41, F!43), A!41)) | (~member(tptp_fun_X1_18(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))))))))),
% 0.42/0.59 inference(modus_ponens,[status(thm)],[208, 207])).
% 0.42/0.59 tff(210,plain,
% 0.42/0.59 (~((~((~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_X2_17(B!40, A!41, F!43), A!41)) | (~member(tptp_fun_X1_18(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)))))))),
% 0.42/0.59 inference(unit_resolution,[status(thm)],[209, 16])).
% 0.42/0.59 tff(211,plain,
% 0.42/0.59 (((~((~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_X2_17(B!40, A!41, F!43), A!41)) | (~member(tptp_fun_X1_18(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))))),
% 0.42/0.59 inference(tautology,[status(thm)],[])).
% 0.42/0.59 tff(212,plain,
% 0.42/0.59 ((~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)))),
% 0.42/0.59 inference(unit_resolution,[status(thm)],[211, 210])).
% 0.42/0.59 tff(213,plain,
% 0.42/0.59 (injective(F!43, A!41, B!40)),
% 0.42/0.59 inference(and_elim,[status(thm)],[71])).
% 0.42/0.59 tff(214,plain,
% 0.42/0.59 ((~((~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)))),
% 0.42/0.59 inference(tautology,[status(thm)],[])).
% 0.42/0.59 tff(215,plain,
% 0.42/0.59 ((~((~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)))),
% 0.42/0.59 inference(unit_resolution,[status(thm)],[214, 213])).
% 0.42/0.59 tff(216,plain,
% 0.42/0.59 (![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)))),
% 0.42/0.59 inference(unit_resolution,[status(thm)],[215, 212])).
% 0.42/0.59 tff(217,plain,
% 0.42/0.59 (((~![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_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)) = tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | (~member(tptp_fun_Y_3(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), B!40)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43))) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, 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_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)) = tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | (~member(tptp_fun_Y_3(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), B!40)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43))) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43))))),
% 0.42/0.59 inference(rewrite,[status(thm)],[])).
% 0.42/0.59 tff(218,plain,
% 0.42/0.59 (((tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)) = tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | (~member(tptp_fun_Y_3(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), B!40)) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43))) | (~member(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43)))) <=> ((~member(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)) = tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | (~member(tptp_fun_Y_3(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), B!40)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43))) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43))))),
% 0.42/0.60 inference(rewrite,[status(thm)],[])).
% 0.42/0.60 tff(219,plain,
% 0.42/0.60 (((~![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_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)) = tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | (~member(tptp_fun_Y_3(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), B!40)) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43))) | (~member(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, 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_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)) = tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | (~member(tptp_fun_Y_3(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), B!40)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43))) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43)))))),
% 0.42/0.60 inference(monotonicity,[status(thm)],[218])).
% 0.42/0.60 tff(220,plain,
% 0.42/0.60 (((~![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_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)) = tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | (~member(tptp_fun_Y_3(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), B!40)) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43))) | (~member(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, 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_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)) = tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | (~member(tptp_fun_Y_3(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), B!40)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43))) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43))))),
% 0.42/0.60 inference(transitivity,[status(thm)],[219, 217])).
% 0.42/0.60 tff(221,plain,
% 0.42/0.60 ((~![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_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)) = tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | (~member(tptp_fun_Y_3(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), B!40)) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43))) | (~member(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43))))),
% 0.42/0.60 inference(quant_inst,[status(thm)],[])).
% 0.42/0.60 tff(222,plain,
% 0.42/0.60 ((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!40)) | (~apply(F!43, X1, Y)) | (~member(X1, A!41)) | (~member(X2, A!41)) | (~apply(F!43, X2, Y)))) | (~member(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)) = tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | (~member(tptp_fun_Y_3(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), B!40)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43))) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43)))),
% 0.42/0.60 inference(modus_ponens,[status(thm)],[221, 220])).
% 0.42/0.60 tff(223,plain,
% 0.42/0.60 (~apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43))),
% 0.42/0.60 inference(unit_resolution,[status(thm)],[222, 216, 135, 39, 203, 187, 185])).
% 0.42/0.60 tff(224,plain,
% 0.42/0.60 ($false),
% 0.42/0.60 inference(unit_resolution,[status(thm)],[223, 201])).
% 0.42/0.60 % SZS output end Proof
% 0.42/0.60 % E exiting
%------------------------------------------------------------------------------