%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET733+4 : TPTP v9.0.0. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:26:14 AM UTC 2025
% Result : Theorem 0.22s 0.41s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : SET733+4 : TPTP v9.0.0. Bugfixed v2.2.1.
% 0.08/0.14 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n013.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Jun 20 05:39:23 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.22/0.41 % SZS status Theorem
% 0.22/0.41 % SZS output start Proof
% 0.22/0.41 tff(apply_type, type, (
% 0.22/0.41 apply: ( $i * $i * $i ) > $o)).
% 0.22/0.41 tff(tptp_fun_X1_18_type, type, (
% 0.22/0.41 tptp_fun_X1_18: ( $i * $i * $i ) > $i)).
% 0.22/0.41 tff(tptp_fun_F_42_type, type, (
% 0.22/0.41 tptp_fun_F_42: $i)).
% 0.22/0.41 tff(tptp_fun_A_40_type, type, (
% 0.22/0.41 tptp_fun_A_40: $i)).
% 0.22/0.41 tff(tptp_fun_B_39_type, type, (
% 0.22/0.41 tptp_fun_B_39: $i)).
% 0.22/0.41 tff(tptp_fun_Y_16_type, type, (
% 0.22/0.41 tptp_fun_Y_16: ( $i * $i * $i ) > $i)).
% 0.22/0.41 tff(tptp_fun_G_41_type, type, (
% 0.22/0.41 tptp_fun_G_41: $i)).
% 0.22/0.41 tff(tptp_fun_Y_8_type, type, (
% 0.22/0.41 tptp_fun_Y_8: ( $i * $i * $i * $i * $i ) > $i)).
% 0.22/0.41 tff(member_type, type, (
% 0.22/0.41 member: ( $i * $i ) > $o)).
% 0.22/0.41 tff(compose_function_type, type, (
% 0.22/0.41 compose_function: ( $i * $i * $i * $i * $i ) > $i)).
% 0.22/0.41 tff(tptp_fun_X2_17_type, type, (
% 0.22/0.41 tptp_fun_X2_17: ( $i * $i * $i ) > $i)).
% 0.22/0.41 tff(injective_type, type, (
% 0.22/0.41 injective: ( $i * $i * $i ) > $o)).
% 0.22/0.41 tff(identity_type, type, (
% 0.22/0.41 identity: ( $i * $i ) > $o)).
% 0.22/0.41 tff(maps_type, type, (
% 0.22/0.41 maps: ( $i * $i * $i ) > $o)).
% 0.22/0.41 tff(tptp_fun_X_15_type, type, (
% 0.22/0.41 tptp_fun_X_15: ( $i * $i ) > $i)).
% 0.22/0.41 tff(tptp_fun_Y_3_type, type, (
% 0.22/0.41 tptp_fun_Y_3: ( $i * $i * $i ) > $i)).
% 0.22/0.41 tff(tptp_fun_Y2_5_type, type, (
% 0.22/0.41 tptp_fun_Y2_5: ( $i * $i * $i ) > $i)).
% 0.22/0.41 tff(tptp_fun_Y1_6_type, type, (
% 0.22/0.41 tptp_fun_Y1_6: ( $i * $i * $i ) > $i)).
% 0.22/0.41 tff(tptp_fun_X_7_type, type, (
% 0.22/0.41 tptp_fun_X_7: ( $i * $i * $i ) > $i)).
% 0.22/0.41 tff(tptp_fun_X_4_type, type, (
% 0.22/0.41 tptp_fun_X_4: ( $i * $i * $i ) > $i)).
% 0.22/0.41 tff(1,plain,
% 0.22/0.41 (^[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)))))))))),
% 0.22/0.41 inference(bind,[status(th)],[])).
% 0.22/0.41 tff(2,plain,
% 0.22/0.41 (![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)))))))) <=> ![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))))))))),
% 0.22/0.41 inference(quant_intro,[status(thm)],[1])).
% 0.22/0.41 tff(3,plain,
% 0.22/0.41 (^[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)))))))))),
% 0.22/0.42 inference(bind,[status(th)],[])).
% 0.22/0.42 tff(4,plain,
% 0.22/0.42 (![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)))))))) <=> ![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))))))))),
% 0.22/0.42 inference(quant_intro,[status(thm)],[3])).
% 0.22/0.42 tff(5,plain,
% 0.22/0.42 (![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)))))))) <=> ![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))))))))),
% 0.22/0.42 inference(transitivity,[status(thm)],[4, 2])).
% 0.22/0.42 tff(6,plain,
% 0.22/0.42 (^[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))))))))))),
% 0.22/0.42 inference(bind,[status(th)],[])).
% 0.22/0.42 tff(7,plain,
% 0.22/0.42 (![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))))))))),
% 0.22/0.42 inference(quant_intro,[status(thm)],[6])).
% 0.22/0.42 tff(8,plain,
% 0.22/0.42 (![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)))))),
% 0.22/0.42 inference(rewrite,[status(thm)],[])).
% 0.22/0.42 tff(9,plain,
% 0.22/0.42 (^[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))))))),
% 0.22/0.42 inference(bind,[status(th)],[])).
% 0.22/0.42 tff(10,plain,
% 0.22/0.42 (![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)))))),
% 0.22/0.42 inference(quant_intro,[status(thm)],[9])).
% 0.22/0.42 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/sandbox/benchmark/Axioms/SET006+1.ax','injective')).
% 0.22/0.42 tff(12,plain,
% 0.22/0.42 (![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)))))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.22/0.42 tff(13,plain,
% 0.22/0.42 (![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)))))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[12, 8])).
% 0.22/0.42 tff(14,plain,(
% 0.22/0.42 ![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)))))))),
% 0.22/0.42 inference(skolemize,[status(sab)],[13])).
% 0.22/0.42 tff(15,plain,
% 0.22/0.42 (![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))))))))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[14, 7])).
% 0.22/0.42 tff(16,plain,
% 0.22/0.42 (![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))))))))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[15, 5])).
% 0.22/0.42 tff(17,plain,
% 0.22/0.42 (((~![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(F!42, A!40, B!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!39)) | (~apply(F!42, X1, Y)) | (~member(X1, A!40)) | (~member(X2, A!40)) | (~apply(F!42, X2, Y))))) | (~(injective(F!42, A!40, B!39) | (~((~member(tptp_fun_Y_16(B!39, A!40, F!42), B!39)) | (~member(tptp_fun_X1_18(B!39, A!40, F!42), A!40)) | (~member(tptp_fun_X2_17(B!39, A!40, F!42), A!40)) | (~apply(F!42, tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_Y_16(B!39, A!40, F!42))) | (~apply(F!42, tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_Y_16(B!39, A!40, F!42))) | (tptp_fun_X1_18(B!39, A!40, F!42) = tptp_fun_X2_17(B!39, A!40, F!42))))))))) <=> ((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(F!42, A!40, B!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!39)) | (~apply(F!42, X1, Y)) | (~member(X1, A!40)) | (~member(X2, A!40)) | (~apply(F!42, X2, Y))))) | (~(injective(F!42, A!40, B!39) | (~((~member(tptp_fun_Y_16(B!39, A!40, F!42), B!39)) | (~member(tptp_fun_X1_18(B!39, A!40, F!42), A!40)) | (~member(tptp_fun_X2_17(B!39, A!40, F!42), A!40)) | (~apply(F!42, tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_Y_16(B!39, A!40, F!42))) | (~apply(F!42, tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_Y_16(B!39, A!40, F!42))) | (tptp_fun_X1_18(B!39, A!40, F!42) = tptp_fun_X2_17(B!39, A!40, F!42)))))))))),
% 0.22/0.42 inference(rewrite,[status(thm)],[])).
% 0.22/0.42 tff(18,plain,
% 0.22/0.42 ((~((~((~injective(F!42, A!40, B!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!42, X1, Y)) | (~member(X2, A!40)) | (~member(X1, A!40)) | (~member(Y, B!39)) | (~apply(F!42, X2, Y))))) | (~(injective(F!42, A!40, B!39) | (~((tptp_fun_X1_18(B!39, A!40, F!42) = tptp_fun_X2_17(B!39, A!40, F!42)) | (~apply(F!42, tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_Y_16(B!39, A!40, F!42))) | (~apply(F!42, tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_Y_16(B!39, A!40, F!42))) | (~member(tptp_fun_X1_18(B!39, A!40, F!42), A!40)) | (~member(tptp_fun_X2_17(B!39, A!40, F!42), A!40)) | (~member(tptp_fun_Y_16(B!39, A!40, F!42), B!39)))))))) <=> (~((~((~injective(F!42, A!40, B!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!39)) | (~apply(F!42, X1, Y)) | (~member(X1, A!40)) | (~member(X2, A!40)) | (~apply(F!42, X2, Y))))) | (~(injective(F!42, A!40, B!39) | (~((~member(tptp_fun_Y_16(B!39, A!40, F!42), B!39)) | (~member(tptp_fun_X1_18(B!39, A!40, F!42), A!40)) | (~member(tptp_fun_X2_17(B!39, A!40, F!42), A!40)) | (~apply(F!42, tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_Y_16(B!39, A!40, F!42))) | (~apply(F!42, tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_Y_16(B!39, A!40, F!42))) | (tptp_fun_X1_18(B!39, A!40, F!42) = tptp_fun_X2_17(B!39, A!40, F!42))))))))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(19,plain,
% 0.22/0.43 (((~![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!42, A!40, B!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!42, X1, Y)) | (~member(X2, A!40)) | (~member(X1, A!40)) | (~member(Y, B!39)) | (~apply(F!42, X2, Y))))) | (~(injective(F!42, A!40, B!39) | (~((tptp_fun_X1_18(B!39, A!40, F!42) = tptp_fun_X2_17(B!39, A!40, F!42)) | (~apply(F!42, tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_Y_16(B!39, A!40, F!42))) | (~apply(F!42, tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_Y_16(B!39, A!40, F!42))) | (~member(tptp_fun_X1_18(B!39, A!40, F!42), A!40)) | (~member(tptp_fun_X2_17(B!39, A!40, F!42), A!40)) | (~member(tptp_fun_Y_16(B!39, A!40, F!42), B!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(F!42, A!40, B!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!39)) | (~apply(F!42, X1, Y)) | (~member(X1, A!40)) | (~member(X2, A!40)) | (~apply(F!42, X2, Y))))) | (~(injective(F!42, A!40, B!39) | (~((~member(tptp_fun_Y_16(B!39, A!40, F!42), B!39)) | (~member(tptp_fun_X1_18(B!39, A!40, F!42), A!40)) | (~member(tptp_fun_X2_17(B!39, A!40, F!42), A!40)) | (~apply(F!42, tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_Y_16(B!39, A!40, F!42))) | (~apply(F!42, tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_Y_16(B!39, A!40, F!42))) | (tptp_fun_X1_18(B!39, A!40, F!42) = tptp_fun_X2_17(B!39, A!40, F!42)))))))))),
% 0.22/0.43 inference(monotonicity,[status(thm)],[18])).
% 0.22/0.43 tff(20,plain,
% 0.22/0.43 (((~![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!42, A!40, B!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!42, X1, Y)) | (~member(X2, A!40)) | (~member(X1, A!40)) | (~member(Y, B!39)) | (~apply(F!42, X2, Y))))) | (~(injective(F!42, A!40, B!39) | (~((tptp_fun_X1_18(B!39, A!40, F!42) = tptp_fun_X2_17(B!39, A!40, F!42)) | (~apply(F!42, tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_Y_16(B!39, A!40, F!42))) | (~apply(F!42, tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_Y_16(B!39, A!40, F!42))) | (~member(tptp_fun_X1_18(B!39, A!40, F!42), A!40)) | (~member(tptp_fun_X2_17(B!39, A!40, F!42), A!40)) | (~member(tptp_fun_Y_16(B!39, A!40, F!42), B!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(F!42, A!40, B!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!39)) | (~apply(F!42, X1, Y)) | (~member(X1, A!40)) | (~member(X2, A!40)) | (~apply(F!42, X2, Y))))) | (~(injective(F!42, A!40, B!39) | (~((~member(tptp_fun_Y_16(B!39, A!40, F!42), B!39)) | (~member(tptp_fun_X1_18(B!39, A!40, F!42), A!40)) | (~member(tptp_fun_X2_17(B!39, A!40, F!42), A!40)) | (~apply(F!42, tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_Y_16(B!39, A!40, F!42))) | (~apply(F!42, tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_Y_16(B!39, A!40, F!42))) | (tptp_fun_X1_18(B!39, A!40, F!42) = tptp_fun_X2_17(B!39, A!40, F!42)))))))))),
% 0.22/0.43 inference(transitivity,[status(thm)],[19, 17])).
% 0.22/0.43 tff(21,plain,
% 0.22/0.43 ((~![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!42, A!40, B!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!42, X1, Y)) | (~member(X2, A!40)) | (~member(X1, A!40)) | (~member(Y, B!39)) | (~apply(F!42, X2, Y))))) | (~(injective(F!42, A!40, B!39) | (~((tptp_fun_X1_18(B!39, A!40, F!42) = tptp_fun_X2_17(B!39, A!40, F!42)) | (~apply(F!42, tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_Y_16(B!39, A!40, F!42))) | (~apply(F!42, tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_Y_16(B!39, A!40, F!42))) | (~member(tptp_fun_X1_18(B!39, A!40, F!42), A!40)) | (~member(tptp_fun_X2_17(B!39, A!40, F!42), A!40)) | (~member(tptp_fun_Y_16(B!39, A!40, F!42), B!39))))))))),
% 0.22/0.43 inference(quant_inst,[status(thm)],[])).
% 0.22/0.43 tff(22,plain,
% 0.22/0.43 ((~![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!42, A!40, B!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!39)) | (~apply(F!42, X1, Y)) | (~member(X1, A!40)) | (~member(X2, A!40)) | (~apply(F!42, X2, Y))))) | (~(injective(F!42, A!40, B!39) | (~((~member(tptp_fun_Y_16(B!39, A!40, F!42), B!39)) | (~member(tptp_fun_X1_18(B!39, A!40, F!42), A!40)) | (~member(tptp_fun_X2_17(B!39, A!40, F!42), A!40)) | (~apply(F!42, tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_Y_16(B!39, A!40, F!42))) | (~apply(F!42, tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_Y_16(B!39, A!40, F!42))) | (tptp_fun_X1_18(B!39, A!40, F!42) = tptp_fun_X2_17(B!39, A!40, F!42))))))))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.22/0.43 tff(23,plain,
% 0.22/0.43 (~((~((~injective(F!42, A!40, B!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!39)) | (~apply(F!42, X1, Y)) | (~member(X1, A!40)) | (~member(X2, A!40)) | (~apply(F!42, X2, Y))))) | (~(injective(F!42, A!40, B!39) | (~((~member(tptp_fun_Y_16(B!39, A!40, F!42), B!39)) | (~member(tptp_fun_X1_18(B!39, A!40, F!42), A!40)) | (~member(tptp_fun_X2_17(B!39, A!40, F!42), A!40)) | (~apply(F!42, tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_Y_16(B!39, A!40, F!42))) | (~apply(F!42, tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_Y_16(B!39, A!40, F!42))) | (tptp_fun_X1_18(B!39, A!40, F!42) = tptp_fun_X2_17(B!39, A!40, F!42)))))))),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[22, 16])).
% 0.22/0.43 tff(24,plain,
% 0.22/0.43 (((~((~injective(F!42, A!40, B!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!39)) | (~apply(F!42, X1, Y)) | (~member(X1, A!40)) | (~member(X2, A!40)) | (~apply(F!42, X2, Y))))) | (~(injective(F!42, A!40, B!39) | (~((~member(tptp_fun_Y_16(B!39, A!40, F!42), B!39)) | (~member(tptp_fun_X1_18(B!39, A!40, F!42), A!40)) | (~member(tptp_fun_X2_17(B!39, A!40, F!42), A!40)) | (~apply(F!42, tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_Y_16(B!39, A!40, F!42))) | (~apply(F!42, tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_Y_16(B!39, A!40, F!42))) | (tptp_fun_X1_18(B!39, A!40, F!42) = tptp_fun_X2_17(B!39, A!40, F!42))))))) | (injective(F!42, A!40, B!39) | (~((~member(tptp_fun_Y_16(B!39, A!40, F!42), B!39)) | (~member(tptp_fun_X1_18(B!39, A!40, F!42), A!40)) | (~member(tptp_fun_X2_17(B!39, A!40, F!42), A!40)) | (~apply(F!42, tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_Y_16(B!39, A!40, F!42))) | (~apply(F!42, tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_Y_16(B!39, A!40, F!42))) | (tptp_fun_X1_18(B!39, A!40, F!42) = tptp_fun_X2_17(B!39, A!40, F!42)))))),
% 0.22/0.43 inference(tautology,[status(thm)],[])).
% 0.22/0.43 tff(25,plain,
% 0.22/0.43 (injective(F!42, A!40, B!39) | (~((~member(tptp_fun_Y_16(B!39, A!40, F!42), B!39)) | (~member(tptp_fun_X1_18(B!39, A!40, F!42), A!40)) | (~member(tptp_fun_X2_17(B!39, A!40, F!42), A!40)) | (~apply(F!42, tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_Y_16(B!39, A!40, F!42))) | (~apply(F!42, tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_Y_16(B!39, A!40, F!42))) | (tptp_fun_X1_18(B!39, A!40, F!42) = tptp_fun_X2_17(B!39, A!40, F!42))))),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[24, 23])).
% 0.22/0.43 tff(26,plain,
% 0.22/0.43 ((~![F: $i, G: $i, A: $i, B: $i] : ((~(maps(F, A, B) & maps(G, B, A) & identity(compose_function(G, F, A, B, A), A))) | injective(F, A, B))) <=> (~![F: $i, G: $i, A: $i, B: $i] : ((~(maps(F, A, B) & maps(G, B, A) & identity(compose_function(G, F, A, B, A), A))) | injective(F, A, B)))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(27,plain,
% 0.22/0.43 ((~![F: $i, G: $i, A: $i, B: $i] : (((maps(F, A, B) & maps(G, B, A)) & identity(compose_function(G, F, A, B, A), A)) => injective(F, A, B))) <=> (~![F: $i, G: $i, A: $i, B: $i] : ((~(maps(F, A, B) & maps(G, B, A) & identity(compose_function(G, F, A, B, A), A))) | injective(F, A, B)))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(28,axiom,(~![F: $i, G: $i, A: $i, B: $i] : (((maps(F, A, B) & maps(G, B, A)) & identity(compose_function(G, F, A, B, A), A)) => injective(F, A, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','thII24')).
% 0.22/0.43 tff(29,plain,
% 0.22/0.43 (~![F: $i, G: $i, A: $i, B: $i] : ((~(maps(F, A, B) & maps(G, B, A) & identity(compose_function(G, F, A, B, A), A))) | injective(F, A, B))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.22/0.43 tff(30,plain,
% 0.22/0.43 (~![F: $i, G: $i, A: $i, B: $i] : ((~(maps(F, A, B) & maps(G, B, A) & identity(compose_function(G, F, A, B, A), A))) | injective(F, A, B))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[29, 26])).
% 0.22/0.43 tff(31,plain,
% 0.22/0.43 (~![F: $i, G: $i, A: $i, B: $i] : ((~(maps(F, A, B) & maps(G, B, A) & identity(compose_function(G, F, A, B, A), A))) | injective(F, A, B))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[30, 26])).
% 0.22/0.44 tff(32,plain,
% 0.22/0.44 (~![F: $i, G: $i, A: $i, B: $i] : ((~(maps(F, A, B) & maps(G, B, A) & identity(compose_function(G, F, A, B, A), A))) | injective(F, A, B))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[31, 26])).
% 0.22/0.44 tff(33,plain,(
% 0.22/0.44 ~((~(maps(F!42, A!40, B!39) & maps(G!41, B!39, A!40) & identity(compose_function(G!41, F!42, A!40, B!39, A!40), A!40))) | injective(F!42, A!40, B!39))),
% 0.22/0.44 inference(skolemize,[status(sab)],[32])).
% 0.22/0.44 tff(34,plain,
% 0.22/0.44 (~injective(F!42, A!40, B!39)),
% 0.22/0.44 inference(or_elim,[status(thm)],[33])).
% 0.22/0.44 tff(35,plain,
% 0.22/0.44 ((~(injective(F!42, A!40, B!39) | (~((~member(tptp_fun_Y_16(B!39, A!40, F!42), B!39)) | (~member(tptp_fun_X1_18(B!39, A!40, F!42), A!40)) | (~member(tptp_fun_X2_17(B!39, A!40, F!42), A!40)) | (~apply(F!42, tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_Y_16(B!39, A!40, F!42))) | (~apply(F!42, tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_Y_16(B!39, A!40, F!42))) | (tptp_fun_X1_18(B!39, A!40, F!42) = tptp_fun_X2_17(B!39, A!40, F!42)))))) | injective(F!42, A!40, B!39) | (~((~member(tptp_fun_Y_16(B!39, A!40, F!42), B!39)) | (~member(tptp_fun_X1_18(B!39, A!40, F!42), A!40)) | (~member(tptp_fun_X2_17(B!39, A!40, F!42), A!40)) | (~apply(F!42, tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_Y_16(B!39, A!40, F!42))) | (~apply(F!42, tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_Y_16(B!39, A!40, F!42))) | (tptp_fun_X1_18(B!39, A!40, F!42) = tptp_fun_X2_17(B!39, A!40, F!42))))),
% 0.22/0.44 inference(tautology,[status(thm)],[])).
% 0.22/0.44 tff(36,plain,
% 0.22/0.44 ((~(injective(F!42, A!40, B!39) | (~((~member(tptp_fun_Y_16(B!39, A!40, F!42), B!39)) | (~member(tptp_fun_X1_18(B!39, A!40, F!42), A!40)) | (~member(tptp_fun_X2_17(B!39, A!40, F!42), A!40)) | (~apply(F!42, tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_Y_16(B!39, A!40, F!42))) | (~apply(F!42, tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_Y_16(B!39, A!40, F!42))) | (tptp_fun_X1_18(B!39, A!40, F!42) = tptp_fun_X2_17(B!39, A!40, F!42)))))) | (~((~member(tptp_fun_Y_16(B!39, A!40, F!42), B!39)) | (~member(tptp_fun_X1_18(B!39, A!40, F!42), A!40)) | (~member(tptp_fun_X2_17(B!39, A!40, F!42), A!40)) | (~apply(F!42, tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_Y_16(B!39, A!40, F!42))) | (~apply(F!42, tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_Y_16(B!39, A!40, F!42))) | (tptp_fun_X1_18(B!39, A!40, F!42) = tptp_fun_X2_17(B!39, A!40, F!42))))),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[35, 34])).
% 0.22/0.44 tff(37,plain,
% 0.22/0.44 (~((~member(tptp_fun_Y_16(B!39, A!40, F!42), B!39)) | (~member(tptp_fun_X1_18(B!39, A!40, F!42), A!40)) | (~member(tptp_fun_X2_17(B!39, A!40, F!42), A!40)) | (~apply(F!42, tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_Y_16(B!39, A!40, F!42))) | (~apply(F!42, tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_Y_16(B!39, A!40, F!42))) | (tptp_fun_X1_18(B!39, A!40, F!42) = tptp_fun_X2_17(B!39, A!40, F!42)))),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[36, 25])).
% 0.22/0.44 tff(38,plain,
% 0.22/0.44 (((~member(tptp_fun_Y_16(B!39, A!40, F!42), B!39)) | (~member(tptp_fun_X1_18(B!39, A!40, F!42), A!40)) | (~member(tptp_fun_X2_17(B!39, A!40, F!42), A!40)) | (~apply(F!42, tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_Y_16(B!39, A!40, F!42))) | (~apply(F!42, tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_Y_16(B!39, A!40, F!42))) | (tptp_fun_X1_18(B!39, A!40, F!42) = tptp_fun_X2_17(B!39, A!40, F!42))) | member(tptp_fun_X1_18(B!39, A!40, F!42), A!40)),
% 0.22/0.44 inference(tautology,[status(thm)],[])).
% 0.22/0.44 tff(39,plain,
% 0.22/0.44 (member(tptp_fun_X1_18(B!39, A!40, F!42), A!40)),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[38, 37])).
% 0.22/0.44 tff(40,plain,
% 0.22/0.44 (^[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)))))))))),
% 0.22/0.44 inference(bind,[status(th)],[])).
% 0.22/0.44 tff(41,plain,
% 0.22/0.44 (![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))))))))),
% 0.22/0.44 inference(quant_intro,[status(thm)],[40])).
% 0.22/0.44 tff(42,plain,
% 0.22/0.44 (^[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)))))))))),
% 0.22/0.44 inference(bind,[status(th)],[])).
% 0.22/0.44 tff(43,plain,
% 0.22/0.44 (![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))))))))),
% 0.22/0.44 inference(quant_intro,[status(thm)],[42])).
% 0.22/0.44 tff(44,plain,
% 0.22/0.44 (![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))))))))),
% 0.22/0.44 inference(transitivity,[status(thm)],[43, 41])).
% 0.22/0.44 tff(45,plain,
% 0.22/0.44 (^[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))))))))))),
% 0.22/0.44 inference(bind,[status(th)],[])).
% 0.22/0.44 tff(46,plain,
% 0.22/0.44 (![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))))))))),
% 0.22/0.44 inference(quant_intro,[status(thm)],[45])).
% 0.22/0.44 tff(47,plain,
% 0.22/0.44 (![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))))),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(48,plain,
% 0.22/0.44 (^[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))))))),
% 0.22/0.44 inference(bind,[status(th)],[])).
% 0.22/0.44 tff(49,plain,
% 0.22/0.44 (![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))))),
% 0.22/0.44 inference(quant_intro,[status(thm)],[48])).
% 0.22/0.44 tff(50,axiom,(![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((member(X, A) & member(Z, C)) => (apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : ((member(Y, B) & apply(F, X, Y)) & apply(G, Y, Z))))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+1.ax','compose_function')).
% 0.22/0.45 tff(51,plain,
% 0.22/0.45 (![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))))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.22/0.45 tff(52,plain,
% 0.22/0.45 (![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))))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[51, 47])).
% 0.22/0.45 tff(53,plain,(
% 0.22/0.45 ![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))))))),
% 0.22/0.45 inference(skolemize,[status(sab)],[52])).
% 0.22/0.45 tff(54,plain,
% 0.22/0.45 (![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[53, 46])).
% 0.22/0.45 tff(55,plain,
% 0.22/0.45 (![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[54, 44])).
% 0.22/0.45 tff(56,plain,
% 0.22/0.45 (((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_X1_18(B!39, A!40, F!42), A!40)) | (~((~(apply(compose_function(G!41, F!42, A!40, B!39, A!40), tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!42, tptp_fun_X1_18(B!39, A!40, F!42), Y)) | (~apply(G!41, Y, tptp_fun_X1_18(B!39, A!40, F!42)))))) | (~((~apply(compose_function(G!41, F!42, A!40, B!39, A!40), tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42), B!39, F!42, G!41), B!39)) | (~apply(F!42, tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42), B!39, F!42, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42), B!39, F!42, G!41), tptp_fun_X1_18(B!39, A!40, F!42))))))))))) <=> ((~![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_X1_18(B!39, A!40, F!42), A!40)) | (~((~(apply(compose_function(G!41, F!42, A!40, B!39, A!40), tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!42, tptp_fun_X1_18(B!39, A!40, F!42), Y)) | (~apply(G!41, Y, tptp_fun_X1_18(B!39, A!40, F!42)))))) | (~((~apply(compose_function(G!41, F!42, A!40, B!39, A!40), tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42), B!39, F!42, G!41), B!39)) | (~apply(F!42, tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42), B!39, F!42, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42), B!39, F!42, G!41), tptp_fun_X1_18(B!39, A!40, F!42))))))))))),
% 0.22/0.45 inference(rewrite,[status(thm)],[])).
% 0.22/0.45 tff(57,plain,
% 0.22/0.45 (((~member(tptp_fun_X1_18(B!39, A!40, F!42), A!40)) | (~member(tptp_fun_X1_18(B!39, A!40, F!42), A!40)) | (~((~(apply(compose_function(G!41, F!42, A!40, B!39, A!40), tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!42, tptp_fun_X1_18(B!39, A!40, F!42), Y)) | (~apply(G!41, Y, tptp_fun_X1_18(B!39, A!40, F!42)))))) | (~((~apply(compose_function(G!41, F!42, A!40, B!39, A!40), tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42), B!39, F!42, G!41), B!39)) | (~apply(F!42, tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42), B!39, F!42, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42), B!39, F!42, G!41), tptp_fun_X1_18(B!39, A!40, F!42)))))))))) <=> ((~member(tptp_fun_X1_18(B!39, A!40, F!42), A!40)) | (~((~(apply(compose_function(G!41, F!42, A!40, B!39, A!40), tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!42, tptp_fun_X1_18(B!39, A!40, F!42), Y)) | (~apply(G!41, Y, tptp_fun_X1_18(B!39, A!40, F!42)))))) | (~((~apply(compose_function(G!41, F!42, A!40, B!39, A!40), tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42), B!39, F!42, G!41), B!39)) | (~apply(F!42, tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42), B!39, F!42, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42), B!39, F!42, G!41), tptp_fun_X1_18(B!39, A!40, F!42))))))))))),
% 0.22/0.45 inference(rewrite,[status(thm)],[])).
% 0.22/0.45 tff(58,plain,
% 0.22/0.45 ((~((~((~apply(compose_function(G!41, F!42, A!40, B!39, A!40), tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42), B!39, F!42, G!41), B!39)) | (~apply(F!42, tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42), B!39, F!42, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42), B!39, F!42, G!41), tptp_fun_X1_18(B!39, A!40, F!42))))))) | (~(apply(compose_function(G!41, F!42, A!40, B!39, A!40), tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!42, tptp_fun_X1_18(B!39, A!40, F!42), Y)) | (~apply(G!41, Y, tptp_fun_X1_18(B!39, A!40, F!42)))))))) <=> (~((~(apply(compose_function(G!41, F!42, A!40, B!39, A!40), tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!42, tptp_fun_X1_18(B!39, A!40, F!42), Y)) | (~apply(G!41, Y, tptp_fun_X1_18(B!39, A!40, F!42)))))) | (~((~apply(compose_function(G!41, F!42, A!40, B!39, A!40), tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42), B!39, F!42, G!41), B!39)) | (~apply(F!42, tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42), B!39, F!42, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42), B!39, F!42, G!41), tptp_fun_X1_18(B!39, A!40, F!42)))))))))),
% 0.22/0.46 inference(rewrite,[status(thm)],[])).
% 0.22/0.46 tff(59,plain,
% 0.22/0.46 (((~member(tptp_fun_X1_18(B!39, A!40, F!42), A!40)) | (~member(tptp_fun_X1_18(B!39, A!40, F!42), A!40)) | (~((~((~apply(compose_function(G!41, F!42, A!40, B!39, A!40), tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42), B!39, F!42, G!41), B!39)) | (~apply(F!42, tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42), B!39, F!42, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42), B!39, F!42, G!41), tptp_fun_X1_18(B!39, A!40, F!42))))))) | (~(apply(compose_function(G!41, F!42, A!40, B!39, A!40), tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!42, tptp_fun_X1_18(B!39, A!40, F!42), Y)) | (~apply(G!41, Y, tptp_fun_X1_18(B!39, A!40, F!42))))))))) <=> ((~member(tptp_fun_X1_18(B!39, A!40, F!42), A!40)) | (~member(tptp_fun_X1_18(B!39, A!40, F!42), A!40)) | (~((~(apply(compose_function(G!41, F!42, A!40, B!39, A!40), tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!42, tptp_fun_X1_18(B!39, A!40, F!42), Y)) | (~apply(G!41, Y, tptp_fun_X1_18(B!39, A!40, F!42)))))) | (~((~apply(compose_function(G!41, F!42, A!40, B!39, A!40), tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42), B!39, F!42, G!41), B!39)) | (~apply(F!42, tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42), B!39, F!42, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42), B!39, F!42, G!41), tptp_fun_X1_18(B!39, A!40, F!42))))))))))),
% 0.22/0.46 inference(monotonicity,[status(thm)],[58])).
% 0.22/0.46 tff(60,plain,
% 0.22/0.46 (((~member(tptp_fun_X1_18(B!39, A!40, F!42), A!40)) | (~member(tptp_fun_X1_18(B!39, A!40, F!42), A!40)) | (~((~((~apply(compose_function(G!41, F!42, A!40, B!39, A!40), tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42), B!39, F!42, G!41), B!39)) | (~apply(F!42, tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42), B!39, F!42, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42), B!39, F!42, G!41), tptp_fun_X1_18(B!39, A!40, F!42))))))) | (~(apply(compose_function(G!41, F!42, A!40, B!39, A!40), tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!42, tptp_fun_X1_18(B!39, A!40, F!42), Y)) | (~apply(G!41, Y, tptp_fun_X1_18(B!39, A!40, F!42))))))))) <=> ((~member(tptp_fun_X1_18(B!39, A!40, F!42), A!40)) | (~((~(apply(compose_function(G!41, F!42, A!40, B!39, A!40), tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!42, tptp_fun_X1_18(B!39, A!40, F!42), Y)) | (~apply(G!41, Y, tptp_fun_X1_18(B!39, A!40, F!42)))))) | (~((~apply(compose_function(G!41, F!42, A!40, B!39, A!40), tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42), B!39, F!42, G!41), B!39)) | (~apply(F!42, tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42), B!39, F!42, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42), B!39, F!42, G!41), tptp_fun_X1_18(B!39, A!40, F!42))))))))))),
% 0.22/0.46 inference(transitivity,[status(thm)],[59, 57])).
% 0.22/0.46 tff(61,plain,
% 0.22/0.46 (((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_X1_18(B!39, A!40, F!42), A!40)) | (~member(tptp_fun_X1_18(B!39, A!40, F!42), A!40)) | (~((~((~apply(compose_function(G!41, F!42, A!40, B!39, A!40), tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42), B!39, F!42, G!41), B!39)) | (~apply(F!42, tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42), B!39, F!42, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42), B!39, F!42, G!41), tptp_fun_X1_18(B!39, A!40, F!42))))))) | (~(apply(compose_function(G!41, F!42, A!40, B!39, A!40), tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!42, tptp_fun_X1_18(B!39, A!40, F!42), Y)) | (~apply(G!41, Y, tptp_fun_X1_18(B!39, A!40, F!42)))))))))) <=> ((~![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_X1_18(B!39, A!40, F!42), A!40)) | (~((~(apply(compose_function(G!41, F!42, A!40, B!39, A!40), tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!42, tptp_fun_X1_18(B!39, A!40, F!42), Y)) | (~apply(G!41, Y, tptp_fun_X1_18(B!39, A!40, F!42)))))) | (~((~apply(compose_function(G!41, F!42, A!40, B!39, A!40), tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42), B!39, F!42, G!41), B!39)) | (~apply(F!42, tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42), B!39, F!42, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42), B!39, F!42, G!41), tptp_fun_X1_18(B!39, A!40, F!42)))))))))))),
% 0.22/0.46 inference(monotonicity,[status(thm)],[60])).
% 0.22/0.46 tff(62,plain,
% 0.22/0.46 (((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_X1_18(B!39, A!40, F!42), A!40)) | (~member(tptp_fun_X1_18(B!39, A!40, F!42), A!40)) | (~((~((~apply(compose_function(G!41, F!42, A!40, B!39, A!40), tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42), B!39, F!42, G!41), B!39)) | (~apply(F!42, tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42), B!39, F!42, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42), B!39, F!42, G!41), tptp_fun_X1_18(B!39, A!40, F!42))))))) | (~(apply(compose_function(G!41, F!42, A!40, B!39, A!40), tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!42, tptp_fun_X1_18(B!39, A!40, F!42), Y)) | (~apply(G!41, Y, tptp_fun_X1_18(B!39, A!40, F!42)))))))))) <=> ((~![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_X1_18(B!39, A!40, F!42), A!40)) | (~((~(apply(compose_function(G!41, F!42, A!40, B!39, A!40), tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!42, tptp_fun_X1_18(B!39, A!40, F!42), Y)) | (~apply(G!41, Y, tptp_fun_X1_18(B!39, A!40, F!42)))))) | (~((~apply(compose_function(G!41, F!42, A!40, B!39, A!40), tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42), B!39, F!42, G!41), B!39)) | (~apply(F!42, tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42), B!39, F!42, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42), B!39, F!42, G!41), tptp_fun_X1_18(B!39, A!40, F!42))))))))))),
% 0.22/0.46 inference(transitivity,[status(thm)],[61, 56])).
% 0.22/0.46 tff(63,plain,
% 0.22/0.46 ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_X1_18(B!39, A!40, F!42), A!40)) | (~member(tptp_fun_X1_18(B!39, A!40, F!42), A!40)) | (~((~((~apply(compose_function(G!41, F!42, A!40, B!39, A!40), tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42), B!39, F!42, G!41), B!39)) | (~apply(F!42, tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42), B!39, F!42, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42), B!39, F!42, G!41), tptp_fun_X1_18(B!39, A!40, F!42))))))) | (~(apply(compose_function(G!41, F!42, A!40, B!39, A!40), tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!42, tptp_fun_X1_18(B!39, A!40, F!42), Y)) | (~apply(G!41, Y, tptp_fun_X1_18(B!39, A!40, F!42)))))))))),
% 0.22/0.46 inference(quant_inst,[status(thm)],[])).
% 0.22/0.46 tff(64,plain,
% 0.22/0.46 ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | (~member(tptp_fun_X1_18(B!39, A!40, F!42), A!40)) | (~((~(apply(compose_function(G!41, F!42, A!40, B!39, A!40), tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!42, tptp_fun_X1_18(B!39, A!40, F!42), Y)) | (~apply(G!41, Y, tptp_fun_X1_18(B!39, A!40, F!42)))))) | (~((~apply(compose_function(G!41, F!42, A!40, B!39, A!40), tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42), B!39, F!42, G!41), B!39)) | (~apply(F!42, tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42), B!39, F!42, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42), B!39, F!42, G!41), tptp_fun_X1_18(B!39, A!40, F!42)))))))))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.22/0.46 tff(65,plain,
% 0.22/0.46 (~((~(apply(compose_function(G!41, F!42, A!40, B!39, A!40), tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!42, tptp_fun_X1_18(B!39, A!40, F!42), Y)) | (~apply(G!41, Y, tptp_fun_X1_18(B!39, A!40, F!42)))))) | (~((~apply(compose_function(G!41, F!42, A!40, B!39, A!40), tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42), B!39, F!42, G!41), B!39)) | (~apply(F!42, tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42), B!39, F!42, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42), B!39, F!42, G!41), tptp_fun_X1_18(B!39, A!40, F!42))))))))),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[64, 55, 39])).
% 0.22/0.47 tff(66,plain,
% 0.22/0.47 (((~(apply(compose_function(G!41, F!42, A!40, B!39, A!40), tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!42, tptp_fun_X1_18(B!39, A!40, F!42), Y)) | (~apply(G!41, Y, tptp_fun_X1_18(B!39, A!40, F!42)))))) | (~((~apply(compose_function(G!41, F!42, A!40, B!39, A!40), tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42), B!39, F!42, G!41), B!39)) | (~apply(F!42, tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42), B!39, F!42, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42), B!39, F!42, G!41), tptp_fun_X1_18(B!39, A!40, F!42)))))))) | ((~apply(compose_function(G!41, F!42, A!40, B!39, A!40), tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42), B!39, F!42, G!41), B!39)) | (~apply(F!42, tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42), B!39, F!42, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42), B!39, F!42, G!41), tptp_fun_X1_18(B!39, A!40, F!42))))))),
% 0.22/0.47 inference(tautology,[status(thm)],[])).
% 0.22/0.47 tff(67,plain,
% 0.22/0.47 ((~apply(compose_function(G!41, F!42, A!40, B!39, A!40), tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42), B!39, F!42, G!41), B!39)) | (~apply(F!42, tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42), B!39, F!42, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42), B!39, F!42, G!41), tptp_fun_X1_18(B!39, A!40, F!42)))))),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[66, 65])).
% 0.22/0.47 tff(68,plain,
% 0.22/0.47 (^[F: $i, A: $i] : refl((~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F)))))))) <=> (~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F)))))))))),
% 0.22/0.47 inference(bind,[status(th)],[])).
% 0.22/0.47 tff(69,plain,
% 0.22/0.47 (![F: $i, A: $i] : (~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F)))))))) <=> ![F: $i, A: $i] : (~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F))))))))),
% 0.22/0.47 inference(quant_intro,[status(thm)],[68])).
% 0.22/0.47 tff(70,plain,
% 0.22/0.47 (^[F: $i, A: $i] : rewrite((~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F)))))))) <=> (~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F)))))))))),
% 0.22/0.47 inference(bind,[status(th)],[])).
% 0.22/0.47 tff(71,plain,
% 0.22/0.47 (![F: $i, A: $i] : (~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F)))))))) <=> ![F: $i, A: $i] : (~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F))))))))),
% 0.22/0.47 inference(quant_intro,[status(thm)],[70])).
% 0.22/0.47 tff(72,plain,
% 0.22/0.47 (![F: $i, A: $i] : (~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F)))))))) <=> ![F: $i, A: $i] : (~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F))))))))),
% 0.22/0.47 inference(transitivity,[status(thm)],[71, 69])).
% 0.22/0.47 tff(73,plain,
% 0.22/0.47 (^[F: $i, A: $i] : trans(monotonicity(rewrite(((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X))) <=> ((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))), rewrite((identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F))))) <=> (identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F)))))), ((((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X))) & (identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F)))))) <=> (((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X))) & (identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F)))))))), rewrite((((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X))) & (identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F)))))) <=> (~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F))))))))), ((((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X))) & (identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F)))))) <=> (~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F))))))))))),
% 0.22/0.47 inference(bind,[status(th)],[])).
% 0.22/0.47 tff(74,plain,
% 0.22/0.47 (![F: $i, A: $i] : (((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X))) & (identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F)))))) <=> ![F: $i, A: $i] : (~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F))))))))),
% 0.22/0.47 inference(quant_intro,[status(thm)],[73])).
% 0.22/0.47 tff(75,plain,
% 0.22/0.47 (![F: $i, A: $i] : (identity(F, A) <=> ![X: $i] : ((~member(X, A)) | apply(F, X, X))) <=> ![F: $i, A: $i] : (identity(F, A) <=> ![X: $i] : ((~member(X, A)) | apply(F, X, X)))),
% 0.22/0.47 inference(rewrite,[status(thm)],[])).
% 0.22/0.47 tff(76,plain,
% 0.22/0.47 (^[F: $i, A: $i] : rewrite((identity(F, A) <=> ![X: $i] : (member(X, A) => apply(F, X, X))) <=> (identity(F, A) <=> ![X: $i] : ((~member(X, A)) | apply(F, X, X))))),
% 0.22/0.47 inference(bind,[status(th)],[])).
% 0.22/0.47 tff(77,plain,
% 0.22/0.47 (![F: $i, A: $i] : (identity(F, A) <=> ![X: $i] : (member(X, A) => apply(F, X, X))) <=> ![F: $i, A: $i] : (identity(F, A) <=> ![X: $i] : ((~member(X, A)) | apply(F, X, X)))),
% 0.22/0.47 inference(quant_intro,[status(thm)],[76])).
% 0.22/0.47 tff(78,axiom,(![F: $i, A: $i] : (identity(F, A) <=> ![X: $i] : (member(X, A) => apply(F, X, X)))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+1.ax','identity')).
% 0.22/0.47 tff(79,plain,
% 0.22/0.47 (![F: $i, A: $i] : (identity(F, A) <=> ![X: $i] : ((~member(X, A)) | apply(F, X, X)))),
% 0.22/0.47 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.22/0.47 tff(80,plain,
% 0.22/0.47 (![F: $i, A: $i] : (identity(F, A) <=> ![X: $i] : ((~member(X, A)) | apply(F, X, X)))),
% 0.22/0.47 inference(modus_ponens,[status(thm)],[79, 75])).
% 0.22/0.47 tff(81,plain,(
% 0.22/0.47 ![F: $i, A: $i] : (((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X))) & (identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F))))))),
% 0.22/0.47 inference(skolemize,[status(sab)],[80])).
% 0.22/0.47 tff(82,plain,
% 0.22/0.47 (![F: $i, A: $i] : (~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F))))))))),
% 0.22/0.47 inference(modus_ponens,[status(thm)],[81, 74])).
% 0.22/0.47 tff(83,plain,
% 0.22/0.47 (![F: $i, A: $i] : (~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F))))))))),
% 0.22/0.47 inference(modus_ponens,[status(thm)],[82, 72])).
% 0.22/0.47 tff(84,plain,
% 0.22/0.47 ((~![F: $i, A: $i] : (~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F))))))))) | (~((~((~identity(compose_function(G!41, F!42, A!40, B!39, A!40), A!40)) | ![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!41, F!42, A!40, B!39, A!40), X, X)))) | (~(identity(compose_function(G!41, F!42, A!40, B!39, A!40), A!40) | (~((~member(tptp_fun_X_15(A!40, compose_function(G!41, F!42, A!40, B!39, A!40)), A!40)) | apply(compose_function(G!41, F!42, A!40, B!39, A!40), tptp_fun_X_15(A!40, compose_function(G!41, F!42, A!40, B!39, A!40)), tptp_fun_X_15(A!40, compose_function(G!41, F!42, A!40, B!39, A!40)))))))))),
% 0.22/0.47 inference(quant_inst,[status(thm)],[])).
% 0.22/0.47 tff(85,plain,
% 0.22/0.47 (~((~((~identity(compose_function(G!41, F!42, A!40, B!39, A!40), A!40)) | ![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!41, F!42, A!40, B!39, A!40), X, X)))) | (~(identity(compose_function(G!41, F!42, A!40, B!39, A!40), A!40) | (~((~member(tptp_fun_X_15(A!40, compose_function(G!41, F!42, A!40, B!39, A!40)), A!40)) | apply(compose_function(G!41, F!42, A!40, B!39, A!40), tptp_fun_X_15(A!40, compose_function(G!41, F!42, A!40, B!39, A!40)), tptp_fun_X_15(A!40, compose_function(G!41, F!42, A!40, B!39, A!40))))))))),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[84, 83])).
% 0.22/0.47 tff(86,plain,
% 0.22/0.47 (((~((~identity(compose_function(G!41, F!42, A!40, B!39, A!40), A!40)) | ![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!41, F!42, A!40, B!39, A!40), X, X)))) | (~(identity(compose_function(G!41, F!42, A!40, B!39, A!40), A!40) | (~((~member(tptp_fun_X_15(A!40, compose_function(G!41, F!42, A!40, B!39, A!40)), A!40)) | apply(compose_function(G!41, F!42, A!40, B!39, A!40), tptp_fun_X_15(A!40, compose_function(G!41, F!42, A!40, B!39, A!40)), tptp_fun_X_15(A!40, compose_function(G!41, F!42, A!40, B!39, A!40)))))))) | ((~identity(compose_function(G!41, F!42, A!40, B!39, A!40), A!40)) | ![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!41, F!42, A!40, B!39, A!40), X, X)))),
% 0.22/0.47 inference(tautology,[status(thm)],[])).
% 0.22/0.47 tff(87,plain,
% 0.22/0.47 ((~identity(compose_function(G!41, F!42, A!40, B!39, A!40), A!40)) | ![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!41, F!42, A!40, B!39, A!40), X, X))),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[86, 85])).
% 0.22/0.47 tff(88,plain,
% 0.22/0.47 (maps(F!42, A!40, B!39) & maps(G!41, B!39, A!40) & identity(compose_function(G!41, F!42, A!40, B!39, A!40), A!40)),
% 0.22/0.47 inference(or_elim,[status(thm)],[33])).
% 0.22/0.47 tff(89,plain,
% 0.22/0.47 (identity(compose_function(G!41, F!42, A!40, B!39, A!40), A!40)),
% 0.22/0.47 inference(and_elim,[status(thm)],[88])).
% 0.22/0.47 tff(90,plain,
% 0.22/0.47 ((~((~identity(compose_function(G!41, F!42, A!40, B!39, A!40), A!40)) | ![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!41, F!42, A!40, B!39, A!40), X, X)))) | (~identity(compose_function(G!41, F!42, A!40, B!39, A!40), A!40)) | ![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!41, F!42, A!40, B!39, A!40), X, X))),
% 0.22/0.48 inference(tautology,[status(thm)],[])).
% 0.22/0.48 tff(91,plain,
% 0.22/0.48 ((~((~identity(compose_function(G!41, F!42, A!40, B!39, A!40), A!40)) | ![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!41, F!42, A!40, B!39, A!40), X, X)))) | ![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!41, F!42, A!40, B!39, A!40), X, X))),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[90, 89])).
% 0.22/0.48 tff(92,plain,
% 0.22/0.48 (![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!41, F!42, A!40, B!39, A!40), X, X))),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[91, 87])).
% 0.22/0.48 tff(93,plain,
% 0.22/0.48 (((~![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!41, F!42, A!40, B!39, A!40), X, X))) | ((~member(tptp_fun_X1_18(B!39, A!40, F!42), A!40)) | apply(compose_function(G!41, F!42, A!40, B!39, A!40), tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42)))) <=> ((~![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!41, F!42, A!40, B!39, A!40), X, X))) | (~member(tptp_fun_X1_18(B!39, A!40, F!42), A!40)) | apply(compose_function(G!41, F!42, A!40, B!39, A!40), tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42)))),
% 0.22/0.48 inference(rewrite,[status(thm)],[])).
% 0.22/0.48 tff(94,plain,
% 0.22/0.48 ((~![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!41, F!42, A!40, B!39, A!40), X, X))) | ((~member(tptp_fun_X1_18(B!39, A!40, F!42), A!40)) | apply(compose_function(G!41, F!42, A!40, B!39, A!40), tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42)))),
% 0.22/0.48 inference(quant_inst,[status(thm)],[])).
% 0.22/0.48 tff(95,plain,
% 0.22/0.48 ((~![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!41, F!42, A!40, B!39, A!40), X, X))) | (~member(tptp_fun_X1_18(B!39, A!40, F!42), A!40)) | apply(compose_function(G!41, F!42, A!40, B!39, A!40), tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42))),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.22/0.48 tff(96,plain,
% 0.22/0.48 (apply(compose_function(G!41, F!42, A!40, B!39, A!40), tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42))),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[95, 92, 39])).
% 0.22/0.48 tff(97,plain,
% 0.22/0.48 ((~((~apply(compose_function(G!41, F!42, A!40, B!39, A!40), tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42), B!39, F!42, G!41), B!39)) | (~apply(F!42, tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42), B!39, F!42, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42), B!39, F!42, G!41), tptp_fun_X1_18(B!39, A!40, F!42))))))) | (~apply(compose_function(G!41, F!42, A!40, B!39, A!40), tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42), B!39, F!42, G!41), B!39)) | (~apply(F!42, tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42), B!39, F!42, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42), B!39, F!42, G!41), tptp_fun_X1_18(B!39, A!40, F!42)))))),
% 0.22/0.48 inference(tautology,[status(thm)],[])).
% 0.22/0.48 tff(98,plain,
% 0.22/0.48 ((~((~apply(compose_function(G!41, F!42, A!40, B!39, A!40), tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42), B!39, F!42, G!41), B!39)) | (~apply(F!42, tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42), B!39, F!42, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42), B!39, F!42, G!41), tptp_fun_X1_18(B!39, A!40, F!42))))))) | (~((~member(tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42), B!39, F!42, G!41), B!39)) | (~apply(F!42, tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42), B!39, F!42, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42), B!39, F!42, G!41), tptp_fun_X1_18(B!39, A!40, F!42)))))),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[97, 96])).
% 0.22/0.48 tff(99,plain,
% 0.22/0.48 (~((~member(tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42), B!39, F!42, G!41), B!39)) | (~apply(F!42, tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42), B!39, F!42, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42), B!39, F!42, G!41), tptp_fun_X1_18(B!39, A!40, F!42))))),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[98, 67])).
% 0.22/0.48 tff(100,plain,
% 0.22/0.48 (((~member(tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42), B!39, F!42, G!41), B!39)) | (~apply(F!42, tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42), B!39, F!42, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42), B!39, F!42, G!41), tptp_fun_X1_18(B!39, A!40, F!42)))) | apply(F!42, tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42), B!39, F!42, G!41))),
% 0.22/0.48 inference(tautology,[status(thm)],[])).
% 0.22/0.48 tff(101,plain,
% 0.22/0.48 (apply(F!42, tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42), B!39, F!42, G!41))),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[100, 99])).
% 0.22/0.48 tff(102,plain,
% 0.22/0.48 (((~member(tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42), B!39, F!42, G!41), B!39)) | (~apply(F!42, tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42), B!39, F!42, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42), B!39, F!42, G!41), tptp_fun_X1_18(B!39, A!40, F!42)))) | member(tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42), B!39, F!42, G!41), B!39)),
% 0.22/0.48 inference(tautology,[status(thm)],[])).
% 0.22/0.48 tff(103,plain,
% 0.22/0.48 (member(tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42), B!39, F!42, G!41), B!39)),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[102, 99])).
% 0.22/0.48 tff(104,plain,
% 0.22/0.48 (((~member(tptp_fun_Y_16(B!39, A!40, F!42), B!39)) | (~member(tptp_fun_X1_18(B!39, A!40, F!42), A!40)) | (~member(tptp_fun_X2_17(B!39, A!40, F!42), A!40)) | (~apply(F!42, tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_Y_16(B!39, A!40, F!42))) | (~apply(F!42, tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_Y_16(B!39, A!40, F!42))) | (tptp_fun_X1_18(B!39, A!40, F!42) = tptp_fun_X2_17(B!39, A!40, F!42))) | apply(F!42, tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_Y_16(B!39, A!40, F!42))),
% 0.22/0.48 inference(tautology,[status(thm)],[])).
% 0.22/0.48 tff(105,plain,
% 0.22/0.48 (apply(F!42, tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_Y_16(B!39, A!40, F!42))),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[104, 37])).
% 0.22/0.48 tff(106,plain,
% 0.22/0.48 (((~member(tptp_fun_Y_16(B!39, A!40, F!42), B!39)) | (~member(tptp_fun_X1_18(B!39, A!40, F!42), A!40)) | (~member(tptp_fun_X2_17(B!39, A!40, F!42), A!40)) | (~apply(F!42, tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_Y_16(B!39, A!40, F!42))) | (~apply(F!42, tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_Y_16(B!39, A!40, F!42))) | (tptp_fun_X1_18(B!39, A!40, F!42) = tptp_fun_X2_17(B!39, A!40, F!42))) | member(tptp_fun_Y_16(B!39, A!40, F!42), B!39)),
% 0.22/0.48 inference(tautology,[status(thm)],[])).
% 0.22/0.48 tff(107,plain,
% 0.22/0.48 (member(tptp_fun_Y_16(B!39, A!40, F!42), B!39)),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[106, 37])).
% 0.22/0.48 tff(108,plain,
% 0.22/0.48 (^[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)))))))))))),
% 0.22/0.48 inference(bind,[status(th)],[])).
% 0.22/0.48 tff(109,plain,
% 0.22/0.48 (![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))))))))))),
% 0.22/0.48 inference(quant_intro,[status(thm)],[108])).
% 0.22/0.48 tff(110,plain,
% 0.22/0.48 (^[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)))))))))),
% 0.22/0.48 inference(bind,[status(th)],[])).
% 0.22/0.48 tff(111,plain,
% 0.22/0.48 (![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))))))))),
% 0.22/0.48 inference(quant_intro,[status(thm)],[110])).
% 0.22/0.48 tff(112,plain,
% 0.22/0.48 (^[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)))))))))),
% 0.22/0.48 inference(bind,[status(th)],[])).
% 0.22/0.48 tff(113,plain,
% 0.22/0.48 (![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))))))))),
% 0.22/0.48 inference(quant_intro,[status(thm)],[112])).
% 0.22/0.48 tff(114,plain,
% 0.22/0.48 (![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))))))))),
% 0.22/0.48 inference(transitivity,[status(thm)],[113, 111])).
% 0.22/0.48 tff(115,plain,
% 0.22/0.48 (^[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))))))))))),
% 0.22/0.48 inference(bind,[status(th)],[])).
% 0.22/0.48 tff(116,plain,
% 0.22/0.48 (![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))))))))),
% 0.22/0.49 inference(quant_intro,[status(thm)],[115])).
% 0.22/0.49 tff(117,plain,
% 0.22/0.49 (^[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))))))))),
% 0.22/0.49 inference(bind,[status(th)],[])).
% 0.22/0.49 tff(118,plain,
% 0.22/0.49 (![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)))))))),
% 0.22/0.49 inference(quant_intro,[status(thm)],[117])).
% 0.22/0.49 tff(119,plain,
% 0.22/0.49 (![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))))))),
% 0.22/0.49 inference(rewrite,[status(thm)],[])).
% 0.22/0.49 tff(120,plain,
% 0.22/0.49 (^[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)))))))),
% 0.22/0.49 inference(bind,[status(th)],[])).
% 0.22/0.49 tff(121,plain,
% 0.22/0.49 (![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))))))),
% 0.22/0.49 inference(quant_intro,[status(thm)],[120])).
% 0.22/0.49 tff(122,axiom,(![F: $i, A: $i, B: $i] : (maps(F, A, B) <=> (![X: $i] : (member(X, A) => ?[Y: $i] : (member(Y, B) & apply(F, X, Y))) & ![X: $i, Y1: $i, Y2: $i] : (((member(X, A) & member(Y1, B)) & member(Y2, B)) => ((apply(F, X, Y1) & apply(F, X, Y2)) => (Y1 = Y2)))))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+1.ax','maps')).
% 0.22/0.49 tff(123,plain,
% 0.22/0.49 (![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))))))),
% 0.22/0.49 inference(modus_ponens,[status(thm)],[122, 121])).
% 0.22/0.49 tff(124,plain,
% 0.22/0.49 (![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))))))),
% 0.22/0.49 inference(modus_ponens,[status(thm)],[123, 119])).
% 0.22/0.49 tff(125,plain,(
% 0.22/0.49 ![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))))))))),
% 0.22/0.49 inference(skolemize,[status(sab)],[124])).
% 0.22/0.49 tff(126,plain,
% 0.22/0.49 (![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)))))))),
% 0.22/0.49 inference(modus_ponens,[status(thm)],[125, 118])).
% 0.22/0.49 tff(127,plain,
% 0.22/0.49 (![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))))))))),
% 0.22/0.49 inference(modus_ponens,[status(thm)],[126, 116])).
% 0.22/0.49 tff(128,plain,
% 0.22/0.49 (![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))))))))),
% 0.22/0.49 inference(modus_ponens,[status(thm)],[127, 114])).
% 0.22/0.49 tff(129,plain,
% 0.22/0.49 (![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))))))))))),
% 0.22/0.49 inference(modus_ponens,[status(thm)],[128, 109])).
% 0.22/0.49 tff(130,plain,
% 0.22/0.49 (((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(F!42, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!42), B!39)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!39, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))))))) | (~(maps(F!42, A!40, B!39) | (~((~member(tptp_fun_X_4(B!39, A!40, F!42), A!40)) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F!42, tptp_fun_X_4(B!39, A!40, F!42), Y)))))) | (~((~member(tptp_fun_Y2_5(B!39, A!40, F!42), B!39)) | (~member(tptp_fun_Y1_6(B!39, A!40, F!42), B!39)) | (~member(tptp_fun_X_7(B!39, A!40, F!42), A!40)) | (~apply(F!42, tptp_fun_X_7(B!39, A!40, F!42), tptp_fun_Y2_5(B!39, A!40, F!42))) | (~apply(F!42, tptp_fun_X_7(B!39, A!40, F!42), tptp_fun_Y1_6(B!39, A!40, F!42))) | (tptp_fun_Y1_6(B!39, A!40, F!42) = tptp_fun_Y2_5(B!39, A!40, F!42))))))))) <=> ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(F!42, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!42), B!39)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!39, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))))))) | (~(maps(F!42, A!40, B!39) | (~((~member(tptp_fun_X_4(B!39, A!40, F!42), A!40)) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F!42, tptp_fun_X_4(B!39, A!40, F!42), Y)))))) | (~((~member(tptp_fun_Y2_5(B!39, A!40, F!42), B!39)) | (~member(tptp_fun_Y1_6(B!39, A!40, F!42), B!39)) | (~member(tptp_fun_X_7(B!39, A!40, F!42), A!40)) | (~apply(F!42, tptp_fun_X_7(B!39, A!40, F!42), tptp_fun_Y2_5(B!39, A!40, F!42))) | (~apply(F!42, tptp_fun_X_7(B!39, A!40, F!42), tptp_fun_Y1_6(B!39, A!40, F!42))) | (tptp_fun_Y1_6(B!39, A!40, F!42) = tptp_fun_Y2_5(B!39, A!40, F!42)))))))))),
% 0.22/0.49 inference(rewrite,[status(thm)],[])).
% 0.22/0.49 tff(131,plain,
% 0.22/0.49 ((~((~((~maps(F!42, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!42), B!39)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!39, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))))))) | (~(maps(F!42, A!40, B!39) | (~((tptp_fun_Y1_6(B!39, A!40, F!42) = tptp_fun_Y2_5(B!39, A!40, F!42)) | (~apply(F!42, tptp_fun_X_7(B!39, A!40, F!42), tptp_fun_Y1_6(B!39, A!40, F!42))) | (~apply(F!42, tptp_fun_X_7(B!39, A!40, F!42), tptp_fun_Y2_5(B!39, A!40, F!42))) | (~member(tptp_fun_X_7(B!39, A!40, F!42), A!40)) | (~member(tptp_fun_Y1_6(B!39, A!40, F!42), B!39)) | (~member(tptp_fun_Y2_5(B!39, A!40, F!42), B!39)))) | (~((~member(tptp_fun_X_4(B!39, A!40, F!42), A!40)) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F!42, tptp_fun_X_4(B!39, A!40, F!42), Y)))))))))) <=> (~((~((~maps(F!42, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!42), B!39)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!39, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))))))) | (~(maps(F!42, A!40, B!39) | (~((~member(tptp_fun_X_4(B!39, A!40, F!42), A!40)) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F!42, tptp_fun_X_4(B!39, A!40, F!42), Y)))))) | (~((~member(tptp_fun_Y2_5(B!39, A!40, F!42), B!39)) | (~member(tptp_fun_Y1_6(B!39, A!40, F!42), B!39)) | (~member(tptp_fun_X_7(B!39, A!40, F!42), A!40)) | (~apply(F!42, tptp_fun_X_7(B!39, A!40, F!42), tptp_fun_Y2_5(B!39, A!40, F!42))) | (~apply(F!42, tptp_fun_X_7(B!39, A!40, F!42), tptp_fun_Y1_6(B!39, A!40, F!42))) | (tptp_fun_Y1_6(B!39, A!40, F!42) = tptp_fun_Y2_5(B!39, A!40, F!42))))))))),
% 0.22/0.49 inference(rewrite,[status(thm)],[])).
% 0.22/0.49 tff(132,plain,
% 0.22/0.49 (((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(F!42, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!42), B!39)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!39, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))))))) | (~(maps(F!42, A!40, B!39) | (~((tptp_fun_Y1_6(B!39, A!40, F!42) = tptp_fun_Y2_5(B!39, A!40, F!42)) | (~apply(F!42, tptp_fun_X_7(B!39, A!40, F!42), tptp_fun_Y1_6(B!39, A!40, F!42))) | (~apply(F!42, tptp_fun_X_7(B!39, A!40, F!42), tptp_fun_Y2_5(B!39, A!40, F!42))) | (~member(tptp_fun_X_7(B!39, A!40, F!42), A!40)) | (~member(tptp_fun_Y1_6(B!39, A!40, F!42), B!39)) | (~member(tptp_fun_Y2_5(B!39, A!40, F!42), B!39)))) | (~((~member(tptp_fun_X_4(B!39, A!40, F!42), A!40)) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F!42, tptp_fun_X_4(B!39, A!40, F!42), Y))))))))))) <=> ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(F!42, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!42), B!39)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!39, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))))))) | (~(maps(F!42, A!40, B!39) | (~((~member(tptp_fun_X_4(B!39, A!40, F!42), A!40)) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F!42, tptp_fun_X_4(B!39, A!40, F!42), Y)))))) | (~((~member(tptp_fun_Y2_5(B!39, A!40, F!42), B!39)) | (~member(tptp_fun_Y1_6(B!39, A!40, F!42), B!39)) | (~member(tptp_fun_X_7(B!39, A!40, F!42), A!40)) | (~apply(F!42, tptp_fun_X_7(B!39, A!40, F!42), tptp_fun_Y2_5(B!39, A!40, F!42))) | (~apply(F!42, tptp_fun_X_7(B!39, A!40, F!42), tptp_fun_Y1_6(B!39, A!40, F!42))) | (tptp_fun_Y1_6(B!39, A!40, F!42) = tptp_fun_Y2_5(B!39, A!40, F!42)))))))))),
% 0.22/0.49 inference(monotonicity,[status(thm)],[131])).
% 0.22/0.49 tff(133,plain,
% 0.22/0.49 (((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(F!42, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!42), B!39)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!39, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))))))) | (~(maps(F!42, A!40, B!39) | (~((tptp_fun_Y1_6(B!39, A!40, F!42) = tptp_fun_Y2_5(B!39, A!40, F!42)) | (~apply(F!42, tptp_fun_X_7(B!39, A!40, F!42), tptp_fun_Y1_6(B!39, A!40, F!42))) | (~apply(F!42, tptp_fun_X_7(B!39, A!40, F!42), tptp_fun_Y2_5(B!39, A!40, F!42))) | (~member(tptp_fun_X_7(B!39, A!40, F!42), A!40)) | (~member(tptp_fun_Y1_6(B!39, A!40, F!42), B!39)) | (~member(tptp_fun_Y2_5(B!39, A!40, F!42), B!39)))) | (~((~member(tptp_fun_X_4(B!39, A!40, F!42), A!40)) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F!42, tptp_fun_X_4(B!39, A!40, F!42), Y))))))))))) <=> ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(F!42, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!42), B!39)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!39, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))))))) | (~(maps(F!42, A!40, B!39) | (~((~member(tptp_fun_X_4(B!39, A!40, F!42), A!40)) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F!42, tptp_fun_X_4(B!39, A!40, F!42), Y)))))) | (~((~member(tptp_fun_Y2_5(B!39, A!40, F!42), B!39)) | (~member(tptp_fun_Y1_6(B!39, A!40, F!42), B!39)) | (~member(tptp_fun_X_7(B!39, A!40, F!42), A!40)) | (~apply(F!42, tptp_fun_X_7(B!39, A!40, F!42), tptp_fun_Y2_5(B!39, A!40, F!42))) | (~apply(F!42, tptp_fun_X_7(B!39, A!40, F!42), tptp_fun_Y1_6(B!39, A!40, F!42))) | (tptp_fun_Y1_6(B!39, A!40, F!42) = tptp_fun_Y2_5(B!39, A!40, F!42)))))))))),
% 0.22/0.50 inference(transitivity,[status(thm)],[132, 130])).
% 0.22/0.50 tff(134,plain,
% 0.22/0.50 ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(F!42, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!42), B!39)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!39, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))))))) | (~(maps(F!42, A!40, B!39) | (~((tptp_fun_Y1_6(B!39, A!40, F!42) = tptp_fun_Y2_5(B!39, A!40, F!42)) | (~apply(F!42, tptp_fun_X_7(B!39, A!40, F!42), tptp_fun_Y1_6(B!39, A!40, F!42))) | (~apply(F!42, tptp_fun_X_7(B!39, A!40, F!42), tptp_fun_Y2_5(B!39, A!40, F!42))) | (~member(tptp_fun_X_7(B!39, A!40, F!42), A!40)) | (~member(tptp_fun_Y1_6(B!39, A!40, F!42), B!39)) | (~member(tptp_fun_Y2_5(B!39, A!40, F!42), B!39)))) | (~((~member(tptp_fun_X_4(B!39, A!40, F!42), A!40)) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F!42, tptp_fun_X_4(B!39, A!40, F!42), Y))))))))))),
% 0.22/0.50 inference(quant_inst,[status(thm)],[])).
% 0.22/0.50 tff(135,plain,
% 0.22/0.50 ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(F!42, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!42), B!39)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!39, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))))))) | (~(maps(F!42, A!40, B!39) | (~((~member(tptp_fun_X_4(B!39, A!40, F!42), A!40)) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F!42, tptp_fun_X_4(B!39, A!40, F!42), Y)))))) | (~((~member(tptp_fun_Y2_5(B!39, A!40, F!42), B!39)) | (~member(tptp_fun_Y1_6(B!39, A!40, F!42), B!39)) | (~member(tptp_fun_X_7(B!39, A!40, F!42), A!40)) | (~apply(F!42, tptp_fun_X_7(B!39, A!40, F!42), tptp_fun_Y2_5(B!39, A!40, F!42))) | (~apply(F!42, tptp_fun_X_7(B!39, A!40, F!42), tptp_fun_Y1_6(B!39, A!40, F!42))) | (tptp_fun_Y1_6(B!39, A!40, F!42) = tptp_fun_Y2_5(B!39, A!40, F!42))))))))),
% 0.22/0.50 inference(modus_ponens,[status(thm)],[134, 133])).
% 0.22/0.50 tff(136,plain,
% 0.22/0.50 (~((~((~maps(F!42, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!42), B!39)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!39, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))))))) | (~(maps(F!42, A!40, B!39) | (~((~member(tptp_fun_X_4(B!39, A!40, F!42), A!40)) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F!42, tptp_fun_X_4(B!39, A!40, F!42), Y)))))) | (~((~member(tptp_fun_Y2_5(B!39, A!40, F!42), B!39)) | (~member(tptp_fun_Y1_6(B!39, A!40, F!42), B!39)) | (~member(tptp_fun_X_7(B!39, A!40, F!42), A!40)) | (~apply(F!42, tptp_fun_X_7(B!39, A!40, F!42), tptp_fun_Y2_5(B!39, A!40, F!42))) | (~apply(F!42, tptp_fun_X_7(B!39, A!40, F!42), tptp_fun_Y1_6(B!39, A!40, F!42))) | (tptp_fun_Y1_6(B!39, A!40, F!42) = tptp_fun_Y2_5(B!39, A!40, F!42)))))))),
% 0.22/0.50 inference(unit_resolution,[status(thm)],[135, 129])).
% 0.22/0.50 tff(137,plain,
% 0.22/0.50 (((~((~maps(F!42, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!42), B!39)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!39, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))))))) | (~(maps(F!42, A!40, B!39) | (~((~member(tptp_fun_X_4(B!39, A!40, F!42), A!40)) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F!42, tptp_fun_X_4(B!39, A!40, F!42), Y)))))) | (~((~member(tptp_fun_Y2_5(B!39, A!40, F!42), B!39)) | (~member(tptp_fun_Y1_6(B!39, A!40, F!42), B!39)) | (~member(tptp_fun_X_7(B!39, A!40, F!42), A!40)) | (~apply(F!42, tptp_fun_X_7(B!39, A!40, F!42), tptp_fun_Y2_5(B!39, A!40, F!42))) | (~apply(F!42, tptp_fun_X_7(B!39, A!40, F!42), tptp_fun_Y1_6(B!39, A!40, F!42))) | (tptp_fun_Y1_6(B!39, A!40, F!42) = tptp_fun_Y2_5(B!39, A!40, F!42))))))) | ((~maps(F!42, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!42), B!39)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!39, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))))))),
% 0.22/0.50 inference(tautology,[status(thm)],[])).
% 0.22/0.50 tff(138,plain,
% 0.22/0.50 ((~maps(F!42, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!42), B!39)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!39, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39))))))),
% 0.22/0.50 inference(unit_resolution,[status(thm)],[137, 136])).
% 0.22/0.50 tff(139,plain,
% 0.22/0.50 (maps(F!42, A!40, B!39)),
% 0.22/0.50 inference(and_elim,[status(thm)],[88])).
% 0.22/0.50 tff(140,plain,
% 0.22/0.50 ((~((~maps(F!42, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!42), B!39)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!39, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))))))) | (~maps(F!42, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!42), B!39)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!39, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39))))))),
% 0.22/0.50 inference(tautology,[status(thm)],[])).
% 0.22/0.50 tff(141,plain,
% 0.22/0.50 ((~((~maps(F!42, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!42), B!39)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!39, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))))))) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!42), B!39)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!39, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39))))))),
% 0.22/0.50 inference(unit_resolution,[status(thm)],[140, 139])).
% 0.22/0.50 tff(142,plain,
% 0.22/0.50 (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!42), B!39)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!39, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))))),
% 0.22/0.50 inference(unit_resolution,[status(thm)],[141, 138])).
% 0.22/0.50 tff(143,plain,
% 0.22/0.50 (((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!42), B!39)) | (~apply(F!42, X, tptp_fun_Y_3(X, B!39, F!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39))))) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))),
% 0.22/0.50 inference(tautology,[status(thm)],[])).
% 0.22/0.50 tff(144,plain,
% 0.22/0.50 (![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))),
% 0.22/0.50 inference(unit_resolution,[status(thm)],[143, 142])).
% 0.22/0.50 tff(145,plain,
% 0.22/0.50 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))) | ((~member(tptp_fun_Y_16(B!39, A!40, F!42), B!39)) | (~member(tptp_fun_X1_18(B!39, A!40, F!42), A!40)) | (~apply(F!42, tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_Y_16(B!39, A!40, F!42))) | (~apply(F!42, tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42), B!39, F!42, G!41))) | (~member(tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42), B!39, F!42, G!41), B!39)) | (tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42), B!39, F!42, G!41) = tptp_fun_Y_16(B!39, A!40, F!42)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))) | (~member(tptp_fun_Y_16(B!39, A!40, F!42), B!39)) | (~member(tptp_fun_X1_18(B!39, A!40, F!42), A!40)) | (~apply(F!42, tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_Y_16(B!39, A!40, F!42))) | (~apply(F!42, tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42), B!39, F!42, G!41))) | (~member(tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42), B!39, F!42, G!41), B!39)) | (tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42), B!39, F!42, G!41) = tptp_fun_Y_16(B!39, A!40, F!42)))),
% 0.22/0.50 inference(rewrite,[status(thm)],[])).
% 0.22/0.50 tff(146,plain,
% 0.22/0.50 (((tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42), B!39, F!42, G!41) = tptp_fun_Y_16(B!39, A!40, F!42)) | (~member(tptp_fun_Y_16(B!39, A!40, F!42), B!39)) | (~apply(F!42, tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42), B!39, F!42, G!41))) | (~apply(F!42, tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_Y_16(B!39, A!40, F!42))) | (~member(tptp_fun_X1_18(B!39, A!40, F!42), A!40)) | (~member(tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42), B!39, F!42, G!41), B!39))) <=> ((~member(tptp_fun_Y_16(B!39, A!40, F!42), B!39)) | (~member(tptp_fun_X1_18(B!39, A!40, F!42), A!40)) | (~apply(F!42, tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_Y_16(B!39, A!40, F!42))) | (~apply(F!42, tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42), B!39, F!42, G!41))) | (~member(tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42), B!39, F!42, G!41), B!39)) | (tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42), B!39, F!42, G!41) = tptp_fun_Y_16(B!39, A!40, F!42)))),
% 0.22/0.50 inference(rewrite,[status(thm)],[])).
% 0.22/0.50 tff(147,plain,
% 0.22/0.50 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))) | ((tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42), B!39, F!42, G!41) = tptp_fun_Y_16(B!39, A!40, F!42)) | (~member(tptp_fun_Y_16(B!39, A!40, F!42), B!39)) | (~apply(F!42, tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42), B!39, F!42, G!41))) | (~apply(F!42, tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_Y_16(B!39, A!40, F!42))) | (~member(tptp_fun_X1_18(B!39, A!40, F!42), A!40)) | (~member(tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42), B!39, F!42, G!41), B!39)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))) | ((~member(tptp_fun_Y_16(B!39, A!40, F!42), B!39)) | (~member(tptp_fun_X1_18(B!39, A!40, F!42), A!40)) | (~apply(F!42, tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_Y_16(B!39, A!40, F!42))) | (~apply(F!42, tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42), B!39, F!42, G!41))) | (~member(tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42), B!39, F!42, G!41), B!39)) | (tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42), B!39, F!42, G!41) = tptp_fun_Y_16(B!39, A!40, F!42))))),
% 0.22/0.50 inference(monotonicity,[status(thm)],[146])).
% 0.22/0.50 tff(148,plain,
% 0.22/0.50 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))) | ((tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42), B!39, F!42, G!41) = tptp_fun_Y_16(B!39, A!40, F!42)) | (~member(tptp_fun_Y_16(B!39, A!40, F!42), B!39)) | (~apply(F!42, tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42), B!39, F!42, G!41))) | (~apply(F!42, tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_Y_16(B!39, A!40, F!42))) | (~member(tptp_fun_X1_18(B!39, A!40, F!42), A!40)) | (~member(tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42), B!39, F!42, G!41), B!39)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))) | (~member(tptp_fun_Y_16(B!39, A!40, F!42), B!39)) | (~member(tptp_fun_X1_18(B!39, A!40, F!42), A!40)) | (~apply(F!42, tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_Y_16(B!39, A!40, F!42))) | (~apply(F!42, tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42), B!39, F!42, G!41))) | (~member(tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42), B!39, F!42, G!41), B!39)) | (tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42), B!39, F!42, G!41) = tptp_fun_Y_16(B!39, A!40, F!42)))),
% 0.22/0.51 inference(transitivity,[status(thm)],[147, 145])).
% 0.22/0.51 tff(149,plain,
% 0.22/0.51 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))) | ((tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42), B!39, F!42, G!41) = tptp_fun_Y_16(B!39, A!40, F!42)) | (~member(tptp_fun_Y_16(B!39, A!40, F!42), B!39)) | (~apply(F!42, tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42), B!39, F!42, G!41))) | (~apply(F!42, tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_Y_16(B!39, A!40, F!42))) | (~member(tptp_fun_X1_18(B!39, A!40, F!42), A!40)) | (~member(tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42), B!39, F!42, G!41), B!39)))),
% 0.22/0.51 inference(quant_inst,[status(thm)],[])).
% 0.22/0.51 tff(150,plain,
% 0.22/0.51 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))) | (~member(tptp_fun_Y_16(B!39, A!40, F!42), B!39)) | (~member(tptp_fun_X1_18(B!39, A!40, F!42), A!40)) | (~apply(F!42, tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_Y_16(B!39, A!40, F!42))) | (~apply(F!42, tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42), B!39, F!42, G!41))) | (~member(tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42), B!39, F!42, G!41), B!39)) | (tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42), B!39, F!42, G!41) = tptp_fun_Y_16(B!39, A!40, F!42))),
% 0.22/0.51 inference(modus_ponens,[status(thm)],[149, 148])).
% 0.22/0.51 tff(151,plain,
% 0.22/0.51 (tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42), B!39, F!42, G!41) = tptp_fun_Y_16(B!39, A!40, F!42)),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[150, 144, 107, 39, 105, 103, 101])).
% 0.22/0.51 tff(152,plain,
% 0.22/0.51 (tptp_fun_Y_16(B!39, A!40, F!42) = tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42), B!39, F!42, G!41)),
% 0.22/0.51 inference(symmetry,[status(thm)],[151])).
% 0.22/0.51 tff(153,plain,
% 0.22/0.51 (apply(G!41, tptp_fun_Y_16(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42)) <=> apply(G!41, tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42), B!39, F!42, G!41), tptp_fun_X1_18(B!39, A!40, F!42))),
% 0.22/0.51 inference(monotonicity,[status(thm)],[152])).
% 0.22/0.51 tff(154,plain,
% 0.22/0.51 (apply(G!41, tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42), B!39, F!42, G!41), tptp_fun_X1_18(B!39, A!40, F!42)) <=> apply(G!41, tptp_fun_Y_16(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42))),
% 0.22/0.51 inference(symmetry,[status(thm)],[153])).
% 0.22/0.51 tff(155,plain,
% 0.22/0.51 (((~member(tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42), B!39, F!42, G!41), B!39)) | (~apply(F!42, tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42), B!39, F!42, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42), B!39, F!42, G!41), tptp_fun_X1_18(B!39, A!40, F!42)))) | apply(G!41, tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42), B!39, F!42, G!41), tptp_fun_X1_18(B!39, A!40, F!42))),
% 0.22/0.51 inference(tautology,[status(thm)],[])).
% 0.22/0.51 tff(156,plain,
% 0.22/0.51 (apply(G!41, tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42), B!39, F!42, G!41), tptp_fun_X1_18(B!39, A!40, F!42))),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[155, 99])).
% 0.22/0.51 tff(157,plain,
% 0.22/0.51 (apply(G!41, tptp_fun_Y_16(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42))),
% 0.22/0.51 inference(modus_ponens,[status(thm)],[156, 154])).
% 0.22/0.51 tff(158,plain,
% 0.22/0.51 (((~member(tptp_fun_Y_16(B!39, A!40, F!42), B!39)) | (~member(tptp_fun_X1_18(B!39, A!40, F!42), A!40)) | (~member(tptp_fun_X2_17(B!39, A!40, F!42), A!40)) | (~apply(F!42, tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_Y_16(B!39, A!40, F!42))) | (~apply(F!42, tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_Y_16(B!39, A!40, F!42))) | (tptp_fun_X1_18(B!39, A!40, F!42) = tptp_fun_X2_17(B!39, A!40, F!42))) | member(tptp_fun_X2_17(B!39, A!40, F!42), A!40)),
% 0.22/0.51 inference(tautology,[status(thm)],[])).
% 0.22/0.51 tff(159,plain,
% 0.22/0.51 (member(tptp_fun_X2_17(B!39, A!40, F!42), A!40)),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[158, 37])).
% 0.22/0.51 tff(160,plain,
% 0.22/0.51 (((~![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_X2_17(B!39, A!40, F!42), A!40)) | (~((~(apply(compose_function(G!41, F!42, A!40, B!39, A!40), tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!42, tptp_fun_X2_17(B!39, A!40, F!42), Y)) | (~apply(G!41, Y, tptp_fun_X2_17(B!39, A!40, F!42)))))) | (~((~apply(compose_function(G!41, F!42, A!40, B!39, A!40), tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42), B!39, F!42, G!41), B!39)) | (~apply(F!42, tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42), B!39, F!42, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42), B!39, F!42, G!41), tptp_fun_X2_17(B!39, A!40, F!42))))))))))) <=> ((~![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_X2_17(B!39, A!40, F!42), A!40)) | (~((~(apply(compose_function(G!41, F!42, A!40, B!39, A!40), tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!42, tptp_fun_X2_17(B!39, A!40, F!42), Y)) | (~apply(G!41, Y, tptp_fun_X2_17(B!39, A!40, F!42)))))) | (~((~apply(compose_function(G!41, F!42, A!40, B!39, A!40), tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42), B!39, F!42, G!41), B!39)) | (~apply(F!42, tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42), B!39, F!42, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42), B!39, F!42, G!41), tptp_fun_X2_17(B!39, A!40, F!42))))))))))),
% 0.22/0.51 inference(rewrite,[status(thm)],[])).
% 0.22/0.51 tff(161,plain,
% 0.22/0.51 (((~member(tptp_fun_X2_17(B!39, A!40, F!42), A!40)) | (~member(tptp_fun_X2_17(B!39, A!40, F!42), A!40)) | (~((~(apply(compose_function(G!41, F!42, A!40, B!39, A!40), tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!42, tptp_fun_X2_17(B!39, A!40, F!42), Y)) | (~apply(G!41, Y, tptp_fun_X2_17(B!39, A!40, F!42)))))) | (~((~apply(compose_function(G!41, F!42, A!40, B!39, A!40), tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42), B!39, F!42, G!41), B!39)) | (~apply(F!42, tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42), B!39, F!42, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42), B!39, F!42, G!41), tptp_fun_X2_17(B!39, A!40, F!42)))))))))) <=> ((~member(tptp_fun_X2_17(B!39, A!40, F!42), A!40)) | (~((~(apply(compose_function(G!41, F!42, A!40, B!39, A!40), tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!42, tptp_fun_X2_17(B!39, A!40, F!42), Y)) | (~apply(G!41, Y, tptp_fun_X2_17(B!39, A!40, F!42)))))) | (~((~apply(compose_function(G!41, F!42, A!40, B!39, A!40), tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42), B!39, F!42, G!41), B!39)) | (~apply(F!42, tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42), B!39, F!42, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42), B!39, F!42, G!41), tptp_fun_X2_17(B!39, A!40, F!42))))))))))),
% 0.22/0.51 inference(rewrite,[status(thm)],[])).
% 0.22/0.51 tff(162,plain,
% 0.22/0.51 ((~((~((~apply(compose_function(G!41, F!42, A!40, B!39, A!40), tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42), B!39, F!42, G!41), B!39)) | (~apply(F!42, tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42), B!39, F!42, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42), B!39, F!42, G!41), tptp_fun_X2_17(B!39, A!40, F!42))))))) | (~(apply(compose_function(G!41, F!42, A!40, B!39, A!40), tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!42, tptp_fun_X2_17(B!39, A!40, F!42), Y)) | (~apply(G!41, Y, tptp_fun_X2_17(B!39, A!40, F!42)))))))) <=> (~((~(apply(compose_function(G!41, F!42, A!40, B!39, A!40), tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!42, tptp_fun_X2_17(B!39, A!40, F!42), Y)) | (~apply(G!41, Y, tptp_fun_X2_17(B!39, A!40, F!42)))))) | (~((~apply(compose_function(G!41, F!42, A!40, B!39, A!40), tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42), B!39, F!42, G!41), B!39)) | (~apply(F!42, tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42), B!39, F!42, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42), B!39, F!42, G!41), tptp_fun_X2_17(B!39, A!40, F!42)))))))))),
% 0.22/0.51 inference(rewrite,[status(thm)],[])).
% 0.22/0.51 tff(163,plain,
% 0.22/0.51 (((~member(tptp_fun_X2_17(B!39, A!40, F!42), A!40)) | (~member(tptp_fun_X2_17(B!39, A!40, F!42), A!40)) | (~((~((~apply(compose_function(G!41, F!42, A!40, B!39, A!40), tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42), B!39, F!42, G!41), B!39)) | (~apply(F!42, tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42), B!39, F!42, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42), B!39, F!42, G!41), tptp_fun_X2_17(B!39, A!40, F!42))))))) | (~(apply(compose_function(G!41, F!42, A!40, B!39, A!40), tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!42, tptp_fun_X2_17(B!39, A!40, F!42), Y)) | (~apply(G!41, Y, tptp_fun_X2_17(B!39, A!40, F!42))))))))) <=> ((~member(tptp_fun_X2_17(B!39, A!40, F!42), A!40)) | (~member(tptp_fun_X2_17(B!39, A!40, F!42), A!40)) | (~((~(apply(compose_function(G!41, F!42, A!40, B!39, A!40), tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!42, tptp_fun_X2_17(B!39, A!40, F!42), Y)) | (~apply(G!41, Y, tptp_fun_X2_17(B!39, A!40, F!42)))))) | (~((~apply(compose_function(G!41, F!42, A!40, B!39, A!40), tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42), B!39, F!42, G!41), B!39)) | (~apply(F!42, tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42), B!39, F!42, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42), B!39, F!42, G!41), tptp_fun_X2_17(B!39, A!40, F!42))))))))))),
% 0.22/0.51 inference(monotonicity,[status(thm)],[162])).
% 0.22/0.51 tff(164,plain,
% 0.22/0.51 (((~member(tptp_fun_X2_17(B!39, A!40, F!42), A!40)) | (~member(tptp_fun_X2_17(B!39, A!40, F!42), A!40)) | (~((~((~apply(compose_function(G!41, F!42, A!40, B!39, A!40), tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42), B!39, F!42, G!41), B!39)) | (~apply(F!42, tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42), B!39, F!42, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42), B!39, F!42, G!41), tptp_fun_X2_17(B!39, A!40, F!42))))))) | (~(apply(compose_function(G!41, F!42, A!40, B!39, A!40), tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!42, tptp_fun_X2_17(B!39, A!40, F!42), Y)) | (~apply(G!41, Y, tptp_fun_X2_17(B!39, A!40, F!42))))))))) <=> ((~member(tptp_fun_X2_17(B!39, A!40, F!42), A!40)) | (~((~(apply(compose_function(G!41, F!42, A!40, B!39, A!40), tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!42, tptp_fun_X2_17(B!39, A!40, F!42), Y)) | (~apply(G!41, Y, tptp_fun_X2_17(B!39, A!40, F!42)))))) | (~((~apply(compose_function(G!41, F!42, A!40, B!39, A!40), tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42), B!39, F!42, G!41), B!39)) | (~apply(F!42, tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42), B!39, F!42, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42), B!39, F!42, G!41), tptp_fun_X2_17(B!39, A!40, F!42))))))))))),
% 0.22/0.51 inference(transitivity,[status(thm)],[163, 161])).
% 0.22/0.51 tff(165,plain,
% 0.22/0.51 (((~![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_X2_17(B!39, A!40, F!42), A!40)) | (~member(tptp_fun_X2_17(B!39, A!40, F!42), A!40)) | (~((~((~apply(compose_function(G!41, F!42, A!40, B!39, A!40), tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42), B!39, F!42, G!41), B!39)) | (~apply(F!42, tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42), B!39, F!42, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42), B!39, F!42, G!41), tptp_fun_X2_17(B!39, A!40, F!42))))))) | (~(apply(compose_function(G!41, F!42, A!40, B!39, A!40), tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!42, tptp_fun_X2_17(B!39, A!40, F!42), Y)) | (~apply(G!41, Y, tptp_fun_X2_17(B!39, A!40, F!42)))))))))) <=> ((~![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_X2_17(B!39, A!40, F!42), A!40)) | (~((~(apply(compose_function(G!41, F!42, A!40, B!39, A!40), tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!42, tptp_fun_X2_17(B!39, A!40, F!42), Y)) | (~apply(G!41, Y, tptp_fun_X2_17(B!39, A!40, F!42)))))) | (~((~apply(compose_function(G!41, F!42, A!40, B!39, A!40), tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42), B!39, F!42, G!41), B!39)) | (~apply(F!42, tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42), B!39, F!42, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42), B!39, F!42, G!41), tptp_fun_X2_17(B!39, A!40, F!42)))))))))))),
% 0.22/0.52 inference(monotonicity,[status(thm)],[164])).
% 0.22/0.52 tff(166,plain,
% 0.22/0.52 (((~![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_X2_17(B!39, A!40, F!42), A!40)) | (~member(tptp_fun_X2_17(B!39, A!40, F!42), A!40)) | (~((~((~apply(compose_function(G!41, F!42, A!40, B!39, A!40), tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42), B!39, F!42, G!41), B!39)) | (~apply(F!42, tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42), B!39, F!42, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42), B!39, F!42, G!41), tptp_fun_X2_17(B!39, A!40, F!42))))))) | (~(apply(compose_function(G!41, F!42, A!40, B!39, A!40), tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!42, tptp_fun_X2_17(B!39, A!40, F!42), Y)) | (~apply(G!41, Y, tptp_fun_X2_17(B!39, A!40, F!42)))))))))) <=> ((~![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_X2_17(B!39, A!40, F!42), A!40)) | (~((~(apply(compose_function(G!41, F!42, A!40, B!39, A!40), tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!42, tptp_fun_X2_17(B!39, A!40, F!42), Y)) | (~apply(G!41, Y, tptp_fun_X2_17(B!39, A!40, F!42)))))) | (~((~apply(compose_function(G!41, F!42, A!40, B!39, A!40), tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42), B!39, F!42, G!41), B!39)) | (~apply(F!42, tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42), B!39, F!42, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42), B!39, F!42, G!41), tptp_fun_X2_17(B!39, A!40, F!42))))))))))),
% 0.22/0.52 inference(transitivity,[status(thm)],[165, 160])).
% 0.22/0.52 tff(167,plain,
% 0.22/0.52 ((~![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_X2_17(B!39, A!40, F!42), A!40)) | (~member(tptp_fun_X2_17(B!39, A!40, F!42), A!40)) | (~((~((~apply(compose_function(G!41, F!42, A!40, B!39, A!40), tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42), B!39, F!42, G!41), B!39)) | (~apply(F!42, tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42), B!39, F!42, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42), B!39, F!42, G!41), tptp_fun_X2_17(B!39, A!40, F!42))))))) | (~(apply(compose_function(G!41, F!42, A!40, B!39, A!40), tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!42, tptp_fun_X2_17(B!39, A!40, F!42), Y)) | (~apply(G!41, Y, tptp_fun_X2_17(B!39, A!40, F!42)))))))))),
% 0.22/0.52 inference(quant_inst,[status(thm)],[])).
% 0.22/0.52 tff(168,plain,
% 0.22/0.52 ((~![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_X2_17(B!39, A!40, F!42), A!40)) | (~((~(apply(compose_function(G!41, F!42, A!40, B!39, A!40), tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!42, tptp_fun_X2_17(B!39, A!40, F!42), Y)) | (~apply(G!41, Y, tptp_fun_X2_17(B!39, A!40, F!42)))))) | (~((~apply(compose_function(G!41, F!42, A!40, B!39, A!40), tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42), B!39, F!42, G!41), B!39)) | (~apply(F!42, tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42), B!39, F!42, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42), B!39, F!42, G!41), tptp_fun_X2_17(B!39, A!40, F!42)))))))))),
% 0.22/0.52 inference(modus_ponens,[status(thm)],[167, 166])).
% 0.22/0.52 tff(169,plain,
% 0.22/0.52 (~((~(apply(compose_function(G!41, F!42, A!40, B!39, A!40), tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!42, tptp_fun_X2_17(B!39, A!40, F!42), Y)) | (~apply(G!41, Y, tptp_fun_X2_17(B!39, A!40, F!42)))))) | (~((~apply(compose_function(G!41, F!42, A!40, B!39, A!40), tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42), B!39, F!42, G!41), B!39)) | (~apply(F!42, tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42), B!39, F!42, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42), B!39, F!42, G!41), tptp_fun_X2_17(B!39, A!40, F!42))))))))),
% 0.22/0.52 inference(unit_resolution,[status(thm)],[168, 55, 159])).
% 0.22/0.52 tff(170,plain,
% 0.22/0.52 (((~(apply(compose_function(G!41, F!42, A!40, B!39, A!40), tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!42, tptp_fun_X2_17(B!39, A!40, F!42), Y)) | (~apply(G!41, Y, tptp_fun_X2_17(B!39, A!40, F!42)))))) | (~((~apply(compose_function(G!41, F!42, A!40, B!39, A!40), tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42), B!39, F!42, G!41), B!39)) | (~apply(F!42, tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42), B!39, F!42, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42), B!39, F!42, G!41), tptp_fun_X2_17(B!39, A!40, F!42)))))))) | ((~apply(compose_function(G!41, F!42, A!40, B!39, A!40), tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42), B!39, F!42, G!41), B!39)) | (~apply(F!42, tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42), B!39, F!42, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42), B!39, F!42, G!41), tptp_fun_X2_17(B!39, A!40, F!42))))))),
% 0.22/0.52 inference(tautology,[status(thm)],[])).
% 0.22/0.52 tff(171,plain,
% 0.22/0.52 ((~apply(compose_function(G!41, F!42, A!40, B!39, A!40), tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42), B!39, F!42, G!41), B!39)) | (~apply(F!42, tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42), B!39, F!42, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42), B!39, F!42, G!41), tptp_fun_X2_17(B!39, A!40, F!42)))))),
% 0.22/0.52 inference(unit_resolution,[status(thm)],[170, 169])).
% 0.22/0.52 tff(172,plain,
% 0.22/0.52 (((~![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!41, F!42, A!40, B!39, A!40), X, X))) | ((~member(tptp_fun_X2_17(B!39, A!40, F!42), A!40)) | apply(compose_function(G!41, F!42, A!40, B!39, A!40), tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42)))) <=> ((~![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!41, F!42, A!40, B!39, A!40), X, X))) | (~member(tptp_fun_X2_17(B!39, A!40, F!42), A!40)) | apply(compose_function(G!41, F!42, A!40, B!39, A!40), tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42)))),
% 0.22/0.52 inference(rewrite,[status(thm)],[])).
% 0.22/0.52 tff(173,plain,
% 0.22/0.52 ((~![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!41, F!42, A!40, B!39, A!40), X, X))) | ((~member(tptp_fun_X2_17(B!39, A!40, F!42), A!40)) | apply(compose_function(G!41, F!42, A!40, B!39, A!40), tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42)))),
% 0.22/0.52 inference(quant_inst,[status(thm)],[])).
% 0.22/0.52 tff(174,plain,
% 0.22/0.52 ((~![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!41, F!42, A!40, B!39, A!40), X, X))) | (~member(tptp_fun_X2_17(B!39, A!40, F!42), A!40)) | apply(compose_function(G!41, F!42, A!40, B!39, A!40), tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42))),
% 0.22/0.52 inference(modus_ponens,[status(thm)],[173, 172])).
% 0.22/0.52 tff(175,plain,
% 0.22/0.52 (apply(compose_function(G!41, F!42, A!40, B!39, A!40), tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42))),
% 0.22/0.52 inference(unit_resolution,[status(thm)],[174, 92, 159])).
% 0.22/0.52 tff(176,plain,
% 0.22/0.52 ((~((~apply(compose_function(G!41, F!42, A!40, B!39, A!40), tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42), B!39, F!42, G!41), B!39)) | (~apply(F!42, tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42), B!39, F!42, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42), B!39, F!42, G!41), tptp_fun_X2_17(B!39, A!40, F!42))))))) | (~apply(compose_function(G!41, F!42, A!40, B!39, A!40), tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42), B!39, F!42, G!41), B!39)) | (~apply(F!42, tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42), B!39, F!42, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42), B!39, F!42, G!41), tptp_fun_X2_17(B!39, A!40, F!42)))))),
% 0.22/0.52 inference(tautology,[status(thm)],[])).
% 0.22/0.52 tff(177,plain,
% 0.22/0.52 ((~((~apply(compose_function(G!41, F!42, A!40, B!39, A!40), tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42), B!39, F!42, G!41), B!39)) | (~apply(F!42, tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42), B!39, F!42, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42), B!39, F!42, G!41), tptp_fun_X2_17(B!39, A!40, F!42))))))) | (~((~member(tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42), B!39, F!42, G!41), B!39)) | (~apply(F!42, tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42), B!39, F!42, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42), B!39, F!42, G!41), tptp_fun_X2_17(B!39, A!40, F!42)))))),
% 0.22/0.52 inference(unit_resolution,[status(thm)],[176, 175])).
% 0.22/0.52 tff(178,plain,
% 0.22/0.52 (~((~member(tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42), B!39, F!42, G!41), B!39)) | (~apply(F!42, tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42), B!39, F!42, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42), B!39, F!42, G!41), tptp_fun_X2_17(B!39, A!40, F!42))))),
% 0.22/0.52 inference(unit_resolution,[status(thm)],[177, 171])).
% 0.22/0.52 tff(179,plain,
% 0.22/0.52 (((~member(tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42), B!39, F!42, G!41), B!39)) | (~apply(F!42, tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42), B!39, F!42, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42), B!39, F!42, G!41), tptp_fun_X2_17(B!39, A!40, F!42)))) | apply(F!42, tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42), B!39, F!42, G!41))),
% 0.22/0.52 inference(tautology,[status(thm)],[])).
% 0.22/0.52 tff(180,plain,
% 0.22/0.52 (apply(F!42, tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42), B!39, F!42, G!41))),
% 0.22/0.52 inference(unit_resolution,[status(thm)],[179, 178])).
% 0.22/0.52 tff(181,plain,
% 0.22/0.52 (((~member(tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42), B!39, F!42, G!41), B!39)) | (~apply(F!42, tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42), B!39, F!42, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42), B!39, F!42, G!41), tptp_fun_X2_17(B!39, A!40, F!42)))) | member(tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42), B!39, F!42, G!41), B!39)),
% 0.22/0.52 inference(tautology,[status(thm)],[])).
% 0.22/0.52 tff(182,plain,
% 0.22/0.52 (member(tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42), B!39, F!42, G!41), B!39)),
% 0.22/0.52 inference(unit_resolution,[status(thm)],[181, 178])).
% 0.22/0.52 tff(183,plain,
% 0.22/0.52 (((~member(tptp_fun_Y_16(B!39, A!40, F!42), B!39)) | (~member(tptp_fun_X1_18(B!39, A!40, F!42), A!40)) | (~member(tptp_fun_X2_17(B!39, A!40, F!42), A!40)) | (~apply(F!42, tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_Y_16(B!39, A!40, F!42))) | (~apply(F!42, tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_Y_16(B!39, A!40, F!42))) | (tptp_fun_X1_18(B!39, A!40, F!42) = tptp_fun_X2_17(B!39, A!40, F!42))) | apply(F!42, tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_Y_16(B!39, A!40, F!42))),
% 0.22/0.53 inference(tautology,[status(thm)],[])).
% 0.22/0.53 tff(184,plain,
% 0.22/0.53 (apply(F!42, tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_Y_16(B!39, A!40, F!42))),
% 0.22/0.53 inference(unit_resolution,[status(thm)],[183, 37])).
% 0.22/0.53 tff(185,plain,
% 0.22/0.53 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))) | ((~member(tptp_fun_Y_16(B!39, A!40, F!42), B!39)) | (~member(tptp_fun_X2_17(B!39, A!40, F!42), A!40)) | (~apply(F!42, tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_Y_16(B!39, A!40, F!42))) | (~apply(F!42, tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42), B!39, F!42, G!41))) | (~member(tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42), B!39, F!42, G!41), B!39)) | (tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42), B!39, F!42, G!41) = tptp_fun_Y_16(B!39, A!40, F!42)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))) | (~member(tptp_fun_Y_16(B!39, A!40, F!42), B!39)) | (~member(tptp_fun_X2_17(B!39, A!40, F!42), A!40)) | (~apply(F!42, tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_Y_16(B!39, A!40, F!42))) | (~apply(F!42, tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42), B!39, F!42, G!41))) | (~member(tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42), B!39, F!42, G!41), B!39)) | (tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42), B!39, F!42, G!41) = tptp_fun_Y_16(B!39, A!40, F!42)))),
% 0.22/0.53 inference(rewrite,[status(thm)],[])).
% 0.22/0.53 tff(186,plain,
% 0.22/0.53 (((tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42), B!39, F!42, G!41) = tptp_fun_Y_16(B!39, A!40, F!42)) | (~member(tptp_fun_Y_16(B!39, A!40, F!42), B!39)) | (~apply(F!42, tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42), B!39, F!42, G!41))) | (~apply(F!42, tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_Y_16(B!39, A!40, F!42))) | (~member(tptp_fun_X2_17(B!39, A!40, F!42), A!40)) | (~member(tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42), B!39, F!42, G!41), B!39))) <=> ((~member(tptp_fun_Y_16(B!39, A!40, F!42), B!39)) | (~member(tptp_fun_X2_17(B!39, A!40, F!42), A!40)) | (~apply(F!42, tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_Y_16(B!39, A!40, F!42))) | (~apply(F!42, tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42), B!39, F!42, G!41))) | (~member(tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42), B!39, F!42, G!41), B!39)) | (tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42), B!39, F!42, G!41) = tptp_fun_Y_16(B!39, A!40, F!42)))),
% 0.22/0.53 inference(rewrite,[status(thm)],[])).
% 0.22/0.53 tff(187,plain,
% 0.22/0.53 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))) | ((tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42), B!39, F!42, G!41) = tptp_fun_Y_16(B!39, A!40, F!42)) | (~member(tptp_fun_Y_16(B!39, A!40, F!42), B!39)) | (~apply(F!42, tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42), B!39, F!42, G!41))) | (~apply(F!42, tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_Y_16(B!39, A!40, F!42))) | (~member(tptp_fun_X2_17(B!39, A!40, F!42), A!40)) | (~member(tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42), B!39, F!42, G!41), B!39)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))) | ((~member(tptp_fun_Y_16(B!39, A!40, F!42), B!39)) | (~member(tptp_fun_X2_17(B!39, A!40, F!42), A!40)) | (~apply(F!42, tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_Y_16(B!39, A!40, F!42))) | (~apply(F!42, tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42), B!39, F!42, G!41))) | (~member(tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42), B!39, F!42, G!41), B!39)) | (tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42), B!39, F!42, G!41) = tptp_fun_Y_16(B!39, A!40, F!42))))),
% 0.22/0.53 inference(monotonicity,[status(thm)],[186])).
% 0.22/0.53 tff(188,plain,
% 0.22/0.53 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))) | ((tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42), B!39, F!42, G!41) = tptp_fun_Y_16(B!39, A!40, F!42)) | (~member(tptp_fun_Y_16(B!39, A!40, F!42), B!39)) | (~apply(F!42, tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42), B!39, F!42, G!41))) | (~apply(F!42, tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_Y_16(B!39, A!40, F!42))) | (~member(tptp_fun_X2_17(B!39, A!40, F!42), A!40)) | (~member(tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42), B!39, F!42, G!41), B!39)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))) | (~member(tptp_fun_Y_16(B!39, A!40, F!42), B!39)) | (~member(tptp_fun_X2_17(B!39, A!40, F!42), A!40)) | (~apply(F!42, tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_Y_16(B!39, A!40, F!42))) | (~apply(F!42, tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42), B!39, F!42, G!41))) | (~member(tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42), B!39, F!42, G!41), B!39)) | (tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42), B!39, F!42, G!41) = tptp_fun_Y_16(B!39, A!40, F!42)))),
% 0.22/0.53 inference(transitivity,[status(thm)],[187, 185])).
% 0.22/0.53 tff(189,plain,
% 0.22/0.53 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))) | ((tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42), B!39, F!42, G!41) = tptp_fun_Y_16(B!39, A!40, F!42)) | (~member(tptp_fun_Y_16(B!39, A!40, F!42), B!39)) | (~apply(F!42, tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42), B!39, F!42, G!41))) | (~apply(F!42, tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_Y_16(B!39, A!40, F!42))) | (~member(tptp_fun_X2_17(B!39, A!40, F!42), A!40)) | (~member(tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42), B!39, F!42, G!41), B!39)))),
% 0.22/0.53 inference(quant_inst,[status(thm)],[])).
% 0.22/0.53 tff(190,plain,
% 0.22/0.53 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!42, X, Y1)) | (~apply(F!42, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))) | (~member(tptp_fun_Y_16(B!39, A!40, F!42), B!39)) | (~member(tptp_fun_X2_17(B!39, A!40, F!42), A!40)) | (~apply(F!42, tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_Y_16(B!39, A!40, F!42))) | (~apply(F!42, tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42), B!39, F!42, G!41))) | (~member(tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42), B!39, F!42, G!41), B!39)) | (tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42), B!39, F!42, G!41) = tptp_fun_Y_16(B!39, A!40, F!42))),
% 0.22/0.53 inference(modus_ponens,[status(thm)],[189, 188])).
% 0.22/0.53 tff(191,plain,
% 0.22/0.53 (tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42), B!39, F!42, G!41) = tptp_fun_Y_16(B!39, A!40, F!42)),
% 0.22/0.53 inference(unit_resolution,[status(thm)],[190, 144, 107, 159, 184, 182, 180])).
% 0.22/0.53 tff(192,plain,
% 0.22/0.53 (tptp_fun_Y_16(B!39, A!40, F!42) = tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42), B!39, F!42, G!41)),
% 0.22/0.53 inference(symmetry,[status(thm)],[191])).
% 0.22/0.53 tff(193,plain,
% 0.22/0.53 (apply(G!41, tptp_fun_Y_16(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42)) <=> apply(G!41, tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42), B!39, F!42, G!41), tptp_fun_X2_17(B!39, A!40, F!42))),
% 0.22/0.53 inference(monotonicity,[status(thm)],[192])).
% 0.22/0.53 tff(194,plain,
% 0.22/0.53 (apply(G!41, tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42), B!39, F!42, G!41), tptp_fun_X2_17(B!39, A!40, F!42)) <=> apply(G!41, tptp_fun_Y_16(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42))),
% 0.22/0.53 inference(symmetry,[status(thm)],[193])).
% 0.22/0.53 tff(195,plain,
% 0.22/0.53 (((~member(tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42), B!39, F!42, G!41), B!39)) | (~apply(F!42, tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42), B!39, F!42, G!41))) | (~apply(G!41, tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42), B!39, F!42, G!41), tptp_fun_X2_17(B!39, A!40, F!42)))) | apply(G!41, tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42), B!39, F!42, G!41), tptp_fun_X2_17(B!39, A!40, F!42))),
% 0.22/0.53 inference(tautology,[status(thm)],[])).
% 0.22/0.53 tff(196,plain,
% 0.22/0.53 (apply(G!41, tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42), B!39, F!42, G!41), tptp_fun_X2_17(B!39, A!40, F!42))),
% 0.22/0.53 inference(unit_resolution,[status(thm)],[195, 178])).
% 0.22/0.53 tff(197,plain,
% 0.22/0.53 (apply(G!41, tptp_fun_Y_16(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42))),
% 0.22/0.53 inference(modus_ponens,[status(thm)],[196, 194])).
% 0.22/0.53 tff(198,plain,
% 0.22/0.53 ((tptp_fun_X2_17(B!39, A!40, F!42) = tptp_fun_X1_18(B!39, A!40, F!42)) <=> (tptp_fun_X1_18(B!39, A!40, F!42) = tptp_fun_X2_17(B!39, A!40, F!42))),
% 0.22/0.53 inference(commutativity,[status(thm)],[])).
% 0.22/0.53 tff(199,plain,
% 0.22/0.53 ((tptp_fun_X1_18(B!39, A!40, F!42) = tptp_fun_X2_17(B!39, A!40, F!42)) <=> (tptp_fun_X2_17(B!39, A!40, F!42) = tptp_fun_X1_18(B!39, A!40, F!42))),
% 0.22/0.53 inference(symmetry,[status(thm)],[198])).
% 0.22/0.53 tff(200,plain,
% 0.22/0.53 ((~(tptp_fun_X1_18(B!39, A!40, F!42) = tptp_fun_X2_17(B!39, A!40, F!42))) <=> (~(tptp_fun_X2_17(B!39, A!40, F!42) = tptp_fun_X1_18(B!39, A!40, F!42)))),
% 0.22/0.53 inference(monotonicity,[status(thm)],[199])).
% 0.22/0.53 tff(201,plain,
% 0.22/0.53 (((~member(tptp_fun_Y_16(B!39, A!40, F!42), B!39)) | (~member(tptp_fun_X1_18(B!39, A!40, F!42), A!40)) | (~member(tptp_fun_X2_17(B!39, A!40, F!42), A!40)) | (~apply(F!42, tptp_fun_X2_17(B!39, A!40, F!42), tptp_fun_Y_16(B!39, A!40, F!42))) | (~apply(F!42, tptp_fun_X1_18(B!39, A!40, F!42), tptp_fun_Y_16(B!39, A!40, F!42))) | (tptp_fun_X1_18(B!39, A!40, F!42) = tptp_fun_X2_17(B!39, A!40, F!42))) | (~(tptp_fun_X1_18(B!39, A!40, F!42) = tptp_fun_X2_17(B!39, A!40, F!42)))),
% 0.22/0.53 inference(tautology,[status(thm)],[])).
% 0.22/0.53 tff(202,plain,
% 0.22/0.53 (~(tptp_fun_X1_18(B!39, A!40, F!42) = tptp_fun_X2_17(B!39, A!40, F!42))),
% 0.22/0.53 inference(unit_resolution,[status(thm)],[201, 37])).
% 0.22/0.53 tff(203,plain,
% 0.22/0.53 (~(tptp_fun_X2_17(B!39, A!40, F!42) = tptp_fun_X1_18(B!39, A!40, F!42))),
% 0.22/0.53 inference(modus_ponens,[status(thm)],[202, 200])).
% 0.22/0.53 tff(204,plain,
% 0.22/0.53 (((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(G!41, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!41), A!40)) | (~apply(G!41, X, tptp_fun_Y_3(X, A!40, G!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!41, X, Y1)) | (~apply(G!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))))))) | (~(maps(G!41, B!39, A!40) | (~((~member(tptp_fun_X_4(A!40, B!39, G!41), B!39)) | (~![Y: $i] : ((~member(Y, A!40)) | (~apply(G!41, tptp_fun_X_4(A!40, B!39, G!41), Y)))))) | (~((~member(tptp_fun_Y2_5(A!40, B!39, G!41), A!40)) | (~member(tptp_fun_Y1_6(A!40, B!39, G!41), A!40)) | (~member(tptp_fun_X_7(A!40, B!39, G!41), B!39)) | (~apply(G!41, tptp_fun_X_7(A!40, B!39, G!41), tptp_fun_Y2_5(A!40, B!39, G!41))) | (~apply(G!41, tptp_fun_X_7(A!40, B!39, G!41), tptp_fun_Y1_6(A!40, B!39, G!41))) | (tptp_fun_Y1_6(A!40, B!39, G!41) = tptp_fun_Y2_5(A!40, B!39, G!41))))))))) <=> ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(G!41, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!41), A!40)) | (~apply(G!41, X, tptp_fun_Y_3(X, A!40, G!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!41, X, Y1)) | (~apply(G!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))))))) | (~(maps(G!41, B!39, A!40) | (~((~member(tptp_fun_X_4(A!40, B!39, G!41), B!39)) | (~![Y: $i] : ((~member(Y, A!40)) | (~apply(G!41, tptp_fun_X_4(A!40, B!39, G!41), Y)))))) | (~((~member(tptp_fun_Y2_5(A!40, B!39, G!41), A!40)) | (~member(tptp_fun_Y1_6(A!40, B!39, G!41), A!40)) | (~member(tptp_fun_X_7(A!40, B!39, G!41), B!39)) | (~apply(G!41, tptp_fun_X_7(A!40, B!39, G!41), tptp_fun_Y2_5(A!40, B!39, G!41))) | (~apply(G!41, tptp_fun_X_7(A!40, B!39, G!41), tptp_fun_Y1_6(A!40, B!39, G!41))) | (tptp_fun_Y1_6(A!40, B!39, G!41) = tptp_fun_Y2_5(A!40, B!39, G!41)))))))))),
% 0.22/0.53 inference(rewrite,[status(thm)],[])).
% 0.22/0.53 tff(205,plain,
% 0.22/0.53 ((~((~((~maps(G!41, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!41), A!40)) | (~apply(G!41, X, tptp_fun_Y_3(X, A!40, G!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G!41, X, Y1)) | (~apply(G!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)) | (~member(Y2, A!40)))))))) | (~(maps(G!41, B!39, A!40) | (~((tptp_fun_Y1_6(A!40, B!39, G!41) = tptp_fun_Y2_5(A!40, B!39, G!41)) | (~apply(G!41, tptp_fun_X_7(A!40, B!39, G!41), tptp_fun_Y1_6(A!40, B!39, G!41))) | (~apply(G!41, tptp_fun_X_7(A!40, B!39, G!41), tptp_fun_Y2_5(A!40, B!39, G!41))) | (~member(tptp_fun_X_7(A!40, B!39, G!41), B!39)) | (~member(tptp_fun_Y1_6(A!40, B!39, G!41), A!40)) | (~member(tptp_fun_Y2_5(A!40, B!39, G!41), A!40)))) | (~((~member(tptp_fun_X_4(A!40, B!39, G!41), B!39)) | (~![Y: $i] : ((~member(Y, A!40)) | (~apply(G!41, tptp_fun_X_4(A!40, B!39, G!41), Y)))))))))) <=> (~((~((~maps(G!41, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!41), A!40)) | (~apply(G!41, X, tptp_fun_Y_3(X, A!40, G!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!41, X, Y1)) | (~apply(G!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))))))) | (~(maps(G!41, B!39, A!40) | (~((~member(tptp_fun_X_4(A!40, B!39, G!41), B!39)) | (~![Y: $i] : ((~member(Y, A!40)) | (~apply(G!41, tptp_fun_X_4(A!40, B!39, G!41), Y)))))) | (~((~member(tptp_fun_Y2_5(A!40, B!39, G!41), A!40)) | (~member(tptp_fun_Y1_6(A!40, B!39, G!41), A!40)) | (~member(tptp_fun_X_7(A!40, B!39, G!41), B!39)) | (~apply(G!41, tptp_fun_X_7(A!40, B!39, G!41), tptp_fun_Y2_5(A!40, B!39, G!41))) | (~apply(G!41, tptp_fun_X_7(A!40, B!39, G!41), tptp_fun_Y1_6(A!40, B!39, G!41))) | (tptp_fun_Y1_6(A!40, B!39, G!41) = tptp_fun_Y2_5(A!40, B!39, G!41))))))))),
% 0.22/0.54 inference(rewrite,[status(thm)],[])).
% 0.22/0.54 tff(206,plain,
% 0.22/0.54 (((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(G!41, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!41), A!40)) | (~apply(G!41, X, tptp_fun_Y_3(X, A!40, G!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G!41, X, Y1)) | (~apply(G!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)) | (~member(Y2, A!40)))))))) | (~(maps(G!41, B!39, A!40) | (~((tptp_fun_Y1_6(A!40, B!39, G!41) = tptp_fun_Y2_5(A!40, B!39, G!41)) | (~apply(G!41, tptp_fun_X_7(A!40, B!39, G!41), tptp_fun_Y1_6(A!40, B!39, G!41))) | (~apply(G!41, tptp_fun_X_7(A!40, B!39, G!41), tptp_fun_Y2_5(A!40, B!39, G!41))) | (~member(tptp_fun_X_7(A!40, B!39, G!41), B!39)) | (~member(tptp_fun_Y1_6(A!40, B!39, G!41), A!40)) | (~member(tptp_fun_Y2_5(A!40, B!39, G!41), A!40)))) | (~((~member(tptp_fun_X_4(A!40, B!39, G!41), B!39)) | (~![Y: $i] : ((~member(Y, A!40)) | (~apply(G!41, tptp_fun_X_4(A!40, B!39, G!41), Y))))))))))) <=> ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(G!41, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!41), A!40)) | (~apply(G!41, X, tptp_fun_Y_3(X, A!40, G!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!41, X, Y1)) | (~apply(G!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))))))) | (~(maps(G!41, B!39, A!40) | (~((~member(tptp_fun_X_4(A!40, B!39, G!41), B!39)) | (~![Y: $i] : ((~member(Y, A!40)) | (~apply(G!41, tptp_fun_X_4(A!40, B!39, G!41), Y)))))) | (~((~member(tptp_fun_Y2_5(A!40, B!39, G!41), A!40)) | (~member(tptp_fun_Y1_6(A!40, B!39, G!41), A!40)) | (~member(tptp_fun_X_7(A!40, B!39, G!41), B!39)) | (~apply(G!41, tptp_fun_X_7(A!40, B!39, G!41), tptp_fun_Y2_5(A!40, B!39, G!41))) | (~apply(G!41, tptp_fun_X_7(A!40, B!39, G!41), tptp_fun_Y1_6(A!40, B!39, G!41))) | (tptp_fun_Y1_6(A!40, B!39, G!41) = tptp_fun_Y2_5(A!40, B!39, G!41)))))))))),
% 0.22/0.54 inference(monotonicity,[status(thm)],[205])).
% 0.22/0.54 tff(207,plain,
% 0.22/0.54 (((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(G!41, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!41), A!40)) | (~apply(G!41, X, tptp_fun_Y_3(X, A!40, G!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G!41, X, Y1)) | (~apply(G!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)) | (~member(Y2, A!40)))))))) | (~(maps(G!41, B!39, A!40) | (~((tptp_fun_Y1_6(A!40, B!39, G!41) = tptp_fun_Y2_5(A!40, B!39, G!41)) | (~apply(G!41, tptp_fun_X_7(A!40, B!39, G!41), tptp_fun_Y1_6(A!40, B!39, G!41))) | (~apply(G!41, tptp_fun_X_7(A!40, B!39, G!41), tptp_fun_Y2_5(A!40, B!39, G!41))) | (~member(tptp_fun_X_7(A!40, B!39, G!41), B!39)) | (~member(tptp_fun_Y1_6(A!40, B!39, G!41), A!40)) | (~member(tptp_fun_Y2_5(A!40, B!39, G!41), A!40)))) | (~((~member(tptp_fun_X_4(A!40, B!39, G!41), B!39)) | (~![Y: $i] : ((~member(Y, A!40)) | (~apply(G!41, tptp_fun_X_4(A!40, B!39, G!41), Y))))))))))) <=> ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(G!41, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!41), A!40)) | (~apply(G!41, X, tptp_fun_Y_3(X, A!40, G!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!41, X, Y1)) | (~apply(G!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))))))) | (~(maps(G!41, B!39, A!40) | (~((~member(tptp_fun_X_4(A!40, B!39, G!41), B!39)) | (~![Y: $i] : ((~member(Y, A!40)) | (~apply(G!41, tptp_fun_X_4(A!40, B!39, G!41), Y)))))) | (~((~member(tptp_fun_Y2_5(A!40, B!39, G!41), A!40)) | (~member(tptp_fun_Y1_6(A!40, B!39, G!41), A!40)) | (~member(tptp_fun_X_7(A!40, B!39, G!41), B!39)) | (~apply(G!41, tptp_fun_X_7(A!40, B!39, G!41), tptp_fun_Y2_5(A!40, B!39, G!41))) | (~apply(G!41, tptp_fun_X_7(A!40, B!39, G!41), tptp_fun_Y1_6(A!40, B!39, G!41))) | (tptp_fun_Y1_6(A!40, B!39, G!41) = tptp_fun_Y2_5(A!40, B!39, G!41)))))))))),
% 0.22/0.54 inference(transitivity,[status(thm)],[206, 204])).
% 0.22/0.54 tff(208,plain,
% 0.22/0.54 ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(G!41, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!41), A!40)) | (~apply(G!41, X, tptp_fun_Y_3(X, A!40, G!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G!41, X, Y1)) | (~apply(G!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)) | (~member(Y2, A!40)))))))) | (~(maps(G!41, B!39, A!40) | (~((tptp_fun_Y1_6(A!40, B!39, G!41) = tptp_fun_Y2_5(A!40, B!39, G!41)) | (~apply(G!41, tptp_fun_X_7(A!40, B!39, G!41), tptp_fun_Y1_6(A!40, B!39, G!41))) | (~apply(G!41, tptp_fun_X_7(A!40, B!39, G!41), tptp_fun_Y2_5(A!40, B!39, G!41))) | (~member(tptp_fun_X_7(A!40, B!39, G!41), B!39)) | (~member(tptp_fun_Y1_6(A!40, B!39, G!41), A!40)) | (~member(tptp_fun_Y2_5(A!40, B!39, G!41), A!40)))) | (~((~member(tptp_fun_X_4(A!40, B!39, G!41), B!39)) | (~![Y: $i] : ((~member(Y, A!40)) | (~apply(G!41, tptp_fun_X_4(A!40, B!39, G!41), Y))))))))))),
% 0.22/0.54 inference(quant_inst,[status(thm)],[])).
% 0.22/0.54 tff(209,plain,
% 0.22/0.54 ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(G!41, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!41), A!40)) | (~apply(G!41, X, tptp_fun_Y_3(X, A!40, G!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!41, X, Y1)) | (~apply(G!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))))))) | (~(maps(G!41, B!39, A!40) | (~((~member(tptp_fun_X_4(A!40, B!39, G!41), B!39)) | (~![Y: $i] : ((~member(Y, A!40)) | (~apply(G!41, tptp_fun_X_4(A!40, B!39, G!41), Y)))))) | (~((~member(tptp_fun_Y2_5(A!40, B!39, G!41), A!40)) | (~member(tptp_fun_Y1_6(A!40, B!39, G!41), A!40)) | (~member(tptp_fun_X_7(A!40, B!39, G!41), B!39)) | (~apply(G!41, tptp_fun_X_7(A!40, B!39, G!41), tptp_fun_Y2_5(A!40, B!39, G!41))) | (~apply(G!41, tptp_fun_X_7(A!40, B!39, G!41), tptp_fun_Y1_6(A!40, B!39, G!41))) | (tptp_fun_Y1_6(A!40, B!39, G!41) = tptp_fun_Y2_5(A!40, B!39, G!41))))))))),
% 0.22/0.54 inference(modus_ponens,[status(thm)],[208, 207])).
% 0.22/0.54 tff(210,plain,
% 0.22/0.54 (~((~((~maps(G!41, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!41), A!40)) | (~apply(G!41, X, tptp_fun_Y_3(X, A!40, G!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!41, X, Y1)) | (~apply(G!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))))))) | (~(maps(G!41, B!39, A!40) | (~((~member(tptp_fun_X_4(A!40, B!39, G!41), B!39)) | (~![Y: $i] : ((~member(Y, A!40)) | (~apply(G!41, tptp_fun_X_4(A!40, B!39, G!41), Y)))))) | (~((~member(tptp_fun_Y2_5(A!40, B!39, G!41), A!40)) | (~member(tptp_fun_Y1_6(A!40, B!39, G!41), A!40)) | (~member(tptp_fun_X_7(A!40, B!39, G!41), B!39)) | (~apply(G!41, tptp_fun_X_7(A!40, B!39, G!41), tptp_fun_Y2_5(A!40, B!39, G!41))) | (~apply(G!41, tptp_fun_X_7(A!40, B!39, G!41), tptp_fun_Y1_6(A!40, B!39, G!41))) | (tptp_fun_Y1_6(A!40, B!39, G!41) = tptp_fun_Y2_5(A!40, B!39, G!41)))))))),
% 0.22/0.54 inference(unit_resolution,[status(thm)],[209, 129])).
% 0.22/0.54 tff(211,plain,
% 0.22/0.54 (((~((~maps(G!41, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!41), A!40)) | (~apply(G!41, X, tptp_fun_Y_3(X, A!40, G!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!41, X, Y1)) | (~apply(G!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))))))) | (~(maps(G!41, B!39, A!40) | (~((~member(tptp_fun_X_4(A!40, B!39, G!41), B!39)) | (~![Y: $i] : ((~member(Y, A!40)) | (~apply(G!41, tptp_fun_X_4(A!40, B!39, G!41), Y)))))) | (~((~member(tptp_fun_Y2_5(A!40, B!39, G!41), A!40)) | (~member(tptp_fun_Y1_6(A!40, B!39, G!41), A!40)) | (~member(tptp_fun_X_7(A!40, B!39, G!41), B!39)) | (~apply(G!41, tptp_fun_X_7(A!40, B!39, G!41), tptp_fun_Y2_5(A!40, B!39, G!41))) | (~apply(G!41, tptp_fun_X_7(A!40, B!39, G!41), tptp_fun_Y1_6(A!40, B!39, G!41))) | (tptp_fun_Y1_6(A!40, B!39, G!41) = tptp_fun_Y2_5(A!40, B!39, G!41))))))) | ((~maps(G!41, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!41), A!40)) | (~apply(G!41, X, tptp_fun_Y_3(X, A!40, G!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!41, X, Y1)) | (~apply(G!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))))))),
% 0.22/0.54 inference(tautology,[status(thm)],[])).
% 0.22/0.54 tff(212,plain,
% 0.22/0.54 ((~maps(G!41, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!41), A!40)) | (~apply(G!41, X, tptp_fun_Y_3(X, A!40, G!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!41, X, Y1)) | (~apply(G!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40))))))),
% 0.22/0.54 inference(unit_resolution,[status(thm)],[211, 210])).
% 0.22/0.54 tff(213,plain,
% 0.22/0.54 (maps(G!41, B!39, A!40)),
% 0.22/0.54 inference(and_elim,[status(thm)],[88])).
% 0.22/0.54 tff(214,plain,
% 0.22/0.54 ((~((~maps(G!41, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!41), A!40)) | (~apply(G!41, X, tptp_fun_Y_3(X, A!40, G!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!41, X, Y1)) | (~apply(G!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))))))) | (~maps(G!41, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!41), A!40)) | (~apply(G!41, X, tptp_fun_Y_3(X, A!40, G!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!41, X, Y1)) | (~apply(G!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40))))))),
% 0.22/0.54 inference(tautology,[status(thm)],[])).
% 0.22/0.54 tff(215,plain,
% 0.22/0.54 ((~((~maps(G!41, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!41), A!40)) | (~apply(G!41, X, tptp_fun_Y_3(X, A!40, G!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!41, X, Y1)) | (~apply(G!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))))))) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!41), A!40)) | (~apply(G!41, X, tptp_fun_Y_3(X, A!40, G!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!41, X, Y1)) | (~apply(G!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40))))))),
% 0.22/0.54 inference(unit_resolution,[status(thm)],[214, 213])).
% 0.22/0.54 tff(216,plain,
% 0.22/0.54 (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!41), A!40)) | (~apply(G!41, X, tptp_fun_Y_3(X, A!40, G!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!41, X, Y1)) | (~apply(G!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))))),
% 0.22/0.54 inference(unit_resolution,[status(thm)],[215, 212])).
% 0.22/0.54 tff(217,plain,
% 0.22/0.54 (((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!41), A!40)) | (~apply(G!41, X, tptp_fun_Y_3(X, A!40, G!41))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!41, X, Y1)) | (~apply(G!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40))))) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!41, X, Y1)) | (~apply(G!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))),
% 0.22/0.54 inference(tautology,[status(thm)],[])).
% 0.22/0.54 tff(218,plain,
% 0.22/0.54 (![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!41, X, Y1)) | (~apply(G!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))),
% 0.22/0.54 inference(unit_resolution,[status(thm)],[217, 216])).
% 0.22/0.54 tff(219,plain,
% 0.22/0.54 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!41, X, Y1)) | (~apply(G!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))) | ((~member(tptp_fun_Y_16(B!39, A!40, F!42), B!39)) | (~member(tptp_fun_X1_18(B!39, A!40, F!42), A!40)) | (~member(tptp_fun_X2_17(B!39, A!40, F!42), A!40)) | (~apply(G!41, tptp_fun_Y_16(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42))) | (tptp_fun_X2_17(B!39, A!40, F!42) = tptp_fun_X1_18(B!39, A!40, F!42)) | (~apply(G!41, tptp_fun_Y_16(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42))))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!41, X, Y1)) | (~apply(G!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))) | (~member(tptp_fun_Y_16(B!39, A!40, F!42), B!39)) | (~member(tptp_fun_X1_18(B!39, A!40, F!42), A!40)) | (~member(tptp_fun_X2_17(B!39, A!40, F!42), A!40)) | (~apply(G!41, tptp_fun_Y_16(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42))) | (tptp_fun_X2_17(B!39, A!40, F!42) = tptp_fun_X1_18(B!39, A!40, F!42)) | (~apply(G!41, tptp_fun_Y_16(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42))))),
% 0.22/0.55 inference(rewrite,[status(thm)],[])).
% 0.22/0.55 tff(220,plain,
% 0.22/0.55 (((tptp_fun_X2_17(B!39, A!40, F!42) = tptp_fun_X1_18(B!39, A!40, F!42)) | (~member(tptp_fun_X1_18(B!39, A!40, F!42), A!40)) | (~apply(G!41, tptp_fun_Y_16(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42))) | (~apply(G!41, tptp_fun_Y_16(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42))) | (~member(tptp_fun_Y_16(B!39, A!40, F!42), B!39)) | (~member(tptp_fun_X2_17(B!39, A!40, F!42), A!40))) <=> ((~member(tptp_fun_Y_16(B!39, A!40, F!42), B!39)) | (~member(tptp_fun_X1_18(B!39, A!40, F!42), A!40)) | (~member(tptp_fun_X2_17(B!39, A!40, F!42), A!40)) | (~apply(G!41, tptp_fun_Y_16(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42))) | (tptp_fun_X2_17(B!39, A!40, F!42) = tptp_fun_X1_18(B!39, A!40, F!42)) | (~apply(G!41, tptp_fun_Y_16(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42))))),
% 0.22/0.55 inference(rewrite,[status(thm)],[])).
% 0.22/0.55 tff(221,plain,
% 0.22/0.55 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!41, X, Y1)) | (~apply(G!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))) | ((tptp_fun_X2_17(B!39, A!40, F!42) = tptp_fun_X1_18(B!39, A!40, F!42)) | (~member(tptp_fun_X1_18(B!39, A!40, F!42), A!40)) | (~apply(G!41, tptp_fun_Y_16(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42))) | (~apply(G!41, tptp_fun_Y_16(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42))) | (~member(tptp_fun_Y_16(B!39, A!40, F!42), B!39)) | (~member(tptp_fun_X2_17(B!39, A!40, F!42), A!40)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!41, X, Y1)) | (~apply(G!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))) | ((~member(tptp_fun_Y_16(B!39, A!40, F!42), B!39)) | (~member(tptp_fun_X1_18(B!39, A!40, F!42), A!40)) | (~member(tptp_fun_X2_17(B!39, A!40, F!42), A!40)) | (~apply(G!41, tptp_fun_Y_16(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42))) | (tptp_fun_X2_17(B!39, A!40, F!42) = tptp_fun_X1_18(B!39, A!40, F!42)) | (~apply(G!41, tptp_fun_Y_16(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42)))))),
% 0.22/0.55 inference(monotonicity,[status(thm)],[220])).
% 0.22/0.55 tff(222,plain,
% 0.22/0.55 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!41, X, Y1)) | (~apply(G!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))) | ((tptp_fun_X2_17(B!39, A!40, F!42) = tptp_fun_X1_18(B!39, A!40, F!42)) | (~member(tptp_fun_X1_18(B!39, A!40, F!42), A!40)) | (~apply(G!41, tptp_fun_Y_16(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42))) | (~apply(G!41, tptp_fun_Y_16(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42))) | (~member(tptp_fun_Y_16(B!39, A!40, F!42), B!39)) | (~member(tptp_fun_X2_17(B!39, A!40, F!42), A!40)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!41, X, Y1)) | (~apply(G!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))) | (~member(tptp_fun_Y_16(B!39, A!40, F!42), B!39)) | (~member(tptp_fun_X1_18(B!39, A!40, F!42), A!40)) | (~member(tptp_fun_X2_17(B!39, A!40, F!42), A!40)) | (~apply(G!41, tptp_fun_Y_16(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42))) | (tptp_fun_X2_17(B!39, A!40, F!42) = tptp_fun_X1_18(B!39, A!40, F!42)) | (~apply(G!41, tptp_fun_Y_16(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42))))),
% 0.22/0.55 inference(transitivity,[status(thm)],[221, 219])).
% 0.22/0.55 tff(223,plain,
% 0.22/0.55 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!41, X, Y1)) | (~apply(G!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))) | ((tptp_fun_X2_17(B!39, A!40, F!42) = tptp_fun_X1_18(B!39, A!40, F!42)) | (~member(tptp_fun_X1_18(B!39, A!40, F!42), A!40)) | (~apply(G!41, tptp_fun_Y_16(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42))) | (~apply(G!41, tptp_fun_Y_16(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42))) | (~member(tptp_fun_Y_16(B!39, A!40, F!42), B!39)) | (~member(tptp_fun_X2_17(B!39, A!40, F!42), A!40)))),
% 0.22/0.55 inference(quant_inst,[status(thm)],[])).
% 0.22/0.55 tff(224,plain,
% 0.22/0.55 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!41, X, Y1)) | (~apply(G!41, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))) | (~member(tptp_fun_Y_16(B!39, A!40, F!42), B!39)) | (~member(tptp_fun_X1_18(B!39, A!40, F!42), A!40)) | (~member(tptp_fun_X2_17(B!39, A!40, F!42), A!40)) | (~apply(G!41, tptp_fun_Y_16(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42))) | (tptp_fun_X2_17(B!39, A!40, F!42) = tptp_fun_X1_18(B!39, A!40, F!42)) | (~apply(G!41, tptp_fun_Y_16(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42)))),
% 0.22/0.55 inference(modus_ponens,[status(thm)],[223, 222])).
% 0.22/0.55 tff(225,plain,
% 0.22/0.55 ((~apply(G!41, tptp_fun_Y_16(B!39, A!40, F!42), tptp_fun_X2_17(B!39, A!40, F!42))) | (tptp_fun_X2_17(B!39, A!40, F!42) = tptp_fun_X1_18(B!39, A!40, F!42)) | (~apply(G!41, tptp_fun_Y_16(B!39, A!40, F!42), tptp_fun_X1_18(B!39, A!40, F!42)))),
% 0.22/0.55 inference(unit_resolution,[status(thm)],[224, 218, 107, 39, 159])).
% 0.22/0.55 tff(226,plain,
% 0.22/0.55 ($false),
% 0.22/0.55 inference(unit_resolution,[status(thm)],[225, 203, 197, 157])).
% 0.22/0.55 % SZS output end Proof
% 0.22/0.55 % E exiting
%------------------------------------------------------------------------------