%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET725+4 : TPTP v9.0.0. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:26:13 AM UTC 2025
% Result : Theorem 0.12s 0.40s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET725+4 : TPTP v9.0.0. Bugfixed v2.2.1.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n010.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 05:40:41 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.40 % SZS status Theorem
% 0.12/0.40 % SZS output start Proof
% 0.12/0.40 tff(apply_type, type, (
% 0.12/0.40 apply: ( $i * $i * $i ) > $o)).
% 0.12/0.40 tff(tptp_fun_X1_18_type, type, (
% 0.12/0.40 tptp_fun_X1_18: ( $i * $i * $i ) > $i)).
% 0.12/0.40 tff(tptp_fun_F_43_type, type, (
% 0.12/0.40 tptp_fun_F_43: $i)).
% 0.12/0.40 tff(tptp_fun_A_40_type, type, (
% 0.12/0.40 tptp_fun_A_40: $i)).
% 0.12/0.40 tff(tptp_fun_B_39_type, type, (
% 0.12/0.40 tptp_fun_B_39: $i)).
% 0.12/0.40 tff(tptp_fun_Y_16_type, type, (
% 0.12/0.40 tptp_fun_Y_16: ( $i * $i * $i ) > $i)).
% 0.12/0.40 tff(tptp_fun_G_42_type, type, (
% 0.12/0.40 tptp_fun_G_42: $i)).
% 0.12/0.40 tff(tptp_fun_Y_8_type, type, (
% 0.12/0.40 tptp_fun_Y_8: ( $i * $i * $i * $i * $i ) > $i)).
% 0.12/0.40 tff(member_type, type, (
% 0.12/0.40 member: ( $i * $i ) > $o)).
% 0.12/0.40 tff(compose_function_type, type, (
% 0.12/0.40 compose_function: ( $i * $i * $i * $i * $i ) > $i)).
% 0.12/0.40 tff(tptp_fun_X2_17_type, type, (
% 0.12/0.40 tptp_fun_X2_17: ( $i * $i * $i ) > $i)).
% 0.12/0.40 tff(injective_type, type, (
% 0.12/0.40 injective: ( $i * $i * $i ) > $o)).
% 0.12/0.40 tff(surjective_type, type, (
% 0.12/0.40 surjective: ( $i * $i * $i ) > $o)).
% 0.12/0.40 tff(tptp_fun_Y_20_type, type, (
% 0.12/0.40 tptp_fun_Y_20: ( $i * $i * $i ) > $i)).
% 0.12/0.40 tff(tptp_fun_E_19_type, type, (
% 0.12/0.40 tptp_fun_E_19: ( $i * $i * $i ) > $i)).
% 0.12/0.40 tff(tptp_fun_H_41_type, type, (
% 0.12/0.40 tptp_fun_H_41: $i)).
% 0.12/0.40 tff(identity_type, type, (
% 0.12/0.40 identity: ( $i * $i ) > $o)).
% 0.12/0.40 tff(tptp_fun_X_15_type, type, (
% 0.12/0.40 tptp_fun_X_15: ( $i * $i ) > $i)).
% 0.12/0.40 tff(maps_type, type, (
% 0.12/0.40 maps: ( $i * $i * $i ) > $o)).
% 0.12/0.40 tff(one_to_one_type, type, (
% 0.12/0.40 one_to_one: ( $i * $i * $i ) > $o)).
% 0.12/0.40 tff(tptp_fun_Y_3_type, type, (
% 0.12/0.40 tptp_fun_Y_3: ( $i * $i * $i ) > $i)).
% 0.12/0.40 tff(tptp_fun_Y2_5_type, type, (
% 0.12/0.40 tptp_fun_Y2_5: ( $i * $i * $i ) > $i)).
% 0.12/0.40 tff(tptp_fun_Y1_6_type, type, (
% 0.12/0.40 tptp_fun_Y1_6: ( $i * $i * $i ) > $i)).
% 0.12/0.40 tff(tptp_fun_X_7_type, type, (
% 0.12/0.40 tptp_fun_X_7: ( $i * $i * $i ) > $i)).
% 0.12/0.40 tff(tptp_fun_X_4_type, type, (
% 0.12/0.40 tptp_fun_X_4: ( $i * $i * $i ) > $i)).
% 0.12/0.40 tff(1,plain,
% 0.12/0.40 (^[F: $i, 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)))))))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(2,plain,
% 0.12/0.40 (![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B)))))))) <=> ![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))))))))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[1])).
% 0.12/0.40 tff(3,plain,
% 0.12/0.40 (^[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)))))))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(4,plain,
% 0.12/0.40 (![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B)))))))) <=> ![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))))))))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[3])).
% 0.12/0.40 tff(5,plain,
% 0.12/0.40 (![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B)))))))) <=> ![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))))))))),
% 0.12/0.40 inference(transitivity,[status(thm)],[4, 2])).
% 0.12/0.40 tff(6,plain,
% 0.12/0.40 (^[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))))))))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(7,plain,
% 0.12/0.40 (![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))))))))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[6])).
% 0.12/0.40 tff(8,plain,
% 0.12/0.40 (![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)))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(9,plain,
% 0.12/0.40 (^[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))))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(10,plain,
% 0.12/0.40 (![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)))))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[9])).
% 0.12/0.40 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')).
% 0.12/0.40 tff(12,plain,
% 0.12/0.40 (![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)))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.12/0.40 tff(13,plain,
% 0.12/0.40 (![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)))))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[12, 8])).
% 0.12/0.41 tff(14,plain,(
% 0.12/0.41 ![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)))))))),
% 0.12/0.41 inference(skolemize,[status(sab)],[13])).
% 0.12/0.41 tff(15,plain,
% 0.12/0.41 (![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))))))))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[14, 7])).
% 0.12/0.41 tff(16,plain,
% 0.12/0.41 (![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))))))))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[15, 5])).
% 0.12/0.41 tff(17,plain,
% 0.12/0.41 (((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(F!43, A!40, B!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!39)) | (~apply(F!43, X1, Y)) | (~member(X1, A!40)) | (~member(X2, A!40)) | (~apply(F!43, X2, Y))))) | (~(injective(F!43, A!40, B!39) | (~((~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_Y_16(B!39, A!40, F!43), B!39)) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (tptp_fun_X1_18(B!39, A!40, F!43) = tptp_fun_X2_17(B!39, A!40, F!43)) | (~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40))))))))) <=> ((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(F!43, A!40, B!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!39)) | (~apply(F!43, X1, Y)) | (~member(X1, A!40)) | (~member(X2, A!40)) | (~apply(F!43, X2, Y))))) | (~(injective(F!43, A!40, B!39) | (~((~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_Y_16(B!39, A!40, F!43), B!39)) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (tptp_fun_X1_18(B!39, A!40, F!43) = tptp_fun_X2_17(B!39, A!40, F!43)) | (~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40)))))))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(18,plain,
% 0.20/0.41 ((~((~((~injective(F!43, A!40, B!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!43, X1, Y)) | (~member(X2, A!40)) | (~member(X1, A!40)) | (~member(Y, B!39)) | (~apply(F!43, X2, Y))))) | (~(injective(F!43, A!40, B!39) | (~((tptp_fun_X1_18(B!39, A!40, F!43) = tptp_fun_X2_17(B!39, A!40, F!43)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_Y_16(B!39, A!40, F!43), B!39)))))))) <=> (~((~((~injective(F!43, A!40, B!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!39)) | (~apply(F!43, X1, Y)) | (~member(X1, A!40)) | (~member(X2, A!40)) | (~apply(F!43, X2, Y))))) | (~(injective(F!43, A!40, B!39) | (~((~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_Y_16(B!39, A!40, F!43), B!39)) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (tptp_fun_X1_18(B!39, A!40, F!43) = tptp_fun_X2_17(B!39, A!40, F!43)) | (~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40))))))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(19,plain,
% 0.20/0.41 (((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(F!43, A!40, B!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!43, X1, Y)) | (~member(X2, A!40)) | (~member(X1, A!40)) | (~member(Y, B!39)) | (~apply(F!43, X2, Y))))) | (~(injective(F!43, A!40, B!39) | (~((tptp_fun_X1_18(B!39, A!40, F!43) = tptp_fun_X2_17(B!39, A!40, F!43)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_Y_16(B!39, A!40, F!43), 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!43, A!40, B!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!39)) | (~apply(F!43, X1, Y)) | (~member(X1, A!40)) | (~member(X2, A!40)) | (~apply(F!43, X2, Y))))) | (~(injective(F!43, A!40, B!39) | (~((~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_Y_16(B!39, A!40, F!43), B!39)) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (tptp_fun_X1_18(B!39, A!40, F!43) = tptp_fun_X2_17(B!39, A!40, F!43)) | (~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40)))))))))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[18])).
% 0.20/0.41 tff(20,plain,
% 0.20/0.41 (((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(F!43, A!40, B!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!43, X1, Y)) | (~member(X2, A!40)) | (~member(X1, A!40)) | (~member(Y, B!39)) | (~apply(F!43, X2, Y))))) | (~(injective(F!43, A!40, B!39) | (~((tptp_fun_X1_18(B!39, A!40, F!43) = tptp_fun_X2_17(B!39, A!40, F!43)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_Y_16(B!39, A!40, F!43), 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!43, A!40, B!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!39)) | (~apply(F!43, X1, Y)) | (~member(X1, A!40)) | (~member(X2, A!40)) | (~apply(F!43, X2, Y))))) | (~(injective(F!43, A!40, B!39) | (~((~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_Y_16(B!39, A!40, F!43), B!39)) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (tptp_fun_X1_18(B!39, A!40, F!43) = tptp_fun_X2_17(B!39, A!40, F!43)) | (~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40)))))))))),
% 0.20/0.41 inference(transitivity,[status(thm)],[19, 17])).
% 0.20/0.41 tff(21,plain,
% 0.20/0.41 ((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(F!43, A!40, B!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!43, X1, Y)) | (~member(X2, A!40)) | (~member(X1, A!40)) | (~member(Y, B!39)) | (~apply(F!43, X2, Y))))) | (~(injective(F!43, A!40, B!39) | (~((tptp_fun_X1_18(B!39, A!40, F!43) = tptp_fun_X2_17(B!39, A!40, F!43)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_Y_16(B!39, A!40, F!43), B!39))))))))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(22,plain,
% 0.20/0.41 ((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(F!43, A!40, B!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!39)) | (~apply(F!43, X1, Y)) | (~member(X1, A!40)) | (~member(X2, A!40)) | (~apply(F!43, X2, Y))))) | (~(injective(F!43, A!40, B!39) | (~((~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_Y_16(B!39, A!40, F!43), B!39)) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (tptp_fun_X1_18(B!39, A!40, F!43) = tptp_fun_X2_17(B!39, A!40, F!43)) | (~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40))))))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.20/0.42 tff(23,plain,
% 0.20/0.42 (~((~((~injective(F!43, A!40, B!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!39)) | (~apply(F!43, X1, Y)) | (~member(X1, A!40)) | (~member(X2, A!40)) | (~apply(F!43, X2, Y))))) | (~(injective(F!43, A!40, B!39) | (~((~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_Y_16(B!39, A!40, F!43), B!39)) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (tptp_fun_X1_18(B!39, A!40, F!43) = tptp_fun_X2_17(B!39, A!40, F!43)) | (~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40)))))))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[22, 16])).
% 0.20/0.42 tff(24,plain,
% 0.20/0.42 (((~((~injective(F!43, A!40, B!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!39)) | (~apply(F!43, X1, Y)) | (~member(X1, A!40)) | (~member(X2, A!40)) | (~apply(F!43, X2, Y))))) | (~(injective(F!43, A!40, B!39) | (~((~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_Y_16(B!39, A!40, F!43), B!39)) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (tptp_fun_X1_18(B!39, A!40, F!43) = tptp_fun_X2_17(B!39, A!40, F!43)) | (~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40))))))) | (injective(F!43, A!40, B!39) | (~((~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_Y_16(B!39, A!40, F!43), B!39)) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (tptp_fun_X1_18(B!39, A!40, F!43) = tptp_fun_X2_17(B!39, A!40, F!43)) | (~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40)))))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(25,plain,
% 0.20/0.42 (injective(F!43, A!40, B!39) | (~((~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_Y_16(B!39, A!40, F!43), B!39)) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (tptp_fun_X1_18(B!39, A!40, F!43) = tptp_fun_X2_17(B!39, A!40, F!43)) | (~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40))))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[24, 23])).
% 0.20/0.42 tff(26,assumption,((~((~surjective(F!43, A!40, B!39)) | ![Y: $i] : ((~member(Y, B!39)) | (~((~member(tptp_fun_E_19(Y, A!40, F!43), A!40)) | (~apply(F!43, tptp_fun_E_19(Y, A!40, F!43), Y))))))) | (~(surjective(F!43, A!40, B!39) | (~((~member(tptp_fun_Y_20(B!39, A!40, F!43), B!39)) | (~![E: $i] : ((~member(E, A!40)) | (~apply(F!43, E, tptp_fun_Y_20(B!39, A!40, F!43)))))))))), introduced(assumption)).
% 0.20/0.42 tff(27,plain,
% 0.20/0.42 (^[F: $i, A: $i, B: $i] : refl((~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))))))) <=> (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(28,plain,
% 0.20/0.42 (![F: $i, A: $i, B: $i] : (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[27])).
% 0.20/0.42 tff(29,plain,
% 0.20/0.42 (^[F: $i, A: $i, B: $i] : rewrite((~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))))))) <=> (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(30,plain,
% 0.20/0.42 (![F: $i, A: $i, B: $i] : (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[29])).
% 0.20/0.42 tff(31,plain,
% 0.20/0.42 (![F: $i, A: $i, B: $i] : (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))))))),
% 0.20/0.42 inference(transitivity,[status(thm)],[30, 28])).
% 0.20/0.42 tff(32,plain,
% 0.20/0.42 (^[F: $i, A: $i, B: $i] : trans(monotonicity(rewrite(((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (member(tptp_fun_E_19(Y, A, F), A) & apply(F, tptp_fun_E_19(Y, A, F), Y)))) <=> ((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))), trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[E: $i] : trans(monotonicity(rewrite((member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F))) <=> (~((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))), ((~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F)))) <=> (~(~((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))), rewrite((~(~((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))) <=> ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))), ((~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F)))) <=> ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))), (![E: $i] : (~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F)))) <=> ![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))), ((member(tptp_fun_Y_20(B, A, F), B) & ![E: $i] : (~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F))))) <=> (member(tptp_fun_Y_20(B, A, F), B) & ![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))), rewrite((member(tptp_fun_Y_20(B, A, F), B) & ![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))) <=> (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))), ((member(tptp_fun_Y_20(B, A, F), B) & ![E: $i] : (~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F))))) <=> (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))))), ((surjective(F, A, B) | (member(tptp_fun_Y_20(B, A, F), B) & ![E: $i] : (~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F)))))) <=> (surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))))), rewrite((surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))) <=> (surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))))), ((surjective(F, A, B) | (member(tptp_fun_Y_20(B, A, F), B) & ![E: $i] : (~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F)))))) <=> (surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))))), ((((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (member(tptp_fun_E_19(Y, A, F), A) & apply(F, tptp_fun_E_19(Y, A, F), Y)))) & (surjective(F, A, B) | (member(tptp_fun_Y_20(B, A, F), B) & ![E: $i] : (~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F))))))) <=> (((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y)))))) & (surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))))))), rewrite((((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y)))))) & (surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))))) <=> (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))))))), ((((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (member(tptp_fun_E_19(Y, A, F), A) & apply(F, tptp_fun_E_19(Y, A, F), Y)))) & (surjective(F, A, B) | (member(tptp_fun_Y_20(B, A, F), B) & ![E: $i] : (~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F))))))) <=> (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(33,plain,
% 0.20/0.42 (![F: $i, A: $i, B: $i] : (((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (member(tptp_fun_E_19(Y, A, F), A) & apply(F, tptp_fun_E_19(Y, A, F), Y)))) & (surjective(F, A, B) | (member(tptp_fun_Y_20(B, A, F), B) & ![E: $i] : (~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[32])).
% 0.20/0.42 tff(34,plain,
% 0.20/0.42 (![F: $i, A: $i, B: $i] : (surjective(F, A, B) <=> ![Y: $i] : ((~member(Y, B)) | ?[E: $i] : (member(E, A) & apply(F, E, Y)))) <=> ![F: $i, A: $i, B: $i] : (surjective(F, A, B) <=> ![Y: $i] : ((~member(Y, B)) | ?[E: $i] : (member(E, A) & apply(F, E, Y))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(35,plain,
% 0.20/0.42 (^[F: $i, A: $i, B: $i] : rewrite((surjective(F, A, B) <=> ![Y: $i] : (member(Y, B) => ?[E: $i] : (member(E, A) & apply(F, E, Y)))) <=> (surjective(F, A, B) <=> ![Y: $i] : ((~member(Y, B)) | ?[E: $i] : (member(E, A) & apply(F, E, Y)))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(36,plain,
% 0.20/0.42 (![F: $i, A: $i, B: $i] : (surjective(F, A, B) <=> ![Y: $i] : (member(Y, B) => ?[E: $i] : (member(E, A) & apply(F, E, Y)))) <=> ![F: $i, A: $i, B: $i] : (surjective(F, A, B) <=> ![Y: $i] : ((~member(Y, B)) | ?[E: $i] : (member(E, A) & apply(F, E, Y))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[35])).
% 0.20/0.42 tff(37,axiom,(![F: $i, A: $i, B: $i] : (surjective(F, A, B) <=> ![Y: $i] : (member(Y, B) => ?[E: $i] : (member(E, A) & apply(F, E, Y))))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+1.ax','surjective')).
% 0.20/0.42 tff(38,plain,
% 0.20/0.42 (![F: $i, A: $i, B: $i] : (surjective(F, A, B) <=> ![Y: $i] : ((~member(Y, B)) | ?[E: $i] : (member(E, A) & apply(F, E, Y))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.20/0.42 tff(39,plain,
% 0.20/0.42 (![F: $i, A: $i, B: $i] : (surjective(F, A, B) <=> ![Y: $i] : ((~member(Y, B)) | ?[E: $i] : (member(E, A) & apply(F, E, Y))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[38, 34])).
% 0.20/0.42 tff(40,plain,(
% 0.20/0.42 ![F: $i, A: $i, B: $i] : (((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (member(tptp_fun_E_19(Y, A, F), A) & apply(F, tptp_fun_E_19(Y, A, F), Y)))) & (surjective(F, A, B) | (member(tptp_fun_Y_20(B, A, F), B) & ![E: $i] : (~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F)))))))),
% 0.20/0.42 inference(skolemize,[status(sab)],[39])).
% 0.20/0.42 tff(41,plain,
% 0.20/0.42 (![F: $i, A: $i, B: $i] : (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[40, 33])).
% 0.20/0.42 tff(42,plain,
% 0.20/0.42 (![F: $i, A: $i, B: $i] : (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[41, 31])).
% 0.20/0.42 tff(43,plain,
% 0.20/0.42 ((~![F: $i, A: $i, B: $i] : (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))))))) | (~((~((~surjective(F!43, A!40, B!39)) | ![Y: $i] : ((~member(Y, B!39)) | (~((~member(tptp_fun_E_19(Y, A!40, F!43), A!40)) | (~apply(F!43, tptp_fun_E_19(Y, A!40, F!43), Y))))))) | (~(surjective(F!43, A!40, B!39) | (~((~member(tptp_fun_Y_20(B!39, A!40, F!43), B!39)) | (~![E: $i] : ((~member(E, A!40)) | (~apply(F!43, E, tptp_fun_Y_20(B!39, A!40, F!43)))))))))))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(44,plain,
% 0.20/0.42 ($false),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[43, 42, 26])).
% 0.20/0.42 tff(45,plain,(~((~((~surjective(F!43, A!40, B!39)) | ![Y: $i] : ((~member(Y, B!39)) | (~((~member(tptp_fun_E_19(Y, A!40, F!43), A!40)) | (~apply(F!43, tptp_fun_E_19(Y, A!40, F!43), Y))))))) | (~(surjective(F!43, A!40, B!39) | (~((~member(tptp_fun_Y_20(B!39, A!40, F!43), B!39)) | (~![E: $i] : ((~member(E, A!40)) | (~apply(F!43, E, tptp_fun_Y_20(B!39, A!40, F!43))))))))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.42 tff(46,plain,
% 0.20/0.42 (((~((~surjective(F!43, A!40, B!39)) | ![Y: $i] : ((~member(Y, B!39)) | (~((~member(tptp_fun_E_19(Y, A!40, F!43), A!40)) | (~apply(F!43, tptp_fun_E_19(Y, A!40, F!43), Y))))))) | (~(surjective(F!43, A!40, B!39) | (~((~member(tptp_fun_Y_20(B!39, A!40, F!43), B!39)) | (~![E: $i] : ((~member(E, A!40)) | (~apply(F!43, E, tptp_fun_Y_20(B!39, A!40, F!43)))))))))) | (surjective(F!43, A!40, B!39) | (~((~member(tptp_fun_Y_20(B!39, A!40, F!43), B!39)) | (~![E: $i] : ((~member(E, A!40)) | (~apply(F!43, E, tptp_fun_Y_20(B!39, A!40, F!43))))))))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(47,plain,
% 0.20/0.43 (surjective(F!43, A!40, B!39) | (~((~member(tptp_fun_Y_20(B!39, A!40, F!43), B!39)) | (~![E: $i] : ((~member(E, A!40)) | (~apply(F!43, E, tptp_fun_Y_20(B!39, A!40, F!43)))))))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[46, 45])).
% 0.20/0.43 tff(48,assumption,(~((~member(tptp_fun_Y_20(B!39, A!40, F!43), B!39)) | (~![E: $i] : ((~member(E, A!40)) | (~apply(F!43, E, tptp_fun_Y_20(B!39, A!40, F!43))))))), introduced(assumption)).
% 0.20/0.43 tff(49,plain,
% 0.20/0.43 (((~member(tptp_fun_Y_20(B!39, A!40, F!43), B!39)) | (~![E: $i] : ((~member(E, A!40)) | (~apply(F!43, E, tptp_fun_Y_20(B!39, A!40, F!43)))))) | member(tptp_fun_Y_20(B!39, A!40, F!43), B!39)),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(50,plain,
% 0.20/0.43 (member(tptp_fun_Y_20(B!39, A!40, F!43), B!39)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[49, 48])).
% 0.20/0.43 tff(51,plain,
% 0.20/0.43 (^[G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : refl(((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z)))))))) <=> ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z)))))))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(52,plain,
% 0.20/0.43 (![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z)))))))) <=> ![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[51])).
% 0.20/0.43 tff(53,plain,
% 0.20/0.43 (^[G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : rewrite(((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z)))))))) <=> ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z)))))))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(54,plain,
% 0.20/0.43 (![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z)))))))) <=> ![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[53])).
% 0.20/0.43 tff(55,plain,
% 0.20/0.43 (![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z)))))))) <=> ![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))),
% 0.20/0.43 inference(transitivity,[status(thm)],[54, 52])).
% 0.20/0.43 tff(56,plain,
% 0.20/0.43 (^[G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : trans(monotonicity(trans(monotonicity(rewrite((member(X, A) & member(Z, C)) <=> (~((~member(Z, C)) | (~member(X, A))))), ((~(member(X, A) & member(Z, C))) <=> (~(~((~member(Z, C)) | (~member(X, A))))))), rewrite((~(~((~member(Z, C)) | (~member(X, A))))) <=> ((~member(Z, C)) | (~member(X, A)))), ((~(member(X, A) & member(Z, C))) <=> ((~member(Z, C)) | (~member(X, A))))), trans(monotonicity(rewrite(((~apply(compose_function(G, F, A, B, C), X, Z)) | (member(tptp_fun_Y_8(Z, X, B, F, G), B) & apply(F, X, tptp_fun_Y_8(Z, X, B, F, G)) & apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z))) <=> ((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))), rewrite((apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y) & apply(G, Y, Z)))) <=> (apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))), ((((~apply(compose_function(G, F, A, B, C), X, Z)) | (member(tptp_fun_Y_8(Z, X, B, F, G), B) & apply(F, X, tptp_fun_Y_8(Z, X, B, F, G)) & apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z))) & (apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y) & apply(G, Y, Z))))) <=> (((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z))))) & (apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))), rewrite((((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z))))) & (apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))) <=> (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z)))))))), ((((~apply(compose_function(G, F, A, B, C), X, Z)) | (member(tptp_fun_Y_8(Z, X, B, F, G), B) & apply(F, X, tptp_fun_Y_8(Z, X, B, F, G)) & apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z))) & (apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y) & apply(G, Y, Z))))) <=> (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))), (((~(member(X, A) & member(Z, C))) | (((~apply(compose_function(G, F, A, B, C), X, Z)) | (member(tptp_fun_Y_8(Z, X, B, F, G), B) & apply(F, X, tptp_fun_Y_8(Z, X, B, F, G)) & apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z))) & (apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y) & apply(G, Y, Z)))))) <=> (((~member(Z, C)) | (~member(X, A))) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z)))))))))), rewrite((((~member(Z, C)) | (~member(X, A))) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z)))))))) <=> ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))), (((~(member(X, A) & member(Z, C))) | (((~apply(compose_function(G, F, A, B, C), X, Z)) | (member(tptp_fun_Y_8(Z, X, B, F, G), B) & apply(F, X, tptp_fun_Y_8(Z, X, B, F, G)) & apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z))) & (apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y) & apply(G, Y, Z)))))) <=> ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(57,plain,
% 0.20/0.43 (![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~(member(X, A) & member(Z, C))) | (((~apply(compose_function(G, F, A, B, C), X, Z)) | (member(tptp_fun_Y_8(Z, X, B, F, G), B) & apply(F, X, tptp_fun_Y_8(Z, X, B, F, G)) & apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z))) & (apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y) & apply(G, Y, Z)))))) <=> ![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[56])).
% 0.20/0.43 tff(58,plain,
% 0.20/0.43 (![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~(member(X, A) & member(Z, C))) | (apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : (member(Y, B) & apply(F, X, Y) & apply(G, Y, Z)))) <=> ![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~(member(X, A) & member(Z, C))) | (apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : (member(Y, B) & apply(F, X, Y) & apply(G, Y, Z))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(59,plain,
% 0.20/0.43 (^[G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : trans(monotonicity(rewrite((apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : ((member(Y, B) & apply(F, X, Y)) & apply(G, Y, Z))) <=> (apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : (member(Y, B) & apply(F, X, Y) & apply(G, Y, Z)))), (((member(X, A) & member(Z, C)) => (apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : ((member(Y, B) & apply(F, X, Y)) & apply(G, Y, Z)))) <=> ((member(X, A) & member(Z, C)) => (apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : (member(Y, B) & apply(F, X, Y) & apply(G, Y, Z)))))), rewrite(((member(X, A) & member(Z, C)) => (apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : (member(Y, B) & apply(F, X, Y) & apply(G, Y, Z)))) <=> ((~(member(X, A) & member(Z, C))) | (apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : (member(Y, B) & apply(F, X, Y) & apply(G, Y, Z))))), (((member(X, A) & member(Z, C)) => (apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : ((member(Y, B) & apply(F, X, Y)) & apply(G, Y, Z)))) <=> ((~(member(X, A) & member(Z, C))) | (apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : (member(Y, B) & apply(F, X, Y) & apply(G, Y, Z))))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(60,plain,
% 0.20/0.43 (![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((member(X, A) & member(Z, C)) => (apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : ((member(Y, B) & apply(F, X, Y)) & apply(G, Y, Z)))) <=> ![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~(member(X, A) & member(Z, C))) | (apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : (member(Y, B) & apply(F, X, Y) & apply(G, Y, Z))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[59])).
% 0.20/0.43 tff(61,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')).
% 0.20/0.43 tff(62,plain,
% 0.20/0.43 (![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~(member(X, A) & member(Z, C))) | (apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : (member(Y, B) & apply(F, X, Y) & apply(G, Y, Z))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.20/0.43 tff(63,plain,
% 0.20/0.43 (![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~(member(X, A) & member(Z, C))) | (apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : (member(Y, B) & apply(F, X, Y) & apply(G, Y, Z))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[62, 58])).
% 0.20/0.43 tff(64,plain,(
% 0.20/0.43 ![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~(member(X, A) & member(Z, C))) | (((~apply(compose_function(G, F, A, B, C), X, Z)) | (member(tptp_fun_Y_8(Z, X, B, F, G), B) & apply(F, X, tptp_fun_Y_8(Z, X, B, F, G)) & apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z))) & (apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y) & apply(G, Y, Z))))))),
% 0.20/0.43 inference(skolemize,[status(sab)],[63])).
% 0.20/0.43 tff(65,plain,
% 0.20/0.43 (![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[64, 57])).
% 0.20/0.43 tff(66,plain,
% 0.20/0.43 (![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[65, 55])).
% 0.20/0.43 tff(67,plain,
% 0.20/0.43 (((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_Y_20(B!39, A!40, F!43), B!39)) | (~((~((~apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43))) | (~((~apply(F!43, tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43), tptp_fun_Y_20(B!39, A!40, F!43))) | (~apply(H!41, tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43))) | (~member(tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43), A!40)))))) | (~(apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43)) | ![Y: $i] : ((~member(Y, A!40)) | (~apply(F!43, Y, tptp_fun_Y_20(B!39, A!40, F!43))) | (~apply(H!41, tptp_fun_Y_20(B!39, A!40, F!43), Y))))))))) <=> ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | (~member(tptp_fun_Y_20(B!39, A!40, F!43), B!39)) | (~((~((~apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43))) | (~((~apply(F!43, tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43), tptp_fun_Y_20(B!39, A!40, F!43))) | (~apply(H!41, tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43))) | (~member(tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43), A!40)))))) | (~(apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43)) | ![Y: $i] : ((~member(Y, A!40)) | (~apply(F!43, Y, tptp_fun_Y_20(B!39, A!40, F!43))) | (~apply(H!41, tptp_fun_Y_20(B!39, A!40, F!43), Y))))))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(68,plain,
% 0.20/0.44 (((~member(tptp_fun_Y_20(B!39, A!40, F!43), B!39)) | (~member(tptp_fun_Y_20(B!39, A!40, F!43), B!39)) | (~((~((~apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43))) | (~((~apply(F!43, tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43), tptp_fun_Y_20(B!39, A!40, F!43))) | (~apply(H!41, tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43))) | (~member(tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43), A!40)))))) | (~(apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43)) | ![Y: $i] : ((~member(Y, A!40)) | (~apply(F!43, Y, tptp_fun_Y_20(B!39, A!40, F!43))) | (~apply(H!41, tptp_fun_Y_20(B!39, A!40, F!43), Y)))))))) <=> ((~member(tptp_fun_Y_20(B!39, A!40, F!43), B!39)) | (~((~((~apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43))) | (~((~apply(F!43, tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43), tptp_fun_Y_20(B!39, A!40, F!43))) | (~apply(H!41, tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43))) | (~member(tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43), A!40)))))) | (~(apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43)) | ![Y: $i] : ((~member(Y, A!40)) | (~apply(F!43, Y, tptp_fun_Y_20(B!39, A!40, F!43))) | (~apply(H!41, tptp_fun_Y_20(B!39, A!40, F!43), Y))))))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(69,plain,
% 0.20/0.44 ((~((~((~apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43), A!40)) | (~apply(H!41, tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43))) | (~apply(F!43, tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43), tptp_fun_Y_20(B!39, A!40, F!43))))))) | (~(apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43)) | ![Y: $i] : ((~member(Y, A!40)) | (~apply(H!41, tptp_fun_Y_20(B!39, A!40, F!43), Y)) | (~apply(F!43, Y, tptp_fun_Y_20(B!39, A!40, F!43)))))))) <=> (~((~((~apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43))) | (~((~apply(F!43, tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43), tptp_fun_Y_20(B!39, A!40, F!43))) | (~apply(H!41, tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43))) | (~member(tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43), A!40)))))) | (~(apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43)) | ![Y: $i] : ((~member(Y, A!40)) | (~apply(F!43, Y, tptp_fun_Y_20(B!39, A!40, F!43))) | (~apply(H!41, tptp_fun_Y_20(B!39, A!40, F!43), Y)))))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(70,plain,
% 0.20/0.44 (((~member(tptp_fun_Y_20(B!39, A!40, F!43), B!39)) | (~member(tptp_fun_Y_20(B!39, A!40, F!43), B!39)) | (~((~((~apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43), A!40)) | (~apply(H!41, tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43))) | (~apply(F!43, tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43), tptp_fun_Y_20(B!39, A!40, F!43))))))) | (~(apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43)) | ![Y: $i] : ((~member(Y, A!40)) | (~apply(H!41, tptp_fun_Y_20(B!39, A!40, F!43), Y)) | (~apply(F!43, Y, tptp_fun_Y_20(B!39, A!40, F!43))))))))) <=> ((~member(tptp_fun_Y_20(B!39, A!40, F!43), B!39)) | (~member(tptp_fun_Y_20(B!39, A!40, F!43), B!39)) | (~((~((~apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43))) | (~((~apply(F!43, tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43), tptp_fun_Y_20(B!39, A!40, F!43))) | (~apply(H!41, tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43))) | (~member(tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43), A!40)))))) | (~(apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43)) | ![Y: $i] : ((~member(Y, A!40)) | (~apply(F!43, Y, tptp_fun_Y_20(B!39, A!40, F!43))) | (~apply(H!41, tptp_fun_Y_20(B!39, A!40, F!43), Y))))))))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[69])).
% 0.20/0.44 tff(71,plain,
% 0.20/0.44 (((~member(tptp_fun_Y_20(B!39, A!40, F!43), B!39)) | (~member(tptp_fun_Y_20(B!39, A!40, F!43), B!39)) | (~((~((~apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43), A!40)) | (~apply(H!41, tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43))) | (~apply(F!43, tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43), tptp_fun_Y_20(B!39, A!40, F!43))))))) | (~(apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43)) | ![Y: $i] : ((~member(Y, A!40)) | (~apply(H!41, tptp_fun_Y_20(B!39, A!40, F!43), Y)) | (~apply(F!43, Y, tptp_fun_Y_20(B!39, A!40, F!43))))))))) <=> ((~member(tptp_fun_Y_20(B!39, A!40, F!43), B!39)) | (~((~((~apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43))) | (~((~apply(F!43, tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43), tptp_fun_Y_20(B!39, A!40, F!43))) | (~apply(H!41, tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43))) | (~member(tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43), A!40)))))) | (~(apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43)) | ![Y: $i] : ((~member(Y, A!40)) | (~apply(F!43, Y, tptp_fun_Y_20(B!39, A!40, F!43))) | (~apply(H!41, tptp_fun_Y_20(B!39, A!40, F!43), Y))))))))),
% 0.20/0.45 inference(transitivity,[status(thm)],[70, 68])).
% 0.20/0.45 tff(72,plain,
% 0.20/0.45 (((~![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_Y_20(B!39, A!40, F!43), B!39)) | (~member(tptp_fun_Y_20(B!39, A!40, F!43), B!39)) | (~((~((~apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43), A!40)) | (~apply(H!41, tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43))) | (~apply(F!43, tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43), tptp_fun_Y_20(B!39, A!40, F!43))))))) | (~(apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43)) | ![Y: $i] : ((~member(Y, A!40)) | (~apply(H!41, tptp_fun_Y_20(B!39, A!40, F!43), Y)) | (~apply(F!43, Y, tptp_fun_Y_20(B!39, A!40, F!43)))))))))) <=> ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_Y_20(B!39, A!40, F!43), B!39)) | (~((~((~apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43))) | (~((~apply(F!43, tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43), tptp_fun_Y_20(B!39, A!40, F!43))) | (~apply(H!41, tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43))) | (~member(tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43), A!40)))))) | (~(apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43)) | ![Y: $i] : ((~member(Y, A!40)) | (~apply(F!43, Y, tptp_fun_Y_20(B!39, A!40, F!43))) | (~apply(H!41, tptp_fun_Y_20(B!39, A!40, F!43), Y)))))))))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[71])).
% 0.20/0.45 tff(73,plain,
% 0.20/0.45 (((~![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_Y_20(B!39, A!40, F!43), B!39)) | (~member(tptp_fun_Y_20(B!39, A!40, F!43), B!39)) | (~((~((~apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43), A!40)) | (~apply(H!41, tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43))) | (~apply(F!43, tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43), tptp_fun_Y_20(B!39, A!40, F!43))))))) | (~(apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43)) | ![Y: $i] : ((~member(Y, A!40)) | (~apply(H!41, tptp_fun_Y_20(B!39, A!40, F!43), Y)) | (~apply(F!43, Y, tptp_fun_Y_20(B!39, A!40, F!43)))))))))) <=> ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | (~member(tptp_fun_Y_20(B!39, A!40, F!43), B!39)) | (~((~((~apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43))) | (~((~apply(F!43, tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43), tptp_fun_Y_20(B!39, A!40, F!43))) | (~apply(H!41, tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43))) | (~member(tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43), A!40)))))) | (~(apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43)) | ![Y: $i] : ((~member(Y, A!40)) | (~apply(F!43, Y, tptp_fun_Y_20(B!39, A!40, F!43))) | (~apply(H!41, tptp_fun_Y_20(B!39, A!40, F!43), Y))))))))),
% 0.20/0.45 inference(transitivity,[status(thm)],[72, 67])).
% 0.20/0.45 tff(74,plain,
% 0.20/0.45 ((~![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_Y_20(B!39, A!40, F!43), B!39)) | (~member(tptp_fun_Y_20(B!39, A!40, F!43), B!39)) | (~((~((~apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43), A!40)) | (~apply(H!41, tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43))) | (~apply(F!43, tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43), tptp_fun_Y_20(B!39, A!40, F!43))))))) | (~(apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43)) | ![Y: $i] : ((~member(Y, A!40)) | (~apply(H!41, tptp_fun_Y_20(B!39, A!40, F!43), Y)) | (~apply(F!43, Y, tptp_fun_Y_20(B!39, A!40, F!43)))))))))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(75,plain,
% 0.20/0.45 ((~![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_Y_20(B!39, A!40, F!43), B!39)) | (~((~((~apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43))) | (~((~apply(F!43, tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43), tptp_fun_Y_20(B!39, A!40, F!43))) | (~apply(H!41, tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43))) | (~member(tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43), A!40)))))) | (~(apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43)) | ![Y: $i] : ((~member(Y, A!40)) | (~apply(F!43, Y, tptp_fun_Y_20(B!39, A!40, F!43))) | (~apply(H!41, tptp_fun_Y_20(B!39, A!40, F!43), Y)))))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.20/0.46 tff(76,plain,
% 0.20/0.46 (~((~((~apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43))) | (~((~apply(F!43, tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43), tptp_fun_Y_20(B!39, A!40, F!43))) | (~apply(H!41, tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43))) | (~member(tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43), A!40)))))) | (~(apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43)) | ![Y: $i] : ((~member(Y, A!40)) | (~apply(F!43, Y, tptp_fun_Y_20(B!39, A!40, F!43))) | (~apply(H!41, tptp_fun_Y_20(B!39, A!40, F!43), Y))))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[75, 66, 50])).
% 0.20/0.46 tff(77,plain,
% 0.20/0.46 (((~((~apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43))) | (~((~apply(F!43, tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43), tptp_fun_Y_20(B!39, A!40, F!43))) | (~apply(H!41, tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43))) | (~member(tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43), A!40)))))) | (~(apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43)) | ![Y: $i] : ((~member(Y, A!40)) | (~apply(F!43, Y, tptp_fun_Y_20(B!39, A!40, F!43))) | (~apply(H!41, tptp_fun_Y_20(B!39, A!40, F!43), Y)))))) | ((~apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43))) | (~((~apply(F!43, tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43), tptp_fun_Y_20(B!39, A!40, F!43))) | (~apply(H!41, tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43))) | (~member(tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43), A!40)))))),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(78,plain,
% 0.20/0.46 ((~apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43))) | (~((~apply(F!43, tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43), tptp_fun_Y_20(B!39, A!40, F!43))) | (~apply(H!41, tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43))) | (~member(tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43), A!40))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[77, 76])).
% 0.20/0.46 tff(79,plain,
% 0.20/0.46 (^[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)))))))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(80,plain,
% 0.20/0.46 (![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))))))))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[79])).
% 0.20/0.46 tff(81,plain,
% 0.20/0.46 (^[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)))))))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(82,plain,
% 0.20/0.46 (![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))))))))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[81])).
% 0.20/0.46 tff(83,plain,
% 0.20/0.46 (![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))))))))),
% 0.20/0.46 inference(transitivity,[status(thm)],[82, 80])).
% 0.20/0.46 tff(84,plain,
% 0.20/0.46 (^[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))))))))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(85,plain,
% 0.20/0.46 (![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))))))))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[84])).
% 0.20/0.46 tff(86,plain,
% 0.20/0.46 (![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)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(87,plain,
% 0.20/0.46 (^[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))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(88,plain,
% 0.20/0.46 (![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)))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[87])).
% 0.20/0.46 tff(89,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')).
% 0.20/0.46 tff(90,plain,
% 0.20/0.46 (![F: $i, A: $i] : (identity(F, A) <=> ![X: $i] : ((~member(X, A)) | apply(F, X, X)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.20/0.46 tff(91,plain,
% 0.20/0.46 (![F: $i, A: $i] : (identity(F, A) <=> ![X: $i] : ((~member(X, A)) | apply(F, X, X)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[90, 86])).
% 0.20/0.46 tff(92,plain,(
% 0.20/0.46 ![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))))))),
% 0.20/0.46 inference(skolemize,[status(sab)],[91])).
% 0.20/0.46 tff(93,plain,
% 0.20/0.46 (![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))))))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[92, 85])).
% 0.20/0.46 tff(94,plain,
% 0.20/0.46 (![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))))))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[93, 83])).
% 0.20/0.46 tff(95,plain,
% 0.20/0.46 ((~![F: $i, A: $i] : (~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F))))))))) | (~((~((~identity(compose_function(F!43, H!41, B!39, A!40, B!39), B!39)) | ![X: $i] : ((~member(X, B!39)) | apply(compose_function(F!43, H!41, B!39, A!40, B!39), X, X)))) | (~(identity(compose_function(F!43, H!41, B!39, A!40, B!39), B!39) | (~((~member(tptp_fun_X_15(B!39, compose_function(F!43, H!41, B!39, A!40, B!39)), B!39)) | apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!43, H!41, B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!43, H!41, B!39, A!40, B!39)))))))))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(96,plain,
% 0.20/0.46 (~((~((~identity(compose_function(F!43, H!41, B!39, A!40, B!39), B!39)) | ![X: $i] : ((~member(X, B!39)) | apply(compose_function(F!43, H!41, B!39, A!40, B!39), X, X)))) | (~(identity(compose_function(F!43, H!41, B!39, A!40, B!39), B!39) | (~((~member(tptp_fun_X_15(B!39, compose_function(F!43, H!41, B!39, A!40, B!39)), B!39)) | apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!43, H!41, B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!43, H!41, B!39, A!40, B!39))))))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[95, 94])).
% 0.20/0.46 tff(97,plain,
% 0.20/0.46 (((~((~identity(compose_function(F!43, H!41, B!39, A!40, B!39), B!39)) | ![X: $i] : ((~member(X, B!39)) | apply(compose_function(F!43, H!41, B!39, A!40, B!39), X, X)))) | (~(identity(compose_function(F!43, H!41, B!39, A!40, B!39), B!39) | (~((~member(tptp_fun_X_15(B!39, compose_function(F!43, H!41, B!39, A!40, B!39)), B!39)) | apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!43, H!41, B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!43, H!41, B!39, A!40, B!39)))))))) | ((~identity(compose_function(F!43, H!41, B!39, A!40, B!39), B!39)) | ![X: $i] : ((~member(X, B!39)) | apply(compose_function(F!43, H!41, B!39, A!40, B!39), X, X)))),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(98,plain,
% 0.20/0.46 ((~identity(compose_function(F!43, H!41, B!39, A!40, B!39), B!39)) | ![X: $i] : ((~member(X, B!39)) | apply(compose_function(F!43, H!41, B!39, A!40, B!39), X, X))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[97, 96])).
% 0.20/0.46 tff(99,plain,
% 0.20/0.46 ((~![F: $i, G: $i, H: $i, A: $i, B: $i] : ((~(maps(F, A, B) & maps(G, B, A) & maps(H, B, A) & identity(compose_function(G, F, A, B, A), A) & identity(compose_function(F, H, B, A, B), B))) | one_to_one(F, A, B))) <=> (~![F: $i, G: $i, H: $i, A: $i, B: $i] : ((~(maps(F, A, B) & maps(G, B, A) & maps(H, B, A) & identity(compose_function(G, F, A, B, A), A) & identity(compose_function(F, H, B, A, B), B))) | one_to_one(F, A, B)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(100,plain,
% 0.20/0.46 ((~![F: $i, G: $i, H: $i, A: $i, B: $i] : (((((maps(F, A, B) & maps(G, B, A)) & maps(H, B, A)) & identity(compose_function(G, F, A, B, A), A)) & identity(compose_function(F, H, B, A, B), B)) => one_to_one(F, A, B))) <=> (~![F: $i, G: $i, H: $i, A: $i, B: $i] : ((~(maps(F, A, B) & maps(G, B, A) & maps(H, B, A) & identity(compose_function(G, F, A, B, A), A) & identity(compose_function(F, H, B, A, B), B))) | one_to_one(F, A, B)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(101,axiom,(~![F: $i, G: $i, H: $i, A: $i, B: $i] : (((((maps(F, A, B) & maps(G, B, A)) & maps(H, B, A)) & identity(compose_function(G, F, A, B, A), A)) & identity(compose_function(F, H, B, A, B), B)) => one_to_one(F, A, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','thII16')).
% 0.20/0.46 tff(102,plain,
% 0.20/0.46 (~![F: $i, G: $i, H: $i, A: $i, B: $i] : ((~(maps(F, A, B) & maps(G, B, A) & maps(H, B, A) & identity(compose_function(G, F, A, B, A), A) & identity(compose_function(F, H, B, A, B), B))) | one_to_one(F, A, B))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[101, 100])).
% 0.20/0.46 tff(103,plain,
% 0.20/0.46 (~![F: $i, G: $i, H: $i, A: $i, B: $i] : ((~(maps(F, A, B) & maps(G, B, A) & maps(H, B, A) & identity(compose_function(G, F, A, B, A), A) & identity(compose_function(F, H, B, A, B), B))) | one_to_one(F, A, B))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[102, 99])).
% 0.20/0.46 tff(104,plain,
% 0.20/0.46 (~![F: $i, G: $i, H: $i, A: $i, B: $i] : ((~(maps(F, A, B) & maps(G, B, A) & maps(H, B, A) & identity(compose_function(G, F, A, B, A), A) & identity(compose_function(F, H, B, A, B), B))) | one_to_one(F, A, B))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[103, 99])).
% 0.20/0.46 tff(105,plain,
% 0.20/0.46 (~![F: $i, G: $i, H: $i, A: $i, B: $i] : ((~(maps(F, A, B) & maps(G, B, A) & maps(H, B, A) & identity(compose_function(G, F, A, B, A), A) & identity(compose_function(F, H, B, A, B), B))) | one_to_one(F, A, B))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[104, 99])).
% 0.20/0.46 tff(106,plain,(
% 0.20/0.46 ~((~(maps(F!43, A!40, B!39) & maps(G!42, B!39, A!40) & maps(H!41, B!39, A!40) & identity(compose_function(G!42, F!43, A!40, B!39, A!40), A!40) & identity(compose_function(F!43, H!41, B!39, A!40, B!39), B!39))) | one_to_one(F!43, A!40, B!39))),
% 0.20/0.46 inference(skolemize,[status(sab)],[105])).
% 0.20/0.46 tff(107,plain,
% 0.20/0.46 (maps(F!43, A!40, B!39) & maps(G!42, B!39, A!40) & maps(H!41, B!39, A!40) & identity(compose_function(G!42, F!43, A!40, B!39, A!40), A!40) & identity(compose_function(F!43, H!41, B!39, A!40, B!39), B!39)),
% 0.20/0.46 inference(or_elim,[status(thm)],[106])).
% 0.20/0.46 tff(108,plain,
% 0.20/0.46 (identity(compose_function(F!43, H!41, B!39, A!40, B!39), B!39)),
% 0.20/0.46 inference(and_elim,[status(thm)],[107])).
% 0.20/0.46 tff(109,plain,
% 0.20/0.46 ((~((~identity(compose_function(F!43, H!41, B!39, A!40, B!39), B!39)) | ![X: $i] : ((~member(X, B!39)) | apply(compose_function(F!43, H!41, B!39, A!40, B!39), X, X)))) | (~identity(compose_function(F!43, H!41, B!39, A!40, B!39), B!39)) | ![X: $i] : ((~member(X, B!39)) | apply(compose_function(F!43, H!41, B!39, A!40, B!39), X, X))),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(110,plain,
% 0.20/0.46 ((~((~identity(compose_function(F!43, H!41, B!39, A!40, B!39), B!39)) | ![X: $i] : ((~member(X, B!39)) | apply(compose_function(F!43, H!41, B!39, A!40, B!39), X, X)))) | ![X: $i] : ((~member(X, B!39)) | apply(compose_function(F!43, H!41, B!39, A!40, B!39), X, X))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[109, 108])).
% 0.20/0.46 tff(111,plain,
% 0.20/0.46 (![X: $i] : ((~member(X, B!39)) | apply(compose_function(F!43, H!41, B!39, A!40, B!39), X, X))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[110, 98])).
% 0.20/0.46 tff(112,plain,
% 0.20/0.46 (((~![X: $i] : ((~member(X, B!39)) | apply(compose_function(F!43, H!41, B!39, A!40, B!39), X, X))) | ((~member(tptp_fun_Y_20(B!39, A!40, F!43), B!39)) | apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43)))) <=> ((~![X: $i] : ((~member(X, B!39)) | apply(compose_function(F!43, H!41, B!39, A!40, B!39), X, X))) | (~member(tptp_fun_Y_20(B!39, A!40, F!43), B!39)) | apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(113,plain,
% 0.20/0.46 ((~![X: $i] : ((~member(X, B!39)) | apply(compose_function(F!43, H!41, B!39, A!40, B!39), X, X))) | ((~member(tptp_fun_Y_20(B!39, A!40, F!43), B!39)) | apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43)))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(114,plain,
% 0.20/0.46 ((~![X: $i] : ((~member(X, B!39)) | apply(compose_function(F!43, H!41, B!39, A!40, B!39), X, X))) | (~member(tptp_fun_Y_20(B!39, A!40, F!43), B!39)) | apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[113, 112])).
% 0.20/0.46 tff(115,plain,
% 0.20/0.46 (apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[114, 111, 50])).
% 0.20/0.46 tff(116,plain,
% 0.20/0.46 ((~((~apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43))) | (~((~apply(F!43, tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43), tptp_fun_Y_20(B!39, A!40, F!43))) | (~apply(H!41, tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43))) | (~member(tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43), A!40)))))) | (~apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43))) | (~((~apply(F!43, tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43), tptp_fun_Y_20(B!39, A!40, F!43))) | (~apply(H!41, tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43))) | (~member(tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43), A!40))))),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(117,plain,
% 0.20/0.46 ((~((~apply(compose_function(F!43, H!41, B!39, A!40, B!39), tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43))) | (~((~apply(F!43, tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43), tptp_fun_Y_20(B!39, A!40, F!43))) | (~apply(H!41, tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43))) | (~member(tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43), A!40)))))) | (~((~apply(F!43, tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43), tptp_fun_Y_20(B!39, A!40, F!43))) | (~apply(H!41, tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43))) | (~member(tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43), A!40))))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[116, 115])).
% 0.20/0.47 tff(118,plain,
% 0.20/0.47 (~((~apply(F!43, tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43), tptp_fun_Y_20(B!39, A!40, F!43))) | (~apply(H!41, tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43))) | (~member(tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43), A!40)))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[117, 78])).
% 0.20/0.47 tff(119,plain,
% 0.20/0.47 (((~apply(F!43, tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43), tptp_fun_Y_20(B!39, A!40, F!43))) | (~apply(H!41, tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43))) | (~member(tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43), A!40))) | member(tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43), A!40)),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(120,plain,
% 0.20/0.47 (member(tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43), A!40)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[119, 118])).
% 0.20/0.47 tff(121,plain,
% 0.20/0.47 (((~apply(F!43, tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43), tptp_fun_Y_20(B!39, A!40, F!43))) | (~apply(H!41, tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43))) | (~member(tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43), A!40))) | apply(F!43, tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43), tptp_fun_Y_20(B!39, A!40, F!43))),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(122,plain,
% 0.20/0.47 (apply(F!43, tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43), tptp_fun_Y_20(B!39, A!40, F!43))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[121, 118])).
% 0.20/0.47 tff(123,plain,
% 0.20/0.47 (((~member(tptp_fun_Y_20(B!39, A!40, F!43), B!39)) | (~![E: $i] : ((~member(E, A!40)) | (~apply(F!43, E, tptp_fun_Y_20(B!39, A!40, F!43)))))) | ![E: $i] : ((~member(E, A!40)) | (~apply(F!43, E, tptp_fun_Y_20(B!39, A!40, F!43))))),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(124,plain,
% 0.20/0.47 (![E: $i] : ((~member(E, A!40)) | (~apply(F!43, E, tptp_fun_Y_20(B!39, A!40, F!43))))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[123, 48])).
% 0.20/0.47 tff(125,plain,
% 0.20/0.47 (((~![E: $i] : ((~member(E, A!40)) | (~apply(F!43, E, tptp_fun_Y_20(B!39, A!40, F!43))))) | ((~member(tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43), A!40)) | (~apply(F!43, tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43), tptp_fun_Y_20(B!39, A!40, F!43))))) <=> ((~![E: $i] : ((~member(E, A!40)) | (~apply(F!43, E, tptp_fun_Y_20(B!39, A!40, F!43))))) | (~member(tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43), A!40)) | (~apply(F!43, tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43), tptp_fun_Y_20(B!39, A!40, F!43))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(126,plain,
% 0.20/0.47 ((~![E: $i] : ((~member(E, A!40)) | (~apply(F!43, E, tptp_fun_Y_20(B!39, A!40, F!43))))) | ((~member(tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43), A!40)) | (~apply(F!43, tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43), tptp_fun_Y_20(B!39, A!40, F!43))))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(127,plain,
% 0.20/0.47 ((~![E: $i] : ((~member(E, A!40)) | (~apply(F!43, E, tptp_fun_Y_20(B!39, A!40, F!43))))) | (~member(tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43), A!40)) | (~apply(F!43, tptp_fun_Y_8(tptp_fun_Y_20(B!39, A!40, F!43), tptp_fun_Y_20(B!39, A!40, F!43), A!40, H!41, F!43), tptp_fun_Y_20(B!39, A!40, F!43)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[126, 125])).
% 0.20/0.47 tff(128,plain,
% 0.20/0.47 ($false),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[127, 124, 122, 120])).
% 0.20/0.47 tff(129,plain,((~member(tptp_fun_Y_20(B!39, A!40, F!43), B!39)) | (~![E: $i] : ((~member(E, A!40)) | (~apply(F!43, E, tptp_fun_Y_20(B!39, A!40, F!43)))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.47 tff(130,plain,
% 0.20/0.47 ((~(surjective(F!43, A!40, B!39) | (~((~member(tptp_fun_Y_20(B!39, A!40, F!43), B!39)) | (~![E: $i] : ((~member(E, A!40)) | (~apply(F!43, E, tptp_fun_Y_20(B!39, A!40, F!43))))))))) | surjective(F!43, A!40, B!39) | (~((~member(tptp_fun_Y_20(B!39, A!40, F!43), B!39)) | (~![E: $i] : ((~member(E, A!40)) | (~apply(F!43, E, tptp_fun_Y_20(B!39, A!40, F!43)))))))),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(131,plain,
% 0.20/0.47 ((~(surjective(F!43, A!40, B!39) | (~((~member(tptp_fun_Y_20(B!39, A!40, F!43), B!39)) | (~![E: $i] : ((~member(E, A!40)) | (~apply(F!43, E, tptp_fun_Y_20(B!39, A!40, F!43))))))))) | surjective(F!43, A!40, B!39)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[130, 129])).
% 0.20/0.47 tff(132,plain,
% 0.20/0.47 (surjective(F!43, A!40, B!39)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[131, 47])).
% 0.20/0.47 tff(133,plain,
% 0.20/0.47 (^[F: $i, A: $i, B: $i] : refl((~(((~injective(F, A, B)) | (~surjective(F, A, B))) <=> one_to_one(F, A, B))) <=> (~(((~injective(F, A, B)) | (~surjective(F, A, B))) <=> one_to_one(F, A, B))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(134,plain,
% 0.20/0.47 (![F: $i, A: $i, B: $i] : (~(((~injective(F, A, B)) | (~surjective(F, A, B))) <=> one_to_one(F, A, B))) <=> ![F: $i, A: $i, B: $i] : (~(((~injective(F, A, B)) | (~surjective(F, A, B))) <=> one_to_one(F, A, B)))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[133])).
% 0.20/0.47 tff(135,plain,
% 0.20/0.47 (^[F: $i, A: $i, B: $i] : trans(trans(monotonicity(rewrite((injective(F, A, B) & surjective(F, A, B)) <=> (~((~injective(F, A, B)) | (~surjective(F, A, B))))), ((one_to_one(F, A, B) <=> (injective(F, A, B) & surjective(F, A, B))) <=> (one_to_one(F, A, B) <=> (~((~injective(F, A, B)) | (~surjective(F, A, B))))))), rewrite((one_to_one(F, A, B) <=> (~((~injective(F, A, B)) | (~surjective(F, A, B))))) <=> (~(((~injective(F, A, B)) | (~surjective(F, A, B))) <=> one_to_one(F, A, B)))), ((one_to_one(F, A, B) <=> (injective(F, A, B) & surjective(F, A, B))) <=> (~(((~injective(F, A, B)) | (~surjective(F, A, B))) <=> one_to_one(F, A, B))))), rewrite((~(((~injective(F, A, B)) | (~surjective(F, A, B))) <=> one_to_one(F, A, B))) <=> (~(((~injective(F, A, B)) | (~surjective(F, A, B))) <=> one_to_one(F, A, B)))), ((one_to_one(F, A, B) <=> (injective(F, A, B) & surjective(F, A, B))) <=> (~(((~injective(F, A, B)) | (~surjective(F, A, B))) <=> one_to_one(F, A, B)))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(136,plain,
% 0.20/0.47 (![F: $i, A: $i, B: $i] : (one_to_one(F, A, B) <=> (injective(F, A, B) & surjective(F, A, B))) <=> ![F: $i, A: $i, B: $i] : (~(((~injective(F, A, B)) | (~surjective(F, A, B))) <=> one_to_one(F, A, B)))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[135])).
% 0.20/0.47 tff(137,plain,
% 0.20/0.47 (![F: $i, A: $i, B: $i] : (one_to_one(F, A, B) <=> (injective(F, A, B) & surjective(F, A, B))) <=> ![F: $i, A: $i, B: $i] : (one_to_one(F, A, B) <=> (injective(F, A, B) & surjective(F, A, B)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(138,axiom,(![F: $i, A: $i, B: $i] : (one_to_one(F, A, B) <=> (injective(F, A, B) & surjective(F, A, B)))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+1.ax','one_to_one')).
% 0.20/0.47 tff(139,plain,
% 0.20/0.47 (![F: $i, A: $i, B: $i] : (one_to_one(F, A, B) <=> (injective(F, A, B) & surjective(F, A, B)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[138, 137])).
% 0.20/0.47 tff(140,plain,(
% 0.20/0.47 ![F: $i, A: $i, B: $i] : (one_to_one(F, A, B) <=> (injective(F, A, B) & surjective(F, A, B)))),
% 0.20/0.47 inference(skolemize,[status(sab)],[139])).
% 0.20/0.47 tff(141,plain,
% 0.20/0.47 (![F: $i, A: $i, B: $i] : (~(((~injective(F, A, B)) | (~surjective(F, A, B))) <=> one_to_one(F, A, B)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[140, 136])).
% 0.20/0.47 tff(142,plain,
% 0.20/0.47 (![F: $i, A: $i, B: $i] : (~(((~injective(F, A, B)) | (~surjective(F, A, B))) <=> one_to_one(F, A, B)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[141, 134])).
% 0.20/0.47 tff(143,plain,
% 0.20/0.47 ((~![F: $i, A: $i, B: $i] : (~(((~injective(F, A, B)) | (~surjective(F, A, B))) <=> one_to_one(F, A, B)))) | (~(((~injective(F!43, A!40, B!39)) | (~surjective(F!43, A!40, B!39))) <=> one_to_one(F!43, A!40, B!39)))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(144,plain,
% 0.20/0.47 (~(((~injective(F!43, A!40, B!39)) | (~surjective(F!43, A!40, B!39))) <=> one_to_one(F!43, A!40, B!39))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[143, 142])).
% 0.20/0.47 tff(145,plain,
% 0.20/0.47 (~one_to_one(F!43, A!40, B!39)),
% 0.20/0.47 inference(or_elim,[status(thm)],[106])).
% 0.20/0.47 tff(146,plain,
% 0.20/0.47 ((((~injective(F!43, A!40, B!39)) | (~surjective(F!43, A!40, B!39))) <=> one_to_one(F!43, A!40, B!39)) | ((~injective(F!43, A!40, B!39)) | (~surjective(F!43, A!40, B!39))) | one_to_one(F!43, A!40, B!39)),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(147,plain,
% 0.20/0.47 ((((~injective(F!43, A!40, B!39)) | (~surjective(F!43, A!40, B!39))) <=> one_to_one(F!43, A!40, B!39)) | ((~injective(F!43, A!40, B!39)) | (~surjective(F!43, A!40, B!39)))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[146, 145])).
% 0.20/0.47 tff(148,plain,
% 0.20/0.47 ((~injective(F!43, A!40, B!39)) | (~surjective(F!43, A!40, B!39))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[147, 144])).
% 0.20/0.47 tff(149,plain,
% 0.20/0.47 ((~((~injective(F!43, A!40, B!39)) | (~surjective(F!43, A!40, B!39)))) | (~injective(F!43, A!40, B!39)) | (~surjective(F!43, A!40, B!39))),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(150,plain,
% 0.20/0.47 ((~injective(F!43, A!40, B!39)) | (~surjective(F!43, A!40, B!39))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[149, 148])).
% 0.20/0.47 tff(151,plain,
% 0.20/0.47 (~injective(F!43, A!40, B!39)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[150, 132])).
% 0.20/0.47 tff(152,plain,
% 0.20/0.47 ((~(injective(F!43, A!40, B!39) | (~((~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_Y_16(B!39, A!40, F!43), B!39)) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (tptp_fun_X1_18(B!39, A!40, F!43) = tptp_fun_X2_17(B!39, A!40, F!43)) | (~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40)))))) | injective(F!43, A!40, B!39) | (~((~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_Y_16(B!39, A!40, F!43), B!39)) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (tptp_fun_X1_18(B!39, A!40, F!43) = tptp_fun_X2_17(B!39, A!40, F!43)) | (~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40))))),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(153,plain,
% 0.20/0.47 ((~(injective(F!43, A!40, B!39) | (~((~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_Y_16(B!39, A!40, F!43), B!39)) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (tptp_fun_X1_18(B!39, A!40, F!43) = tptp_fun_X2_17(B!39, A!40, F!43)) | (~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40)))))) | (~((~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_Y_16(B!39, A!40, F!43), B!39)) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (tptp_fun_X1_18(B!39, A!40, F!43) = tptp_fun_X2_17(B!39, A!40, F!43)) | (~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40))))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[152, 151])).
% 0.20/0.47 tff(154,plain,
% 0.20/0.47 (~((~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_Y_16(B!39, A!40, F!43), B!39)) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (tptp_fun_X1_18(B!39, A!40, F!43) = tptp_fun_X2_17(B!39, A!40, F!43)) | (~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40)))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[153, 25])).
% 0.20/0.47 tff(155,plain,
% 0.20/0.47 (((~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_Y_16(B!39, A!40, F!43), B!39)) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (tptp_fun_X1_18(B!39, A!40, F!43) = tptp_fun_X2_17(B!39, A!40, F!43)) | (~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40))) | member(tptp_fun_X1_18(B!39, A!40, F!43), A!40)),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(156,plain,
% 0.20/0.47 (member(tptp_fun_X1_18(B!39, A!40, F!43), A!40)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[155, 154])).
% 0.20/0.47 tff(157,plain,
% 0.20/0.47 (((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40)) | (~((~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), Y)) | (~apply(G!42, Y, tptp_fun_X1_18(B!39, A!40, F!43)))))) | (~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42), tptp_fun_X1_18(B!39, A!40, F!43))))))))))) <=> ((~![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!43), A!40)) | (~((~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), Y)) | (~apply(G!42, Y, tptp_fun_X1_18(B!39, A!40, F!43)))))) | (~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42), tptp_fun_X1_18(B!39, A!40, F!43))))))))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(158,plain,
% 0.20/0.47 (((~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40)) | (~((~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), Y)) | (~apply(G!42, Y, tptp_fun_X1_18(B!39, A!40, F!43)))))) | (~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42), tptp_fun_X1_18(B!39, A!40, F!43)))))))))) <=> ((~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40)) | (~((~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), Y)) | (~apply(G!42, Y, tptp_fun_X1_18(B!39, A!40, F!43)))))) | (~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42), tptp_fun_X1_18(B!39, A!40, F!43))))))))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(159,plain,
% 0.20/0.48 ((~((~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42), tptp_fun_X1_18(B!39, A!40, F!43))))))) | (~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), Y)) | (~apply(G!42, Y, tptp_fun_X1_18(B!39, A!40, F!43)))))))) <=> (~((~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), Y)) | (~apply(G!42, Y, tptp_fun_X1_18(B!39, A!40, F!43)))))) | (~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42), tptp_fun_X1_18(B!39, A!40, F!43)))))))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(160,plain,
% 0.20/0.48 (((~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40)) | (~((~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42), tptp_fun_X1_18(B!39, A!40, F!43))))))) | (~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), Y)) | (~apply(G!42, Y, tptp_fun_X1_18(B!39, A!40, F!43))))))))) <=> ((~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40)) | (~((~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), Y)) | (~apply(G!42, Y, tptp_fun_X1_18(B!39, A!40, F!43)))))) | (~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42), tptp_fun_X1_18(B!39, A!40, F!43))))))))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[159])).
% 0.20/0.48 tff(161,plain,
% 0.20/0.48 (((~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40)) | (~((~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42), tptp_fun_X1_18(B!39, A!40, F!43))))))) | (~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), Y)) | (~apply(G!42, Y, tptp_fun_X1_18(B!39, A!40, F!43))))))))) <=> ((~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40)) | (~((~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), Y)) | (~apply(G!42, Y, tptp_fun_X1_18(B!39, A!40, F!43)))))) | (~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42), tptp_fun_X1_18(B!39, A!40, F!43))))))))))),
% 0.20/0.48 inference(transitivity,[status(thm)],[160, 158])).
% 0.20/0.48 tff(162,plain,
% 0.20/0.48 (((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40)) | (~((~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42), tptp_fun_X1_18(B!39, A!40, F!43))))))) | (~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), Y)) | (~apply(G!42, Y, tptp_fun_X1_18(B!39, A!40, F!43)))))))))) <=> ((~![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!43), A!40)) | (~((~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), Y)) | (~apply(G!42, Y, tptp_fun_X1_18(B!39, A!40, F!43)))))) | (~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42), tptp_fun_X1_18(B!39, A!40, F!43)))))))))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[161])).
% 0.20/0.48 tff(163,plain,
% 0.20/0.48 (((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40)) | (~((~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42), tptp_fun_X1_18(B!39, A!40, F!43))))))) | (~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), Y)) | (~apply(G!42, Y, tptp_fun_X1_18(B!39, A!40, F!43)))))))))) <=> ((~![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!43), A!40)) | (~((~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), Y)) | (~apply(G!42, Y, tptp_fun_X1_18(B!39, A!40, F!43)))))) | (~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42), tptp_fun_X1_18(B!39, A!40, F!43))))))))))),
% 0.20/0.48 inference(transitivity,[status(thm)],[162, 157])).
% 0.20/0.48 tff(164,plain,
% 0.20/0.48 ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40)) | (~((~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42), tptp_fun_X1_18(B!39, A!40, F!43))))))) | (~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), Y)) | (~apply(G!42, Y, tptp_fun_X1_18(B!39, A!40, F!43)))))))))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(165,plain,
% 0.20/0.48 ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | (~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40)) | (~((~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), Y)) | (~apply(G!42, Y, tptp_fun_X1_18(B!39, A!40, F!43)))))) | (~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42), tptp_fun_X1_18(B!39, A!40, F!43)))))))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[164, 163])).
% 0.20/0.48 tff(166,plain,
% 0.20/0.48 (~((~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), Y)) | (~apply(G!42, Y, tptp_fun_X1_18(B!39, A!40, F!43)))))) | (~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42), tptp_fun_X1_18(B!39, A!40, F!43))))))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[165, 66, 156])).
% 0.20/0.48 tff(167,plain,
% 0.20/0.48 (((~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), Y)) | (~apply(G!42, Y, tptp_fun_X1_18(B!39, A!40, F!43)))))) | (~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42), tptp_fun_X1_18(B!39, A!40, F!43)))))))) | ((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42), tptp_fun_X1_18(B!39, A!40, F!43))))))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(168,plain,
% 0.20/0.49 ((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42), tptp_fun_X1_18(B!39, A!40, F!43)))))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[167, 166])).
% 0.20/0.49 tff(169,plain,
% 0.20/0.49 ((~![F: $i, A: $i] : (~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F))))))))) | (~((~((~identity(compose_function(G!42, F!43, A!40, B!39, A!40), A!40)) | ![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!42, F!43, A!40, B!39, A!40), X, X)))) | (~(identity(compose_function(G!42, F!43, A!40, B!39, A!40), A!40) | (~((~member(tptp_fun_X_15(A!40, compose_function(G!42, F!43, A!40, B!39, A!40)), A!40)) | apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X_15(A!40, compose_function(G!42, F!43, A!40, B!39, A!40)), tptp_fun_X_15(A!40, compose_function(G!42, F!43, A!40, B!39, A!40)))))))))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(170,plain,
% 0.20/0.49 (~((~((~identity(compose_function(G!42, F!43, A!40, B!39, A!40), A!40)) | ![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!42, F!43, A!40, B!39, A!40), X, X)))) | (~(identity(compose_function(G!42, F!43, A!40, B!39, A!40), A!40) | (~((~member(tptp_fun_X_15(A!40, compose_function(G!42, F!43, A!40, B!39, A!40)), A!40)) | apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X_15(A!40, compose_function(G!42, F!43, A!40, B!39, A!40)), tptp_fun_X_15(A!40, compose_function(G!42, F!43, A!40, B!39, A!40))))))))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[169, 94])).
% 0.20/0.49 tff(171,plain,
% 0.20/0.49 (((~((~identity(compose_function(G!42, F!43, A!40, B!39, A!40), A!40)) | ![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!42, F!43, A!40, B!39, A!40), X, X)))) | (~(identity(compose_function(G!42, F!43, A!40, B!39, A!40), A!40) | (~((~member(tptp_fun_X_15(A!40, compose_function(G!42, F!43, A!40, B!39, A!40)), A!40)) | apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X_15(A!40, compose_function(G!42, F!43, A!40, B!39, A!40)), tptp_fun_X_15(A!40, compose_function(G!42, F!43, A!40, B!39, A!40)))))))) | ((~identity(compose_function(G!42, F!43, A!40, B!39, A!40), A!40)) | ![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!42, F!43, A!40, B!39, A!40), X, X)))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(172,plain,
% 0.20/0.49 ((~identity(compose_function(G!42, F!43, A!40, B!39, A!40), A!40)) | ![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!42, F!43, A!40, B!39, A!40), X, X))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[171, 170])).
% 0.20/0.49 tff(173,plain,
% 0.20/0.49 (identity(compose_function(G!42, F!43, A!40, B!39, A!40), A!40)),
% 0.20/0.49 inference(and_elim,[status(thm)],[107])).
% 0.20/0.49 tff(174,plain,
% 0.20/0.49 ((~((~identity(compose_function(G!42, F!43, A!40, B!39, A!40), A!40)) | ![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!42, F!43, A!40, B!39, A!40), X, X)))) | (~identity(compose_function(G!42, F!43, A!40, B!39, A!40), A!40)) | ![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!42, F!43, A!40, B!39, A!40), X, X))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(175,plain,
% 0.20/0.49 ((~((~identity(compose_function(G!42, F!43, A!40, B!39, A!40), A!40)) | ![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!42, F!43, A!40, B!39, A!40), X, X)))) | ![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!42, F!43, A!40, B!39, A!40), X, X))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[174, 173])).
% 0.20/0.49 tff(176,plain,
% 0.20/0.49 (![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!42, F!43, A!40, B!39, A!40), X, X))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[175, 172])).
% 0.20/0.49 tff(177,plain,
% 0.20/0.49 (((~![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!42, F!43, A!40, B!39, A!40), X, X))) | ((~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40)) | apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43)))) <=> ((~![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!42, F!43, A!40, B!39, A!40), X, X))) | (~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40)) | apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(178,plain,
% 0.20/0.49 ((~![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!42, F!43, A!40, B!39, A!40), X, X))) | ((~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40)) | apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43)))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(179,plain,
% 0.20/0.49 ((~![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!42, F!43, A!40, B!39, A!40), X, X))) | (~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40)) | apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[178, 177])).
% 0.20/0.49 tff(180,plain,
% 0.20/0.49 (apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[179, 176, 156])).
% 0.20/0.49 tff(181,plain,
% 0.20/0.49 ((~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42), tptp_fun_X1_18(B!39, A!40, F!43))))))) | (~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42), tptp_fun_X1_18(B!39, A!40, F!43)))))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(182,plain,
% 0.20/0.49 ((~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42), tptp_fun_X1_18(B!39, A!40, F!43))))))) | (~((~member(tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42), tptp_fun_X1_18(B!39, A!40, F!43)))))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[181, 180])).
% 0.20/0.49 tff(183,plain,
% 0.20/0.49 (~((~member(tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42), tptp_fun_X1_18(B!39, A!40, F!43))))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[182, 168])).
% 0.20/0.49 tff(184,plain,
% 0.20/0.49 (((~member(tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42), tptp_fun_X1_18(B!39, A!40, F!43)))) | apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(185,plain,
% 0.20/0.49 (apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[184, 183])).
% 0.20/0.49 tff(186,plain,
% 0.20/0.49 (((~member(tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42), tptp_fun_X1_18(B!39, A!40, F!43)))) | member(tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42), B!39)),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(187,plain,
% 0.20/0.49 (member(tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42), B!39)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[186, 183])).
% 0.20/0.49 tff(188,plain,
% 0.20/0.49 (((~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_Y_16(B!39, A!40, F!43), B!39)) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (tptp_fun_X1_18(B!39, A!40, F!43) = tptp_fun_X2_17(B!39, A!40, F!43)) | (~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40))) | apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(189,plain,
% 0.20/0.49 (apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[188, 154])).
% 0.20/0.49 tff(190,plain,
% 0.20/0.49 (((~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_Y_16(B!39, A!40, F!43), B!39)) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (tptp_fun_X1_18(B!39, A!40, F!43) = tptp_fun_X2_17(B!39, A!40, F!43)) | (~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40))) | member(tptp_fun_Y_16(B!39, A!40, F!43), B!39)),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(191,plain,
% 0.20/0.49 (member(tptp_fun_Y_16(B!39, A!40, F!43), B!39)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[190, 154])).
% 0.20/0.49 tff(192,plain,
% 0.20/0.49 (^[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) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_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)))))))))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(193,plain,
% 0.20/0.49 (![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) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_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))))))))))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[192])).
% 0.20/0.49 tff(194,plain,
% 0.20/0.49 (^[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)))))))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(195,plain,
% 0.20/0.50 (![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))))))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[194])).
% 0.20/0.50 tff(196,plain,
% 0.20/0.50 (^[F: $i, A: $i, B: $i] : rewrite((~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))) <=> (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~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)))))))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(197,plain,
% 0.20/0.50 (![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))))))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[196])).
% 0.20/0.50 tff(198,plain,
% 0.20/0.50 (![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))))))),
% 0.20/0.50 inference(transitivity,[status(thm)],[197, 195])).
% 0.20/0.50 tff(199,plain,
% 0.20/0.50 (^[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))))))))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(200,plain,
% 0.20/0.50 (![F: $i, A: $i, B: $i] : (((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) & (maps(F, A, B) | (member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))))))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[199])).
% 0.20/0.50 tff(201,plain,
% 0.20/0.50 (^[F: $i, A: $i, B: $i] : rewrite((((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) & (maps(F, A, B) | ((member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B)))))))) <=> (((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) & (maps(F, A, B) | (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))))))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(202,plain,
% 0.20/0.50 (![F: $i, A: $i, B: $i] : (((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) & (maps(F, A, B) | ((member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B)))))))) <=> ![F: $i, A: $i, B: $i] : (((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) & (maps(F, A, B) | (member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B)))))))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[201])).
% 0.20/0.50 tff(203,plain,
% 0.20/0.50 (![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))))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(204,plain,
% 0.20/0.50 (^[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)))))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(205,plain,
% 0.20/0.50 (![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))))))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[204])).
% 0.20/0.50 tff(206,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')).
% 0.20/0.50 tff(207,plain,
% 0.20/0.50 (![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))))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[206, 205])).
% 0.20/0.50 tff(208,plain,
% 0.20/0.50 (![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))))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[207, 203])).
% 0.20/0.50 tff(209,plain,(
% 0.20/0.50 ![F: $i, A: $i, B: $i] : (((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) & (maps(F, A, B) | ((member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B))))))))),
% 0.20/0.50 inference(skolemize,[status(sab)],[208])).
% 0.20/0.50 tff(210,plain,
% 0.20/0.50 (![F: $i, A: $i, B: $i] : (((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) & (maps(F, A, B) | (member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B)))))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[209, 202])).
% 0.20/0.50 tff(211,plain,
% 0.20/0.50 (![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[210, 200])).
% 0.20/0.50 tff(212,plain,
% 0.20/0.50 (![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[211, 198])).
% 0.20/0.50 tff(213,plain,
% 0.20/0.50 (![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))))))))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[212, 193])).
% 0.20/0.50 tff(214,plain,
% 0.20/0.50 (((~![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!43, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!43), B!39)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!39, F!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))))))) | (~(maps(F!43, A!40, B!39) | (~((~member(tptp_fun_X_4(B!39, A!40, F!43), A!40)) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_X_4(B!39, A!40, F!43), Y)))))) | (~((~member(tptp_fun_Y2_5(B!39, A!40, F!43), B!39)) | (~member(tptp_fun_Y1_6(B!39, A!40, F!43), B!39)) | (~member(tptp_fun_X_7(B!39, A!40, F!43), A!40)) | (~apply(F!43, tptp_fun_X_7(B!39, A!40, F!43), tptp_fun_Y2_5(B!39, A!40, F!43))) | (~apply(F!43, tptp_fun_X_7(B!39, A!40, F!43), tptp_fun_Y1_6(B!39, A!40, F!43))) | (tptp_fun_Y1_6(B!39, A!40, F!43) = tptp_fun_Y2_5(B!39, A!40, F!43))))))))) <=> ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(F!43, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!43), B!39)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!39, F!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))))))) | (~(maps(F!43, A!40, B!39) | (~((~member(tptp_fun_X_4(B!39, A!40, F!43), A!40)) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_X_4(B!39, A!40, F!43), Y)))))) | (~((~member(tptp_fun_Y2_5(B!39, A!40, F!43), B!39)) | (~member(tptp_fun_Y1_6(B!39, A!40, F!43), B!39)) | (~member(tptp_fun_X_7(B!39, A!40, F!43), A!40)) | (~apply(F!43, tptp_fun_X_7(B!39, A!40, F!43), tptp_fun_Y2_5(B!39, A!40, F!43))) | (~apply(F!43, tptp_fun_X_7(B!39, A!40, F!43), tptp_fun_Y1_6(B!39, A!40, F!43))) | (tptp_fun_Y1_6(B!39, A!40, F!43) = tptp_fun_Y2_5(B!39, A!40, F!43)))))))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(215,plain,
% 0.20/0.50 ((~((~((~maps(F!43, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!43), B!39)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!39, F!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))))))) | (~(maps(F!43, A!40, B!39) | (~((tptp_fun_Y1_6(B!39, A!40, F!43) = tptp_fun_Y2_5(B!39, A!40, F!43)) | (~apply(F!43, tptp_fun_X_7(B!39, A!40, F!43), tptp_fun_Y1_6(B!39, A!40, F!43))) | (~apply(F!43, tptp_fun_X_7(B!39, A!40, F!43), tptp_fun_Y2_5(B!39, A!40, F!43))) | (~member(tptp_fun_X_7(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_Y1_6(B!39, A!40, F!43), B!39)) | (~member(tptp_fun_Y2_5(B!39, A!40, F!43), B!39)))) | (~((~member(tptp_fun_X_4(B!39, A!40, F!43), A!40)) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_X_4(B!39, A!40, F!43), Y)))))))))) <=> (~((~((~maps(F!43, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!43), B!39)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!39, F!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))))))) | (~(maps(F!43, A!40, B!39) | (~((~member(tptp_fun_X_4(B!39, A!40, F!43), A!40)) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_X_4(B!39, A!40, F!43), Y)))))) | (~((~member(tptp_fun_Y2_5(B!39, A!40, F!43), B!39)) | (~member(tptp_fun_Y1_6(B!39, A!40, F!43), B!39)) | (~member(tptp_fun_X_7(B!39, A!40, F!43), A!40)) | (~apply(F!43, tptp_fun_X_7(B!39, A!40, F!43), tptp_fun_Y2_5(B!39, A!40, F!43))) | (~apply(F!43, tptp_fun_X_7(B!39, A!40, F!43), tptp_fun_Y1_6(B!39, A!40, F!43))) | (tptp_fun_Y1_6(B!39, A!40, F!43) = tptp_fun_Y2_5(B!39, A!40, F!43))))))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(216,plain,
% 0.20/0.51 (((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(F!43, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!43), B!39)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!39, F!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))))))) | (~(maps(F!43, A!40, B!39) | (~((tptp_fun_Y1_6(B!39, A!40, F!43) = tptp_fun_Y2_5(B!39, A!40, F!43)) | (~apply(F!43, tptp_fun_X_7(B!39, A!40, F!43), tptp_fun_Y1_6(B!39, A!40, F!43))) | (~apply(F!43, tptp_fun_X_7(B!39, A!40, F!43), tptp_fun_Y2_5(B!39, A!40, F!43))) | (~member(tptp_fun_X_7(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_Y1_6(B!39, A!40, F!43), B!39)) | (~member(tptp_fun_Y2_5(B!39, A!40, F!43), B!39)))) | (~((~member(tptp_fun_X_4(B!39, A!40, F!43), A!40)) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_X_4(B!39, A!40, F!43), Y))))))))))) <=> ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(F!43, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!43), B!39)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!39, F!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))))))) | (~(maps(F!43, A!40, B!39) | (~((~member(tptp_fun_X_4(B!39, A!40, F!43), A!40)) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_X_4(B!39, A!40, F!43), Y)))))) | (~((~member(tptp_fun_Y2_5(B!39, A!40, F!43), B!39)) | (~member(tptp_fun_Y1_6(B!39, A!40, F!43), B!39)) | (~member(tptp_fun_X_7(B!39, A!40, F!43), A!40)) | (~apply(F!43, tptp_fun_X_7(B!39, A!40, F!43), tptp_fun_Y2_5(B!39, A!40, F!43))) | (~apply(F!43, tptp_fun_X_7(B!39, A!40, F!43), tptp_fun_Y1_6(B!39, A!40, F!43))) | (tptp_fun_Y1_6(B!39, A!40, F!43) = tptp_fun_Y2_5(B!39, A!40, F!43)))))))))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[215])).
% 0.20/0.51 tff(217,plain,
% 0.20/0.51 (((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(F!43, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!43), B!39)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!39, F!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))))))) | (~(maps(F!43, A!40, B!39) | (~((tptp_fun_Y1_6(B!39, A!40, F!43) = tptp_fun_Y2_5(B!39, A!40, F!43)) | (~apply(F!43, tptp_fun_X_7(B!39, A!40, F!43), tptp_fun_Y1_6(B!39, A!40, F!43))) | (~apply(F!43, tptp_fun_X_7(B!39, A!40, F!43), tptp_fun_Y2_5(B!39, A!40, F!43))) | (~member(tptp_fun_X_7(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_Y1_6(B!39, A!40, F!43), B!39)) | (~member(tptp_fun_Y2_5(B!39, A!40, F!43), B!39)))) | (~((~member(tptp_fun_X_4(B!39, A!40, F!43), A!40)) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_X_4(B!39, A!40, F!43), Y))))))))))) <=> ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(F!43, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!43), B!39)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!39, F!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))))))) | (~(maps(F!43, A!40, B!39) | (~((~member(tptp_fun_X_4(B!39, A!40, F!43), A!40)) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_X_4(B!39, A!40, F!43), Y)))))) | (~((~member(tptp_fun_Y2_5(B!39, A!40, F!43), B!39)) | (~member(tptp_fun_Y1_6(B!39, A!40, F!43), B!39)) | (~member(tptp_fun_X_7(B!39, A!40, F!43), A!40)) | (~apply(F!43, tptp_fun_X_7(B!39, A!40, F!43), tptp_fun_Y2_5(B!39, A!40, F!43))) | (~apply(F!43, tptp_fun_X_7(B!39, A!40, F!43), tptp_fun_Y1_6(B!39, A!40, F!43))) | (tptp_fun_Y1_6(B!39, A!40, F!43) = tptp_fun_Y2_5(B!39, A!40, F!43)))))))))),
% 0.20/0.51 inference(transitivity,[status(thm)],[216, 214])).
% 0.20/0.51 tff(218,plain,
% 0.20/0.51 ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(F!43, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!43), B!39)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!39, F!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)) | (~member(Y2, B!39)))))))) | (~(maps(F!43, A!40, B!39) | (~((tptp_fun_Y1_6(B!39, A!40, F!43) = tptp_fun_Y2_5(B!39, A!40, F!43)) | (~apply(F!43, tptp_fun_X_7(B!39, A!40, F!43), tptp_fun_Y1_6(B!39, A!40, F!43))) | (~apply(F!43, tptp_fun_X_7(B!39, A!40, F!43), tptp_fun_Y2_5(B!39, A!40, F!43))) | (~member(tptp_fun_X_7(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_Y1_6(B!39, A!40, F!43), B!39)) | (~member(tptp_fun_Y2_5(B!39, A!40, F!43), B!39)))) | (~((~member(tptp_fun_X_4(B!39, A!40, F!43), A!40)) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_X_4(B!39, A!40, F!43), Y))))))))))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(219,plain,
% 0.20/0.51 ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(F!43, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!43), B!39)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!39, F!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))))))) | (~(maps(F!43, A!40, B!39) | (~((~member(tptp_fun_X_4(B!39, A!40, F!43), A!40)) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_X_4(B!39, A!40, F!43), Y)))))) | (~((~member(tptp_fun_Y2_5(B!39, A!40, F!43), B!39)) | (~member(tptp_fun_Y1_6(B!39, A!40, F!43), B!39)) | (~member(tptp_fun_X_7(B!39, A!40, F!43), A!40)) | (~apply(F!43, tptp_fun_X_7(B!39, A!40, F!43), tptp_fun_Y2_5(B!39, A!40, F!43))) | (~apply(F!43, tptp_fun_X_7(B!39, A!40, F!43), tptp_fun_Y1_6(B!39, A!40, F!43))) | (tptp_fun_Y1_6(B!39, A!40, F!43) = tptp_fun_Y2_5(B!39, A!40, F!43))))))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[218, 217])).
% 0.20/0.51 tff(220,plain,
% 0.20/0.51 (~((~((~maps(F!43, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!43), B!39)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!39, F!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))))))) | (~(maps(F!43, A!40, B!39) | (~((~member(tptp_fun_X_4(B!39, A!40, F!43), A!40)) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_X_4(B!39, A!40, F!43), Y)))))) | (~((~member(tptp_fun_Y2_5(B!39, A!40, F!43), B!39)) | (~member(tptp_fun_Y1_6(B!39, A!40, F!43), B!39)) | (~member(tptp_fun_X_7(B!39, A!40, F!43), A!40)) | (~apply(F!43, tptp_fun_X_7(B!39, A!40, F!43), tptp_fun_Y2_5(B!39, A!40, F!43))) | (~apply(F!43, tptp_fun_X_7(B!39, A!40, F!43), tptp_fun_Y1_6(B!39, A!40, F!43))) | (tptp_fun_Y1_6(B!39, A!40, F!43) = tptp_fun_Y2_5(B!39, A!40, F!43)))))))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[219, 213])).
% 0.20/0.51 tff(221,plain,
% 0.20/0.51 (((~((~maps(F!43, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!43), B!39)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!39, F!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))))))) | (~(maps(F!43, A!40, B!39) | (~((~member(tptp_fun_X_4(B!39, A!40, F!43), A!40)) | (~![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_X_4(B!39, A!40, F!43), Y)))))) | (~((~member(tptp_fun_Y2_5(B!39, A!40, F!43), B!39)) | (~member(tptp_fun_Y1_6(B!39, A!40, F!43), B!39)) | (~member(tptp_fun_X_7(B!39, A!40, F!43), A!40)) | (~apply(F!43, tptp_fun_X_7(B!39, A!40, F!43), tptp_fun_Y2_5(B!39, A!40, F!43))) | (~apply(F!43, tptp_fun_X_7(B!39, A!40, F!43), tptp_fun_Y1_6(B!39, A!40, F!43))) | (tptp_fun_Y1_6(B!39, A!40, F!43) = tptp_fun_Y2_5(B!39, A!40, F!43))))))) | ((~maps(F!43, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!43), B!39)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!39, F!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))))))),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(222,plain,
% 0.20/0.51 ((~maps(F!43, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!43), B!39)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!39, F!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39))))))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[221, 220])).
% 0.20/0.51 tff(223,plain,
% 0.20/0.51 (maps(F!43, A!40, B!39)),
% 0.20/0.51 inference(and_elim,[status(thm)],[107])).
% 0.20/0.51 tff(224,plain,
% 0.20/0.51 ((~((~maps(F!43, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!43), B!39)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!39, F!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))))))) | (~maps(F!43, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!43), B!39)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!39, F!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39))))))),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(225,plain,
% 0.20/0.51 ((~((~maps(F!43, A!40, B!39)) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!43), B!39)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!39, F!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))))))) | (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!43), B!39)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!39, F!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39))))))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[224, 223])).
% 0.20/0.51 tff(226,plain,
% 0.20/0.51 (~((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!43), B!39)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!39, F!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[225, 222])).
% 0.20/0.51 tff(227,plain,
% 0.20/0.51 (((~![X: $i] : ((~member(X, A!40)) | (~((~member(tptp_fun_Y_3(X, B!39, F!43), B!39)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!39, F!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39))))) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(228,plain,
% 0.20/0.51 (![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[227, 226])).
% 0.20/0.51 tff(229,plain,
% 0.20/0.51 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))) | ((~member(tptp_fun_Y_16(B!39, A!40, F!43), B!39)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42))) | (~member(tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42), B!39)) | (tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42) = tptp_fun_Y_16(B!39, A!40, F!43)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))) | (~member(tptp_fun_Y_16(B!39, A!40, F!43), B!39)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42))) | (~member(tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42), B!39)) | (tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42) = tptp_fun_Y_16(B!39, A!40, F!43)))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(230,plain,
% 0.20/0.52 (((tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42) = tptp_fun_Y_16(B!39, A!40, F!43)) | (~member(tptp_fun_Y_16(B!39, A!40, F!43), B!39)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42))) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42), B!39))) <=> ((~member(tptp_fun_Y_16(B!39, A!40, F!43), B!39)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42))) | (~member(tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42), B!39)) | (tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42) = tptp_fun_Y_16(B!39, A!40, F!43)))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(231,plain,
% 0.20/0.52 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))) | ((tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42) = tptp_fun_Y_16(B!39, A!40, F!43)) | (~member(tptp_fun_Y_16(B!39, A!40, F!43), B!39)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42))) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42), B!39)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))) | ((~member(tptp_fun_Y_16(B!39, A!40, F!43), B!39)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42))) | (~member(tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42), B!39)) | (tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42) = tptp_fun_Y_16(B!39, A!40, F!43))))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[230])).
% 0.20/0.52 tff(232,plain,
% 0.20/0.52 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))) | ((tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42) = tptp_fun_Y_16(B!39, A!40, F!43)) | (~member(tptp_fun_Y_16(B!39, A!40, F!43), B!39)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42))) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42), B!39)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))) | (~member(tptp_fun_Y_16(B!39, A!40, F!43), B!39)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42))) | (~member(tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42), B!39)) | (tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42) = tptp_fun_Y_16(B!39, A!40, F!43)))),
% 0.20/0.52 inference(transitivity,[status(thm)],[231, 229])).
% 0.20/0.52 tff(233,plain,
% 0.20/0.52 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))) | ((tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42) = tptp_fun_Y_16(B!39, A!40, F!43)) | (~member(tptp_fun_Y_16(B!39, A!40, F!43), B!39)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42))) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42), B!39)))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(234,plain,
% 0.20/0.52 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))) | (~member(tptp_fun_Y_16(B!39, A!40, F!43), B!39)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42))) | (~member(tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42), B!39)) | (tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42) = tptp_fun_Y_16(B!39, A!40, F!43))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[233, 232])).
% 0.20/0.52 tff(235,plain,
% 0.20/0.52 (tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42) = tptp_fun_Y_16(B!39, A!40, F!43)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[234, 228, 191, 189, 156, 187, 185])).
% 0.20/0.52 tff(236,plain,
% 0.20/0.52 (tptp_fun_Y_16(B!39, A!40, F!43) = tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42)),
% 0.20/0.52 inference(symmetry,[status(thm)],[235])).
% 0.20/0.52 tff(237,plain,
% 0.20/0.52 (apply(G!42, tptp_fun_Y_16(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43)) <=> apply(G!42, tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42), tptp_fun_X1_18(B!39, A!40, F!43))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[236])).
% 0.20/0.52 tff(238,plain,
% 0.20/0.52 (apply(G!42, tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42), tptp_fun_X1_18(B!39, A!40, F!43)) <=> apply(G!42, tptp_fun_Y_16(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43))),
% 0.20/0.52 inference(symmetry,[status(thm)],[237])).
% 0.20/0.52 tff(239,plain,
% 0.20/0.52 (((~member(tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42), tptp_fun_X1_18(B!39, A!40, F!43)))) | apply(G!42, tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42), tptp_fun_X1_18(B!39, A!40, F!43))),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(240,plain,
% 0.20/0.52 (apply(G!42, tptp_fun_Y_8(tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43), B!39, F!43, G!42), tptp_fun_X1_18(B!39, A!40, F!43))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[239, 183])).
% 0.20/0.52 tff(241,plain,
% 0.20/0.52 (apply(G!42, tptp_fun_Y_16(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[240, 238])).
% 0.20/0.52 tff(242,plain,
% 0.20/0.52 (((~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_Y_16(B!39, A!40, F!43), B!39)) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (tptp_fun_X1_18(B!39, A!40, F!43) = tptp_fun_X2_17(B!39, A!40, F!43)) | (~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40))) | member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(243,plain,
% 0.20/0.52 (member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[242, 154])).
% 0.20/0.52 tff(244,plain,
% 0.20/0.52 (((~![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!43), A!40)) | (~((~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), Y)) | (~apply(G!42, Y, tptp_fun_X2_17(B!39, A!40, F!43)))))) | (~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42), tptp_fun_X2_17(B!39, A!40, F!43))))))))))) <=> ((~![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!43), A!40)) | (~((~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), Y)) | (~apply(G!42, Y, tptp_fun_X2_17(B!39, A!40, F!43)))))) | (~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42), tptp_fun_X2_17(B!39, A!40, F!43))))))))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(245,plain,
% 0.20/0.52 (((~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)) | (~((~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), Y)) | (~apply(G!42, Y, tptp_fun_X2_17(B!39, A!40, F!43)))))) | (~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42), tptp_fun_X2_17(B!39, A!40, F!43)))))))))) <=> ((~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)) | (~((~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), Y)) | (~apply(G!42, Y, tptp_fun_X2_17(B!39, A!40, F!43)))))) | (~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42), tptp_fun_X2_17(B!39, A!40, F!43))))))))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(246,plain,
% 0.20/0.52 ((~((~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42), tptp_fun_X2_17(B!39, A!40, F!43))))))) | (~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), Y)) | (~apply(G!42, Y, tptp_fun_X2_17(B!39, A!40, F!43)))))))) <=> (~((~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), Y)) | (~apply(G!42, Y, tptp_fun_X2_17(B!39, A!40, F!43)))))) | (~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42), tptp_fun_X2_17(B!39, A!40, F!43)))))))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(247,plain,
% 0.20/0.52 (((~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)) | (~((~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42), tptp_fun_X2_17(B!39, A!40, F!43))))))) | (~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), Y)) | (~apply(G!42, Y, tptp_fun_X2_17(B!39, A!40, F!43))))))))) <=> ((~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)) | (~((~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), Y)) | (~apply(G!42, Y, tptp_fun_X2_17(B!39, A!40, F!43)))))) | (~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42), tptp_fun_X2_17(B!39, A!40, F!43))))))))))),
% 0.20/0.53 inference(monotonicity,[status(thm)],[246])).
% 0.20/0.53 tff(248,plain,
% 0.20/0.53 (((~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)) | (~((~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42), tptp_fun_X2_17(B!39, A!40, F!43))))))) | (~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), Y)) | (~apply(G!42, Y, tptp_fun_X2_17(B!39, A!40, F!43))))))))) <=> ((~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)) | (~((~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), Y)) | (~apply(G!42, Y, tptp_fun_X2_17(B!39, A!40, F!43)))))) | (~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42), tptp_fun_X2_17(B!39, A!40, F!43))))))))))),
% 0.20/0.53 inference(transitivity,[status(thm)],[247, 245])).
% 0.20/0.53 tff(249,plain,
% 0.20/0.53 (((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)) | (~((~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42), tptp_fun_X2_17(B!39, A!40, F!43))))))) | (~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), Y)) | (~apply(G!42, Y, tptp_fun_X2_17(B!39, A!40, F!43)))))))))) <=> ((~![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!43), A!40)) | (~((~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), Y)) | (~apply(G!42, Y, tptp_fun_X2_17(B!39, A!40, F!43)))))) | (~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42), tptp_fun_X2_17(B!39, A!40, F!43)))))))))))),
% 0.20/0.53 inference(monotonicity,[status(thm)],[248])).
% 0.20/0.53 tff(250,plain,
% 0.20/0.53 (((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)) | (~((~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42), tptp_fun_X2_17(B!39, A!40, F!43))))))) | (~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), Y)) | (~apply(G!42, Y, tptp_fun_X2_17(B!39, A!40, F!43)))))))))) <=> ((~![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!43), A!40)) | (~((~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), Y)) | (~apply(G!42, Y, tptp_fun_X2_17(B!39, A!40, F!43)))))) | (~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42), tptp_fun_X2_17(B!39, A!40, F!43))))))))))),
% 0.20/0.53 inference(transitivity,[status(thm)],[249, 244])).
% 0.20/0.53 tff(251,plain,
% 0.20/0.53 ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)) | (~((~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42), tptp_fun_X2_17(B!39, A!40, F!43))))))) | (~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), Y)) | (~apply(G!42, Y, tptp_fun_X2_17(B!39, A!40, F!43)))))))))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(252,plain,
% 0.20/0.53 ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | (~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)) | (~((~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), Y)) | (~apply(G!42, Y, tptp_fun_X2_17(B!39, A!40, F!43)))))) | (~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42), tptp_fun_X2_17(B!39, A!40, F!43)))))))))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[251, 250])).
% 0.20/0.53 tff(253,plain,
% 0.20/0.53 (~((~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), Y)) | (~apply(G!42, Y, tptp_fun_X2_17(B!39, A!40, F!43)))))) | (~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42), tptp_fun_X2_17(B!39, A!40, F!43))))))))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[252, 66, 243])).
% 0.20/0.53 tff(254,plain,
% 0.20/0.53 (((~(apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43)) | ![Y: $i] : ((~member(Y, B!39)) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), Y)) | (~apply(G!42, Y, tptp_fun_X2_17(B!39, A!40, F!43)))))) | (~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42), tptp_fun_X2_17(B!39, A!40, F!43)))))))) | ((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42), tptp_fun_X2_17(B!39, A!40, F!43))))))),
% 0.20/0.53 inference(tautology,[status(thm)],[])).
% 0.20/0.53 tff(255,plain,
% 0.20/0.53 ((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42), tptp_fun_X2_17(B!39, A!40, F!43)))))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[254, 253])).
% 0.20/0.53 tff(256,plain,
% 0.20/0.53 (((~![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!42, F!43, A!40, B!39, A!40), X, X))) | ((~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)) | apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43)))) <=> ((~![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!42, F!43, A!40, B!39, A!40), X, X))) | (~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)) | apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43)))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(257,plain,
% 0.20/0.53 ((~![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!42, F!43, A!40, B!39, A!40), X, X))) | ((~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)) | apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43)))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(258,plain,
% 0.20/0.53 ((~![X: $i] : ((~member(X, A!40)) | apply(compose_function(G!42, F!43, A!40, B!39, A!40), X, X))) | (~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)) | apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[257, 256])).
% 0.20/0.53 tff(259,plain,
% 0.20/0.53 (apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[258, 176, 243])).
% 0.20/0.54 tff(260,plain,
% 0.20/0.54 ((~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42), tptp_fun_X2_17(B!39, A!40, F!43))))))) | (~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42), tptp_fun_X2_17(B!39, A!40, F!43)))))),
% 0.20/0.54 inference(tautology,[status(thm)],[])).
% 0.20/0.54 tff(261,plain,
% 0.20/0.54 ((~((~apply(compose_function(G!42, F!43, A!40, B!39, A!40), tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42), tptp_fun_X2_17(B!39, A!40, F!43))))))) | (~((~member(tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42), tptp_fun_X2_17(B!39, A!40, F!43)))))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[260, 259])).
% 0.20/0.54 tff(262,plain,
% 0.20/0.54 (~((~member(tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42), tptp_fun_X2_17(B!39, A!40, F!43))))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[261, 255])).
% 0.20/0.54 tff(263,plain,
% 0.20/0.54 (((~member(tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42), tptp_fun_X2_17(B!39, A!40, F!43)))) | apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42))),
% 0.20/0.54 inference(tautology,[status(thm)],[])).
% 0.20/0.54 tff(264,plain,
% 0.20/0.54 (apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[263, 262])).
% 0.20/0.54 tff(265,plain,
% 0.20/0.54 (((~member(tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42), tptp_fun_X2_17(B!39, A!40, F!43)))) | member(tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42), B!39)),
% 0.20/0.54 inference(tautology,[status(thm)],[])).
% 0.20/0.54 tff(266,plain,
% 0.20/0.54 (member(tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42), B!39)),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[265, 262])).
% 0.20/0.54 tff(267,plain,
% 0.20/0.54 (((~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_Y_16(B!39, A!40, F!43), B!39)) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (tptp_fun_X1_18(B!39, A!40, F!43) = tptp_fun_X2_17(B!39, A!40, F!43)) | (~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40))) | apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))),
% 0.20/0.54 inference(tautology,[status(thm)],[])).
% 0.20/0.54 tff(268,plain,
% 0.20/0.54 (apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[267, 154])).
% 0.20/0.54 tff(269,plain,
% 0.20/0.54 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))) | ((~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_Y_16(B!39, A!40, F!43), B!39)) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42))) | (~member(tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42), B!39)) | (tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42) = tptp_fun_Y_16(B!39, A!40, F!43)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))) | (~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_Y_16(B!39, A!40, F!43), B!39)) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42))) | (~member(tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42), B!39)) | (tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42) = tptp_fun_Y_16(B!39, A!40, F!43)))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(270,plain,
% 0.20/0.54 (((tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42) = tptp_fun_Y_16(B!39, A!40, F!43)) | (~member(tptp_fun_Y_16(B!39, A!40, F!43), B!39)) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42))) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42), B!39))) <=> ((~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_Y_16(B!39, A!40, F!43), B!39)) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42))) | (~member(tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42), B!39)) | (tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42) = tptp_fun_Y_16(B!39, A!40, F!43)))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(271,plain,
% 0.20/0.54 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))) | ((tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42) = tptp_fun_Y_16(B!39, A!40, F!43)) | (~member(tptp_fun_Y_16(B!39, A!40, F!43), B!39)) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42))) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42), B!39)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))) | ((~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_Y_16(B!39, A!40, F!43), B!39)) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42))) | (~member(tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42), B!39)) | (tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42) = tptp_fun_Y_16(B!39, A!40, F!43))))),
% 0.20/0.54 inference(monotonicity,[status(thm)],[270])).
% 0.20/0.54 tff(272,plain,
% 0.20/0.54 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))) | ((tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42) = tptp_fun_Y_16(B!39, A!40, F!43)) | (~member(tptp_fun_Y_16(B!39, A!40, F!43), B!39)) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42))) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42), B!39)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))) | (~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_Y_16(B!39, A!40, F!43), B!39)) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42))) | (~member(tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42), B!39)) | (tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42) = tptp_fun_Y_16(B!39, A!40, F!43)))),
% 0.20/0.54 inference(transitivity,[status(thm)],[271, 269])).
% 0.20/0.54 tff(273,plain,
% 0.20/0.54 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))) | ((tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42) = tptp_fun_Y_16(B!39, A!40, F!43)) | (~member(tptp_fun_Y_16(B!39, A!40, F!43), B!39)) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42))) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42), B!39)))),
% 0.20/0.54 inference(quant_inst,[status(thm)],[])).
% 0.20/0.54 tff(274,plain,
% 0.20/0.54 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!39)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!40)) | (~member(Y1, B!39)))) | (~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_Y_16(B!39, A!40, F!43), B!39)) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42))) | (~member(tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42), B!39)) | (tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42) = tptp_fun_Y_16(B!39, A!40, F!43))),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[273, 272])).
% 0.20/0.55 tff(275,plain,
% 0.20/0.55 (tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42) = tptp_fun_Y_16(B!39, A!40, F!43)),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[274, 228, 243, 191, 268, 266, 264])).
% 0.20/0.55 tff(276,plain,
% 0.20/0.55 (tptp_fun_Y_16(B!39, A!40, F!43) = tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42)),
% 0.20/0.55 inference(symmetry,[status(thm)],[275])).
% 0.20/0.55 tff(277,plain,
% 0.20/0.55 (apply(G!42, tptp_fun_Y_16(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43)) <=> apply(G!42, tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42), tptp_fun_X2_17(B!39, A!40, F!43))),
% 0.20/0.55 inference(monotonicity,[status(thm)],[276])).
% 0.20/0.55 tff(278,plain,
% 0.20/0.55 (apply(G!42, tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42), tptp_fun_X2_17(B!39, A!40, F!43)) <=> apply(G!42, tptp_fun_Y_16(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43))),
% 0.20/0.55 inference(symmetry,[status(thm)],[277])).
% 0.20/0.55 tff(279,plain,
% 0.20/0.55 (((~member(tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42), B!39)) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42), tptp_fun_X2_17(B!39, A!40, F!43)))) | apply(G!42, tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42), tptp_fun_X2_17(B!39, A!40, F!43))),
% 0.20/0.55 inference(tautology,[status(thm)],[])).
% 0.20/0.55 tff(280,plain,
% 0.20/0.55 (apply(G!42, tptp_fun_Y_8(tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43), B!39, F!43, G!42), tptp_fun_X2_17(B!39, A!40, F!43))),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[279, 262])).
% 0.20/0.55 tff(281,plain,
% 0.20/0.55 (apply(G!42, tptp_fun_Y_16(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43))),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[280, 278])).
% 0.20/0.55 tff(282,plain,
% 0.20/0.55 (((~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_Y_16(B!39, A!40, F!43), B!39)) | (~apply(F!43, tptp_fun_X2_17(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (~apply(F!43, tptp_fun_X1_18(B!39, A!40, F!43), tptp_fun_Y_16(B!39, A!40, F!43))) | (tptp_fun_X1_18(B!39, A!40, F!43) = tptp_fun_X2_17(B!39, A!40, F!43)) | (~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40))) | (~(tptp_fun_X1_18(B!39, A!40, F!43) = tptp_fun_X2_17(B!39, A!40, F!43)))),
% 0.20/0.55 inference(tautology,[status(thm)],[])).
% 0.20/0.55 tff(283,plain,
% 0.20/0.55 (~(tptp_fun_X1_18(B!39, A!40, F!43) = tptp_fun_X2_17(B!39, A!40, F!43))),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[282, 154])).
% 0.20/0.55 tff(284,plain,
% 0.20/0.55 (((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(G!42, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!42), A!40)) | (~apply(G!42, X, tptp_fun_Y_3(X, A!40, G!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))))))) | (~(maps(G!42, B!39, A!40) | (~((~member(tptp_fun_X_4(A!40, B!39, G!42), B!39)) | (~![Y: $i] : ((~member(Y, A!40)) | (~apply(G!42, tptp_fun_X_4(A!40, B!39, G!42), Y)))))) | (~((~member(tptp_fun_Y2_5(A!40, B!39, G!42), A!40)) | (~member(tptp_fun_Y1_6(A!40, B!39, G!42), A!40)) | (~member(tptp_fun_X_7(A!40, B!39, G!42), B!39)) | (~apply(G!42, tptp_fun_X_7(A!40, B!39, G!42), tptp_fun_Y2_5(A!40, B!39, G!42))) | (~apply(G!42, tptp_fun_X_7(A!40, B!39, G!42), tptp_fun_Y1_6(A!40, B!39, G!42))) | (tptp_fun_Y1_6(A!40, B!39, G!42) = tptp_fun_Y2_5(A!40, B!39, G!42))))))))) <=> ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(G!42, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!42), A!40)) | (~apply(G!42, X, tptp_fun_Y_3(X, A!40, G!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))))))) | (~(maps(G!42, B!39, A!40) | (~((~member(tptp_fun_X_4(A!40, B!39, G!42), B!39)) | (~![Y: $i] : ((~member(Y, A!40)) | (~apply(G!42, tptp_fun_X_4(A!40, B!39, G!42), Y)))))) | (~((~member(tptp_fun_Y2_5(A!40, B!39, G!42), A!40)) | (~member(tptp_fun_Y1_6(A!40, B!39, G!42), A!40)) | (~member(tptp_fun_X_7(A!40, B!39, G!42), B!39)) | (~apply(G!42, tptp_fun_X_7(A!40, B!39, G!42), tptp_fun_Y2_5(A!40, B!39, G!42))) | (~apply(G!42, tptp_fun_X_7(A!40, B!39, G!42), tptp_fun_Y1_6(A!40, B!39, G!42))) | (tptp_fun_Y1_6(A!40, B!39, G!42) = tptp_fun_Y2_5(A!40, B!39, G!42)))))))))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(285,plain,
% 0.20/0.55 ((~((~((~maps(G!42, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!42), A!40)) | (~apply(G!42, X, tptp_fun_Y_3(X, A!40, G!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)) | (~member(Y2, A!40)))))))) | (~(maps(G!42, B!39, A!40) | (~((tptp_fun_Y1_6(A!40, B!39, G!42) = tptp_fun_Y2_5(A!40, B!39, G!42)) | (~apply(G!42, tptp_fun_X_7(A!40, B!39, G!42), tptp_fun_Y1_6(A!40, B!39, G!42))) | (~apply(G!42, tptp_fun_X_7(A!40, B!39, G!42), tptp_fun_Y2_5(A!40, B!39, G!42))) | (~member(tptp_fun_X_7(A!40, B!39, G!42), B!39)) | (~member(tptp_fun_Y1_6(A!40, B!39, G!42), A!40)) | (~member(tptp_fun_Y2_5(A!40, B!39, G!42), A!40)))) | (~((~member(tptp_fun_X_4(A!40, B!39, G!42), B!39)) | (~![Y: $i] : ((~member(Y, A!40)) | (~apply(G!42, tptp_fun_X_4(A!40, B!39, G!42), Y)))))))))) <=> (~((~((~maps(G!42, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!42), A!40)) | (~apply(G!42, X, tptp_fun_Y_3(X, A!40, G!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))))))) | (~(maps(G!42, B!39, A!40) | (~((~member(tptp_fun_X_4(A!40, B!39, G!42), B!39)) | (~![Y: $i] : ((~member(Y, A!40)) | (~apply(G!42, tptp_fun_X_4(A!40, B!39, G!42), Y)))))) | (~((~member(tptp_fun_Y2_5(A!40, B!39, G!42), A!40)) | (~member(tptp_fun_Y1_6(A!40, B!39, G!42), A!40)) | (~member(tptp_fun_X_7(A!40, B!39, G!42), B!39)) | (~apply(G!42, tptp_fun_X_7(A!40, B!39, G!42), tptp_fun_Y2_5(A!40, B!39, G!42))) | (~apply(G!42, tptp_fun_X_7(A!40, B!39, G!42), tptp_fun_Y1_6(A!40, B!39, G!42))) | (tptp_fun_Y1_6(A!40, B!39, G!42) = tptp_fun_Y2_5(A!40, B!39, G!42))))))))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(286,plain,
% 0.20/0.55 (((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(G!42, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!42), A!40)) | (~apply(G!42, X, tptp_fun_Y_3(X, A!40, G!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)) | (~member(Y2, A!40)))))))) | (~(maps(G!42, B!39, A!40) | (~((tptp_fun_Y1_6(A!40, B!39, G!42) = tptp_fun_Y2_5(A!40, B!39, G!42)) | (~apply(G!42, tptp_fun_X_7(A!40, B!39, G!42), tptp_fun_Y1_6(A!40, B!39, G!42))) | (~apply(G!42, tptp_fun_X_7(A!40, B!39, G!42), tptp_fun_Y2_5(A!40, B!39, G!42))) | (~member(tptp_fun_X_7(A!40, B!39, G!42), B!39)) | (~member(tptp_fun_Y1_6(A!40, B!39, G!42), A!40)) | (~member(tptp_fun_Y2_5(A!40, B!39, G!42), A!40)))) | (~((~member(tptp_fun_X_4(A!40, B!39, G!42), B!39)) | (~![Y: $i] : ((~member(Y, A!40)) | (~apply(G!42, tptp_fun_X_4(A!40, B!39, G!42), Y))))))))))) <=> ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(G!42, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!42), A!40)) | (~apply(G!42, X, tptp_fun_Y_3(X, A!40, G!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))))))) | (~(maps(G!42, B!39, A!40) | (~((~member(tptp_fun_X_4(A!40, B!39, G!42), B!39)) | (~![Y: $i] : ((~member(Y, A!40)) | (~apply(G!42, tptp_fun_X_4(A!40, B!39, G!42), Y)))))) | (~((~member(tptp_fun_Y2_5(A!40, B!39, G!42), A!40)) | (~member(tptp_fun_Y1_6(A!40, B!39, G!42), A!40)) | (~member(tptp_fun_X_7(A!40, B!39, G!42), B!39)) | (~apply(G!42, tptp_fun_X_7(A!40, B!39, G!42), tptp_fun_Y2_5(A!40, B!39, G!42))) | (~apply(G!42, tptp_fun_X_7(A!40, B!39, G!42), tptp_fun_Y1_6(A!40, B!39, G!42))) | (tptp_fun_Y1_6(A!40, B!39, G!42) = tptp_fun_Y2_5(A!40, B!39, G!42)))))))))),
% 0.20/0.55 inference(monotonicity,[status(thm)],[285])).
% 0.20/0.55 tff(287,plain,
% 0.20/0.55 (((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(G!42, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!42), A!40)) | (~apply(G!42, X, tptp_fun_Y_3(X, A!40, G!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)) | (~member(Y2, A!40)))))))) | (~(maps(G!42, B!39, A!40) | (~((tptp_fun_Y1_6(A!40, B!39, G!42) = tptp_fun_Y2_5(A!40, B!39, G!42)) | (~apply(G!42, tptp_fun_X_7(A!40, B!39, G!42), tptp_fun_Y1_6(A!40, B!39, G!42))) | (~apply(G!42, tptp_fun_X_7(A!40, B!39, G!42), tptp_fun_Y2_5(A!40, B!39, G!42))) | (~member(tptp_fun_X_7(A!40, B!39, G!42), B!39)) | (~member(tptp_fun_Y1_6(A!40, B!39, G!42), A!40)) | (~member(tptp_fun_Y2_5(A!40, B!39, G!42), A!40)))) | (~((~member(tptp_fun_X_4(A!40, B!39, G!42), B!39)) | (~![Y: $i] : ((~member(Y, A!40)) | (~apply(G!42, tptp_fun_X_4(A!40, B!39, G!42), Y))))))))))) <=> ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(G!42, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!42), A!40)) | (~apply(G!42, X, tptp_fun_Y_3(X, A!40, G!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))))))) | (~(maps(G!42, B!39, A!40) | (~((~member(tptp_fun_X_4(A!40, B!39, G!42), B!39)) | (~![Y: $i] : ((~member(Y, A!40)) | (~apply(G!42, tptp_fun_X_4(A!40, B!39, G!42), Y)))))) | (~((~member(tptp_fun_Y2_5(A!40, B!39, G!42), A!40)) | (~member(tptp_fun_Y1_6(A!40, B!39, G!42), A!40)) | (~member(tptp_fun_X_7(A!40, B!39, G!42), B!39)) | (~apply(G!42, tptp_fun_X_7(A!40, B!39, G!42), tptp_fun_Y2_5(A!40, B!39, G!42))) | (~apply(G!42, tptp_fun_X_7(A!40, B!39, G!42), tptp_fun_Y1_6(A!40, B!39, G!42))) | (tptp_fun_Y1_6(A!40, B!39, G!42) = tptp_fun_Y2_5(A!40, B!39, G!42)))))))))),
% 0.20/0.55 inference(transitivity,[status(thm)],[286, 284])).
% 0.20/0.55 tff(288,plain,
% 0.20/0.55 ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(G!42, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!42), A!40)) | (~apply(G!42, X, tptp_fun_Y_3(X, A!40, G!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)) | (~member(Y2, A!40)))))))) | (~(maps(G!42, B!39, A!40) | (~((tptp_fun_Y1_6(A!40, B!39, G!42) = tptp_fun_Y2_5(A!40, B!39, G!42)) | (~apply(G!42, tptp_fun_X_7(A!40, B!39, G!42), tptp_fun_Y1_6(A!40, B!39, G!42))) | (~apply(G!42, tptp_fun_X_7(A!40, B!39, G!42), tptp_fun_Y2_5(A!40, B!39, G!42))) | (~member(tptp_fun_X_7(A!40, B!39, G!42), B!39)) | (~member(tptp_fun_Y1_6(A!40, B!39, G!42), A!40)) | (~member(tptp_fun_Y2_5(A!40, B!39, G!42), A!40)))) | (~((~member(tptp_fun_X_4(A!40, B!39, G!42), B!39)) | (~![Y: $i] : ((~member(Y, A!40)) | (~apply(G!42, tptp_fun_X_4(A!40, B!39, G!42), Y))))))))))),
% 0.20/0.55 inference(quant_inst,[status(thm)],[])).
% 0.20/0.55 tff(289,plain,
% 0.20/0.55 ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(G!42, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!42), A!40)) | (~apply(G!42, X, tptp_fun_Y_3(X, A!40, G!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))))))) | (~(maps(G!42, B!39, A!40) | (~((~member(tptp_fun_X_4(A!40, B!39, G!42), B!39)) | (~![Y: $i] : ((~member(Y, A!40)) | (~apply(G!42, tptp_fun_X_4(A!40, B!39, G!42), Y)))))) | (~((~member(tptp_fun_Y2_5(A!40, B!39, G!42), A!40)) | (~member(tptp_fun_Y1_6(A!40, B!39, G!42), A!40)) | (~member(tptp_fun_X_7(A!40, B!39, G!42), B!39)) | (~apply(G!42, tptp_fun_X_7(A!40, B!39, G!42), tptp_fun_Y2_5(A!40, B!39, G!42))) | (~apply(G!42, tptp_fun_X_7(A!40, B!39, G!42), tptp_fun_Y1_6(A!40, B!39, G!42))) | (tptp_fun_Y1_6(A!40, B!39, G!42) = tptp_fun_Y2_5(A!40, B!39, G!42))))))))),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[288, 287])).
% 0.20/0.55 tff(290,plain,
% 0.20/0.55 (~((~((~maps(G!42, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!42), A!40)) | (~apply(G!42, X, tptp_fun_Y_3(X, A!40, G!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))))))) | (~(maps(G!42, B!39, A!40) | (~((~member(tptp_fun_X_4(A!40, B!39, G!42), B!39)) | (~![Y: $i] : ((~member(Y, A!40)) | (~apply(G!42, tptp_fun_X_4(A!40, B!39, G!42), Y)))))) | (~((~member(tptp_fun_Y2_5(A!40, B!39, G!42), A!40)) | (~member(tptp_fun_Y1_6(A!40, B!39, G!42), A!40)) | (~member(tptp_fun_X_7(A!40, B!39, G!42), B!39)) | (~apply(G!42, tptp_fun_X_7(A!40, B!39, G!42), tptp_fun_Y2_5(A!40, B!39, G!42))) | (~apply(G!42, tptp_fun_X_7(A!40, B!39, G!42), tptp_fun_Y1_6(A!40, B!39, G!42))) | (tptp_fun_Y1_6(A!40, B!39, G!42) = tptp_fun_Y2_5(A!40, B!39, G!42)))))))),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[289, 213])).
% 0.20/0.55 tff(291,plain,
% 0.20/0.55 (((~((~maps(G!42, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!42), A!40)) | (~apply(G!42, X, tptp_fun_Y_3(X, A!40, G!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))))))) | (~(maps(G!42, B!39, A!40) | (~((~member(tptp_fun_X_4(A!40, B!39, G!42), B!39)) | (~![Y: $i] : ((~member(Y, A!40)) | (~apply(G!42, tptp_fun_X_4(A!40, B!39, G!42), Y)))))) | (~((~member(tptp_fun_Y2_5(A!40, B!39, G!42), A!40)) | (~member(tptp_fun_Y1_6(A!40, B!39, G!42), A!40)) | (~member(tptp_fun_X_7(A!40, B!39, G!42), B!39)) | (~apply(G!42, tptp_fun_X_7(A!40, B!39, G!42), tptp_fun_Y2_5(A!40, B!39, G!42))) | (~apply(G!42, tptp_fun_X_7(A!40, B!39, G!42), tptp_fun_Y1_6(A!40, B!39, G!42))) | (tptp_fun_Y1_6(A!40, B!39, G!42) = tptp_fun_Y2_5(A!40, B!39, G!42))))))) | ((~maps(G!42, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!42), A!40)) | (~apply(G!42, X, tptp_fun_Y_3(X, A!40, G!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))))))),
% 0.20/0.56 inference(tautology,[status(thm)],[])).
% 0.20/0.56 tff(292,plain,
% 0.20/0.56 ((~maps(G!42, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!42), A!40)) | (~apply(G!42, X, tptp_fun_Y_3(X, A!40, G!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40))))))),
% 0.20/0.56 inference(unit_resolution,[status(thm)],[291, 290])).
% 0.20/0.56 tff(293,plain,
% 0.20/0.56 (maps(G!42, B!39, A!40)),
% 0.20/0.56 inference(and_elim,[status(thm)],[107])).
% 0.20/0.56 tff(294,plain,
% 0.20/0.56 ((~((~maps(G!42, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!42), A!40)) | (~apply(G!42, X, tptp_fun_Y_3(X, A!40, G!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))))))) | (~maps(G!42, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!42), A!40)) | (~apply(G!42, X, tptp_fun_Y_3(X, A!40, G!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40))))))),
% 0.20/0.56 inference(tautology,[status(thm)],[])).
% 0.20/0.56 tff(295,plain,
% 0.20/0.56 ((~((~maps(G!42, B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!42), A!40)) | (~apply(G!42, X, tptp_fun_Y_3(X, A!40, G!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))))))) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!42), A!40)) | (~apply(G!42, X, tptp_fun_Y_3(X, A!40, G!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40))))))),
% 0.20/0.56 inference(unit_resolution,[status(thm)],[294, 293])).
% 0.20/0.56 tff(296,plain,
% 0.20/0.56 (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!42), A!40)) | (~apply(G!42, X, tptp_fun_Y_3(X, A!40, G!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))))),
% 0.20/0.56 inference(unit_resolution,[status(thm)],[295, 292])).
% 0.20/0.56 tff(297,plain,
% 0.20/0.56 (((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, G!42), A!40)) | (~apply(G!42, X, tptp_fun_Y_3(X, A!40, G!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40))))) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))),
% 0.20/0.56 inference(tautology,[status(thm)],[])).
% 0.20/0.56 tff(298,plain,
% 0.20/0.56 (![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))),
% 0.20/0.56 inference(unit_resolution,[status(thm)],[297, 296])).
% 0.20/0.56 tff(299,plain,
% 0.20/0.56 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))) | ((~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_Y_16(B!39, A!40, F!43), B!39)) | (tptp_fun_X1_18(B!39, A!40, F!43) = tptp_fun_X2_17(B!39, A!40, F!43)) | (~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40)) | (~apply(G!42, tptp_fun_Y_16(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43))) | (~apply(G!42, tptp_fun_Y_16(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43))))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))) | (~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_Y_16(B!39, A!40, F!43), B!39)) | (tptp_fun_X1_18(B!39, A!40, F!43) = tptp_fun_X2_17(B!39, A!40, F!43)) | (~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40)) | (~apply(G!42, tptp_fun_Y_16(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43))) | (~apply(G!42, tptp_fun_Y_16(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43))))),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(300,plain,
% 0.20/0.56 (((tptp_fun_X1_18(B!39, A!40, F!43) = tptp_fun_X2_17(B!39, A!40, F!43)) | (~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)) | (~apply(G!42, tptp_fun_Y_16(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43))) | (~apply(G!42, tptp_fun_Y_16(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43))) | (~member(tptp_fun_Y_16(B!39, A!40, F!43), B!39)) | (~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40))) <=> ((~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_Y_16(B!39, A!40, F!43), B!39)) | (tptp_fun_X1_18(B!39, A!40, F!43) = tptp_fun_X2_17(B!39, A!40, F!43)) | (~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40)) | (~apply(G!42, tptp_fun_Y_16(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43))) | (~apply(G!42, tptp_fun_Y_16(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43))))),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(301,plain,
% 0.20/0.56 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))) | ((tptp_fun_X1_18(B!39, A!40, F!43) = tptp_fun_X2_17(B!39, A!40, F!43)) | (~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)) | (~apply(G!42, tptp_fun_Y_16(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43))) | (~apply(G!42, tptp_fun_Y_16(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43))) | (~member(tptp_fun_Y_16(B!39, A!40, F!43), B!39)) | (~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))) | ((~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_Y_16(B!39, A!40, F!43), B!39)) | (tptp_fun_X1_18(B!39, A!40, F!43) = tptp_fun_X2_17(B!39, A!40, F!43)) | (~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40)) | (~apply(G!42, tptp_fun_Y_16(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43))) | (~apply(G!42, tptp_fun_Y_16(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43)))))),
% 0.20/0.56 inference(monotonicity,[status(thm)],[300])).
% 0.20/0.56 tff(302,plain,
% 0.20/0.56 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))) | ((tptp_fun_X1_18(B!39, A!40, F!43) = tptp_fun_X2_17(B!39, A!40, F!43)) | (~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)) | (~apply(G!42, tptp_fun_Y_16(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43))) | (~apply(G!42, tptp_fun_Y_16(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43))) | (~member(tptp_fun_Y_16(B!39, A!40, F!43), B!39)) | (~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))) | (~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_Y_16(B!39, A!40, F!43), B!39)) | (tptp_fun_X1_18(B!39, A!40, F!43) = tptp_fun_X2_17(B!39, A!40, F!43)) | (~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40)) | (~apply(G!42, tptp_fun_Y_16(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43))) | (~apply(G!42, tptp_fun_Y_16(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43))))),
% 0.20/0.56 inference(transitivity,[status(thm)],[301, 299])).
% 0.20/0.56 tff(303,plain,
% 0.20/0.56 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))) | ((tptp_fun_X1_18(B!39, A!40, F!43) = tptp_fun_X2_17(B!39, A!40, F!43)) | (~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)) | (~apply(G!42, tptp_fun_Y_16(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43))) | (~apply(G!42, tptp_fun_Y_16(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43))) | (~member(tptp_fun_Y_16(B!39, A!40, F!43), B!39)) | (~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40)))),
% 0.20/0.56 inference(quant_inst,[status(thm)],[])).
% 0.20/0.56 tff(304,plain,
% 0.20/0.56 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))) | (~member(tptp_fun_X2_17(B!39, A!40, F!43), A!40)) | (~member(tptp_fun_Y_16(B!39, A!40, F!43), B!39)) | (tptp_fun_X1_18(B!39, A!40, F!43) = tptp_fun_X2_17(B!39, A!40, F!43)) | (~member(tptp_fun_X1_18(B!39, A!40, F!43), A!40)) | (~apply(G!42, tptp_fun_Y_16(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43))) | (~apply(G!42, tptp_fun_Y_16(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43)))),
% 0.20/0.56 inference(modus_ponens,[status(thm)],[303, 302])).
% 0.20/0.56 tff(305,plain,
% 0.20/0.56 ((~apply(G!42, tptp_fun_Y_16(B!39, A!40, F!43), tptp_fun_X1_18(B!39, A!40, F!43))) | (~apply(G!42, tptp_fun_Y_16(B!39, A!40, F!43), tptp_fun_X2_17(B!39, A!40, F!43)))),
% 0.20/0.56 inference(unit_resolution,[status(thm)],[304, 298, 243, 191, 283, 156])).
% 0.20/0.56 tff(306,plain,
% 0.20/0.56 ($false),
% 0.20/0.56 inference(unit_resolution,[status(thm)],[305, 281, 241])).
% 0.20/0.56 % SZS output end Proof
% 0.20/0.56 % E exiting
%------------------------------------------------------------------------------