%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET744+4 : TPTP v9.0.0. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:26:15 AM UTC 2025
% Result : Theorem 21.82s 21.97s
% Output : Proof 22.29s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET744+4 : TPTP v9.0.0. Bugfixed v2.2.1.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n003.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 05:39:24 EDT 2025
% 0.12/0.33 % CPUTime :
% 21.82/21.97 % SZS status Theorem
% 21.82/21.97 % SZS output start Proof
% 21.82/21.97 tff(apply_type, type, (
% 21.82/21.97 apply: ( $i * $i * $i ) > $o)).
% 21.82/21.97 tff(tptp_fun_Y_16_type, type, (
% 21.82/21.97 tptp_fun_Y_16: ( $i * $i * $i ) > $i)).
% 21.82/21.97 tff(tptp_fun_H_42_type, type, (
% 21.82/21.97 tptp_fun_H_42: $i)).
% 21.82/21.97 tff(tptp_fun_C_39_type, type, (
% 21.82/21.97 tptp_fun_C_39: $i)).
% 21.82/21.97 tff(tptp_fun_A_41_type, type, (
% 21.82/21.97 tptp_fun_A_41: $i)).
% 21.82/21.97 tff(tptp_fun_Y_3_type, type, (
% 21.82/21.97 tptp_fun_Y_3: ( $i * $i * $i ) > $i)).
% 21.82/21.97 tff(tptp_fun_G_43_type, type, (
% 21.82/21.97 tptp_fun_G_43: $i)).
% 21.82/21.97 tff(tptp_fun_Y_8_type, type, (
% 21.82/21.97 tptp_fun_Y_8: ( $i * $i * $i * $i * $i ) > $i)).
% 21.82/21.97 tff(tptp_fun_F_44_type, type, (
% 21.82/21.97 tptp_fun_F_44: $i)).
% 21.82/21.97 tff(tptp_fun_B_40_type, type, (
% 21.82/21.97 tptp_fun_B_40: $i)).
% 21.82/21.97 tff(tptp_fun_E_19_type, type, (
% 21.82/21.97 tptp_fun_E_19: ( $i * $i * $i ) > $i)).
% 21.82/21.97 tff(compose_function_type, type, (
% 21.82/21.97 compose_function: ( $i * $i * $i * $i * $i ) > $i)).
% 21.82/21.97 tff(tptp_fun_X2_17_type, type, (
% 21.82/21.97 tptp_fun_X2_17: ( $i * $i * $i ) > $i)).
% 21.82/21.97 tff(member_type, type, (
% 21.82/21.97 member: ( $i * $i ) > $o)).
% 21.82/21.97 tff(tptp_fun_X1_18_type, type, (
% 21.82/21.97 tptp_fun_X1_18: ( $i * $i * $i ) > $i)).
% 21.82/21.97 tff(injective_type, type, (
% 21.82/21.97 injective: ( $i * $i * $i ) > $o)).
% 21.82/21.97 tff(surjective_type, type, (
% 21.82/21.97 surjective: ( $i * $i * $i ) > $o)).
% 21.82/21.97 tff(tptp_fun_Y_20_type, type, (
% 21.82/21.97 tptp_fun_Y_20: ( $i * $i * $i ) > $i)).
% 21.82/21.97 tff(one_to_one_type, type, (
% 21.82/21.97 one_to_one: ( $i * $i * $i ) > $o)).
% 21.82/21.97 tff(maps_type, type, (
% 21.82/21.97 maps: ( $i * $i * $i ) > $o)).
% 21.82/21.97 tff(tptp_fun_Y2_5_type, type, (
% 21.82/21.97 tptp_fun_Y2_5: ( $i * $i * $i ) > $i)).
% 21.82/21.97 tff(tptp_fun_Y1_6_type, type, (
% 21.82/21.97 tptp_fun_Y1_6: ( $i * $i * $i ) > $i)).
% 21.82/21.97 tff(tptp_fun_X_7_type, type, (
% 21.82/21.97 tptp_fun_X_7: ( $i * $i * $i ) > $i)).
% 21.82/21.97 tff(tptp_fun_X_4_type, type, (
% 21.82/21.97 tptp_fun_X_4: ( $i * $i * $i ) > $i)).
% 21.82/21.97 tff(1,plain,
% 21.82/21.97 (^[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)))))))))),
% 21.82/21.97 inference(bind,[status(th)],[])).
% 21.82/21.97 tff(2,plain,
% 21.82/21.97 (![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))))))))),
% 21.82/21.97 inference(quant_intro,[status(thm)],[1])).
% 21.82/21.97 tff(3,plain,
% 21.82/21.97 (^[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)))))))))),
% 21.82/21.97 inference(bind,[status(th)],[])).
% 21.82/21.97 tff(4,plain,
% 21.82/21.97 (![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))))))))),
% 21.82/21.97 inference(quant_intro,[status(thm)],[3])).
% 21.82/21.97 tff(5,plain,
% 21.82/21.97 (![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))))))))),
% 21.82/21.97 inference(transitivity,[status(thm)],[4, 2])).
% 21.82/21.97 tff(6,plain,
% 21.82/21.97 (^[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))))))))))),
% 21.82/21.97 inference(bind,[status(th)],[])).
% 21.82/21.97 tff(7,plain,
% 21.82/21.97 (![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))))))))),
% 21.82/21.97 inference(quant_intro,[status(thm)],[6])).
% 21.82/21.97 tff(8,plain,
% 21.82/21.97 (![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)))))),
% 21.82/21.97 inference(rewrite,[status(thm)],[])).
% 21.82/21.97 tff(9,plain,
% 21.82/21.97 (^[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))))))),
% 21.82/21.97 inference(bind,[status(th)],[])).
% 21.82/21.97 tff(10,plain,
% 21.82/21.97 (![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)))))),
% 21.82/21.97 inference(quant_intro,[status(thm)],[9])).
% 21.82/21.97 tff(11,axiom,(![F: $i, A: $i, B: $i] : (injective(F, A, B) <=> ![X1: $i, X2: $i, Y: $i] : (((member(X1, A) & member(X2, A)) & member(Y, B)) => ((apply(F, X1, Y) & apply(F, X2, Y)) => (X1 = X2))))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+1.ax','injective')).
% 21.82/21.97 tff(12,plain,
% 21.82/21.97 (![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)))))),
% 21.82/21.97 inference(modus_ponens,[status(thm)],[11, 10])).
% 21.82/21.97 tff(13,plain,
% 21.82/21.97 (![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)))))),
% 21.82/21.97 inference(modus_ponens,[status(thm)],[12, 8])).
% 21.82/21.97 tff(14,plain,(
% 21.82/21.97 ![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)))))))),
% 21.82/21.97 inference(skolemize,[status(sab)],[13])).
% 21.82/21.97 tff(15,plain,
% 21.82/21.97 (![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))))))))),
% 21.82/21.97 inference(modus_ponens,[status(thm)],[14, 7])).
% 21.82/21.97 tff(16,plain,
% 21.82/21.97 (![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))))))))),
% 21.82/21.97 inference(modus_ponens,[status(thm)],[15, 5])).
% 21.82/21.97 tff(17,plain,
% 21.82/21.97 (((~![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(H!42, C!39, A!41)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, A!41)) | (~member(X2, C!39)) | (~apply(H!42, X1, Y)) | (~member(X1, C!39)) | (~apply(H!42, X2, Y))))) | (~(injective(H!42, C!39, A!41) | (~((~member(tptp_fun_X2_17(A!41, C!39, H!42), C!39)) | (~member(tptp_fun_Y_16(A!41, C!39, H!42), A!41)) | (~member(tptp_fun_X1_18(A!41, C!39, H!42), C!39)) | (~apply(H!42, tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_Y_16(A!41, C!39, H!42))) | (~apply(H!42, tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_Y_16(A!41, C!39, H!42))) | (tptp_fun_X1_18(A!41, C!39, H!42) = tptp_fun_X2_17(A!41, C!39, H!42))))))))) <=> ((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(H!42, C!39, A!41)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, A!41)) | (~member(X2, C!39)) | (~apply(H!42, X1, Y)) | (~member(X1, C!39)) | (~apply(H!42, X2, Y))))) | (~(injective(H!42, C!39, A!41) | (~((~member(tptp_fun_X2_17(A!41, C!39, H!42), C!39)) | (~member(tptp_fun_Y_16(A!41, C!39, H!42), A!41)) | (~member(tptp_fun_X1_18(A!41, C!39, H!42), C!39)) | (~apply(H!42, tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_Y_16(A!41, C!39, H!42))) | (~apply(H!42, tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_Y_16(A!41, C!39, H!42))) | (tptp_fun_X1_18(A!41, C!39, H!42) = tptp_fun_X2_17(A!41, C!39, H!42)))))))))),
% 21.82/21.97 inference(rewrite,[status(thm)],[])).
% 21.82/21.97 tff(18,plain,
% 21.82/21.97 ((~((~((~injective(H!42, C!39, A!41)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(H!42, X1, Y)) | (~member(X2, C!39)) | (~member(X1, C!39)) | (~member(Y, A!41)) | (~apply(H!42, X2, Y))))) | (~(injective(H!42, C!39, A!41) | (~((tptp_fun_X1_18(A!41, C!39, H!42) = tptp_fun_X2_17(A!41, C!39, H!42)) | (~apply(H!42, tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_Y_16(A!41, C!39, H!42))) | (~apply(H!42, tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_Y_16(A!41, C!39, H!42))) | (~member(tptp_fun_X1_18(A!41, C!39, H!42), C!39)) | (~member(tptp_fun_X2_17(A!41, C!39, H!42), C!39)) | (~member(tptp_fun_Y_16(A!41, C!39, H!42), A!41)))))))) <=> (~((~((~injective(H!42, C!39, A!41)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, A!41)) | (~member(X2, C!39)) | (~apply(H!42, X1, Y)) | (~member(X1, C!39)) | (~apply(H!42, X2, Y))))) | (~(injective(H!42, C!39, A!41) | (~((~member(tptp_fun_X2_17(A!41, C!39, H!42), C!39)) | (~member(tptp_fun_Y_16(A!41, C!39, H!42), A!41)) | (~member(tptp_fun_X1_18(A!41, C!39, H!42), C!39)) | (~apply(H!42, tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_Y_16(A!41, C!39, H!42))) | (~apply(H!42, tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_Y_16(A!41, C!39, H!42))) | (tptp_fun_X1_18(A!41, C!39, H!42) = tptp_fun_X2_17(A!41, C!39, H!42))))))))),
% 21.82/21.97 inference(rewrite,[status(thm)],[])).
% 21.82/21.97 tff(19,plain,
% 21.82/21.97 (((~![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(H!42, C!39, A!41)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(H!42, X1, Y)) | (~member(X2, C!39)) | (~member(X1, C!39)) | (~member(Y, A!41)) | (~apply(H!42, X2, Y))))) | (~(injective(H!42, C!39, A!41) | (~((tptp_fun_X1_18(A!41, C!39, H!42) = tptp_fun_X2_17(A!41, C!39, H!42)) | (~apply(H!42, tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_Y_16(A!41, C!39, H!42))) | (~apply(H!42, tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_Y_16(A!41, C!39, H!42))) | (~member(tptp_fun_X1_18(A!41, C!39, H!42), C!39)) | (~member(tptp_fun_X2_17(A!41, C!39, H!42), C!39)) | (~member(tptp_fun_Y_16(A!41, C!39, H!42), A!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(H!42, C!39, A!41)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, A!41)) | (~member(X2, C!39)) | (~apply(H!42, X1, Y)) | (~member(X1, C!39)) | (~apply(H!42, X2, Y))))) | (~(injective(H!42, C!39, A!41) | (~((~member(tptp_fun_X2_17(A!41, C!39, H!42), C!39)) | (~member(tptp_fun_Y_16(A!41, C!39, H!42), A!41)) | (~member(tptp_fun_X1_18(A!41, C!39, H!42), C!39)) | (~apply(H!42, tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_Y_16(A!41, C!39, H!42))) | (~apply(H!42, tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_Y_16(A!41, C!39, H!42))) | (tptp_fun_X1_18(A!41, C!39, H!42) = tptp_fun_X2_17(A!41, C!39, H!42)))))))))),
% 21.82/21.97 inference(monotonicity,[status(thm)],[18])).
% 21.82/21.97 tff(20,plain,
% 21.82/21.97 (((~![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(H!42, C!39, A!41)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(H!42, X1, Y)) | (~member(X2, C!39)) | (~member(X1, C!39)) | (~member(Y, A!41)) | (~apply(H!42, X2, Y))))) | (~(injective(H!42, C!39, A!41) | (~((tptp_fun_X1_18(A!41, C!39, H!42) = tptp_fun_X2_17(A!41, C!39, H!42)) | (~apply(H!42, tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_Y_16(A!41, C!39, H!42))) | (~apply(H!42, tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_Y_16(A!41, C!39, H!42))) | (~member(tptp_fun_X1_18(A!41, C!39, H!42), C!39)) | (~member(tptp_fun_X2_17(A!41, C!39, H!42), C!39)) | (~member(tptp_fun_Y_16(A!41, C!39, H!42), A!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(H!42, C!39, A!41)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, A!41)) | (~member(X2, C!39)) | (~apply(H!42, X1, Y)) | (~member(X1, C!39)) | (~apply(H!42, X2, Y))))) | (~(injective(H!42, C!39, A!41) | (~((~member(tptp_fun_X2_17(A!41, C!39, H!42), C!39)) | (~member(tptp_fun_Y_16(A!41, C!39, H!42), A!41)) | (~member(tptp_fun_X1_18(A!41, C!39, H!42), C!39)) | (~apply(H!42, tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_Y_16(A!41, C!39, H!42))) | (~apply(H!42, tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_Y_16(A!41, C!39, H!42))) | (tptp_fun_X1_18(A!41, C!39, H!42) = tptp_fun_X2_17(A!41, C!39, H!42)))))))))),
% 21.82/21.97 inference(transitivity,[status(thm)],[19, 17])).
% 21.82/21.97 tff(21,plain,
% 21.82/21.97 ((~![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(H!42, C!39, A!41)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(H!42, X1, Y)) | (~member(X2, C!39)) | (~member(X1, C!39)) | (~member(Y, A!41)) | (~apply(H!42, X2, Y))))) | (~(injective(H!42, C!39, A!41) | (~((tptp_fun_X1_18(A!41, C!39, H!42) = tptp_fun_X2_17(A!41, C!39, H!42)) | (~apply(H!42, tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_Y_16(A!41, C!39, H!42))) | (~apply(H!42, tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_Y_16(A!41, C!39, H!42))) | (~member(tptp_fun_X1_18(A!41, C!39, H!42), C!39)) | (~member(tptp_fun_X2_17(A!41, C!39, H!42), C!39)) | (~member(tptp_fun_Y_16(A!41, C!39, H!42), A!41))))))))),
% 21.82/21.97 inference(quant_inst,[status(thm)],[])).
% 21.82/21.97 tff(22,plain,
% 21.82/21.97 ((~![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(H!42, C!39, A!41)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, A!41)) | (~member(X2, C!39)) | (~apply(H!42, X1, Y)) | (~member(X1, C!39)) | (~apply(H!42, X2, Y))))) | (~(injective(H!42, C!39, A!41) | (~((~member(tptp_fun_X2_17(A!41, C!39, H!42), C!39)) | (~member(tptp_fun_Y_16(A!41, C!39, H!42), A!41)) | (~member(tptp_fun_X1_18(A!41, C!39, H!42), C!39)) | (~apply(H!42, tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_Y_16(A!41, C!39, H!42))) | (~apply(H!42, tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_Y_16(A!41, C!39, H!42))) | (tptp_fun_X1_18(A!41, C!39, H!42) = tptp_fun_X2_17(A!41, C!39, H!42))))))))),
% 21.82/21.97 inference(modus_ponens,[status(thm)],[21, 20])).
% 21.82/21.97 tff(23,plain,
% 21.82/21.97 (~((~((~injective(H!42, C!39, A!41)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, A!41)) | (~member(X2, C!39)) | (~apply(H!42, X1, Y)) | (~member(X1, C!39)) | (~apply(H!42, X2, Y))))) | (~(injective(H!42, C!39, A!41) | (~((~member(tptp_fun_X2_17(A!41, C!39, H!42), C!39)) | (~member(tptp_fun_Y_16(A!41, C!39, H!42), A!41)) | (~member(tptp_fun_X1_18(A!41, C!39, H!42), C!39)) | (~apply(H!42, tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_Y_16(A!41, C!39, H!42))) | (~apply(H!42, tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_Y_16(A!41, C!39, H!42))) | (tptp_fun_X1_18(A!41, C!39, H!42) = tptp_fun_X2_17(A!41, C!39, H!42)))))))),
% 21.82/21.97 inference(unit_resolution,[status(thm)],[22, 16])).
% 21.82/21.97 tff(24,plain,
% 21.82/21.97 (((~((~injective(H!42, C!39, A!41)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, A!41)) | (~member(X2, C!39)) | (~apply(H!42, X1, Y)) | (~member(X1, C!39)) | (~apply(H!42, X2, Y))))) | (~(injective(H!42, C!39, A!41) | (~((~member(tptp_fun_X2_17(A!41, C!39, H!42), C!39)) | (~member(tptp_fun_Y_16(A!41, C!39, H!42), A!41)) | (~member(tptp_fun_X1_18(A!41, C!39, H!42), C!39)) | (~apply(H!42, tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_Y_16(A!41, C!39, H!42))) | (~apply(H!42, tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_Y_16(A!41, C!39, H!42))) | (tptp_fun_X1_18(A!41, C!39, H!42) = tptp_fun_X2_17(A!41, C!39, H!42))))))) | (injective(H!42, C!39, A!41) | (~((~member(tptp_fun_X2_17(A!41, C!39, H!42), C!39)) | (~member(tptp_fun_Y_16(A!41, C!39, H!42), A!41)) | (~member(tptp_fun_X1_18(A!41, C!39, H!42), C!39)) | (~apply(H!42, tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_Y_16(A!41, C!39, H!42))) | (~apply(H!42, tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_Y_16(A!41, C!39, H!42))) | (tptp_fun_X1_18(A!41, C!39, H!42) = tptp_fun_X2_17(A!41, C!39, H!42)))))),
% 21.82/21.97 inference(tautology,[status(thm)],[])).
% 21.82/21.97 tff(25,plain,
% 21.82/21.97 (injective(H!42, C!39, A!41) | (~((~member(tptp_fun_X2_17(A!41, C!39, H!42), C!39)) | (~member(tptp_fun_Y_16(A!41, C!39, H!42), A!41)) | (~member(tptp_fun_X1_18(A!41, C!39, H!42), C!39)) | (~apply(H!42, tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_Y_16(A!41, C!39, H!42))) | (~apply(H!42, tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_Y_16(A!41, C!39, H!42))) | (tptp_fun_X1_18(A!41, C!39, H!42) = tptp_fun_X2_17(A!41, C!39, H!42))))),
% 21.82/21.97 inference(unit_resolution,[status(thm)],[24, 23])).
% 21.82/21.97 tff(26,assumption,((~((~surjective(H!42, C!39, A!41)) | ![Y: $i] : ((~member(Y, A!41)) | (~((~member(tptp_fun_E_19(Y, C!39, H!42), C!39)) | (~apply(H!42, tptp_fun_E_19(Y, C!39, H!42), Y))))))) | (~(surjective(H!42, C!39, A!41) | (~((~member(tptp_fun_Y_20(A!41, C!39, H!42), A!41)) | (~![E: $i] : ((~member(E, C!39)) | (~apply(H!42, E, tptp_fun_Y_20(A!41, C!39, H!42)))))))))), introduced(assumption)).
% 21.82/21.97 tff(27,plain,
% 21.82/21.97 (^[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))))))))))))),
% 21.82/21.97 inference(bind,[status(th)],[])).
% 21.82/21.97 tff(28,plain,
% 21.82/21.97 (![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)))))))))))),
% 21.82/21.98 inference(quant_intro,[status(thm)],[27])).
% 21.82/21.98 tff(29,plain,
% 21.82/21.98 (^[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))))))))))))),
% 21.82/21.98 inference(bind,[status(th)],[])).
% 21.82/21.98 tff(30,plain,
% 21.82/21.98 (![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)))))))))))),
% 21.82/21.98 inference(quant_intro,[status(thm)],[29])).
% 21.82/21.98 tff(31,plain,
% 21.82/21.98 (![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)))))))))))),
% 21.82/21.98 inference(transitivity,[status(thm)],[30, 28])).
% 21.82/21.98 tff(32,plain,
% 21.82/21.98 (^[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)))))))))))))),
% 21.82/21.98 inference(bind,[status(th)],[])).
% 21.82/21.98 tff(33,plain,
% 21.82/21.98 (![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)))))))))))),
% 21.82/21.98 inference(quant_intro,[status(thm)],[32])).
% 21.82/21.98 tff(34,plain,
% 21.82/21.98 (![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))))),
% 21.82/21.98 inference(rewrite,[status(thm)],[])).
% 21.82/21.98 tff(35,plain,
% 21.82/21.98 (^[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)))))),
% 21.82/21.98 inference(bind,[status(th)],[])).
% 21.82/21.98 tff(36,plain,
% 21.82/21.98 (![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))))),
% 21.82/21.98 inference(quant_intro,[status(thm)],[35])).
% 21.82/21.98 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/sandbox2/benchmark/Axioms/SET006+1.ax','surjective')).
% 21.82/21.98 tff(38,plain,
% 21.82/21.98 (![F: $i, A: $i, B: $i] : (surjective(F, A, B) <=> ![Y: $i] : ((~member(Y, B)) | ?[E: $i] : (member(E, A) & apply(F, E, Y))))),
% 21.82/21.98 inference(modus_ponens,[status(thm)],[37, 36])).
% 21.82/21.98 tff(39,plain,
% 21.82/21.98 (![F: $i, A: $i, B: $i] : (surjective(F, A, B) <=> ![Y: $i] : ((~member(Y, B)) | ?[E: $i] : (member(E, A) & apply(F, E, Y))))),
% 21.82/21.98 inference(modus_ponens,[status(thm)],[38, 34])).
% 21.82/21.98 tff(40,plain,(
% 21.82/21.98 ![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)))))))),
% 21.82/21.98 inference(skolemize,[status(sab)],[39])).
% 21.82/21.98 tff(41,plain,
% 21.82/21.98 (![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)))))))))))),
% 21.82/21.98 inference(modus_ponens,[status(thm)],[40, 33])).
% 21.82/21.98 tff(42,plain,
% 21.82/21.98 (![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)))))))))))),
% 21.82/21.98 inference(modus_ponens,[status(thm)],[41, 31])).
% 21.82/21.98 tff(43,plain,
% 21.82/21.98 ((~![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(H!42, C!39, A!41)) | ![Y: $i] : ((~member(Y, A!41)) | (~((~member(tptp_fun_E_19(Y, C!39, H!42), C!39)) | (~apply(H!42, tptp_fun_E_19(Y, C!39, H!42), Y))))))) | (~(surjective(H!42, C!39, A!41) | (~((~member(tptp_fun_Y_20(A!41, C!39, H!42), A!41)) | (~![E: $i] : ((~member(E, C!39)) | (~apply(H!42, E, tptp_fun_Y_20(A!41, C!39, H!42)))))))))))),
% 21.82/21.98 inference(quant_inst,[status(thm)],[])).
% 21.82/21.98 tff(44,plain,
% 21.82/21.98 ($false),
% 21.82/21.98 inference(unit_resolution,[status(thm)],[43, 42, 26])).
% 21.82/21.98 tff(45,plain,(~((~((~surjective(H!42, C!39, A!41)) | ![Y: $i] : ((~member(Y, A!41)) | (~((~member(tptp_fun_E_19(Y, C!39, H!42), C!39)) | (~apply(H!42, tptp_fun_E_19(Y, C!39, H!42), Y))))))) | (~(surjective(H!42, C!39, A!41) | (~((~member(tptp_fun_Y_20(A!41, C!39, H!42), A!41)) | (~![E: $i] : ((~member(E, C!39)) | (~apply(H!42, E, tptp_fun_Y_20(A!41, C!39, H!42))))))))))), inference(lemma,lemma(discharge,[]))).
% 21.82/21.98 tff(46,plain,
% 21.82/21.98 (((~((~surjective(H!42, C!39, A!41)) | ![Y: $i] : ((~member(Y, A!41)) | (~((~member(tptp_fun_E_19(Y, C!39, H!42), C!39)) | (~apply(H!42, tptp_fun_E_19(Y, C!39, H!42), Y))))))) | (~(surjective(H!42, C!39, A!41) | (~((~member(tptp_fun_Y_20(A!41, C!39, H!42), A!41)) | (~![E: $i] : ((~member(E, C!39)) | (~apply(H!42, E, tptp_fun_Y_20(A!41, C!39, H!42)))))))))) | (surjective(H!42, C!39, A!41) | (~((~member(tptp_fun_Y_20(A!41, C!39, H!42), A!41)) | (~![E: $i] : ((~member(E, C!39)) | (~apply(H!42, E, tptp_fun_Y_20(A!41, C!39, H!42))))))))),
% 21.82/21.98 inference(tautology,[status(thm)],[])).
% 21.82/21.98 tff(47,plain,
% 21.82/21.98 (surjective(H!42, C!39, A!41) | (~((~member(tptp_fun_Y_20(A!41, C!39, H!42), A!41)) | (~![E: $i] : ((~member(E, C!39)) | (~apply(H!42, E, tptp_fun_Y_20(A!41, C!39, H!42)))))))),
% 21.82/21.98 inference(unit_resolution,[status(thm)],[46, 45])).
% 21.82/21.98 tff(48,assumption,(~((~member(tptp_fun_Y_20(A!41, C!39, H!42), A!41)) | (~![E: $i] : ((~member(E, C!39)) | (~apply(H!42, E, tptp_fun_Y_20(A!41, C!39, H!42))))))), introduced(assumption)).
% 21.82/21.98 tff(49,plain,
% 21.82/21.98 (((~member(tptp_fun_Y_20(A!41, C!39, H!42), A!41)) | (~![E: $i] : ((~member(E, C!39)) | (~apply(H!42, E, tptp_fun_Y_20(A!41, C!39, H!42)))))) | member(tptp_fun_Y_20(A!41, C!39, H!42), A!41)),
% 21.82/21.98 inference(tautology,[status(thm)],[])).
% 21.82/21.98 tff(50,plain,
% 21.82/21.98 (member(tptp_fun_Y_20(A!41, C!39, H!42), A!41)),
% 21.82/21.98 inference(unit_resolution,[status(thm)],[49, 48])).
% 21.82/21.98 tff(51,plain,
% 21.82/21.98 ((~![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(compose_function(H!42, G!43, B!40, C!39, A!41), B!40, A!41)) | ![Y: $i] : ((~member(Y, A!41)) | (~((~member(tptp_fun_E_19(Y, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_E_19(Y, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), Y))))))) | (~(surjective(compose_function(H!42, G!43, B!40, C!39, A!41), B!40, A!41) | (~((~member(tptp_fun_Y_20(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~![E: $i] : ((~member(E, B!40)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), E, tptp_fun_Y_20(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41))))))))))))),
% 21.82/21.98 inference(quant_inst,[status(thm)],[])).
% 21.82/21.98 tff(52,plain,
% 21.82/21.98 (~((~((~surjective(compose_function(H!42, G!43, B!40, C!39, A!41), B!40, A!41)) | ![Y: $i] : ((~member(Y, A!41)) | (~((~member(tptp_fun_E_19(Y, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_E_19(Y, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), Y))))))) | (~(surjective(compose_function(H!42, G!43, B!40, C!39, A!41), B!40, A!41) | (~((~member(tptp_fun_Y_20(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~![E: $i] : ((~member(E, B!40)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), E, tptp_fun_Y_20(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))))))))))),
% 21.82/21.98 inference(unit_resolution,[status(thm)],[51, 42])).
% 21.82/21.98 tff(53,plain,
% 21.82/21.98 (((~((~surjective(compose_function(H!42, G!43, B!40, C!39, A!41), B!40, A!41)) | ![Y: $i] : ((~member(Y, A!41)) | (~((~member(tptp_fun_E_19(Y, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_E_19(Y, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), Y))))))) | (~(surjective(compose_function(H!42, G!43, B!40, C!39, A!41), B!40, A!41) | (~((~member(tptp_fun_Y_20(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~![E: $i] : ((~member(E, B!40)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), E, tptp_fun_Y_20(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41))))))))))) | ((~surjective(compose_function(H!42, G!43, B!40, C!39, A!41), B!40, A!41)) | ![Y: $i] : ((~member(Y, A!41)) | (~((~member(tptp_fun_E_19(Y, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_E_19(Y, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), Y))))))),
% 21.82/21.98 inference(tautology,[status(thm)],[])).
% 21.82/21.98 tff(54,plain,
% 21.82/21.98 ((~surjective(compose_function(H!42, G!43, B!40, C!39, A!41), B!40, A!41)) | ![Y: $i] : ((~member(Y, A!41)) | (~((~member(tptp_fun_E_19(Y, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_E_19(Y, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), Y)))))),
% 21.82/21.98 inference(unit_resolution,[status(thm)],[53, 52])).
% 21.82/21.98 tff(55,plain,
% 21.82/21.98 (^[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))))),
% 21.82/21.98 inference(bind,[status(th)],[])).
% 21.82/21.98 tff(56,plain,
% 21.82/21.98 (![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)))),
% 21.82/21.98 inference(quant_intro,[status(thm)],[55])).
% 21.82/21.98 tff(57,plain,
% 21.82/21.98 (^[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)))))),
% 21.82/21.98 inference(bind,[status(th)],[])).
% 21.82/21.98 tff(58,plain,
% 21.82/21.98 (![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)))),
% 21.82/21.98 inference(quant_intro,[status(thm)],[57])).
% 21.82/21.98 tff(59,plain,
% 21.82/21.98 (![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)))),
% 21.82/21.98 inference(rewrite,[status(thm)],[])).
% 21.82/21.98 tff(60,axiom,(![F: $i, A: $i, B: $i] : (one_to_one(F, A, B) <=> (injective(F, A, B) & surjective(F, A, B)))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+1.ax','one_to_one')).
% 21.82/21.98 tff(61,plain,
% 21.82/21.98 (![F: $i, A: $i, B: $i] : (one_to_one(F, A, B) <=> (injective(F, A, B) & surjective(F, A, B)))),
% 21.82/21.98 inference(modus_ponens,[status(thm)],[60, 59])).
% 21.82/21.98 tff(62,plain,(
% 21.82/21.98 ![F: $i, A: $i, B: $i] : (one_to_one(F, A, B) <=> (injective(F, A, B) & surjective(F, A, B)))),
% 21.82/21.98 inference(skolemize,[status(sab)],[61])).
% 21.82/21.98 tff(63,plain,
% 21.82/21.98 (![F: $i, A: $i, B: $i] : (~(((~injective(F, A, B)) | (~surjective(F, A, B))) <=> one_to_one(F, A, B)))),
% 21.82/21.98 inference(modus_ponens,[status(thm)],[62, 58])).
% 21.82/21.98 tff(64,plain,
% 21.82/21.98 (![F: $i, A: $i, B: $i] : (~(((~injective(F, A, B)) | (~surjective(F, A, B))) <=> one_to_one(F, A, B)))),
% 21.82/21.98 inference(modus_ponens,[status(thm)],[63, 56])).
% 21.82/21.98 tff(65,plain,
% 21.82/21.98 ((~![F: $i, A: $i, B: $i] : (~(((~injective(F, A, B)) | (~surjective(F, A, B))) <=> one_to_one(F, A, B)))) | (~(((~injective(compose_function(H!42, G!43, B!40, C!39, A!41), B!40, A!41)) | (~surjective(compose_function(H!42, G!43, B!40, C!39, A!41), B!40, A!41))) <=> one_to_one(compose_function(H!42, G!43, B!40, C!39, A!41), B!40, A!41)))),
% 21.82/21.98 inference(quant_inst,[status(thm)],[])).
% 21.82/21.98 tff(66,plain,
% 21.82/21.98 (~(((~injective(compose_function(H!42, G!43, B!40, C!39, A!41), B!40, A!41)) | (~surjective(compose_function(H!42, G!43, B!40, C!39, A!41), B!40, A!41))) <=> one_to_one(compose_function(H!42, G!43, B!40, C!39, A!41), B!40, A!41))),
% 21.82/21.98 inference(unit_resolution,[status(thm)],[65, 64])).
% 21.82/21.98 tff(67,plain,
% 21.82/21.98 ((~![F: $i, G: $i, H: $i, A: $i, B: $i, C: $i] : ((~(maps(F, A, B) & maps(G, B, C) & maps(H, C, A) & one_to_one(compose_function(G, F, A, B, C), A, C) & one_to_one(compose_function(H, G, B, C, A), B, A))) | one_to_one(H, C, A))) <=> (~![F: $i, G: $i, H: $i, A: $i, B: $i, C: $i] : ((~(maps(F, A, B) & maps(G, B, C) & maps(H, C, A) & one_to_one(compose_function(G, F, A, B, C), A, C) & one_to_one(compose_function(H, G, B, C, A), B, A))) | one_to_one(H, C, A)))),
% 21.82/21.98 inference(rewrite,[status(thm)],[])).
% 21.82/21.98 tff(68,plain,
% 21.82/21.98 ((~![F: $i, G: $i, H: $i, A: $i, B: $i, C: $i] : (((((maps(F, A, B) & maps(G, B, C)) & maps(H, C, A)) & one_to_one(compose_function(G, F, A, B, C), A, C)) & one_to_one(compose_function(H, G, B, C, A), B, A)) => one_to_one(H, C, A))) <=> (~![F: $i, G: $i, H: $i, A: $i, B: $i, C: $i] : ((~(maps(F, A, B) & maps(G, B, C) & maps(H, C, A) & one_to_one(compose_function(G, F, A, B, C), A, C) & one_to_one(compose_function(H, G, B, C, A), B, A))) | one_to_one(H, C, A)))),
% 21.82/21.98 inference(rewrite,[status(thm)],[])).
% 21.82/21.98 tff(69,axiom,(~![F: $i, G: $i, H: $i, A: $i, B: $i, C: $i] : (((((maps(F, A, B) & maps(G, B, C)) & maps(H, C, A)) & one_to_one(compose_function(G, F, A, B, C), A, C)) & one_to_one(compose_function(H, G, B, C, A), B, A)) => one_to_one(H, C, A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thII35')).
% 21.82/21.98 tff(70,plain,
% 21.82/21.98 (~![F: $i, G: $i, H: $i, A: $i, B: $i, C: $i] : ((~(maps(F, A, B) & maps(G, B, C) & maps(H, C, A) & one_to_one(compose_function(G, F, A, B, C), A, C) & one_to_one(compose_function(H, G, B, C, A), B, A))) | one_to_one(H, C, A))),
% 21.82/21.98 inference(modus_ponens,[status(thm)],[69, 68])).
% 21.82/21.98 tff(71,plain,
% 21.82/21.98 (~![F: $i, G: $i, H: $i, A: $i, B: $i, C: $i] : ((~(maps(F, A, B) & maps(G, B, C) & maps(H, C, A) & one_to_one(compose_function(G, F, A, B, C), A, C) & one_to_one(compose_function(H, G, B, C, A), B, A))) | one_to_one(H, C, A))),
% 21.82/21.98 inference(modus_ponens,[status(thm)],[70, 67])).
% 21.82/21.98 tff(72,plain,
% 21.82/21.98 (~![F: $i, G: $i, H: $i, A: $i, B: $i, C: $i] : ((~(maps(F, A, B) & maps(G, B, C) & maps(H, C, A) & one_to_one(compose_function(G, F, A, B, C), A, C) & one_to_one(compose_function(H, G, B, C, A), B, A))) | one_to_one(H, C, A))),
% 21.82/21.98 inference(modus_ponens,[status(thm)],[71, 67])).
% 21.82/21.98 tff(73,plain,
% 21.82/21.98 (~![F: $i, G: $i, H: $i, A: $i, B: $i, C: $i] : ((~(maps(F, A, B) & maps(G, B, C) & maps(H, C, A) & one_to_one(compose_function(G, F, A, B, C), A, C) & one_to_one(compose_function(H, G, B, C, A), B, A))) | one_to_one(H, C, A))),
% 21.82/21.98 inference(modus_ponens,[status(thm)],[72, 67])).
% 21.82/21.98 tff(74,plain,(
% 21.82/21.98 ~((~(maps(F!44, A!41, B!40) & maps(G!43, B!40, C!39) & maps(H!42, C!39, A!41) & one_to_one(compose_function(G!43, F!44, A!41, B!40, C!39), A!41, C!39) & one_to_one(compose_function(H!42, G!43, B!40, C!39, A!41), B!40, A!41))) | one_to_one(H!42, C!39, A!41))),
% 21.82/21.98 inference(skolemize,[status(sab)],[73])).
% 21.82/21.98 tff(75,plain,
% 21.82/21.98 (maps(F!44, A!41, B!40) & maps(G!43, B!40, C!39) & maps(H!42, C!39, A!41) & one_to_one(compose_function(G!43, F!44, A!41, B!40, C!39), A!41, C!39) & one_to_one(compose_function(H!42, G!43, B!40, C!39, A!41), B!40, A!41)),
% 21.82/21.98 inference(or_elim,[status(thm)],[74])).
% 21.82/21.98 tff(76,plain,
% 21.82/21.98 (one_to_one(compose_function(H!42, G!43, B!40, C!39, A!41), B!40, A!41)),
% 21.82/21.98 inference(and_elim,[status(thm)],[75])).
% 21.82/21.98 tff(77,plain,
% 21.82/21.98 ((((~injective(compose_function(H!42, G!43, B!40, C!39, A!41), B!40, A!41)) | (~surjective(compose_function(H!42, G!43, B!40, C!39, A!41), B!40, A!41))) <=> one_to_one(compose_function(H!42, G!43, B!40, C!39, A!41), B!40, A!41)) | (~((~injective(compose_function(H!42, G!43, B!40, C!39, A!41), B!40, A!41)) | (~surjective(compose_function(H!42, G!43, B!40, C!39, A!41), B!40, A!41)))) | (~one_to_one(compose_function(H!42, G!43, B!40, C!39, A!41), B!40, A!41))),
% 21.82/21.98 inference(tautology,[status(thm)],[])).
% 21.82/21.98 tff(78,plain,
% 21.82/21.98 ((((~injective(compose_function(H!42, G!43, B!40, C!39, A!41), B!40, A!41)) | (~surjective(compose_function(H!42, G!43, B!40, C!39, A!41), B!40, A!41))) <=> one_to_one(compose_function(H!42, G!43, B!40, C!39, A!41), B!40, A!41)) | (~((~injective(compose_function(H!42, G!43, B!40, C!39, A!41), B!40, A!41)) | (~surjective(compose_function(H!42, G!43, B!40, C!39, A!41), B!40, A!41))))),
% 21.82/21.98 inference(unit_resolution,[status(thm)],[77, 76])).
% 21.82/21.98 tff(79,plain,
% 21.82/21.98 (~((~injective(compose_function(H!42, G!43, B!40, C!39, A!41), B!40, A!41)) | (~surjective(compose_function(H!42, G!43, B!40, C!39, A!41), B!40, A!41)))),
% 21.82/21.98 inference(unit_resolution,[status(thm)],[78, 66])).
% 21.82/21.98 tff(80,plain,
% 21.82/21.98 (((~injective(compose_function(H!42, G!43, B!40, C!39, A!41), B!40, A!41)) | (~surjective(compose_function(H!42, G!43, B!40, C!39, A!41), B!40, A!41))) | surjective(compose_function(H!42, G!43, B!40, C!39, A!41), B!40, A!41)),
% 21.82/21.98 inference(tautology,[status(thm)],[])).
% 21.82/21.98 tff(81,plain,
% 21.82/21.98 (surjective(compose_function(H!42, G!43, B!40, C!39, A!41), B!40, A!41)),
% 21.82/21.98 inference(unit_resolution,[status(thm)],[80, 79])).
% 21.82/21.98 tff(82,plain,
% 21.82/21.98 ((~((~surjective(compose_function(H!42, G!43, B!40, C!39, A!41), B!40, A!41)) | ![Y: $i] : ((~member(Y, A!41)) | (~((~member(tptp_fun_E_19(Y, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_E_19(Y, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), Y))))))) | (~surjective(compose_function(H!42, G!43, B!40, C!39, A!41), B!40, A!41)) | ![Y: $i] : ((~member(Y, A!41)) | (~((~member(tptp_fun_E_19(Y, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_E_19(Y, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), Y)))))),
% 21.82/21.98 inference(tautology,[status(thm)],[])).
% 21.82/21.98 tff(83,plain,
% 21.82/21.98 ((~((~surjective(compose_function(H!42, G!43, B!40, C!39, A!41), B!40, A!41)) | ![Y: $i] : ((~member(Y, A!41)) | (~((~member(tptp_fun_E_19(Y, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_E_19(Y, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), Y))))))) | ![Y: $i] : ((~member(Y, A!41)) | (~((~member(tptp_fun_E_19(Y, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_E_19(Y, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), Y)))))),
% 21.82/21.98 inference(unit_resolution,[status(thm)],[82, 81])).
% 21.82/21.98 tff(84,plain,
% 21.82/21.98 (![Y: $i] : ((~member(Y, A!41)) | (~((~member(tptp_fun_E_19(Y, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_E_19(Y, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), Y)))))),
% 21.82/21.98 inference(unit_resolution,[status(thm)],[83, 54])).
% 21.82/21.98 tff(85,plain,
% 21.82/21.98 (((~![Y: $i] : ((~member(Y, A!41)) | (~((~member(tptp_fun_E_19(Y, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_E_19(Y, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), Y)))))) | ((~member(tptp_fun_Y_20(A!41, C!39, H!42), A!41)) | (~((~member(tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_20(A!41, C!39, H!42))))))) <=> ((~![Y: $i] : ((~member(Y, A!41)) | (~((~member(tptp_fun_E_19(Y, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_E_19(Y, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), Y)))))) | (~member(tptp_fun_Y_20(A!41, C!39, H!42), A!41)) | (~((~member(tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_20(A!41, C!39, H!42))))))),
% 21.82/21.98 inference(rewrite,[status(thm)],[])).
% 21.82/21.98 tff(86,plain,
% 21.82/21.98 ((~![Y: $i] : ((~member(Y, A!41)) | (~((~member(tptp_fun_E_19(Y, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_E_19(Y, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), Y)))))) | ((~member(tptp_fun_Y_20(A!41, C!39, H!42), A!41)) | (~((~member(tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_20(A!41, C!39, H!42))))))),
% 21.82/21.99 inference(quant_inst,[status(thm)],[])).
% 21.82/21.99 tff(87,plain,
% 21.82/21.99 ((~![Y: $i] : ((~member(Y, A!41)) | (~((~member(tptp_fun_E_19(Y, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_E_19(Y, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), Y)))))) | (~member(tptp_fun_Y_20(A!41, C!39, H!42), A!41)) | (~((~member(tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_20(A!41, C!39, H!42)))))),
% 21.82/21.99 inference(modus_ponens,[status(thm)],[86, 85])).
% 21.82/21.99 tff(88,plain,
% 21.82/21.99 (~((~member(tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_20(A!41, C!39, H!42))))),
% 21.82/21.99 inference(unit_resolution,[status(thm)],[87, 84, 50])).
% 21.82/21.99 tff(89,plain,
% 21.82/21.99 (((~member(tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_20(A!41, C!39, H!42)))) | member(tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)),
% 21.82/21.99 inference(tautology,[status(thm)],[])).
% 21.82/21.99 tff(90,plain,
% 21.82/21.99 (member(tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)),
% 21.82/21.99 inference(unit_resolution,[status(thm)],[89, 88])).
% 21.82/21.99 tff(91,plain,
% 21.82/21.99 (^[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)))))))))),
% 21.82/21.99 inference(bind,[status(th)],[])).
% 21.82/21.99 tff(92,plain,
% 21.82/21.99 (![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))))))))),
% 21.82/21.99 inference(quant_intro,[status(thm)],[91])).
% 21.82/21.99 tff(93,plain,
% 21.82/21.99 (^[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)))))))))),
% 21.82/21.99 inference(bind,[status(th)],[])).
% 21.82/21.99 tff(94,plain,
% 21.82/21.99 (![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))))))))),
% 21.82/21.99 inference(quant_intro,[status(thm)],[93])).
% 21.82/21.99 tff(95,plain,
% 21.82/21.99 (![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))))))))),
% 21.82/21.99 inference(transitivity,[status(thm)],[94, 92])).
% 21.82/21.99 tff(96,plain,
% 21.82/21.99 (^[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))))))))))),
% 21.82/21.99 inference(bind,[status(th)],[])).
% 21.82/21.99 tff(97,plain,
% 21.82/21.99 (![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))))))))),
% 21.82/21.99 inference(quant_intro,[status(thm)],[96])).
% 21.82/21.99 tff(98,plain,
% 21.82/21.99 (![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))))),
% 21.82/21.99 inference(rewrite,[status(thm)],[])).
% 21.82/21.99 tff(99,plain,
% 21.82/21.99 (^[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))))))),
% 21.82/21.99 inference(bind,[status(th)],[])).
% 21.82/21.99 tff(100,plain,
% 21.82/21.99 (![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))))),
% 21.82/21.99 inference(quant_intro,[status(thm)],[99])).
% 21.82/21.99 tff(101,axiom,(![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((member(X, A) & member(Z, C)) => (apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : ((member(Y, B) & apply(F, X, Y)) & apply(G, Y, Z))))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+1.ax','compose_function')).
% 21.82/21.99 tff(102,plain,
% 21.82/21.99 (![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))))),
% 21.82/21.99 inference(modus_ponens,[status(thm)],[101, 100])).
% 21.82/21.99 tff(103,plain,
% 21.82/21.99 (![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))))),
% 21.82/21.99 inference(modus_ponens,[status(thm)],[102, 98])).
% 21.82/21.99 tff(104,plain,(
% 21.82/21.99 ![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))))))),
% 21.82/21.99 inference(skolemize,[status(sab)],[103])).
% 21.82/21.99 tff(105,plain,
% 21.82/21.99 (![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))))))))),
% 21.82/21.99 inference(modus_ponens,[status(thm)],[104, 97])).
% 21.82/21.99 tff(106,plain,
% 21.82/21.99 (![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))))))))),
% 21.82/21.99 inference(modus_ponens,[status(thm)],[105, 95])).
% 21.82/21.99 tff(107,plain,
% 21.82/21.99 (((~![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(A!41, C!39, H!42), A!41)) | (~member(tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~((~((~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_20(A!41, C!39, H!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_20(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), C!39)) | (~apply(G!43, tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_Y_20(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42))) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y_20(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), tptp_fun_Y_20(A!41, C!39, H!42))))))) | (~(apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_20(A!41, C!39, H!42)) | ![Y: $i] : ((~member(Y, C!39)) | (~apply(H!42, Y, tptp_fun_Y_20(A!41, C!39, H!42))) | (~apply(G!43, tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), 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(A!41, C!39, H!42), A!41)) | (~member(tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~((~((~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_20(A!41, C!39, H!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_20(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), C!39)) | (~apply(G!43, tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_Y_20(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42))) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y_20(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), tptp_fun_Y_20(A!41, C!39, H!42))))))) | (~(apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_20(A!41, C!39, H!42)) | ![Y: $i] : ((~member(Y, C!39)) | (~apply(H!42, Y, tptp_fun_Y_20(A!41, C!39, H!42))) | (~apply(G!43, tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), Y))))))))),
% 21.82/21.99 inference(rewrite,[status(thm)],[])).
% 21.82/21.99 tff(108,plain,
% 21.82/21.99 (((~member(tptp_fun_Y_20(A!41, C!39, H!42), A!41)) | (~member(tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~((~((~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_20(A!41, C!39, H!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_20(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), C!39)) | (~apply(G!43, tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_Y_20(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42))) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y_20(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), tptp_fun_Y_20(A!41, C!39, H!42))))))) | (~(apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_20(A!41, C!39, H!42)) | ![Y: $i] : ((~member(Y, C!39)) | (~apply(G!43, tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), Y)) | (~apply(H!42, Y, tptp_fun_Y_20(A!41, C!39, H!42))))))))) <=> ((~member(tptp_fun_Y_20(A!41, C!39, H!42), A!41)) | (~member(tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~((~((~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_20(A!41, C!39, H!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_20(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), C!39)) | (~apply(G!43, tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_Y_20(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42))) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y_20(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), tptp_fun_Y_20(A!41, C!39, H!42))))))) | (~(apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_20(A!41, C!39, H!42)) | ![Y: $i] : ((~member(Y, C!39)) | (~apply(H!42, Y, tptp_fun_Y_20(A!41, C!39, H!42))) | (~apply(G!43, tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), Y))))))))),
% 21.82/21.99 inference(rewrite,[status(thm)],[])).
% 21.82/21.99 tff(109,plain,
% 21.82/21.99 (((~![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(A!41, C!39, H!42), A!41)) | (~member(tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~((~((~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_20(A!41, C!39, H!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_20(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), C!39)) | (~apply(G!43, tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_Y_20(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42))) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y_20(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), tptp_fun_Y_20(A!41, C!39, H!42))))))) | (~(apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_20(A!41, C!39, H!42)) | ![Y: $i] : ((~member(Y, C!39)) | (~apply(G!43, tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), Y)) | (~apply(H!42, Y, tptp_fun_Y_20(A!41, C!39, H!42)))))))))) <=> ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_Y_20(A!41, C!39, H!42), A!41)) | (~member(tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~((~((~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_20(A!41, C!39, H!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_20(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), C!39)) | (~apply(G!43, tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_Y_20(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42))) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y_20(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), tptp_fun_Y_20(A!41, C!39, H!42))))))) | (~(apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_20(A!41, C!39, H!42)) | ![Y: $i] : ((~member(Y, C!39)) | (~apply(H!42, Y, tptp_fun_Y_20(A!41, C!39, H!42))) | (~apply(G!43, tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), Y)))))))))),
% 21.82/21.99 inference(monotonicity,[status(thm)],[108])).
% 21.82/21.99 tff(110,plain,
% 21.82/21.99 (((~![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(A!41, C!39, H!42), A!41)) | (~member(tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~((~((~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_20(A!41, C!39, H!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_20(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), C!39)) | (~apply(G!43, tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_Y_20(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42))) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y_20(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), tptp_fun_Y_20(A!41, C!39, H!42))))))) | (~(apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_20(A!41, C!39, H!42)) | ![Y: $i] : ((~member(Y, C!39)) | (~apply(G!43, tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), Y)) | (~apply(H!42, Y, tptp_fun_Y_20(A!41, C!39, H!42)))))))))) <=> ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | (~member(tptp_fun_Y_20(A!41, C!39, H!42), A!41)) | (~member(tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~((~((~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_20(A!41, C!39, H!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_20(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), C!39)) | (~apply(G!43, tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_Y_20(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42))) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y_20(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), tptp_fun_Y_20(A!41, C!39, H!42))))))) | (~(apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_20(A!41, C!39, H!42)) | ![Y: $i] : ((~member(Y, C!39)) | (~apply(H!42, Y, tptp_fun_Y_20(A!41, C!39, H!42))) | (~apply(G!43, tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), Y))))))))),
% 21.82/22.00 inference(transitivity,[status(thm)],[109, 107])).
% 21.82/22.00 tff(111,plain,
% 21.82/22.00 ((~![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(A!41, C!39, H!42), A!41)) | (~member(tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~((~((~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_20(A!41, C!39, H!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_20(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), C!39)) | (~apply(G!43, tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_Y_20(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42))) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y_20(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), tptp_fun_Y_20(A!41, C!39, H!42))))))) | (~(apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_20(A!41, C!39, H!42)) | ![Y: $i] : ((~member(Y, C!39)) | (~apply(G!43, tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), Y)) | (~apply(H!42, Y, tptp_fun_Y_20(A!41, C!39, H!42)))))))))),
% 21.82/22.00 inference(quant_inst,[status(thm)],[])).
% 21.82/22.00 tff(112,plain,
% 21.82/22.00 ((~![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(A!41, C!39, H!42), A!41)) | (~member(tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~((~((~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_20(A!41, C!39, H!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_20(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), C!39)) | (~apply(G!43, tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_Y_20(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42))) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y_20(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), tptp_fun_Y_20(A!41, C!39, H!42))))))) | (~(apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_20(A!41, C!39, H!42)) | ![Y: $i] : ((~member(Y, C!39)) | (~apply(H!42, Y, tptp_fun_Y_20(A!41, C!39, H!42))) | (~apply(G!43, tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), Y)))))))),
% 21.82/22.00 inference(modus_ponens,[status(thm)],[111, 110])).
% 21.82/22.00 tff(113,plain,
% 21.82/22.00 (~((~((~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_20(A!41, C!39, H!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_20(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), C!39)) | (~apply(G!43, tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_Y_20(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42))) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y_20(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), tptp_fun_Y_20(A!41, C!39, H!42))))))) | (~(apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_20(A!41, C!39, H!42)) | ![Y: $i] : ((~member(Y, C!39)) | (~apply(H!42, Y, tptp_fun_Y_20(A!41, C!39, H!42))) | (~apply(G!43, tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), Y))))))),
% 21.82/22.00 inference(unit_resolution,[status(thm)],[112, 106, 50, 90])).
% 21.82/22.00 tff(114,plain,
% 21.82/22.00 (((~((~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_20(A!41, C!39, H!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_20(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), C!39)) | (~apply(G!43, tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_Y_20(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42))) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y_20(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), tptp_fun_Y_20(A!41, C!39, H!42))))))) | (~(apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_20(A!41, C!39, H!42)) | ![Y: $i] : ((~member(Y, C!39)) | (~apply(H!42, Y, tptp_fun_Y_20(A!41, C!39, H!42))) | (~apply(G!43, tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), Y)))))) | ((~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_20(A!41, C!39, H!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_20(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), C!39)) | (~apply(G!43, tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_Y_20(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42))) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y_20(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), tptp_fun_Y_20(A!41, C!39, H!42))))))),
% 21.82/22.00 inference(tautology,[status(thm)],[])).
% 21.82/22.00 tff(115,plain,
% 21.82/22.00 ((~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_20(A!41, C!39, H!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_20(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), C!39)) | (~apply(G!43, tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_Y_20(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42))) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y_20(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), tptp_fun_Y_20(A!41, C!39, H!42)))))),
% 21.82/22.00 inference(unit_resolution,[status(thm)],[114, 113])).
% 21.82/22.00 tff(116,plain,
% 21.82/22.00 (((~member(tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_20(A!41, C!39, H!42)))) | apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_20(A!41, C!39, H!42))),
% 21.82/22.00 inference(tautology,[status(thm)],[])).
% 21.82/22.00 tff(117,plain,
% 21.82/22.00 (apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_20(A!41, C!39, H!42))),
% 21.82/22.00 inference(unit_resolution,[status(thm)],[116, 88])).
% 21.82/22.00 tff(118,plain,
% 21.82/22.00 ((~((~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_20(A!41, C!39, H!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_20(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), C!39)) | (~apply(G!43, tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_Y_20(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42))) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y_20(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), tptp_fun_Y_20(A!41, C!39, H!42))))))) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_20(A!41, C!39, H!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_20(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), C!39)) | (~apply(G!43, tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_Y_20(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42))) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y_20(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), tptp_fun_Y_20(A!41, C!39, H!42)))))),
% 21.82/22.00 inference(tautology,[status(thm)],[])).
% 21.82/22.00 tff(119,plain,
% 21.82/22.00 ((~((~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_20(A!41, C!39, H!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_20(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), C!39)) | (~apply(G!43, tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_Y_20(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42))) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y_20(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), tptp_fun_Y_20(A!41, C!39, H!42))))))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_20(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), C!39)) | (~apply(G!43, tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_Y_20(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42))) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y_20(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), tptp_fun_Y_20(A!41, C!39, H!42)))))),
% 21.82/22.00 inference(unit_resolution,[status(thm)],[118, 117])).
% 21.82/22.00 tff(120,plain,
% 21.82/22.00 (~((~member(tptp_fun_Y_8(tptp_fun_Y_20(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), C!39)) | (~apply(G!43, tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_Y_20(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42))) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y_20(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), tptp_fun_Y_20(A!41, C!39, H!42))))),
% 21.82/22.01 inference(unit_resolution,[status(thm)],[119, 115])).
% 21.82/22.01 tff(121,plain,
% 21.82/22.01 (((~member(tptp_fun_Y_8(tptp_fun_Y_20(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), C!39)) | (~apply(G!43, tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_Y_20(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42))) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y_20(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), tptp_fun_Y_20(A!41, C!39, H!42)))) | apply(H!42, tptp_fun_Y_8(tptp_fun_Y_20(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), tptp_fun_Y_20(A!41, C!39, H!42))),
% 21.82/22.01 inference(tautology,[status(thm)],[])).
% 21.82/22.01 tff(122,plain,
% 21.82/22.01 (apply(H!42, tptp_fun_Y_8(tptp_fun_Y_20(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), tptp_fun_Y_20(A!41, C!39, H!42))),
% 21.82/22.01 inference(unit_resolution,[status(thm)],[121, 120])).
% 21.82/22.01 tff(123,plain,
% 21.82/22.01 (((~member(tptp_fun_Y_8(tptp_fun_Y_20(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), C!39)) | (~apply(G!43, tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_Y_20(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42))) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y_20(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), tptp_fun_Y_20(A!41, C!39, H!42)))) | member(tptp_fun_Y_8(tptp_fun_Y_20(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), C!39)),
% 21.82/22.01 inference(tautology,[status(thm)],[])).
% 21.82/22.01 tff(124,plain,
% 21.82/22.01 (member(tptp_fun_Y_8(tptp_fun_Y_20(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), C!39)),
% 21.82/22.01 inference(unit_resolution,[status(thm)],[123, 120])).
% 21.82/22.01 tff(125,plain,
% 21.82/22.01 (((~member(tptp_fun_Y_20(A!41, C!39, H!42), A!41)) | (~![E: $i] : ((~member(E, C!39)) | (~apply(H!42, E, tptp_fun_Y_20(A!41, C!39, H!42)))))) | ![E: $i] : ((~member(E, C!39)) | (~apply(H!42, E, tptp_fun_Y_20(A!41, C!39, H!42))))),
% 21.82/22.01 inference(tautology,[status(thm)],[])).
% 21.82/22.01 tff(126,plain,
% 21.82/22.01 (![E: $i] : ((~member(E, C!39)) | (~apply(H!42, E, tptp_fun_Y_20(A!41, C!39, H!42))))),
% 21.82/22.01 inference(unit_resolution,[status(thm)],[125, 48])).
% 21.82/22.01 tff(127,plain,
% 21.82/22.01 (((~![E: $i] : ((~member(E, C!39)) | (~apply(H!42, E, tptp_fun_Y_20(A!41, C!39, H!42))))) | ((~member(tptp_fun_Y_8(tptp_fun_Y_20(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), C!39)) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y_20(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), tptp_fun_Y_20(A!41, C!39, H!42))))) <=> ((~![E: $i] : ((~member(E, C!39)) | (~apply(H!42, E, tptp_fun_Y_20(A!41, C!39, H!42))))) | (~member(tptp_fun_Y_8(tptp_fun_Y_20(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), C!39)) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y_20(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), tptp_fun_Y_20(A!41, C!39, H!42))))),
% 21.82/22.01 inference(rewrite,[status(thm)],[])).
% 21.82/22.01 tff(128,plain,
% 21.82/22.01 ((~![E: $i] : ((~member(E, C!39)) | (~apply(H!42, E, tptp_fun_Y_20(A!41, C!39, H!42))))) | ((~member(tptp_fun_Y_8(tptp_fun_Y_20(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), C!39)) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y_20(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), tptp_fun_Y_20(A!41, C!39, H!42))))),
% 21.82/22.01 inference(quant_inst,[status(thm)],[])).
% 21.82/22.01 tff(129,plain,
% 21.82/22.01 ((~![E: $i] : ((~member(E, C!39)) | (~apply(H!42, E, tptp_fun_Y_20(A!41, C!39, H!42))))) | (~member(tptp_fun_Y_8(tptp_fun_Y_20(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), C!39)) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y_20(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_Y_20(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), tptp_fun_Y_20(A!41, C!39, H!42)))),
% 21.82/22.01 inference(modus_ponens,[status(thm)],[128, 127])).
% 21.82/22.01 tff(130,plain,
% 21.82/22.01 ($false),
% 21.82/22.01 inference(unit_resolution,[status(thm)],[129, 126, 124, 122])).
% 21.82/22.01 tff(131,plain,((~member(tptp_fun_Y_20(A!41, C!39, H!42), A!41)) | (~![E: $i] : ((~member(E, C!39)) | (~apply(H!42, E, tptp_fun_Y_20(A!41, C!39, H!42)))))), inference(lemma,lemma(discharge,[]))).
% 21.82/22.01 tff(132,plain,
% 21.82/22.01 ((~(surjective(H!42, C!39, A!41) | (~((~member(tptp_fun_Y_20(A!41, C!39, H!42), A!41)) | (~![E: $i] : ((~member(E, C!39)) | (~apply(H!42, E, tptp_fun_Y_20(A!41, C!39, H!42))))))))) | surjective(H!42, C!39, A!41) | (~((~member(tptp_fun_Y_20(A!41, C!39, H!42), A!41)) | (~![E: $i] : ((~member(E, C!39)) | (~apply(H!42, E, tptp_fun_Y_20(A!41, C!39, H!42)))))))),
% 21.82/22.01 inference(tautology,[status(thm)],[])).
% 21.82/22.01 tff(133,plain,
% 21.82/22.01 ((~(surjective(H!42, C!39, A!41) | (~((~member(tptp_fun_Y_20(A!41, C!39, H!42), A!41)) | (~![E: $i] : ((~member(E, C!39)) | (~apply(H!42, E, tptp_fun_Y_20(A!41, C!39, H!42))))))))) | surjective(H!42, C!39, A!41)),
% 21.82/22.01 inference(unit_resolution,[status(thm)],[132, 131])).
% 21.82/22.01 tff(134,plain,
% 21.82/22.01 (surjective(H!42, C!39, A!41)),
% 21.82/22.01 inference(unit_resolution,[status(thm)],[133, 47])).
% 21.82/22.01 tff(135,plain,
% 21.82/22.01 ((~![F: $i, A: $i, B: $i] : (~(((~injective(F, A, B)) | (~surjective(F, A, B))) <=> one_to_one(F, A, B)))) | (~(((~injective(H!42, C!39, A!41)) | (~surjective(H!42, C!39, A!41))) <=> one_to_one(H!42, C!39, A!41)))),
% 21.82/22.01 inference(quant_inst,[status(thm)],[])).
% 21.82/22.01 tff(136,plain,
% 21.82/22.01 (~(((~injective(H!42, C!39, A!41)) | (~surjective(H!42, C!39, A!41))) <=> one_to_one(H!42, C!39, A!41))),
% 21.82/22.01 inference(unit_resolution,[status(thm)],[135, 64])).
% 21.82/22.01 tff(137,plain,
% 21.82/22.01 (~one_to_one(H!42, C!39, A!41)),
% 21.82/22.01 inference(or_elim,[status(thm)],[74])).
% 21.82/22.01 tff(138,plain,
% 21.82/22.01 ((((~injective(H!42, C!39, A!41)) | (~surjective(H!42, C!39, A!41))) <=> one_to_one(H!42, C!39, A!41)) | ((~injective(H!42, C!39, A!41)) | (~surjective(H!42, C!39, A!41))) | one_to_one(H!42, C!39, A!41)),
% 21.82/22.01 inference(tautology,[status(thm)],[])).
% 21.82/22.01 tff(139,plain,
% 21.82/22.01 ((((~injective(H!42, C!39, A!41)) | (~surjective(H!42, C!39, A!41))) <=> one_to_one(H!42, C!39, A!41)) | ((~injective(H!42, C!39, A!41)) | (~surjective(H!42, C!39, A!41)))),
% 21.82/22.01 inference(unit_resolution,[status(thm)],[138, 137])).
% 21.82/22.01 tff(140,plain,
% 21.82/22.01 ((~injective(H!42, C!39, A!41)) | (~surjective(H!42, C!39, A!41))),
% 21.82/22.01 inference(unit_resolution,[status(thm)],[139, 136])).
% 21.82/22.01 tff(141,plain,
% 21.82/22.01 ((~((~injective(H!42, C!39, A!41)) | (~surjective(H!42, C!39, A!41)))) | (~injective(H!42, C!39, A!41)) | (~surjective(H!42, C!39, A!41))),
% 21.82/22.01 inference(tautology,[status(thm)],[])).
% 21.82/22.01 tff(142,plain,
% 21.82/22.01 ((~injective(H!42, C!39, A!41)) | (~surjective(H!42, C!39, A!41))),
% 21.82/22.01 inference(unit_resolution,[status(thm)],[141, 140])).
% 21.82/22.01 tff(143,plain,
% 21.82/22.01 (~injective(H!42, C!39, A!41)),
% 21.82/22.01 inference(unit_resolution,[status(thm)],[142, 134])).
% 21.82/22.01 tff(144,plain,
% 21.82/22.01 ((~(injective(H!42, C!39, A!41) | (~((~member(tptp_fun_X2_17(A!41, C!39, H!42), C!39)) | (~member(tptp_fun_Y_16(A!41, C!39, H!42), A!41)) | (~member(tptp_fun_X1_18(A!41, C!39, H!42), C!39)) | (~apply(H!42, tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_Y_16(A!41, C!39, H!42))) | (~apply(H!42, tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_Y_16(A!41, C!39, H!42))) | (tptp_fun_X1_18(A!41, C!39, H!42) = tptp_fun_X2_17(A!41, C!39, H!42)))))) | injective(H!42, C!39, A!41) | (~((~member(tptp_fun_X2_17(A!41, C!39, H!42), C!39)) | (~member(tptp_fun_Y_16(A!41, C!39, H!42), A!41)) | (~member(tptp_fun_X1_18(A!41, C!39, H!42), C!39)) | (~apply(H!42, tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_Y_16(A!41, C!39, H!42))) | (~apply(H!42, tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_Y_16(A!41, C!39, H!42))) | (tptp_fun_X1_18(A!41, C!39, H!42) = tptp_fun_X2_17(A!41, C!39, H!42))))),
% 21.82/22.01 inference(tautology,[status(thm)],[])).
% 21.82/22.01 tff(145,plain,
% 21.82/22.01 ((~(injective(H!42, C!39, A!41) | (~((~member(tptp_fun_X2_17(A!41, C!39, H!42), C!39)) | (~member(tptp_fun_Y_16(A!41, C!39, H!42), A!41)) | (~member(tptp_fun_X1_18(A!41, C!39, H!42), C!39)) | (~apply(H!42, tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_Y_16(A!41, C!39, H!42))) | (~apply(H!42, tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_Y_16(A!41, C!39, H!42))) | (tptp_fun_X1_18(A!41, C!39, H!42) = tptp_fun_X2_17(A!41, C!39, H!42)))))) | (~((~member(tptp_fun_X2_17(A!41, C!39, H!42), C!39)) | (~member(tptp_fun_Y_16(A!41, C!39, H!42), A!41)) | (~member(tptp_fun_X1_18(A!41, C!39, H!42), C!39)) | (~apply(H!42, tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_Y_16(A!41, C!39, H!42))) | (~apply(H!42, tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_Y_16(A!41, C!39, H!42))) | (tptp_fun_X1_18(A!41, C!39, H!42) = tptp_fun_X2_17(A!41, C!39, H!42))))),
% 21.82/22.01 inference(unit_resolution,[status(thm)],[144, 143])).
% 21.82/22.01 tff(146,plain,
% 21.82/22.01 (~((~member(tptp_fun_X2_17(A!41, C!39, H!42), C!39)) | (~member(tptp_fun_Y_16(A!41, C!39, H!42), A!41)) | (~member(tptp_fun_X1_18(A!41, C!39, H!42), C!39)) | (~apply(H!42, tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_Y_16(A!41, C!39, H!42))) | (~apply(H!42, tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_Y_16(A!41, C!39, H!42))) | (tptp_fun_X1_18(A!41, C!39, H!42) = tptp_fun_X2_17(A!41, C!39, H!42)))),
% 21.82/22.01 inference(unit_resolution,[status(thm)],[145, 25])).
% 21.82/22.01 tff(147,plain,
% 21.82/22.01 (((~member(tptp_fun_X2_17(A!41, C!39, H!42), C!39)) | (~member(tptp_fun_Y_16(A!41, C!39, H!42), A!41)) | (~member(tptp_fun_X1_18(A!41, C!39, H!42), C!39)) | (~apply(H!42, tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_Y_16(A!41, C!39, H!42))) | (~apply(H!42, tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_Y_16(A!41, C!39, H!42))) | (tptp_fun_X1_18(A!41, C!39, H!42) = tptp_fun_X2_17(A!41, C!39, H!42))) | member(tptp_fun_X2_17(A!41, C!39, H!42), C!39)),
% 21.82/22.01 inference(tautology,[status(thm)],[])).
% 21.82/22.01 tff(148,plain,
% 21.82/22.01 (member(tptp_fun_X2_17(A!41, C!39, H!42), C!39)),
% 21.82/22.01 inference(unit_resolution,[status(thm)],[147, 146])).
% 21.82/22.01 tff(149,plain,
% 21.82/22.01 ((~![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(compose_function(G!43, F!44, A!41, B!40, C!39), A!41, C!39)) | ![Y: $i] : ((~member(Y, C!39)) | (~((~member(tptp_fun_E_19(Y, A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), A!41)) | (~apply(compose_function(G!43, F!44, A!41, B!40, C!39), tptp_fun_E_19(Y, A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), Y))))))) | (~(surjective(compose_function(G!43, F!44, A!41, B!40, C!39), A!41, C!39) | (~((~member(tptp_fun_Y_20(C!39, A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), C!39)) | (~![E: $i] : ((~member(E, A!41)) | (~apply(compose_function(G!43, F!44, A!41, B!40, C!39), E, tptp_fun_Y_20(C!39, A!41, compose_function(G!43, F!44, A!41, B!40, C!39))))))))))))),
% 21.82/22.01 inference(quant_inst,[status(thm)],[])).
% 21.82/22.01 tff(150,plain,
% 21.82/22.01 (~((~((~surjective(compose_function(G!43, F!44, A!41, B!40, C!39), A!41, C!39)) | ![Y: $i] : ((~member(Y, C!39)) | (~((~member(tptp_fun_E_19(Y, A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), A!41)) | (~apply(compose_function(G!43, F!44, A!41, B!40, C!39), tptp_fun_E_19(Y, A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), Y))))))) | (~(surjective(compose_function(G!43, F!44, A!41, B!40, C!39), A!41, C!39) | (~((~member(tptp_fun_Y_20(C!39, A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), C!39)) | (~![E: $i] : ((~member(E, A!41)) | (~apply(compose_function(G!43, F!44, A!41, B!40, C!39), E, tptp_fun_Y_20(C!39, A!41, compose_function(G!43, F!44, A!41, B!40, C!39)))))))))))),
% 21.82/22.01 inference(unit_resolution,[status(thm)],[149, 42])).
% 21.82/22.01 tff(151,plain,
% 21.82/22.01 (((~((~surjective(compose_function(G!43, F!44, A!41, B!40, C!39), A!41, C!39)) | ![Y: $i] : ((~member(Y, C!39)) | (~((~member(tptp_fun_E_19(Y, A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), A!41)) | (~apply(compose_function(G!43, F!44, A!41, B!40, C!39), tptp_fun_E_19(Y, A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), Y))))))) | (~(surjective(compose_function(G!43, F!44, A!41, B!40, C!39), A!41, C!39) | (~((~member(tptp_fun_Y_20(C!39, A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), C!39)) | (~![E: $i] : ((~member(E, A!41)) | (~apply(compose_function(G!43, F!44, A!41, B!40, C!39), E, tptp_fun_Y_20(C!39, A!41, compose_function(G!43, F!44, A!41, B!40, C!39))))))))))) | ((~surjective(compose_function(G!43, F!44, A!41, B!40, C!39), A!41, C!39)) | ![Y: $i] : ((~member(Y, C!39)) | (~((~member(tptp_fun_E_19(Y, A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), A!41)) | (~apply(compose_function(G!43, F!44, A!41, B!40, C!39), tptp_fun_E_19(Y, A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), Y))))))),
% 21.82/22.01 inference(tautology,[status(thm)],[])).
% 21.82/22.01 tff(152,plain,
% 21.82/22.01 ((~surjective(compose_function(G!43, F!44, A!41, B!40, C!39), A!41, C!39)) | ![Y: $i] : ((~member(Y, C!39)) | (~((~member(tptp_fun_E_19(Y, A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), A!41)) | (~apply(compose_function(G!43, F!44, A!41, B!40, C!39), tptp_fun_E_19(Y, A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), Y)))))),
% 21.82/22.01 inference(unit_resolution,[status(thm)],[151, 150])).
% 21.82/22.01 tff(153,plain,
% 21.82/22.01 ((~![F: $i, A: $i, B: $i] : (~(((~injective(F, A, B)) | (~surjective(F, A, B))) <=> one_to_one(F, A, B)))) | (~(((~injective(compose_function(G!43, F!44, A!41, B!40, C!39), A!41, C!39)) | (~surjective(compose_function(G!43, F!44, A!41, B!40, C!39), A!41, C!39))) <=> one_to_one(compose_function(G!43, F!44, A!41, B!40, C!39), A!41, C!39)))),
% 21.82/22.01 inference(quant_inst,[status(thm)],[])).
% 21.82/22.01 tff(154,plain,
% 21.82/22.01 (~(((~injective(compose_function(G!43, F!44, A!41, B!40, C!39), A!41, C!39)) | (~surjective(compose_function(G!43, F!44, A!41, B!40, C!39), A!41, C!39))) <=> one_to_one(compose_function(G!43, F!44, A!41, B!40, C!39), A!41, C!39))),
% 21.82/22.01 inference(unit_resolution,[status(thm)],[153, 64])).
% 21.82/22.01 tff(155,plain,
% 21.82/22.01 (one_to_one(compose_function(G!43, F!44, A!41, B!40, C!39), A!41, C!39)),
% 21.82/22.01 inference(and_elim,[status(thm)],[75])).
% 21.82/22.01 tff(156,plain,
% 21.82/22.01 ((((~injective(compose_function(G!43, F!44, A!41, B!40, C!39), A!41, C!39)) | (~surjective(compose_function(G!43, F!44, A!41, B!40, C!39), A!41, C!39))) <=> one_to_one(compose_function(G!43, F!44, A!41, B!40, C!39), A!41, C!39)) | (~((~injective(compose_function(G!43, F!44, A!41, B!40, C!39), A!41, C!39)) | (~surjective(compose_function(G!43, F!44, A!41, B!40, C!39), A!41, C!39)))) | (~one_to_one(compose_function(G!43, F!44, A!41, B!40, C!39), A!41, C!39))),
% 21.82/22.01 inference(tautology,[status(thm)],[])).
% 21.82/22.01 tff(157,plain,
% 21.82/22.01 ((((~injective(compose_function(G!43, F!44, A!41, B!40, C!39), A!41, C!39)) | (~surjective(compose_function(G!43, F!44, A!41, B!40, C!39), A!41, C!39))) <=> one_to_one(compose_function(G!43, F!44, A!41, B!40, C!39), A!41, C!39)) | (~((~injective(compose_function(G!43, F!44, A!41, B!40, C!39), A!41, C!39)) | (~surjective(compose_function(G!43, F!44, A!41, B!40, C!39), A!41, C!39))))),
% 21.82/22.01 inference(unit_resolution,[status(thm)],[156, 155])).
% 21.82/22.01 tff(158,plain,
% 21.82/22.01 (~((~injective(compose_function(G!43, F!44, A!41, B!40, C!39), A!41, C!39)) | (~surjective(compose_function(G!43, F!44, A!41, B!40, C!39), A!41, C!39)))),
% 21.82/22.01 inference(unit_resolution,[status(thm)],[157, 154])).
% 21.82/22.01 tff(159,plain,
% 21.82/22.01 (((~injective(compose_function(G!43, F!44, A!41, B!40, C!39), A!41, C!39)) | (~surjective(compose_function(G!43, F!44, A!41, B!40, C!39), A!41, C!39))) | surjective(compose_function(G!43, F!44, A!41, B!40, C!39), A!41, C!39)),
% 21.82/22.01 inference(tautology,[status(thm)],[])).
% 21.82/22.01 tff(160,plain,
% 21.82/22.01 (surjective(compose_function(G!43, F!44, A!41, B!40, C!39), A!41, C!39)),
% 21.82/22.01 inference(unit_resolution,[status(thm)],[159, 158])).
% 21.82/22.01 tff(161,plain,
% 21.82/22.01 ((~((~surjective(compose_function(G!43, F!44, A!41, B!40, C!39), A!41, C!39)) | ![Y: $i] : ((~member(Y, C!39)) | (~((~member(tptp_fun_E_19(Y, A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), A!41)) | (~apply(compose_function(G!43, F!44, A!41, B!40, C!39), tptp_fun_E_19(Y, A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), Y))))))) | (~surjective(compose_function(G!43, F!44, A!41, B!40, C!39), A!41, C!39)) | ![Y: $i] : ((~member(Y, C!39)) | (~((~member(tptp_fun_E_19(Y, A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), A!41)) | (~apply(compose_function(G!43, F!44, A!41, B!40, C!39), tptp_fun_E_19(Y, A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), Y)))))),
% 21.82/22.01 inference(tautology,[status(thm)],[])).
% 21.82/22.01 tff(162,plain,
% 21.82/22.01 ((~((~surjective(compose_function(G!43, F!44, A!41, B!40, C!39), A!41, C!39)) | ![Y: $i] : ((~member(Y, C!39)) | (~((~member(tptp_fun_E_19(Y, A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), A!41)) | (~apply(compose_function(G!43, F!44, A!41, B!40, C!39), tptp_fun_E_19(Y, A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), Y))))))) | ![Y: $i] : ((~member(Y, C!39)) | (~((~member(tptp_fun_E_19(Y, A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), A!41)) | (~apply(compose_function(G!43, F!44, A!41, B!40, C!39), tptp_fun_E_19(Y, A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), Y)))))),
% 21.82/22.01 inference(unit_resolution,[status(thm)],[161, 160])).
% 21.82/22.01 tff(163,plain,
% 21.82/22.01 (![Y: $i] : ((~member(Y, C!39)) | (~((~member(tptp_fun_E_19(Y, A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), A!41)) | (~apply(compose_function(G!43, F!44, A!41, B!40, C!39), tptp_fun_E_19(Y, A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), Y)))))),
% 21.82/22.01 inference(unit_resolution,[status(thm)],[162, 152])).
% 21.82/22.01 tff(164,plain,
% 21.82/22.01 (((~![Y: $i] : ((~member(Y, C!39)) | (~((~member(tptp_fun_E_19(Y, A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), A!41)) | (~apply(compose_function(G!43, F!44, A!41, B!40, C!39), tptp_fun_E_19(Y, A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), Y)))))) | ((~member(tptp_fun_X2_17(A!41, C!39, H!42), C!39)) | (~((~member(tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), A!41)) | (~apply(compose_function(G!43, F!44, A!41, B!40, C!39), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), tptp_fun_X2_17(A!41, C!39, H!42))))))) <=> ((~![Y: $i] : ((~member(Y, C!39)) | (~((~member(tptp_fun_E_19(Y, A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), A!41)) | (~apply(compose_function(G!43, F!44, A!41, B!40, C!39), tptp_fun_E_19(Y, A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), Y)))))) | (~member(tptp_fun_X2_17(A!41, C!39, H!42), C!39)) | (~((~member(tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), A!41)) | (~apply(compose_function(G!43, F!44, A!41, B!40, C!39), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), tptp_fun_X2_17(A!41, C!39, H!42))))))),
% 21.82/22.01 inference(rewrite,[status(thm)],[])).
% 21.82/22.01 tff(165,plain,
% 21.82/22.01 ((~![Y: $i] : ((~member(Y, C!39)) | (~((~member(tptp_fun_E_19(Y, A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), A!41)) | (~apply(compose_function(G!43, F!44, A!41, B!40, C!39), tptp_fun_E_19(Y, A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), Y)))))) | ((~member(tptp_fun_X2_17(A!41, C!39, H!42), C!39)) | (~((~member(tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), A!41)) | (~apply(compose_function(G!43, F!44, A!41, B!40, C!39), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), tptp_fun_X2_17(A!41, C!39, H!42))))))),
% 21.82/22.02 inference(quant_inst,[status(thm)],[])).
% 21.82/22.02 tff(166,plain,
% 21.82/22.02 ((~![Y: $i] : ((~member(Y, C!39)) | (~((~member(tptp_fun_E_19(Y, A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), A!41)) | (~apply(compose_function(G!43, F!44, A!41, B!40, C!39), tptp_fun_E_19(Y, A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), Y)))))) | (~member(tptp_fun_X2_17(A!41, C!39, H!42), C!39)) | (~((~member(tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), A!41)) | (~apply(compose_function(G!43, F!44, A!41, B!40, C!39), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), tptp_fun_X2_17(A!41, C!39, H!42)))))),
% 21.82/22.02 inference(modus_ponens,[status(thm)],[165, 164])).
% 21.82/22.02 tff(167,plain,
% 21.82/22.02 (~((~member(tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), A!41)) | (~apply(compose_function(G!43, F!44, A!41, B!40, C!39), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), tptp_fun_X2_17(A!41, C!39, H!42))))),
% 21.82/22.02 inference(unit_resolution,[status(thm)],[166, 163, 148])).
% 21.82/22.02 tff(168,plain,
% 21.82/22.02 (((~member(tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), A!41)) | (~apply(compose_function(G!43, F!44, A!41, B!40, C!39), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), tptp_fun_X2_17(A!41, C!39, H!42)))) | member(tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), A!41)),
% 21.82/22.02 inference(tautology,[status(thm)],[])).
% 21.82/22.02 tff(169,plain,
% 21.82/22.02 (member(tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), A!41)),
% 21.82/22.02 inference(unit_resolution,[status(thm)],[168, 167])).
% 21.82/22.02 tff(170,plain,
% 21.82/22.02 (((~![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(A!41, C!39, H!42), C!39)) | (~member(tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), A!41)) | (~((~(apply(compose_function(G!43, F!44, A!41, B!40, C!39), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), tptp_fun_X2_17(A!41, C!39, H!42)) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!44, tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), Y)) | (~apply(G!43, Y, tptp_fun_X2_17(A!41, C!39, H!42)))))) | (~((~apply(compose_function(G!43, F!44, A!41, B!40, C!39), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), tptp_fun_X2_17(A!41, C!39, H!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), B!40)) | (~apply(F!44, tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43))) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_X2_17(A!41, C!39, H!42))))))))))) <=> ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | (~member(tptp_fun_X2_17(A!41, C!39, H!42), C!39)) | (~member(tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), A!41)) | (~((~(apply(compose_function(G!43, F!44, A!41, B!40, C!39), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), tptp_fun_X2_17(A!41, C!39, H!42)) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!44, tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), Y)) | (~apply(G!43, Y, tptp_fun_X2_17(A!41, C!39, H!42)))))) | (~((~apply(compose_function(G!43, F!44, A!41, B!40, C!39), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), tptp_fun_X2_17(A!41, C!39, H!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), B!40)) | (~apply(F!44, tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43))) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_X2_17(A!41, C!39, H!42))))))))))),
% 21.82/22.02 inference(rewrite,[status(thm)],[])).
% 21.82/22.02 tff(171,plain,
% 21.82/22.02 (((~member(tptp_fun_X2_17(A!41, C!39, H!42), C!39)) | (~member(tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), A!41)) | (~((~((~apply(compose_function(G!43, F!44, A!41, B!40, C!39), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), tptp_fun_X2_17(A!41, C!39, H!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), B!40)) | (~apply(F!44, tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43))) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_X2_17(A!41, C!39, H!42))))))) | (~(apply(compose_function(G!43, F!44, A!41, B!40, C!39), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), tptp_fun_X2_17(A!41, C!39, H!42)) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!44, tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), Y)) | (~apply(G!43, Y, tptp_fun_X2_17(A!41, C!39, H!42))))))))) <=> ((~member(tptp_fun_X2_17(A!41, C!39, H!42), C!39)) | (~member(tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), A!41)) | (~((~(apply(compose_function(G!43, F!44, A!41, B!40, C!39), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), tptp_fun_X2_17(A!41, C!39, H!42)) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!44, tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), Y)) | (~apply(G!43, Y, tptp_fun_X2_17(A!41, C!39, H!42)))))) | (~((~apply(compose_function(G!43, F!44, A!41, B!40, C!39), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), tptp_fun_X2_17(A!41, C!39, H!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), B!40)) | (~apply(F!44, tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43))) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_X2_17(A!41, C!39, H!42))))))))))),
% 21.82/22.02 inference(rewrite,[status(thm)],[])).
% 21.82/22.02 tff(172,plain,
% 21.82/22.02 (((~![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(A!41, C!39, H!42), C!39)) | (~member(tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), A!41)) | (~((~((~apply(compose_function(G!43, F!44, A!41, B!40, C!39), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), tptp_fun_X2_17(A!41, C!39, H!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), B!40)) | (~apply(F!44, tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43))) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_X2_17(A!41, C!39, H!42))))))) | (~(apply(compose_function(G!43, F!44, A!41, B!40, C!39), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), tptp_fun_X2_17(A!41, C!39, H!42)) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!44, tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), Y)) | (~apply(G!43, Y, tptp_fun_X2_17(A!41, C!39, H!42)))))))))) <=> ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_X2_17(A!41, C!39, H!42), C!39)) | (~member(tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), A!41)) | (~((~(apply(compose_function(G!43, F!44, A!41, B!40, C!39), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), tptp_fun_X2_17(A!41, C!39, H!42)) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!44, tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), Y)) | (~apply(G!43, Y, tptp_fun_X2_17(A!41, C!39, H!42)))))) | (~((~apply(compose_function(G!43, F!44, A!41, B!40, C!39), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), tptp_fun_X2_17(A!41, C!39, H!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), B!40)) | (~apply(F!44, tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43))) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_X2_17(A!41, C!39, H!42)))))))))))),
% 21.82/22.02 inference(monotonicity,[status(thm)],[171])).
% 21.82/22.02 tff(173,plain,
% 21.82/22.02 (((~![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(A!41, C!39, H!42), C!39)) | (~member(tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), A!41)) | (~((~((~apply(compose_function(G!43, F!44, A!41, B!40, C!39), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), tptp_fun_X2_17(A!41, C!39, H!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), B!40)) | (~apply(F!44, tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43))) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_X2_17(A!41, C!39, H!42))))))) | (~(apply(compose_function(G!43, F!44, A!41, B!40, C!39), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), tptp_fun_X2_17(A!41, C!39, H!42)) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!44, tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), Y)) | (~apply(G!43, Y, tptp_fun_X2_17(A!41, C!39, H!42)))))))))) <=> ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | (~member(tptp_fun_X2_17(A!41, C!39, H!42), C!39)) | (~member(tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), A!41)) | (~((~(apply(compose_function(G!43, F!44, A!41, B!40, C!39), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), tptp_fun_X2_17(A!41, C!39, H!42)) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!44, tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), Y)) | (~apply(G!43, Y, tptp_fun_X2_17(A!41, C!39, H!42)))))) | (~((~apply(compose_function(G!43, F!44, A!41, B!40, C!39), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), tptp_fun_X2_17(A!41, C!39, H!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), B!40)) | (~apply(F!44, tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43))) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_X2_17(A!41, C!39, H!42))))))))))),
% 21.82/22.02 inference(transitivity,[status(thm)],[172, 170])).
% 21.82/22.02 tff(174,plain,
% 21.82/22.02 ((~![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(A!41, C!39, H!42), C!39)) | (~member(tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), A!41)) | (~((~((~apply(compose_function(G!43, F!44, A!41, B!40, C!39), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), tptp_fun_X2_17(A!41, C!39, H!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), B!40)) | (~apply(F!44, tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43))) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_X2_17(A!41, C!39, H!42))))))) | (~(apply(compose_function(G!43, F!44, A!41, B!40, C!39), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), tptp_fun_X2_17(A!41, C!39, H!42)) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!44, tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), Y)) | (~apply(G!43, Y, tptp_fun_X2_17(A!41, C!39, H!42)))))))))),
% 21.82/22.03 inference(quant_inst,[status(thm)],[])).
% 21.82/22.03 tff(175,plain,
% 21.82/22.03 ((~![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(A!41, C!39, H!42), C!39)) | (~member(tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), A!41)) | (~((~(apply(compose_function(G!43, F!44, A!41, B!40, C!39), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), tptp_fun_X2_17(A!41, C!39, H!42)) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!44, tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), Y)) | (~apply(G!43, Y, tptp_fun_X2_17(A!41, C!39, H!42)))))) | (~((~apply(compose_function(G!43, F!44, A!41, B!40, C!39), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), tptp_fun_X2_17(A!41, C!39, H!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), B!40)) | (~apply(F!44, tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43))) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_X2_17(A!41, C!39, H!42)))))))))),
% 21.82/22.03 inference(modus_ponens,[status(thm)],[174, 173])).
% 21.82/22.03 tff(176,plain,
% 21.82/22.03 (~((~(apply(compose_function(G!43, F!44, A!41, B!40, C!39), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), tptp_fun_X2_17(A!41, C!39, H!42)) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!44, tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), Y)) | (~apply(G!43, Y, tptp_fun_X2_17(A!41, C!39, H!42)))))) | (~((~apply(compose_function(G!43, F!44, A!41, B!40, C!39), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), tptp_fun_X2_17(A!41, C!39, H!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), B!40)) | (~apply(F!44, tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43))) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_X2_17(A!41, C!39, H!42))))))))),
% 21.82/22.03 inference(unit_resolution,[status(thm)],[175, 106, 148, 169])).
% 21.82/22.03 tff(177,plain,
% 21.82/22.03 (((~(apply(compose_function(G!43, F!44, A!41, B!40, C!39), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), tptp_fun_X2_17(A!41, C!39, H!42)) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!44, tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), Y)) | (~apply(G!43, Y, tptp_fun_X2_17(A!41, C!39, H!42)))))) | (~((~apply(compose_function(G!43, F!44, A!41, B!40, C!39), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), tptp_fun_X2_17(A!41, C!39, H!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), B!40)) | (~apply(F!44, tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43))) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_X2_17(A!41, C!39, H!42)))))))) | ((~apply(compose_function(G!43, F!44, A!41, B!40, C!39), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), tptp_fun_X2_17(A!41, C!39, H!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), B!40)) | (~apply(F!44, tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43))) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_X2_17(A!41, C!39, H!42))))))),
% 21.82/22.03 inference(tautology,[status(thm)],[])).
% 21.82/22.03 tff(178,plain,
% 21.82/22.03 ((~apply(compose_function(G!43, F!44, A!41, B!40, C!39), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), tptp_fun_X2_17(A!41, C!39, H!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), B!40)) | (~apply(F!44, tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43))) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_X2_17(A!41, C!39, H!42)))))),
% 21.82/22.03 inference(unit_resolution,[status(thm)],[177, 176])).
% 21.82/22.03 tff(179,plain,
% 21.82/22.03 (((~member(tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), A!41)) | (~apply(compose_function(G!43, F!44, A!41, B!40, C!39), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), tptp_fun_X2_17(A!41, C!39, H!42)))) | apply(compose_function(G!43, F!44, A!41, B!40, C!39), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), tptp_fun_X2_17(A!41, C!39, H!42))),
% 21.82/22.03 inference(tautology,[status(thm)],[])).
% 21.82/22.03 tff(180,plain,
% 21.82/22.03 (apply(compose_function(G!43, F!44, A!41, B!40, C!39), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), tptp_fun_X2_17(A!41, C!39, H!42))),
% 21.82/22.03 inference(unit_resolution,[status(thm)],[179, 167])).
% 21.82/22.03 tff(181,plain,
% 21.82/22.03 ((~((~apply(compose_function(G!43, F!44, A!41, B!40, C!39), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), tptp_fun_X2_17(A!41, C!39, H!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), B!40)) | (~apply(F!44, tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43))) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_X2_17(A!41, C!39, H!42))))))) | (~apply(compose_function(G!43, F!44, A!41, B!40, C!39), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), tptp_fun_X2_17(A!41, C!39, H!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), B!40)) | (~apply(F!44, tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43))) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_X2_17(A!41, C!39, H!42)))))),
% 21.82/22.03 inference(tautology,[status(thm)],[])).
% 21.82/22.03 tff(182,plain,
% 21.82/22.03 ((~((~apply(compose_function(G!43, F!44, A!41, B!40, C!39), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), tptp_fun_X2_17(A!41, C!39, H!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), B!40)) | (~apply(F!44, tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43))) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_X2_17(A!41, C!39, H!42))))))) | (~((~member(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), B!40)) | (~apply(F!44, tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43))) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_X2_17(A!41, C!39, H!42)))))),
% 21.82/22.03 inference(unit_resolution,[status(thm)],[181, 180])).
% 21.82/22.03 tff(183,plain,
% 21.82/22.03 (~((~member(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), B!40)) | (~apply(F!44, tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43))) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_X2_17(A!41, C!39, H!42))))),
% 21.82/22.03 inference(unit_resolution,[status(thm)],[182, 178])).
% 21.82/22.03 tff(184,plain,
% 21.82/22.03 (((~member(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), B!40)) | (~apply(F!44, tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43))) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_X2_17(A!41, C!39, H!42)))) | member(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), B!40)),
% 21.82/22.03 inference(tautology,[status(thm)],[])).
% 21.82/22.03 tff(185,plain,
% 21.82/22.03 (member(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), B!40)),
% 21.82/22.03 inference(unit_resolution,[status(thm)],[184, 183])).
% 21.82/22.03 tff(186,plain,
% 21.82/22.03 (^[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)))))))))))),
% 21.82/22.03 inference(bind,[status(th)],[])).
% 21.82/22.03 tff(187,plain,
% 21.82/22.03 (![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))))))))))),
% 21.82/22.03 inference(quant_intro,[status(thm)],[186])).
% 21.82/22.03 tff(188,plain,
% 21.82/22.03 (^[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)))))))))),
% 21.82/22.03 inference(bind,[status(th)],[])).
% 21.82/22.03 tff(189,plain,
% 21.82/22.03 (![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))))))))),
% 21.82/22.03 inference(quant_intro,[status(thm)],[188])).
% 21.82/22.03 tff(190,plain,
% 21.82/22.03 (^[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)))))))))),
% 21.82/22.03 inference(bind,[status(th)],[])).
% 21.82/22.03 tff(191,plain,
% 21.82/22.03 (![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))))))))),
% 21.82/22.03 inference(quant_intro,[status(thm)],[190])).
% 21.82/22.03 tff(192,plain,
% 21.82/22.03 (![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))))))))),
% 21.82/22.03 inference(transitivity,[status(thm)],[191, 189])).
% 21.82/22.03 tff(193,plain,
% 21.82/22.03 (^[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))))))))))),
% 21.82/22.04 inference(bind,[status(th)],[])).
% 21.82/22.04 tff(194,plain,
% 21.82/22.04 (![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))))))))),
% 21.82/22.04 inference(quant_intro,[status(thm)],[193])).
% 21.82/22.04 tff(195,plain,
% 21.82/22.04 (^[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))))))))),
% 21.82/22.04 inference(bind,[status(th)],[])).
% 21.82/22.04 tff(196,plain,
% 21.82/22.04 (![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)))))))),
% 21.82/22.04 inference(quant_intro,[status(thm)],[195])).
% 21.82/22.04 tff(197,plain,
% 21.82/22.04 (![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))))))),
% 21.82/22.04 inference(rewrite,[status(thm)],[])).
% 21.82/22.04 tff(198,plain,
% 21.82/22.04 (^[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)))))))),
% 21.89/22.04 inference(bind,[status(th)],[])).
% 21.89/22.04 tff(199,plain,
% 21.89/22.04 (![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))))))),
% 21.89/22.04 inference(quant_intro,[status(thm)],[198])).
% 21.89/22.04 tff(200,axiom,(![F: $i, A: $i, B: $i] : (maps(F, A, B) <=> (![X: $i] : (member(X, A) => ?[Y: $i] : (member(Y, B) & apply(F, X, Y))) & ![X: $i, Y1: $i, Y2: $i] : (((member(X, A) & member(Y1, B)) & member(Y2, B)) => ((apply(F, X, Y1) & apply(F, X, Y2)) => (Y1 = Y2)))))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+1.ax','maps')).
% 21.89/22.04 tff(201,plain,
% 21.89/22.04 (![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))))))),
% 21.89/22.04 inference(modus_ponens,[status(thm)],[200, 199])).
% 21.89/22.04 tff(202,plain,
% 21.89/22.04 (![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))))))),
% 21.89/22.04 inference(modus_ponens,[status(thm)],[201, 197])).
% 21.89/22.04 tff(203,plain,(
% 21.89/22.04 ![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))))))))),
% 21.89/22.04 inference(skolemize,[status(sab)],[202])).
% 21.89/22.04 tff(204,plain,
% 21.89/22.04 (![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)))))))),
% 21.89/22.04 inference(modus_ponens,[status(thm)],[203, 196])).
% 21.89/22.04 tff(205,plain,
% 21.89/22.04 (![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))))))))),
% 21.89/22.04 inference(modus_ponens,[status(thm)],[204, 194])).
% 21.89/22.04 tff(206,plain,
% 21.89/22.04 (![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))))))))),
% 21.89/22.04 inference(modus_ponens,[status(thm)],[205, 192])).
% 21.89/22.04 tff(207,plain,
% 21.89/22.04 (![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))))))))))),
% 21.89/22.04 inference(modus_ponens,[status(thm)],[206, 187])).
% 21.89/22.04 tff(208,plain,
% 21.89/22.04 (((~![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!43, B!40, C!39)) | (~((~![X: $i] : ((~member(X, B!40)) | (~((~member(tptp_fun_Y_3(X, C!39, G!43), C!39)) | (~apply(G!43, X, tptp_fun_Y_3(X, C!39, G!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, C!39)) | (~apply(G!43, X, Y1)) | (~apply(G!43, X, Y2)) | (~member(X, B!40)) | (~member(Y1, C!39)))))))) | (~(maps(G!43, B!40, C!39) | (~((~member(tptp_fun_X_4(C!39, B!40, G!43), B!40)) | (~![Y: $i] : ((~member(Y, C!39)) | (~apply(G!43, tptp_fun_X_4(C!39, B!40, G!43), Y)))))) | (~((~member(tptp_fun_Y2_5(C!39, B!40, G!43), C!39)) | (~member(tptp_fun_Y1_6(C!39, B!40, G!43), C!39)) | (~member(tptp_fun_X_7(C!39, B!40, G!43), B!40)) | (~apply(G!43, tptp_fun_X_7(C!39, B!40, G!43), tptp_fun_Y2_5(C!39, B!40, G!43))) | (~apply(G!43, tptp_fun_X_7(C!39, B!40, G!43), tptp_fun_Y1_6(C!39, B!40, G!43))) | (tptp_fun_Y1_6(C!39, B!40, G!43) = tptp_fun_Y2_5(C!39, B!40, G!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(G!43, B!40, C!39)) | (~((~![X: $i] : ((~member(X, B!40)) | (~((~member(tptp_fun_Y_3(X, C!39, G!43), C!39)) | (~apply(G!43, X, tptp_fun_Y_3(X, C!39, G!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, C!39)) | (~apply(G!43, X, Y1)) | (~apply(G!43, X, Y2)) | (~member(X, B!40)) | (~member(Y1, C!39)))))))) | (~(maps(G!43, B!40, C!39) | (~((~member(tptp_fun_X_4(C!39, B!40, G!43), B!40)) | (~![Y: $i] : ((~member(Y, C!39)) | (~apply(G!43, tptp_fun_X_4(C!39, B!40, G!43), Y)))))) | (~((~member(tptp_fun_Y2_5(C!39, B!40, G!43), C!39)) | (~member(tptp_fun_Y1_6(C!39, B!40, G!43), C!39)) | (~member(tptp_fun_X_7(C!39, B!40, G!43), B!40)) | (~apply(G!43, tptp_fun_X_7(C!39, B!40, G!43), tptp_fun_Y2_5(C!39, B!40, G!43))) | (~apply(G!43, tptp_fun_X_7(C!39, B!40, G!43), tptp_fun_Y1_6(C!39, B!40, G!43))) | (tptp_fun_Y1_6(C!39, B!40, G!43) = tptp_fun_Y2_5(C!39, B!40, G!43)))))))))),
% 21.89/22.04 inference(rewrite,[status(thm)],[])).
% 21.89/22.04 tff(209,plain,
% 21.89/22.04 ((~((~((~maps(G!43, B!40, C!39)) | (~((~![X: $i] : ((~member(X, B!40)) | (~((~member(tptp_fun_Y_3(X, C!39, G!43), C!39)) | (~apply(G!43, X, tptp_fun_Y_3(X, C!39, G!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G!43, X, Y1)) | (~apply(G!43, X, Y2)) | (~member(X, B!40)) | (~member(Y1, C!39)) | (~member(Y2, C!39)))))))) | (~(maps(G!43, B!40, C!39) | (~((tptp_fun_Y1_6(C!39, B!40, G!43) = tptp_fun_Y2_5(C!39, B!40, G!43)) | (~apply(G!43, tptp_fun_X_7(C!39, B!40, G!43), tptp_fun_Y1_6(C!39, B!40, G!43))) | (~apply(G!43, tptp_fun_X_7(C!39, B!40, G!43), tptp_fun_Y2_5(C!39, B!40, G!43))) | (~member(tptp_fun_X_7(C!39, B!40, G!43), B!40)) | (~member(tptp_fun_Y1_6(C!39, B!40, G!43), C!39)) | (~member(tptp_fun_Y2_5(C!39, B!40, G!43), C!39)))) | (~((~member(tptp_fun_X_4(C!39, B!40, G!43), B!40)) | (~![Y: $i] : ((~member(Y, C!39)) | (~apply(G!43, tptp_fun_X_4(C!39, B!40, G!43), Y)))))))))) <=> (~((~((~maps(G!43, B!40, C!39)) | (~((~![X: $i] : ((~member(X, B!40)) | (~((~member(tptp_fun_Y_3(X, C!39, G!43), C!39)) | (~apply(G!43, X, tptp_fun_Y_3(X, C!39, G!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, C!39)) | (~apply(G!43, X, Y1)) | (~apply(G!43, X, Y2)) | (~member(X, B!40)) | (~member(Y1, C!39)))))))) | (~(maps(G!43, B!40, C!39) | (~((~member(tptp_fun_X_4(C!39, B!40, G!43), B!40)) | (~![Y: $i] : ((~member(Y, C!39)) | (~apply(G!43, tptp_fun_X_4(C!39, B!40, G!43), Y)))))) | (~((~member(tptp_fun_Y2_5(C!39, B!40, G!43), C!39)) | (~member(tptp_fun_Y1_6(C!39, B!40, G!43), C!39)) | (~member(tptp_fun_X_7(C!39, B!40, G!43), B!40)) | (~apply(G!43, tptp_fun_X_7(C!39, B!40, G!43), tptp_fun_Y2_5(C!39, B!40, G!43))) | (~apply(G!43, tptp_fun_X_7(C!39, B!40, G!43), tptp_fun_Y1_6(C!39, B!40, G!43))) | (tptp_fun_Y1_6(C!39, B!40, G!43) = tptp_fun_Y2_5(C!39, B!40, G!43))))))))),
% 21.89/22.04 inference(rewrite,[status(thm)],[])).
% 21.89/22.04 tff(210,plain,
% 21.89/22.04 (((~![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!43, B!40, C!39)) | (~((~![X: $i] : ((~member(X, B!40)) | (~((~member(tptp_fun_Y_3(X, C!39, G!43), C!39)) | (~apply(G!43, X, tptp_fun_Y_3(X, C!39, G!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G!43, X, Y1)) | (~apply(G!43, X, Y2)) | (~member(X, B!40)) | (~member(Y1, C!39)) | (~member(Y2, C!39)))))))) | (~(maps(G!43, B!40, C!39) | (~((tptp_fun_Y1_6(C!39, B!40, G!43) = tptp_fun_Y2_5(C!39, B!40, G!43)) | (~apply(G!43, tptp_fun_X_7(C!39, B!40, G!43), tptp_fun_Y1_6(C!39, B!40, G!43))) | (~apply(G!43, tptp_fun_X_7(C!39, B!40, G!43), tptp_fun_Y2_5(C!39, B!40, G!43))) | (~member(tptp_fun_X_7(C!39, B!40, G!43), B!40)) | (~member(tptp_fun_Y1_6(C!39, B!40, G!43), C!39)) | (~member(tptp_fun_Y2_5(C!39, B!40, G!43), C!39)))) | (~((~member(tptp_fun_X_4(C!39, B!40, G!43), B!40)) | (~![Y: $i] : ((~member(Y, C!39)) | (~apply(G!43, tptp_fun_X_4(C!39, B!40, G!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(G!43, B!40, C!39)) | (~((~![X: $i] : ((~member(X, B!40)) | (~((~member(tptp_fun_Y_3(X, C!39, G!43), C!39)) | (~apply(G!43, X, tptp_fun_Y_3(X, C!39, G!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, C!39)) | (~apply(G!43, X, Y1)) | (~apply(G!43, X, Y2)) | (~member(X, B!40)) | (~member(Y1, C!39)))))))) | (~(maps(G!43, B!40, C!39) | (~((~member(tptp_fun_X_4(C!39, B!40, G!43), B!40)) | (~![Y: $i] : ((~member(Y, C!39)) | (~apply(G!43, tptp_fun_X_4(C!39, B!40, G!43), Y)))))) | (~((~member(tptp_fun_Y2_5(C!39, B!40, G!43), C!39)) | (~member(tptp_fun_Y1_6(C!39, B!40, G!43), C!39)) | (~member(tptp_fun_X_7(C!39, B!40, G!43), B!40)) | (~apply(G!43, tptp_fun_X_7(C!39, B!40, G!43), tptp_fun_Y2_5(C!39, B!40, G!43))) | (~apply(G!43, tptp_fun_X_7(C!39, B!40, G!43), tptp_fun_Y1_6(C!39, B!40, G!43))) | (tptp_fun_Y1_6(C!39, B!40, G!43) = tptp_fun_Y2_5(C!39, B!40, G!43)))))))))),
% 21.89/22.04 inference(monotonicity,[status(thm)],[209])).
% 21.89/22.04 tff(211,plain,
% 21.89/22.04 (((~![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!43, B!40, C!39)) | (~((~![X: $i] : ((~member(X, B!40)) | (~((~member(tptp_fun_Y_3(X, C!39, G!43), C!39)) | (~apply(G!43, X, tptp_fun_Y_3(X, C!39, G!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G!43, X, Y1)) | (~apply(G!43, X, Y2)) | (~member(X, B!40)) | (~member(Y1, C!39)) | (~member(Y2, C!39)))))))) | (~(maps(G!43, B!40, C!39) | (~((tptp_fun_Y1_6(C!39, B!40, G!43) = tptp_fun_Y2_5(C!39, B!40, G!43)) | (~apply(G!43, tptp_fun_X_7(C!39, B!40, G!43), tptp_fun_Y1_6(C!39, B!40, G!43))) | (~apply(G!43, tptp_fun_X_7(C!39, B!40, G!43), tptp_fun_Y2_5(C!39, B!40, G!43))) | (~member(tptp_fun_X_7(C!39, B!40, G!43), B!40)) | (~member(tptp_fun_Y1_6(C!39, B!40, G!43), C!39)) | (~member(tptp_fun_Y2_5(C!39, B!40, G!43), C!39)))) | (~((~member(tptp_fun_X_4(C!39, B!40, G!43), B!40)) | (~![Y: $i] : ((~member(Y, C!39)) | (~apply(G!43, tptp_fun_X_4(C!39, B!40, G!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(G!43, B!40, C!39)) | (~((~![X: $i] : ((~member(X, B!40)) | (~((~member(tptp_fun_Y_3(X, C!39, G!43), C!39)) | (~apply(G!43, X, tptp_fun_Y_3(X, C!39, G!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, C!39)) | (~apply(G!43, X, Y1)) | (~apply(G!43, X, Y2)) | (~member(X, B!40)) | (~member(Y1, C!39)))))))) | (~(maps(G!43, B!40, C!39) | (~((~member(tptp_fun_X_4(C!39, B!40, G!43), B!40)) | (~![Y: $i] : ((~member(Y, C!39)) | (~apply(G!43, tptp_fun_X_4(C!39, B!40, G!43), Y)))))) | (~((~member(tptp_fun_Y2_5(C!39, B!40, G!43), C!39)) | (~member(tptp_fun_Y1_6(C!39, B!40, G!43), C!39)) | (~member(tptp_fun_X_7(C!39, B!40, G!43), B!40)) | (~apply(G!43, tptp_fun_X_7(C!39, B!40, G!43), tptp_fun_Y2_5(C!39, B!40, G!43))) | (~apply(G!43, tptp_fun_X_7(C!39, B!40, G!43), tptp_fun_Y1_6(C!39, B!40, G!43))) | (tptp_fun_Y1_6(C!39, B!40, G!43) = tptp_fun_Y2_5(C!39, B!40, G!43)))))))))),
% 21.89/22.04 inference(transitivity,[status(thm)],[210, 208])).
% 21.89/22.04 tff(212,plain,
% 21.89/22.04 ((~![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!43, B!40, C!39)) | (~((~![X: $i] : ((~member(X, B!40)) | (~((~member(tptp_fun_Y_3(X, C!39, G!43), C!39)) | (~apply(G!43, X, tptp_fun_Y_3(X, C!39, G!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G!43, X, Y1)) | (~apply(G!43, X, Y2)) | (~member(X, B!40)) | (~member(Y1, C!39)) | (~member(Y2, C!39)))))))) | (~(maps(G!43, B!40, C!39) | (~((tptp_fun_Y1_6(C!39, B!40, G!43) = tptp_fun_Y2_5(C!39, B!40, G!43)) | (~apply(G!43, tptp_fun_X_7(C!39, B!40, G!43), tptp_fun_Y1_6(C!39, B!40, G!43))) | (~apply(G!43, tptp_fun_X_7(C!39, B!40, G!43), tptp_fun_Y2_5(C!39, B!40, G!43))) | (~member(tptp_fun_X_7(C!39, B!40, G!43), B!40)) | (~member(tptp_fun_Y1_6(C!39, B!40, G!43), C!39)) | (~member(tptp_fun_Y2_5(C!39, B!40, G!43), C!39)))) | (~((~member(tptp_fun_X_4(C!39, B!40, G!43), B!40)) | (~![Y: $i] : ((~member(Y, C!39)) | (~apply(G!43, tptp_fun_X_4(C!39, B!40, G!43), Y))))))))))),
% 21.89/22.04 inference(quant_inst,[status(thm)],[])).
% 21.89/22.04 tff(213,plain,
% 21.89/22.04 ((~![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!43, B!40, C!39)) | (~((~![X: $i] : ((~member(X, B!40)) | (~((~member(tptp_fun_Y_3(X, C!39, G!43), C!39)) | (~apply(G!43, X, tptp_fun_Y_3(X, C!39, G!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, C!39)) | (~apply(G!43, X, Y1)) | (~apply(G!43, X, Y2)) | (~member(X, B!40)) | (~member(Y1, C!39)))))))) | (~(maps(G!43, B!40, C!39) | (~((~member(tptp_fun_X_4(C!39, B!40, G!43), B!40)) | (~![Y: $i] : ((~member(Y, C!39)) | (~apply(G!43, tptp_fun_X_4(C!39, B!40, G!43), Y)))))) | (~((~member(tptp_fun_Y2_5(C!39, B!40, G!43), C!39)) | (~member(tptp_fun_Y1_6(C!39, B!40, G!43), C!39)) | (~member(tptp_fun_X_7(C!39, B!40, G!43), B!40)) | (~apply(G!43, tptp_fun_X_7(C!39, B!40, G!43), tptp_fun_Y2_5(C!39, B!40, G!43))) | (~apply(G!43, tptp_fun_X_7(C!39, B!40, G!43), tptp_fun_Y1_6(C!39, B!40, G!43))) | (tptp_fun_Y1_6(C!39, B!40, G!43) = tptp_fun_Y2_5(C!39, B!40, G!43))))))))),
% 21.89/22.05 inference(modus_ponens,[status(thm)],[212, 211])).
% 21.89/22.05 tff(214,plain,
% 21.89/22.05 (~((~((~maps(G!43, B!40, C!39)) | (~((~![X: $i] : ((~member(X, B!40)) | (~((~member(tptp_fun_Y_3(X, C!39, G!43), C!39)) | (~apply(G!43, X, tptp_fun_Y_3(X, C!39, G!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, C!39)) | (~apply(G!43, X, Y1)) | (~apply(G!43, X, Y2)) | (~member(X, B!40)) | (~member(Y1, C!39)))))))) | (~(maps(G!43, B!40, C!39) | (~((~member(tptp_fun_X_4(C!39, B!40, G!43), B!40)) | (~![Y: $i] : ((~member(Y, C!39)) | (~apply(G!43, tptp_fun_X_4(C!39, B!40, G!43), Y)))))) | (~((~member(tptp_fun_Y2_5(C!39, B!40, G!43), C!39)) | (~member(tptp_fun_Y1_6(C!39, B!40, G!43), C!39)) | (~member(tptp_fun_X_7(C!39, B!40, G!43), B!40)) | (~apply(G!43, tptp_fun_X_7(C!39, B!40, G!43), tptp_fun_Y2_5(C!39, B!40, G!43))) | (~apply(G!43, tptp_fun_X_7(C!39, B!40, G!43), tptp_fun_Y1_6(C!39, B!40, G!43))) | (tptp_fun_Y1_6(C!39, B!40, G!43) = tptp_fun_Y2_5(C!39, B!40, G!43)))))))),
% 21.89/22.05 inference(unit_resolution,[status(thm)],[213, 207])).
% 21.89/22.05 tff(215,plain,
% 21.89/22.05 (((~((~maps(G!43, B!40, C!39)) | (~((~![X: $i] : ((~member(X, B!40)) | (~((~member(tptp_fun_Y_3(X, C!39, G!43), C!39)) | (~apply(G!43, X, tptp_fun_Y_3(X, C!39, G!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, C!39)) | (~apply(G!43, X, Y1)) | (~apply(G!43, X, Y2)) | (~member(X, B!40)) | (~member(Y1, C!39)))))))) | (~(maps(G!43, B!40, C!39) | (~((~member(tptp_fun_X_4(C!39, B!40, G!43), B!40)) | (~![Y: $i] : ((~member(Y, C!39)) | (~apply(G!43, tptp_fun_X_4(C!39, B!40, G!43), Y)))))) | (~((~member(tptp_fun_Y2_5(C!39, B!40, G!43), C!39)) | (~member(tptp_fun_Y1_6(C!39, B!40, G!43), C!39)) | (~member(tptp_fun_X_7(C!39, B!40, G!43), B!40)) | (~apply(G!43, tptp_fun_X_7(C!39, B!40, G!43), tptp_fun_Y2_5(C!39, B!40, G!43))) | (~apply(G!43, tptp_fun_X_7(C!39, B!40, G!43), tptp_fun_Y1_6(C!39, B!40, G!43))) | (tptp_fun_Y1_6(C!39, B!40, G!43) = tptp_fun_Y2_5(C!39, B!40, G!43))))))) | ((~maps(G!43, B!40, C!39)) | (~((~![X: $i] : ((~member(X, B!40)) | (~((~member(tptp_fun_Y_3(X, C!39, G!43), C!39)) | (~apply(G!43, X, tptp_fun_Y_3(X, C!39, G!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, C!39)) | (~apply(G!43, X, Y1)) | (~apply(G!43, X, Y2)) | (~member(X, B!40)) | (~member(Y1, C!39)))))))),
% 21.89/22.05 inference(tautology,[status(thm)],[])).
% 21.89/22.05 tff(216,plain,
% 21.89/22.05 ((~maps(G!43, B!40, C!39)) | (~((~![X: $i] : ((~member(X, B!40)) | (~((~member(tptp_fun_Y_3(X, C!39, G!43), C!39)) | (~apply(G!43, X, tptp_fun_Y_3(X, C!39, G!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, C!39)) | (~apply(G!43, X, Y1)) | (~apply(G!43, X, Y2)) | (~member(X, B!40)) | (~member(Y1, C!39))))))),
% 21.89/22.05 inference(unit_resolution,[status(thm)],[215, 214])).
% 21.89/22.05 tff(217,plain,
% 21.89/22.05 (maps(G!43, B!40, C!39)),
% 21.89/22.05 inference(and_elim,[status(thm)],[75])).
% 21.89/22.05 tff(218,plain,
% 21.89/22.05 ((~((~maps(G!43, B!40, C!39)) | (~((~![X: $i] : ((~member(X, B!40)) | (~((~member(tptp_fun_Y_3(X, C!39, G!43), C!39)) | (~apply(G!43, X, tptp_fun_Y_3(X, C!39, G!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, C!39)) | (~apply(G!43, X, Y1)) | (~apply(G!43, X, Y2)) | (~member(X, B!40)) | (~member(Y1, C!39)))))))) | (~maps(G!43, B!40, C!39)) | (~((~![X: $i] : ((~member(X, B!40)) | (~((~member(tptp_fun_Y_3(X, C!39, G!43), C!39)) | (~apply(G!43, X, tptp_fun_Y_3(X, C!39, G!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, C!39)) | (~apply(G!43, X, Y1)) | (~apply(G!43, X, Y2)) | (~member(X, B!40)) | (~member(Y1, C!39))))))),
% 21.89/22.05 inference(tautology,[status(thm)],[])).
% 21.89/22.05 tff(219,plain,
% 21.89/22.05 ((~((~maps(G!43, B!40, C!39)) | (~((~![X: $i] : ((~member(X, B!40)) | (~((~member(tptp_fun_Y_3(X, C!39, G!43), C!39)) | (~apply(G!43, X, tptp_fun_Y_3(X, C!39, G!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, C!39)) | (~apply(G!43, X, Y1)) | (~apply(G!43, X, Y2)) | (~member(X, B!40)) | (~member(Y1, C!39)))))))) | (~((~![X: $i] : ((~member(X, B!40)) | (~((~member(tptp_fun_Y_3(X, C!39, G!43), C!39)) | (~apply(G!43, X, tptp_fun_Y_3(X, C!39, G!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, C!39)) | (~apply(G!43, X, Y1)) | (~apply(G!43, X, Y2)) | (~member(X, B!40)) | (~member(Y1, C!39))))))),
% 21.89/22.05 inference(unit_resolution,[status(thm)],[218, 217])).
% 21.89/22.05 tff(220,plain,
% 21.89/22.05 (~((~![X: $i] : ((~member(X, B!40)) | (~((~member(tptp_fun_Y_3(X, C!39, G!43), C!39)) | (~apply(G!43, X, tptp_fun_Y_3(X, C!39, G!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, C!39)) | (~apply(G!43, X, Y1)) | (~apply(G!43, X, Y2)) | (~member(X, B!40)) | (~member(Y1, C!39)))))),
% 21.89/22.05 inference(unit_resolution,[status(thm)],[219, 216])).
% 21.89/22.05 tff(221,plain,
% 21.89/22.05 (((~![X: $i] : ((~member(X, B!40)) | (~((~member(tptp_fun_Y_3(X, C!39, G!43), C!39)) | (~apply(G!43, X, tptp_fun_Y_3(X, C!39, G!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, C!39)) | (~apply(G!43, X, Y1)) | (~apply(G!43, X, Y2)) | (~member(X, B!40)) | (~member(Y1, C!39))))) | ![X: $i] : ((~member(X, B!40)) | (~((~member(tptp_fun_Y_3(X, C!39, G!43), C!39)) | (~apply(G!43, X, tptp_fun_Y_3(X, C!39, G!43))))))),
% 21.89/22.05 inference(tautology,[status(thm)],[])).
% 21.89/22.05 tff(222,plain,
% 21.89/22.05 (![X: $i] : ((~member(X, B!40)) | (~((~member(tptp_fun_Y_3(X, C!39, G!43), C!39)) | (~apply(G!43, X, tptp_fun_Y_3(X, C!39, G!43))))))),
% 21.89/22.05 inference(unit_resolution,[status(thm)],[221, 220])).
% 21.89/22.05 tff(223,plain,
% 21.89/22.05 (((~![X: $i] : ((~member(X, B!40)) | (~((~member(tptp_fun_Y_3(X, C!39, G!43), C!39)) | (~apply(G!43, X, tptp_fun_Y_3(X, C!39, G!43))))))) | ((~member(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), B!40)) | (~((~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43), C!39)) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43))))))) <=> ((~![X: $i] : ((~member(X, B!40)) | (~((~member(tptp_fun_Y_3(X, C!39, G!43), C!39)) | (~apply(G!43, X, tptp_fun_Y_3(X, C!39, G!43))))))) | (~member(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), B!40)) | (~((~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43), C!39)) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43))))))),
% 21.89/22.05 inference(rewrite,[status(thm)],[])).
% 21.89/22.05 tff(224,plain,
% 21.89/22.05 ((~![X: $i] : ((~member(X, B!40)) | (~((~member(tptp_fun_Y_3(X, C!39, G!43), C!39)) | (~apply(G!43, X, tptp_fun_Y_3(X, C!39, G!43))))))) | ((~member(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), B!40)) | (~((~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43), C!39)) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43))))))),
% 21.89/22.05 inference(quant_inst,[status(thm)],[])).
% 21.89/22.05 tff(225,plain,
% 21.89/22.05 ((~![X: $i] : ((~member(X, B!40)) | (~((~member(tptp_fun_Y_3(X, C!39, G!43), C!39)) | (~apply(G!43, X, tptp_fun_Y_3(X, C!39, G!43))))))) | (~member(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), B!40)) | (~((~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43), C!39)) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43)))))),
% 21.89/22.05 inference(modus_ponens,[status(thm)],[224, 223])).
% 21.89/22.05 tff(226,plain,
% 21.89/22.05 (~((~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43), C!39)) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43))))),
% 21.89/22.05 inference(unit_resolution,[status(thm)],[225, 222, 185])).
% 21.89/22.05 tff(227,plain,
% 21.89/22.05 (((~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43), C!39)) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43)))) | apply(G!43, tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43))),
% 21.89/22.05 inference(tautology,[status(thm)],[])).
% 21.89/22.05 tff(228,plain,
% 21.89/22.05 (apply(G!43, tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43))),
% 21.89/22.05 inference(unit_resolution,[status(thm)],[227, 226])).
% 21.89/22.05 tff(229,plain,
% 21.89/22.05 (((~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43), C!39)) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43)))) | member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43), C!39)),
% 21.89/22.05 inference(tautology,[status(thm)],[])).
% 21.89/22.05 tff(230,plain,
% 21.89/22.05 (member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43), C!39)),
% 21.89/22.05 inference(unit_resolution,[status(thm)],[229, 226])).
% 21.89/22.05 tff(231,plain,
% 21.89/22.05 (((~member(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), B!40)) | (~apply(F!44, tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43))) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_X2_17(A!41, C!39, H!42)))) | apply(G!43, tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_X2_17(A!41, C!39, H!42))),
% 21.89/22.05 inference(tautology,[status(thm)],[])).
% 21.89/22.05 tff(232,plain,
% 21.89/22.05 (apply(G!43, tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_X2_17(A!41, C!39, H!42))),
% 21.89/22.05 inference(unit_resolution,[status(thm)],[231, 183])).
% 21.89/22.05 tff(233,plain,
% 21.89/22.05 (((~![X: $i] : ((~member(X, B!40)) | (~((~member(tptp_fun_Y_3(X, C!39, G!43), C!39)) | (~apply(G!43, X, tptp_fun_Y_3(X, C!39, G!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, C!39)) | (~apply(G!43, X, Y1)) | (~apply(G!43, X, Y2)) | (~member(X, B!40)) | (~member(Y1, C!39))))) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, C!39)) | (~apply(G!43, X, Y1)) | (~apply(G!43, X, Y2)) | (~member(X, B!40)) | (~member(Y1, C!39)))),
% 21.89/22.05 inference(tautology,[status(thm)],[])).
% 21.89/22.05 tff(234,plain,
% 21.89/22.05 (![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, C!39)) | (~apply(G!43, X, Y1)) | (~apply(G!43, X, Y2)) | (~member(X, B!40)) | (~member(Y1, C!39)))),
% 21.89/22.05 inference(unit_resolution,[status(thm)],[233, 220])).
% 21.89/22.05 tff(235,plain,
% 21.89/22.05 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, C!39)) | (~apply(G!43, X, Y1)) | (~apply(G!43, X, Y2)) | (~member(X, B!40)) | (~member(Y1, C!39)))) | ((~member(tptp_fun_X2_17(A!41, C!39, H!42), C!39)) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_X2_17(A!41, C!39, H!42))) | (~member(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), B!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43), C!39)) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43))) | (tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43) = tptp_fun_X2_17(A!41, C!39, H!42)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, C!39)) | (~apply(G!43, X, Y1)) | (~apply(G!43, X, Y2)) | (~member(X, B!40)) | (~member(Y1, C!39)))) | (~member(tptp_fun_X2_17(A!41, C!39, H!42), C!39)) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_X2_17(A!41, C!39, H!42))) | (~member(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), B!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43), C!39)) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43))) | (tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43) = tptp_fun_X2_17(A!41, C!39, H!42)))),
% 21.89/22.05 inference(rewrite,[status(thm)],[])).
% 21.89/22.05 tff(236,plain,
% 21.89/22.05 (((tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43) = tptp_fun_X2_17(A!41, C!39, H!42)) | (~member(tptp_fun_X2_17(A!41, C!39, H!42), C!39)) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43))) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_X2_17(A!41, C!39, H!42))) | (~member(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), B!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43), C!39))) <=> ((~member(tptp_fun_X2_17(A!41, C!39, H!42), C!39)) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_X2_17(A!41, C!39, H!42))) | (~member(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), B!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43), C!39)) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43))) | (tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43) = tptp_fun_X2_17(A!41, C!39, H!42)))),
% 21.89/22.06 inference(rewrite,[status(thm)],[])).
% 21.89/22.06 tff(237,plain,
% 21.89/22.06 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, C!39)) | (~apply(G!43, X, Y1)) | (~apply(G!43, X, Y2)) | (~member(X, B!40)) | (~member(Y1, C!39)))) | ((tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43) = tptp_fun_X2_17(A!41, C!39, H!42)) | (~member(tptp_fun_X2_17(A!41, C!39, H!42), C!39)) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43))) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_X2_17(A!41, C!39, H!42))) | (~member(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), B!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43), C!39)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, C!39)) | (~apply(G!43, X, Y1)) | (~apply(G!43, X, Y2)) | (~member(X, B!40)) | (~member(Y1, C!39)))) | ((~member(tptp_fun_X2_17(A!41, C!39, H!42), C!39)) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_X2_17(A!41, C!39, H!42))) | (~member(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), B!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43), C!39)) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43))) | (tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43) = tptp_fun_X2_17(A!41, C!39, H!42))))),
% 21.89/22.06 inference(monotonicity,[status(thm)],[236])).
% 21.89/22.06 tff(238,plain,
% 21.89/22.06 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, C!39)) | (~apply(G!43, X, Y1)) | (~apply(G!43, X, Y2)) | (~member(X, B!40)) | (~member(Y1, C!39)))) | ((tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43) = tptp_fun_X2_17(A!41, C!39, H!42)) | (~member(tptp_fun_X2_17(A!41, C!39, H!42), C!39)) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43))) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_X2_17(A!41, C!39, H!42))) | (~member(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), B!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43), C!39)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, C!39)) | (~apply(G!43, X, Y1)) | (~apply(G!43, X, Y2)) | (~member(X, B!40)) | (~member(Y1, C!39)))) | (~member(tptp_fun_X2_17(A!41, C!39, H!42), C!39)) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_X2_17(A!41, C!39, H!42))) | (~member(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), B!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43), C!39)) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43))) | (tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43) = tptp_fun_X2_17(A!41, C!39, H!42)))),
% 21.89/22.06 inference(transitivity,[status(thm)],[237, 235])).
% 21.89/22.06 tff(239,plain,
% 21.89/22.06 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, C!39)) | (~apply(G!43, X, Y1)) | (~apply(G!43, X, Y2)) | (~member(X, B!40)) | (~member(Y1, C!39)))) | ((tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43) = tptp_fun_X2_17(A!41, C!39, H!42)) | (~member(tptp_fun_X2_17(A!41, C!39, H!42), C!39)) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43))) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_X2_17(A!41, C!39, H!42))) | (~member(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), B!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43), C!39)))),
% 21.89/22.06 inference(quant_inst,[status(thm)],[])).
% 21.89/22.06 tff(240,plain,
% 21.89/22.06 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, C!39)) | (~apply(G!43, X, Y1)) | (~apply(G!43, X, Y2)) | (~member(X, B!40)) | (~member(Y1, C!39)))) | (~member(tptp_fun_X2_17(A!41, C!39, H!42), C!39)) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_X2_17(A!41, C!39, H!42))) | (~member(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), B!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43), C!39)) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43))) | (tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43) = tptp_fun_X2_17(A!41, C!39, H!42))),
% 21.89/22.06 inference(modus_ponens,[status(thm)],[239, 238])).
% 21.89/22.06 tff(241,plain,
% 21.89/22.06 (tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43) = tptp_fun_X2_17(A!41, C!39, H!42)),
% 21.89/22.06 inference(unit_resolution,[status(thm)],[240, 234, 148, 185, 232, 230, 228])).
% 21.89/22.06 tff(242,plain,
% 21.89/22.06 (apply(H!42, tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43), tptp_fun_Y_16(A!41, C!39, H!42)) <=> apply(H!42, tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_Y_16(A!41, C!39, H!42))),
% 21.89/22.06 inference(monotonicity,[status(thm)],[241])).
% 21.89/22.06 tff(243,plain,
% 21.89/22.06 (apply(H!42, tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_Y_16(A!41, C!39, H!42)) <=> apply(H!42, tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43), tptp_fun_Y_16(A!41, C!39, H!42))),
% 21.89/22.06 inference(symmetry,[status(thm)],[242])).
% 21.89/22.06 tff(244,plain,
% 21.89/22.06 (((~member(tptp_fun_X2_17(A!41, C!39, H!42), C!39)) | (~member(tptp_fun_Y_16(A!41, C!39, H!42), A!41)) | (~member(tptp_fun_X1_18(A!41, C!39, H!42), C!39)) | (~apply(H!42, tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_Y_16(A!41, C!39, H!42))) | (~apply(H!42, tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_Y_16(A!41, C!39, H!42))) | (tptp_fun_X1_18(A!41, C!39, H!42) = tptp_fun_X2_17(A!41, C!39, H!42))) | apply(H!42, tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_Y_16(A!41, C!39, H!42))),
% 21.89/22.06 inference(tautology,[status(thm)],[])).
% 21.89/22.06 tff(245,plain,
% 21.89/22.06 (apply(H!42, tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_Y_16(A!41, C!39, H!42))),
% 21.89/22.06 inference(unit_resolution,[status(thm)],[244, 146])).
% 21.89/22.06 tff(246,plain,
% 21.89/22.06 (apply(H!42, tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43), tptp_fun_Y_16(A!41, C!39, H!42))),
% 21.89/22.06 inference(modus_ponens,[status(thm)],[245, 243])).
% 21.89/22.06 tff(247,assumption,((~((~maps(compose_function(H!42, G!43, B!40, C!39, A!41), B!40, A!41)) | (~((~![X: $i] : ((~member(X, B!40)) | (~((~member(tptp_fun_Y_3(X, A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), X, tptp_fun_Y_3(X, A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!41)) | (~member(X, B!40)) | (~member(Y1, A!41)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), X, Y2)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), X, Y1)))))))) | (~(maps(compose_function(H!42, G!43, B!40, C!39, A!41), B!40, A!41) | (~((~member(tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~member(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)) = tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41))) | (~member(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)))) | (~((~member(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~![Y: $i] : ((~member(Y, A!41)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), Y))))))))), introduced(assumption)).
% 21.89/22.06 tff(248,plain,
% 21.89/22.06 (((~![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(compose_function(H!42, G!43, B!40, C!39, A!41), B!40, A!41)) | (~((~![X: $i] : ((~member(X, B!40)) | (~((~member(tptp_fun_Y_3(X, A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), X, tptp_fun_Y_3(X, A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!41)) | (~member(X, B!40)) | (~member(Y1, A!41)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), X, Y2)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), X, Y1)))))))) | (~(maps(compose_function(H!42, G!43, B!40, C!39, A!41), B!40, A!41) | (~((~member(tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~member(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)) = tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41))) | (~member(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)))) | (~((~member(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~![Y: $i] : ((~member(Y, A!41)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), Y))))))))))) <=> ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(compose_function(H!42, G!43, B!40, C!39, A!41), B!40, A!41)) | (~((~![X: $i] : ((~member(X, B!40)) | (~((~member(tptp_fun_Y_3(X, A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), X, tptp_fun_Y_3(X, A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!41)) | (~member(X, B!40)) | (~member(Y1, A!41)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), X, Y2)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), X, Y1)))))))) | (~(maps(compose_function(H!42, G!43, B!40, C!39, A!41), B!40, A!41) | (~((~member(tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~member(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)) = tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41))) | (~member(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)))) | (~((~member(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~![Y: $i] : ((~member(Y, A!41)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), Y)))))))))))),
% 21.89/22.07 inference(rewrite,[status(thm)],[])).
% 21.89/22.07 tff(249,plain,
% 21.89/22.07 ((~((~((~maps(compose_function(H!42, G!43, B!40, C!39, A!41), B!40, A!41)) | (~((~![X: $i] : ((~member(X, B!40)) | (~((~member(tptp_fun_Y_3(X, A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), X, tptp_fun_Y_3(X, A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), X, Y1)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), X, Y2)) | (~member(X, B!40)) | (~member(Y1, A!41)) | (~member(Y2, A!41)))))))) | (~(maps(compose_function(H!42, G!43, B!40, C!39, A!41), B!40, A!41) | (~((tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)) = tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41))) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~member(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~member(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~member(tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)))) | (~((~member(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~![Y: $i] : ((~member(Y, A!41)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), Y)))))))))) <=> (~((~((~maps(compose_function(H!42, G!43, B!40, C!39, A!41), B!40, A!41)) | (~((~![X: $i] : ((~member(X, B!40)) | (~((~member(tptp_fun_Y_3(X, A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), X, tptp_fun_Y_3(X, A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!41)) | (~member(X, B!40)) | (~member(Y1, A!41)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), X, Y2)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), X, Y1)))))))) | (~(maps(compose_function(H!42, G!43, B!40, C!39, A!41), B!40, A!41) | (~((~member(tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~member(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)) = tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41))) | (~member(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)))) | (~((~member(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~![Y: $i] : ((~member(Y, A!41)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), Y))))))))))),
% 21.89/22.07 inference(rewrite,[status(thm)],[])).
% 21.89/22.07 tff(250,plain,
% 21.89/22.07 (((~![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(compose_function(H!42, G!43, B!40, C!39, A!41), B!40, A!41)) | (~((~![X: $i] : ((~member(X, B!40)) | (~((~member(tptp_fun_Y_3(X, A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), X, tptp_fun_Y_3(X, A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), X, Y1)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), X, Y2)) | (~member(X, B!40)) | (~member(Y1, A!41)) | (~member(Y2, A!41)))))))) | (~(maps(compose_function(H!42, G!43, B!40, C!39, A!41), B!40, A!41) | (~((tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)) = tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41))) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~member(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~member(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~member(tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)))) | (~((~member(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~![Y: $i] : ((~member(Y, A!41)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), Y))))))))))) <=> ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(compose_function(H!42, G!43, B!40, C!39, A!41), B!40, A!41)) | (~((~![X: $i] : ((~member(X, B!40)) | (~((~member(tptp_fun_Y_3(X, A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), X, tptp_fun_Y_3(X, A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!41)) | (~member(X, B!40)) | (~member(Y1, A!41)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), X, Y2)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), X, Y1)))))))) | (~(maps(compose_function(H!42, G!43, B!40, C!39, A!41), B!40, A!41) | (~((~member(tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~member(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)) = tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41))) | (~member(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)))) | (~((~member(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~![Y: $i] : ((~member(Y, A!41)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), Y)))))))))))),
% 21.89/22.07 inference(monotonicity,[status(thm)],[249])).
% 21.89/22.07 tff(251,plain,
% 21.89/22.07 (((~![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(compose_function(H!42, G!43, B!40, C!39, A!41), B!40, A!41)) | (~((~![X: $i] : ((~member(X, B!40)) | (~((~member(tptp_fun_Y_3(X, A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), X, tptp_fun_Y_3(X, A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), X, Y1)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), X, Y2)) | (~member(X, B!40)) | (~member(Y1, A!41)) | (~member(Y2, A!41)))))))) | (~(maps(compose_function(H!42, G!43, B!40, C!39, A!41), B!40, A!41) | (~((tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)) = tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41))) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~member(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~member(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~member(tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)))) | (~((~member(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~![Y: $i] : ((~member(Y, A!41)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), Y))))))))))) <=> ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(compose_function(H!42, G!43, B!40, C!39, A!41), B!40, A!41)) | (~((~![X: $i] : ((~member(X, B!40)) | (~((~member(tptp_fun_Y_3(X, A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), X, tptp_fun_Y_3(X, A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!41)) | (~member(X, B!40)) | (~member(Y1, A!41)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), X, Y2)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), X, Y1)))))))) | (~(maps(compose_function(H!42, G!43, B!40, C!39, A!41), B!40, A!41) | (~((~member(tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~member(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)) = tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41))) | (~member(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)))) | (~((~member(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~![Y: $i] : ((~member(Y, A!41)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), Y)))))))))))),
% 21.93/22.07 inference(transitivity,[status(thm)],[250, 248])).
% 21.93/22.07 tff(252,plain,
% 21.93/22.07 ((~![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(compose_function(H!42, G!43, B!40, C!39, A!41), B!40, A!41)) | (~((~![X: $i] : ((~member(X, B!40)) | (~((~member(tptp_fun_Y_3(X, A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), X, tptp_fun_Y_3(X, A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), X, Y1)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), X, Y2)) | (~member(X, B!40)) | (~member(Y1, A!41)) | (~member(Y2, A!41)))))))) | (~(maps(compose_function(H!42, G!43, B!40, C!39, A!41), B!40, A!41) | (~((tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)) = tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41))) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~member(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~member(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~member(tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)))) | (~((~member(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~![Y: $i] : ((~member(Y, A!41)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), Y))))))))))),
% 21.93/22.07 inference(quant_inst,[status(thm)],[])).
% 21.93/22.07 tff(253,plain,
% 21.93/22.07 ((~![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(compose_function(H!42, G!43, B!40, C!39, A!41), B!40, A!41)) | (~((~![X: $i] : ((~member(X, B!40)) | (~((~member(tptp_fun_Y_3(X, A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), X, tptp_fun_Y_3(X, A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!41)) | (~member(X, B!40)) | (~member(Y1, A!41)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), X, Y2)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), X, Y1)))))))) | (~(maps(compose_function(H!42, G!43, B!40, C!39, A!41), B!40, A!41) | (~((~member(tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~member(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)) = tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41))) | (~member(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)))) | (~((~member(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~![Y: $i] : ((~member(Y, A!41)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), Y))))))))))),
% 21.93/22.08 inference(modus_ponens,[status(thm)],[252, 251])).
% 21.93/22.08 tff(254,plain,
% 21.93/22.08 ($false),
% 21.93/22.08 inference(unit_resolution,[status(thm)],[253, 207, 247])).
% 21.93/22.08 tff(255,plain,(~((~((~maps(compose_function(H!42, G!43, B!40, C!39, A!41), B!40, A!41)) | (~((~![X: $i] : ((~member(X, B!40)) | (~((~member(tptp_fun_Y_3(X, A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), X, tptp_fun_Y_3(X, A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!41)) | (~member(X, B!40)) | (~member(Y1, A!41)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), X, Y2)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), X, Y1)))))))) | (~(maps(compose_function(H!42, G!43, B!40, C!39, A!41), B!40, A!41) | (~((~member(tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~member(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)) = tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41))) | (~member(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)))) | (~((~member(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~![Y: $i] : ((~member(Y, A!41)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), Y)))))))))), inference(lemma,lemma(discharge,[]))).
% 21.93/22.08 tff(256,plain,
% 21.93/22.08 (((~((~maps(compose_function(H!42, G!43, B!40, C!39, A!41), B!40, A!41)) | (~((~![X: $i] : ((~member(X, B!40)) | (~((~member(tptp_fun_Y_3(X, A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), X, tptp_fun_Y_3(X, A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!41)) | (~member(X, B!40)) | (~member(Y1, A!41)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), X, Y2)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), X, Y1)))))))) | (~(maps(compose_function(H!42, G!43, B!40, C!39, A!41), B!40, A!41) | (~((~member(tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~member(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)) = tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41))) | (~member(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)))) | (~((~member(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~![Y: $i] : ((~member(Y, A!41)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), Y))))))))) | ((~maps(compose_function(H!42, G!43, B!40, C!39, A!41), B!40, A!41)) | (~((~![X: $i] : ((~member(X, B!40)) | (~((~member(tptp_fun_Y_3(X, A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), X, tptp_fun_Y_3(X, A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!41)) | (~member(X, B!40)) | (~member(Y1, A!41)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), X, Y2)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), X, Y1)))))))),
% 21.93/22.08 inference(tautology,[status(thm)],[])).
% 21.93/22.08 tff(257,plain,
% 21.93/22.08 ((~maps(compose_function(H!42, G!43, B!40, C!39, A!41), B!40, A!41)) | (~((~![X: $i] : ((~member(X, B!40)) | (~((~member(tptp_fun_Y_3(X, A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), X, tptp_fun_Y_3(X, A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!41)) | (~member(X, B!40)) | (~member(Y1, A!41)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), X, Y2)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), X, Y1))))))),
% 21.93/22.08 inference(unit_resolution,[status(thm)],[256, 255])).
% 21.93/22.08 tff(258,plain,
% 21.93/22.08 (((~((~maps(compose_function(H!42, G!43, B!40, C!39, A!41), B!40, A!41)) | (~((~![X: $i] : ((~member(X, B!40)) | (~((~member(tptp_fun_Y_3(X, A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), X, tptp_fun_Y_3(X, A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!41)) | (~member(X, B!40)) | (~member(Y1, A!41)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), X, Y2)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), X, Y1)))))))) | (~(maps(compose_function(H!42, G!43, B!40, C!39, A!41), B!40, A!41) | (~((~member(tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~member(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)) = tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41))) | (~member(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)))) | (~((~member(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~![Y: $i] : ((~member(Y, A!41)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), Y))))))))) | (maps(compose_function(H!42, G!43, B!40, C!39, A!41), B!40, A!41) | (~((~member(tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~member(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)) = tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41))) | (~member(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)))) | (~((~member(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~![Y: $i] : ((~member(Y, A!41)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), Y)))))))),
% 21.93/22.08 inference(tautology,[status(thm)],[])).
% 21.93/22.08 tff(259,plain,
% 21.93/22.08 (maps(compose_function(H!42, G!43, B!40, C!39, A!41), B!40, A!41) | (~((~member(tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~member(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)) = tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41))) | (~member(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)))) | (~((~member(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~![Y: $i] : ((~member(Y, A!41)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), Y))))))),
% 21.93/22.08 inference(unit_resolution,[status(thm)],[258, 255])).
% 21.93/22.08 tff(260,assumption,(~((~member(tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~member(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)) = tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41))) | (~member(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)))), introduced(assumption)).
% 21.93/22.08 tff(261,plain,
% 21.93/22.08 (((~member(tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~member(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)) = tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41))) | (~member(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41))) | member(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)),
% 21.93/22.08 inference(tautology,[status(thm)],[])).
% 21.93/22.08 tff(262,plain,
% 21.93/22.08 (member(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)),
% 21.93/22.08 inference(unit_resolution,[status(thm)],[261, 260])).
% 21.93/22.08 tff(263,plain,
% 21.93/22.08 (((~member(tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~member(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)) = tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41))) | (~member(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41))) | member(tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)),
% 21.93/22.08 inference(tautology,[status(thm)],[])).
% 21.93/22.08 tff(264,plain,
% 21.93/22.08 (member(tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)),
% 21.93/22.08 inference(unit_resolution,[status(thm)],[263, 260])).
% 21.93/22.08 tff(265,plain,
% 21.93/22.08 (((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~member(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~((~((~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), C!39)) | (~apply(G!43, tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42))) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))))))) | (~(apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41))) | ![Y: $i] : ((~member(Y, C!39)) | (~apply(G!43, tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), Y)) | (~apply(H!42, Y, tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41))))))))))) <=> ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | (~member(tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~member(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~((~((~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), C!39)) | (~apply(G!43, tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42))) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))))))) | (~(apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41))) | ![Y: $i] : ((~member(Y, C!39)) | (~apply(G!43, tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), Y)) | (~apply(H!42, Y, tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41))))))))))),
% 21.93/22.08 inference(rewrite,[status(thm)],[])).
% 21.93/22.08 tff(266,plain,
% 21.93/22.08 ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~member(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~((~((~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), C!39)) | (~apply(G!43, tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42))) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))))))) | (~(apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41))) | ![Y: $i] : ((~member(Y, C!39)) | (~apply(G!43, tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), Y)) | (~apply(H!42, Y, tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41))))))))))),
% 21.93/22.08 inference(quant_inst,[status(thm)],[])).
% 21.93/22.08 tff(267,plain,
% 21.93/22.08 ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | (~member(tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~member(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~((~((~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), C!39)) | (~apply(G!43, tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42))) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))))))) | (~(apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41))) | ![Y: $i] : ((~member(Y, C!39)) | (~apply(G!43, tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), Y)) | (~apply(H!42, Y, tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))))))))),
% 21.93/22.09 inference(modus_ponens,[status(thm)],[266, 265])).
% 21.93/22.09 tff(268,plain,
% 21.93/22.09 (~((~((~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), C!39)) | (~apply(G!43, tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42))) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))))))) | (~(apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41))) | ![Y: $i] : ((~member(Y, C!39)) | (~apply(G!43, tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), Y)) | (~apply(H!42, Y, tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41))))))))),
% 21.93/22.09 inference(unit_resolution,[status(thm)],[267, 106, 264, 262])).
% 21.93/22.09 tff(269,plain,
% 21.93/22.09 (((~((~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), C!39)) | (~apply(G!43, tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42))) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))))))) | (~(apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41))) | ![Y: $i] : ((~member(Y, C!39)) | (~apply(G!43, tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), Y)) | (~apply(H!42, Y, tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))))))) | ((~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), C!39)) | (~apply(G!43, tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42))) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))))))),
% 21.93/22.09 inference(tautology,[status(thm)],[])).
% 21.93/22.09 tff(270,plain,
% 21.93/22.09 ((~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), C!39)) | (~apply(G!43, tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42))) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41))))))),
% 21.93/22.09 inference(unit_resolution,[status(thm)],[269, 268])).
% 21.93/22.09 tff(271,plain,
% 21.93/22.09 (((~member(tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~member(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)) = tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41))) | (~member(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41))) | apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))),
% 21.93/22.09 inference(tautology,[status(thm)],[])).
% 21.93/22.09 tff(272,plain,
% 21.93/22.09 (apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))),
% 21.93/22.09 inference(unit_resolution,[status(thm)],[271, 260])).
% 21.93/22.09 tff(273,plain,
% 21.93/22.09 ((~((~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), C!39)) | (~apply(G!43, tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42))) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))))))) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), C!39)) | (~apply(G!43, tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42))) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41))))))),
% 21.93/22.09 inference(tautology,[status(thm)],[])).
% 21.93/22.09 tff(274,plain,
% 21.93/22.09 ((~((~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), C!39)) | (~apply(G!43, tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42))) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))))))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), C!39)) | (~apply(G!43, tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42))) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41))))))),
% 21.93/22.09 inference(unit_resolution,[status(thm)],[273, 272])).
% 21.93/22.09 tff(275,plain,
% 21.93/22.09 (~((~member(tptp_fun_Y_8(tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), C!39)) | (~apply(G!43, tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42))) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))))),
% 21.93/22.09 inference(unit_resolution,[status(thm)],[274, 270])).
% 21.93/22.09 tff(276,plain,
% 21.93/22.09 (((~member(tptp_fun_Y_8(tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), C!39)) | (~apply(G!43, tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42))) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41))))) | apply(G!43, tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42))),
% 21.93/22.09 inference(tautology,[status(thm)],[])).
% 21.93/22.09 tff(277,plain,
% 21.93/22.09 (apply(G!43, tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42))),
% 21.93/22.09 inference(unit_resolution,[status(thm)],[276, 275])).
% 21.93/22.09 tff(278,plain,
% 21.93/22.09 (((~member(tptp_fun_Y_8(tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), C!39)) | (~apply(G!43, tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42))) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41))))) | member(tptp_fun_Y_8(tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), C!39)),
% 21.93/22.09 inference(tautology,[status(thm)],[])).
% 21.93/22.09 tff(279,plain,
% 21.93/22.09 (member(tptp_fun_Y_8(tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), C!39)),
% 21.93/22.09 inference(unit_resolution,[status(thm)],[278, 275])).
% 21.93/22.09 tff(280,plain,
% 21.93/22.09 (((~![X: $i] : ((~member(X, B!40)) | (~((~member(tptp_fun_Y_3(X, C!39, G!43), C!39)) | (~apply(G!43, X, tptp_fun_Y_3(X, C!39, G!43))))))) | ((~member(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~((~member(tptp_fun_Y_3(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), C!39)) | (~apply(G!43, tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_3(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43))))))) <=> ((~![X: $i] : ((~member(X, B!40)) | (~((~member(tptp_fun_Y_3(X, C!39, G!43), C!39)) | (~apply(G!43, X, tptp_fun_Y_3(X, C!39, G!43))))))) | (~member(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~((~member(tptp_fun_Y_3(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), C!39)) | (~apply(G!43, tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_3(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43))))))),
% 21.93/22.09 inference(rewrite,[status(thm)],[])).
% 21.93/22.09 tff(281,plain,
% 21.93/22.09 ((~![X: $i] : ((~member(X, B!40)) | (~((~member(tptp_fun_Y_3(X, C!39, G!43), C!39)) | (~apply(G!43, X, tptp_fun_Y_3(X, C!39, G!43))))))) | ((~member(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~((~member(tptp_fun_Y_3(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), C!39)) | (~apply(G!43, tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_3(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43))))))),
% 21.93/22.10 inference(quant_inst,[status(thm)],[])).
% 21.93/22.10 tff(282,plain,
% 21.93/22.10 ((~![X: $i] : ((~member(X, B!40)) | (~((~member(tptp_fun_Y_3(X, C!39, G!43), C!39)) | (~apply(G!43, X, tptp_fun_Y_3(X, C!39, G!43))))))) | (~member(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~((~member(tptp_fun_Y_3(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), C!39)) | (~apply(G!43, tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_3(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43)))))),
% 21.93/22.10 inference(modus_ponens,[status(thm)],[281, 280])).
% 21.93/22.10 tff(283,plain,
% 21.93/22.10 (~((~member(tptp_fun_Y_3(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), C!39)) | (~apply(G!43, tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_3(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43))))),
% 21.93/22.10 inference(unit_resolution,[status(thm)],[282, 222, 262])).
% 21.93/22.10 tff(284,plain,
% 21.93/22.10 (((~member(tptp_fun_Y_3(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), C!39)) | (~apply(G!43, tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_3(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43)))) | apply(G!43, tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_3(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43))),
% 21.93/22.10 inference(tautology,[status(thm)],[])).
% 21.93/22.10 tff(285,plain,
% 21.93/22.10 (apply(G!43, tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_3(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43))),
% 21.93/22.10 inference(unit_resolution,[status(thm)],[284, 283])).
% 21.93/22.10 tff(286,plain,
% 21.93/22.10 (((~member(tptp_fun_Y_3(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), C!39)) | (~apply(G!43, tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_3(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43)))) | member(tptp_fun_Y_3(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), C!39)),
% 21.93/22.10 inference(tautology,[status(thm)],[])).
% 21.93/22.10 tff(287,plain,
% 21.93/22.10 (member(tptp_fun_Y_3(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), C!39)),
% 21.93/22.10 inference(unit_resolution,[status(thm)],[286, 283])).
% 21.93/22.10 tff(288,plain,
% 21.93/22.10 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, C!39)) | (~apply(G!43, X, Y1)) | (~apply(G!43, X, Y2)) | (~member(X, B!40)) | (~member(Y1, C!39)))) | ((~member(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~apply(G!43, tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42))) | (~apply(G!43, tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_3(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43))) | (~member(tptp_fun_Y_3(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), C!39)) | (~member(tptp_fun_Y_8(tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), C!39)) | (tptp_fun_Y_3(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43) = tptp_fun_Y_8(tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, C!39)) | (~apply(G!43, X, Y1)) | (~apply(G!43, X, Y2)) | (~member(X, B!40)) | (~member(Y1, C!39)))) | (~member(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~apply(G!43, tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42))) | (~apply(G!43, tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_3(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43))) | (~member(tptp_fun_Y_3(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), C!39)) | (~member(tptp_fun_Y_8(tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), C!39)) | (tptp_fun_Y_3(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43) = tptp_fun_Y_8(tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42)))),
% 21.93/22.10 inference(rewrite,[status(thm)],[])).
% 21.93/22.10 tff(289,plain,
% 21.93/22.10 (((tptp_fun_Y_3(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43) = tptp_fun_Y_8(tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42)) | (~member(tptp_fun_Y_8(tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), C!39)) | (~apply(G!43, tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_3(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43))) | (~apply(G!43, tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42))) | (~member(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~member(tptp_fun_Y_3(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), C!39))) <=> ((~member(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~apply(G!43, tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42))) | (~apply(G!43, tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_3(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43))) | (~member(tptp_fun_Y_3(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), C!39)) | (~member(tptp_fun_Y_8(tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), C!39)) | (tptp_fun_Y_3(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43) = tptp_fun_Y_8(tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42)))),
% 21.93/22.10 inference(rewrite,[status(thm)],[])).
% 21.93/22.10 tff(290,plain,
% 21.93/22.10 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, C!39)) | (~apply(G!43, X, Y1)) | (~apply(G!43, X, Y2)) | (~member(X, B!40)) | (~member(Y1, C!39)))) | ((tptp_fun_Y_3(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43) = tptp_fun_Y_8(tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42)) | (~member(tptp_fun_Y_8(tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), C!39)) | (~apply(G!43, tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_3(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43))) | (~apply(G!43, tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42))) | (~member(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~member(tptp_fun_Y_3(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), C!39)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, C!39)) | (~apply(G!43, X, Y1)) | (~apply(G!43, X, Y2)) | (~member(X, B!40)) | (~member(Y1, C!39)))) | ((~member(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~apply(G!43, tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42))) | (~apply(G!43, tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_3(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43))) | (~member(tptp_fun_Y_3(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), C!39)) | (~member(tptp_fun_Y_8(tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), C!39)) | (tptp_fun_Y_3(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43) = tptp_fun_Y_8(tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42))))),
% 21.93/22.10 inference(monotonicity,[status(thm)],[289])).
% 21.93/22.10 tff(291,plain,
% 21.93/22.10 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, C!39)) | (~apply(G!43, X, Y1)) | (~apply(G!43, X, Y2)) | (~member(X, B!40)) | (~member(Y1, C!39)))) | ((tptp_fun_Y_3(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43) = tptp_fun_Y_8(tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42)) | (~member(tptp_fun_Y_8(tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), C!39)) | (~apply(G!43, tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_3(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43))) | (~apply(G!43, tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42))) | (~member(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~member(tptp_fun_Y_3(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), C!39)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, C!39)) | (~apply(G!43, X, Y1)) | (~apply(G!43, X, Y2)) | (~member(X, B!40)) | (~member(Y1, C!39)))) | (~member(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~apply(G!43, tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42))) | (~apply(G!43, tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_3(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43))) | (~member(tptp_fun_Y_3(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), C!39)) | (~member(tptp_fun_Y_8(tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), C!39)) | (tptp_fun_Y_3(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43) = tptp_fun_Y_8(tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42)))),
% 21.93/22.10 inference(transitivity,[status(thm)],[290, 288])).
% 21.93/22.10 tff(292,plain,
% 21.93/22.10 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, C!39)) | (~apply(G!43, X, Y1)) | (~apply(G!43, X, Y2)) | (~member(X, B!40)) | (~member(Y1, C!39)))) | ((tptp_fun_Y_3(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43) = tptp_fun_Y_8(tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42)) | (~member(tptp_fun_Y_8(tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), C!39)) | (~apply(G!43, tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_3(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43))) | (~apply(G!43, tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42))) | (~member(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~member(tptp_fun_Y_3(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), C!39)))),
% 21.93/22.10 inference(quant_inst,[status(thm)],[])).
% 21.93/22.10 tff(293,plain,
% 21.93/22.10 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, C!39)) | (~apply(G!43, X, Y1)) | (~apply(G!43, X, Y2)) | (~member(X, B!40)) | (~member(Y1, C!39)))) | (~member(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~apply(G!43, tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42))) | (~apply(G!43, tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_3(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43))) | (~member(tptp_fun_Y_3(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), C!39)) | (~member(tptp_fun_Y_8(tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), C!39)) | (tptp_fun_Y_3(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43) = tptp_fun_Y_8(tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42))),
% 21.93/22.10 inference(modus_ponens,[status(thm)],[292, 291])).
% 21.93/22.10 tff(294,plain,
% 21.93/22.10 (tptp_fun_Y_3(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43) = tptp_fun_Y_8(tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42)),
% 21.93/22.11 inference(unit_resolution,[status(thm)],[293, 234, 262, 287, 285, 279, 277])).
% 21.93/22.11 tff(295,plain,
% 21.93/22.11 (((~member(tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~member(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)) = tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41))) | (~member(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41))) | member(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)),
% 21.93/22.11 inference(tautology,[status(thm)],[])).
% 21.93/22.11 tff(296,plain,
% 21.93/22.11 (member(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)),
% 21.93/22.11 inference(unit_resolution,[status(thm)],[295, 260])).
% 21.93/22.11 tff(297,plain,
% 21.93/22.11 (((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~member(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~((~(apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41))) | ![Y: $i] : ((~member(Y, C!39)) | (~apply(G!43, tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), Y)) | (~apply(H!42, Y, tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41))))))) | (~((~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), C!39)) | (~apply(G!43, tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42))) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))))))))))) <=> ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | (~member(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~member(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~((~(apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41))) | ![Y: $i] : ((~member(Y, C!39)) | (~apply(G!43, tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), Y)) | (~apply(H!42, Y, tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41))))))) | (~((~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), C!39)) | (~apply(G!43, tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42))) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))))))))))),
% 21.93/22.11 inference(rewrite,[status(thm)],[])).
% 21.93/22.11 tff(298,plain,
% 21.93/22.11 (((~member(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~member(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~((~(apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41))) | ![Y: $i] : ((~member(Y, C!39)) | (~apply(G!43, tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), Y)) | (~apply(H!42, Y, tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41))))))) | (~((~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), C!39)) | (~apply(G!43, tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42))) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41))))))))))) <=> ((~member(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~member(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~((~(apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41))) | ![Y: $i] : ((~member(Y, C!39)) | (~apply(G!43, tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), Y)) | (~apply(H!42, Y, tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41))))))) | (~((~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), C!39)) | (~apply(G!43, tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42))) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))))))))))),
% 21.93/22.11 inference(rewrite,[status(thm)],[])).
% 21.93/22.11 tff(299,plain,
% 21.93/22.11 ((~((~((~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), C!39)) | (~apply(G!43, tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42))) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))))))) | (~(apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41))) | ![Y: $i] : ((~member(Y, C!39)) | (~apply(G!43, tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), Y)) | (~apply(H!42, Y, tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41))))))))) <=> (~((~(apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41))) | ![Y: $i] : ((~member(Y, C!39)) | (~apply(G!43, tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), Y)) | (~apply(H!42, Y, tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41))))))) | (~((~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), C!39)) | (~apply(G!43, tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42))) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41))))))))))),
% 21.93/22.11 inference(rewrite,[status(thm)],[])).
% 21.93/22.11 tff(300,plain,
% 21.93/22.11 (((~member(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~member(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~((~((~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), C!39)) | (~apply(G!43, tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42))) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))))))) | (~(apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41))) | ![Y: $i] : ((~member(Y, C!39)) | (~apply(G!43, tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), Y)) | (~apply(H!42, Y, tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))))))))) <=> ((~member(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~member(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~((~(apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41))) | ![Y: $i] : ((~member(Y, C!39)) | (~apply(G!43, tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), Y)) | (~apply(H!42, Y, tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41))))))) | (~((~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), C!39)) | (~apply(G!43, tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42))) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))))))))))),
% 21.93/22.11 inference(monotonicity,[status(thm)],[299])).
% 21.93/22.11 tff(301,plain,
% 21.93/22.11 (((~member(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~member(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~((~((~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), C!39)) | (~apply(G!43, tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42))) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))))))) | (~(apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41))) | ![Y: $i] : ((~member(Y, C!39)) | (~apply(G!43, tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), Y)) | (~apply(H!42, Y, tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))))))))) <=> ((~member(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~member(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~((~(apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41))) | ![Y: $i] : ((~member(Y, C!39)) | (~apply(G!43, tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), Y)) | (~apply(H!42, Y, tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41))))))) | (~((~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), C!39)) | (~apply(G!43, tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42))) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))))))))))),
% 21.93/22.12 inference(transitivity,[status(thm)],[300, 298])).
% 21.93/22.12 tff(302,plain,
% 21.93/22.12 (((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~member(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~((~((~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), C!39)) | (~apply(G!43, tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42))) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))))))) | (~(apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41))) | ![Y: $i] : ((~member(Y, C!39)) | (~apply(G!43, tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), Y)) | (~apply(H!42, Y, tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41))))))))))) <=> ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~member(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~((~(apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41))) | ![Y: $i] : ((~member(Y, C!39)) | (~apply(G!43, tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), Y)) | (~apply(H!42, Y, tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41))))))) | (~((~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), C!39)) | (~apply(G!43, tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42))) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41))))))))))))),
% 21.93/22.12 inference(monotonicity,[status(thm)],[301])).
% 21.93/22.12 tff(303,plain,
% 21.93/22.12 (((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~member(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~((~((~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), C!39)) | (~apply(G!43, tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42))) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))))))) | (~(apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41))) | ![Y: $i] : ((~member(Y, C!39)) | (~apply(G!43, tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), Y)) | (~apply(H!42, Y, tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41))))))))))) <=> ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | (~member(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~member(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~((~(apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41))) | ![Y: $i] : ((~member(Y, C!39)) | (~apply(G!43, tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), Y)) | (~apply(H!42, Y, tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41))))))) | (~((~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), C!39)) | (~apply(G!43, tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42))) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))))))))))),
% 21.93/22.12 inference(transitivity,[status(thm)],[302, 297])).
% 21.93/22.12 tff(304,plain,
% 21.93/22.12 ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~member(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~((~((~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), C!39)) | (~apply(G!43, tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42))) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))))))) | (~(apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41))) | ![Y: $i] : ((~member(Y, C!39)) | (~apply(G!43, tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), Y)) | (~apply(H!42, Y, tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41))))))))))),
% 21.93/22.12 inference(quant_inst,[status(thm)],[])).
% 21.93/22.12 tff(305,plain,
% 21.93/22.12 ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | (~member(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~member(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~((~(apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41))) | ![Y: $i] : ((~member(Y, C!39)) | (~apply(G!43, tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), Y)) | (~apply(H!42, Y, tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41))))))) | (~((~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), C!39)) | (~apply(G!43, tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42))) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41))))))))))),
% 21.93/22.12 inference(modus_ponens,[status(thm)],[304, 303])).
% 21.93/22.12 tff(306,plain,
% 21.93/22.12 (~((~(apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41))) | ![Y: $i] : ((~member(Y, C!39)) | (~apply(G!43, tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), Y)) | (~apply(H!42, Y, tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41))))))) | (~((~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), C!39)) | (~apply(G!43, tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42))) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))))))))),
% 21.93/22.12 inference(unit_resolution,[status(thm)],[305, 106, 262, 296])).
% 21.93/22.12 tff(307,plain,
% 21.93/22.12 (((~(apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41))) | ![Y: $i] : ((~member(Y, C!39)) | (~apply(G!43, tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), Y)) | (~apply(H!42, Y, tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41))))))) | (~((~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), C!39)) | (~apply(G!43, tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42))) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41))))))))) | ((~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), C!39)) | (~apply(G!43, tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42))) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))))))),
% 21.93/22.13 inference(tautology,[status(thm)],[])).
% 21.93/22.13 tff(308,plain,
% 21.93/22.13 ((~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), C!39)) | (~apply(G!43, tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42))) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41))))))),
% 21.93/22.13 inference(unit_resolution,[status(thm)],[307, 306])).
% 21.93/22.13 tff(309,plain,
% 21.93/22.13 (((~member(tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~member(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)) = tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41))) | (~member(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41))) | apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))),
% 21.93/22.13 inference(tautology,[status(thm)],[])).
% 21.93/22.13 tff(310,plain,
% 21.93/22.13 (apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))),
% 21.93/22.13 inference(unit_resolution,[status(thm)],[309, 260])).
% 21.93/22.13 tff(311,plain,
% 21.93/22.13 ((~((~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), C!39)) | (~apply(G!43, tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42))) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))))))) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), C!39)) | (~apply(G!43, tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42))) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41))))))),
% 21.93/22.13 inference(tautology,[status(thm)],[])).
% 21.93/22.13 tff(312,plain,
% 21.93/22.13 ((~((~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), C!39)) | (~apply(G!43, tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42))) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))))))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), C!39)) | (~apply(G!43, tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42))) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41))))))),
% 21.93/22.13 inference(unit_resolution,[status(thm)],[311, 310])).
% 21.93/22.13 tff(313,plain,
% 21.93/22.13 (~((~member(tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), C!39)) | (~apply(G!43, tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42))) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))))),
% 21.99/22.13 inference(unit_resolution,[status(thm)],[312, 308])).
% 21.99/22.13 tff(314,plain,
% 21.99/22.13 (((~member(tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), C!39)) | (~apply(G!43, tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42))) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41))))) | apply(G!43, tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42))),
% 21.99/22.13 inference(tautology,[status(thm)],[])).
% 21.99/22.13 tff(315,plain,
% 21.99/22.13 (apply(G!43, tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42))),
% 21.99/22.13 inference(unit_resolution,[status(thm)],[314, 313])).
% 21.99/22.13 tff(316,plain,
% 21.99/22.13 (((~member(tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), C!39)) | (~apply(G!43, tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42))) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41))))) | member(tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), C!39)),
% 21.99/22.13 inference(tautology,[status(thm)],[])).
% 21.99/22.13 tff(317,plain,
% 21.99/22.13 (member(tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), C!39)),
% 21.99/22.13 inference(unit_resolution,[status(thm)],[316, 313])).
% 21.99/22.13 tff(318,plain,
% 21.99/22.13 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, C!39)) | (~apply(G!43, X, Y1)) | (~apply(G!43, X, Y2)) | (~member(X, B!40)) | (~member(Y1, C!39)))) | ((~member(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~apply(G!43, tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_3(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43))) | (~member(tptp_fun_Y_3(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), C!39)) | (tptp_fun_Y_3(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43) = tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42)) | (~apply(G!43, tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42))) | (~member(tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), C!39)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, C!39)) | (~apply(G!43, X, Y1)) | (~apply(G!43, X, Y2)) | (~member(X, B!40)) | (~member(Y1, C!39)))) | (~member(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~apply(G!43, tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_3(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43))) | (~member(tptp_fun_Y_3(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), C!39)) | (tptp_fun_Y_3(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43) = tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42)) | (~apply(G!43, tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42))) | (~member(tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), C!39)))),
% 21.99/22.13 inference(rewrite,[status(thm)],[])).
% 21.99/22.13 tff(319,plain,
% 21.99/22.13 (((tptp_fun_Y_3(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43) = tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42)) | (~member(tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), C!39)) | (~apply(G!43, tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_3(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43))) | (~apply(G!43, tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42))) | (~member(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~member(tptp_fun_Y_3(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), C!39))) <=> ((~member(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~apply(G!43, tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_3(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43))) | (~member(tptp_fun_Y_3(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), C!39)) | (tptp_fun_Y_3(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43) = tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42)) | (~apply(G!43, tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42))) | (~member(tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), C!39)))),
% 21.99/22.13 inference(rewrite,[status(thm)],[])).
% 21.99/22.13 tff(320,plain,
% 21.99/22.14 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, C!39)) | (~apply(G!43, X, Y1)) | (~apply(G!43, X, Y2)) | (~member(X, B!40)) | (~member(Y1, C!39)))) | ((tptp_fun_Y_3(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43) = tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42)) | (~member(tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), C!39)) | (~apply(G!43, tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_3(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43))) | (~apply(G!43, tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42))) | (~member(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~member(tptp_fun_Y_3(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), C!39)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, C!39)) | (~apply(G!43, X, Y1)) | (~apply(G!43, X, Y2)) | (~member(X, B!40)) | (~member(Y1, C!39)))) | ((~member(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~apply(G!43, tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_3(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43))) | (~member(tptp_fun_Y_3(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), C!39)) | (tptp_fun_Y_3(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43) = tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42)) | (~apply(G!43, tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42))) | (~member(tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), C!39))))),
% 21.99/22.14 inference(monotonicity,[status(thm)],[319])).
% 21.99/22.14 tff(321,plain,
% 21.99/22.14 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, C!39)) | (~apply(G!43, X, Y1)) | (~apply(G!43, X, Y2)) | (~member(X, B!40)) | (~member(Y1, C!39)))) | ((tptp_fun_Y_3(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43) = tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42)) | (~member(tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), C!39)) | (~apply(G!43, tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_3(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43))) | (~apply(G!43, tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42))) | (~member(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~member(tptp_fun_Y_3(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), C!39)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, C!39)) | (~apply(G!43, X, Y1)) | (~apply(G!43, X, Y2)) | (~member(X, B!40)) | (~member(Y1, C!39)))) | (~member(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~apply(G!43, tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_3(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43))) | (~member(tptp_fun_Y_3(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), C!39)) | (tptp_fun_Y_3(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43) = tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42)) | (~apply(G!43, tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42))) | (~member(tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), C!39)))),
% 21.99/22.14 inference(transitivity,[status(thm)],[320, 318])).
% 21.99/22.14 tff(322,plain,
% 21.99/22.14 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, C!39)) | (~apply(G!43, X, Y1)) | (~apply(G!43, X, Y2)) | (~member(X, B!40)) | (~member(Y1, C!39)))) | ((tptp_fun_Y_3(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43) = tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42)) | (~member(tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), C!39)) | (~apply(G!43, tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_3(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43))) | (~apply(G!43, tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42))) | (~member(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~member(tptp_fun_Y_3(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), C!39)))),
% 21.99/22.14 inference(quant_inst,[status(thm)],[])).
% 21.99/22.14 tff(323,plain,
% 21.99/22.14 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, C!39)) | (~apply(G!43, X, Y1)) | (~apply(G!43, X, Y2)) | (~member(X, B!40)) | (~member(Y1, C!39)))) | (~member(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~apply(G!43, tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_3(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43))) | (~member(tptp_fun_Y_3(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), C!39)) | (tptp_fun_Y_3(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43) = tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42)) | (~apply(G!43, tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42))) | (~member(tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), C!39))),
% 21.99/22.14 inference(modus_ponens,[status(thm)],[322, 321])).
% 21.99/22.14 tff(324,plain,
% 21.99/22.14 (tptp_fun_Y_3(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43) = tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42)),
% 21.99/22.14 inference(unit_resolution,[status(thm)],[323, 234, 262, 287, 285, 317, 315])).
% 21.99/22.14 tff(325,plain,
% 21.99/22.14 (tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42) = tptp_fun_Y_3(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43)),
% 21.99/22.14 inference(symmetry,[status(thm)],[324])).
% 21.99/22.14 tff(326,plain,
% 21.99/22.14 (tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42) = tptp_fun_Y_8(tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42)),
% 21.99/22.14 inference(transitivity,[status(thm)],[325, 294])).
% 21.99/22.14 tff(327,plain,
% 21.99/22.14 (apply(H!42, tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41))) <=> apply(H!42, tptp_fun_Y_8(tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))),
% 21.99/22.14 inference(monotonicity,[status(thm)],[326])).
% 21.99/22.14 tff(328,plain,
% 21.99/22.14 (apply(H!42, tptp_fun_Y_8(tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41))) <=> apply(H!42, tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))),
% 21.99/22.14 inference(symmetry,[status(thm)],[327])).
% 21.99/22.14 tff(329,plain,
% 21.99/22.14 (((~member(tptp_fun_Y_8(tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), C!39)) | (~apply(G!43, tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42))) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41))))) | apply(H!42, tptp_fun_Y_8(tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))),
% 21.99/22.14 inference(tautology,[status(thm)],[])).
% 21.99/22.14 tff(330,plain,
% 21.99/22.14 (apply(H!42, tptp_fun_Y_8(tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))),
% 21.99/22.14 inference(unit_resolution,[status(thm)],[329, 275])).
% 21.99/22.14 tff(331,plain,
% 21.99/22.14 (apply(H!42, tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))),
% 21.99/22.14 inference(modus_ponens,[status(thm)],[330, 328])).
% 21.99/22.14 tff(332,plain,
% 21.99/22.14 (((~member(tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), C!39)) | (~apply(G!43, tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42))) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41))))) | apply(H!42, tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))),
% 21.99/22.14 inference(tautology,[status(thm)],[])).
% 21.99/22.14 tff(333,plain,
% 21.99/22.14 (apply(H!42, tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))),
% 21.99/22.14 inference(unit_resolution,[status(thm)],[332, 313])).
% 21.99/22.14 tff(334,plain,
% 21.99/22.14 (((~member(tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~member(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)) = tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41))) | (~member(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41))) | (~(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)) = tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41))))),
% 21.99/22.14 inference(tautology,[status(thm)],[])).
% 21.99/22.14 tff(335,plain,
% 21.99/22.14 (~(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)) = tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))),
% 21.99/22.14 inference(unit_resolution,[status(thm)],[334, 260])).
% 21.99/22.14 tff(336,plain,
% 21.99/22.14 (((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(H!42, C!39, A!41)) | (~((~![X: $i] : ((~member(X, C!39)) | (~((~member(tptp_fun_Y_3(X, A!41, H!42), A!41)) | (~apply(H!42, X, tptp_fun_Y_3(X, A!41, H!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!41)) | (~apply(H!42, X, Y1)) | (~apply(H!42, X, Y2)) | (~member(X, C!39)) | (~member(Y1, A!41)))))))) | (~(maps(H!42, C!39, A!41) | (~((~member(tptp_fun_X_4(A!41, C!39, H!42), C!39)) | (~![Y: $i] : ((~member(Y, A!41)) | (~apply(H!42, tptp_fun_X_4(A!41, C!39, H!42), Y)))))) | (~((~member(tptp_fun_Y2_5(A!41, C!39, H!42), A!41)) | (~member(tptp_fun_Y1_6(A!41, C!39, H!42), A!41)) | (~member(tptp_fun_X_7(A!41, C!39, H!42), C!39)) | (~apply(H!42, tptp_fun_X_7(A!41, C!39, H!42), tptp_fun_Y2_5(A!41, C!39, H!42))) | (~apply(H!42, tptp_fun_X_7(A!41, C!39, H!42), tptp_fun_Y1_6(A!41, C!39, H!42))) | (tptp_fun_Y1_6(A!41, C!39, H!42) = tptp_fun_Y2_5(A!41, C!39, H!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(H!42, C!39, A!41)) | (~((~![X: $i] : ((~member(X, C!39)) | (~((~member(tptp_fun_Y_3(X, A!41, H!42), A!41)) | (~apply(H!42, X, tptp_fun_Y_3(X, A!41, H!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!41)) | (~apply(H!42, X, Y1)) | (~apply(H!42, X, Y2)) | (~member(X, C!39)) | (~member(Y1, A!41)))))))) | (~(maps(H!42, C!39, A!41) | (~((~member(tptp_fun_X_4(A!41, C!39, H!42), C!39)) | (~![Y: $i] : ((~member(Y, A!41)) | (~apply(H!42, tptp_fun_X_4(A!41, C!39, H!42), Y)))))) | (~((~member(tptp_fun_Y2_5(A!41, C!39, H!42), A!41)) | (~member(tptp_fun_Y1_6(A!41, C!39, H!42), A!41)) | (~member(tptp_fun_X_7(A!41, C!39, H!42), C!39)) | (~apply(H!42, tptp_fun_X_7(A!41, C!39, H!42), tptp_fun_Y2_5(A!41, C!39, H!42))) | (~apply(H!42, tptp_fun_X_7(A!41, C!39, H!42), tptp_fun_Y1_6(A!41, C!39, H!42))) | (tptp_fun_Y1_6(A!41, C!39, H!42) = tptp_fun_Y2_5(A!41, C!39, H!42)))))))))),
% 21.99/22.14 inference(rewrite,[status(thm)],[])).
% 21.99/22.14 tff(337,plain,
% 21.99/22.14 ((~((~((~maps(H!42, C!39, A!41)) | (~((~![X: $i] : ((~member(X, C!39)) | (~((~member(tptp_fun_Y_3(X, A!41, H!42), A!41)) | (~apply(H!42, X, tptp_fun_Y_3(X, A!41, H!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(H!42, X, Y1)) | (~apply(H!42, X, Y2)) | (~member(X, C!39)) | (~member(Y1, A!41)) | (~member(Y2, A!41)))))))) | (~(maps(H!42, C!39, A!41) | (~((tptp_fun_Y1_6(A!41, C!39, H!42) = tptp_fun_Y2_5(A!41, C!39, H!42)) | (~apply(H!42, tptp_fun_X_7(A!41, C!39, H!42), tptp_fun_Y1_6(A!41, C!39, H!42))) | (~apply(H!42, tptp_fun_X_7(A!41, C!39, H!42), tptp_fun_Y2_5(A!41, C!39, H!42))) | (~member(tptp_fun_X_7(A!41, C!39, H!42), C!39)) | (~member(tptp_fun_Y1_6(A!41, C!39, H!42), A!41)) | (~member(tptp_fun_Y2_5(A!41, C!39, H!42), A!41)))) | (~((~member(tptp_fun_X_4(A!41, C!39, H!42), C!39)) | (~![Y: $i] : ((~member(Y, A!41)) | (~apply(H!42, tptp_fun_X_4(A!41, C!39, H!42), Y)))))))))) <=> (~((~((~maps(H!42, C!39, A!41)) | (~((~![X: $i] : ((~member(X, C!39)) | (~((~member(tptp_fun_Y_3(X, A!41, H!42), A!41)) | (~apply(H!42, X, tptp_fun_Y_3(X, A!41, H!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!41)) | (~apply(H!42, X, Y1)) | (~apply(H!42, X, Y2)) | (~member(X, C!39)) | (~member(Y1, A!41)))))))) | (~(maps(H!42, C!39, A!41) | (~((~member(tptp_fun_X_4(A!41, C!39, H!42), C!39)) | (~![Y: $i] : ((~member(Y, A!41)) | (~apply(H!42, tptp_fun_X_4(A!41, C!39, H!42), Y)))))) | (~((~member(tptp_fun_Y2_5(A!41, C!39, H!42), A!41)) | (~member(tptp_fun_Y1_6(A!41, C!39, H!42), A!41)) | (~member(tptp_fun_X_7(A!41, C!39, H!42), C!39)) | (~apply(H!42, tptp_fun_X_7(A!41, C!39, H!42), tptp_fun_Y2_5(A!41, C!39, H!42))) | (~apply(H!42, tptp_fun_X_7(A!41, C!39, H!42), tptp_fun_Y1_6(A!41, C!39, H!42))) | (tptp_fun_Y1_6(A!41, C!39, H!42) = tptp_fun_Y2_5(A!41, C!39, H!42))))))))),
% 21.99/22.14 inference(rewrite,[status(thm)],[])).
% 21.99/22.14 tff(338,plain,
% 21.99/22.14 (((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(H!42, C!39, A!41)) | (~((~![X: $i] : ((~member(X, C!39)) | (~((~member(tptp_fun_Y_3(X, A!41, H!42), A!41)) | (~apply(H!42, X, tptp_fun_Y_3(X, A!41, H!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(H!42, X, Y1)) | (~apply(H!42, X, Y2)) | (~member(X, C!39)) | (~member(Y1, A!41)) | (~member(Y2, A!41)))))))) | (~(maps(H!42, C!39, A!41) | (~((tptp_fun_Y1_6(A!41, C!39, H!42) = tptp_fun_Y2_5(A!41, C!39, H!42)) | (~apply(H!42, tptp_fun_X_7(A!41, C!39, H!42), tptp_fun_Y1_6(A!41, C!39, H!42))) | (~apply(H!42, tptp_fun_X_7(A!41, C!39, H!42), tptp_fun_Y2_5(A!41, C!39, H!42))) | (~member(tptp_fun_X_7(A!41, C!39, H!42), C!39)) | (~member(tptp_fun_Y1_6(A!41, C!39, H!42), A!41)) | (~member(tptp_fun_Y2_5(A!41, C!39, H!42), A!41)))) | (~((~member(tptp_fun_X_4(A!41, C!39, H!42), C!39)) | (~![Y: $i] : ((~member(Y, A!41)) | (~apply(H!42, tptp_fun_X_4(A!41, C!39, H!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(H!42, C!39, A!41)) | (~((~![X: $i] : ((~member(X, C!39)) | (~((~member(tptp_fun_Y_3(X, A!41, H!42), A!41)) | (~apply(H!42, X, tptp_fun_Y_3(X, A!41, H!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!41)) | (~apply(H!42, X, Y1)) | (~apply(H!42, X, Y2)) | (~member(X, C!39)) | (~member(Y1, A!41)))))))) | (~(maps(H!42, C!39, A!41) | (~((~member(tptp_fun_X_4(A!41, C!39, H!42), C!39)) | (~![Y: $i] : ((~member(Y, A!41)) | (~apply(H!42, tptp_fun_X_4(A!41, C!39, H!42), Y)))))) | (~((~member(tptp_fun_Y2_5(A!41, C!39, H!42), A!41)) | (~member(tptp_fun_Y1_6(A!41, C!39, H!42), A!41)) | (~member(tptp_fun_X_7(A!41, C!39, H!42), C!39)) | (~apply(H!42, tptp_fun_X_7(A!41, C!39, H!42), tptp_fun_Y2_5(A!41, C!39, H!42))) | (~apply(H!42, tptp_fun_X_7(A!41, C!39, H!42), tptp_fun_Y1_6(A!41, C!39, H!42))) | (tptp_fun_Y1_6(A!41, C!39, H!42) = tptp_fun_Y2_5(A!41, C!39, H!42)))))))))),
% 21.99/22.15 inference(monotonicity,[status(thm)],[337])).
% 21.99/22.15 tff(339,plain,
% 21.99/22.15 (((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(H!42, C!39, A!41)) | (~((~![X: $i] : ((~member(X, C!39)) | (~((~member(tptp_fun_Y_3(X, A!41, H!42), A!41)) | (~apply(H!42, X, tptp_fun_Y_3(X, A!41, H!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(H!42, X, Y1)) | (~apply(H!42, X, Y2)) | (~member(X, C!39)) | (~member(Y1, A!41)) | (~member(Y2, A!41)))))))) | (~(maps(H!42, C!39, A!41) | (~((tptp_fun_Y1_6(A!41, C!39, H!42) = tptp_fun_Y2_5(A!41, C!39, H!42)) | (~apply(H!42, tptp_fun_X_7(A!41, C!39, H!42), tptp_fun_Y1_6(A!41, C!39, H!42))) | (~apply(H!42, tptp_fun_X_7(A!41, C!39, H!42), tptp_fun_Y2_5(A!41, C!39, H!42))) | (~member(tptp_fun_X_7(A!41, C!39, H!42), C!39)) | (~member(tptp_fun_Y1_6(A!41, C!39, H!42), A!41)) | (~member(tptp_fun_Y2_5(A!41, C!39, H!42), A!41)))) | (~((~member(tptp_fun_X_4(A!41, C!39, H!42), C!39)) | (~![Y: $i] : ((~member(Y, A!41)) | (~apply(H!42, tptp_fun_X_4(A!41, C!39, H!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(H!42, C!39, A!41)) | (~((~![X: $i] : ((~member(X, C!39)) | (~((~member(tptp_fun_Y_3(X, A!41, H!42), A!41)) | (~apply(H!42, X, tptp_fun_Y_3(X, A!41, H!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!41)) | (~apply(H!42, X, Y1)) | (~apply(H!42, X, Y2)) | (~member(X, C!39)) | (~member(Y1, A!41)))))))) | (~(maps(H!42, C!39, A!41) | (~((~member(tptp_fun_X_4(A!41, C!39, H!42), C!39)) | (~![Y: $i] : ((~member(Y, A!41)) | (~apply(H!42, tptp_fun_X_4(A!41, C!39, H!42), Y)))))) | (~((~member(tptp_fun_Y2_5(A!41, C!39, H!42), A!41)) | (~member(tptp_fun_Y1_6(A!41, C!39, H!42), A!41)) | (~member(tptp_fun_X_7(A!41, C!39, H!42), C!39)) | (~apply(H!42, tptp_fun_X_7(A!41, C!39, H!42), tptp_fun_Y2_5(A!41, C!39, H!42))) | (~apply(H!42, tptp_fun_X_7(A!41, C!39, H!42), tptp_fun_Y1_6(A!41, C!39, H!42))) | (tptp_fun_Y1_6(A!41, C!39, H!42) = tptp_fun_Y2_5(A!41, C!39, H!42)))))))))),
% 21.99/22.15 inference(transitivity,[status(thm)],[338, 336])).
% 21.99/22.15 tff(340,plain,
% 21.99/22.15 ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(H!42, C!39, A!41)) | (~((~![X: $i] : ((~member(X, C!39)) | (~((~member(tptp_fun_Y_3(X, A!41, H!42), A!41)) | (~apply(H!42, X, tptp_fun_Y_3(X, A!41, H!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(H!42, X, Y1)) | (~apply(H!42, X, Y2)) | (~member(X, C!39)) | (~member(Y1, A!41)) | (~member(Y2, A!41)))))))) | (~(maps(H!42, C!39, A!41) | (~((tptp_fun_Y1_6(A!41, C!39, H!42) = tptp_fun_Y2_5(A!41, C!39, H!42)) | (~apply(H!42, tptp_fun_X_7(A!41, C!39, H!42), tptp_fun_Y1_6(A!41, C!39, H!42))) | (~apply(H!42, tptp_fun_X_7(A!41, C!39, H!42), tptp_fun_Y2_5(A!41, C!39, H!42))) | (~member(tptp_fun_X_7(A!41, C!39, H!42), C!39)) | (~member(tptp_fun_Y1_6(A!41, C!39, H!42), A!41)) | (~member(tptp_fun_Y2_5(A!41, C!39, H!42), A!41)))) | (~((~member(tptp_fun_X_4(A!41, C!39, H!42), C!39)) | (~![Y: $i] : ((~member(Y, A!41)) | (~apply(H!42, tptp_fun_X_4(A!41, C!39, H!42), Y))))))))))),
% 21.99/22.15 inference(quant_inst,[status(thm)],[])).
% 21.99/22.15 tff(341,plain,
% 21.99/22.15 ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(H!42, C!39, A!41)) | (~((~![X: $i] : ((~member(X, C!39)) | (~((~member(tptp_fun_Y_3(X, A!41, H!42), A!41)) | (~apply(H!42, X, tptp_fun_Y_3(X, A!41, H!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!41)) | (~apply(H!42, X, Y1)) | (~apply(H!42, X, Y2)) | (~member(X, C!39)) | (~member(Y1, A!41)))))))) | (~(maps(H!42, C!39, A!41) | (~((~member(tptp_fun_X_4(A!41, C!39, H!42), C!39)) | (~![Y: $i] : ((~member(Y, A!41)) | (~apply(H!42, tptp_fun_X_4(A!41, C!39, H!42), Y)))))) | (~((~member(tptp_fun_Y2_5(A!41, C!39, H!42), A!41)) | (~member(tptp_fun_Y1_6(A!41, C!39, H!42), A!41)) | (~member(tptp_fun_X_7(A!41, C!39, H!42), C!39)) | (~apply(H!42, tptp_fun_X_7(A!41, C!39, H!42), tptp_fun_Y2_5(A!41, C!39, H!42))) | (~apply(H!42, tptp_fun_X_7(A!41, C!39, H!42), tptp_fun_Y1_6(A!41, C!39, H!42))) | (tptp_fun_Y1_6(A!41, C!39, H!42) = tptp_fun_Y2_5(A!41, C!39, H!42))))))))),
% 21.99/22.15 inference(modus_ponens,[status(thm)],[340, 339])).
% 21.99/22.15 tff(342,plain,
% 21.99/22.15 (~((~((~maps(H!42, C!39, A!41)) | (~((~![X: $i] : ((~member(X, C!39)) | (~((~member(tptp_fun_Y_3(X, A!41, H!42), A!41)) | (~apply(H!42, X, tptp_fun_Y_3(X, A!41, H!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!41)) | (~apply(H!42, X, Y1)) | (~apply(H!42, X, Y2)) | (~member(X, C!39)) | (~member(Y1, A!41)))))))) | (~(maps(H!42, C!39, A!41) | (~((~member(tptp_fun_X_4(A!41, C!39, H!42), C!39)) | (~![Y: $i] : ((~member(Y, A!41)) | (~apply(H!42, tptp_fun_X_4(A!41, C!39, H!42), Y)))))) | (~((~member(tptp_fun_Y2_5(A!41, C!39, H!42), A!41)) | (~member(tptp_fun_Y1_6(A!41, C!39, H!42), A!41)) | (~member(tptp_fun_X_7(A!41, C!39, H!42), C!39)) | (~apply(H!42, tptp_fun_X_7(A!41, C!39, H!42), tptp_fun_Y2_5(A!41, C!39, H!42))) | (~apply(H!42, tptp_fun_X_7(A!41, C!39, H!42), tptp_fun_Y1_6(A!41, C!39, H!42))) | (tptp_fun_Y1_6(A!41, C!39, H!42) = tptp_fun_Y2_5(A!41, C!39, H!42)))))))),
% 21.99/22.15 inference(unit_resolution,[status(thm)],[341, 207])).
% 21.99/22.15 tff(343,plain,
% 21.99/22.15 (((~((~maps(H!42, C!39, A!41)) | (~((~![X: $i] : ((~member(X, C!39)) | (~((~member(tptp_fun_Y_3(X, A!41, H!42), A!41)) | (~apply(H!42, X, tptp_fun_Y_3(X, A!41, H!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!41)) | (~apply(H!42, X, Y1)) | (~apply(H!42, X, Y2)) | (~member(X, C!39)) | (~member(Y1, A!41)))))))) | (~(maps(H!42, C!39, A!41) | (~((~member(tptp_fun_X_4(A!41, C!39, H!42), C!39)) | (~![Y: $i] : ((~member(Y, A!41)) | (~apply(H!42, tptp_fun_X_4(A!41, C!39, H!42), Y)))))) | (~((~member(tptp_fun_Y2_5(A!41, C!39, H!42), A!41)) | (~member(tptp_fun_Y1_6(A!41, C!39, H!42), A!41)) | (~member(tptp_fun_X_7(A!41, C!39, H!42), C!39)) | (~apply(H!42, tptp_fun_X_7(A!41, C!39, H!42), tptp_fun_Y2_5(A!41, C!39, H!42))) | (~apply(H!42, tptp_fun_X_7(A!41, C!39, H!42), tptp_fun_Y1_6(A!41, C!39, H!42))) | (tptp_fun_Y1_6(A!41, C!39, H!42) = tptp_fun_Y2_5(A!41, C!39, H!42))))))) | ((~maps(H!42, C!39, A!41)) | (~((~![X: $i] : ((~member(X, C!39)) | (~((~member(tptp_fun_Y_3(X, A!41, H!42), A!41)) | (~apply(H!42, X, tptp_fun_Y_3(X, A!41, H!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!41)) | (~apply(H!42, X, Y1)) | (~apply(H!42, X, Y2)) | (~member(X, C!39)) | (~member(Y1, A!41)))))))),
% 21.99/22.15 inference(tautology,[status(thm)],[])).
% 21.99/22.15 tff(344,plain,
% 21.99/22.15 ((~maps(H!42, C!39, A!41)) | (~((~![X: $i] : ((~member(X, C!39)) | (~((~member(tptp_fun_Y_3(X, A!41, H!42), A!41)) | (~apply(H!42, X, tptp_fun_Y_3(X, A!41, H!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!41)) | (~apply(H!42, X, Y1)) | (~apply(H!42, X, Y2)) | (~member(X, C!39)) | (~member(Y1, A!41))))))),
% 21.99/22.15 inference(unit_resolution,[status(thm)],[343, 342])).
% 21.99/22.15 tff(345,plain,
% 21.99/22.15 (maps(H!42, C!39, A!41)),
% 21.99/22.15 inference(and_elim,[status(thm)],[75])).
% 21.99/22.15 tff(346,plain,
% 21.99/22.15 ((~((~maps(H!42, C!39, A!41)) | (~((~![X: $i] : ((~member(X, C!39)) | (~((~member(tptp_fun_Y_3(X, A!41, H!42), A!41)) | (~apply(H!42, X, tptp_fun_Y_3(X, A!41, H!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!41)) | (~apply(H!42, X, Y1)) | (~apply(H!42, X, Y2)) | (~member(X, C!39)) | (~member(Y1, A!41)))))))) | (~maps(H!42, C!39, A!41)) | (~((~![X: $i] : ((~member(X, C!39)) | (~((~member(tptp_fun_Y_3(X, A!41, H!42), A!41)) | (~apply(H!42, X, tptp_fun_Y_3(X, A!41, H!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!41)) | (~apply(H!42, X, Y1)) | (~apply(H!42, X, Y2)) | (~member(X, C!39)) | (~member(Y1, A!41))))))),
% 21.99/22.15 inference(tautology,[status(thm)],[])).
% 21.99/22.15 tff(347,plain,
% 21.99/22.15 ((~((~maps(H!42, C!39, A!41)) | (~((~![X: $i] : ((~member(X, C!39)) | (~((~member(tptp_fun_Y_3(X, A!41, H!42), A!41)) | (~apply(H!42, X, tptp_fun_Y_3(X, A!41, H!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!41)) | (~apply(H!42, X, Y1)) | (~apply(H!42, X, Y2)) | (~member(X, C!39)) | (~member(Y1, A!41)))))))) | (~((~![X: $i] : ((~member(X, C!39)) | (~((~member(tptp_fun_Y_3(X, A!41, H!42), A!41)) | (~apply(H!42, X, tptp_fun_Y_3(X, A!41, H!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!41)) | (~apply(H!42, X, Y1)) | (~apply(H!42, X, Y2)) | (~member(X, C!39)) | (~member(Y1, A!41))))))),
% 21.99/22.15 inference(unit_resolution,[status(thm)],[346, 345])).
% 21.99/22.15 tff(348,plain,
% 21.99/22.15 (~((~![X: $i] : ((~member(X, C!39)) | (~((~member(tptp_fun_Y_3(X, A!41, H!42), A!41)) | (~apply(H!42, X, tptp_fun_Y_3(X, A!41, H!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!41)) | (~apply(H!42, X, Y1)) | (~apply(H!42, X, Y2)) | (~member(X, C!39)) | (~member(Y1, A!41)))))),
% 21.99/22.15 inference(unit_resolution,[status(thm)],[347, 344])).
% 21.99/22.15 tff(349,plain,
% 21.99/22.15 (((~![X: $i] : ((~member(X, C!39)) | (~((~member(tptp_fun_Y_3(X, A!41, H!42), A!41)) | (~apply(H!42, X, tptp_fun_Y_3(X, A!41, H!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!41)) | (~apply(H!42, X, Y1)) | (~apply(H!42, X, Y2)) | (~member(X, C!39)) | (~member(Y1, A!41))))) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!41)) | (~apply(H!42, X, Y1)) | (~apply(H!42, X, Y2)) | (~member(X, C!39)) | (~member(Y1, A!41)))),
% 21.99/22.15 inference(tautology,[status(thm)],[])).
% 21.99/22.15 tff(350,plain,
% 21.99/22.15 (![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!41)) | (~apply(H!42, X, Y1)) | (~apply(H!42, X, Y2)) | (~member(X, C!39)) | (~member(Y1, A!41)))),
% 21.99/22.15 inference(unit_resolution,[status(thm)],[349, 348])).
% 21.99/22.15 tff(351,plain,
% 21.99/22.15 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!41)) | (~apply(H!42, X, Y1)) | (~apply(H!42, X, Y2)) | (~member(X, C!39)) | (~member(Y1, A!41)))) | ((~member(tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)) = tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41))) | (~member(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~member(tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), C!39)) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!41)) | (~apply(H!42, X, Y1)) | (~apply(H!42, X, Y2)) | (~member(X, C!39)) | (~member(Y1, A!41)))) | (~member(tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)) = tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41))) | (~member(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~member(tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), C!39)) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))))),
% 21.99/22.15 inference(rewrite,[status(thm)],[])).
% 21.99/22.15 tff(352,plain,
% 21.99/22.15 (((tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)) = tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41))) | (~member(tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~member(tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), C!39)) | (~member(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41))) <=> ((~member(tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)) = tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41))) | (~member(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~member(tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), C!39)) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))))),
% 21.99/22.15 inference(rewrite,[status(thm)],[])).
% 21.99/22.15 tff(353,plain,
% 21.99/22.15 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!41)) | (~apply(H!42, X, Y1)) | (~apply(H!42, X, Y2)) | (~member(X, C!39)) | (~member(Y1, A!41)))) | ((tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)) = tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41))) | (~member(tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~member(tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), C!39)) | (~member(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!41)) | (~apply(H!42, X, Y1)) | (~apply(H!42, X, Y2)) | (~member(X, C!39)) | (~member(Y1, A!41)))) | ((~member(tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)) = tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41))) | (~member(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~member(tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), C!39)) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41))))))),
% 22.01/22.16 inference(monotonicity,[status(thm)],[352])).
% 22.01/22.16 tff(354,plain,
% 22.01/22.16 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!41)) | (~apply(H!42, X, Y1)) | (~apply(H!42, X, Y2)) | (~member(X, C!39)) | (~member(Y1, A!41)))) | ((tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)) = tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41))) | (~member(tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~member(tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), C!39)) | (~member(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!41)) | (~apply(H!42, X, Y1)) | (~apply(H!42, X, Y2)) | (~member(X, C!39)) | (~member(Y1, A!41)))) | (~member(tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)) = tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41))) | (~member(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~member(tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), C!39)) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))))),
% 22.01/22.16 inference(transitivity,[status(thm)],[353, 351])).
% 22.01/22.16 tff(355,plain,
% 22.01/22.16 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!41)) | (~apply(H!42, X, Y1)) | (~apply(H!42, X, Y2)) | (~member(X, C!39)) | (~member(Y1, A!41)))) | ((tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)) = tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41))) | (~member(tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~member(tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), C!39)) | (~member(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)))),
% 22.01/22.16 inference(quant_inst,[status(thm)],[])).
% 22.01/22.16 tff(356,plain,
% 22.01/22.16 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!41)) | (~apply(H!42, X, Y1)) | (~apply(H!42, X, Y2)) | (~member(X, C!39)) | (~member(Y1, A!41)))) | (~member(tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)) = tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41))) | (~member(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~member(tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), C!39)) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41))))),
% 22.01/22.16 inference(modus_ponens,[status(thm)],[355, 354])).
% 22.01/22.16 tff(357,plain,
% 22.01/22.16 (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))),
% 22.01/22.16 inference(unit_resolution,[status(thm)],[356, 350, 264, 335, 296, 317, 333])).
% 22.01/22.16 tff(358,plain,
% 22.01/22.16 ($false),
% 22.01/22.16 inference(unit_resolution,[status(thm)],[357, 331])).
% 22.01/22.16 tff(359,plain,((~member(tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~member(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)) = tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41))) | (~member(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41))), inference(lemma,lemma(discharge,[]))).
% 22.01/22.16 tff(360,assumption,(~((~member(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~![Y: $i] : ((~member(Y, A!41)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), Y)))))), introduced(assumption)).
% 22.01/22.16 tff(361,plain,
% 22.01/22.16 (((~member(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~![Y: $i] : ((~member(Y, A!41)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), Y))))) | member(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)),
% 22.01/22.16 inference(tautology,[status(thm)],[])).
% 22.01/22.16 tff(362,plain,
% 22.01/22.16 (member(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)),
% 22.01/22.16 inference(unit_resolution,[status(thm)],[361, 360])).
% 22.01/22.16 tff(363,plain,
% 22.01/22.16 (((~![X: $i] : ((~member(X, B!40)) | (~((~member(tptp_fun_Y_3(X, C!39, G!43), C!39)) | (~apply(G!43, X, tptp_fun_Y_3(X, C!39, G!43))))))) | ((~member(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~((~member(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), C!39)) | (~apply(G!43, tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43))))))) <=> ((~![X: $i] : ((~member(X, B!40)) | (~((~member(tptp_fun_Y_3(X, C!39, G!43), C!39)) | (~apply(G!43, X, tptp_fun_Y_3(X, C!39, G!43))))))) | (~member(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~((~member(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), C!39)) | (~apply(G!43, tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43))))))),
% 22.01/22.16 inference(rewrite,[status(thm)],[])).
% 22.01/22.16 tff(364,plain,
% 22.01/22.16 ((~![X: $i] : ((~member(X, B!40)) | (~((~member(tptp_fun_Y_3(X, C!39, G!43), C!39)) | (~apply(G!43, X, tptp_fun_Y_3(X, C!39, G!43))))))) | ((~member(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~((~member(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), C!39)) | (~apply(G!43, tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43))))))),
% 22.01/22.16 inference(quant_inst,[status(thm)],[])).
% 22.01/22.16 tff(365,plain,
% 22.01/22.16 ((~![X: $i] : ((~member(X, B!40)) | (~((~member(tptp_fun_Y_3(X, C!39, G!43), C!39)) | (~apply(G!43, X, tptp_fun_Y_3(X, C!39, G!43))))))) | (~member(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~((~member(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), C!39)) | (~apply(G!43, tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43)))))),
% 22.01/22.16 inference(modus_ponens,[status(thm)],[364, 363])).
% 22.01/22.16 tff(366,plain,
% 22.01/22.16 (~((~member(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), C!39)) | (~apply(G!43, tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43))))),
% 22.01/22.16 inference(unit_resolution,[status(thm)],[365, 222, 362])).
% 22.01/22.16 tff(367,plain,
% 22.01/22.16 (((~member(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), C!39)) | (~apply(G!43, tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43)))) | member(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), C!39)),
% 22.01/22.16 inference(tautology,[status(thm)],[])).
% 22.01/22.16 tff(368,plain,
% 22.01/22.16 (member(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), C!39)),
% 22.01/22.16 inference(unit_resolution,[status(thm)],[367, 366])).
% 22.01/22.16 tff(369,plain,
% 22.01/22.16 (((~![X: $i] : ((~member(X, C!39)) | (~((~member(tptp_fun_Y_3(X, A!41, H!42), A!41)) | (~apply(H!42, X, tptp_fun_Y_3(X, A!41, H!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!41)) | (~apply(H!42, X, Y1)) | (~apply(H!42, X, Y2)) | (~member(X, C!39)) | (~member(Y1, A!41))))) | ![X: $i] : ((~member(X, C!39)) | (~((~member(tptp_fun_Y_3(X, A!41, H!42), A!41)) | (~apply(H!42, X, tptp_fun_Y_3(X, A!41, H!42))))))),
% 22.01/22.16 inference(tautology,[status(thm)],[])).
% 22.01/22.16 tff(370,plain,
% 22.01/22.16 (![X: $i] : ((~member(X, C!39)) | (~((~member(tptp_fun_Y_3(X, A!41, H!42), A!41)) | (~apply(H!42, X, tptp_fun_Y_3(X, A!41, H!42))))))),
% 22.01/22.16 inference(unit_resolution,[status(thm)],[369, 348])).
% 22.01/22.16 tff(371,plain,
% 22.01/22.16 (((~![X: $i] : ((~member(X, C!39)) | (~((~member(tptp_fun_Y_3(X, A!41, H!42), A!41)) | (~apply(H!42, X, tptp_fun_Y_3(X, A!41, H!42))))))) | ((~member(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), C!39)) | (~((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42), A!41)) | (~apply(H!42, tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42))))))) <=> ((~![X: $i] : ((~member(X, C!39)) | (~((~member(tptp_fun_Y_3(X, A!41, H!42), A!41)) | (~apply(H!42, X, tptp_fun_Y_3(X, A!41, H!42))))))) | (~member(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), C!39)) | (~((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42), A!41)) | (~apply(H!42, tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42))))))),
% 22.01/22.16 inference(rewrite,[status(thm)],[])).
% 22.01/22.16 tff(372,plain,
% 22.01/22.16 ((~![X: $i] : ((~member(X, C!39)) | (~((~member(tptp_fun_Y_3(X, A!41, H!42), A!41)) | (~apply(H!42, X, tptp_fun_Y_3(X, A!41, H!42))))))) | ((~member(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), C!39)) | (~((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42), A!41)) | (~apply(H!42, tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42))))))),
% 22.01/22.16 inference(quant_inst,[status(thm)],[])).
% 22.01/22.16 tff(373,plain,
% 22.01/22.16 ((~![X: $i] : ((~member(X, C!39)) | (~((~member(tptp_fun_Y_3(X, A!41, H!42), A!41)) | (~apply(H!42, X, tptp_fun_Y_3(X, A!41, H!42))))))) | (~member(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), C!39)) | (~((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42), A!41)) | (~apply(H!42, tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42)))))),
% 22.01/22.16 inference(modus_ponens,[status(thm)],[372, 371])).
% 22.01/22.16 tff(374,plain,
% 22.01/22.16 (~((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42), A!41)) | (~apply(H!42, tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42))))),
% 22.01/22.16 inference(unit_resolution,[status(thm)],[373, 370, 368])).
% 22.01/22.16 tff(375,plain,
% 22.01/22.16 (((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42), A!41)) | (~apply(H!42, tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42)))) | member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42), A!41)),
% 22.01/22.16 inference(tautology,[status(thm)],[])).
% 22.01/22.16 tff(376,plain,
% 22.01/22.16 (member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42), A!41)),
% 22.01/22.16 inference(unit_resolution,[status(thm)],[375, 374])).
% 22.01/22.16 tff(377,plain,
% 22.01/22.16 (((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42), A!41)) | (~((~((~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42), tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), C!39)) | (~apply(G!43, tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42), tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42))) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42), tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42))))))) | (~(apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42)) | ![Y: $i] : ((~member(Y, C!39)) | (~apply(G!43, tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), Y)) | (~apply(H!42, Y, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42)))))))))) <=> ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | (~member(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42), A!41)) | (~((~((~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42), tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), C!39)) | (~apply(G!43, tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42), tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42))) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42), tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42))))))) | (~(apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42)) | ![Y: $i] : ((~member(Y, C!39)) | (~apply(G!43, tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), Y)) | (~apply(H!42, Y, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42)))))))))),
% 22.01/22.17 inference(rewrite,[status(thm)],[])).
% 22.01/22.17 tff(378,plain,
% 22.01/22.17 (((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42), A!41)) | (~member(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~((~((~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42), tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), C!39)) | (~apply(G!43, tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42), tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42))) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42), tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42))))))) | (~(apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42)) | ![Y: $i] : ((~member(Y, C!39)) | (~apply(G!43, tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), Y)) | (~apply(H!42, Y, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42))))))))) <=> ((~member(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42), A!41)) | (~((~((~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42), tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), C!39)) | (~apply(G!43, tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42), tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42))) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42), tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42))))))) | (~(apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42)) | ![Y: $i] : ((~member(Y, C!39)) | (~apply(G!43, tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), Y)) | (~apply(H!42, Y, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42)))))))))),
% 22.01/22.17 inference(rewrite,[status(thm)],[])).
% 22.01/22.17 tff(379,plain,
% 22.01/22.17 ((~((~((~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42), tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), C!39)) | (~apply(G!43, tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42), tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42))) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42), tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42))))))) | (~(apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42)) | ![Y: $i] : ((~member(Y, C!39)) | (~apply(G!43, tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), Y)) | (~apply(H!42, Y, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42)))))))) <=> (~((~((~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42), tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), C!39)) | (~apply(G!43, tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42), tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42))) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42), tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42))))))) | (~(apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42)) | ![Y: $i] : ((~member(Y, C!39)) | (~apply(G!43, tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), Y)) | (~apply(H!42, Y, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42))))))))),
% 22.01/22.17 inference(rewrite,[status(thm)],[])).
% 22.01/22.17 tff(380,plain,
% 22.01/22.17 (((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42), A!41)) | (~member(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~((~((~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42), tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), C!39)) | (~apply(G!43, tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42), tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42))) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42), tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42))))))) | (~(apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42)) | ![Y: $i] : ((~member(Y, C!39)) | (~apply(G!43, tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), Y)) | (~apply(H!42, Y, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42))))))))) <=> ((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42), A!41)) | (~member(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~((~((~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42), tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), C!39)) | (~apply(G!43, tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42), tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42))) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42), tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42))))))) | (~(apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42)) | ![Y: $i] : ((~member(Y, C!39)) | (~apply(G!43, tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), Y)) | (~apply(H!42, Y, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42)))))))))),
% 22.01/22.17 inference(monotonicity,[status(thm)],[379])).
% 22.01/22.17 tff(381,plain,
% 22.01/22.17 (((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42), A!41)) | (~member(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~((~((~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42), tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), C!39)) | (~apply(G!43, tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42), tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42))) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42), tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42))))))) | (~(apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42)) | ![Y: $i] : ((~member(Y, C!39)) | (~apply(G!43, tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), Y)) | (~apply(H!42, Y, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42))))))))) <=> ((~member(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42), A!41)) | (~((~((~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42), tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), C!39)) | (~apply(G!43, tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42), tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42))) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42), tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42))))))) | (~(apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42)) | ![Y: $i] : ((~member(Y, C!39)) | (~apply(G!43, tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), Y)) | (~apply(H!42, Y, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42)))))))))),
% 22.01/22.18 inference(transitivity,[status(thm)],[380, 378])).
% 22.01/22.18 tff(382,plain,
% 22.01/22.18 (((~![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_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42), A!41)) | (~member(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~((~((~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42), tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), C!39)) | (~apply(G!43, tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42), tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42))) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42), tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42))))))) | (~(apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42)) | ![Y: $i] : ((~member(Y, C!39)) | (~apply(G!43, tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), Y)) | (~apply(H!42, Y, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42)))))))))) <=> ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42), A!41)) | (~((~((~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42), tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), C!39)) | (~apply(G!43, tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42), tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42))) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42), tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42))))))) | (~(apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42)) | ![Y: $i] : ((~member(Y, C!39)) | (~apply(G!43, tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), Y)) | (~apply(H!42, Y, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42))))))))))),
% 22.01/22.18 inference(monotonicity,[status(thm)],[381])).
% 22.01/22.18 tff(383,plain,
% 22.01/22.18 (((~![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_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42), A!41)) | (~member(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~((~((~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42), tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), C!39)) | (~apply(G!43, tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42), tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42))) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42), tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42))))))) | (~(apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42)) | ![Y: $i] : ((~member(Y, C!39)) | (~apply(G!43, tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), Y)) | (~apply(H!42, Y, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42)))))))))) <=> ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | (~member(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42), A!41)) | (~((~((~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42), tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), C!39)) | (~apply(G!43, tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42), tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42))) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42), tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42))))))) | (~(apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42)) | ![Y: $i] : ((~member(Y, C!39)) | (~apply(G!43, tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), Y)) | (~apply(H!42, Y, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42)))))))))),
% 22.01/22.18 inference(transitivity,[status(thm)],[382, 377])).
% 22.01/22.18 tff(384,plain,
% 22.01/22.18 ((~![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_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42), A!41)) | (~member(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~((~((~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42), tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), C!39)) | (~apply(G!43, tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42), tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42))) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42), tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42))))))) | (~(apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42)) | ![Y: $i] : ((~member(Y, C!39)) | (~apply(G!43, tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), Y)) | (~apply(H!42, Y, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42)))))))))),
% 22.01/22.18 inference(quant_inst,[status(thm)],[])).
% 22.01/22.18 tff(385,plain,
% 22.01/22.18 ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | (~member(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42), A!41)) | (~((~((~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42), tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), C!39)) | (~apply(G!43, tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42), tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42))) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42), tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42))))))) | (~(apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42)) | ![Y: $i] : ((~member(Y, C!39)) | (~apply(G!43, tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), Y)) | (~apply(H!42, Y, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42))))))))),
% 22.01/22.19 inference(modus_ponens,[status(thm)],[384, 383])).
% 22.01/22.19 tff(386,plain,
% 22.01/22.19 (~((~((~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42), tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), C!39)) | (~apply(G!43, tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42), tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42))) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42), tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42))))))) | (~(apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42)) | ![Y: $i] : ((~member(Y, C!39)) | (~apply(G!43, tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), Y)) | (~apply(H!42, Y, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42)))))))),
% 22.01/22.19 inference(unit_resolution,[status(thm)],[385, 106, 362, 376])).
% 22.01/22.19 tff(387,plain,
% 22.01/22.19 (((~((~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42), tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), C!39)) | (~apply(G!43, tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42), tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42))) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42), tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43, H!42), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42))))))) | (~(apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42)) | ![Y: $i] : ((~member(Y, C!39)) | (~apply(G!43, tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), Y)) | (~apply(H!42, Y, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42))))))) | (apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42)) | ![Y: $i] : ((~member(Y, C!39)) | (~apply(G!43, tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), Y)) | (~apply(H!42, Y, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42)))))),
% 22.01/22.19 inference(tautology,[status(thm)],[])).
% 22.01/22.19 tff(388,plain,
% 22.01/22.19 (apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42)) | ![Y: $i] : ((~member(Y, C!39)) | (~apply(G!43, tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), Y)) | (~apply(H!42, Y, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42))))),
% 22.01/22.19 inference(unit_resolution,[status(thm)],[387, 386])).
% 22.01/22.19 tff(389,plain,
% 22.01/22.19 (((~member(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~![Y: $i] : ((~member(Y, A!41)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), Y))))) | ![Y: $i] : ((~member(Y, A!41)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), Y)))),
% 22.01/22.19 inference(tautology,[status(thm)],[])).
% 22.01/22.19 tff(390,plain,
% 22.01/22.19 (![Y: $i] : ((~member(Y, A!41)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), Y)))),
% 22.01/22.19 inference(unit_resolution,[status(thm)],[389, 360])).
% 22.01/22.19 tff(391,plain,
% 22.01/22.19 (((~![Y: $i] : ((~member(Y, A!41)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), Y)))) | ((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42), A!41)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42))))) <=> ((~![Y: $i] : ((~member(Y, A!41)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), Y)))) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42), A!41)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42))))),
% 22.01/22.19 inference(rewrite,[status(thm)],[])).
% 22.01/22.19 tff(392,plain,
% 22.01/22.19 ((~![Y: $i] : ((~member(Y, A!41)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), Y)))) | ((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42), A!41)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42))))),
% 22.01/22.19 inference(quant_inst,[status(thm)],[])).
% 22.01/22.19 tff(393,plain,
% 22.01/22.19 ((~![Y: $i] : ((~member(Y, A!41)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), Y)))) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42), A!41)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42)))),
% 22.01/22.19 inference(modus_ponens,[status(thm)],[392, 391])).
% 22.01/22.19 tff(394,plain,
% 22.01/22.19 (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42))),
% 22.01/22.19 inference(unit_resolution,[status(thm)],[393, 390, 376])).
% 22.01/22.19 tff(395,plain,
% 22.01/22.19 ((~(apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42)) | ![Y: $i] : ((~member(Y, C!39)) | (~apply(G!43, tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), Y)) | (~apply(H!42, Y, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42)))))) | apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42)) | ![Y: $i] : ((~member(Y, C!39)) | (~apply(G!43, tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), Y)) | (~apply(H!42, Y, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42))))),
% 22.01/22.19 inference(tautology,[status(thm)],[])).
% 22.01/22.19 tff(396,plain,
% 22.01/22.19 ((~(apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42)) | ![Y: $i] : ((~member(Y, C!39)) | (~apply(G!43, tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), Y)) | (~apply(H!42, Y, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42)))))) | ![Y: $i] : ((~member(Y, C!39)) | (~apply(G!43, tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), Y)) | (~apply(H!42, Y, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42))))),
% 22.01/22.19 inference(unit_resolution,[status(thm)],[395, 394])).
% 22.01/22.19 tff(397,plain,
% 22.01/22.19 (![Y: $i] : ((~member(Y, C!39)) | (~apply(G!43, tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), Y)) | (~apply(H!42, Y, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42))))),
% 22.01/22.19 inference(unit_resolution,[status(thm)],[396, 388])).
% 22.01/22.19 tff(398,plain,
% 22.01/22.19 (((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42), A!41)) | (~apply(H!42, tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42)))) | apply(H!42, tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42))),
% 22.01/22.19 inference(tautology,[status(thm)],[])).
% 22.01/22.19 tff(399,plain,
% 22.01/22.19 (apply(H!42, tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42))),
% 22.01/22.19 inference(unit_resolution,[status(thm)],[398, 374])).
% 22.01/22.19 tff(400,plain,
% 22.01/22.19 (((~member(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), C!39)) | (~apply(G!43, tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43)))) | apply(G!43, tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43))),
% 22.01/22.19 inference(tautology,[status(thm)],[])).
% 22.01/22.19 tff(401,plain,
% 22.01/22.19 (apply(G!43, tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43))),
% 22.01/22.19 inference(unit_resolution,[status(thm)],[400, 366])).
% 22.01/22.19 tff(402,plain,
% 22.01/22.19 (((~![Y: $i] : ((~member(Y, C!39)) | (~apply(G!43, tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), Y)) | (~apply(H!42, Y, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42))))) | ((~member(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), C!39)) | (~apply(G!43, tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43))) | (~apply(H!42, tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42))))) <=> ((~![Y: $i] : ((~member(Y, C!39)) | (~apply(G!43, tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), Y)) | (~apply(H!42, Y, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42))))) | (~member(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), C!39)) | (~apply(G!43, tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43))) | (~apply(H!42, tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42))))),
% 22.01/22.19 inference(rewrite,[status(thm)],[])).
% 22.01/22.19 tff(403,plain,
% 22.01/22.19 ((~![Y: $i] : ((~member(Y, C!39)) | (~apply(G!43, tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), Y)) | (~apply(H!42, Y, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42))))) | ((~member(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), C!39)) | (~apply(G!43, tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43))) | (~apply(H!42, tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42))))),
% 22.01/22.19 inference(quant_inst,[status(thm)],[])).
% 22.01/22.19 tff(404,plain,
% 22.01/22.19 ((~![Y: $i] : ((~member(Y, C!39)) | (~apply(G!43, tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), Y)) | (~apply(H!42, Y, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42))))) | (~member(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), C!39)) | (~apply(G!43, tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43))) | (~apply(H!42, tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43), A!41, H!42)))),
% 22.01/22.19 inference(modus_ponens,[status(thm)],[403, 402])).
% 22.01/22.19 tff(405,plain,
% 22.01/22.19 ($false),
% 22.01/22.19 inference(unit_resolution,[status(thm)],[404, 368, 401, 399, 397])).
% 22.01/22.19 tff(406,plain,((~member(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~![Y: $i] : ((~member(Y, A!41)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), Y))))), inference(lemma,lemma(discharge,[]))).
% 22.01/22.19 tff(407,plain,
% 22.01/22.19 ((~(maps(compose_function(H!42, G!43, B!40, C!39, A!41), B!40, A!41) | (~((~member(tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~member(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)) = tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41))) | (~member(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)))) | (~((~member(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~![Y: $i] : ((~member(Y, A!41)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), Y)))))))) | maps(compose_function(H!42, G!43, B!40, C!39, A!41), B!40, A!41) | (~((~member(tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~member(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)) = tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41))) | (~member(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)))) | (~((~member(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~![Y: $i] : ((~member(Y, A!41)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), Y))))))),
% 22.01/22.19 inference(tautology,[status(thm)],[])).
% 22.01/22.19 tff(408,plain,
% 22.01/22.19 ((~(maps(compose_function(H!42, G!43, B!40, C!39, A!41), B!40, A!41) | (~((~member(tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~member(tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_7(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)) = tptp_fun_Y2_5(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41))) | (~member(tptp_fun_Y1_6(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)))) | (~((~member(tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~![Y: $i] : ((~member(Y, A!41)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X_4(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), Y)))))))) | maps(compose_function(H!42, G!43, B!40, C!39, A!41), B!40, A!41)),
% 22.01/22.20 inference(unit_resolution,[status(thm)],[407, 406, 359])).
% 22.01/22.20 tff(409,plain,
% 22.01/22.20 (maps(compose_function(H!42, G!43, B!40, C!39, A!41), B!40, A!41)),
% 22.01/22.20 inference(unit_resolution,[status(thm)],[408, 259])).
% 22.01/22.20 tff(410,plain,
% 22.01/22.20 ((~((~maps(compose_function(H!42, G!43, B!40, C!39, A!41), B!40, A!41)) | (~((~![X: $i] : ((~member(X, B!40)) | (~((~member(tptp_fun_Y_3(X, A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), X, tptp_fun_Y_3(X, A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!41)) | (~member(X, B!40)) | (~member(Y1, A!41)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), X, Y2)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), X, Y1)))))))) | (~maps(compose_function(H!42, G!43, B!40, C!39, A!41), B!40, A!41)) | (~((~![X: $i] : ((~member(X, B!40)) | (~((~member(tptp_fun_Y_3(X, A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), X, tptp_fun_Y_3(X, A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!41)) | (~member(X, B!40)) | (~member(Y1, A!41)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), X, Y2)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), X, Y1))))))),
% 22.01/22.20 inference(tautology,[status(thm)],[])).
% 22.01/22.20 tff(411,plain,
% 22.01/22.20 (~((~![X: $i] : ((~member(X, B!40)) | (~((~member(tptp_fun_Y_3(X, A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), X, tptp_fun_Y_3(X, A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!41)) | (~member(X, B!40)) | (~member(Y1, A!41)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), X, Y2)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), X, Y1)))))),
% 22.01/22.20 inference(unit_resolution,[status(thm)],[410, 409, 257])).
% 22.01/22.20 tff(412,plain,
% 22.01/22.20 (((~![X: $i] : ((~member(X, B!40)) | (~((~member(tptp_fun_Y_3(X, A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), X, tptp_fun_Y_3(X, A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!41)) | (~member(X, B!40)) | (~member(Y1, A!41)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), X, Y2)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), X, Y1))))) | ![X: $i] : ((~member(X, B!40)) | (~((~member(tptp_fun_Y_3(X, A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), X, tptp_fun_Y_3(X, A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))))))),
% 22.01/22.20 inference(tautology,[status(thm)],[])).
% 22.01/22.20 tff(413,plain,
% 22.01/22.20 (![X: $i] : ((~member(X, B!40)) | (~((~member(tptp_fun_Y_3(X, A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), X, tptp_fun_Y_3(X, A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))))))),
% 22.01/22.20 inference(unit_resolution,[status(thm)],[412, 411])).
% 22.01/22.20 tff(414,plain,
% 22.01/22.20 (((~![X: $i] : ((~member(X, B!40)) | (~((~member(tptp_fun_Y_3(X, A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), X, tptp_fun_Y_3(X, A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))))))) | ((~member(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), B!40)) | (~((~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))))))) <=> ((~![X: $i] : ((~member(X, B!40)) | (~((~member(tptp_fun_Y_3(X, A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), X, tptp_fun_Y_3(X, A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))))))) | (~member(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), B!40)) | (~((~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))))))),
% 22.01/22.20 inference(rewrite,[status(thm)],[])).
% 22.01/22.20 tff(415,plain,
% 22.01/22.20 ((~![X: $i] : ((~member(X, B!40)) | (~((~member(tptp_fun_Y_3(X, A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), X, tptp_fun_Y_3(X, A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))))))) | ((~member(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), B!40)) | (~((~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))))))),
% 22.01/22.20 inference(quant_inst,[status(thm)],[])).
% 22.01/22.20 tff(416,plain,
% 22.01/22.20 ((~![X: $i] : ((~member(X, B!40)) | (~((~member(tptp_fun_Y_3(X, A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), X, tptp_fun_Y_3(X, A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))))))) | (~member(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), B!40)) | (~((~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41))))))),
% 22.01/22.20 inference(modus_ponens,[status(thm)],[415, 414])).
% 22.01/22.20 tff(417,plain,
% 22.01/22.20 (~((~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))))),
% 22.01/22.20 inference(unit_resolution,[status(thm)],[416, 185, 413])).
% 22.01/22.20 tff(418,plain,
% 22.01/22.20 (((~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41))))) | member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)),
% 22.01/22.20 inference(tautology,[status(thm)],[])).
% 22.01/22.20 tff(419,plain,
% 22.01/22.20 (member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)),
% 22.01/22.20 inference(unit_resolution,[status(thm)],[418, 417])).
% 22.01/22.20 tff(420,plain,
% 22.01/22.20 (((~![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_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), B!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~((~((~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42), C!39)) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, 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B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41))))))))))) <=> ((~![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_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), B!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~((~((~apply(compose_function(H!42, 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tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))))))) | (~(apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41))) | ![Y: $i] : ((~member(Y, C!39)) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), Y)) | (~apply(H!42, Y, tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, 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% 22.01/22.21 inference(rewrite,[status(thm)],[])).
% 22.01/22.21 tff(421,plain,
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H!42))) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))))))) | (~(apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41))) | ![Y: $i] : ((~member(Y, C!39)) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), Y)) | (~apply(H!42, Y, tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))))))))) <=> ((~member(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), B!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~((~((~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42), C!39)) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42))) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))))))) | (~(apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41))) | ![Y: $i] : ((~member(Y, C!39)) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), Y)) | (~apply(H!42, Y, tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41))))))))))),
% 22.01/22.21 inference(rewrite,[status(thm)],[])).
% 22.01/22.21 tff(422,plain,
% 22.01/22.21 ((~((~((~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42), C!39)) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, 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tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41))))))))) <=> (~((~((~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), 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((~member(Y, C!39)) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), Y)) | (~apply(H!42, Y, tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))))))))),
% 22.01/22.21 inference(rewrite,[status(thm)],[])).
% 22.01/22.21 tff(423,plain,
% 22.01/22.21 (((~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~member(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), B!40)) | (~((~((~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42), C!39)) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42))) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))))))) | (~(apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41))) | ![Y: $i] : ((~member(Y, C!39)) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), Y)) | (~apply(H!42, Y, tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))))))))) <=> ((~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~member(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), B!40)) | (~((~((~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42), C!39)) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42))) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))))))) | (~(apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41))) | ![Y: $i] : ((~member(Y, C!39)) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), Y)) | (~apply(H!42, Y, tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41))))))))))),
% 22.01/22.22 inference(monotonicity,[status(thm)],[422])).
% 22.01/22.22 tff(424,plain,
% 22.01/22.22 (((~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~member(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), B!40)) | (~((~((~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, 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F!44, G!43), C!39, G!43, H!42), C!39)) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42))) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))))))) | (~(apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41))) | ![Y: $i] : ((~member(Y, C!39)) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), Y)) | (~apply(H!42, Y, tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41))))))))))),
% 22.01/22.22 inference(transitivity,[status(thm)],[423, 421])).
% 22.01/22.22 tff(425,plain,
% 22.01/22.22 (((~![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_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~member(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), B!40)) | (~((~((~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42), C!39)) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42))) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))))))) | (~(apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41))) | ![Y: $i] : ((~member(Y, C!39)) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), Y)) | (~apply(H!42, Y, tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41))))))))))) <=> ((~![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_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), B!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~((~((~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42), C!39)) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42))) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))))))) | (~(apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41))) | ![Y: $i] : ((~member(Y, C!39)) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), Y)) | (~apply(H!42, Y, tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))))))))))),
% 22.01/22.23 inference(monotonicity,[status(thm)],[424])).
% 22.01/22.23 tff(426,plain,
% 22.01/22.23 (((~![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_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~member(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), B!40)) | (~((~((~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42), C!39)) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42))) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))))))) | (~(apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41))) | ![Y: $i] : ((~member(Y, C!39)) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), Y)) | (~apply(H!42, Y, tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41))))))))))) <=> ((~![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_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), B!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~((~((~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42), C!39)) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42))) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))))))) | (~(apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41))) | ![Y: $i] : ((~member(Y, C!39)) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), Y)) | (~apply(H!42, Y, tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41))))))))))),
% 22.01/22.23 inference(transitivity,[status(thm)],[425, 420])).
% 22.01/22.23 tff(427,plain,
% 22.01/22.23 ((~![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_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~member(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), B!40)) | (~((~((~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42), C!39)) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42))) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))))))) | (~(apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41))) | ![Y: $i] : ((~member(Y, C!39)) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), Y)) | (~apply(H!42, Y, tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41))))))))))),
% 22.01/22.23 inference(quant_inst,[status(thm)],[])).
% 22.01/22.23 tff(428,plain,
% 22.01/22.23 ((~![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_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), B!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~((~((~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42), C!39)) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42))) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))))))) | (~(apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41))) | ![Y: $i] : ((~member(Y, C!39)) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), Y)) | (~apply(H!42, Y, tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))))))))),
% 22.01/22.24 inference(modus_ponens,[status(thm)],[427, 426])).
% 22.01/22.24 tff(429,plain,
% 22.01/22.24 (~((~((~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42), C!39)) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42))) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))))))) | (~(apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41))) | ![Y: $i] : ((~member(Y, C!39)) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), Y)) | (~apply(H!42, Y, tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41))))))))),
% 22.09/22.24 inference(unit_resolution,[status(thm)],[428, 106, 185, 419])).
% 22.09/22.24 tff(430,plain,
% 22.09/22.24 (((~((~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42), C!39)) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, 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G!43), C!39, G!43, H!42), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))))))) | (~(apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41))) | ![Y: $i] : ((~member(Y, C!39)) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), Y)) | (~apply(H!42, Y, 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B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))))))),
% 22.09/22.24 inference(tautology,[status(thm)],[])).
% 22.09/22.24 tff(431,plain,
% 22.09/22.24 ((~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42), C!39)) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42))) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41))))))),
% 22.09/22.24 inference(unit_resolution,[status(thm)],[430, 429])).
% 22.09/22.24 tff(432,plain,
% 22.09/22.24 (((~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41))))) | apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))),
% 22.09/22.24 inference(tautology,[status(thm)],[])).
% 22.09/22.24 tff(433,plain,
% 22.09/22.24 (apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))),
% 22.09/22.24 inference(unit_resolution,[status(thm)],[432, 417])).
% 22.09/22.24 tff(434,plain,
% 22.09/22.24 ((~((~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42), C!39)) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42))) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))))))) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42), C!39)) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42))) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41))))))),
% 22.09/22.25 inference(tautology,[status(thm)],[])).
% 22.09/22.25 tff(435,plain,
% 22.09/22.25 ((~((~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42), C!39)) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42))) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))))))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42), C!39)) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42))) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41))))))),
% 22.09/22.25 inference(unit_resolution,[status(thm)],[434, 433])).
% 22.09/22.25 tff(436,plain,
% 22.09/22.25 (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42), C!39)) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42))) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))))),
% 22.09/22.25 inference(unit_resolution,[status(thm)],[435, 431])).
% 22.09/22.25 tff(437,plain,
% 22.09/22.25 (((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42), C!39)) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42))) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41))))) | apply(G!43, tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42))),
% 22.09/22.25 inference(tautology,[status(thm)],[])).
% 22.09/22.25 tff(438,plain,
% 22.09/22.25 (apply(G!43, tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42))),
% 22.09/22.25 inference(unit_resolution,[status(thm)],[437, 436])).
% 22.09/22.25 tff(439,plain,
% 22.09/22.25 (((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42), C!39)) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42))) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41))))) | member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42), C!39)),
% 22.09/22.25 inference(tautology,[status(thm)],[])).
% 22.09/22.25 tff(440,plain,
% 22.09/22.25 (member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42), C!39)),
% 22.09/22.25 inference(unit_resolution,[status(thm)],[439, 436])).
% 22.09/22.25 tff(441,plain,
% 22.09/22.25 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, C!39)) | (~apply(G!43, X, Y1)) | (~apply(G!43, X, Y2)) | (~member(X, B!40)) | (~member(Y1, C!39)))) | ((~member(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), B!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43), C!39)) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43))) | (~apply(G!43, 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A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42), C!39)) | (tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42) = tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, C!39)) | (~apply(G!43, X, Y1)) | (~apply(G!43, X, Y2)) | (~member(X, B!40)) | (~member(Y1, C!39)))) | (~member(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), B!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43), C!39)) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43))) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42))) | (~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42), C!39)) | (tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42) = tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43)))),
% 22.09/22.26 inference(rewrite,[status(thm)],[])).
% 22.09/22.26 tff(442,plain,
% 22.09/22.26 (((tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42) = tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43)) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43), C!39)) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42))) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43))) | (~member(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), B!40)) | (~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42), C!39))) <=> ((~member(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), B!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43), C!39)) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43))) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42))) | (~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42), C!39)) | (tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42) = tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43)))),
% 22.09/22.26 inference(rewrite,[status(thm)],[])).
% 22.09/22.26 tff(443,plain,
% 22.09/22.26 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, C!39)) | (~apply(G!43, X, Y1)) | (~apply(G!43, X, Y2)) | (~member(X, B!40)) | (~member(Y1, C!39)))) | ((tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42) = tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43)) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43), C!39)) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42))) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43))) | (~member(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), B!40)) | (~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42), C!39)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, C!39)) | (~apply(G!43, X, Y1)) | (~apply(G!43, X, Y2)) | (~member(X, B!40)) | (~member(Y1, C!39)))) | ((~member(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), B!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43), C!39)) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43))) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42))) | (~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42), C!39)) | (tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42) = tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43))))),
% 22.09/22.26 inference(monotonicity,[status(thm)],[442])).
% 22.09/22.26 tff(444,plain,
% 22.09/22.26 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, C!39)) | (~apply(G!43, X, Y1)) | (~apply(G!43, X, Y2)) | (~member(X, B!40)) | (~member(Y1, C!39)))) | ((tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42) = tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43)) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43), C!39)) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42))) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43))) | (~member(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), B!40)) | (~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42), C!39)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, C!39)) | (~apply(G!43, X, Y1)) | (~apply(G!43, X, Y2)) | (~member(X, B!40)) | (~member(Y1, C!39)))) | (~member(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), B!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43), C!39)) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43))) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42))) | (~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42), C!39)) | (tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42) = tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43)))),
% 22.09/22.27 inference(transitivity,[status(thm)],[443, 441])).
% 22.09/22.27 tff(445,plain,
% 22.09/22.27 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, C!39)) | (~apply(G!43, X, Y1)) | (~apply(G!43, X, Y2)) | (~member(X, B!40)) | (~member(Y1, C!39)))) | ((tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42) = tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43)) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43), C!39)) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42))) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43))) | (~member(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), B!40)) | (~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42), C!39)))),
% 22.09/22.27 inference(quant_inst,[status(thm)],[])).
% 22.09/22.27 tff(446,plain,
% 22.09/22.27 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, C!39)) | (~apply(G!43, X, Y1)) | (~apply(G!43, X, Y2)) | (~member(X, B!40)) | (~member(Y1, C!39)))) | (~member(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), B!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43), C!39)) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43))) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42))) | (~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42), C!39)) | (tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42) = tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43))),
% 22.09/22.27 inference(modus_ponens,[status(thm)],[445, 444])).
% 22.09/22.27 tff(447,plain,
% 22.09/22.27 (tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42) = tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43)),
% 22.09/22.27 inference(unit_resolution,[status(thm)],[446, 234, 185, 230, 228, 440, 438])).
% 22.09/22.27 tff(448,plain,
% 22.09/22.27 (tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43) = tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42)),
% 22.09/22.27 inference(symmetry,[status(thm)],[447])).
% 22.09/22.27 tff(449,plain,
% 22.09/22.27 (apply(H!42, tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41))) <=> apply(H!42, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))),
% 22.09/22.27 inference(monotonicity,[status(thm)],[448])).
% 22.09/22.27 tff(450,plain,
% 22.09/22.27 (apply(H!42, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41))) <=> apply(H!42, tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))),
% 22.09/22.27 inference(symmetry,[status(thm)],[449])).
% 22.09/22.27 tff(451,plain,
% 22.09/22.27 (((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42), C!39)) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42))) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41))))) | apply(H!42, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))),
% 22.09/22.27 inference(tautology,[status(thm)],[])).
% 22.09/22.27 tff(452,plain,
% 22.09/22.27 (apply(H!42, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))),
% 22.09/22.27 inference(unit_resolution,[status(thm)],[451, 436])).
% 22.09/22.27 tff(453,plain,
% 22.09/22.27 (apply(H!42, tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))),
% 22.09/22.28 inference(modus_ponens,[status(thm)],[452, 450])).
% 22.09/22.28 tff(454,assumption,(apply(H!42, tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43), tptp_fun_Y_16(A!41, C!39, H!42))), introduced(assumption)).
% 22.09/22.28 tff(455,plain,
% 22.09/22.28 (((~member(tptp_fun_X2_17(A!41, C!39, H!42), C!39)) | (~member(tptp_fun_Y_16(A!41, C!39, H!42), A!41)) | (~member(tptp_fun_X1_18(A!41, C!39, H!42), C!39)) | (~apply(H!42, tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_Y_16(A!41, C!39, H!42))) | (~apply(H!42, tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_Y_16(A!41, C!39, H!42))) | (tptp_fun_X1_18(A!41, C!39, H!42) = tptp_fun_X2_17(A!41, C!39, H!42))) | member(tptp_fun_Y_16(A!41, C!39, H!42), A!41)),
% 22.09/22.28 inference(tautology,[status(thm)],[])).
% 22.09/22.28 tff(456,plain,
% 22.09/22.28 (member(tptp_fun_Y_16(A!41, C!39, H!42), A!41)),
% 22.09/22.28 inference(unit_resolution,[status(thm)],[455, 146])).
% 22.09/22.28 tff(457,plain,
% 22.09/22.28 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!41)) | (~apply(H!42, X, Y1)) | (~apply(H!42, X, Y2)) | (~member(X, C!39)) | (~member(Y1, A!41)))) | ((~member(tptp_fun_Y_16(A!41, C!39, H!42), A!41)) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43), C!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~apply(H!42, tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43), tptp_fun_Y_16(A!41, C!39, H!42))) | (tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)) = tptp_fun_Y_16(A!41, C!39, H!42)) | (~apply(H!42, tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!41)) | (~apply(H!42, X, Y1)) | (~apply(H!42, X, Y2)) | (~member(X, C!39)) | (~member(Y1, A!41)))) | (~member(tptp_fun_Y_16(A!41, C!39, H!42), A!41)) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43), C!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~apply(H!42, tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43), tptp_fun_Y_16(A!41, C!39, H!42))) | (tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)) = tptp_fun_Y_16(A!41, C!39, H!42)) | (~apply(H!42, tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))))),
% 22.09/22.28 inference(rewrite,[status(thm)],[])).
% 22.09/22.28 tff(458,plain,
% 22.09/22.28 (((tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)) = tptp_fun_Y_16(A!41, C!39, H!42)) | (~member(tptp_fun_Y_16(A!41, C!39, H!42), A!41)) | (~apply(H!42, tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~apply(H!42, tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43), tptp_fun_Y_16(A!41, C!39, H!42))) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43), C!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41))) <=> ((~member(tptp_fun_Y_16(A!41, C!39, H!42), A!41)) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43), C!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~apply(H!42, tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43), tptp_fun_Y_16(A!41, C!39, H!42))) | (tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)) = tptp_fun_Y_16(A!41, C!39, H!42)) | (~apply(H!42, tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))))),
% 22.09/22.28 inference(rewrite,[status(thm)],[])).
% 22.09/22.28 tff(459,plain,
% 22.09/22.28 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!41)) | (~apply(H!42, X, Y1)) | (~apply(H!42, X, Y2)) | (~member(X, C!39)) | (~member(Y1, A!41)))) | ((tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)) = tptp_fun_Y_16(A!41, C!39, H!42)) | (~member(tptp_fun_Y_16(A!41, C!39, H!42), A!41)) | (~apply(H!42, tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~apply(H!42, tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43), tptp_fun_Y_16(A!41, C!39, H!42))) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43), C!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!41)) | (~apply(H!42, X, Y1)) | (~apply(H!42, X, Y2)) | (~member(X, C!39)) | (~member(Y1, A!41)))) | ((~member(tptp_fun_Y_16(A!41, C!39, H!42), A!41)) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43), C!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~apply(H!42, tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43), tptp_fun_Y_16(A!41, C!39, H!42))) | (tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)) = tptp_fun_Y_16(A!41, C!39, H!42)) | (~apply(H!42, tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41))))))),
% 22.13/22.28 inference(monotonicity,[status(thm)],[458])).
% 22.13/22.28 tff(460,plain,
% 22.13/22.28 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!41)) | (~apply(H!42, X, Y1)) | (~apply(H!42, X, Y2)) | (~member(X, C!39)) | (~member(Y1, A!41)))) | ((tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)) = tptp_fun_Y_16(A!41, C!39, H!42)) | (~member(tptp_fun_Y_16(A!41, C!39, H!42), A!41)) | (~apply(H!42, tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~apply(H!42, tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43), tptp_fun_Y_16(A!41, C!39, H!42))) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43), C!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!41)) | (~apply(H!42, X, Y1)) | (~apply(H!42, X, Y2)) | (~member(X, C!39)) | (~member(Y1, A!41)))) | (~member(tptp_fun_Y_16(A!41, C!39, H!42), A!41)) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43), C!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~apply(H!42, tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43), tptp_fun_Y_16(A!41, C!39, H!42))) | (tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)) = tptp_fun_Y_16(A!41, C!39, H!42)) | (~apply(H!42, tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))))),
% 22.13/22.28 inference(transitivity,[status(thm)],[459, 457])).
% 22.13/22.28 tff(461,plain,
% 22.13/22.28 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!41)) | (~apply(H!42, X, Y1)) | (~apply(H!42, X, Y2)) | (~member(X, C!39)) | (~member(Y1, A!41)))) | ((tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)) = tptp_fun_Y_16(A!41, C!39, H!42)) | (~member(tptp_fun_Y_16(A!41, C!39, H!42), A!41)) | (~apply(H!42, tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~apply(H!42, tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43), tptp_fun_Y_16(A!41, C!39, H!42))) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43), C!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)))),
% 22.13/22.28 inference(quant_inst,[status(thm)],[])).
% 22.13/22.28 tff(462,plain,
% 22.13/22.28 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!41)) | (~apply(H!42, X, Y1)) | (~apply(H!42, X, Y2)) | (~member(X, C!39)) | (~member(Y1, A!41)))) | (~member(tptp_fun_Y_16(A!41, C!39, H!42), A!41)) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43), C!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~apply(H!42, tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43), tptp_fun_Y_16(A!41, C!39, H!42))) | (tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)) = tptp_fun_Y_16(A!41, C!39, H!42)) | (~apply(H!42, tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41))))),
% 22.13/22.29 inference(modus_ponens,[status(thm)],[461, 460])).
% 22.13/22.29 tff(463,plain,
% 22.13/22.29 ((tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)) = tptp_fun_Y_16(A!41, C!39, H!42)) | (~apply(H!42, tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41))))),
% 22.13/22.29 inference(unit_resolution,[status(thm)],[462, 350, 456, 230, 454, 419])).
% 22.13/22.29 tff(464,plain,
% 22.13/22.29 (tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)) = tptp_fun_Y_16(A!41, C!39, H!42)),
% 22.13/22.29 inference(unit_resolution,[status(thm)],[463, 453])).
% 22.13/22.29 tff(465,plain,
% 22.13/22.29 (tptp_fun_E_19(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)) = tptp_fun_E_19(tptp_fun_Y_16(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41))),
% 22.13/22.29 inference(monotonicity,[status(thm)],[464])).
% 22.13/22.29 tff(466,plain,
% 22.13/22.29 (((~![Y: $i] : ((~member(Y, A!41)) | (~((~member(tptp_fun_E_19(Y, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_E_19(Y, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), Y)))))) | ((~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~((~member(tptp_fun_E_19(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_E_19(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))))))) <=> ((~![Y: $i] : ((~member(Y, A!41)) | (~((~member(tptp_fun_E_19(Y, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_E_19(Y, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), Y)))))) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~((~member(tptp_fun_E_19(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_E_19(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))))))),
% 22.13/22.29 inference(rewrite,[status(thm)],[])).
% 22.13/22.29 tff(467,plain,
% 22.13/22.29 ((~![Y: $i] : ((~member(Y, A!41)) | (~((~member(tptp_fun_E_19(Y, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_E_19(Y, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), Y)))))) | ((~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~((~member(tptp_fun_E_19(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_E_19(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))))))),
% 22.13/22.29 inference(quant_inst,[status(thm)],[])).
% 22.13/22.29 tff(468,plain,
% 22.13/22.29 ((~![Y: $i] : ((~member(Y, A!41)) | (~((~member(tptp_fun_E_19(Y, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_E_19(Y, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), Y)))))) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~((~member(tptp_fun_E_19(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_E_19(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41))))))),
% 22.13/22.29 inference(modus_ponens,[status(thm)],[467, 466])).
% 22.13/22.29 tff(469,plain,
% 22.13/22.29 (~((~member(tptp_fun_E_19(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_E_19(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))))),
% 22.13/22.29 inference(unit_resolution,[status(thm)],[468, 84, 419])).
% 22.13/22.29 tff(470,plain,
% 22.13/22.29 (((~member(tptp_fun_E_19(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_E_19(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41))))) | apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_E_19(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))),
% 22.13/22.29 inference(tautology,[status(thm)],[])).
% 22.13/22.29 tff(471,plain,
% 22.13/22.29 (apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_E_19(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))),
% 22.13/22.29 inference(unit_resolution,[status(thm)],[470, 469])).
% 22.13/22.29 tff(472,plain,
% 22.13/22.29 (((~member(tptp_fun_E_19(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_E_19(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41))))) | member(tptp_fun_E_19(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)),
% 22.13/22.29 inference(tautology,[status(thm)],[])).
% 22.13/22.29 tff(473,plain,
% 22.13/22.29 (member(tptp_fun_E_19(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)),
% 22.13/22.29 inference(unit_resolution,[status(thm)],[472, 469])).
% 22.13/22.29 tff(474,plain,
% 22.13/22.29 (((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(compose_function(H!42, G!43, B!40, C!39, A!41), B!40, A!41)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, B!40)) | (~member(Y, A!41)) | (~member(X1, B!40)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), X1, Y)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), X2, Y))))) | (~(injective(compose_function(H!42, G!43, B!40, C!39, A!41), B!40, A!41) | (~((~member(tptp_fun_Y_16(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~member(tptp_fun_X2_17(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~member(tptp_fun_X1_18(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X2_17(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_16(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X1_18(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_16(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (tptp_fun_X1_18(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)) = tptp_fun_X2_17(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))))))))) <=> ((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(compose_function(H!42, G!43, B!40, C!39, A!41), B!40, A!41)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, B!40)) | (~member(Y, A!41)) | (~member(X1, B!40)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), X1, Y)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), X2, Y))))) | (~(injective(compose_function(H!42, G!43, B!40, C!39, A!41), B!40, A!41) | (~((~member(tptp_fun_Y_16(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~member(tptp_fun_X2_17(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~member(tptp_fun_X1_18(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X2_17(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_16(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X1_18(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_16(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (tptp_fun_X1_18(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)) = tptp_fun_X2_17(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41))))))))))),
% 22.13/22.29 inference(rewrite,[status(thm)],[])).
% 22.13/22.29 tff(475,plain,
% 22.13/22.29 ((~((~((~injective(compose_function(H!42, G!43, B!40, C!39, A!41), B!40, A!41)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), X1, Y)) | (~member(X2, B!40)) | (~member(X1, B!40)) | (~member(Y, A!41)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), X2, Y))))) | (~(injective(compose_function(H!42, G!43, B!40, C!39, A!41), B!40, A!41) | (~((tptp_fun_X1_18(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)) = tptp_fun_X2_17(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41))) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X1_18(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_16(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X2_17(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_16(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~member(tptp_fun_X1_18(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~member(tptp_fun_X2_17(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~member(tptp_fun_Y_16(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)))))))) <=> (~((~((~injective(compose_function(H!42, G!43, B!40, C!39, A!41), B!40, A!41)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, B!40)) | (~member(Y, A!41)) | (~member(X1, B!40)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), X1, Y)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), X2, Y))))) | (~(injective(compose_function(H!42, G!43, B!40, C!39, A!41), B!40, A!41) | (~((~member(tptp_fun_Y_16(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~member(tptp_fun_X2_17(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~member(tptp_fun_X1_18(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X2_17(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_16(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X1_18(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_16(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (tptp_fun_X1_18(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)) = tptp_fun_X2_17(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))))))))),
% 22.13/22.29 inference(rewrite,[status(thm)],[])).
% 22.13/22.29 tff(476,plain,
% 22.13/22.29 (((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(compose_function(H!42, G!43, B!40, C!39, A!41), B!40, A!41)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), X1, Y)) | (~member(X2, B!40)) | (~member(X1, B!40)) | (~member(Y, A!41)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), X2, Y))))) | (~(injective(compose_function(H!42, G!43, B!40, C!39, A!41), B!40, A!41) | (~((tptp_fun_X1_18(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)) = tptp_fun_X2_17(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41))) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X1_18(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_16(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X2_17(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_16(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~member(tptp_fun_X1_18(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~member(tptp_fun_X2_17(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~member(tptp_fun_Y_16(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41))))))))) <=> ((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(compose_function(H!42, G!43, B!40, C!39, A!41), B!40, A!41)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, B!40)) | (~member(Y, A!41)) | (~member(X1, B!40)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), X1, Y)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), X2, Y))))) | (~(injective(compose_function(H!42, G!43, B!40, C!39, A!41), B!40, A!41) | (~((~member(tptp_fun_Y_16(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~member(tptp_fun_X2_17(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~member(tptp_fun_X1_18(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X2_17(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_16(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X1_18(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_16(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (tptp_fun_X1_18(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)) = tptp_fun_X2_17(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41))))))))))),
% 22.13/22.30 inference(monotonicity,[status(thm)],[475])).
% 22.13/22.30 tff(477,plain,
% 22.13/22.30 (((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(compose_function(H!42, G!43, B!40, C!39, A!41), B!40, A!41)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), X1, Y)) | (~member(X2, B!40)) | (~member(X1, B!40)) | (~member(Y, A!41)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), X2, Y))))) | (~(injective(compose_function(H!42, G!43, B!40, C!39, A!41), B!40, A!41) | (~((tptp_fun_X1_18(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)) = tptp_fun_X2_17(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41))) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X1_18(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_16(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X2_17(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_16(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~member(tptp_fun_X1_18(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~member(tptp_fun_X2_17(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~member(tptp_fun_Y_16(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41))))))))) <=> ((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(compose_function(H!42, G!43, B!40, C!39, A!41), B!40, A!41)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, B!40)) | (~member(Y, A!41)) | (~member(X1, B!40)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), X1, Y)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), X2, Y))))) | (~(injective(compose_function(H!42, G!43, B!40, C!39, A!41), B!40, A!41) | (~((~member(tptp_fun_Y_16(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~member(tptp_fun_X2_17(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~member(tptp_fun_X1_18(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X2_17(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_16(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X1_18(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_16(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (tptp_fun_X1_18(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)) = tptp_fun_X2_17(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41))))))))))),
% 22.13/22.30 inference(transitivity,[status(thm)],[476, 474])).
% 22.13/22.30 tff(478,plain,
% 22.13/22.30 ((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(compose_function(H!42, G!43, B!40, C!39, A!41), B!40, A!41)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), X1, Y)) | (~member(X2, B!40)) | (~member(X1, B!40)) | (~member(Y, A!41)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), X2, Y))))) | (~(injective(compose_function(H!42, G!43, B!40, C!39, A!41), B!40, A!41) | (~((tptp_fun_X1_18(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)) = tptp_fun_X2_17(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41))) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X1_18(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_16(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X2_17(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_16(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~member(tptp_fun_X1_18(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~member(tptp_fun_X2_17(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~member(tptp_fun_Y_16(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41))))))))),
% 22.13/22.30 inference(quant_inst,[status(thm)],[])).
% 22.13/22.30 tff(479,plain,
% 22.13/22.30 ((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(compose_function(H!42, G!43, B!40, C!39, A!41), B!40, A!41)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, B!40)) | (~member(Y, A!41)) | (~member(X1, B!40)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), X1, Y)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), X2, Y))))) | (~(injective(compose_function(H!42, G!43, B!40, C!39, A!41), B!40, A!41) | (~((~member(tptp_fun_Y_16(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~member(tptp_fun_X2_17(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~member(tptp_fun_X1_18(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X2_17(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_16(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X1_18(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_16(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (tptp_fun_X1_18(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)) = tptp_fun_X2_17(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))))))))),
% 22.13/22.30 inference(modus_ponens,[status(thm)],[478, 477])).
% 22.13/22.30 tff(480,plain,
% 22.13/22.30 (~((~((~injective(compose_function(H!42, G!43, B!40, C!39, A!41), B!40, A!41)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, B!40)) | (~member(Y, A!41)) | (~member(X1, B!40)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), X1, Y)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), X2, Y))))) | (~(injective(compose_function(H!42, G!43, B!40, C!39, A!41), B!40, A!41) | (~((~member(tptp_fun_Y_16(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~member(tptp_fun_X2_17(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~member(tptp_fun_X1_18(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X2_17(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_16(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X1_18(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_16(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (tptp_fun_X1_18(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)) = tptp_fun_X2_17(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41))))))))),
% 22.13/22.30 inference(unit_resolution,[status(thm)],[479, 16])).
% 22.13/22.30 tff(481,plain,
% 22.13/22.30 (((~((~injective(compose_function(H!42, G!43, B!40, C!39, A!41), B!40, A!41)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, B!40)) | (~member(Y, A!41)) | (~member(X1, B!40)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), X1, Y)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), X2, Y))))) | (~(injective(compose_function(H!42, G!43, B!40, C!39, A!41), B!40, A!41) | (~((~member(tptp_fun_Y_16(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~member(tptp_fun_X2_17(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~member(tptp_fun_X1_18(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X2_17(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_16(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_X1_18(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_16(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (tptp_fun_X1_18(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)) = tptp_fun_X2_17(A!41, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)))))))) | ((~injective(compose_function(H!42, G!43, B!40, C!39, A!41), B!40, A!41)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, B!40)) | (~member(Y, A!41)) | (~member(X1, B!40)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), X1, Y)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), X2, Y))))),
% 22.13/22.30 inference(tautology,[status(thm)],[])).
% 22.13/22.30 tff(482,plain,
% 22.13/22.30 ((~injective(compose_function(H!42, G!43, B!40, C!39, A!41), B!40, A!41)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, B!40)) | (~member(Y, A!41)) | (~member(X1, B!40)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), X1, Y)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), X2, Y)))),
% 22.13/22.30 inference(unit_resolution,[status(thm)],[481, 480])).
% 22.13/22.30 tff(483,plain,
% 22.13/22.30 (((~injective(compose_function(H!42, G!43, B!40, C!39, A!41), B!40, A!41)) | (~surjective(compose_function(H!42, G!43, B!40, C!39, A!41), B!40, A!41))) | injective(compose_function(H!42, G!43, B!40, C!39, A!41), B!40, A!41)),
% 22.13/22.30 inference(tautology,[status(thm)],[])).
% 22.13/22.30 tff(484,plain,
% 22.13/22.30 (injective(compose_function(H!42, G!43, B!40, C!39, A!41), B!40, A!41)),
% 22.13/22.30 inference(unit_resolution,[status(thm)],[483, 79])).
% 22.13/22.30 tff(485,plain,
% 22.13/22.30 ((~((~injective(compose_function(H!42, G!43, B!40, C!39, A!41), B!40, A!41)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, B!40)) | (~member(Y, A!41)) | (~member(X1, B!40)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), X1, Y)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), X2, Y))))) | (~injective(compose_function(H!42, G!43, B!40, C!39, A!41), B!40, A!41)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, B!40)) | (~member(Y, A!41)) | (~member(X1, B!40)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), X1, Y)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), X2, Y)))),
% 22.13/22.30 inference(tautology,[status(thm)],[])).
% 22.13/22.30 tff(486,plain,
% 22.13/22.30 ((~((~injective(compose_function(H!42, G!43, B!40, C!39, A!41), B!40, A!41)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, B!40)) | (~member(Y, A!41)) | (~member(X1, B!40)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), X1, Y)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), X2, Y))))) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, B!40)) | (~member(Y, A!41)) | (~member(X1, B!40)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), X1, Y)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), X2, Y)))),
% 22.13/22.30 inference(unit_resolution,[status(thm)],[485, 484])).
% 22.13/22.30 tff(487,plain,
% 22.13/22.30 (![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, B!40)) | (~member(Y, A!41)) | (~member(X1, B!40)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), X1, Y)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), X2, Y)))),
% 22.13/22.30 inference(unit_resolution,[status(thm)],[486, 482])).
% 22.13/22.30 tff(488,plain,
% 22.13/22.30 (((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, B!40)) | (~member(Y, A!41)) | (~member(X1, B!40)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), X1, Y)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), X2, Y)))) | ((~member(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), B!40)) | (tptp_fun_E_19(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)) = tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), 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B!40, F!44, G!43), B!40)) | (tptp_fun_E_19(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)) = tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_E_19(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, 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% 22.13/22.31 inference(rewrite,[status(thm)],[])).
% 22.13/22.31 tff(489,plain,
% 22.13/22.31 (((tptp_fun_E_19(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)) = tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43)) | (~member(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), B!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~member(tptp_fun_E_19(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_E_19(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41))))) <=> ((~member(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), B!40)) | (tptp_fun_E_19(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)) = tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_E_19(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~member(tptp_fun_E_19(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)))),
% 22.13/22.31 inference(rewrite,[status(thm)],[])).
% 22.13/22.31 tff(490,plain,
% 22.13/22.31 (((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, B!40)) | (~member(Y, A!41)) | (~member(X1, B!40)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), X1, Y)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), X2, Y)))) | ((tptp_fun_E_19(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)) = tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43)) | (~member(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), B!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), 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B!40, F!44, G!43), B!40)) | (tptp_fun_E_19(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)) = tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_E_19(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, 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% 22.13/22.31 inference(monotonicity,[status(thm)],[489])).
% 22.13/22.31 tff(491,plain,
% 22.13/22.31 (((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, B!40)) | (~member(Y, A!41)) | (~member(X1, B!40)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), X1, Y)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), X2, Y)))) | ((tptp_fun_E_19(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)) = tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43)) | (~member(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), B!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~member(tptp_fun_E_19(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_E_19(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, 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B!40, F!44, G!43), B!40)) | (tptp_fun_E_19(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)) = tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_E_19(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, 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% 22.13/22.31 inference(transitivity,[status(thm)],[490, 488])).
% 22.13/22.31 tff(492,plain,
% 22.13/22.31 ((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, B!40)) | (~member(Y, A!41)) | (~member(X1, B!40)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), X1, Y)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), X2, Y)))) | ((tptp_fun_E_19(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)) = tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43)) | (~member(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), B!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~member(tptp_fun_E_19(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_E_19(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))))),
% 22.13/22.32 inference(quant_inst,[status(thm)],[])).
% 22.13/22.32 tff(493,plain,
% 22.13/22.32 ((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, B!40)) | (~member(Y, A!41)) | (~member(X1, B!40)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), X1, Y)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), X2, Y)))) | (~member(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), B!40)) | (tptp_fun_E_19(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)) = tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_E_19(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~member(tptp_fun_E_19(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40))),
% 22.13/22.32 inference(modus_ponens,[status(thm)],[492, 491])).
% 22.13/22.32 tff(494,plain,
% 22.13/22.32 (tptp_fun_E_19(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)) = tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43)),
% 22.13/22.32 inference(unit_resolution,[status(thm)],[493, 487, 185, 419, 433, 473, 471])).
% 22.13/22.32 tff(495,plain,
% 22.13/22.32 (tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43) = tptp_fun_E_19(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40, compose_function(H!42, G!43, B!40, C!39, A!41))),
% 22.13/22.32 inference(symmetry,[status(thm)],[494])).
% 22.13/22.32 tff(496,plain,
% 22.13/22.32 (tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43) = tptp_fun_E_19(tptp_fun_Y_16(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41))),
% 22.13/22.32 inference(transitivity,[status(thm)],[495, 465])).
% 22.13/22.32 tff(497,plain,
% 22.13/22.32 (tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43) = tptp_fun_Y_3(tptp_fun_E_19(tptp_fun_Y_16(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43)),
% 22.13/22.32 inference(monotonicity,[status(thm)],[496])).
% 22.13/22.32 tff(498,plain,
% 22.13/22.32 (tptp_fun_Y_3(tptp_fun_E_19(tptp_fun_Y_16(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43) = tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43)),
% 22.13/22.32 inference(symmetry,[status(thm)],[497])).
% 22.13/22.32 tff(499,plain,
% 22.13/22.32 (((~member(tptp_fun_X2_17(A!41, C!39, H!42), C!39)) | (~member(tptp_fun_Y_16(A!41, C!39, H!42), A!41)) | (~member(tptp_fun_X1_18(A!41, C!39, H!42), C!39)) | (~apply(H!42, tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_Y_16(A!41, C!39, H!42))) | (~apply(H!42, tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_Y_16(A!41, C!39, H!42))) | (tptp_fun_X1_18(A!41, C!39, H!42) = tptp_fun_X2_17(A!41, C!39, H!42))) | member(tptp_fun_X1_18(A!41, C!39, H!42), C!39)),
% 22.13/22.32 inference(tautology,[status(thm)],[])).
% 22.13/22.32 tff(500,plain,
% 22.13/22.32 (member(tptp_fun_X1_18(A!41, C!39, H!42), C!39)),
% 22.13/22.32 inference(unit_resolution,[status(thm)],[499, 146])).
% 22.13/22.32 tff(501,plain,
% 22.13/22.32 (((~![Y: $i] : ((~member(Y, C!39)) | (~((~member(tptp_fun_E_19(Y, A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), A!41)) | (~apply(compose_function(G!43, F!44, A!41, B!40, C!39), tptp_fun_E_19(Y, A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), Y)))))) | ((~member(tptp_fun_X1_18(A!41, C!39, H!42), C!39)) | (~((~member(tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), A!41)) | (~apply(compose_function(G!43, F!44, A!41, B!40, C!39), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), tptp_fun_X1_18(A!41, C!39, H!42))))))) <=> ((~![Y: $i] : ((~member(Y, C!39)) | (~((~member(tptp_fun_E_19(Y, A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), A!41)) | (~apply(compose_function(G!43, F!44, A!41, B!40, C!39), tptp_fun_E_19(Y, A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), Y)))))) | (~member(tptp_fun_X1_18(A!41, C!39, H!42), C!39)) | (~((~member(tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), A!41)) | (~apply(compose_function(G!43, F!44, A!41, B!40, C!39), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), tptp_fun_X1_18(A!41, C!39, H!42))))))),
% 22.13/22.32 inference(rewrite,[status(thm)],[])).
% 22.13/22.32 tff(502,plain,
% 22.13/22.32 ((~![Y: $i] : ((~member(Y, C!39)) | (~((~member(tptp_fun_E_19(Y, A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), A!41)) | (~apply(compose_function(G!43, F!44, A!41, B!40, C!39), tptp_fun_E_19(Y, A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), Y)))))) | ((~member(tptp_fun_X1_18(A!41, C!39, H!42), C!39)) | (~((~member(tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), A!41)) | (~apply(compose_function(G!43, F!44, A!41, B!40, C!39), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), tptp_fun_X1_18(A!41, C!39, H!42))))))),
% 22.13/22.32 inference(quant_inst,[status(thm)],[])).
% 22.13/22.32 tff(503,plain,
% 22.13/22.32 ((~![Y: $i] : ((~member(Y, C!39)) | (~((~member(tptp_fun_E_19(Y, A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), A!41)) | (~apply(compose_function(G!43, F!44, A!41, B!40, C!39), tptp_fun_E_19(Y, A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), Y)))))) | (~member(tptp_fun_X1_18(A!41, C!39, H!42), C!39)) | (~((~member(tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), A!41)) | (~apply(compose_function(G!43, F!44, A!41, B!40, C!39), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), tptp_fun_X1_18(A!41, C!39, H!42)))))),
% 22.13/22.32 inference(modus_ponens,[status(thm)],[502, 501])).
% 22.13/22.32 tff(504,plain,
% 22.13/22.32 (~((~member(tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), A!41)) | (~apply(compose_function(G!43, F!44, A!41, B!40, C!39), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), tptp_fun_X1_18(A!41, C!39, H!42))))),
% 22.13/22.32 inference(unit_resolution,[status(thm)],[503, 163, 500])).
% 22.13/22.32 tff(505,plain,
% 22.13/22.32 (((~member(tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), A!41)) | (~apply(compose_function(G!43, F!44, A!41, B!40, C!39), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), tptp_fun_X1_18(A!41, C!39, H!42)))) | member(tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), A!41)),
% 22.13/22.32 inference(tautology,[status(thm)],[])).
% 22.13/22.32 tff(506,plain,
% 22.13/22.32 (member(tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), A!41)),
% 22.13/22.32 inference(unit_resolution,[status(thm)],[505, 504])).
% 22.13/22.32 tff(507,plain,
% 22.13/22.32 (((~![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(A!41, C!39, H!42), C!39)) | (~member(tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), A!41)) | (~((~(apply(compose_function(G!43, F!44, A!41, B!40, C!39), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), tptp_fun_X1_18(A!41, C!39, H!42)) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!44, tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), Y)) | (~apply(G!43, Y, tptp_fun_X1_18(A!41, C!39, H!42)))))) | (~((~apply(compose_function(G!43, F!44, A!41, B!40, C!39), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), tptp_fun_X1_18(A!41, C!39, H!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), B!40)) | (~apply(F!44, tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43))) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_X1_18(A!41, C!39, H!42))))))))))) <=> ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | (~member(tptp_fun_X1_18(A!41, C!39, H!42), C!39)) | (~member(tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), A!41)) | (~((~(apply(compose_function(G!43, F!44, A!41, B!40, C!39), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), tptp_fun_X1_18(A!41, C!39, H!42)) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!44, tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), Y)) | (~apply(G!43, Y, tptp_fun_X1_18(A!41, C!39, H!42)))))) | (~((~apply(compose_function(G!43, F!44, A!41, B!40, C!39), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), tptp_fun_X1_18(A!41, C!39, H!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), B!40)) | (~apply(F!44, tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43))) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_X1_18(A!41, C!39, H!42))))))))))),
% 22.13/22.32 inference(rewrite,[status(thm)],[])).
% 22.13/22.32 tff(508,plain,
% 22.13/22.32 (((~member(tptp_fun_X1_18(A!41, C!39, H!42), C!39)) | (~member(tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), A!41)) | (~((~((~apply(compose_function(G!43, F!44, A!41, B!40, C!39), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), tptp_fun_X1_18(A!41, C!39, H!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), B!40)) | (~apply(F!44, tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43))) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_X1_18(A!41, C!39, H!42))))))) | (~(apply(compose_function(G!43, F!44, A!41, B!40, C!39), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), tptp_fun_X1_18(A!41, C!39, H!42)) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!44, tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), Y)) | (~apply(G!43, Y, tptp_fun_X1_18(A!41, C!39, H!42))))))))) <=> ((~member(tptp_fun_X1_18(A!41, C!39, H!42), C!39)) | (~member(tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), A!41)) | (~((~(apply(compose_function(G!43, F!44, A!41, B!40, C!39), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), tptp_fun_X1_18(A!41, C!39, H!42)) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!44, tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), Y)) | (~apply(G!43, Y, tptp_fun_X1_18(A!41, C!39, H!42)))))) | (~((~apply(compose_function(G!43, F!44, A!41, B!40, C!39), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), tptp_fun_X1_18(A!41, C!39, H!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), B!40)) | (~apply(F!44, tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43))) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_X1_18(A!41, C!39, H!42))))))))))),
% 22.13/22.32 inference(rewrite,[status(thm)],[])).
% 22.13/22.32 tff(509,plain,
% 22.13/22.32 (((~![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(A!41, C!39, H!42), C!39)) | (~member(tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), A!41)) | (~((~((~apply(compose_function(G!43, F!44, A!41, B!40, C!39), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), tptp_fun_X1_18(A!41, C!39, H!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), B!40)) | (~apply(F!44, tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43))) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_X1_18(A!41, C!39, H!42))))))) | (~(apply(compose_function(G!43, F!44, A!41, B!40, C!39), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), tptp_fun_X1_18(A!41, C!39, H!42)) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!44, tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), Y)) | (~apply(G!43, Y, tptp_fun_X1_18(A!41, C!39, H!42)))))))))) <=> ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_X1_18(A!41, C!39, H!42), C!39)) | (~member(tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), A!41)) | (~((~(apply(compose_function(G!43, F!44, A!41, B!40, C!39), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), tptp_fun_X1_18(A!41, C!39, H!42)) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!44, tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), Y)) | (~apply(G!43, Y, tptp_fun_X1_18(A!41, C!39, H!42)))))) | (~((~apply(compose_function(G!43, F!44, A!41, B!40, C!39), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), tptp_fun_X1_18(A!41, C!39, H!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), B!40)) | (~apply(F!44, tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43))) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_X1_18(A!41, C!39, H!42)))))))))))),
% 22.13/22.33 inference(monotonicity,[status(thm)],[508])).
% 22.13/22.33 tff(510,plain,
% 22.13/22.33 (((~![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(A!41, C!39, H!42), C!39)) | (~member(tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), A!41)) | (~((~((~apply(compose_function(G!43, F!44, A!41, B!40, C!39), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), tptp_fun_X1_18(A!41, C!39, H!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), B!40)) | (~apply(F!44, tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43))) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_X1_18(A!41, C!39, H!42))))))) | (~(apply(compose_function(G!43, F!44, A!41, B!40, C!39), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), tptp_fun_X1_18(A!41, C!39, H!42)) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!44, tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), Y)) | (~apply(G!43, Y, tptp_fun_X1_18(A!41, C!39, H!42)))))))))) <=> ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | (~member(tptp_fun_X1_18(A!41, C!39, H!42), C!39)) | (~member(tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), A!41)) | (~((~(apply(compose_function(G!43, F!44, A!41, B!40, C!39), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), tptp_fun_X1_18(A!41, C!39, H!42)) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!44, tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), Y)) | (~apply(G!43, Y, tptp_fun_X1_18(A!41, C!39, H!42)))))) | (~((~apply(compose_function(G!43, F!44, A!41, B!40, C!39), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), tptp_fun_X1_18(A!41, C!39, H!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), B!40)) | (~apply(F!44, tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43))) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_X1_18(A!41, C!39, H!42))))))))))),
% 22.13/22.33 inference(transitivity,[status(thm)],[509, 507])).
% 22.13/22.33 tff(511,plain,
% 22.13/22.33 ((~![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(A!41, C!39, H!42), C!39)) | (~member(tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), A!41)) | (~((~((~apply(compose_function(G!43, F!44, A!41, B!40, C!39), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), tptp_fun_X1_18(A!41, C!39, H!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), B!40)) | (~apply(F!44, tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43))) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_X1_18(A!41, C!39, H!42))))))) | (~(apply(compose_function(G!43, F!44, A!41, B!40, C!39), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), tptp_fun_X1_18(A!41, C!39, H!42)) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!44, tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), Y)) | (~apply(G!43, Y, tptp_fun_X1_18(A!41, C!39, H!42)))))))))),
% 22.13/22.33 inference(quant_inst,[status(thm)],[])).
% 22.13/22.33 tff(512,plain,
% 22.13/22.33 ((~![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(A!41, C!39, H!42), C!39)) | (~member(tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), A!41)) | (~((~(apply(compose_function(G!43, F!44, A!41, B!40, C!39), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), tptp_fun_X1_18(A!41, C!39, H!42)) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!44, tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), Y)) | (~apply(G!43, Y, tptp_fun_X1_18(A!41, C!39, H!42)))))) | (~((~apply(compose_function(G!43, F!44, A!41, B!40, C!39), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), tptp_fun_X1_18(A!41, C!39, H!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), B!40)) | (~apply(F!44, tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43))) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_X1_18(A!41, C!39, H!42)))))))))),
% 22.13/22.33 inference(modus_ponens,[status(thm)],[511, 510])).
% 22.13/22.33 tff(513,plain,
% 22.13/22.33 (~((~(apply(compose_function(G!43, F!44, A!41, B!40, C!39), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), tptp_fun_X1_18(A!41, C!39, H!42)) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!44, tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), Y)) | (~apply(G!43, Y, tptp_fun_X1_18(A!41, C!39, H!42)))))) | (~((~apply(compose_function(G!43, F!44, A!41, B!40, C!39), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), tptp_fun_X1_18(A!41, C!39, H!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), B!40)) | (~apply(F!44, tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43))) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_X1_18(A!41, C!39, H!42))))))))),
% 22.13/22.33 inference(unit_resolution,[status(thm)],[512, 106, 500, 506])).
% 22.13/22.33 tff(514,plain,
% 22.13/22.33 (((~(apply(compose_function(G!43, F!44, A!41, B!40, C!39), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), tptp_fun_X1_18(A!41, C!39, H!42)) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!44, tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), Y)) | (~apply(G!43, Y, tptp_fun_X1_18(A!41, C!39, H!42)))))) | (~((~apply(compose_function(G!43, F!44, A!41, B!40, C!39), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), tptp_fun_X1_18(A!41, C!39, H!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), B!40)) | (~apply(F!44, tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43))) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_X1_18(A!41, C!39, H!42)))))))) | ((~apply(compose_function(G!43, F!44, A!41, B!40, C!39), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), tptp_fun_X1_18(A!41, C!39, H!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), B!40)) | (~apply(F!44, tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43))) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_X1_18(A!41, C!39, H!42))))))),
% 22.13/22.33 inference(tautology,[status(thm)],[])).
% 22.13/22.33 tff(515,plain,
% 22.13/22.33 ((~apply(compose_function(G!43, F!44, A!41, B!40, C!39), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), tptp_fun_X1_18(A!41, C!39, H!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), B!40)) | (~apply(F!44, tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43))) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_X1_18(A!41, C!39, H!42)))))),
% 22.13/22.33 inference(unit_resolution,[status(thm)],[514, 513])).
% 22.13/22.33 tff(516,plain,
% 22.13/22.33 (((~member(tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), A!41)) | (~apply(compose_function(G!43, F!44, A!41, B!40, C!39), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), tptp_fun_X1_18(A!41, C!39, H!42)))) | apply(compose_function(G!43, F!44, A!41, B!40, C!39), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), tptp_fun_X1_18(A!41, C!39, H!42))),
% 22.13/22.33 inference(tautology,[status(thm)],[])).
% 22.13/22.33 tff(517,plain,
% 22.13/22.33 (apply(compose_function(G!43, F!44, A!41, B!40, C!39), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), tptp_fun_X1_18(A!41, C!39, H!42))),
% 22.13/22.33 inference(unit_resolution,[status(thm)],[516, 504])).
% 22.13/22.33 tff(518,plain,
% 22.13/22.33 ((~((~apply(compose_function(G!43, F!44, A!41, B!40, C!39), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), tptp_fun_X1_18(A!41, C!39, H!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), B!40)) | (~apply(F!44, tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43))) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_X1_18(A!41, C!39, H!42))))))) | (~apply(compose_function(G!43, F!44, A!41, B!40, C!39), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), tptp_fun_X1_18(A!41, C!39, H!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), B!40)) | (~apply(F!44, tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43))) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_X1_18(A!41, C!39, H!42)))))),
% 22.13/22.34 inference(tautology,[status(thm)],[])).
% 22.13/22.34 tff(519,plain,
% 22.13/22.34 ((~((~apply(compose_function(G!43, F!44, A!41, B!40, C!39), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), tptp_fun_X1_18(A!41, C!39, H!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), B!40)) | (~apply(F!44, tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43))) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_X1_18(A!41, C!39, H!42))))))) | (~((~member(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), B!40)) | (~apply(F!44, tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43))) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_X1_18(A!41, C!39, H!42)))))),
% 22.13/22.34 inference(unit_resolution,[status(thm)],[518, 517])).
% 22.13/22.34 tff(520,plain,
% 22.13/22.34 (~((~member(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), B!40)) | (~apply(F!44, tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43))) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_X1_18(A!41, C!39, H!42))))),
% 22.13/22.34 inference(unit_resolution,[status(thm)],[519, 515])).
% 22.13/22.34 tff(521,plain,
% 22.13/22.34 (((~member(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), B!40)) | (~apply(F!44, tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43))) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_X1_18(A!41, C!39, H!42)))) | member(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), B!40)),
% 22.13/22.34 inference(tautology,[status(thm)],[])).
% 22.13/22.34 tff(522,plain,
% 22.13/22.34 (member(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), B!40)),
% 22.13/22.34 inference(unit_resolution,[status(thm)],[521, 520])).
% 22.13/22.34 tff(523,plain,
% 22.13/22.34 (((~![X: $i] : ((~member(X, B!40)) | (~((~member(tptp_fun_Y_3(X, A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), X, tptp_fun_Y_3(X, A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))))))) | ((~member(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), B!40)) | (~((~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))))))) <=> ((~![X: $i] : ((~member(X, B!40)) | (~((~member(tptp_fun_Y_3(X, A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), X, tptp_fun_Y_3(X, A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))))))) | (~member(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), B!40)) | (~((~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))))))),
% 22.13/22.34 inference(rewrite,[status(thm)],[])).
% 22.13/22.34 tff(524,plain,
% 22.13/22.34 ((~![X: $i] : ((~member(X, B!40)) | (~((~member(tptp_fun_Y_3(X, A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), X, tptp_fun_Y_3(X, A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))))))) | ((~member(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), B!40)) | (~((~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))))))),
% 22.13/22.34 inference(quant_inst,[status(thm)],[])).
% 22.13/22.34 tff(525,plain,
% 22.13/22.34 ((~![X: $i] : ((~member(X, B!40)) | (~((~member(tptp_fun_Y_3(X, A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), X, tptp_fun_Y_3(X, A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))))))) | (~member(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), B!40)) | (~((~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41))))))),
% 22.13/22.34 inference(modus_ponens,[status(thm)],[524, 523])).
% 22.13/22.34 tff(526,plain,
% 22.13/22.34 (~((~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))))),
% 22.13/22.34 inference(unit_resolution,[status(thm)],[525, 522, 413])).
% 22.13/22.34 tff(527,plain,
% 22.13/22.34 (((~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41))))) | member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)),
% 22.13/22.34 inference(tautology,[status(thm)],[])).
% 22.13/22.34 tff(528,plain,
% 22.13/22.34 (member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)),
% 22.13/22.34 inference(unit_resolution,[status(thm)],[527, 526])).
% 22.13/22.34 tff(529,plain,
% 22.13/22.34 (((~![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_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), B!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~((~(apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), 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A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))))))))))) <=> ((~![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_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), B!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~((~(apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41))) | ![Y: $i] : ((~member(Y, C!39)) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), Y)) | (~apply(H!42, Y, tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41))))))) | (~((~apply(compose_function(H!42, G!43, B!40, 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compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42))) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))))))))))),
% 22.13/22.34 inference(rewrite,[status(thm)],[])).
% 22.13/22.34 tff(530,plain,
% 22.13/22.34 (((~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~member(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), B!40)) | (~((~(apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41))) | ![Y: $i] : ((~member(Y, C!39)) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), Y)) | (~apply(H!42, Y, tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41))))))) | (~((~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), 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B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41))))))) | (~((~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42), C!39)) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42))) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))))))))))),
% 22.13/22.35 inference(rewrite,[status(thm)],[])).
% 22.13/22.35 tff(531,plain,
% 22.13/22.35 ((~((~((~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42), C!39)) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, 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% 22.21/22.35 inference(rewrite,[status(thm)],[])).
% 22.21/22.35 tff(532,plain,
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C!39)) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42))) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))))))))))),
% 22.21/22.36 inference(monotonicity,[status(thm)],[531])).
% 22.21/22.36 tff(533,plain,
% 22.21/22.36 (((~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~member(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), B!40)) | (~((~((~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, 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H!42))) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))))))) | (~(apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), 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A!41, compose_function(H!42, G!43, B!40, C!39, A!41))))))) | (~((~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42), C!39)) | 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% 22.21/22.36 inference(transitivity,[status(thm)],[532, 530])).
% 22.21/22.36 tff(534,plain,
% 22.21/22.36 (((~![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_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~member(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), B!40)) | (~((~((~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), 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G!43), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42))) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))))))) | (~(apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41))) | ![Y: $i] : ((~member(Y, C!39)) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), Y)) | (~apply(H!42, Y, tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41))))))))))) <=> ((~![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_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), B!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~((~(apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41))) | ![Y: $i] : ((~member(Y, C!39)) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), Y)) | (~apply(H!42, Y, tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41))))))) | (~((~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42), C!39)) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42))) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41))))))))))))),
% 22.21/22.37 inference(monotonicity,[status(thm)],[533])).
% 22.21/22.37 tff(535,plain,
% 22.21/22.37 (((~![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_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~member(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), B!40)) | (~((~((~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), 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B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41))))))))))) <=> ((~![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_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), B!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~((~(apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41))) | ![Y: $i] : ((~member(Y, C!39)) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), Y)) | (~apply(H!42, Y, tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41))))))) | (~((~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42), C!39)) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42))) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))))))))))),
% 22.23/22.37 inference(transitivity,[status(thm)],[534, 529])).
% 22.23/22.37 tff(536,plain,
% 22.23/22.37 ((~![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_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~member(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), B!40)) | (~((~((~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42), C!39)) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42))) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))))))) | (~(apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41))) | ![Y: $i] : ((~member(Y, C!39)) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), Y)) | (~apply(H!42, Y, tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41))))))))))),
% 22.23/22.37 inference(quant_inst,[status(thm)],[])).
% 22.23/22.37 tff(537,plain,
% 22.23/22.37 ((~![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_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), B!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~((~(apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41))) | ![Y: $i] : ((~member(Y, C!39)) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), Y)) | (~apply(H!42, Y, tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41))))))) | (~((~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42), C!39)) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42))) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41))))))))))),
% 22.23/22.38 inference(modus_ponens,[status(thm)],[536, 535])).
% 22.23/22.38 tff(538,plain,
% 22.23/22.38 (~((~(apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41))) | ![Y: $i] : ((~member(Y, C!39)) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), Y)) | (~apply(H!42, Y, tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41))))))) | (~((~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42), C!39)) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42))) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))))))))),
% 22.23/22.38 inference(unit_resolution,[status(thm)],[537, 106, 522, 528])).
% 22.23/22.38 tff(539,plain,
% 22.23/22.38 (((~(apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41))) | ![Y: $i] : ((~member(Y, C!39)) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), Y)) | (~apply(H!42, Y, tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41))))))) | (~((~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42), C!39)) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42))) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41))))))))) | ((~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42), C!39)) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42))) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))))))),
% 22.23/22.38 inference(tautology,[status(thm)],[])).
% 22.23/22.38 tff(540,plain,
% 22.23/22.38 ((~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42), C!39)) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42))) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41))))))),
% 22.23/22.38 inference(unit_resolution,[status(thm)],[539, 538])).
% 22.23/22.38 tff(541,plain,
% 22.23/22.38 (((~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41))))) | apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))),
% 22.23/22.38 inference(tautology,[status(thm)],[])).
% 22.23/22.38 tff(542,plain,
% 22.23/22.38 (apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))),
% 22.23/22.38 inference(unit_resolution,[status(thm)],[541, 526])).
% 22.23/22.38 tff(543,plain,
% 22.23/22.38 ((~((~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42), C!39)) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42))) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))))))) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42), C!39)) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42))) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41))))))),
% 22.23/22.39 inference(tautology,[status(thm)],[])).
% 22.23/22.39 tff(544,plain,
% 22.23/22.39 ((~((~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42), C!39)) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42))) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))))))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42), C!39)) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42))) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41))))))),
% 22.23/22.39 inference(unit_resolution,[status(thm)],[543, 542])).
% 22.23/22.39 tff(545,plain,
% 22.23/22.39 (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42), C!39)) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42))) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))))),
% 22.23/22.39 inference(unit_resolution,[status(thm)],[544, 540])).
% 22.23/22.39 tff(546,plain,
% 22.23/22.39 (((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42), C!39)) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42))) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41))))) | apply(G!43, tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42))),
% 22.23/22.39 inference(tautology,[status(thm)],[])).
% 22.23/22.39 tff(547,plain,
% 22.23/22.39 (apply(G!43, tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42))),
% 22.23/22.39 inference(unit_resolution,[status(thm)],[546, 545])).
% 22.23/22.39 tff(548,plain,
% 22.23/22.39 (((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42), C!39)) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42))) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41))))) | member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42), C!39)),
% 22.23/22.39 inference(tautology,[status(thm)],[])).
% 22.23/22.39 tff(549,plain,
% 22.23/22.39 (member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42), C!39)),
% 22.23/22.39 inference(unit_resolution,[status(thm)],[548, 545])).
% 22.23/22.39 tff(550,plain,
% 22.23/22.39 (((~![X: $i] : ((~member(X, B!40)) | (~((~member(tptp_fun_Y_3(X, C!39, G!43), C!39)) | (~apply(G!43, X, tptp_fun_Y_3(X, C!39, G!43))))))) | ((~member(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), B!40)) | (~((~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43), C!39)) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43))))))) <=> ((~![X: $i] : ((~member(X, B!40)) | (~((~member(tptp_fun_Y_3(X, C!39, G!43), C!39)) | (~apply(G!43, X, tptp_fun_Y_3(X, C!39, G!43))))))) | (~member(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), B!40)) | (~((~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43), C!39)) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43))))))),
% 22.23/22.40 inference(rewrite,[status(thm)],[])).
% 22.23/22.40 tff(551,plain,
% 22.23/22.40 ((~![X: $i] : ((~member(X, B!40)) | (~((~member(tptp_fun_Y_3(X, C!39, G!43), C!39)) | (~apply(G!43, X, tptp_fun_Y_3(X, C!39, G!43))))))) | ((~member(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), B!40)) | (~((~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43), C!39)) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43))))))),
% 22.23/22.40 inference(quant_inst,[status(thm)],[])).
% 22.23/22.40 tff(552,plain,
% 22.23/22.40 ((~![X: $i] : ((~member(X, B!40)) | (~((~member(tptp_fun_Y_3(X, C!39, G!43), C!39)) | (~apply(G!43, X, tptp_fun_Y_3(X, C!39, G!43))))))) | (~member(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), B!40)) | (~((~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43), C!39)) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43)))))),
% 22.23/22.40 inference(modus_ponens,[status(thm)],[551, 550])).
% 22.23/22.40 tff(553,plain,
% 22.23/22.40 (~((~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43), C!39)) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43))))),
% 22.23/22.40 inference(unit_resolution,[status(thm)],[552, 222, 522])).
% 22.23/22.40 tff(554,plain,
% 22.23/22.40 (((~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43), C!39)) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43)))) | apply(G!43, tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43))),
% 22.23/22.40 inference(tautology,[status(thm)],[])).
% 22.23/22.40 tff(555,plain,
% 22.23/22.40 (apply(G!43, tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43))),
% 22.23/22.40 inference(unit_resolution,[status(thm)],[554, 553])).
% 22.23/22.40 tff(556,plain,
% 22.23/22.40 (((~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43), C!39)) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43)))) | member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43), C!39)),
% 22.23/22.40 inference(tautology,[status(thm)],[])).
% 22.23/22.40 tff(557,plain,
% 22.23/22.40 (member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43), C!39)),
% 22.23/22.40 inference(unit_resolution,[status(thm)],[556, 553])).
% 22.23/22.40 tff(558,plain,
% 22.23/22.40 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, C!39)) | (~apply(G!43, X, Y1)) | (~apply(G!43, X, Y2)) | (~member(X, B!40)) | (~member(Y1, C!39)))) | ((~member(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), B!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43), C!39)) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43))) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42))) | (~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42), C!39)) | (tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42) = tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, C!39)) | (~apply(G!43, X, Y1)) | (~apply(G!43, X, Y2)) | (~member(X, B!40)) | (~member(Y1, C!39)))) | (~member(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), B!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43), C!39)) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43))) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42))) | (~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42), C!39)) | (tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42) = tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43)))),
% 22.23/22.40 inference(rewrite,[status(thm)],[])).
% 22.23/22.40 tff(559,plain,
% 22.23/22.40 (((tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42) = tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43)) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43), C!39)) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42))) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43))) | (~member(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), B!40)) | (~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42), C!39))) <=> ((~member(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), B!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43), C!39)) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43))) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42))) | (~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42), C!39)) | (tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42) = tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43)))),
% 22.23/22.41 inference(rewrite,[status(thm)],[])).
% 22.23/22.41 tff(560,plain,
% 22.23/22.41 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, C!39)) | (~apply(G!43, X, Y1)) | (~apply(G!43, X, Y2)) | (~member(X, B!40)) | (~member(Y1, C!39)))) | ((tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42) = tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43)) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43), C!39)) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42))) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43))) | (~member(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), B!40)) | (~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42), C!39)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, C!39)) | (~apply(G!43, X, Y1)) | (~apply(G!43, X, Y2)) | (~member(X, B!40)) | (~member(Y1, C!39)))) | ((~member(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), B!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43), C!39)) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43))) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42))) | (~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42), C!39)) | (tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42) = tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43))))),
% 22.23/22.41 inference(monotonicity,[status(thm)],[559])).
% 22.23/22.41 tff(561,plain,
% 22.23/22.41 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, C!39)) | (~apply(G!43, X, Y1)) | (~apply(G!43, X, Y2)) | (~member(X, B!40)) | (~member(Y1, C!39)))) | ((tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42) = tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43)) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43), C!39)) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42))) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43))) | (~member(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), B!40)) | (~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42), C!39)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, C!39)) | (~apply(G!43, X, Y1)) | (~apply(G!43, X, Y2)) | (~member(X, B!40)) | (~member(Y1, C!39)))) | (~member(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), B!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43), C!39)) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43))) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42))) | (~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42), C!39)) | (tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42) = tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43)))),
% 22.23/22.41 inference(transitivity,[status(thm)],[560, 558])).
% 22.23/22.41 tff(562,plain,
% 22.23/22.41 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, C!39)) | (~apply(G!43, X, Y1)) | (~apply(G!43, X, Y2)) | (~member(X, B!40)) | (~member(Y1, C!39)))) | ((tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42) = tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43)) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43), C!39)) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42))) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43))) | (~member(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), B!40)) | (~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42), C!39)))),
% 22.27/22.41 inference(quant_inst,[status(thm)],[])).
% 22.27/22.41 tff(563,plain,
% 22.27/22.41 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, C!39)) | (~apply(G!43, X, Y1)) | (~apply(G!43, X, Y2)) | (~member(X, B!40)) | (~member(Y1, C!39)))) | (~member(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), B!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43), C!39)) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43))) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42))) | (~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42), C!39)) | (tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42) = tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43))),
% 22.27/22.42 inference(modus_ponens,[status(thm)],[562, 561])).
% 22.27/22.42 tff(564,plain,
% 22.27/22.42 (tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42) = tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43)),
% 22.27/22.42 inference(unit_resolution,[status(thm)],[563, 234, 522, 557, 555, 549, 547])).
% 22.27/22.42 tff(565,plain,
% 22.27/22.42 (tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43) = tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42)),
% 22.27/22.42 inference(symmetry,[status(thm)],[564])).
% 22.27/22.42 tff(566,plain,
% 22.27/22.42 (apply(H!42, tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41))) <=> apply(H!42, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))),
% 22.27/22.42 inference(monotonicity,[status(thm)],[565])).
% 22.27/22.42 tff(567,plain,
% 22.27/22.42 (apply(H!42, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41))) <=> apply(H!42, tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))),
% 22.27/22.42 inference(symmetry,[status(thm)],[566])).
% 22.27/22.42 tff(568,plain,
% 22.27/22.42 (((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42), C!39)) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42))) | (~apply(H!42, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41))))) | apply(H!42, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))),
% 22.27/22.42 inference(tautology,[status(thm)],[])).
% 22.27/22.42 tff(569,plain,
% 22.27/22.42 (apply(H!42, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43, H!42), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))),
% 22.27/22.42 inference(unit_resolution,[status(thm)],[568, 545])).
% 22.27/22.42 tff(570,plain,
% 22.27/22.42 (apply(H!42, tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))),
% 22.27/22.42 inference(modus_ponens,[status(thm)],[569, 567])).
% 22.27/22.42 tff(571,plain,
% 22.27/22.42 (((~member(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), B!40)) | (~apply(F!44, tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43))) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_X1_18(A!41, C!39, H!42)))) | apply(G!43, tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_X1_18(A!41, C!39, H!42))),
% 22.27/22.42 inference(tautology,[status(thm)],[])).
% 22.27/22.42 tff(572,plain,
% 22.27/22.42 (apply(G!43, tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_X1_18(A!41, C!39, H!42))),
% 22.27/22.42 inference(unit_resolution,[status(thm)],[571, 520])).
% 22.27/22.42 tff(573,plain,
% 22.27/22.42 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, C!39)) | (~apply(G!43, X, Y1)) | (~apply(G!43, X, Y2)) | (~member(X, B!40)) | (~member(Y1, C!39)))) | ((~member(tptp_fun_X1_18(A!41, C!39, H!42), C!39)) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_X1_18(A!41, C!39, H!42))) | (~member(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), B!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43), C!39)) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43))) | (tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43) = tptp_fun_X1_18(A!41, C!39, H!42)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, C!39)) | (~apply(G!43, X, Y1)) | (~apply(G!43, X, Y2)) | (~member(X, B!40)) | (~member(Y1, C!39)))) | (~member(tptp_fun_X1_18(A!41, C!39, H!42), C!39)) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_X1_18(A!41, C!39, H!42))) | (~member(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), B!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43), C!39)) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43))) | (tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43) = tptp_fun_X1_18(A!41, C!39, H!42)))),
% 22.27/22.42 inference(rewrite,[status(thm)],[])).
% 22.27/22.42 tff(574,plain,
% 22.27/22.42 (((tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43) = tptp_fun_X1_18(A!41, C!39, H!42)) | (~member(tptp_fun_X1_18(A!41, C!39, H!42), C!39)) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43))) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_X1_18(A!41, C!39, H!42))) | (~member(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), B!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43), C!39))) <=> ((~member(tptp_fun_X1_18(A!41, C!39, H!42), C!39)) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_X1_18(A!41, C!39, H!42))) | (~member(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), B!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43), C!39)) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43))) | (tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43) = tptp_fun_X1_18(A!41, C!39, H!42)))),
% 22.27/22.42 inference(rewrite,[status(thm)],[])).
% 22.27/22.42 tff(575,plain,
% 22.27/22.42 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, C!39)) | (~apply(G!43, X, Y1)) | (~apply(G!43, X, Y2)) | (~member(X, B!40)) | (~member(Y1, C!39)))) | ((tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43) = tptp_fun_X1_18(A!41, C!39, H!42)) | (~member(tptp_fun_X1_18(A!41, C!39, H!42), C!39)) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43))) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_X1_18(A!41, C!39, H!42))) | (~member(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), B!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43), C!39)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, C!39)) | (~apply(G!43, X, Y1)) | (~apply(G!43, X, Y2)) | (~member(X, B!40)) | (~member(Y1, C!39)))) | ((~member(tptp_fun_X1_18(A!41, C!39, H!42), C!39)) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_X1_18(A!41, C!39, H!42))) | (~member(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), B!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43), C!39)) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43))) | (tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43) = tptp_fun_X1_18(A!41, C!39, H!42))))),
% 22.27/22.42 inference(monotonicity,[status(thm)],[574])).
% 22.27/22.42 tff(576,plain,
% 22.27/22.42 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, C!39)) | (~apply(G!43, X, Y1)) | (~apply(G!43, X, Y2)) | (~member(X, B!40)) | (~member(Y1, C!39)))) | ((tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43) = tptp_fun_X1_18(A!41, C!39, H!42)) | (~member(tptp_fun_X1_18(A!41, C!39, H!42), C!39)) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43))) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_X1_18(A!41, C!39, H!42))) | (~member(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), B!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43), C!39)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, C!39)) | (~apply(G!43, X, Y1)) | (~apply(G!43, X, Y2)) | (~member(X, B!40)) | (~member(Y1, C!39)))) | (~member(tptp_fun_X1_18(A!41, C!39, H!42), C!39)) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_X1_18(A!41, C!39, H!42))) | (~member(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), B!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43), C!39)) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43))) | (tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43) = tptp_fun_X1_18(A!41, C!39, H!42)))),
% 22.27/22.43 inference(transitivity,[status(thm)],[575, 573])).
% 22.27/22.43 tff(577,plain,
% 22.27/22.43 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, C!39)) | (~apply(G!43, X, Y1)) | (~apply(G!43, X, Y2)) | (~member(X, B!40)) | (~member(Y1, C!39)))) | ((tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43) = tptp_fun_X1_18(A!41, C!39, H!42)) | (~member(tptp_fun_X1_18(A!41, C!39, H!42), C!39)) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43))) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_X1_18(A!41, C!39, H!42))) | (~member(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), B!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43), C!39)))),
% 22.27/22.43 inference(quant_inst,[status(thm)],[])).
% 22.27/22.43 tff(578,plain,
% 22.27/22.43 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, C!39)) | (~apply(G!43, X, Y1)) | (~apply(G!43, X, Y2)) | (~member(X, B!40)) | (~member(Y1, C!39)))) | (~member(tptp_fun_X1_18(A!41, C!39, H!42), C!39)) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_X1_18(A!41, C!39, H!42))) | (~member(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), B!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43), C!39)) | (~apply(G!43, tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43))) | (tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43) = tptp_fun_X1_18(A!41, C!39, H!42))),
% 22.27/22.43 inference(modus_ponens,[status(thm)],[577, 576])).
% 22.27/22.43 tff(579,plain,
% 22.27/22.43 (tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43) = tptp_fun_X1_18(A!41, C!39, H!42)),
% 22.27/22.43 inference(unit_resolution,[status(thm)],[578, 234, 500, 522, 572, 557, 555])).
% 22.27/22.43 tff(580,plain,
% 22.27/22.43 (apply(H!42, tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43), tptp_fun_Y_16(A!41, C!39, H!42)) <=> apply(H!42, tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_Y_16(A!41, C!39, H!42))),
% 22.27/22.43 inference(monotonicity,[status(thm)],[579])).
% 22.27/22.43 tff(581,plain,
% 22.27/22.43 (apply(H!42, tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_Y_16(A!41, C!39, H!42)) <=> apply(H!42, tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43), tptp_fun_Y_16(A!41, C!39, H!42))),
% 22.27/22.43 inference(symmetry,[status(thm)],[580])).
% 22.27/22.43 tff(582,plain,
% 22.27/22.43 (((~member(tptp_fun_X2_17(A!41, C!39, H!42), C!39)) | (~member(tptp_fun_Y_16(A!41, C!39, H!42), A!41)) | (~member(tptp_fun_X1_18(A!41, C!39, H!42), C!39)) | (~apply(H!42, tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_Y_16(A!41, C!39, H!42))) | (~apply(H!42, tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_Y_16(A!41, C!39, H!42))) | (tptp_fun_X1_18(A!41, C!39, H!42) = tptp_fun_X2_17(A!41, C!39, H!42))) | apply(H!42, tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_Y_16(A!41, C!39, H!42))),
% 22.27/22.43 inference(tautology,[status(thm)],[])).
% 22.27/22.43 tff(583,plain,
% 22.27/22.43 (apply(H!42, tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_Y_16(A!41, C!39, H!42))),
% 22.27/22.43 inference(unit_resolution,[status(thm)],[582, 146])).
% 22.27/22.43 tff(584,plain,
% 22.27/22.43 (apply(H!42, tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43), tptp_fun_Y_16(A!41, C!39, H!42))),
% 22.27/22.43 inference(modus_ponens,[status(thm)],[583, 581])).
% 22.27/22.43 tff(585,plain,
% 22.27/22.43 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!41)) | (~apply(H!42, X, Y1)) | (~apply(H!42, X, Y2)) | (~member(X, C!39)) | (~member(Y1, A!41)))) | ((~member(tptp_fun_Y_16(A!41, C!39, H!42), A!41)) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43), C!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~apply(H!42, tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43), tptp_fun_Y_16(A!41, C!39, H!42))) | (tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)) = tptp_fun_Y_16(A!41, C!39, H!42)) | (~apply(H!42, tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!41)) | (~apply(H!42, X, Y1)) | (~apply(H!42, X, Y2)) | (~member(X, C!39)) | (~member(Y1, A!41)))) | (~member(tptp_fun_Y_16(A!41, C!39, H!42), A!41)) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43), C!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~apply(H!42, tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43), tptp_fun_Y_16(A!41, C!39, H!42))) | (tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)) = tptp_fun_Y_16(A!41, C!39, H!42)) | (~apply(H!42, tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))))),
% 22.27/22.43 inference(rewrite,[status(thm)],[])).
% 22.27/22.43 tff(586,plain,
% 22.27/22.43 (((tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)) = tptp_fun_Y_16(A!41, C!39, H!42)) | (~member(tptp_fun_Y_16(A!41, C!39, H!42), A!41)) | (~apply(H!42, tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~apply(H!42, tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43), tptp_fun_Y_16(A!41, C!39, H!42))) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43), C!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41))) <=> ((~member(tptp_fun_Y_16(A!41, C!39, H!42), A!41)) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43), C!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~apply(H!42, tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43), tptp_fun_Y_16(A!41, C!39, H!42))) | (tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)) = tptp_fun_Y_16(A!41, C!39, H!42)) | (~apply(H!42, tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))))),
% 22.27/22.43 inference(rewrite,[status(thm)],[])).
% 22.27/22.43 tff(587,plain,
% 22.27/22.43 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!41)) | (~apply(H!42, X, Y1)) | (~apply(H!42, X, Y2)) | (~member(X, C!39)) | (~member(Y1, A!41)))) | ((tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)) = tptp_fun_Y_16(A!41, C!39, H!42)) | (~member(tptp_fun_Y_16(A!41, C!39, H!42), A!41)) | (~apply(H!42, tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~apply(H!42, tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43), tptp_fun_Y_16(A!41, C!39, H!42))) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43), C!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!41)) | (~apply(H!42, X, Y1)) | (~apply(H!42, X, Y2)) | (~member(X, C!39)) | (~member(Y1, A!41)))) | ((~member(tptp_fun_Y_16(A!41, C!39, H!42), A!41)) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43), C!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~apply(H!42, tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43), tptp_fun_Y_16(A!41, C!39, H!42))) | (tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)) = tptp_fun_Y_16(A!41, C!39, H!42)) | (~apply(H!42, tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41))))))),
% 22.27/22.43 inference(monotonicity,[status(thm)],[586])).
% 22.27/22.43 tff(588,plain,
% 22.27/22.43 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!41)) | (~apply(H!42, X, Y1)) | (~apply(H!42, X, Y2)) | (~member(X, C!39)) | (~member(Y1, A!41)))) | ((tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)) = tptp_fun_Y_16(A!41, C!39, H!42)) | (~member(tptp_fun_Y_16(A!41, C!39, H!42), A!41)) | (~apply(H!42, tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~apply(H!42, tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43), tptp_fun_Y_16(A!41, C!39, H!42))) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43), C!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!41)) | (~apply(H!42, X, Y1)) | (~apply(H!42, X, Y2)) | (~member(X, C!39)) | (~member(Y1, A!41)))) | (~member(tptp_fun_Y_16(A!41, C!39, H!42), A!41)) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43), C!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~apply(H!42, tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43), tptp_fun_Y_16(A!41, C!39, H!42))) | (tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)) = tptp_fun_Y_16(A!41, C!39, H!42)) | (~apply(H!42, tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))))),
% 22.27/22.44 inference(transitivity,[status(thm)],[587, 585])).
% 22.27/22.44 tff(589,plain,
% 22.27/22.44 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!41)) | (~apply(H!42, X, Y1)) | (~apply(H!42, X, Y2)) | (~member(X, C!39)) | (~member(Y1, A!41)))) | ((tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)) = tptp_fun_Y_16(A!41, C!39, H!42)) | (~member(tptp_fun_Y_16(A!41, C!39, H!42), A!41)) | (~apply(H!42, tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~apply(H!42, tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43), tptp_fun_Y_16(A!41, C!39, H!42))) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43), C!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)))),
% 22.29/22.44 inference(quant_inst,[status(thm)],[])).
% 22.29/22.44 tff(590,plain,
% 22.29/22.44 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!41)) | (~apply(H!42, X, Y1)) | (~apply(H!42, X, Y2)) | (~member(X, C!39)) | (~member(Y1, A!41)))) | (~member(tptp_fun_Y_16(A!41, C!39, H!42), A!41)) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43), C!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~apply(H!42, tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43), tptp_fun_Y_16(A!41, C!39, H!42))) | (tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)) = tptp_fun_Y_16(A!41, C!39, H!42)) | (~apply(H!42, tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41))))),
% 22.29/22.44 inference(modus_ponens,[status(thm)],[589, 588])).
% 22.29/22.44 tff(591,plain,
% 22.29/22.44 ((tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)) = tptp_fun_Y_16(A!41, C!39, H!42)) | (~apply(H!42, tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41))))),
% 22.29/22.44 inference(unit_resolution,[status(thm)],[590, 350, 456, 557, 584, 528])).
% 22.29/22.44 tff(592,plain,
% 22.29/22.44 (tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)) = tptp_fun_Y_16(A!41, C!39, H!42)),
% 22.29/22.44 inference(unit_resolution,[status(thm)],[591, 570])).
% 22.29/22.44 tff(593,plain,
% 22.29/22.44 (tptp_fun_E_19(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)) = tptp_fun_E_19(tptp_fun_Y_16(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41))),
% 22.29/22.44 inference(monotonicity,[status(thm)],[592])).
% 22.29/22.44 tff(594,plain,
% 22.29/22.44 (((~![Y: $i] : ((~member(Y, A!41)) | (~((~member(tptp_fun_E_19(Y, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_E_19(Y, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), Y)))))) | ((~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~((~member(tptp_fun_E_19(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_E_19(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))))))) <=> ((~![Y: $i] : ((~member(Y, A!41)) | (~((~member(tptp_fun_E_19(Y, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_E_19(Y, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), Y)))))) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~((~member(tptp_fun_E_19(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_E_19(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))))))),
% 22.29/22.44 inference(rewrite,[status(thm)],[])).
% 22.29/22.44 tff(595,plain,
% 22.29/22.44 ((~![Y: $i] : ((~member(Y, A!41)) | (~((~member(tptp_fun_E_19(Y, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_E_19(Y, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), Y)))))) | ((~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~((~member(tptp_fun_E_19(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_E_19(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))))))),
% 22.29/22.44 inference(quant_inst,[status(thm)],[])).
% 22.29/22.44 tff(596,plain,
% 22.29/22.44 ((~![Y: $i] : ((~member(Y, A!41)) | (~((~member(tptp_fun_E_19(Y, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_E_19(Y, B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), Y)))))) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~((~member(tptp_fun_E_19(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_E_19(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41))))))),
% 22.29/22.44 inference(modus_ponens,[status(thm)],[595, 594])).
% 22.29/22.44 tff(597,plain,
% 22.29/22.44 (~((~member(tptp_fun_E_19(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_E_19(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))))),
% 22.29/22.44 inference(unit_resolution,[status(thm)],[596, 84, 528])).
% 22.29/22.44 tff(598,plain,
% 22.29/22.44 (((~member(tptp_fun_E_19(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_E_19(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41))))) | apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_E_19(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))),
% 22.29/22.45 inference(tautology,[status(thm)],[])).
% 22.29/22.45 tff(599,plain,
% 22.29/22.45 (apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_E_19(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))),
% 22.29/22.45 inference(unit_resolution,[status(thm)],[598, 597])).
% 22.29/22.45 tff(600,plain,
% 22.29/22.45 (((~member(tptp_fun_E_19(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_E_19(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41))))) | member(tptp_fun_E_19(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)),
% 22.29/22.45 inference(tautology,[status(thm)],[])).
% 22.29/22.45 tff(601,plain,
% 22.29/22.45 (member(tptp_fun_E_19(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)),
% 22.29/22.45 inference(unit_resolution,[status(thm)],[600, 597])).
% 22.29/22.45 tff(602,plain,
% 22.29/22.45 (((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, B!40)) | (~member(Y, A!41)) | (~member(X1, B!40)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), X1, Y)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), X2, Y)))) | ((~member(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), B!40)) | (~member(tptp_fun_E_19(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_E_19(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, 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| (~member(tptp_fun_E_19(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, 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% 22.29/22.45 inference(rewrite,[status(thm)],[])).
% 22.29/22.45 tff(603,plain,
% 22.29/22.45 (((tptp_fun_E_19(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)) = tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43)) | (~member(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), B!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~member(tptp_fun_E_19(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_E_19(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41))))) <=> ((~member(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), B!40)) | (~member(tptp_fun_E_19(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_E_19(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (tptp_fun_E_19(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)) = tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43)))),
% 22.29/22.45 inference(rewrite,[status(thm)],[])).
% 22.29/22.45 tff(604,plain,
% 22.29/22.45 (((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, B!40)) | (~member(Y, A!41)) | (~member(X1, B!40)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), X1, Y)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), X2, Y)))) | ((tptp_fun_E_19(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)) = tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43)) | (~member(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), B!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), 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B!40, F!44, G!43), B!40)) | (~member(tptp_fun_E_19(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_E_19(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (tptp_fun_E_19(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)) = tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43))))),
% 22.29/22.46 inference(monotonicity,[status(thm)],[603])).
% 22.29/22.46 tff(605,plain,
% 22.29/22.46 (((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, B!40)) | (~member(Y, A!41)) | (~member(X1, B!40)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), X1, Y)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), X2, Y)))) | ((tptp_fun_E_19(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)) = tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43)) | (~member(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), B!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), 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B!40, F!44, G!43), B!40)) | (~member(tptp_fun_E_19(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_E_19(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (tptp_fun_E_19(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)) = 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% 22.29/22.46 inference(transitivity,[status(thm)],[604, 602])).
% 22.29/22.46 tff(606,plain,
% 22.29/22.46 ((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, B!40)) | (~member(Y, A!41)) | (~member(X1, B!40)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), X1, Y)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), X2, Y)))) | ((tptp_fun_E_19(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)) = tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43)) | (~member(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), B!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~member(tptp_fun_E_19(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_E_19(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))))),
% 22.29/22.46 inference(quant_inst,[status(thm)],[])).
% 22.29/22.46 tff(607,plain,
% 22.29/22.46 ((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, B!40)) | (~member(Y, A!41)) | (~member(X1, B!40)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), X1, Y)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), X2, Y)))) | (~member(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), B!40)) | (~member(tptp_fun_E_19(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), A!41)) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (~apply(compose_function(H!42, G!43, B!40, C!39, A!41), tptp_fun_E_19(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)))) | (tptp_fun_E_19(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)) = tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43))),
% 22.29/22.46 inference(modus_ponens,[status(thm)],[606, 605])).
% 22.29/22.46 tff(608,plain,
% 22.29/22.46 (tptp_fun_E_19(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)) = tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43)),
% 22.29/22.47 inference(unit_resolution,[status(thm)],[607, 487, 522, 528, 542, 601, 599])).
% 22.29/22.47 tff(609,plain,
% 22.29/22.47 (tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43) = tptp_fun_E_19(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), A!41, compose_function(H!42, G!43, B!40, C!39, A!41)), B!40, compose_function(H!42, G!43, B!40, C!39, A!41))),
% 22.29/22.47 inference(symmetry,[status(thm)],[608])).
% 22.29/22.47 tff(610,plain,
% 22.29/22.47 (tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43) = tptp_fun_E_19(tptp_fun_Y_16(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41))),
% 22.29/22.47 inference(transitivity,[status(thm)],[609, 593])).
% 22.29/22.47 tff(611,plain,
% 22.29/22.47 (tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43) = tptp_fun_Y_3(tptp_fun_E_19(tptp_fun_Y_16(A!41, C!39, H!42), B!40, compose_function(H!42, G!43, B!40, C!39, A!41)), C!39, G!43)),
% 22.29/22.47 inference(monotonicity,[status(thm)],[610])).
% 22.29/22.47 tff(612,plain,
% 22.29/22.47 (tptp_fun_X1_18(A!41, C!39, H!42) = tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X1_18(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43)),
% 22.29/22.47 inference(symmetry,[status(thm)],[579])).
% 22.29/22.47 tff(613,plain,
% 22.29/22.47 (tptp_fun_X1_18(A!41, C!39, H!42) = tptp_fun_X2_17(A!41, C!39, H!42)),
% 22.29/22.47 inference(transitivity,[status(thm)],[612, 611, 498, 241])).
% 22.29/22.47 tff(614,plain,
% 22.29/22.47 (((~member(tptp_fun_X2_17(A!41, C!39, H!42), C!39)) | (~member(tptp_fun_Y_16(A!41, C!39, H!42), A!41)) | (~member(tptp_fun_X1_18(A!41, C!39, H!42), C!39)) | (~apply(H!42, tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_Y_16(A!41, C!39, H!42))) | (~apply(H!42, tptp_fun_X1_18(A!41, C!39, H!42), tptp_fun_Y_16(A!41, C!39, H!42))) | (tptp_fun_X1_18(A!41, C!39, H!42) = tptp_fun_X2_17(A!41, C!39, H!42))) | (~(tptp_fun_X1_18(A!41, C!39, H!42) = tptp_fun_X2_17(A!41, C!39, H!42)))),
% 22.29/22.47 inference(tautology,[status(thm)],[])).
% 22.29/22.47 tff(615,plain,
% 22.29/22.47 (~(tptp_fun_X1_18(A!41, C!39, H!42) = tptp_fun_X2_17(A!41, C!39, H!42))),
% 22.29/22.47 inference(unit_resolution,[status(thm)],[614, 146])).
% 22.29/22.47 tff(616,plain,
% 22.29/22.47 ($false),
% 22.29/22.47 inference(unit_resolution,[status(thm)],[615, 613])).
% 22.29/22.47 tff(617,plain,(~apply(H!42, tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_X2_17(A!41, C!39, H!42), tptp_fun_E_19(tptp_fun_X2_17(A!41, C!39, H!42), A!41, compose_function(G!43, F!44, A!41, B!40, C!39)), B!40, F!44, G!43), C!39, G!43), tptp_fun_Y_16(A!41, C!39, H!42))), inference(lemma,lemma(discharge,[]))).
% 22.29/22.47 tff(618,plain,
% 22.29/22.47 ($false),
% 22.29/22.47 inference(unit_resolution,[status(thm)],[617, 246])).
% 22.29/22.47 % SZS output end Proof
% 22.29/22.48 % E exiting
%------------------------------------------------------------------------------