%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET729+4 : TPTP v9.0.0. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:26:14 AM UTC 2025
% Result : Theorem 0.23s 0.43s
% Output : Proof 0.72s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14 % Problem : SET729+4 : TPTP v9.0.0. Bugfixed v2.2.1.
% 0.04/0.14 % Command : run_E %s %d THM
% 0.14/0.35 % Computer : n002.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri Jun 20 05:40:31 EDT 2025
% 0.14/0.36 % CPUTime :
% 0.23/0.43 % SZS status Theorem
% 0.23/0.43 % SZS output start Proof
% 0.23/0.43 tff(apply_type, type, (
% 0.23/0.43 apply: ( $i * $i * $i ) > $o)).
% 0.23/0.43 tff(tptp_fun_X1_18_type, type, (
% 0.23/0.43 tptp_fun_X1_18: ( $i * $i * $i ) > $i)).
% 0.23/0.43 tff(tptp_fun_F_40_type, type, (
% 0.23/0.43 tptp_fun_F_40: $i)).
% 0.23/0.43 tff(tptp_fun_A_39_type, type, (
% 0.23/0.43 tptp_fun_A_39: $i)).
% 0.23/0.43 tff(tptp_fun_Y_16_type, type, (
% 0.23/0.43 tptp_fun_Y_16: ( $i * $i * $i ) > $i)).
% 0.23/0.43 tff(tptp_fun_Y_8_type, type, (
% 0.23/0.43 tptp_fun_Y_8: ( $i * $i * $i * $i * $i ) > $i)).
% 0.23/0.43 tff(member_type, type, (
% 0.23/0.43 member: ( $i * $i ) > $o)).
% 0.23/0.43 tff(compose_function_type, type, (
% 0.23/0.43 compose_function: ( $i * $i * $i * $i * $i ) > $i)).
% 0.23/0.43 tff(tptp_fun_X2_17_type, type, (
% 0.23/0.43 tptp_fun_X2_17: ( $i * $i * $i ) > $i)).
% 0.23/0.43 tff(injective_type, type, (
% 0.23/0.43 injective: ( $i * $i * $i ) > $o)).
% 0.23/0.43 tff(surjective_type, type, (
% 0.23/0.43 surjective: ( $i * $i * $i ) > $o)).
% 0.23/0.43 tff(one_to_one_type, type, (
% 0.23/0.43 one_to_one: ( $i * $i * $i ) > $o)).
% 0.23/0.43 tff(inverse_predicate_type, type, (
% 0.23/0.43 inverse_predicate: ( $i * $i * $i * $i ) > $o)).
% 0.23/0.43 tff(tptp_fun_X_22_type, type, (
% 0.23/0.43 tptp_fun_X_22: ( $i * $i * $i * $i ) > $i)).
% 0.23/0.43 tff(tptp_fun_Y_21_type, type, (
% 0.23/0.43 tptp_fun_Y_21: ( $i * $i * $i * $i ) > $i)).
% 0.23/0.43 tff(tptp_fun_Y_3_type, type, (
% 0.23/0.43 tptp_fun_Y_3: ( $i * $i * $i ) > $i)).
% 0.23/0.43 tff(maps_type, type, (
% 0.23/0.43 maps: ( $i * $i * $i ) > $o)).
% 0.23/0.43 tff(tptp_fun_Y2_5_type, type, (
% 0.23/0.43 tptp_fun_Y2_5: ( $i * $i * $i ) > $i)).
% 0.23/0.43 tff(tptp_fun_Y1_6_type, type, (
% 0.23/0.43 tptp_fun_Y1_6: ( $i * $i * $i ) > $i)).
% 0.23/0.43 tff(tptp_fun_X_7_type, type, (
% 0.23/0.43 tptp_fun_X_7: ( $i * $i * $i ) > $i)).
% 0.23/0.43 tff(tptp_fun_X_4_type, type, (
% 0.23/0.43 tptp_fun_X_4: ( $i * $i * $i ) > $i)).
% 0.23/0.43 tff(identity_type, type, (
% 0.23/0.43 identity: ( $i * $i ) > $o)).
% 0.23/0.43 tff(tptp_fun_X_15_type, type, (
% 0.23/0.43 tptp_fun_X_15: ( $i * $i ) > $i)).
% 0.23/0.43 tff(tptp_fun_Y_20_type, type, (
% 0.23/0.43 tptp_fun_Y_20: ( $i * $i * $i ) > $i)).
% 0.23/0.43 tff(tptp_fun_E_19_type, type, (
% 0.23/0.43 tptp_fun_E_19: ( $i * $i * $i ) > $i)).
% 0.23/0.43 tff(1,plain,
% 0.23/0.43 (^[F: $i, A: $i, B: $i] : refl((~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B)))))))) <=> (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B)))))))))),
% 0.23/0.43 inference(bind,[status(th)],[])).
% 0.23/0.43 tff(2,plain,
% 0.23/0.43 (![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B)))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))),
% 0.23/0.43 inference(quant_intro,[status(thm)],[1])).
% 0.23/0.43 tff(3,plain,
% 0.23/0.43 (^[F: $i, A: $i, B: $i] : rewrite((~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B)))))))) <=> (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B)))))))))),
% 0.23/0.43 inference(bind,[status(th)],[])).
% 0.23/0.43 tff(4,plain,
% 0.23/0.43 (![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B)))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))),
% 0.23/0.43 inference(quant_intro,[status(thm)],[3])).
% 0.23/0.43 tff(5,plain,
% 0.23/0.43 (![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B)))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))),
% 0.23/0.43 inference(transitivity,[status(thm)],[4, 2])).
% 0.23/0.43 tff(6,plain,
% 0.23/0.43 (^[F: $i, A: $i, B: $i] : trans(monotonicity(rewrite(((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~(apply(F, X1, Y) & apply(F, X2, Y))) | (~(member(X1, A) & member(X2, A) & member(Y, B))))) <=> ((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))), trans(monotonicity(rewrite((~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~(apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F)) & apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F)))) | (~(member(tptp_fun_X1_18(B, A, F), A) & member(tptp_fun_X2_17(B, A, F), A) & member(tptp_fun_Y_16(B, A, F), B))))) <=> (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))), ((injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~(apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F)) & apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F)))) | (~(member(tptp_fun_X1_18(B, A, F), A) & member(tptp_fun_X2_17(B, A, F), A) & member(tptp_fun_Y_16(B, A, F), B)))))) <=> (injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))), rewrite((injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))) <=> (injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B)))))), ((injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~(apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F)) & apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F)))) | (~(member(tptp_fun_X1_18(B, A, F), A) & member(tptp_fun_X2_17(B, A, F), A) & member(tptp_fun_Y_16(B, A, F), B)))))) <=> (injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))), ((((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~(apply(F, X1, Y) & apply(F, X2, Y))) | (~(member(X1, A) & member(X2, A) & member(Y, B))))) & (injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~(apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F)) & apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F)))) | (~(member(tptp_fun_X1_18(B, A, F), A) & member(tptp_fun_X2_17(B, A, F), A) & member(tptp_fun_Y_16(B, A, F), B))))))) <=> (((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y)))) & (injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B)))))))), rewrite((((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y)))) & (injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B)))))) <=> (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))), ((((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~(apply(F, X1, Y) & apply(F, X2, Y))) | (~(member(X1, A) & member(X2, A) & member(Y, B))))) & (injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~(apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F)) & apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F)))) | (~(member(tptp_fun_X1_18(B, A, F), A) & member(tptp_fun_X2_17(B, A, F), A) & member(tptp_fun_Y_16(B, A, F), B))))))) <=> (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))))),
% 0.23/0.43 inference(bind,[status(th)],[])).
% 0.23/0.43 tff(7,plain,
% 0.23/0.43 (![F: $i, A: $i, B: $i] : (((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~(apply(F, X1, Y) & apply(F, X2, Y))) | (~(member(X1, A) & member(X2, A) & member(Y, B))))) & (injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~(apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F)) & apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F)))) | (~(member(tptp_fun_X1_18(B, A, F), A) & member(tptp_fun_X2_17(B, A, F), A) & member(tptp_fun_Y_16(B, A, F), B))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))),
% 0.23/0.43 inference(quant_intro,[status(thm)],[6])).
% 0.23/0.43 tff(8,plain,
% 0.23/0.43 (![F: $i, A: $i, B: $i] : (injective(F, A, B) <=> ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~(apply(F, X1, Y) & apply(F, X2, Y))) | (~(member(X1, A) & member(X2, A) & member(Y, B))))) <=> ![F: $i, A: $i, B: $i] : (injective(F, A, B) <=> ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~(apply(F, X1, Y) & apply(F, X2, Y))) | (~(member(X1, A) & member(X2, A) & member(Y, B)))))),
% 0.23/0.43 inference(rewrite,[status(thm)],[])).
% 0.23/0.43 tff(9,plain,
% 0.23/0.43 (^[F: $i, A: $i, B: $i] : rewrite((injective(F, A, B) <=> ![X1: $i, X2: $i, Y: $i] : (((member(X1, A) & member(X2, A)) & member(Y, B)) => ((apply(F, X1, Y) & apply(F, X2, Y)) => (X1 = X2)))) <=> (injective(F, A, B) <=> ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~(apply(F, X1, Y) & apply(F, X2, Y))) | (~(member(X1, A) & member(X2, A) & member(Y, B))))))),
% 0.23/0.43 inference(bind,[status(th)],[])).
% 0.23/0.43 tff(10,plain,
% 0.23/0.43 (![F: $i, A: $i, B: $i] : (injective(F, A, B) <=> ![X1: $i, X2: $i, Y: $i] : (((member(X1, A) & member(X2, A)) & member(Y, B)) => ((apply(F, X1, Y) & apply(F, X2, Y)) => (X1 = X2)))) <=> ![F: $i, A: $i, B: $i] : (injective(F, A, B) <=> ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~(apply(F, X1, Y) & apply(F, X2, Y))) | (~(member(X1, A) & member(X2, A) & member(Y, B)))))),
% 0.23/0.43 inference(quant_intro,[status(thm)],[9])).
% 0.23/0.43 tff(11,axiom,(![F: $i, A: $i, B: $i] : (injective(F, A, B) <=> ![X1: $i, X2: $i, Y: $i] : (((member(X1, A) & member(X2, A)) & member(Y, B)) => ((apply(F, X1, Y) & apply(F, X2, Y)) => (X1 = X2))))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+1.ax','injective')).
% 0.23/0.43 tff(12,plain,
% 0.23/0.43 (![F: $i, A: $i, B: $i] : (injective(F, A, B) <=> ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~(apply(F, X1, Y) & apply(F, X2, Y))) | (~(member(X1, A) & member(X2, A) & member(Y, B)))))),
% 0.23/0.43 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.23/0.43 tff(13,plain,
% 0.23/0.43 (![F: $i, A: $i, B: $i] : (injective(F, A, B) <=> ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~(apply(F, X1, Y) & apply(F, X2, Y))) | (~(member(X1, A) & member(X2, A) & member(Y, B)))))),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[12, 8])).
% 0.23/0.44 tff(14,plain,(
% 0.23/0.44 ![F: $i, A: $i, B: $i] : (((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~(apply(F, X1, Y) & apply(F, X2, Y))) | (~(member(X1, A) & member(X2, A) & member(Y, B))))) & (injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~(apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F)) & apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F)))) | (~(member(tptp_fun_X1_18(B, A, F), A) & member(tptp_fun_X2_17(B, A, F), A) & member(tptp_fun_Y_16(B, A, F), B)))))))),
% 0.23/0.44 inference(skolemize,[status(sab)],[13])).
% 0.23/0.44 tff(15,plain,
% 0.23/0.44 (![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[14, 7])).
% 0.23/0.44 tff(16,plain,
% 0.23/0.44 (![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[15, 5])).
% 0.23/0.44 tff(17,plain,
% 0.23/0.44 (((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(F!40, A!39, A!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, A!39)) | (~apply(F!40, X1, Y)) | (~member(X1, A!39)) | (~member(X2, A!39)) | (~apply(F!40, X2, Y))))) | (~(injective(F!40, A!39, A!39) | (~((~member(tptp_fun_Y_16(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_X1_18(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_X2_17(A!39, A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))) | (tptp_fun_X1_18(A!39, A!39, F!40) = tptp_fun_X2_17(A!39, A!39, F!40))))))))) <=> ((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(F!40, A!39, A!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, A!39)) | (~apply(F!40, X1, Y)) | (~member(X1, A!39)) | (~member(X2, A!39)) | (~apply(F!40, X2, Y))))) | (~(injective(F!40, A!39, A!39) | (~((~member(tptp_fun_Y_16(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_X1_18(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_X2_17(A!39, A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))) | (tptp_fun_X1_18(A!39, A!39, F!40) = tptp_fun_X2_17(A!39, A!39, F!40)))))))))),
% 0.23/0.44 inference(rewrite,[status(thm)],[])).
% 0.23/0.44 tff(18,plain,
% 0.23/0.44 ((~((~((~injective(F!40, A!39, A!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!40, X1, Y)) | (~member(X2, A!39)) | (~member(X1, A!39)) | (~member(Y, A!39)) | (~apply(F!40, X2, Y))))) | (~(injective(F!40, A!39, A!39) | (~((tptp_fun_X1_18(A!39, A!39, F!40) = tptp_fun_X2_17(A!39, A!39, F!40)) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))) | (~member(tptp_fun_X1_18(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_X2_17(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_Y_16(A!39, A!39, F!40), A!39)))))))) <=> (~((~((~injective(F!40, A!39, A!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, A!39)) | (~apply(F!40, X1, Y)) | (~member(X1, A!39)) | (~member(X2, A!39)) | (~apply(F!40, X2, Y))))) | (~(injective(F!40, A!39, A!39) | (~((~member(tptp_fun_Y_16(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_X1_18(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_X2_17(A!39, A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))) | (tptp_fun_X1_18(A!39, A!39, F!40) = tptp_fun_X2_17(A!39, A!39, F!40))))))))),
% 0.23/0.44 inference(rewrite,[status(thm)],[])).
% 0.23/0.44 tff(19,plain,
% 0.23/0.44 (((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(F!40, A!39, A!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!40, X1, Y)) | (~member(X2, A!39)) | (~member(X1, A!39)) | (~member(Y, A!39)) | (~apply(F!40, X2, Y))))) | (~(injective(F!40, A!39, A!39) | (~((tptp_fun_X1_18(A!39, A!39, F!40) = tptp_fun_X2_17(A!39, A!39, F!40)) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))) | (~member(tptp_fun_X1_18(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_X2_17(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_Y_16(A!39, A!39, F!40), A!39))))))))) <=> ((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(F!40, A!39, A!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, A!39)) | (~apply(F!40, X1, Y)) | (~member(X1, A!39)) | (~member(X2, A!39)) | (~apply(F!40, X2, Y))))) | (~(injective(F!40, A!39, A!39) | (~((~member(tptp_fun_Y_16(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_X1_18(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_X2_17(A!39, A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))) | (tptp_fun_X1_18(A!39, A!39, F!40) = tptp_fun_X2_17(A!39, A!39, F!40)))))))))),
% 0.23/0.44 inference(monotonicity,[status(thm)],[18])).
% 0.23/0.44 tff(20,plain,
% 0.23/0.44 (((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(F!40, A!39, A!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!40, X1, Y)) | (~member(X2, A!39)) | (~member(X1, A!39)) | (~member(Y, A!39)) | (~apply(F!40, X2, Y))))) | (~(injective(F!40, A!39, A!39) | (~((tptp_fun_X1_18(A!39, A!39, F!40) = tptp_fun_X2_17(A!39, A!39, F!40)) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))) | (~member(tptp_fun_X1_18(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_X2_17(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_Y_16(A!39, A!39, F!40), A!39))))))))) <=> ((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(F!40, A!39, A!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, A!39)) | (~apply(F!40, X1, Y)) | (~member(X1, A!39)) | (~member(X2, A!39)) | (~apply(F!40, X2, Y))))) | (~(injective(F!40, A!39, A!39) | (~((~member(tptp_fun_Y_16(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_X1_18(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_X2_17(A!39, A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))) | (tptp_fun_X1_18(A!39, A!39, F!40) = tptp_fun_X2_17(A!39, A!39, F!40)))))))))),
% 0.23/0.44 inference(transitivity,[status(thm)],[19, 17])).
% 0.23/0.44 tff(21,plain,
% 0.23/0.44 ((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(F!40, A!39, A!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!40, X1, Y)) | (~member(X2, A!39)) | (~member(X1, A!39)) | (~member(Y, A!39)) | (~apply(F!40, X2, Y))))) | (~(injective(F!40, A!39, A!39) | (~((tptp_fun_X1_18(A!39, A!39, F!40) = tptp_fun_X2_17(A!39, A!39, F!40)) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))) | (~member(tptp_fun_X1_18(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_X2_17(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_Y_16(A!39, A!39, F!40), A!39))))))))),
% 0.23/0.44 inference(quant_inst,[status(thm)],[])).
% 0.23/0.44 tff(22,plain,
% 0.23/0.44 ((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(F!40, A!39, A!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, A!39)) | (~apply(F!40, X1, Y)) | (~member(X1, A!39)) | (~member(X2, A!39)) | (~apply(F!40, X2, Y))))) | (~(injective(F!40, A!39, A!39) | (~((~member(tptp_fun_Y_16(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_X1_18(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_X2_17(A!39, A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))) | (tptp_fun_X1_18(A!39, A!39, F!40) = tptp_fun_X2_17(A!39, A!39, F!40))))))))),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.23/0.45 tff(23,plain,
% 0.23/0.45 (~((~((~injective(F!40, A!39, A!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, A!39)) | (~apply(F!40, X1, Y)) | (~member(X1, A!39)) | (~member(X2, A!39)) | (~apply(F!40, X2, Y))))) | (~(injective(F!40, A!39, A!39) | (~((~member(tptp_fun_Y_16(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_X1_18(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_X2_17(A!39, A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))) | (tptp_fun_X1_18(A!39, A!39, F!40) = tptp_fun_X2_17(A!39, A!39, F!40)))))))),
% 0.23/0.45 inference(unit_resolution,[status(thm)],[22, 16])).
% 0.23/0.45 tff(24,plain,
% 0.23/0.45 (((~((~injective(F!40, A!39, A!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, A!39)) | (~apply(F!40, X1, Y)) | (~member(X1, A!39)) | (~member(X2, A!39)) | (~apply(F!40, X2, Y))))) | (~(injective(F!40, A!39, A!39) | (~((~member(tptp_fun_Y_16(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_X1_18(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_X2_17(A!39, A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))) | (tptp_fun_X1_18(A!39, A!39, F!40) = tptp_fun_X2_17(A!39, A!39, F!40))))))) | (injective(F!40, A!39, A!39) | (~((~member(tptp_fun_Y_16(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_X1_18(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_X2_17(A!39, A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))) | (tptp_fun_X1_18(A!39, A!39, F!40) = tptp_fun_X2_17(A!39, A!39, F!40)))))),
% 0.23/0.45 inference(tautology,[status(thm)],[])).
% 0.23/0.45 tff(25,plain,
% 0.23/0.45 (injective(F!40, A!39, A!39) | (~((~member(tptp_fun_Y_16(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_X1_18(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_X2_17(A!39, A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))) | (tptp_fun_X1_18(A!39, A!39, F!40) = tptp_fun_X2_17(A!39, A!39, F!40))))),
% 0.23/0.45 inference(unit_resolution,[status(thm)],[24, 23])).
% 0.23/0.45 tff(26,plain,
% 0.23/0.45 (^[F: $i, A: $i, B: $i] : refl((~(((~injective(F, A, B)) | (~surjective(F, A, B))) <=> one_to_one(F, A, B))) <=> (~(((~injective(F, A, B)) | (~surjective(F, A, B))) <=> one_to_one(F, A, B))))),
% 0.23/0.45 inference(bind,[status(th)],[])).
% 0.23/0.45 tff(27,plain,
% 0.23/0.45 (![F: $i, A: $i, B: $i] : (~(((~injective(F, A, B)) | (~surjective(F, A, B))) <=> one_to_one(F, A, B))) <=> ![F: $i, A: $i, B: $i] : (~(((~injective(F, A, B)) | (~surjective(F, A, B))) <=> one_to_one(F, A, B)))),
% 0.23/0.45 inference(quant_intro,[status(thm)],[26])).
% 0.23/0.45 tff(28,plain,
% 0.23/0.45 (^[F: $i, A: $i, B: $i] : trans(trans(monotonicity(rewrite((injective(F, A, B) & surjective(F, A, B)) <=> (~((~injective(F, A, B)) | (~surjective(F, A, B))))), ((one_to_one(F, A, B) <=> (injective(F, A, B) & surjective(F, A, B))) <=> (one_to_one(F, A, B) <=> (~((~injective(F, A, B)) | (~surjective(F, A, B))))))), rewrite((one_to_one(F, A, B) <=> (~((~injective(F, A, B)) | (~surjective(F, A, B))))) <=> (~(((~injective(F, A, B)) | (~surjective(F, A, B))) <=> one_to_one(F, A, B)))), ((one_to_one(F, A, B) <=> (injective(F, A, B) & surjective(F, A, B))) <=> (~(((~injective(F, A, B)) | (~surjective(F, A, B))) <=> one_to_one(F, A, B))))), rewrite((~(((~injective(F, A, B)) | (~surjective(F, A, B))) <=> one_to_one(F, A, B))) <=> (~(((~injective(F, A, B)) | (~surjective(F, A, B))) <=> one_to_one(F, A, B)))), ((one_to_one(F, A, B) <=> (injective(F, A, B) & surjective(F, A, B))) <=> (~(((~injective(F, A, B)) | (~surjective(F, A, B))) <=> one_to_one(F, A, B)))))),
% 0.23/0.45 inference(bind,[status(th)],[])).
% 0.23/0.45 tff(29,plain,
% 0.23/0.45 (![F: $i, A: $i, B: $i] : (one_to_one(F, A, B) <=> (injective(F, A, B) & surjective(F, A, B))) <=> ![F: $i, A: $i, B: $i] : (~(((~injective(F, A, B)) | (~surjective(F, A, B))) <=> one_to_one(F, A, B)))),
% 0.23/0.45 inference(quant_intro,[status(thm)],[28])).
% 0.23/0.45 tff(30,plain,
% 0.23/0.45 (![F: $i, A: $i, B: $i] : (one_to_one(F, A, B) <=> (injective(F, A, B) & surjective(F, A, B))) <=> ![F: $i, A: $i, B: $i] : (one_to_one(F, A, B) <=> (injective(F, A, B) & surjective(F, A, B)))),
% 0.23/0.45 inference(rewrite,[status(thm)],[])).
% 0.23/0.45 tff(31,axiom,(![F: $i, A: $i, B: $i] : (one_to_one(F, A, B) <=> (injective(F, A, B) & surjective(F, A, B)))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+1.ax','one_to_one')).
% 0.23/0.45 tff(32,plain,
% 0.23/0.45 (![F: $i, A: $i, B: $i] : (one_to_one(F, A, B) <=> (injective(F, A, B) & surjective(F, A, B)))),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.23/0.45 tff(33,plain,(
% 0.23/0.45 ![F: $i, A: $i, B: $i] : (one_to_one(F, A, B) <=> (injective(F, A, B) & surjective(F, A, B)))),
% 0.23/0.45 inference(skolemize,[status(sab)],[32])).
% 0.23/0.45 tff(34,plain,
% 0.23/0.45 (![F: $i, A: $i, B: $i] : (~(((~injective(F, A, B)) | (~surjective(F, A, B))) <=> one_to_one(F, A, B)))),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[33, 29])).
% 0.23/0.45 tff(35,plain,
% 0.23/0.45 (![F: $i, A: $i, B: $i] : (~(((~injective(F, A, B)) | (~surjective(F, A, B))) <=> one_to_one(F, A, B)))),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[34, 27])).
% 0.23/0.45 tff(36,plain,
% 0.23/0.45 ((~![F: $i, A: $i, B: $i] : (~(((~injective(F, A, B)) | (~surjective(F, A, B))) <=> one_to_one(F, A, B)))) | (~(((~injective(F!40, A!39, A!39)) | (~surjective(F!40, A!39, A!39))) <=> one_to_one(F!40, A!39, A!39)))),
% 0.23/0.45 inference(quant_inst,[status(thm)],[])).
% 0.23/0.45 tff(37,plain,
% 0.23/0.45 (~(((~injective(F!40, A!39, A!39)) | (~surjective(F!40, A!39, A!39))) <=> one_to_one(F!40, A!39, A!39))),
% 0.23/0.45 inference(unit_resolution,[status(thm)],[36, 35])).
% 0.23/0.45 tff(38,assumption,((~((~inverse_predicate(F!40, F!40, A!39, A!39)) | ![X: $i, Y: $i] : ((~member(Y, A!39)) | (~member(X, A!39)) | (apply(F!40, X, Y) <=> apply(F!40, Y, X))))) | (~(inverse_predicate(F!40, F!40, A!39, A!39) | (~((~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | (apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40)) <=> apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))) | (~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39))))))), introduced(assumption)).
% 0.23/0.45 tff(39,plain,
% 0.23/0.45 (^[G: $i, F: $i, A: $i, B: $i] : refl((~((~((~inverse_predicate(G, F, A, B)) | ![X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(G, Y, X)) | (~member(Y, B)) | (~member(X, A))))) | (~(inverse_predicate(G, F, A, B) | (~((apply(F, tptp_fun_X_22(B, A, F, G), tptp_fun_Y_21(B, A, F, G)) <=> apply(G, tptp_fun_Y_21(B, A, F, G), tptp_fun_X_22(B, A, F, G))) | (~member(tptp_fun_X_22(B, A, F, G), A)) | (~member(tptp_fun_Y_21(B, A, F, G), B)))))))) <=> (~((~((~inverse_predicate(G, F, A, B)) | ![X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(G, Y, X)) | (~member(Y, B)) | (~member(X, A))))) | (~(inverse_predicate(G, F, A, B) | (~((apply(F, tptp_fun_X_22(B, A, F, G), tptp_fun_Y_21(B, A, F, G)) <=> apply(G, tptp_fun_Y_21(B, A, F, G), tptp_fun_X_22(B, A, F, G))) | (~member(tptp_fun_X_22(B, A, F, G), A)) | (~member(tptp_fun_Y_21(B, A, F, G), B)))))))))),
% 0.23/0.45 inference(bind,[status(th)],[])).
% 0.23/0.45 tff(40,plain,
% 0.23/0.45 (![G: $i, F: $i, A: $i, B: $i] : (~((~((~inverse_predicate(G, F, A, B)) | ![X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(G, Y, X)) | (~member(Y, B)) | (~member(X, A))))) | (~(inverse_predicate(G, F, A, B) | (~((apply(F, tptp_fun_X_22(B, A, F, G), tptp_fun_Y_21(B, A, F, G)) <=> apply(G, tptp_fun_Y_21(B, A, F, G), tptp_fun_X_22(B, A, F, G))) | (~member(tptp_fun_X_22(B, A, F, G), A)) | (~member(tptp_fun_Y_21(B, A, F, G), B)))))))) <=> ![G: $i, F: $i, A: $i, B: $i] : (~((~((~inverse_predicate(G, F, A, B)) | ![X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(G, Y, X)) | (~member(Y, B)) | (~member(X, A))))) | (~(inverse_predicate(G, F, A, B) | (~((apply(F, tptp_fun_X_22(B, A, F, G), tptp_fun_Y_21(B, A, F, G)) <=> apply(G, tptp_fun_Y_21(B, A, F, G), tptp_fun_X_22(B, A, F, G))) | (~member(tptp_fun_X_22(B, A, F, G), A)) | (~member(tptp_fun_Y_21(B, A, F, G), B))))))))),
% 0.23/0.45 inference(quant_intro,[status(thm)],[39])).
% 0.23/0.45 tff(41,plain,
% 0.23/0.45 (^[G: $i, F: $i, A: $i, B: $i] : rewrite((~((~((~inverse_predicate(G, F, A, B)) | ![X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(G, Y, X)) | (~member(Y, B)) | (~member(X, A))))) | (~(inverse_predicate(G, F, A, B) | (~((apply(F, tptp_fun_X_22(B, A, F, G), tptp_fun_Y_21(B, A, F, G)) <=> apply(G, tptp_fun_Y_21(B, A, F, G), tptp_fun_X_22(B, A, F, G))) | (~member(tptp_fun_X_22(B, A, F, G), A)) | (~member(tptp_fun_Y_21(B, A, F, G), B)))))))) <=> (~((~((~inverse_predicate(G, F, A, B)) | ![X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(G, Y, X)) | (~member(Y, B)) | (~member(X, A))))) | (~(inverse_predicate(G, F, A, B) | (~((apply(F, tptp_fun_X_22(B, A, F, G), tptp_fun_Y_21(B, A, F, G)) <=> apply(G, tptp_fun_Y_21(B, A, F, G), tptp_fun_X_22(B, A, F, G))) | (~member(tptp_fun_X_22(B, A, F, G), A)) | (~member(tptp_fun_Y_21(B, A, F, G), B)))))))))),
% 0.23/0.45 inference(bind,[status(th)],[])).
% 0.23/0.45 tff(42,plain,
% 0.23/0.45 (![G: $i, F: $i, A: $i, B: $i] : (~((~((~inverse_predicate(G, F, A, B)) | ![X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(G, Y, X)) | (~member(Y, B)) | (~member(X, A))))) | (~(inverse_predicate(G, F, A, B) | (~((apply(F, tptp_fun_X_22(B, A, F, G), tptp_fun_Y_21(B, A, F, G)) <=> apply(G, tptp_fun_Y_21(B, A, F, G), tptp_fun_X_22(B, A, F, G))) | (~member(tptp_fun_X_22(B, A, F, G), A)) | (~member(tptp_fun_Y_21(B, A, F, G), B)))))))) <=> ![G: $i, F: $i, A: $i, B: $i] : (~((~((~inverse_predicate(G, F, A, B)) | ![X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(G, Y, X)) | (~member(Y, B)) | (~member(X, A))))) | (~(inverse_predicate(G, F, A, B) | (~((apply(F, tptp_fun_X_22(B, A, F, G), tptp_fun_Y_21(B, A, F, G)) <=> apply(G, tptp_fun_Y_21(B, A, F, G), tptp_fun_X_22(B, A, F, G))) | (~member(tptp_fun_X_22(B, A, F, G), A)) | (~member(tptp_fun_Y_21(B, A, F, G), B))))))))),
% 0.23/0.45 inference(quant_intro,[status(thm)],[41])).
% 0.23/0.45 tff(43,plain,
% 0.23/0.45 (![G: $i, F: $i, A: $i, B: $i] : (~((~((~inverse_predicate(G, F, A, B)) | ![X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(G, Y, X)) | (~member(Y, B)) | (~member(X, A))))) | (~(inverse_predicate(G, F, A, B) | (~((apply(F, tptp_fun_X_22(B, A, F, G), tptp_fun_Y_21(B, A, F, G)) <=> apply(G, tptp_fun_Y_21(B, A, F, G), tptp_fun_X_22(B, A, F, G))) | (~member(tptp_fun_X_22(B, A, F, G), A)) | (~member(tptp_fun_Y_21(B, A, F, G), B)))))))) <=> ![G: $i, F: $i, A: $i, B: $i] : (~((~((~inverse_predicate(G, F, A, B)) | ![X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(G, Y, X)) | (~member(Y, B)) | (~member(X, A))))) | (~(inverse_predicate(G, F, A, B) | (~((apply(F, tptp_fun_X_22(B, A, F, G), tptp_fun_Y_21(B, A, F, G)) <=> apply(G, tptp_fun_Y_21(B, A, F, G), tptp_fun_X_22(B, A, F, G))) | (~member(tptp_fun_X_22(B, A, F, G), A)) | (~member(tptp_fun_Y_21(B, A, F, G), B))))))))),
% 0.23/0.45 inference(transitivity,[status(thm)],[42, 40])).
% 0.23/0.45 tff(44,plain,
% 0.23/0.45 (^[G: $i, F: $i, A: $i, B: $i] : trans(monotonicity(rewrite(((~inverse_predicate(G, F, A, B)) | ![X: $i, Y: $i] : ((~(member(X, A) & member(Y, B))) | (apply(F, X, Y) <=> apply(G, Y, X)))) <=> ((~inverse_predicate(G, F, A, B)) | ![X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(G, Y, X)) | (~member(Y, B)) | (~member(X, A))))), trans(monotonicity(rewrite((~((~(member(tptp_fun_X_22(B, A, F, G), A) & member(tptp_fun_Y_21(B, A, F, G), B))) | (apply(F, tptp_fun_X_22(B, A, F, G), tptp_fun_Y_21(B, A, F, G)) <=> apply(G, tptp_fun_Y_21(B, A, F, G), tptp_fun_X_22(B, A, F, G))))) <=> (~((apply(F, tptp_fun_X_22(B, A, F, G), tptp_fun_Y_21(B, A, F, G)) <=> apply(G, tptp_fun_Y_21(B, A, F, G), tptp_fun_X_22(B, A, F, G))) | (~member(tptp_fun_X_22(B, A, F, G), A)) | (~member(tptp_fun_Y_21(B, A, F, G), B))))), ((inverse_predicate(G, F, A, B) | (~((~(member(tptp_fun_X_22(B, A, F, G), A) & member(tptp_fun_Y_21(B, A, F, G), B))) | (apply(F, tptp_fun_X_22(B, A, F, G), tptp_fun_Y_21(B, A, F, G)) <=> apply(G, tptp_fun_Y_21(B, A, F, G), tptp_fun_X_22(B, A, F, G)))))) <=> (inverse_predicate(G, F, A, B) | (~((apply(F, tptp_fun_X_22(B, A, F, G), tptp_fun_Y_21(B, A, F, G)) <=> apply(G, tptp_fun_Y_21(B, A, F, G), tptp_fun_X_22(B, A, F, G))) | (~member(tptp_fun_X_22(B, A, F, G), A)) | (~member(tptp_fun_Y_21(B, A, F, G), B))))))), rewrite((inverse_predicate(G, F, A, B) | (~((apply(F, tptp_fun_X_22(B, A, F, G), tptp_fun_Y_21(B, A, F, G)) <=> apply(G, tptp_fun_Y_21(B, A, F, G), tptp_fun_X_22(B, A, F, G))) | (~member(tptp_fun_X_22(B, A, F, G), A)) | (~member(tptp_fun_Y_21(B, A, F, G), B))))) <=> (inverse_predicate(G, F, A, B) | (~((apply(F, tptp_fun_X_22(B, A, F, G), tptp_fun_Y_21(B, A, F, G)) <=> apply(G, tptp_fun_Y_21(B, A, F, G), tptp_fun_X_22(B, A, F, G))) | (~member(tptp_fun_X_22(B, A, F, G), A)) | (~member(tptp_fun_Y_21(B, A, F, G), B)))))), ((inverse_predicate(G, F, A, B) | (~((~(member(tptp_fun_X_22(B, A, F, G), A) & member(tptp_fun_Y_21(B, A, F, G), B))) | (apply(F, tptp_fun_X_22(B, A, F, G), tptp_fun_Y_21(B, A, F, G)) <=> apply(G, tptp_fun_Y_21(B, A, F, G), tptp_fun_X_22(B, A, F, G)))))) <=> (inverse_predicate(G, F, A, B) | (~((apply(F, tptp_fun_X_22(B, A, F, G), tptp_fun_Y_21(B, A, F, G)) <=> apply(G, tptp_fun_Y_21(B, A, F, G), tptp_fun_X_22(B, A, F, G))) | (~member(tptp_fun_X_22(B, A, F, G), A)) | (~member(tptp_fun_Y_21(B, A, F, G), B))))))), ((((~inverse_predicate(G, F, A, B)) | ![X: $i, Y: $i] : ((~(member(X, A) & member(Y, B))) | (apply(F, X, Y) <=> apply(G, Y, X)))) & (inverse_predicate(G, F, A, B) | (~((~(member(tptp_fun_X_22(B, A, F, G), A) & member(tptp_fun_Y_21(B, A, F, G), B))) | (apply(F, tptp_fun_X_22(B, A, F, G), tptp_fun_Y_21(B, A, F, G)) <=> apply(G, tptp_fun_Y_21(B, A, F, G), tptp_fun_X_22(B, A, F, G))))))) <=> (((~inverse_predicate(G, F, A, B)) | ![X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(G, Y, X)) | (~member(Y, B)) | (~member(X, A)))) & (inverse_predicate(G, F, A, B) | (~((apply(F, tptp_fun_X_22(B, A, F, G), tptp_fun_Y_21(B, A, F, G)) <=> apply(G, tptp_fun_Y_21(B, A, F, G), tptp_fun_X_22(B, A, F, G))) | (~member(tptp_fun_X_22(B, A, F, G), A)) | (~member(tptp_fun_Y_21(B, A, F, G), B)))))))), rewrite((((~inverse_predicate(G, F, A, B)) | ![X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(G, Y, X)) | (~member(Y, B)) | (~member(X, A)))) & (inverse_predicate(G, F, A, B) | (~((apply(F, tptp_fun_X_22(B, A, F, G), tptp_fun_Y_21(B, A, F, G)) <=> apply(G, tptp_fun_Y_21(B, A, F, G), tptp_fun_X_22(B, A, F, G))) | (~member(tptp_fun_X_22(B, A, F, G), A)) | (~member(tptp_fun_Y_21(B, A, F, G), B)))))) <=> (~((~((~inverse_predicate(G, F, A, B)) | ![X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(G, Y, X)) | (~member(Y, B)) | (~member(X, A))))) | (~(inverse_predicate(G, F, A, B) | (~((apply(F, tptp_fun_X_22(B, A, F, G), tptp_fun_Y_21(B, A, F, G)) <=> apply(G, tptp_fun_Y_21(B, A, F, G), tptp_fun_X_22(B, A, F, G))) | (~member(tptp_fun_X_22(B, A, F, G), A)) | (~member(tptp_fun_Y_21(B, A, F, G), B))))))))), ((((~inverse_predicate(G, F, A, B)) | ![X: $i, Y: $i] : ((~(member(X, A) & member(Y, B))) | (apply(F, X, Y) <=> apply(G, Y, X)))) & (inverse_predicate(G, F, A, B) | (~((~(member(tptp_fun_X_22(B, A, F, G), A) & member(tptp_fun_Y_21(B, A, F, G), B))) | (apply(F, tptp_fun_X_22(B, A, F, G), tptp_fun_Y_21(B, A, F, G)) <=> apply(G, tptp_fun_Y_21(B, A, F, G), tptp_fun_X_22(B, A, F, G))))))) <=> (~((~((~inverse_predicate(G, F, A, B)) | ![X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(G, Y, X)) | (~member(Y, B)) | (~member(X, A))))) | (~(inverse_predicate(G, F, A, B) | (~((apply(F, tptp_fun_X_22(B, A, F, G), tptp_fun_Y_21(B, A, F, G)) <=> apply(G, tptp_fun_Y_21(B, A, F, G), tptp_fun_X_22(B, A, F, G))) | (~member(tptp_fun_X_22(B, A, F, G), A)) | (~member(tptp_fun_Y_21(B, A, F, G), B))))))))))),
% 0.23/0.45 inference(bind,[status(th)],[])).
% 0.23/0.45 tff(45,plain,
% 0.23/0.45 (![G: $i, F: $i, A: $i, B: $i] : (((~inverse_predicate(G, F, A, B)) | ![X: $i, Y: $i] : ((~(member(X, A) & member(Y, B))) | (apply(F, X, Y) <=> apply(G, Y, X)))) & (inverse_predicate(G, F, A, B) | (~((~(member(tptp_fun_X_22(B, A, F, G), A) & member(tptp_fun_Y_21(B, A, F, G), B))) | (apply(F, tptp_fun_X_22(B, A, F, G), tptp_fun_Y_21(B, A, F, G)) <=> apply(G, tptp_fun_Y_21(B, A, F, G), tptp_fun_X_22(B, A, F, G))))))) <=> ![G: $i, F: $i, A: $i, B: $i] : (~((~((~inverse_predicate(G, F, A, B)) | ![X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(G, Y, X)) | (~member(Y, B)) | (~member(X, A))))) | (~(inverse_predicate(G, F, A, B) | (~((apply(F, tptp_fun_X_22(B, A, F, G), tptp_fun_Y_21(B, A, F, G)) <=> apply(G, tptp_fun_Y_21(B, A, F, G), tptp_fun_X_22(B, A, F, G))) | (~member(tptp_fun_X_22(B, A, F, G), A)) | (~member(tptp_fun_Y_21(B, A, F, G), B))))))))),
% 0.23/0.45 inference(quant_intro,[status(thm)],[44])).
% 0.23/0.45 tff(46,plain,
% 0.23/0.45 (![G: $i, F: $i, A: $i, B: $i] : (inverse_predicate(G, F, A, B) <=> ![X: $i, Y: $i] : ((~(member(X, A) & member(Y, B))) | (apply(F, X, Y) <=> apply(G, Y, X)))) <=> ![G: $i, F: $i, A: $i, B: $i] : (inverse_predicate(G, F, A, B) <=> ![X: $i, Y: $i] : ((~(member(X, A) & member(Y, B))) | (apply(F, X, Y) <=> apply(G, Y, X))))),
% 0.23/0.45 inference(rewrite,[status(thm)],[])).
% 0.23/0.45 tff(47,plain,
% 0.23/0.45 (^[G: $i, F: $i, A: $i, B: $i] : rewrite((inverse_predicate(G, F, A, B) <=> ![X: $i, Y: $i] : ((member(X, A) & member(Y, B)) => (apply(F, X, Y) <=> apply(G, Y, X)))) <=> (inverse_predicate(G, F, A, B) <=> ![X: $i, Y: $i] : ((~(member(X, A) & member(Y, B))) | (apply(F, X, Y) <=> apply(G, Y, X)))))),
% 0.23/0.45 inference(bind,[status(th)],[])).
% 0.23/0.45 tff(48,plain,
% 0.23/0.45 (![G: $i, F: $i, A: $i, B: $i] : (inverse_predicate(G, F, A, B) <=> ![X: $i, Y: $i] : ((member(X, A) & member(Y, B)) => (apply(F, X, Y) <=> apply(G, Y, X)))) <=> ![G: $i, F: $i, A: $i, B: $i] : (inverse_predicate(G, F, A, B) <=> ![X: $i, Y: $i] : ((~(member(X, A) & member(Y, B))) | (apply(F, X, Y) <=> apply(G, Y, X))))),
% 0.23/0.45 inference(quant_intro,[status(thm)],[47])).
% 0.23/0.45 tff(49,axiom,(![G: $i, F: $i, A: $i, B: $i] : (inverse_predicate(G, F, A, B) <=> ![X: $i, Y: $i] : ((member(X, A) & member(Y, B)) => (apply(F, X, Y) <=> apply(G, Y, X))))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+1.ax','inverse_predicate')).
% 0.23/0.45 tff(50,plain,
% 0.23/0.45 (![G: $i, F: $i, A: $i, B: $i] : (inverse_predicate(G, F, A, B) <=> ![X: $i, Y: $i] : ((~(member(X, A) & member(Y, B))) | (apply(F, X, Y) <=> apply(G, Y, X))))),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.23/0.45 tff(51,plain,
% 0.23/0.45 (![G: $i, F: $i, A: $i, B: $i] : (inverse_predicate(G, F, A, B) <=> ![X: $i, Y: $i] : ((~(member(X, A) & member(Y, B))) | (apply(F, X, Y) <=> apply(G, Y, X))))),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[50, 46])).
% 0.23/0.45 tff(52,plain,(
% 0.23/0.45 ![G: $i, F: $i, A: $i, B: $i] : (((~inverse_predicate(G, F, A, B)) | ![X: $i, Y: $i] : ((~(member(X, A) & member(Y, B))) | (apply(F, X, Y) <=> apply(G, Y, X)))) & (inverse_predicate(G, F, A, B) | (~((~(member(tptp_fun_X_22(B, A, F, G), A) & member(tptp_fun_Y_21(B, A, F, G), B))) | (apply(F, tptp_fun_X_22(B, A, F, G), tptp_fun_Y_21(B, A, F, G)) <=> apply(G, tptp_fun_Y_21(B, A, F, G), tptp_fun_X_22(B, A, F, G)))))))),
% 0.23/0.45 inference(skolemize,[status(sab)],[51])).
% 0.23/0.45 tff(53,plain,
% 0.23/0.45 (![G: $i, F: $i, A: $i, B: $i] : (~((~((~inverse_predicate(G, F, A, B)) | ![X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(G, Y, X)) | (~member(Y, B)) | (~member(X, A))))) | (~(inverse_predicate(G, F, A, B) | (~((apply(F, tptp_fun_X_22(B, A, F, G), tptp_fun_Y_21(B, A, F, G)) <=> apply(G, tptp_fun_Y_21(B, A, F, G), tptp_fun_X_22(B, A, F, G))) | (~member(tptp_fun_X_22(B, A, F, G), A)) | (~member(tptp_fun_Y_21(B, A, F, G), B))))))))),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[52, 45])).
% 0.23/0.45 tff(54,plain,
% 0.23/0.45 (![G: $i, F: $i, A: $i, B: $i] : (~((~((~inverse_predicate(G, F, A, B)) | ![X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(G, Y, X)) | (~member(Y, B)) | (~member(X, A))))) | (~(inverse_predicate(G, F, A, B) | (~((apply(F, tptp_fun_X_22(B, A, F, G), tptp_fun_Y_21(B, A, F, G)) <=> apply(G, tptp_fun_Y_21(B, A, F, G), tptp_fun_X_22(B, A, F, G))) | (~member(tptp_fun_X_22(B, A, F, G), A)) | (~member(tptp_fun_Y_21(B, A, F, G), B))))))))),
% 0.23/0.46 inference(modus_ponens,[status(thm)],[53, 43])).
% 0.23/0.46 tff(55,plain,
% 0.23/0.46 (((~![G: $i, F: $i, A: $i, B: $i] : (~((~((~inverse_predicate(G, F, A, B)) | ![X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(G, Y, X)) | (~member(Y, B)) | (~member(X, A))))) | (~(inverse_predicate(G, F, A, B) | (~((apply(F, tptp_fun_X_22(B, A, F, G), tptp_fun_Y_21(B, A, F, G)) <=> apply(G, tptp_fun_Y_21(B, A, F, G), tptp_fun_X_22(B, A, F, G))) | (~member(tptp_fun_X_22(B, A, F, G), A)) | (~member(tptp_fun_Y_21(B, A, F, G), B))))))))) | (~((~((~inverse_predicate(F!40, F!40, A!39, A!39)) | ![X: $i, Y: $i] : ((~member(Y, A!39)) | (~member(X, A!39)) | (apply(F!40, X, Y) <=> apply(F!40, Y, X))))) | (~(inverse_predicate(F!40, F!40, A!39, A!39) | (~((~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | (apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40)) <=> apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))) | (~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39))))))))) <=> ((~![G: $i, F: $i, A: $i, B: $i] : (~((~((~inverse_predicate(G, F, A, B)) | ![X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(G, Y, X)) | (~member(Y, B)) | (~member(X, A))))) | (~(inverse_predicate(G, F, A, B) | (~((apply(F, tptp_fun_X_22(B, A, F, G), tptp_fun_Y_21(B, A, F, G)) <=> apply(G, tptp_fun_Y_21(B, A, F, G), tptp_fun_X_22(B, A, F, G))) | (~member(tptp_fun_X_22(B, A, F, G), A)) | (~member(tptp_fun_Y_21(B, A, F, G), B))))))))) | (~((~((~inverse_predicate(F!40, F!40, A!39, A!39)) | ![X: $i, Y: $i] : ((~member(Y, A!39)) | (~member(X, A!39)) | (apply(F!40, X, Y) <=> apply(F!40, Y, X))))) | (~(inverse_predicate(F!40, F!40, A!39, A!39) | (~((~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | (apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40)) <=> apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))) | (~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)))))))))),
% 0.23/0.46 inference(rewrite,[status(thm)],[])).
% 0.23/0.46 tff(56,plain,
% 0.23/0.46 ((~((~((~inverse_predicate(F!40, F!40, A!39, A!39)) | ![X: $i, Y: $i] : ((apply(F!40, X, Y) <=> apply(F!40, Y, X)) | (~member(Y, A!39)) | (~member(X, A!39))))) | (~(inverse_predicate(F!40, F!40, A!39, A!39) | (~((apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40)) <=> apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))) | (~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)))))))) <=> (~((~((~inverse_predicate(F!40, F!40, A!39, A!39)) | ![X: $i, Y: $i] : ((~member(Y, A!39)) | (~member(X, A!39)) | (apply(F!40, X, Y) <=> apply(F!40, Y, X))))) | (~(inverse_predicate(F!40, F!40, A!39, A!39) | (~((~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | (apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40)) <=> apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))) | (~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39))))))))),
% 0.23/0.46 inference(rewrite,[status(thm)],[])).
% 0.23/0.46 tff(57,plain,
% 0.23/0.46 (((~![G: $i, F: $i, A: $i, B: $i] : (~((~((~inverse_predicate(G, F, A, B)) | ![X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(G, Y, X)) | (~member(Y, B)) | (~member(X, A))))) | (~(inverse_predicate(G, F, A, B) | (~((apply(F, tptp_fun_X_22(B, A, F, G), tptp_fun_Y_21(B, A, F, G)) <=> apply(G, tptp_fun_Y_21(B, A, F, G), tptp_fun_X_22(B, A, F, G))) | (~member(tptp_fun_X_22(B, A, F, G), A)) | (~member(tptp_fun_Y_21(B, A, F, G), B))))))))) | (~((~((~inverse_predicate(F!40, F!40, A!39, A!39)) | ![X: $i, Y: $i] : ((apply(F!40, X, Y) <=> apply(F!40, Y, X)) | (~member(Y, A!39)) | (~member(X, A!39))))) | (~(inverse_predicate(F!40, F!40, A!39, A!39) | (~((apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40)) <=> apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))) | (~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39))))))))) <=> ((~![G: $i, F: $i, A: $i, B: $i] : (~((~((~inverse_predicate(G, F, A, B)) | ![X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(G, Y, X)) | (~member(Y, B)) | (~member(X, A))))) | (~(inverse_predicate(G, F, A, B) | (~((apply(F, tptp_fun_X_22(B, A, F, G), tptp_fun_Y_21(B, A, F, G)) <=> apply(G, tptp_fun_Y_21(B, A, F, G), tptp_fun_X_22(B, A, F, G))) | (~member(tptp_fun_X_22(B, A, F, G), A)) | (~member(tptp_fun_Y_21(B, A, F, G), B))))))))) | (~((~((~inverse_predicate(F!40, F!40, A!39, A!39)) | ![X: $i, Y: $i] : ((~member(Y, A!39)) | (~member(X, A!39)) | (apply(F!40, X, Y) <=> apply(F!40, Y, X))))) | (~(inverse_predicate(F!40, F!40, A!39, A!39) | (~((~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | (apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40)) <=> apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))) | (~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)))))))))),
% 0.23/0.46 inference(monotonicity,[status(thm)],[56])).
% 0.23/0.46 tff(58,plain,
% 0.23/0.46 (((~![G: $i, F: $i, A: $i, B: $i] : (~((~((~inverse_predicate(G, F, A, B)) | ![X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(G, Y, X)) | (~member(Y, B)) | (~member(X, A))))) | (~(inverse_predicate(G, F, A, B) | (~((apply(F, tptp_fun_X_22(B, A, F, G), tptp_fun_Y_21(B, A, F, G)) <=> apply(G, tptp_fun_Y_21(B, A, F, G), tptp_fun_X_22(B, A, F, G))) | (~member(tptp_fun_X_22(B, A, F, G), A)) | (~member(tptp_fun_Y_21(B, A, F, G), B))))))))) | (~((~((~inverse_predicate(F!40, F!40, A!39, A!39)) | ![X: $i, Y: $i] : ((apply(F!40, X, Y) <=> apply(F!40, Y, X)) | (~member(Y, A!39)) | (~member(X, A!39))))) | (~(inverse_predicate(F!40, F!40, A!39, A!39) | (~((apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40)) <=> apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))) | (~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39))))))))) <=> ((~![G: $i, F: $i, A: $i, B: $i] : (~((~((~inverse_predicate(G, F, A, B)) | ![X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(G, Y, X)) | (~member(Y, B)) | (~member(X, A))))) | (~(inverse_predicate(G, F, A, B) | (~((apply(F, tptp_fun_X_22(B, A, F, G), tptp_fun_Y_21(B, A, F, G)) <=> apply(G, tptp_fun_Y_21(B, A, F, G), tptp_fun_X_22(B, A, F, G))) | (~member(tptp_fun_X_22(B, A, F, G), A)) | (~member(tptp_fun_Y_21(B, A, F, G), B))))))))) | (~((~((~inverse_predicate(F!40, F!40, A!39, A!39)) | ![X: $i, Y: $i] : ((~member(Y, A!39)) | (~member(X, A!39)) | (apply(F!40, X, Y) <=> apply(F!40, Y, X))))) | (~(inverse_predicate(F!40, F!40, A!39, A!39) | (~((~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | (apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40)) <=> apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))) | (~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)))))))))),
% 0.23/0.46 inference(transitivity,[status(thm)],[57, 55])).
% 0.23/0.46 tff(59,plain,
% 0.23/0.46 ((~![G: $i, F: $i, A: $i, B: $i] : (~((~((~inverse_predicate(G, F, A, B)) | ![X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(G, Y, X)) | (~member(Y, B)) | (~member(X, A))))) | (~(inverse_predicate(G, F, A, B) | (~((apply(F, tptp_fun_X_22(B, A, F, G), tptp_fun_Y_21(B, A, F, G)) <=> apply(G, tptp_fun_Y_21(B, A, F, G), tptp_fun_X_22(B, A, F, G))) | (~member(tptp_fun_X_22(B, A, F, G), A)) | (~member(tptp_fun_Y_21(B, A, F, G), B))))))))) | (~((~((~inverse_predicate(F!40, F!40, A!39, A!39)) | ![X: $i, Y: $i] : ((apply(F!40, X, Y) <=> apply(F!40, Y, X)) | (~member(Y, A!39)) | (~member(X, A!39))))) | (~(inverse_predicate(F!40, F!40, A!39, A!39) | (~((apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40)) <=> apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))) | (~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39))))))))),
% 0.23/0.46 inference(quant_inst,[status(thm)],[])).
% 0.23/0.46 tff(60,plain,
% 0.23/0.47 ((~![G: $i, F: $i, A: $i, B: $i] : (~((~((~inverse_predicate(G, F, A, B)) | ![X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(G, Y, X)) | (~member(Y, B)) | (~member(X, A))))) | (~(inverse_predicate(G, F, A, B) | (~((apply(F, tptp_fun_X_22(B, A, F, G), tptp_fun_Y_21(B, A, F, G)) <=> apply(G, tptp_fun_Y_21(B, A, F, G), tptp_fun_X_22(B, A, F, G))) | (~member(tptp_fun_X_22(B, A, F, G), A)) | (~member(tptp_fun_Y_21(B, A, F, G), B))))))))) | (~((~((~inverse_predicate(F!40, F!40, A!39, A!39)) | ![X: $i, Y: $i] : ((~member(Y, A!39)) | (~member(X, A!39)) | (apply(F!40, X, Y) <=> apply(F!40, Y, X))))) | (~(inverse_predicate(F!40, F!40, A!39, A!39) | (~((~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | (apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40)) <=> apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))) | (~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39))))))))),
% 0.23/0.47 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.23/0.47 tff(61,plain,
% 0.23/0.47 ($false),
% 0.23/0.47 inference(unit_resolution,[status(thm)],[60, 54, 38])).
% 0.23/0.47 tff(62,plain,(~((~((~inverse_predicate(F!40, F!40, A!39, A!39)) | ![X: $i, Y: $i] : ((~member(Y, A!39)) | (~member(X, A!39)) | (apply(F!40, X, Y) <=> apply(F!40, Y, X))))) | (~(inverse_predicate(F!40, F!40, A!39, A!39) | (~((~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | (apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40)) <=> apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))) | (~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)))))))), inference(lemma,lemma(discharge,[]))).
% 0.23/0.47 tff(63,plain,
% 0.23/0.47 (((~((~inverse_predicate(F!40, F!40, A!39, A!39)) | ![X: $i, Y: $i] : ((~member(Y, A!39)) | (~member(X, A!39)) | (apply(F!40, X, Y) <=> apply(F!40, Y, X))))) | (~(inverse_predicate(F!40, F!40, A!39, A!39) | (~((~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | (apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40)) <=> apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))) | (~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39))))))) | (inverse_predicate(F!40, F!40, A!39, A!39) | (~((~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | (apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40)) <=> apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))) | (~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)))))),
% 0.23/0.47 inference(tautology,[status(thm)],[])).
% 0.23/0.47 tff(64,plain,
% 0.23/0.47 (inverse_predicate(F!40, F!40, A!39, A!39) | (~((~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | (apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40)) <=> apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))) | (~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39))))),
% 0.23/0.47 inference(unit_resolution,[status(thm)],[63, 62])).
% 0.23/0.47 tff(65,assumption,(~((~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | (apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40)) <=> apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))) | (~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)))), introduced(assumption)).
% 0.23/0.47 tff(66,plain,
% 0.23/0.47 (((~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | (apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40)) <=> apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))) | (~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39))) | member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)),
% 0.23/0.47 inference(tautology,[status(thm)],[])).
% 0.23/0.47 tff(67,plain,
% 0.23/0.47 (member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)),
% 0.23/0.47 inference(unit_resolution,[status(thm)],[66, 65])).
% 0.23/0.47 tff(68,plain,
% 0.23/0.47 (^[F: $i, A: $i, B: $i] : rewrite((~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))) <=> (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))))))))),
% 0.23/0.47 inference(bind,[status(th)],[])).
% 0.23/0.47 tff(69,plain,
% 0.23/0.47 (![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))),
% 0.23/0.47 inference(quant_intro,[status(thm)],[68])).
% 0.23/0.47 tff(70,plain,
% 0.23/0.47 (^[F: $i, A: $i, B: $i] : refl((~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))) <=> (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))))),
% 0.23/0.47 inference(bind,[status(th)],[])).
% 0.23/0.47 tff(71,plain,
% 0.23/0.47 (![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))))))),
% 0.23/0.47 inference(quant_intro,[status(thm)],[70])).
% 0.23/0.47 tff(72,plain,
% 0.23/0.47 (^[F: $i, A: $i, B: $i] : rewrite((~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))) <=> (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))))),
% 0.23/0.47 inference(bind,[status(th)],[])).
% 0.23/0.47 tff(73,plain,
% 0.23/0.47 (![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))))))),
% 0.23/0.47 inference(quant_intro,[status(thm)],[72])).
% 0.23/0.47 tff(74,plain,
% 0.23/0.47 (![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))))))),
% 0.23/0.47 inference(transitivity,[status(thm)],[73, 71])).
% 0.23/0.47 tff(75,plain,
% 0.23/0.47 (^[F: $i, A: $i, B: $i] : trans(monotonicity(rewrite(((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) <=> ((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))), trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[Y: $i] : trans(monotonicity(rewrite((member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)) <=> (~((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))), ((~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y))) <=> (~(~((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))), rewrite((~(~((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))) <=> ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))), ((~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y))) <=> ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))), (![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y))) <=> ![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))), ((member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) <=> (member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))), rewrite((member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))) <=> (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))), ((member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) <=> (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))))), rewrite((~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B))))) <=> (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))), ((maps(F, A, B) | (member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B)))))) <=> (maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))))), rewrite((maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))) <=> (maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))), ((maps(F, A, B) | (member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B)))))) <=> (maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))))), ((((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) & (maps(F, A, B) | (member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B))))))) <=> (((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B))))))) & (maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))), rewrite((((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B))))))) & (maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))) <=> (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))))))), ((((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) & (maps(F, A, B) | (member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B))))))) <=> (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))))))))),
% 0.23/0.47 inference(bind,[status(th)],[])).
% 0.23/0.47 tff(76,plain,
% 0.23/0.47 (![F: $i, A: $i, B: $i] : (((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) & (maps(F, A, B) | (member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))))))),
% 0.23/0.48 inference(quant_intro,[status(thm)],[75])).
% 0.23/0.48 tff(77,plain,
% 0.23/0.48 (^[F: $i, A: $i, B: $i] : rewrite((((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) & (maps(F, A, B) | ((member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B)))))))) <=> (((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) & (maps(F, A, B) | (member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B))))))))),
% 0.23/0.48 inference(bind,[status(th)],[])).
% 0.23/0.48 tff(78,plain,
% 0.23/0.48 (![F: $i, A: $i, B: $i] : (((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) & (maps(F, A, B) | ((member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B)))))))) <=> ![F: $i, A: $i, B: $i] : (((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) & (maps(F, A, B) | (member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B)))))))),
% 0.23/0.48 inference(quant_intro,[status(thm)],[77])).
% 0.23/0.48 tff(79,plain,
% 0.23/0.48 (![F: $i, A: $i, B: $i] : (maps(F, A, B) <=> (![X: $i] : ((~member(X, A)) | ?[Y: $i] : (member(Y, B) & apply(F, X, Y))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) <=> ![F: $i, A: $i, B: $i] : (maps(F, A, B) <=> (![X: $i] : ((~member(X, A)) | ?[Y: $i] : (member(Y, B) & apply(F, X, Y))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B))))))),
% 0.23/0.48 inference(rewrite,[status(thm)],[])).
% 0.23/0.48 tff(80,plain,
% 0.23/0.48 (^[F: $i, A: $i, B: $i] : rewrite((maps(F, A, B) <=> (![X: $i] : (member(X, A) => ?[Y: $i] : (member(Y, B) & apply(F, X, Y))) & ![X: $i, Y1: $i, Y2: $i] : (((member(X, A) & member(Y1, B)) & member(Y2, B)) => ((apply(F, X, Y1) & apply(F, X, Y2)) => (Y1 = Y2))))) <=> (maps(F, A, B) <=> (![X: $i] : ((~member(X, A)) | ?[Y: $i] : (member(Y, B) & apply(F, X, Y))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))))),
% 0.23/0.48 inference(bind,[status(th)],[])).
% 0.23/0.48 tff(81,plain,
% 0.23/0.48 (![F: $i, A: $i, B: $i] : (maps(F, A, B) <=> (![X: $i] : (member(X, A) => ?[Y: $i] : (member(Y, B) & apply(F, X, Y))) & ![X: $i, Y1: $i, Y2: $i] : (((member(X, A) & member(Y1, B)) & member(Y2, B)) => ((apply(F, X, Y1) & apply(F, X, Y2)) => (Y1 = Y2))))) <=> ![F: $i, A: $i, B: $i] : (maps(F, A, B) <=> (![X: $i] : ((~member(X, A)) | ?[Y: $i] : (member(Y, B) & apply(F, X, Y))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B))))))),
% 0.23/0.48 inference(quant_intro,[status(thm)],[80])).
% 0.23/0.48 tff(82,axiom,(![F: $i, A: $i, B: $i] : (maps(F, A, B) <=> (![X: $i] : (member(X, A) => ?[Y: $i] : (member(Y, B) & apply(F, X, Y))) & ![X: $i, Y1: $i, Y2: $i] : (((member(X, A) & member(Y1, B)) & member(Y2, B)) => ((apply(F, X, Y1) & apply(F, X, Y2)) => (Y1 = Y2)))))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+1.ax','maps')).
% 0.23/0.48 tff(83,plain,
% 0.23/0.48 (![F: $i, A: $i, B: $i] : (maps(F, A, B) <=> (![X: $i] : ((~member(X, A)) | ?[Y: $i] : (member(Y, B) & apply(F, X, Y))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B))))))),
% 0.23/0.48 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.23/0.48 tff(84,plain,
% 0.23/0.48 (![F: $i, A: $i, B: $i] : (maps(F, A, B) <=> (![X: $i] : ((~member(X, A)) | ?[Y: $i] : (member(Y, B) & apply(F, X, Y))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B))))))),
% 0.23/0.48 inference(modus_ponens,[status(thm)],[83, 79])).
% 0.23/0.48 tff(85,plain,(
% 0.23/0.48 ![F: $i, A: $i, B: $i] : (((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) & (maps(F, A, B) | ((member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B))))))))),
% 0.23/0.48 inference(skolemize,[status(sab)],[84])).
% 0.23/0.48 tff(86,plain,
% 0.23/0.48 (![F: $i, A: $i, B: $i] : (((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) & (maps(F, A, B) | (member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B)))))))),
% 0.23/0.48 inference(modus_ponens,[status(thm)],[85, 78])).
% 0.23/0.48 tff(87,plain,
% 0.23/0.48 (![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))))))),
% 0.23/0.48 inference(modus_ponens,[status(thm)],[86, 76])).
% 0.23/0.48 tff(88,plain,
% 0.23/0.48 (![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))))))),
% 0.23/0.48 inference(modus_ponens,[status(thm)],[87, 74])).
% 0.23/0.48 tff(89,plain,
% 0.23/0.48 (![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))),
% 0.23/0.48 inference(modus_ponens,[status(thm)],[88, 69])).
% 0.23/0.48 tff(90,plain,
% 0.23/0.48 (((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(F!40, A!39, A!39)) | (~((~![X: $i] : ((~member(X, A!39)) | (~((~member(tptp_fun_Y_3(X, A!39, F!40), A!39)) | (~apply(F!40, X, tptp_fun_Y_3(X, A!39, F!40))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))))))) | (~(maps(F!40, A!39, A!39) | (~((~member(tptp_fun_X_4(A!39, A!39, F!40), A!39)) | (~![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X_4(A!39, A!39, F!40), Y)))))) | (~((~member(tptp_fun_Y2_5(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_Y1_6(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_X_7(A!39, A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_X_7(A!39, A!39, F!40), tptp_fun_Y2_5(A!39, A!39, F!40))) | (~apply(F!40, tptp_fun_X_7(A!39, A!39, F!40), tptp_fun_Y1_6(A!39, A!39, F!40))) | (tptp_fun_Y1_6(A!39, A!39, F!40) = tptp_fun_Y2_5(A!39, A!39, F!40))))))))) <=> ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(F!40, A!39, A!39)) | (~((~![X: $i] : ((~member(X, A!39)) | (~((~member(tptp_fun_Y_3(X, A!39, F!40), A!39)) | (~apply(F!40, X, tptp_fun_Y_3(X, A!39, F!40))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))))))) | (~(maps(F!40, A!39, A!39) | (~((~member(tptp_fun_X_4(A!39, A!39, F!40), A!39)) | (~![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X_4(A!39, A!39, F!40), Y)))))) | (~((~member(tptp_fun_Y2_5(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_Y1_6(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_X_7(A!39, A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_X_7(A!39, A!39, F!40), tptp_fun_Y2_5(A!39, A!39, F!40))) | (~apply(F!40, tptp_fun_X_7(A!39, A!39, F!40), tptp_fun_Y1_6(A!39, A!39, F!40))) | (tptp_fun_Y1_6(A!39, A!39, F!40) = tptp_fun_Y2_5(A!39, A!39, F!40)))))))))),
% 0.23/0.49 inference(rewrite,[status(thm)],[])).
% 0.23/0.49 tff(91,plain,
% 0.23/0.49 ((~((~((~maps(F!40, A!39, A!39)) | (~((~![X: $i] : ((~member(X, A!39)) | (~((~member(tptp_fun_Y_3(X, A!39, F!40), A!39)) | (~apply(F!40, X, tptp_fun_Y_3(X, A!39, F!40))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)) | (~member(Y2, A!39)))))))) | (~(maps(F!40, A!39, A!39) | (~((tptp_fun_Y1_6(A!39, A!39, F!40) = tptp_fun_Y2_5(A!39, A!39, F!40)) | (~apply(F!40, tptp_fun_X_7(A!39, A!39, F!40), tptp_fun_Y1_6(A!39, A!39, F!40))) | (~apply(F!40, tptp_fun_X_7(A!39, A!39, F!40), tptp_fun_Y2_5(A!39, A!39, F!40))) | (~member(tptp_fun_X_7(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_Y1_6(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_Y2_5(A!39, A!39, F!40), A!39)))) | (~((~member(tptp_fun_X_4(A!39, A!39, F!40), A!39)) | (~![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X_4(A!39, A!39, F!40), Y)))))))))) <=> (~((~((~maps(F!40, A!39, A!39)) | (~((~![X: $i] : ((~member(X, A!39)) | (~((~member(tptp_fun_Y_3(X, A!39, F!40), A!39)) | (~apply(F!40, X, tptp_fun_Y_3(X, A!39, F!40))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))))))) | (~(maps(F!40, A!39, A!39) | (~((~member(tptp_fun_X_4(A!39, A!39, F!40), A!39)) | (~![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X_4(A!39, A!39, F!40), Y)))))) | (~((~member(tptp_fun_Y2_5(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_Y1_6(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_X_7(A!39, A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_X_7(A!39, A!39, F!40), tptp_fun_Y2_5(A!39, A!39, F!40))) | (~apply(F!40, tptp_fun_X_7(A!39, A!39, F!40), tptp_fun_Y1_6(A!39, A!39, F!40))) | (tptp_fun_Y1_6(A!39, A!39, F!40) = tptp_fun_Y2_5(A!39, A!39, F!40))))))))),
% 0.23/0.49 inference(rewrite,[status(thm)],[])).
% 0.23/0.49 tff(92,plain,
% 0.23/0.49 (((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(F!40, A!39, A!39)) | (~((~![X: $i] : ((~member(X, A!39)) | (~((~member(tptp_fun_Y_3(X, A!39, F!40), A!39)) | (~apply(F!40, X, tptp_fun_Y_3(X, A!39, F!40))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)) | (~member(Y2, A!39)))))))) | (~(maps(F!40, A!39, A!39) | (~((tptp_fun_Y1_6(A!39, A!39, F!40) = tptp_fun_Y2_5(A!39, A!39, F!40)) | (~apply(F!40, tptp_fun_X_7(A!39, A!39, F!40), tptp_fun_Y1_6(A!39, A!39, F!40))) | (~apply(F!40, tptp_fun_X_7(A!39, A!39, F!40), tptp_fun_Y2_5(A!39, A!39, F!40))) | (~member(tptp_fun_X_7(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_Y1_6(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_Y2_5(A!39, A!39, F!40), A!39)))) | (~((~member(tptp_fun_X_4(A!39, A!39, F!40), A!39)) | (~![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X_4(A!39, A!39, F!40), Y))))))))))) <=> ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(F!40, A!39, A!39)) | (~((~![X: $i] : ((~member(X, A!39)) | (~((~member(tptp_fun_Y_3(X, A!39, F!40), A!39)) | (~apply(F!40, X, tptp_fun_Y_3(X, A!39, F!40))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))))))) | (~(maps(F!40, A!39, A!39) | (~((~member(tptp_fun_X_4(A!39, A!39, F!40), A!39)) | (~![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X_4(A!39, A!39, F!40), Y)))))) | (~((~member(tptp_fun_Y2_5(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_Y1_6(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_X_7(A!39, A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_X_7(A!39, A!39, F!40), tptp_fun_Y2_5(A!39, A!39, F!40))) | (~apply(F!40, tptp_fun_X_7(A!39, A!39, F!40), tptp_fun_Y1_6(A!39, A!39, F!40))) | (tptp_fun_Y1_6(A!39, A!39, F!40) = tptp_fun_Y2_5(A!39, A!39, F!40)))))))))),
% 0.23/0.49 inference(monotonicity,[status(thm)],[91])).
% 0.23/0.49 tff(93,plain,
% 0.23/0.49 (((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(F!40, A!39, A!39)) | (~((~![X: $i] : ((~member(X, A!39)) | (~((~member(tptp_fun_Y_3(X, A!39, F!40), A!39)) | (~apply(F!40, X, tptp_fun_Y_3(X, A!39, F!40))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)) | (~member(Y2, A!39)))))))) | (~(maps(F!40, A!39, A!39) | (~((tptp_fun_Y1_6(A!39, A!39, F!40) = tptp_fun_Y2_5(A!39, A!39, F!40)) | (~apply(F!40, tptp_fun_X_7(A!39, A!39, F!40), tptp_fun_Y1_6(A!39, A!39, F!40))) | (~apply(F!40, tptp_fun_X_7(A!39, A!39, F!40), tptp_fun_Y2_5(A!39, A!39, F!40))) | (~member(tptp_fun_X_7(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_Y1_6(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_Y2_5(A!39, A!39, F!40), A!39)))) | (~((~member(tptp_fun_X_4(A!39, A!39, F!40), A!39)) | (~![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X_4(A!39, A!39, F!40), Y))))))))))) <=> ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(F!40, A!39, A!39)) | (~((~![X: $i] : ((~member(X, A!39)) | (~((~member(tptp_fun_Y_3(X, A!39, F!40), A!39)) | (~apply(F!40, X, tptp_fun_Y_3(X, A!39, F!40))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))))))) | (~(maps(F!40, A!39, A!39) | (~((~member(tptp_fun_X_4(A!39, A!39, F!40), A!39)) | (~![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X_4(A!39, A!39, F!40), Y)))))) | (~((~member(tptp_fun_Y2_5(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_Y1_6(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_X_7(A!39, A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_X_7(A!39, A!39, F!40), tptp_fun_Y2_5(A!39, A!39, F!40))) | (~apply(F!40, tptp_fun_X_7(A!39, A!39, F!40), tptp_fun_Y1_6(A!39, A!39, F!40))) | (tptp_fun_Y1_6(A!39, A!39, F!40) = tptp_fun_Y2_5(A!39, A!39, F!40)))))))))),
% 0.23/0.49 inference(transitivity,[status(thm)],[92, 90])).
% 0.23/0.49 tff(94,plain,
% 0.23/0.49 ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(F!40, A!39, A!39)) | (~((~![X: $i] : ((~member(X, A!39)) | (~((~member(tptp_fun_Y_3(X, A!39, F!40), A!39)) | (~apply(F!40, X, tptp_fun_Y_3(X, A!39, F!40))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)) | (~member(Y2, A!39)))))))) | (~(maps(F!40, A!39, A!39) | (~((tptp_fun_Y1_6(A!39, A!39, F!40) = tptp_fun_Y2_5(A!39, A!39, F!40)) | (~apply(F!40, tptp_fun_X_7(A!39, A!39, F!40), tptp_fun_Y1_6(A!39, A!39, F!40))) | (~apply(F!40, tptp_fun_X_7(A!39, A!39, F!40), tptp_fun_Y2_5(A!39, A!39, F!40))) | (~member(tptp_fun_X_7(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_Y1_6(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_Y2_5(A!39, A!39, F!40), A!39)))) | (~((~member(tptp_fun_X_4(A!39, A!39, F!40), A!39)) | (~![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X_4(A!39, A!39, F!40), Y))))))))))),
% 0.23/0.50 inference(quant_inst,[status(thm)],[])).
% 0.23/0.50 tff(95,plain,
% 0.23/0.50 ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(F!40, A!39, A!39)) | (~((~![X: $i] : ((~member(X, A!39)) | (~((~member(tptp_fun_Y_3(X, A!39, F!40), A!39)) | (~apply(F!40, X, tptp_fun_Y_3(X, A!39, F!40))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))))))) | (~(maps(F!40, A!39, A!39) | (~((~member(tptp_fun_X_4(A!39, A!39, F!40), A!39)) | (~![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X_4(A!39, A!39, F!40), Y)))))) | (~((~member(tptp_fun_Y2_5(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_Y1_6(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_X_7(A!39, A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_X_7(A!39, A!39, F!40), tptp_fun_Y2_5(A!39, A!39, F!40))) | (~apply(F!40, tptp_fun_X_7(A!39, A!39, F!40), tptp_fun_Y1_6(A!39, A!39, F!40))) | (tptp_fun_Y1_6(A!39, A!39, F!40) = tptp_fun_Y2_5(A!39, A!39, F!40))))))))),
% 0.23/0.50 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.23/0.50 tff(96,plain,
% 0.23/0.50 (~((~((~maps(F!40, A!39, A!39)) | (~((~![X: $i] : ((~member(X, A!39)) | (~((~member(tptp_fun_Y_3(X, A!39, F!40), A!39)) | (~apply(F!40, X, tptp_fun_Y_3(X, A!39, F!40))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))))))) | (~(maps(F!40, A!39, A!39) | (~((~member(tptp_fun_X_4(A!39, A!39, F!40), A!39)) | (~![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X_4(A!39, A!39, F!40), Y)))))) | (~((~member(tptp_fun_Y2_5(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_Y1_6(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_X_7(A!39, A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_X_7(A!39, A!39, F!40), tptp_fun_Y2_5(A!39, A!39, F!40))) | (~apply(F!40, tptp_fun_X_7(A!39, A!39, F!40), tptp_fun_Y1_6(A!39, A!39, F!40))) | (tptp_fun_Y1_6(A!39, A!39, F!40) = tptp_fun_Y2_5(A!39, A!39, F!40)))))))),
% 0.23/0.50 inference(unit_resolution,[status(thm)],[95, 89])).
% 0.23/0.50 tff(97,plain,
% 0.23/0.50 (((~((~maps(F!40, A!39, A!39)) | (~((~![X: $i] : ((~member(X, A!39)) | (~((~member(tptp_fun_Y_3(X, A!39, F!40), A!39)) | (~apply(F!40, X, tptp_fun_Y_3(X, A!39, F!40))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))))))) | (~(maps(F!40, A!39, A!39) | (~((~member(tptp_fun_X_4(A!39, A!39, F!40), A!39)) | (~![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X_4(A!39, A!39, F!40), Y)))))) | (~((~member(tptp_fun_Y2_5(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_Y1_6(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_X_7(A!39, A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_X_7(A!39, A!39, F!40), tptp_fun_Y2_5(A!39, A!39, F!40))) | (~apply(F!40, tptp_fun_X_7(A!39, A!39, F!40), tptp_fun_Y1_6(A!39, A!39, F!40))) | (tptp_fun_Y1_6(A!39, A!39, F!40) = tptp_fun_Y2_5(A!39, A!39, F!40))))))) | ((~maps(F!40, A!39, A!39)) | (~((~![X: $i] : ((~member(X, A!39)) | (~((~member(tptp_fun_Y_3(X, A!39, F!40), A!39)) | (~apply(F!40, X, tptp_fun_Y_3(X, A!39, F!40))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))))))),
% 0.23/0.50 inference(tautology,[status(thm)],[])).
% 0.23/0.50 tff(98,plain,
% 0.23/0.50 ((~maps(F!40, A!39, A!39)) | (~((~![X: $i] : ((~member(X, A!39)) | (~((~member(tptp_fun_Y_3(X, A!39, F!40), A!39)) | (~apply(F!40, X, tptp_fun_Y_3(X, A!39, F!40))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39))))))),
% 0.23/0.50 inference(unit_resolution,[status(thm)],[97, 96])).
% 0.23/0.50 tff(99,plain,
% 0.23/0.50 ((~![F: $i, A: $i] : ((~maps(F, A, A)) | ((one_to_one(F, A, A) & inverse_predicate(F, F, A, A)) <=> identity(compose_function(F, F, A, A, A), A)))) <=> (~![F: $i, A: $i] : ((~maps(F, A, A)) | ((one_to_one(F, A, A) & inverse_predicate(F, F, A, A)) <=> identity(compose_function(F, F, A, A, A), A))))),
% 0.23/0.50 inference(rewrite,[status(thm)],[])).
% 0.23/0.50 tff(100,plain,
% 0.23/0.50 ((~![F: $i, A: $i] : (maps(F, A, A) => ((one_to_one(F, A, A) & inverse_predicate(F, F, A, A)) <=> identity(compose_function(F, F, A, A, A), A)))) <=> (~![F: $i, A: $i] : ((~maps(F, A, A)) | ((one_to_one(F, A, A) & inverse_predicate(F, F, A, A)) <=> identity(compose_function(F, F, A, A, A), A))))),
% 0.23/0.50 inference(rewrite,[status(thm)],[])).
% 0.23/0.50 tff(101,axiom,(~![F: $i, A: $i] : (maps(F, A, A) => ((one_to_one(F, A, A) & inverse_predicate(F, F, A, A)) <=> identity(compose_function(F, F, A, A, A), A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thII20')).
% 0.23/0.50 tff(102,plain,
% 0.23/0.50 (~![F: $i, A: $i] : ((~maps(F, A, A)) | ((one_to_one(F, A, A) & inverse_predicate(F, F, A, A)) <=> identity(compose_function(F, F, A, A, A), A)))),
% 0.23/0.50 inference(modus_ponens,[status(thm)],[101, 100])).
% 0.23/0.50 tff(103,plain,
% 0.23/0.50 (~![F: $i, A: $i] : ((~maps(F, A, A)) | ((one_to_one(F, A, A) & inverse_predicate(F, F, A, A)) <=> identity(compose_function(F, F, A, A, A), A)))),
% 0.23/0.50 inference(modus_ponens,[status(thm)],[102, 99])).
% 0.23/0.50 tff(104,plain,
% 0.23/0.50 (~![F: $i, A: $i] : ((~maps(F, A, A)) | ((one_to_one(F, A, A) & inverse_predicate(F, F, A, A)) <=> identity(compose_function(F, F, A, A, A), A)))),
% 0.23/0.50 inference(modus_ponens,[status(thm)],[103, 99])).
% 0.23/0.50 tff(105,plain,
% 0.23/0.50 (~![F: $i, A: $i] : ((~maps(F, A, A)) | ((one_to_one(F, A, A) & inverse_predicate(F, F, A, A)) <=> identity(compose_function(F, F, A, A, A), A)))),
% 0.23/0.50 inference(modus_ponens,[status(thm)],[104, 99])).
% 0.23/0.50 tff(106,plain,(
% 0.23/0.50 ~((~maps(F!40, A!39, A!39)) | ((one_to_one(F!40, A!39, A!39) & inverse_predicate(F!40, F!40, A!39, A!39)) <=> identity(compose_function(F!40, F!40, A!39, A!39, A!39), A!39)))),
% 0.23/0.50 inference(skolemize,[status(sab)],[105])).
% 0.23/0.50 tff(107,plain,
% 0.23/0.50 (maps(F!40, A!39, A!39)),
% 0.23/0.50 inference(or_elim,[status(thm)],[106])).
% 0.23/0.50 tff(108,plain,
% 0.23/0.50 ((~((~maps(F!40, A!39, A!39)) | (~((~![X: $i] : ((~member(X, A!39)) | (~((~member(tptp_fun_Y_3(X, A!39, F!40), A!39)) | (~apply(F!40, X, tptp_fun_Y_3(X, A!39, F!40))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))))))) | (~maps(F!40, A!39, A!39)) | (~((~![X: $i] : ((~member(X, A!39)) | (~((~member(tptp_fun_Y_3(X, A!39, F!40), A!39)) | (~apply(F!40, X, tptp_fun_Y_3(X, A!39, F!40))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39))))))),
% 0.23/0.50 inference(tautology,[status(thm)],[])).
% 0.23/0.50 tff(109,plain,
% 0.23/0.50 ((~((~maps(F!40, A!39, A!39)) | (~((~![X: $i] : ((~member(X, A!39)) | (~((~member(tptp_fun_Y_3(X, A!39, F!40), A!39)) | (~apply(F!40, X, tptp_fun_Y_3(X, A!39, F!40))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))))))) | (~((~![X: $i] : ((~member(X, A!39)) | (~((~member(tptp_fun_Y_3(X, A!39, F!40), A!39)) | (~apply(F!40, X, tptp_fun_Y_3(X, A!39, F!40))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39))))))),
% 0.23/0.50 inference(unit_resolution,[status(thm)],[108, 107])).
% 0.23/0.50 tff(110,plain,
% 0.23/0.50 (~((~![X: $i] : ((~member(X, A!39)) | (~((~member(tptp_fun_Y_3(X, A!39, F!40), A!39)) | (~apply(F!40, X, tptp_fun_Y_3(X, A!39, F!40))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))))),
% 0.23/0.50 inference(unit_resolution,[status(thm)],[109, 98])).
% 0.23/0.50 tff(111,plain,
% 0.23/0.50 (((~![X: $i] : ((~member(X, A!39)) | (~((~member(tptp_fun_Y_3(X, A!39, F!40), A!39)) | (~apply(F!40, X, tptp_fun_Y_3(X, A!39, F!40))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39))))) | ![X: $i] : ((~member(X, A!39)) | (~((~member(tptp_fun_Y_3(X, A!39, F!40), A!39)) | (~apply(F!40, X, tptp_fun_Y_3(X, A!39, F!40))))))),
% 0.23/0.50 inference(tautology,[status(thm)],[])).
% 0.23/0.50 tff(112,plain,
% 0.23/0.50 (![X: $i] : ((~member(X, A!39)) | (~((~member(tptp_fun_Y_3(X, A!39, F!40), A!39)) | (~apply(F!40, X, tptp_fun_Y_3(X, A!39, F!40))))))),
% 0.23/0.50 inference(unit_resolution,[status(thm)],[111, 110])).
% 0.23/0.50 tff(113,plain,
% 0.23/0.50 (((~![X: $i] : ((~member(X, A!39)) | (~((~member(tptp_fun_Y_3(X, A!39, F!40), A!39)) | (~apply(F!40, X, tptp_fun_Y_3(X, A!39, F!40))))))) | ((~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | (~((~member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))))))) <=> ((~![X: $i] : ((~member(X, A!39)) | (~((~member(tptp_fun_Y_3(X, A!39, F!40), A!39)) | (~apply(F!40, X, tptp_fun_Y_3(X, A!39, F!40))))))) | (~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | (~((~member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))))))),
% 0.23/0.50 inference(rewrite,[status(thm)],[])).
% 0.23/0.50 tff(114,plain,
% 0.23/0.50 ((~![X: $i] : ((~member(X, A!39)) | (~((~member(tptp_fun_Y_3(X, A!39, F!40), A!39)) | (~apply(F!40, X, tptp_fun_Y_3(X, A!39, F!40))))))) | ((~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | (~((~member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))))))),
% 0.23/0.50 inference(quant_inst,[status(thm)],[])).
% 0.23/0.50 tff(115,plain,
% 0.23/0.50 ((~![X: $i] : ((~member(X, A!39)) | (~((~member(tptp_fun_Y_3(X, A!39, F!40), A!39)) | (~apply(F!40, X, tptp_fun_Y_3(X, A!39, F!40))))))) | (~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | (~((~member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40)))))),
% 0.23/0.50 inference(modus_ponens,[status(thm)],[114, 113])).
% 0.23/0.50 tff(116,plain,
% 0.23/0.50 (~((~member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))))),
% 0.23/0.50 inference(unit_resolution,[status(thm)],[115, 112, 67])).
% 0.23/0.50 tff(117,plain,
% 0.23/0.50 (((~member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40)))) | member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)),
% 0.23/0.50 inference(tautology,[status(thm)],[])).
% 0.23/0.50 tff(118,plain,
% 0.23/0.50 (member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)),
% 0.23/0.50 inference(unit_resolution,[status(thm)],[117, 116])).
% 0.23/0.50 tff(119,plain,
% 0.23/0.50 (^[G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : refl(((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z)))))))) <=> ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z)))))))))),
% 0.23/0.50 inference(bind,[status(th)],[])).
% 0.23/0.50 tff(120,plain,
% 0.23/0.50 (![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z)))))))) <=> ![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))),
% 0.23/0.50 inference(quant_intro,[status(thm)],[119])).
% 0.23/0.50 tff(121,plain,
% 0.23/0.50 (^[G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : rewrite(((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z)))))))) <=> ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z)))))))))),
% 0.23/0.50 inference(bind,[status(th)],[])).
% 0.23/0.50 tff(122,plain,
% 0.23/0.50 (![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z)))))))) <=> ![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))),
% 0.23/0.50 inference(quant_intro,[status(thm)],[121])).
% 0.23/0.50 tff(123,plain,
% 0.23/0.50 (![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z)))))))) <=> ![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))),
% 0.23/0.50 inference(transitivity,[status(thm)],[122, 120])).
% 0.23/0.50 tff(124,plain,
% 0.23/0.50 (^[G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : trans(monotonicity(trans(monotonicity(rewrite((member(X, A) & member(Z, C)) <=> (~((~member(Z, C)) | (~member(X, A))))), ((~(member(X, A) & member(Z, C))) <=> (~(~((~member(Z, C)) | (~member(X, A))))))), rewrite((~(~((~member(Z, C)) | (~member(X, A))))) <=> ((~member(Z, C)) | (~member(X, A)))), ((~(member(X, A) & member(Z, C))) <=> ((~member(Z, C)) | (~member(X, A))))), trans(monotonicity(rewrite(((~apply(compose_function(G, F, A, B, C), X, Z)) | (member(tptp_fun_Y_8(Z, X, B, F, G), B) & apply(F, X, tptp_fun_Y_8(Z, X, B, F, G)) & apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z))) <=> ((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))), rewrite((apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y) & apply(G, Y, Z)))) <=> (apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))), ((((~apply(compose_function(G, F, A, B, C), X, Z)) | (member(tptp_fun_Y_8(Z, X, B, F, G), B) & apply(F, X, tptp_fun_Y_8(Z, X, B, F, G)) & apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z))) & (apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y) & apply(G, Y, Z))))) <=> (((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z))))) & (apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))), rewrite((((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z))))) & (apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))) <=> (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z)))))))), ((((~apply(compose_function(G, F, A, B, C), X, Z)) | (member(tptp_fun_Y_8(Z, X, B, F, G), B) & apply(F, X, tptp_fun_Y_8(Z, X, B, F, G)) & apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z))) & (apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y) & apply(G, Y, Z))))) <=> (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))), (((~(member(X, A) & member(Z, C))) | (((~apply(compose_function(G, F, A, B, C), X, Z)) | (member(tptp_fun_Y_8(Z, X, B, F, G), B) & apply(F, X, tptp_fun_Y_8(Z, X, B, F, G)) & apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z))) & (apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y) & apply(G, Y, Z)))))) <=> (((~member(Z, C)) | (~member(X, A))) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z)))))))))), rewrite((((~member(Z, C)) | (~member(X, A))) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z)))))))) <=> ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))), (((~(member(X, A) & member(Z, C))) | (((~apply(compose_function(G, F, A, B, C), X, Z)) | (member(tptp_fun_Y_8(Z, X, B, F, G), B) & apply(F, X, tptp_fun_Y_8(Z, X, B, F, G)) & apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z))) & (apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y) & apply(G, Y, Z)))))) <=> ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))))),
% 0.23/0.51 inference(bind,[status(th)],[])).
% 0.23/0.51 tff(125,plain,
% 0.23/0.51 (![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~(member(X, A) & member(Z, C))) | (((~apply(compose_function(G, F, A, B, C), X, Z)) | (member(tptp_fun_Y_8(Z, X, B, F, G), B) & apply(F, X, tptp_fun_Y_8(Z, X, B, F, G)) & apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z))) & (apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y) & apply(G, Y, Z)))))) <=> ![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))),
% 0.23/0.51 inference(quant_intro,[status(thm)],[124])).
% 0.23/0.51 tff(126,plain,
% 0.23/0.51 (![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~(member(X, A) & member(Z, C))) | (apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : (member(Y, B) & apply(F, X, Y) & apply(G, Y, Z)))) <=> ![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~(member(X, A) & member(Z, C))) | (apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : (member(Y, B) & apply(F, X, Y) & apply(G, Y, Z))))),
% 0.23/0.51 inference(rewrite,[status(thm)],[])).
% 0.23/0.51 tff(127,plain,
% 0.23/0.51 (^[G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : trans(monotonicity(rewrite((apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : ((member(Y, B) & apply(F, X, Y)) & apply(G, Y, Z))) <=> (apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : (member(Y, B) & apply(F, X, Y) & apply(G, Y, Z)))), (((member(X, A) & member(Z, C)) => (apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : ((member(Y, B) & apply(F, X, Y)) & apply(G, Y, Z)))) <=> ((member(X, A) & member(Z, C)) => (apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : (member(Y, B) & apply(F, X, Y) & apply(G, Y, Z)))))), rewrite(((member(X, A) & member(Z, C)) => (apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : (member(Y, B) & apply(F, X, Y) & apply(G, Y, Z)))) <=> ((~(member(X, A) & member(Z, C))) | (apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : (member(Y, B) & apply(F, X, Y) & apply(G, Y, Z))))), (((member(X, A) & member(Z, C)) => (apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : ((member(Y, B) & apply(F, X, Y)) & apply(G, Y, Z)))) <=> ((~(member(X, A) & member(Z, C))) | (apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : (member(Y, B) & apply(F, X, Y) & apply(G, Y, Z))))))),
% 0.23/0.51 inference(bind,[status(th)],[])).
% 0.23/0.51 tff(128,plain,
% 0.23/0.51 (![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((member(X, A) & member(Z, C)) => (apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : ((member(Y, B) & apply(F, X, Y)) & apply(G, Y, Z)))) <=> ![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~(member(X, A) & member(Z, C))) | (apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : (member(Y, B) & apply(F, X, Y) & apply(G, Y, Z))))),
% 0.23/0.51 inference(quant_intro,[status(thm)],[127])).
% 0.23/0.51 tff(129,axiom,(![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((member(X, A) & member(Z, C)) => (apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : ((member(Y, B) & apply(F, X, Y)) & apply(G, Y, Z))))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+1.ax','compose_function')).
% 0.23/0.51 tff(130,plain,
% 0.23/0.51 (![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~(member(X, A) & member(Z, C))) | (apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : (member(Y, B) & apply(F, X, Y) & apply(G, Y, Z))))),
% 0.23/0.51 inference(modus_ponens,[status(thm)],[129, 128])).
% 0.23/0.51 tff(131,plain,
% 0.23/0.51 (![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~(member(X, A) & member(Z, C))) | (apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : (member(Y, B) & apply(F, X, Y) & apply(G, Y, Z))))),
% 0.23/0.51 inference(modus_ponens,[status(thm)],[130, 126])).
% 0.23/0.51 tff(132,plain,(
% 0.23/0.51 ![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~(member(X, A) & member(Z, C))) | (((~apply(compose_function(G, F, A, B, C), X, Z)) | (member(tptp_fun_Y_8(Z, X, B, F, G), B) & apply(F, X, tptp_fun_Y_8(Z, X, B, F, G)) & apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z))) & (apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y) & apply(G, Y, Z))))))),
% 0.23/0.51 inference(skolemize,[status(sab)],[131])).
% 0.23/0.51 tff(133,plain,
% 0.23/0.51 (![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))),
% 0.23/0.51 inference(modus_ponens,[status(thm)],[132, 125])).
% 0.23/0.51 tff(134,plain,
% 0.23/0.51 (![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))),
% 0.23/0.51 inference(modus_ponens,[status(thm)],[133, 123])).
% 0.23/0.51 tff(135,plain,
% 0.23/0.51 (((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~((~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40)))))) | (~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))))))))))) <=> ((~![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_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~((~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40)))))) | (~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))))))))))),
% 0.23/0.51 inference(rewrite,[status(thm)],[])).
% 0.23/0.51 tff(136,plain,
% 0.23/0.51 (((~member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~((~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40)))))) | (~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40)))))))))) <=> ((~member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~((~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40)))))) | (~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))))))))))),
% 0.23/0.51 inference(rewrite,[status(thm)],[])).
% 0.23/0.51 tff(137,plain,
% 0.23/0.51 ((~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40)))))))) <=> (~((~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40)))))) | (~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40)))))))))),
% 0.23/0.51 inference(rewrite,[status(thm)],[])).
% 0.23/0.51 tff(138,plain,
% 0.23/0.51 (((~member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))))))))) <=> ((~member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~((~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40)))))) | (~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))))))))))),
% 0.23/0.52 inference(monotonicity,[status(thm)],[137])).
% 0.23/0.52 tff(139,plain,
% 0.23/0.52 (((~member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))))))))) <=> ((~member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~((~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40)))))) | (~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))))))))))),
% 0.23/0.52 inference(transitivity,[status(thm)],[138, 136])).
% 0.23/0.52 tff(140,plain,
% 0.23/0.52 (((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40)))))))))) <=> ((~![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_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~((~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40)))))) | (~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40)))))))))))),
% 0.23/0.52 inference(monotonicity,[status(thm)],[139])).
% 0.23/0.52 tff(141,plain,
% 0.23/0.52 (((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40)))))))))) <=> ((~![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_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~((~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40)))))) | (~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))))))))))),
% 0.23/0.52 inference(transitivity,[status(thm)],[140, 135])).
% 0.23/0.52 tff(142,plain,
% 0.23/0.52 ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40)))))))))),
% 0.23/0.52 inference(quant_inst,[status(thm)],[])).
% 0.23/0.52 tff(143,plain,
% 0.23/0.52 ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | (~member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~((~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40)))))) | (~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40)))))))))),
% 0.23/0.52 inference(modus_ponens,[status(thm)],[142, 141])).
% 0.23/0.52 tff(144,plain,
% 0.23/0.52 (~((~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40)))))) | (~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))))))))),
% 0.23/0.53 inference(unit_resolution,[status(thm)],[143, 134, 118])).
% 0.23/0.53 tff(145,plain,
% 0.23/0.53 (((~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40)))))) | (~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40)))))))) | ((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))))))),
% 0.23/0.53 inference(tautology,[status(thm)],[])).
% 0.23/0.53 tff(146,plain,
% 0.23/0.53 ((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40)))))),
% 0.23/0.53 inference(unit_resolution,[status(thm)],[145, 144])).
% 0.23/0.53 tff(147,assumption,(~identity(compose_function(F!40, F!40, A!39, A!39, A!39), A!39)), introduced(assumption)).
% 0.23/0.53 tff(148,plain,
% 0.23/0.53 (^[F: $i, A: $i] : refl((~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F)))))))) <=> (~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F)))))))))),
% 0.23/0.53 inference(bind,[status(th)],[])).
% 0.23/0.53 tff(149,plain,
% 0.23/0.53 (![F: $i, A: $i] : (~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F)))))))) <=> ![F: $i, A: $i] : (~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F))))))))),
% 0.23/0.53 inference(quant_intro,[status(thm)],[148])).
% 0.23/0.53 tff(150,plain,
% 0.23/0.53 (^[F: $i, A: $i] : rewrite((~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F)))))))) <=> (~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F)))))))))),
% 0.23/0.53 inference(bind,[status(th)],[])).
% 0.23/0.53 tff(151,plain,
% 0.23/0.53 (![F: $i, A: $i] : (~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F)))))))) <=> ![F: $i, A: $i] : (~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F))))))))),
% 0.23/0.53 inference(quant_intro,[status(thm)],[150])).
% 0.23/0.53 tff(152,plain,
% 0.23/0.53 (![F: $i, A: $i] : (~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F)))))))) <=> ![F: $i, A: $i] : (~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F))))))))),
% 0.23/0.53 inference(transitivity,[status(thm)],[151, 149])).
% 0.23/0.53 tff(153,plain,
% 0.23/0.53 (^[F: $i, A: $i] : trans(monotonicity(rewrite(((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X))) <=> ((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))), rewrite((identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F))))) <=> (identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F)))))), ((((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X))) & (identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F)))))) <=> (((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X))) & (identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F)))))))), rewrite((((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X))) & (identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F)))))) <=> (~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F))))))))), ((((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X))) & (identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F)))))) <=> (~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F))))))))))),
% 0.23/0.53 inference(bind,[status(th)],[])).
% 0.23/0.53 tff(154,plain,
% 0.23/0.53 (![F: $i, A: $i] : (((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X))) & (identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F)))))) <=> ![F: $i, A: $i] : (~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F))))))))),
% 0.23/0.53 inference(quant_intro,[status(thm)],[153])).
% 0.23/0.53 tff(155,plain,
% 0.23/0.53 (![F: $i, A: $i] : (identity(F, A) <=> ![X: $i] : ((~member(X, A)) | apply(F, X, X))) <=> ![F: $i, A: $i] : (identity(F, A) <=> ![X: $i] : ((~member(X, A)) | apply(F, X, X)))),
% 0.23/0.53 inference(rewrite,[status(thm)],[])).
% 0.23/0.53 tff(156,plain,
% 0.23/0.53 (^[F: $i, A: $i] : rewrite((identity(F, A) <=> ![X: $i] : (member(X, A) => apply(F, X, X))) <=> (identity(F, A) <=> ![X: $i] : ((~member(X, A)) | apply(F, X, X))))),
% 0.23/0.53 inference(bind,[status(th)],[])).
% 0.23/0.53 tff(157,plain,
% 0.23/0.53 (![F: $i, A: $i] : (identity(F, A) <=> ![X: $i] : (member(X, A) => apply(F, X, X))) <=> ![F: $i, A: $i] : (identity(F, A) <=> ![X: $i] : ((~member(X, A)) | apply(F, X, X)))),
% 0.23/0.53 inference(quant_intro,[status(thm)],[156])).
% 0.23/0.53 tff(158,axiom,(![F: $i, A: $i] : (identity(F, A) <=> ![X: $i] : (member(X, A) => apply(F, X, X)))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+1.ax','identity')).
% 0.23/0.53 tff(159,plain,
% 0.23/0.53 (![F: $i, A: $i] : (identity(F, A) <=> ![X: $i] : ((~member(X, A)) | apply(F, X, X)))),
% 0.23/0.53 inference(modus_ponens,[status(thm)],[158, 157])).
% 0.23/0.53 tff(160,plain,
% 0.23/0.53 (![F: $i, A: $i] : (identity(F, A) <=> ![X: $i] : ((~member(X, A)) | apply(F, X, X)))),
% 0.23/0.53 inference(modus_ponens,[status(thm)],[159, 155])).
% 0.23/0.53 tff(161,plain,(
% 0.23/0.53 ![F: $i, A: $i] : (((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X))) & (identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F))))))),
% 0.23/0.53 inference(skolemize,[status(sab)],[160])).
% 0.23/0.53 tff(162,plain,
% 0.23/0.53 (![F: $i, A: $i] : (~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F))))))))),
% 0.23/0.53 inference(modus_ponens,[status(thm)],[161, 154])).
% 0.23/0.53 tff(163,plain,
% 0.23/0.53 (![F: $i, A: $i] : (~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F))))))))),
% 0.23/0.53 inference(modus_ponens,[status(thm)],[162, 152])).
% 0.23/0.53 tff(164,plain,
% 0.23/0.53 ((~![F: $i, A: $i] : (~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F))))))))) | (~((~((~identity(compose_function(F!40, F!40, A!39, A!39, A!39), A!39)) | ![X: $i] : ((~member(X, A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), X, X)))) | (~(identity(compose_function(F!40, F!40, A!39, A!39, A!39), A!39) | (~((~member(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)))))))))),
% 0.23/0.53 inference(quant_inst,[status(thm)],[])).
% 0.23/0.53 tff(165,plain,
% 0.23/0.53 (~((~((~identity(compose_function(F!40, F!40, A!39, A!39, A!39), A!39)) | ![X: $i] : ((~member(X, A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), X, X)))) | (~(identity(compose_function(F!40, F!40, A!39, A!39, A!39), A!39) | (~((~member(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39))))))))),
% 0.23/0.53 inference(unit_resolution,[status(thm)],[164, 163])).
% 0.23/0.53 tff(166,plain,
% 0.23/0.53 (((~((~identity(compose_function(F!40, F!40, A!39, A!39, A!39), A!39)) | ![X: $i] : ((~member(X, A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), X, X)))) | (~(identity(compose_function(F!40, F!40, A!39, A!39, A!39), A!39) | (~((~member(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)))))))) | (identity(compose_function(F!40, F!40, A!39, A!39, A!39), A!39) | (~((~member(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39))))))),
% 0.23/0.53 inference(tautology,[status(thm)],[])).
% 0.23/0.53 tff(167,plain,
% 0.23/0.53 (identity(compose_function(F!40, F!40, A!39, A!39, A!39), A!39) | (~((~member(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)))))),
% 0.23/0.53 inference(unit_resolution,[status(thm)],[166, 165])).
% 0.23/0.53 tff(168,plain,
% 0.23/0.53 ((~(identity(compose_function(F!40, F!40, A!39, A!39, A!39), A!39) | (~((~member(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39))))))) | identity(compose_function(F!40, F!40, A!39, A!39, A!39), A!39) | (~((~member(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)))))),
% 0.23/0.53 inference(tautology,[status(thm)],[])).
% 0.23/0.53 tff(169,plain,
% 0.23/0.53 (identity(compose_function(F!40, F!40, A!39, A!39, A!39), A!39) | (~((~member(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)))))),
% 0.23/0.53 inference(unit_resolution,[status(thm)],[168, 167])).
% 0.23/0.53 tff(170,plain,
% 0.23/0.53 (~((~member(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39))))),
% 0.23/0.53 inference(unit_resolution,[status(thm)],[169, 147])).
% 0.23/0.53 tff(171,plain,
% 0.23/0.53 (((~member(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)))) | member(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39)),
% 0.23/0.53 inference(tautology,[status(thm)],[])).
% 0.23/0.53 tff(172,plain,
% 0.23/0.53 (member(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39)),
% 0.23/0.53 inference(unit_resolution,[status(thm)],[171, 170])).
% 0.23/0.53 tff(173,plain,
% 0.23/0.53 (((~![X: $i] : ((~member(X, A!39)) | (~((~member(tptp_fun_Y_3(X, A!39, F!40), A!39)) | (~apply(F!40, X, tptp_fun_Y_3(X, A!39, F!40))))))) | ((~member(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39)) | (~((~member(tptp_fun_Y_3(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_Y_3(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40))))))) <=> ((~![X: $i] : ((~member(X, A!39)) | (~((~member(tptp_fun_Y_3(X, A!39, F!40), A!39)) | (~apply(F!40, X, tptp_fun_Y_3(X, A!39, F!40))))))) | (~member(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39)) | (~((~member(tptp_fun_Y_3(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_Y_3(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40))))))),
% 0.23/0.54 inference(rewrite,[status(thm)],[])).
% 0.23/0.54 tff(174,plain,
% 0.23/0.54 ((~![X: $i] : ((~member(X, A!39)) | (~((~member(tptp_fun_Y_3(X, A!39, F!40), A!39)) | (~apply(F!40, X, tptp_fun_Y_3(X, A!39, F!40))))))) | ((~member(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39)) | (~((~member(tptp_fun_Y_3(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_Y_3(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40))))))),
% 0.23/0.54 inference(quant_inst,[status(thm)],[])).
% 0.23/0.54 tff(175,plain,
% 0.23/0.54 ((~![X: $i] : ((~member(X, A!39)) | (~((~member(tptp_fun_Y_3(X, A!39, F!40), A!39)) | (~apply(F!40, X, tptp_fun_Y_3(X, A!39, F!40))))))) | (~member(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39)) | (~((~member(tptp_fun_Y_3(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_Y_3(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40)))))),
% 0.23/0.54 inference(modus_ponens,[status(thm)],[174, 173])).
% 0.23/0.54 tff(176,plain,
% 0.23/0.54 (~((~member(tptp_fun_Y_3(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_Y_3(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40))))),
% 0.23/0.54 inference(unit_resolution,[status(thm)],[175, 112, 172])).
% 0.23/0.54 tff(177,plain,
% 0.23/0.54 (((~member(tptp_fun_Y_3(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_Y_3(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40)))) | apply(F!40, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_Y_3(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40))),
% 0.23/0.54 inference(tautology,[status(thm)],[])).
% 0.23/0.54 tff(178,plain,
% 0.23/0.54 (apply(F!40, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_Y_3(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40))),
% 0.23/0.54 inference(unit_resolution,[status(thm)],[177, 176])).
% 0.23/0.54 tff(179,plain,
% 0.23/0.54 (((~member(tptp_fun_Y_3(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_Y_3(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40)))) | member(tptp_fun_Y_3(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40), A!39)),
% 0.23/0.54 inference(tautology,[status(thm)],[])).
% 0.23/0.54 tff(180,plain,
% 0.23/0.54 (member(tptp_fun_Y_3(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40), A!39)),
% 0.23/0.54 inference(unit_resolution,[status(thm)],[179, 176])).
% 0.23/0.54 tff(181,plain,
% 0.23/0.54 (((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39)) | (~((~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39))) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), Y)) | (~apply(F!40, Y, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39))))))) | (~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_Y_8(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40, F!40), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)))))))))))) <=> ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | (~member(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39)) | (~((~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39))) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), Y)) | (~apply(F!40, Y, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39))))))) | (~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_Y_8(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40, F!40), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)))))))))))),
% 0.23/0.54 inference(rewrite,[status(thm)],[])).
% 0.23/0.54 tff(182,plain,
% 0.23/0.54 (((~member(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39)) | (~member(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39)) | (~((~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39))) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), Y)) | (~apply(F!40, Y, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39))))))) | (~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_Y_8(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40, F!40), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39))))))))))) <=> ((~member(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39)) | (~((~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39))) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), Y)) | (~apply(F!40, Y, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39))))))) | (~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_Y_8(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40, F!40), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)))))))))))),
% 0.39/0.54 inference(rewrite,[status(thm)],[])).
% 0.39/0.54 tff(183,plain,
% 0.39/0.54 ((~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_Y_8(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40, F!40), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39))) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), Y)) | (~apply(F!40, Y, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39))))))))) <=> (~((~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39))) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), Y)) | (~apply(F!40, Y, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39))))))) | (~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_Y_8(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40, F!40), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39))))))))))),
% 0.39/0.54 inference(rewrite,[status(thm)],[])).
% 0.39/0.54 tff(184,plain,
% 0.39/0.54 (((~member(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39)) | (~member(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_Y_8(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40, F!40), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39))) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), Y)) | (~apply(F!40, Y, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)))))))))) <=> ((~member(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39)) | (~member(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39)) | (~((~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39))) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), Y)) | (~apply(F!40, Y, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39))))))) | (~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_Y_8(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40, F!40), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)))))))))))),
% 0.39/0.54 inference(monotonicity,[status(thm)],[183])).
% 0.39/0.54 tff(185,plain,
% 0.39/0.54 (((~member(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39)) | (~member(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_Y_8(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40, F!40), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39))) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), Y)) | (~apply(F!40, Y, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)))))))))) <=> ((~member(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39)) | (~((~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39))) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), Y)) | (~apply(F!40, Y, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39))))))) | (~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_Y_8(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40, F!40), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)))))))))))),
% 0.39/0.55 inference(transitivity,[status(thm)],[184, 182])).
% 0.39/0.55 tff(186,plain,
% 0.39/0.55 (((~![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_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39)) | (~member(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_Y_8(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40, F!40), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39))) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), Y)) | (~apply(F!40, Y, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39))))))))))) <=> ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39)) | (~((~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39))) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), Y)) | (~apply(F!40, Y, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39))))))) | (~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_Y_8(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40, F!40), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39))))))))))))),
% 0.39/0.55 inference(monotonicity,[status(thm)],[185])).
% 0.39/0.55 tff(187,plain,
% 0.39/0.55 (((~![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_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39)) | (~member(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_Y_8(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40, F!40), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39))) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), Y)) | (~apply(F!40, Y, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39))))))))))) <=> ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | (~member(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39)) | (~((~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39))) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), Y)) | (~apply(F!40, Y, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39))))))) | (~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_Y_8(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40, F!40), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)))))))))))),
% 0.39/0.55 inference(transitivity,[status(thm)],[186, 181])).
% 0.39/0.55 tff(188,plain,
% 0.39/0.55 ((~![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_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39)) | (~member(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_Y_8(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40, F!40), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39))) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), Y)) | (~apply(F!40, Y, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39))))))))))),
% 0.39/0.55 inference(quant_inst,[status(thm)],[])).
% 0.39/0.55 tff(189,plain,
% 0.39/0.55 ((~![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_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39)) | (~((~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39))) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), Y)) | (~apply(F!40, Y, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39))))))) | (~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_Y_8(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40, F!40), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39))))))))))),
% 0.39/0.56 inference(modus_ponens,[status(thm)],[188, 187])).
% 0.39/0.56 tff(190,plain,
% 0.39/0.56 (~((~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39))) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), Y)) | (~apply(F!40, Y, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39))))))) | (~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_Y_8(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40, F!40), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)))))))))),
% 0.39/0.56 inference(unit_resolution,[status(thm)],[189, 134, 172])).
% 0.39/0.56 tff(191,plain,
% 0.39/0.56 (((~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39))) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), Y)) | (~apply(F!40, Y, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39))))))) | (~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_Y_8(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40, F!40), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39))))))))) | (apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39))) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), Y)) | (~apply(F!40, Y, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39))))))),
% 0.39/0.56 inference(tautology,[status(thm)],[])).
% 0.39/0.56 tff(192,plain,
% 0.39/0.56 (apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39))) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), Y)) | (~apply(F!40, Y, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)))))),
% 0.39/0.56 inference(unit_resolution,[status(thm)],[191, 190])).
% 0.39/0.56 tff(193,plain,
% 0.39/0.56 (((~member(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)))) | (~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39))))),
% 0.39/0.56 inference(tautology,[status(thm)],[])).
% 0.39/0.56 tff(194,plain,
% 0.39/0.56 (~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)))),
% 0.39/0.56 inference(unit_resolution,[status(thm)],[193, 170])).
% 0.39/0.56 tff(195,plain,
% 0.39/0.56 ((~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39))) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), Y)) | (~apply(F!40, Y, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39))))))) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39))) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), Y)) | (~apply(F!40, Y, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)))))),
% 0.39/0.56 inference(tautology,[status(thm)],[])).
% 0.39/0.56 tff(196,plain,
% 0.39/0.56 ((~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39))) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), Y)) | (~apply(F!40, Y, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39))))))) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), Y)) | (~apply(F!40, Y, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)))))),
% 0.39/0.56 inference(unit_resolution,[status(thm)],[195, 194])).
% 0.39/0.56 tff(197,plain,
% 0.39/0.56 (![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), Y)) | (~apply(F!40, Y, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)))))),
% 0.39/0.56 inference(unit_resolution,[status(thm)],[196, 192])).
% 0.39/0.56 tff(198,plain,
% 0.39/0.56 (((~![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), Y)) | (~apply(F!40, Y, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)))))) | ((~member(tptp_fun_Y_3(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_Y_3(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40))) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)))))) <=> ((~![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), Y)) | (~apply(F!40, Y, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)))))) | (~member(tptp_fun_Y_3(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_Y_3(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40))) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)))))),
% 0.41/0.56 inference(rewrite,[status(thm)],[])).
% 0.41/0.56 tff(199,plain,
% 0.41/0.56 ((~![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), Y)) | (~apply(F!40, Y, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)))))) | ((~member(tptp_fun_Y_3(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_Y_3(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40))) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)))))),
% 0.41/0.56 inference(quant_inst,[status(thm)],[])).
% 0.41/0.56 tff(200,plain,
% 0.41/0.56 ((~![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), Y)) | (~apply(F!40, Y, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)))))) | (~member(tptp_fun_Y_3(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_Y_3(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40))) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39))))),
% 0.41/0.56 inference(modus_ponens,[status(thm)],[199, 198])).
% 0.41/0.56 tff(201,plain,
% 0.41/0.56 (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)))),
% 0.41/0.56 inference(unit_resolution,[status(thm)],[200, 197, 180, 178])).
% 0.41/0.56 tff(202,plain,
% 0.41/0.56 ((~(apply(F!40, tptp_fun_Y_3(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39))) <=> apply(F!40, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_Y_3(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40)))) | apply(F!40, tptp_fun_Y_3(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39))) | (~apply(F!40, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_Y_3(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40)))),
% 0.41/0.56 inference(tautology,[status(thm)],[])).
% 0.41/0.56 tff(203,plain,
% 0.41/0.56 (~(apply(F!40, tptp_fun_Y_3(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39))) <=> apply(F!40, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_Y_3(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40)))),
% 0.41/0.56 inference(unit_resolution,[status(thm)],[202, 178, 201])).
% 0.41/0.56 tff(204,plain,
% 0.41/0.56 (~((~((~inverse_predicate(F!40, F!40, A!39, A!39)) | ![X: $i, Y: $i] : ((~member(Y, A!39)) | (~member(X, A!39)) | (apply(F!40, X, Y) <=> apply(F!40, Y, X))))) | (~(inverse_predicate(F!40, F!40, A!39, A!39) | (~((~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | (apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40)) <=> apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))) | (~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)))))))),
% 0.41/0.56 inference(unit_resolution,[status(thm)],[60, 54])).
% 0.41/0.56 tff(205,plain,
% 0.41/0.56 (((~((~inverse_predicate(F!40, F!40, A!39, A!39)) | ![X: $i, Y: $i] : ((~member(Y, A!39)) | (~member(X, A!39)) | (apply(F!40, X, Y) <=> apply(F!40, Y, X))))) | (~(inverse_predicate(F!40, F!40, A!39, A!39) | (~((~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | (apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40)) <=> apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))) | (~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39))))))) | ((~inverse_predicate(F!40, F!40, A!39, A!39)) | ![X: $i, Y: $i] : ((~member(Y, A!39)) | (~member(X, A!39)) | (apply(F!40, X, Y) <=> apply(F!40, Y, X))))),
% 0.41/0.56 inference(tautology,[status(thm)],[])).
% 0.41/0.56 tff(206,plain,
% 0.41/0.56 ((~inverse_predicate(F!40, F!40, A!39, A!39)) | ![X: $i, Y: $i] : ((~member(Y, A!39)) | (~member(X, A!39)) | (apply(F!40, X, Y) <=> apply(F!40, Y, X)))),
% 0.41/0.56 inference(unit_resolution,[status(thm)],[205, 204])).
% 0.41/0.56 tff(207,plain,
% 0.41/0.56 ((~(~(((~one_to_one(F!40, A!39, A!39)) | (~inverse_predicate(F!40, F!40, A!39, A!39))) <=> identity(compose_function(F!40, F!40, A!39, A!39, A!39), A!39)))) <=> (((~one_to_one(F!40, A!39, A!39)) | (~inverse_predicate(F!40, F!40, A!39, A!39))) <=> identity(compose_function(F!40, F!40, A!39, A!39, A!39), A!39))),
% 0.41/0.56 inference(rewrite,[status(thm)],[])).
% 0.41/0.56 tff(208,plain,
% 0.41/0.56 ((~(((~one_to_one(F!40, A!39, A!39)) | (~inverse_predicate(F!40, F!40, A!39, A!39))) <=> identity(compose_function(F!40, F!40, A!39, A!39, A!39), A!39))) <=> (~(((~one_to_one(F!40, A!39, A!39)) | (~inverse_predicate(F!40, F!40, A!39, A!39))) <=> identity(compose_function(F!40, F!40, A!39, A!39, A!39), A!39)))),
% 0.41/0.56 inference(rewrite,[status(thm)],[])).
% 0.41/0.56 tff(209,plain,
% 0.41/0.56 (((~((~one_to_one(F!40, A!39, A!39)) | (~inverse_predicate(F!40, F!40, A!39, A!39)))) <=> identity(compose_function(F!40, F!40, A!39, A!39, A!39), A!39)) <=> (~(((~one_to_one(F!40, A!39, A!39)) | (~inverse_predicate(F!40, F!40, A!39, A!39))) <=> identity(compose_function(F!40, F!40, A!39, A!39, A!39), A!39)))),
% 0.41/0.56 inference(rewrite,[status(thm)],[])).
% 0.41/0.56 tff(210,plain,
% 0.41/0.56 ((one_to_one(F!40, A!39, A!39) & inverse_predicate(F!40, F!40, A!39, A!39)) <=> (~((~one_to_one(F!40, A!39, A!39)) | (~inverse_predicate(F!40, F!40, A!39, A!39))))),
% 0.41/0.56 inference(rewrite,[status(thm)],[])).
% 0.41/0.56 tff(211,plain,
% 0.41/0.56 (((one_to_one(F!40, A!39, A!39) & inverse_predicate(F!40, F!40, A!39, A!39)) <=> identity(compose_function(F!40, F!40, A!39, A!39, A!39), A!39)) <=> ((~((~one_to_one(F!40, A!39, A!39)) | (~inverse_predicate(F!40, F!40, A!39, A!39)))) <=> identity(compose_function(F!40, F!40, A!39, A!39, A!39), A!39))),
% 0.41/0.56 inference(monotonicity,[status(thm)],[210])).
% 0.41/0.56 tff(212,plain,
% 0.41/0.56 (((one_to_one(F!40, A!39, A!39) & inverse_predicate(F!40, F!40, A!39, A!39)) <=> identity(compose_function(F!40, F!40, A!39, A!39, A!39), A!39)) <=> (~(((~one_to_one(F!40, A!39, A!39)) | (~inverse_predicate(F!40, F!40, A!39, A!39))) <=> identity(compose_function(F!40, F!40, A!39, A!39, A!39), A!39)))),
% 0.41/0.56 inference(transitivity,[status(thm)],[211, 209])).
% 0.41/0.56 tff(213,plain,
% 0.41/0.56 (((one_to_one(F!40, A!39, A!39) & inverse_predicate(F!40, F!40, A!39, A!39)) <=> identity(compose_function(F!40, F!40, A!39, A!39, A!39), A!39)) <=> (~(((~one_to_one(F!40, A!39, A!39)) | (~inverse_predicate(F!40, F!40, A!39, A!39))) <=> identity(compose_function(F!40, F!40, A!39, A!39, A!39), A!39)))),
% 0.41/0.57 inference(transitivity,[status(thm)],[212, 208])).
% 0.41/0.57 tff(214,plain,
% 0.41/0.57 ((~((one_to_one(F!40, A!39, A!39) & inverse_predicate(F!40, F!40, A!39, A!39)) <=> identity(compose_function(F!40, F!40, A!39, A!39, A!39), A!39))) <=> (~(~(((~one_to_one(F!40, A!39, A!39)) | (~inverse_predicate(F!40, F!40, A!39, A!39))) <=> identity(compose_function(F!40, F!40, A!39, A!39, A!39), A!39))))),
% 0.41/0.57 inference(monotonicity,[status(thm)],[213])).
% 0.41/0.57 tff(215,plain,
% 0.41/0.57 ((~((one_to_one(F!40, A!39, A!39) & inverse_predicate(F!40, F!40, A!39, A!39)) <=> identity(compose_function(F!40, F!40, A!39, A!39, A!39), A!39))) <=> (((~one_to_one(F!40, A!39, A!39)) | (~inverse_predicate(F!40, F!40, A!39, A!39))) <=> identity(compose_function(F!40, F!40, A!39, A!39, A!39), A!39))),
% 0.41/0.57 inference(transitivity,[status(thm)],[214, 207])).
% 0.41/0.57 tff(216,plain,
% 0.41/0.57 (~((one_to_one(F!40, A!39, A!39) & inverse_predicate(F!40, F!40, A!39, A!39)) <=> identity(compose_function(F!40, F!40, A!39, A!39, A!39), A!39))),
% 0.41/0.57 inference(or_elim,[status(thm)],[106])).
% 0.41/0.57 tff(217,plain,
% 0.41/0.57 (((~one_to_one(F!40, A!39, A!39)) | (~inverse_predicate(F!40, F!40, A!39, A!39))) <=> identity(compose_function(F!40, F!40, A!39, A!39, A!39), A!39)),
% 0.41/0.57 inference(modus_ponens,[status(thm)],[216, 215])).
% 0.41/0.57 tff(218,plain,
% 0.41/0.57 ((~((~one_to_one(F!40, A!39, A!39)) | (~inverse_predicate(F!40, F!40, A!39, A!39)))) | identity(compose_function(F!40, F!40, A!39, A!39, A!39), A!39) | (~(((~one_to_one(F!40, A!39, A!39)) | (~inverse_predicate(F!40, F!40, A!39, A!39))) <=> identity(compose_function(F!40, F!40, A!39, A!39, A!39), A!39)))),
% 0.41/0.57 inference(tautology,[status(thm)],[])).
% 0.41/0.57 tff(219,plain,
% 0.41/0.57 ((~((~one_to_one(F!40, A!39, A!39)) | (~inverse_predicate(F!40, F!40, A!39, A!39)))) | identity(compose_function(F!40, F!40, A!39, A!39, A!39), A!39)),
% 0.41/0.57 inference(unit_resolution,[status(thm)],[218, 217])).
% 0.41/0.57 tff(220,plain,
% 0.41/0.57 (~((~one_to_one(F!40, A!39, A!39)) | (~inverse_predicate(F!40, F!40, A!39, A!39)))),
% 0.41/0.57 inference(unit_resolution,[status(thm)],[219, 147])).
% 0.41/0.57 tff(221,plain,
% 0.41/0.57 (((~one_to_one(F!40, A!39, A!39)) | (~inverse_predicate(F!40, F!40, A!39, A!39))) | inverse_predicate(F!40, F!40, A!39, A!39)),
% 0.41/0.57 inference(tautology,[status(thm)],[])).
% 0.41/0.57 tff(222,plain,
% 0.41/0.57 (inverse_predicate(F!40, F!40, A!39, A!39)),
% 0.41/0.57 inference(unit_resolution,[status(thm)],[221, 220])).
% 0.41/0.57 tff(223,plain,
% 0.41/0.57 ((~((~inverse_predicate(F!40, F!40, A!39, A!39)) | ![X: $i, Y: $i] : ((~member(Y, A!39)) | (~member(X, A!39)) | (apply(F!40, X, Y) <=> apply(F!40, Y, X))))) | (~inverse_predicate(F!40, F!40, A!39, A!39)) | ![X: $i, Y: $i] : ((~member(Y, A!39)) | (~member(X, A!39)) | (apply(F!40, X, Y) <=> apply(F!40, Y, X)))),
% 0.41/0.57 inference(tautology,[status(thm)],[])).
% 0.41/0.57 tff(224,plain,
% 0.41/0.57 ((~((~inverse_predicate(F!40, F!40, A!39, A!39)) | ![X: $i, Y: $i] : ((~member(Y, A!39)) | (~member(X, A!39)) | (apply(F!40, X, Y) <=> apply(F!40, Y, X))))) | ![X: $i, Y: $i] : ((~member(Y, A!39)) | (~member(X, A!39)) | (apply(F!40, X, Y) <=> apply(F!40, Y, X)))),
% 0.41/0.57 inference(unit_resolution,[status(thm)],[223, 222])).
% 0.41/0.57 tff(225,plain,
% 0.41/0.57 (![X: $i, Y: $i] : ((~member(Y, A!39)) | (~member(X, A!39)) | (apply(F!40, X, Y) <=> apply(F!40, Y, X)))),
% 0.41/0.57 inference(unit_resolution,[status(thm)],[224, 206])).
% 0.41/0.57 tff(226,plain,
% 0.41/0.57 (((~![X: $i, Y: $i] : ((~member(Y, A!39)) | (~member(X, A!39)) | (apply(F!40, X, Y) <=> apply(F!40, Y, X)))) | ((~member(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40), A!39)) | (apply(F!40, tptp_fun_Y_3(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39))) <=> apply(F!40, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_Y_3(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40))))) <=> ((~![X: $i, Y: $i] : ((~member(Y, A!39)) | (~member(X, A!39)) | (apply(F!40, X, Y) <=> apply(F!40, Y, X)))) | (~member(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40), A!39)) | (apply(F!40, tptp_fun_Y_3(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39))) <=> apply(F!40, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_Y_3(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40))))),
% 0.41/0.57 inference(rewrite,[status(thm)],[])).
% 0.41/0.57 tff(227,plain,
% 0.41/0.57 ((~![X: $i, Y: $i] : ((~member(Y, A!39)) | (~member(X, A!39)) | (apply(F!40, X, Y) <=> apply(F!40, Y, X)))) | ((~member(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40), A!39)) | (apply(F!40, tptp_fun_Y_3(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39))) <=> apply(F!40, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_Y_3(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40))))),
% 0.41/0.57 inference(quant_inst,[status(thm)],[])).
% 0.41/0.57 tff(228,plain,
% 0.41/0.57 ((~![X: $i, Y: $i] : ((~member(Y, A!39)) | (~member(X, A!39)) | (apply(F!40, X, Y) <=> apply(F!40, Y, X)))) | (~member(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40), A!39)) | (apply(F!40, tptp_fun_Y_3(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39))) <=> apply(F!40, tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_Y_3(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39, F!40)))),
% 0.41/0.57 inference(modus_ponens,[status(thm)],[227, 226])).
% 0.41/0.57 tff(229,plain,
% 0.41/0.57 ($false),
% 0.41/0.57 inference(unit_resolution,[status(thm)],[228, 172, 225, 180, 203])).
% 0.41/0.57 tff(230,plain,(identity(compose_function(F!40, F!40, A!39, A!39, A!39), A!39)), inference(lemma,lemma(discharge,[]))).
% 0.41/0.57 tff(231,plain,
% 0.41/0.57 (((~((~identity(compose_function(F!40, F!40, A!39, A!39, A!39), A!39)) | ![X: $i] : ((~member(X, A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), X, X)))) | (~(identity(compose_function(F!40, F!40, A!39, A!39, A!39), A!39) | (~((~member(tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)), tptp_fun_X_15(A!39, compose_function(F!40, F!40, A!39, A!39, A!39)))))))) | ((~identity(compose_function(F!40, F!40, A!39, A!39, A!39), A!39)) | ![X: $i] : ((~member(X, A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), X, X)))),
% 0.41/0.57 inference(tautology,[status(thm)],[])).
% 0.41/0.57 tff(232,plain,
% 0.41/0.57 ((~identity(compose_function(F!40, F!40, A!39, A!39, A!39), A!39)) | ![X: $i] : ((~member(X, A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), X, X))),
% 0.41/0.57 inference(unit_resolution,[status(thm)],[231, 165])).
% 0.41/0.57 tff(233,plain,
% 0.41/0.57 ((~((~identity(compose_function(F!40, F!40, A!39, A!39, A!39), A!39)) | ![X: $i] : ((~member(X, A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), X, X)))) | (~identity(compose_function(F!40, F!40, A!39, A!39, A!39), A!39)) | ![X: $i] : ((~member(X, A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), X, X))),
% 0.41/0.57 inference(tautology,[status(thm)],[])).
% 0.41/0.57 tff(234,plain,
% 0.41/0.57 ((~identity(compose_function(F!40, F!40, A!39, A!39, A!39), A!39)) | ![X: $i] : ((~member(X, A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), X, X))),
% 0.41/0.57 inference(unit_resolution,[status(thm)],[233, 232])).
% 0.41/0.57 tff(235,plain,
% 0.41/0.57 (![X: $i] : ((~member(X, A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), X, X))),
% 0.41/0.57 inference(unit_resolution,[status(thm)],[234, 230])).
% 0.41/0.57 tff(236,plain,
% 0.41/0.57 (((~![X: $i] : ((~member(X, A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), X, X))) | ((~member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40)))) <=> ((~![X: $i] : ((~member(X, A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), X, X))) | (~member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40)))),
% 0.41/0.57 inference(rewrite,[status(thm)],[])).
% 0.41/0.57 tff(237,plain,
% 0.41/0.57 ((~![X: $i] : ((~member(X, A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), X, X))) | ((~member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40)))),
% 0.41/0.57 inference(quant_inst,[status(thm)],[])).
% 0.41/0.57 tff(238,plain,
% 0.41/0.57 ((~![X: $i] : ((~member(X, A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), X, X))) | (~member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))),
% 0.41/0.57 inference(modus_ponens,[status(thm)],[237, 236])).
% 0.41/0.57 tff(239,plain,
% 0.41/0.57 (apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))),
% 0.41/0.57 inference(unit_resolution,[status(thm)],[238, 235, 118])).
% 0.41/0.57 tff(240,plain,
% 0.41/0.57 ((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))))))) | (~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40)))))),
% 0.41/0.57 inference(tautology,[status(thm)],[])).
% 0.41/0.57 tff(241,plain,
% 0.41/0.57 ((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))))))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40)))))),
% 0.41/0.57 inference(unit_resolution,[status(thm)],[240, 239])).
% 0.41/0.57 tff(242,plain,
% 0.41/0.57 (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))))),
% 0.41/0.57 inference(unit_resolution,[status(thm)],[241, 146])).
% 0.41/0.57 tff(243,plain,
% 0.41/0.57 (((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40)))) | apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))),
% 0.41/0.57 inference(tautology,[status(thm)],[])).
% 0.41/0.57 tff(244,plain,
% 0.41/0.57 (apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))),
% 0.41/0.57 inference(unit_resolution,[status(thm)],[243, 242])).
% 0.41/0.57 tff(245,plain,
% 0.41/0.57 (((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40)))) | member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)),
% 0.41/0.58 inference(tautology,[status(thm)],[])).
% 0.41/0.58 tff(246,plain,
% 0.41/0.58 (member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)),
% 0.41/0.58 inference(unit_resolution,[status(thm)],[245, 242])).
% 0.41/0.58 tff(247,plain,
% 0.41/0.58 (((~![X: $i] : ((~member(X, A!39)) | (~((~member(tptp_fun_Y_3(X, A!39, F!40), A!39)) | (~apply(F!40, X, tptp_fun_Y_3(X, A!39, F!40))))))) | ((~member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))))))) <=> ((~![X: $i] : ((~member(X, A!39)) | (~((~member(tptp_fun_Y_3(X, A!39, F!40), A!39)) | (~apply(F!40, X, tptp_fun_Y_3(X, A!39, F!40))))))) | (~member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))))))),
% 0.41/0.58 inference(rewrite,[status(thm)],[])).
% 0.41/0.58 tff(248,plain,
% 0.41/0.58 ((~![X: $i] : ((~member(X, A!39)) | (~((~member(tptp_fun_Y_3(X, A!39, F!40), A!39)) | (~apply(F!40, X, tptp_fun_Y_3(X, A!39, F!40))))))) | ((~member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))))))),
% 0.41/0.58 inference(quant_inst,[status(thm)],[])).
% 0.41/0.58 tff(249,plain,
% 0.41/0.58 ((~![X: $i] : ((~member(X, A!39)) | (~((~member(tptp_fun_Y_3(X, A!39, F!40), A!39)) | (~apply(F!40, X, tptp_fun_Y_3(X, A!39, F!40))))))) | (~member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)))))),
% 0.41/0.58 inference(modus_ponens,[status(thm)],[248, 247])).
% 0.41/0.58 tff(250,plain,
% 0.41/0.58 (~((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))))),
% 0.41/0.58 inference(unit_resolution,[status(thm)],[249, 112, 118])).
% 0.41/0.58 tff(251,plain,
% 0.41/0.58 (((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)))) | apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))),
% 0.41/0.58 inference(tautology,[status(thm)],[])).
% 0.41/0.58 tff(252,plain,
% 0.41/0.58 (apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))),
% 0.41/0.58 inference(unit_resolution,[status(thm)],[251, 250])).
% 0.41/0.58 tff(253,plain,
% 0.41/0.58 (((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)))) | member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)),
% 0.41/0.58 inference(tautology,[status(thm)],[])).
% 0.41/0.58 tff(254,plain,
% 0.41/0.58 (member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)),
% 0.41/0.58 inference(unit_resolution,[status(thm)],[253, 250])).
% 0.41/0.58 tff(255,plain,
% 0.41/0.58 (((~![X: $i] : ((~member(X, A!39)) | (~((~member(tptp_fun_Y_3(X, A!39, F!40), A!39)) | (~apply(F!40, X, tptp_fun_Y_3(X, A!39, F!40))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39))))) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))),
% 0.41/0.58 inference(tautology,[status(thm)],[])).
% 0.41/0.58 tff(256,plain,
% 0.41/0.58 (![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))),
% 0.41/0.58 inference(unit_resolution,[status(thm)],[255, 110])).
% 0.41/0.58 tff(257,plain,
% 0.41/0.58 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | ((~member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | (~member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)))),
% 0.41/0.58 inference(rewrite,[status(thm)],[])).
% 0.41/0.58 tff(258,plain,
% 0.41/0.58 (((tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))) | (~member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39))) <=> ((~member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)))),
% 0.41/0.58 inference(rewrite,[status(thm)],[])).
% 0.41/0.58 tff(259,plain,
% 0.41/0.58 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | ((tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))) | (~member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | ((~member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))))),
% 0.41/0.59 inference(monotonicity,[status(thm)],[258])).
% 0.41/0.59 tff(260,plain,
% 0.41/0.59 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | ((tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))) | (~member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | (~member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)))),
% 0.41/0.59 inference(transitivity,[status(thm)],[259, 257])).
% 0.41/0.59 tff(261,plain,
% 0.41/0.59 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | ((tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))) | (~member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)))),
% 0.41/0.59 inference(quant_inst,[status(thm)],[])).
% 0.41/0.59 tff(262,plain,
% 0.41/0.59 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | (~member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))),
% 0.41/0.59 inference(modus_ponens,[status(thm)],[261, 260])).
% 0.41/0.59 tff(263,plain,
% 0.41/0.59 (tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)),
% 0.41/0.59 inference(unit_resolution,[status(thm)],[262, 256, 118, 254, 252, 246, 244])).
% 0.41/0.59 tff(264,plain,
% 0.41/0.59 (((~![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_21(A!39, A!39, F!40, F!40), A!39)) | (~((~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_21(A!39, A!39, F!40, F!40)))))) | (~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40))))))))))) <=> ((~![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_21(A!39, A!39, F!40, F!40), A!39)) | (~((~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_21(A!39, A!39, F!40, F!40)))))) | (~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40))))))))))),
% 0.41/0.59 inference(rewrite,[status(thm)],[])).
% 0.41/0.59 tff(265,plain,
% 0.41/0.59 (((~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | (~((~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_21(A!39, A!39, F!40, F!40)))))) | (~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40)))))))))) <=> ((~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | (~((~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_21(A!39, A!39, F!40, F!40)))))) | (~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40))))))))))),
% 0.41/0.59 inference(rewrite,[status(thm)],[])).
% 0.41/0.59 tff(266,plain,
% 0.41/0.59 ((~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_21(A!39, A!39, F!40, F!40)))))))) <=> (~((~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_21(A!39, A!39, F!40, F!40)))))) | (~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40)))))))))),
% 0.41/0.59 inference(rewrite,[status(thm)],[])).
% 0.41/0.60 tff(267,plain,
% 0.41/0.60 (((~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_21(A!39, A!39, F!40, F!40))))))))) <=> ((~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | (~((~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_21(A!39, A!39, F!40, F!40)))))) | (~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40))))))))))),
% 0.41/0.60 inference(monotonicity,[status(thm)],[266])).
% 0.41/0.60 tff(268,plain,
% 0.41/0.60 (((~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_21(A!39, A!39, F!40, F!40))))))))) <=> ((~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | (~((~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_21(A!39, A!39, F!40, F!40)))))) | (~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40))))))))))),
% 0.41/0.60 inference(transitivity,[status(thm)],[267, 265])).
% 0.41/0.60 tff(269,plain,
% 0.41/0.60 (((~![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_21(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_21(A!39, A!39, F!40, F!40)))))))))) <=> ((~![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_21(A!39, A!39, F!40, F!40), A!39)) | (~((~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_21(A!39, A!39, F!40, F!40)))))) | (~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40)))))))))))),
% 0.41/0.60 inference(monotonicity,[status(thm)],[268])).
% 0.41/0.60 tff(270,plain,
% 0.41/0.60 (((~![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_21(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_21(A!39, A!39, F!40, F!40)))))))))) <=> ((~![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_21(A!39, A!39, F!40, F!40), A!39)) | (~((~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_21(A!39, A!39, F!40, F!40)))))) | (~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40))))))))))),
% 0.41/0.60 inference(transitivity,[status(thm)],[269, 264])).
% 0.41/0.60 tff(271,plain,
% 0.41/0.60 ((~![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_21(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_21(A!39, A!39, F!40, F!40)))))))))),
% 0.41/0.60 inference(quant_inst,[status(thm)],[])).
% 0.41/0.60 tff(272,plain,
% 0.41/0.60 ((~![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_21(A!39, A!39, F!40, F!40), A!39)) | (~((~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_21(A!39, A!39, F!40, F!40)))))) | (~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40)))))))))),
% 0.41/0.60 inference(modus_ponens,[status(thm)],[271, 270])).
% 0.41/0.60 tff(273,plain,
% 0.41/0.60 (~((~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_21(A!39, A!39, F!40, F!40)))))) | (~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40))))))))),
% 0.41/0.60 inference(unit_resolution,[status(thm)],[272, 134, 67])).
% 0.41/0.60 tff(274,plain,
% 0.41/0.60 (((~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_21(A!39, A!39, F!40, F!40)))))) | (~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40)))))))) | ((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40))))))),
% 0.41/0.60 inference(tautology,[status(thm)],[])).
% 0.41/0.60 tff(275,plain,
% 0.41/0.60 ((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40)))))),
% 0.41/0.60 inference(unit_resolution,[status(thm)],[274, 273])).
% 0.41/0.60 tff(276,plain,
% 0.41/0.60 (((~![X: $i] : ((~member(X, A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), X, X))) | ((~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40)))) <=> ((~![X: $i] : ((~member(X, A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), X, X))) | (~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40)))),
% 0.41/0.61 inference(rewrite,[status(thm)],[])).
% 0.41/0.61 tff(277,plain,
% 0.41/0.61 ((~![X: $i] : ((~member(X, A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), X, X))) | ((~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40)))),
% 0.41/0.61 inference(quant_inst,[status(thm)],[])).
% 0.41/0.61 tff(278,plain,
% 0.41/0.61 ((~![X: $i] : ((~member(X, A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), X, X))) | (~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40))),
% 0.41/0.61 inference(modus_ponens,[status(thm)],[277, 276])).
% 0.41/0.61 tff(279,plain,
% 0.41/0.61 (apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40))),
% 0.41/0.61 inference(unit_resolution,[status(thm)],[278, 235, 67])).
% 0.41/0.61 tff(280,plain,
% 0.41/0.61 ((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40))))))) | (~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40)))))),
% 0.41/0.61 inference(tautology,[status(thm)],[])).
% 0.41/0.61 tff(281,plain,
% 0.41/0.61 ((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40))))))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40)))))),
% 0.41/0.61 inference(unit_resolution,[status(thm)],[280, 279])).
% 0.41/0.61 tff(282,plain,
% 0.41/0.61 (~((~member(tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40))))),
% 0.41/0.61 inference(unit_resolution,[status(thm)],[281, 275])).
% 0.41/0.61 tff(283,plain,
% 0.41/0.61 (((~member(tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40)))) | apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40))),
% 0.41/0.61 inference(tautology,[status(thm)],[])).
% 0.41/0.61 tff(284,plain,
% 0.41/0.61 (apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40))),
% 0.41/0.61 inference(unit_resolution,[status(thm)],[283, 282])).
% 0.41/0.61 tff(285,plain,
% 0.41/0.61 (((~member(tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40)))) | member(tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)),
% 0.41/0.61 inference(tautology,[status(thm)],[])).
% 0.41/0.61 tff(286,plain,
% 0.41/0.61 (member(tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)),
% 0.41/0.61 inference(unit_resolution,[status(thm)],[285, 282])).
% 0.41/0.61 tff(287,plain,
% 0.41/0.61 (((~member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40)))) | apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))),
% 0.41/0.61 inference(tautology,[status(thm)],[])).
% 0.41/0.61 tff(288,plain,
% 0.41/0.61 (apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))),
% 0.41/0.61 inference(unit_resolution,[status(thm)],[287, 116])).
% 0.41/0.61 tff(289,plain,
% 0.41/0.61 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | ((~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (~member(tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)) | (tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40) = tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | (~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (~member(tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)) | (tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40) = tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40)))),
% 0.41/0.61 inference(rewrite,[status(thm)],[])).
% 0.41/0.61 tff(290,plain,
% 0.41/0.61 (((tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40) = tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))) | (~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39))) <=> ((~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (~member(tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)) | (tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40) = tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40)))),
% 0.41/0.61 inference(rewrite,[status(thm)],[])).
% 0.41/0.61 tff(291,plain,
% 0.41/0.61 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | ((tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40) = tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))) | (~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | ((~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (~member(tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)) | (tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40) = tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))))),
% 0.41/0.61 inference(monotonicity,[status(thm)],[290])).
% 0.41/0.61 tff(292,plain,
% 0.41/0.61 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | ((tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40) = tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))) | (~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | (~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (~member(tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)) | (tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40) = tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40)))),
% 0.41/0.62 inference(transitivity,[status(thm)],[291, 289])).
% 0.41/0.62 tff(293,plain,
% 0.41/0.62 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | ((tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40) = tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))) | (~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)))),
% 0.41/0.62 inference(quant_inst,[status(thm)],[])).
% 0.41/0.62 tff(294,plain,
% 0.41/0.62 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | (~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (~member(tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)) | (tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40) = tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))),
% 0.41/0.62 inference(modus_ponens,[status(thm)],[293, 292])).
% 0.41/0.62 tff(295,plain,
% 0.41/0.62 (tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40) = tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40)),
% 0.41/0.62 inference(unit_resolution,[status(thm)],[294, 256, 67, 118, 288, 286, 284])).
% 0.41/0.62 tff(296,plain,
% 0.41/0.62 (tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40) = tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40)),
% 0.41/0.62 inference(symmetry,[status(thm)],[295])).
% 0.41/0.62 tff(297,plain,
% 0.41/0.62 (apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40)) <=> apply(F!40, tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40))),
% 0.41/0.62 inference(monotonicity,[status(thm)],[296])).
% 0.41/0.62 tff(298,plain,
% 0.41/0.62 (apply(F!40, tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40)) <=> apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40))),
% 0.41/0.62 inference(symmetry,[status(thm)],[297])).
% 0.41/0.62 tff(299,plain,
% 0.41/0.62 (((~member(tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40)))) | apply(F!40, tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40))),
% 0.41/0.62 inference(tautology,[status(thm)],[])).
% 0.41/0.62 tff(300,plain,
% 0.41/0.62 (apply(F!40, tptp_fun_Y_8(tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40))),
% 0.41/0.62 inference(unit_resolution,[status(thm)],[299, 282])).
% 0.41/0.62 tff(301,plain,
% 0.41/0.62 (apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40))),
% 0.41/0.62 inference(modus_ponens,[status(thm)],[300, 298])).
% 0.41/0.62 tff(302,plain,
% 0.41/0.62 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | ((~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_21(A!39, A!39, F!40, F!40)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40))))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | (~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_21(A!39, A!39, F!40, F!40)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40))))),
% 0.41/0.62 inference(rewrite,[status(thm)],[])).
% 0.41/0.62 tff(303,plain,
% 0.41/0.62 (((tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_21(A!39, A!39, F!40, F!40)) | (~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40))) | (~member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39))) <=> ((~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_21(A!39, A!39, F!40, F!40)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40))))),
% 0.41/0.62 inference(rewrite,[status(thm)],[])).
% 0.41/0.62 tff(304,plain,
% 0.41/0.62 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | ((tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_21(A!39, A!39, F!40, F!40)) | (~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40))) | (~member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | ((~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_21(A!39, A!39, F!40, F!40)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40)))))),
% 0.41/0.62 inference(monotonicity,[status(thm)],[303])).
% 0.41/0.62 tff(305,plain,
% 0.41/0.62 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | ((tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_21(A!39, A!39, F!40, F!40)) | (~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40))) | (~member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | (~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_21(A!39, A!39, F!40, F!40)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40))))),
% 0.41/0.63 inference(transitivity,[status(thm)],[304, 302])).
% 0.41/0.63 tff(306,plain,
% 0.41/0.63 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | ((tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_21(A!39, A!39, F!40, F!40)) | (~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40))) | (~member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)))),
% 0.41/0.63 inference(quant_inst,[status(thm)],[])).
% 0.41/0.63 tff(307,plain,
% 0.41/0.63 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | (~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_21(A!39, A!39, F!40, F!40)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40)))),
% 0.41/0.63 inference(modus_ponens,[status(thm)],[306, 305])).
% 0.41/0.63 tff(308,plain,
% 0.41/0.63 ((tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_21(A!39, A!39, F!40, F!40)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40)))),
% 0.41/0.63 inference(unit_resolution,[status(thm)],[307, 256, 67, 118, 246, 244])).
% 0.41/0.63 tff(309,plain,
% 0.41/0.63 (tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_21(A!39, A!39, F!40, F!40)),
% 0.41/0.63 inference(unit_resolution,[status(thm)],[308, 301])).
% 0.41/0.63 tff(310,plain,
% 0.41/0.63 (tptp_fun_Y_21(A!39, A!39, F!40, F!40) = tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40)),
% 0.41/0.63 inference(symmetry,[status(thm)],[309])).
% 0.41/0.63 tff(311,plain,
% 0.41/0.63 (tptp_fun_Y_21(A!39, A!39, F!40, F!40) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)),
% 0.41/0.63 inference(transitivity,[status(thm)],[310, 263])).
% 0.41/0.63 tff(312,plain,
% 0.41/0.63 (((~![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_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~((~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)))))) | (~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))))))))))) <=> ((~![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_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~((~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)))))) | (~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))))))))))),
% 0.41/0.63 inference(rewrite,[status(thm)],[])).
% 0.41/0.63 tff(313,plain,
% 0.41/0.63 (((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~((~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)))))) | (~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)))))))))) <=> ((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~((~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)))))) | (~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))))))))))),
% 0.49/0.64 inference(rewrite,[status(thm)],[])).
% 0.49/0.64 tff(314,plain,
% 0.49/0.64 ((~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)))))))) <=> (~((~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)))))) | (~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)))))))))),
% 0.49/0.64 inference(rewrite,[status(thm)],[])).
% 0.49/0.64 tff(315,plain,
% 0.49/0.64 (((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))))))))) <=> ((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~((~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)))))) | (~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))))))))))),
% 0.49/0.64 inference(monotonicity,[status(thm)],[314])).
% 0.49/0.64 tff(316,plain,
% 0.49/0.64 (((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))))))))) <=> ((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~((~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)))))) | (~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))))))))))),
% 0.49/0.64 inference(transitivity,[status(thm)],[315, 313])).
% 0.49/0.64 tff(317,plain,
% 0.49/0.64 (((~![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_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)))))))))) <=> ((~![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_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~((~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)))))) | (~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)))))))))))),
% 0.49/0.64 inference(monotonicity,[status(thm)],[316])).
% 0.49/0.64 tff(318,plain,
% 0.49/0.64 (((~![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_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)))))))))) <=> ((~![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_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~((~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)))))) | (~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))))))))))),
% 0.49/0.65 inference(transitivity,[status(thm)],[317, 312])).
% 0.49/0.65 tff(319,plain,
% 0.49/0.65 ((~![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_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)))))))))),
% 0.49/0.65 inference(quant_inst,[status(thm)],[])).
% 0.49/0.65 tff(320,plain,
% 0.49/0.65 ((~![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_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~((~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)))))) | (~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)))))))))),
% 0.49/0.65 inference(modus_ponens,[status(thm)],[319, 318])).
% 0.49/0.65 tff(321,plain,
% 0.49/0.65 (~((~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)))))) | (~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))))))))),
% 0.49/0.65 inference(unit_resolution,[status(thm)],[320, 134, 254])).
% 0.49/0.65 tff(322,plain,
% 0.49/0.65 (((~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)))))) | (~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)))))))) | ((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))))))),
% 0.49/0.66 inference(tautology,[status(thm)],[])).
% 0.49/0.66 tff(323,plain,
% 0.49/0.66 ((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)))))),
% 0.49/0.66 inference(unit_resolution,[status(thm)],[322, 321])).
% 0.49/0.66 tff(324,plain,
% 0.49/0.66 (((~![X: $i] : ((~member(X, A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), X, X))) | ((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)))) <=> ((~![X: $i] : ((~member(X, A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), X, X))) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)))),
% 0.49/0.66 inference(rewrite,[status(thm)],[])).
% 0.49/0.66 tff(325,plain,
% 0.49/0.66 ((~![X: $i] : ((~member(X, A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), X, X))) | ((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)))),
% 0.49/0.66 inference(quant_inst,[status(thm)],[])).
% 0.49/0.66 tff(326,plain,
% 0.49/0.66 ((~![X: $i] : ((~member(X, A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), X, X))) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))),
% 0.49/0.66 inference(modus_ponens,[status(thm)],[325, 324])).
% 0.49/0.66 tff(327,plain,
% 0.49/0.66 (apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))),
% 0.49/0.66 inference(unit_resolution,[status(thm)],[326, 235, 254])).
% 0.49/0.66 tff(328,plain,
% 0.49/0.66 ((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))))))) | (~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)))))),
% 0.49/0.66 inference(tautology,[status(thm)],[])).
% 0.49/0.66 tff(329,plain,
% 0.49/0.66 ((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))))))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)))))),
% 0.49/0.66 inference(unit_resolution,[status(thm)],[328, 327])).
% 0.49/0.66 tff(330,plain,
% 0.49/0.66 (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))))),
% 0.49/0.66 inference(unit_resolution,[status(thm)],[329, 323])).
% 0.49/0.66 tff(331,plain,
% 0.49/0.66 (((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)))) | apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))),
% 0.49/0.66 inference(tautology,[status(thm)],[])).
% 0.49/0.66 tff(332,plain,
% 0.49/0.66 (apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))),
% 0.49/0.66 inference(unit_resolution,[status(thm)],[331, 330])).
% 0.49/0.66 tff(333,plain,
% 0.49/0.66 (((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)))) | member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)),
% 0.49/0.66 inference(tautology,[status(thm)],[])).
% 0.49/0.66 tff(334,plain,
% 0.49/0.66 (member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)),
% 0.49/0.66 inference(unit_resolution,[status(thm)],[333, 330])).
% 0.49/0.66 tff(335,plain,
% 0.49/0.66 (((~![X: $i] : ((~member(X, A!39)) | (~((~member(tptp_fun_Y_3(X, A!39, F!40), A!39)) | (~apply(F!40, X, tptp_fun_Y_3(X, A!39, F!40))))))) | ((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40))))))) <=> ((~![X: $i] : ((~member(X, A!39)) | (~((~member(tptp_fun_Y_3(X, A!39, F!40), A!39)) | (~apply(F!40, X, tptp_fun_Y_3(X, A!39, F!40))))))) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40))))))),
% 0.49/0.66 inference(rewrite,[status(thm)],[])).
% 0.49/0.66 tff(336,plain,
% 0.49/0.66 ((~![X: $i] : ((~member(X, A!39)) | (~((~member(tptp_fun_Y_3(X, A!39, F!40), A!39)) | (~apply(F!40, X, tptp_fun_Y_3(X, A!39, F!40))))))) | ((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40))))))),
% 0.49/0.66 inference(quant_inst,[status(thm)],[])).
% 0.49/0.66 tff(337,plain,
% 0.49/0.66 ((~![X: $i] : ((~member(X, A!39)) | (~((~member(tptp_fun_Y_3(X, A!39, F!40), A!39)) | (~apply(F!40, X, tptp_fun_Y_3(X, A!39, F!40))))))) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40)))))),
% 0.49/0.66 inference(modus_ponens,[status(thm)],[336, 335])).
% 0.49/0.66 tff(338,plain,
% 0.49/0.66 (~((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40))))),
% 0.49/0.66 inference(unit_resolution,[status(thm)],[337, 112, 254])).
% 0.49/0.66 tff(339,plain,
% 0.49/0.66 (((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40)))) | apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40))),
% 0.49/0.67 inference(tautology,[status(thm)],[])).
% 0.49/0.67 tff(340,plain,
% 0.49/0.67 (apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40))),
% 0.49/0.67 inference(unit_resolution,[status(thm)],[339, 338])).
% 0.49/0.67 tff(341,plain,
% 0.49/0.67 (((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40)))) | member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40), A!39)),
% 0.49/0.67 inference(tautology,[status(thm)],[])).
% 0.49/0.67 tff(342,plain,
% 0.49/0.67 (member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40), A!39)),
% 0.49/0.67 inference(unit_resolution,[status(thm)],[341, 338])).
% 0.49/0.67 tff(343,plain,
% 0.49/0.67 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | ((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40))) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40))) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40)))),
% 0.53/0.67 inference(rewrite,[status(thm)],[])).
% 0.53/0.67 tff(344,plain,
% 0.53/0.67 (((tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40))) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39))) <=> ((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40))) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40)))),
% 0.53/0.67 inference(rewrite,[status(thm)],[])).
% 0.53/0.67 tff(345,plain,
% 0.53/0.67 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | ((tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40))) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | ((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40))) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40))))),
% 0.53/0.67 inference(monotonicity,[status(thm)],[344])).
% 0.53/0.67 tff(346,plain,
% 0.53/0.67 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | ((tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40))) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40))) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40)))),
% 0.53/0.68 inference(transitivity,[status(thm)],[345, 343])).
% 0.53/0.68 tff(347,plain,
% 0.53/0.68 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | ((tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40))) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)))),
% 0.53/0.68 inference(quant_inst,[status(thm)],[])).
% 0.53/0.68 tff(348,plain,
% 0.53/0.68 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40))) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40))),
% 0.53/0.68 inference(modus_ponens,[status(thm)],[347, 346])).
% 0.53/0.68 tff(349,plain,
% 0.53/0.68 (tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40)),
% 0.53/0.68 inference(unit_resolution,[status(thm)],[348, 256, 254, 342, 340, 334, 332])).
% 0.53/0.68 tff(350,plain,
% 0.53/0.68 (tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40) = tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40)),
% 0.53/0.68 inference(symmetry,[status(thm)],[349])).
% 0.53/0.68 tff(351,plain,
% 0.53/0.68 (tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40) = tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40)),
% 0.53/0.68 inference(symmetry,[status(thm)],[263])).
% 0.53/0.68 tff(352,plain,
% 0.53/0.68 (tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40) = tptp_fun_Y_21(A!39, A!39, F!40, F!40)),
% 0.53/0.68 inference(transitivity,[status(thm)],[351, 309])).
% 0.53/0.68 tff(353,plain,
% 0.53/0.68 (tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40) = tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40)),
% 0.53/0.68 inference(monotonicity,[status(thm)],[352])).
% 0.53/0.68 tff(354,plain,
% 0.53/0.68 (tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40)),
% 0.53/0.68 inference(symmetry,[status(thm)],[353])).
% 0.53/0.68 tff(355,plain,
% 0.53/0.68 (((~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | (apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40)) <=> apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))) | (~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39))) | (~(apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40)) <=> apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))))),
% 0.53/0.68 inference(tautology,[status(thm)],[])).
% 0.53/0.68 tff(356,plain,
% 0.53/0.68 (~(apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40)) <=> apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40)))),
% 0.53/0.68 inference(unit_resolution,[status(thm)],[355, 65])).
% 0.53/0.68 tff(357,plain,
% 0.53/0.68 (((~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | (apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40)) <=> apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))) | (~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39))) | member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)),
% 0.53/0.68 inference(tautology,[status(thm)],[])).
% 0.53/0.68 tff(358,plain,
% 0.53/0.68 (member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)),
% 0.53/0.68 inference(unit_resolution,[status(thm)],[357, 65])).
% 0.53/0.68 tff(359,assumption,(member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)), introduced(assumption)).
% 0.53/0.68 tff(360,plain,
% 0.53/0.68 (((~![X: $i] : ((~member(X, A!39)) | (~((~member(tptp_fun_Y_3(X, A!39, F!40), A!39)) | (~apply(F!40, X, tptp_fun_Y_3(X, A!39, F!40))))))) | ((~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~((~member(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))))))) <=> ((~![X: $i] : ((~member(X, A!39)) | (~((~member(tptp_fun_Y_3(X, A!39, F!40), A!39)) | (~apply(F!40, X, tptp_fun_Y_3(X, A!39, F!40))))))) | (~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~((~member(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))))))),
% 0.53/0.68 inference(rewrite,[status(thm)],[])).
% 0.53/0.68 tff(361,plain,
% 0.53/0.68 ((~![X: $i] : ((~member(X, A!39)) | (~((~member(tptp_fun_Y_3(X, A!39, F!40), A!39)) | (~apply(F!40, X, tptp_fun_Y_3(X, A!39, F!40))))))) | ((~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~((~member(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))))))),
% 0.53/0.68 inference(quant_inst,[status(thm)],[])).
% 0.53/0.68 tff(362,plain,
% 0.53/0.68 ((~![X: $i] : ((~member(X, A!39)) | (~((~member(tptp_fun_Y_3(X, A!39, F!40), A!39)) | (~apply(F!40, X, tptp_fun_Y_3(X, A!39, F!40))))))) | (~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~((~member(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40)))))),
% 0.53/0.68 inference(modus_ponens,[status(thm)],[361, 360])).
% 0.53/0.68 tff(363,plain,
% 0.53/0.68 (~((~member(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))))),
% 0.53/0.68 inference(unit_resolution,[status(thm)],[362, 112, 359])).
% 0.53/0.68 tff(364,plain,
% 0.53/0.68 (((~member(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40)))) | member(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)),
% 0.53/0.68 inference(tautology,[status(thm)],[])).
% 0.53/0.68 tff(365,plain,
% 0.53/0.68 (member(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)),
% 0.53/0.68 inference(unit_resolution,[status(thm)],[364, 363])).
% 0.53/0.68 tff(366,plain,
% 0.53/0.68 (((~![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_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~((~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40)))))) | (~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))))))))))) <=> ((~![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_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~((~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40)))))) | (~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))))))))))),
% 0.53/0.68 inference(rewrite,[status(thm)],[])).
% 0.53/0.68 tff(367,plain,
% 0.53/0.68 (((~member(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~((~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40)))))) | (~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40)))))))))) <=> ((~member(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~((~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40)))))) | (~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))))))))))),
% 0.53/0.69 inference(rewrite,[status(thm)],[])).
% 0.53/0.69 tff(368,plain,
% 0.53/0.69 ((~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40)))))))) <=> (~((~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40)))))) | (~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40)))))))))),
% 0.53/0.69 inference(rewrite,[status(thm)],[])).
% 0.53/0.69 tff(369,plain,
% 0.53/0.69 (((~member(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))))))))) <=> ((~member(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~((~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40)))))) | (~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))))))))))),
% 0.53/0.69 inference(monotonicity,[status(thm)],[368])).
% 0.53/0.69 tff(370,plain,
% 0.53/0.69 (((~member(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))))))))) <=> ((~member(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~((~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40)))))) | (~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))))))))))),
% 0.53/0.69 inference(transitivity,[status(thm)],[369, 367])).
% 0.53/0.69 tff(371,plain,
% 0.53/0.69 (((~![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_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40)))))))))) <=> ((~![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_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~((~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40)))))) | (~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40)))))))))))),
% 0.53/0.70 inference(monotonicity,[status(thm)],[370])).
% 0.53/0.70 tff(372,plain,
% 0.53/0.70 (((~![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_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40)))))))))) <=> ((~![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_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~((~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40)))))) | (~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))))))))))),
% 0.53/0.70 inference(transitivity,[status(thm)],[371, 366])).
% 0.53/0.70 tff(373,plain,
% 0.53/0.70 ((~![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_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40)))))))))),
% 0.53/0.70 inference(quant_inst,[status(thm)],[])).
% 0.53/0.70 tff(374,plain,
% 0.53/0.70 ((~![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_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~((~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40)))))) | (~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40)))))))))),
% 0.53/0.70 inference(modus_ponens,[status(thm)],[373, 372])).
% 0.53/0.70 tff(375,plain,
% 0.53/0.70 (~((~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40)))))) | (~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))))))))),
% 0.53/0.70 inference(unit_resolution,[status(thm)],[374, 134, 365])).
% 0.53/0.70 tff(376,plain,
% 0.53/0.70 (((~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40)))))) | (~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40)))))))) | ((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))))))),
% 0.53/0.70 inference(tautology,[status(thm)],[])).
% 0.53/0.70 tff(377,plain,
% 0.53/0.70 ((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40)))))),
% 0.53/0.70 inference(unit_resolution,[status(thm)],[376, 375])).
% 0.53/0.70 tff(378,plain,
% 0.53/0.70 (((~![X: $i] : ((~member(X, A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), X, X))) | ((~member(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40)))) <=> ((~![X: $i] : ((~member(X, A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), X, X))) | (~member(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40)))),
% 0.53/0.70 inference(rewrite,[status(thm)],[])).
% 0.53/0.70 tff(379,plain,
% 0.53/0.70 ((~![X: $i] : ((~member(X, A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), X, X))) | ((~member(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40)))),
% 0.53/0.70 inference(quant_inst,[status(thm)],[])).
% 0.53/0.70 tff(380,plain,
% 0.53/0.70 ((~![X: $i] : ((~member(X, A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), X, X))) | (~member(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))),
% 0.53/0.70 inference(modus_ponens,[status(thm)],[379, 378])).
% 0.53/0.70 tff(381,plain,
% 0.53/0.70 (apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))),
% 0.53/0.70 inference(unit_resolution,[status(thm)],[380, 235, 365])).
% 0.53/0.70 tff(382,plain,
% 0.53/0.70 ((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))))))) | (~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40)))))),
% 0.53/0.70 inference(tautology,[status(thm)],[])).
% 0.53/0.70 tff(383,plain,
% 0.53/0.70 ((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))))))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40)))))),
% 0.53/0.71 inference(unit_resolution,[status(thm)],[382, 381])).
% 0.53/0.71 tff(384,plain,
% 0.53/0.71 (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))))),
% 0.53/0.71 inference(unit_resolution,[status(thm)],[383, 377])).
% 0.53/0.71 tff(385,plain,
% 0.53/0.71 (((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40)))) | apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))),
% 0.53/0.71 inference(tautology,[status(thm)],[])).
% 0.53/0.71 tff(386,plain,
% 0.53/0.71 (apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))),
% 0.53/0.71 inference(unit_resolution,[status(thm)],[385, 384])).
% 0.53/0.71 tff(387,plain,
% 0.53/0.71 (((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40)))) | member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)),
% 0.53/0.71 inference(tautology,[status(thm)],[])).
% 0.53/0.71 tff(388,plain,
% 0.53/0.71 (member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)),
% 0.53/0.71 inference(unit_resolution,[status(thm)],[387, 384])).
% 0.53/0.71 tff(389,plain,
% 0.53/0.71 (((~![X: $i] : ((~member(X, A!39)) | (~((~member(tptp_fun_Y_3(X, A!39, F!40), A!39)) | (~apply(F!40, X, tptp_fun_Y_3(X, A!39, F!40))))))) | ((~member(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))))))) <=> ((~![X: $i] : ((~member(X, A!39)) | (~((~member(tptp_fun_Y_3(X, A!39, F!40), A!39)) | (~apply(F!40, X, tptp_fun_Y_3(X, A!39, F!40))))))) | (~member(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))))))),
% 0.53/0.71 inference(rewrite,[status(thm)],[])).
% 0.53/0.71 tff(390,plain,
% 0.53/0.71 ((~![X: $i] : ((~member(X, A!39)) | (~((~member(tptp_fun_Y_3(X, A!39, F!40), A!39)) | (~apply(F!40, X, tptp_fun_Y_3(X, A!39, F!40))))))) | ((~member(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))))))),
% 0.53/0.71 inference(quant_inst,[status(thm)],[])).
% 0.53/0.71 tff(391,plain,
% 0.53/0.71 ((~![X: $i] : ((~member(X, A!39)) | (~((~member(tptp_fun_Y_3(X, A!39, F!40), A!39)) | (~apply(F!40, X, tptp_fun_Y_3(X, A!39, F!40))))))) | (~member(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)))))),
% 0.53/0.71 inference(modus_ponens,[status(thm)],[390, 389])).
% 0.53/0.71 tff(392,plain,
% 0.53/0.71 (~((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))))),
% 0.53/0.71 inference(unit_resolution,[status(thm)],[391, 112, 365])).
% 0.53/0.71 tff(393,plain,
% 0.53/0.71 (((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)))) | apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))),
% 0.53/0.71 inference(tautology,[status(thm)],[])).
% 0.53/0.71 tff(394,plain,
% 0.53/0.71 (apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))),
% 0.53/0.71 inference(unit_resolution,[status(thm)],[393, 392])).
% 0.53/0.71 tff(395,plain,
% 0.53/0.71 (((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)))) | member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)),
% 0.53/0.71 inference(tautology,[status(thm)],[])).
% 0.53/0.71 tff(396,plain,
% 0.53/0.71 (member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)),
% 0.53/0.71 inference(unit_resolution,[status(thm)],[395, 392])).
% 0.53/0.71 tff(397,plain,
% 0.53/0.71 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | ((~member(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | (~member(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)))),
% 0.53/0.71 inference(rewrite,[status(thm)],[])).
% 0.53/0.71 tff(398,plain,
% 0.53/0.71 (((tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))) | (~member(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39))) <=> ((~member(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)))),
% 0.53/0.72 inference(rewrite,[status(thm)],[])).
% 0.53/0.72 tff(399,plain,
% 0.53/0.72 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | ((tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))) | (~member(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | ((~member(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))))),
% 0.53/0.72 inference(monotonicity,[status(thm)],[398])).
% 0.53/0.72 tff(400,plain,
% 0.53/0.72 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | ((tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))) | (~member(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | (~member(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)))),
% 0.53/0.72 inference(transitivity,[status(thm)],[399, 397])).
% 0.53/0.72 tff(401,plain,
% 0.53/0.72 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | ((tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))) | (~member(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)))),
% 0.53/0.72 inference(quant_inst,[status(thm)],[])).
% 0.53/0.72 tff(402,plain,
% 0.53/0.72 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | (~member(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))),
% 0.53/0.72 inference(modus_ponens,[status(thm)],[401, 400])).
% 0.53/0.72 tff(403,plain,
% 0.53/0.72 (tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)),
% 0.53/0.72 inference(unit_resolution,[status(thm)],[402, 256, 365, 396, 394, 388, 386])).
% 0.53/0.72 tff(404,plain,
% 0.53/0.72 (((~![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_22(A!39, A!39, F!40, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), Y)) | (~apply(F!40, Y, tptp_fun_X_22(A!39, A!39, F!40, F!40)))))))))) <=> ((~![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_22(A!39, A!39, F!40, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), Y)) | (~apply(F!40, Y, tptp_fun_X_22(A!39, A!39, F!40, F!40)))))))))),
% 0.53/0.72 inference(rewrite,[status(thm)],[])).
% 0.53/0.72 tff(405,plain,
% 0.53/0.72 (((~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), Y)) | (~apply(F!40, Y, tptp_fun_X_22(A!39, A!39, F!40, F!40))))))))) <=> ((~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), Y)) | (~apply(F!40, Y, tptp_fun_X_22(A!39, A!39, F!40, F!40)))))))))),
% 0.53/0.73 inference(rewrite,[status(thm)],[])).
% 0.53/0.73 tff(406,plain,
% 0.53/0.73 ((~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), Y)) | (~apply(F!40, Y, tptp_fun_X_22(A!39, A!39, F!40, F!40)))))))) <=> (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), Y)) | (~apply(F!40, Y, tptp_fun_X_22(A!39, A!39, F!40, F!40))))))))),
% 0.53/0.73 inference(rewrite,[status(thm)],[])).
% 0.53/0.73 tff(407,plain,
% 0.53/0.73 (((~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), Y)) | (~apply(F!40, Y, tptp_fun_X_22(A!39, A!39, F!40, F!40))))))))) <=> ((~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), Y)) | (~apply(F!40, Y, tptp_fun_X_22(A!39, A!39, F!40, F!40)))))))))),
% 0.53/0.73 inference(monotonicity,[status(thm)],[406])).
% 0.53/0.73 tff(408,plain,
% 0.53/0.73 (((~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), Y)) | (~apply(F!40, Y, tptp_fun_X_22(A!39, A!39, F!40, F!40))))))))) <=> ((~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), Y)) | (~apply(F!40, Y, tptp_fun_X_22(A!39, A!39, F!40, F!40)))))))))),
% 0.53/0.73 inference(transitivity,[status(thm)],[407, 405])).
% 0.53/0.73 tff(409,plain,
% 0.53/0.73 (((~![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_22(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), Y)) | (~apply(F!40, Y, tptp_fun_X_22(A!39, A!39, F!40, F!40)))))))))) <=> ((~![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_22(A!39, A!39, F!40, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), Y)) | (~apply(F!40, Y, tptp_fun_X_22(A!39, A!39, F!40, F!40))))))))))),
% 0.53/0.73 inference(monotonicity,[status(thm)],[408])).
% 0.53/0.73 tff(410,plain,
% 0.53/0.73 (((~![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_22(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), Y)) | (~apply(F!40, Y, tptp_fun_X_22(A!39, A!39, F!40, F!40)))))))))) <=> ((~![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_22(A!39, A!39, F!40, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), Y)) | (~apply(F!40, Y, tptp_fun_X_22(A!39, A!39, F!40, F!40)))))))))),
% 0.59/0.73 inference(transitivity,[status(thm)],[409, 404])).
% 0.59/0.73 tff(411,plain,
% 0.59/0.73 ((~![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_22(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), Y)) | (~apply(F!40, Y, tptp_fun_X_22(A!39, A!39, F!40, F!40)))))))))),
% 0.59/0.73 inference(quant_inst,[status(thm)],[])).
% 0.59/0.73 tff(412,plain,
% 0.59/0.73 ((~![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_22(A!39, A!39, F!40, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), Y)) | (~apply(F!40, Y, tptp_fun_X_22(A!39, A!39, F!40, F!40))))))))),
% 0.59/0.73 inference(modus_ponens,[status(thm)],[411, 410])).
% 0.59/0.73 tff(413,plain,
% 0.59/0.73 (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), Y)) | (~apply(F!40, Y, tptp_fun_X_22(A!39, A!39, F!40, F!40)))))))),
% 0.59/0.74 inference(unit_resolution,[status(thm)],[412, 134, 359])).
% 0.59/0.74 tff(414,plain,
% 0.59/0.74 (((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), Y)) | (~apply(F!40, Y, tptp_fun_X_22(A!39, A!39, F!40, F!40))))))) | ((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))))))),
% 0.59/0.74 inference(tautology,[status(thm)],[])).
% 0.59/0.74 tff(415,plain,
% 0.59/0.74 ((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40)))))),
% 0.59/0.74 inference(unit_resolution,[status(thm)],[414, 413])).
% 0.59/0.74 tff(416,plain,
% 0.59/0.74 (((~![X: $i] : ((~member(X, A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), X, X))) | ((~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40)))) <=> ((~![X: $i] : ((~member(X, A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), X, X))) | (~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40)))),
% 0.59/0.74 inference(rewrite,[status(thm)],[])).
% 0.59/0.74 tff(417,plain,
% 0.59/0.74 ((~![X: $i] : ((~member(X, A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), X, X))) | ((~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40)))),
% 0.59/0.74 inference(quant_inst,[status(thm)],[])).
% 0.59/0.74 tff(418,plain,
% 0.59/0.74 ((~![X: $i] : ((~member(X, A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), X, X))) | (~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))),
% 0.59/0.74 inference(modus_ponens,[status(thm)],[417, 416])).
% 0.59/0.74 tff(419,plain,
% 0.59/0.74 (apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))),
% 0.59/0.74 inference(unit_resolution,[status(thm)],[418, 235, 359])).
% 0.59/0.74 tff(420,plain,
% 0.59/0.74 ((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))))))) | (~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40)))))),
% 0.59/0.74 inference(tautology,[status(thm)],[])).
% 0.59/0.74 tff(421,plain,
% 0.59/0.74 ((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))))))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40)))))),
% 0.59/0.74 inference(unit_resolution,[status(thm)],[420, 419])).
% 0.59/0.74 tff(422,plain,
% 0.59/0.74 (~((~member(tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))))),
% 0.59/0.74 inference(unit_resolution,[status(thm)],[421, 415])).
% 0.59/0.74 tff(423,plain,
% 0.59/0.74 (((~member(tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40)))) | apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40))),
% 0.59/0.74 inference(tautology,[status(thm)],[])).
% 0.59/0.74 tff(424,plain,
% 0.59/0.74 (apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40))),
% 0.59/0.74 inference(unit_resolution,[status(thm)],[423, 422])).
% 0.59/0.74 tff(425,plain,
% 0.59/0.74 (((~member(tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40)))) | member(tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)),
% 0.59/0.74 inference(tautology,[status(thm)],[])).
% 0.59/0.74 tff(426,plain,
% 0.59/0.74 (member(tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)),
% 0.59/0.74 inference(unit_resolution,[status(thm)],[425, 422])).
% 0.59/0.74 tff(427,plain,
% 0.59/0.74 (((~member(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40)))) | apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))),
% 0.59/0.74 inference(tautology,[status(thm)],[])).
% 0.59/0.74 tff(428,plain,
% 0.59/0.74 (apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))),
% 0.59/0.74 inference(unit_resolution,[status(thm)],[427, 363])).
% 0.59/0.74 tff(429,plain,
% 0.59/0.74 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | ((~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (~member(tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)) | (tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40) = tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | (~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (~member(tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)) | (tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40) = tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40)))),
% 0.59/0.74 inference(rewrite,[status(thm)],[])).
% 0.59/0.74 tff(430,plain,
% 0.59/0.74 (((tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40) = tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40)) | (~member(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))) | (~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39))) <=> ((~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (~member(tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)) | (tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40) = tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40)))),
% 0.59/0.75 inference(rewrite,[status(thm)],[])).
% 0.59/0.75 tff(431,plain,
% 0.59/0.75 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | ((tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40) = tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40)) | (~member(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))) | (~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | ((~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (~member(tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)) | (tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40) = tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))))),
% 0.59/0.75 inference(monotonicity,[status(thm)],[430])).
% 0.59/0.75 tff(432,plain,
% 0.59/0.75 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | ((tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40) = tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40)) | (~member(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))) | (~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | (~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (~member(tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)) | (tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40) = tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40)))),
% 0.59/0.75 inference(transitivity,[status(thm)],[431, 429])).
% 0.59/0.75 tff(433,plain,
% 0.59/0.75 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | ((tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40) = tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40)) | (~member(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))) | (~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)))),
% 0.59/0.75 inference(quant_inst,[status(thm)],[])).
% 0.59/0.75 tff(434,plain,
% 0.59/0.75 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | (~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (~member(tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)) | (tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40) = tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))),
% 0.59/0.75 inference(modus_ponens,[status(thm)],[433, 432])).
% 0.59/0.75 tff(435,plain,
% 0.59/0.75 (tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40) = tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40)),
% 0.59/0.75 inference(unit_resolution,[status(thm)],[434, 256, 359, 365, 428, 426, 424])).
% 0.59/0.75 tff(436,plain,
% 0.59/0.75 (tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40) = tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40)),
% 0.59/0.75 inference(symmetry,[status(thm)],[435])).
% 0.59/0.75 tff(437,plain,
% 0.59/0.75 (apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40)) <=> apply(F!40, tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))),
% 0.59/0.75 inference(monotonicity,[status(thm)],[436])).
% 0.59/0.75 tff(438,plain,
% 0.59/0.75 (apply(F!40, tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40)) <=> apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))),
% 0.59/0.75 inference(symmetry,[status(thm)],[437])).
% 0.59/0.75 tff(439,plain,
% 0.59/0.75 (((~member(tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40)))) | apply(F!40, tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))),
% 0.59/0.75 inference(tautology,[status(thm)],[])).
% 0.59/0.75 tff(440,plain,
% 0.59/0.75 (apply(F!40, tptp_fun_Y_8(tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))),
% 0.59/0.75 inference(unit_resolution,[status(thm)],[439, 422])).
% 0.59/0.75 tff(441,plain,
% 0.59/0.75 (apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))),
% 0.59/0.75 inference(modus_ponens,[status(thm)],[440, 438])).
% 0.59/0.75 tff(442,plain,
% 0.59/0.75 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | ((~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40) = tptp_fun_X_22(A!39, A!39, F!40, F!40)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | (~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40) = tptp_fun_X_22(A!39, A!39, F!40, F!40)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))))),
% 0.59/0.75 inference(rewrite,[status(thm)],[])).
% 0.59/0.75 tff(443,plain,
% 0.59/0.75 (((tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40) = tptp_fun_X_22(A!39, A!39, F!40, F!40)) | (~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))) | (~member(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39))) <=> ((~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40) = tptp_fun_X_22(A!39, A!39, F!40, F!40)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))))),
% 0.59/0.76 inference(rewrite,[status(thm)],[])).
% 0.59/0.76 tff(444,plain,
% 0.59/0.76 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | ((tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40) = tptp_fun_X_22(A!39, A!39, F!40, F!40)) | (~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))) | (~member(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | ((~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40) = tptp_fun_X_22(A!39, A!39, F!40, F!40)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40)))))),
% 0.59/0.76 inference(monotonicity,[status(thm)],[443])).
% 0.59/0.76 tff(445,plain,
% 0.59/0.76 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | ((tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40) = tptp_fun_X_22(A!39, A!39, F!40, F!40)) | (~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))) | (~member(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | (~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40) = tptp_fun_X_22(A!39, A!39, F!40, F!40)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))))),
% 0.62/0.76 inference(transitivity,[status(thm)],[444, 442])).
% 0.62/0.76 tff(446,plain,
% 0.62/0.76 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | ((tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40) = tptp_fun_X_22(A!39, A!39, F!40, F!40)) | (~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))) | (~member(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)))),
% 0.62/0.76 inference(quant_inst,[status(thm)],[])).
% 0.62/0.76 tff(447,plain,
% 0.62/0.76 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | (~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40))) | (~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40) = tptp_fun_X_22(A!39, A!39, F!40, F!40)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40)))),
% 0.62/0.76 inference(modus_ponens,[status(thm)],[446, 445])).
% 0.62/0.76 tff(448,plain,
% 0.62/0.76 ((tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40) = tptp_fun_X_22(A!39, A!39, F!40, F!40)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40)))),
% 0.62/0.76 inference(unit_resolution,[status(thm)],[447, 256, 359, 365, 388, 386])).
% 0.62/0.76 tff(449,plain,
% 0.62/0.76 (tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40) = tptp_fun_X_22(A!39, A!39, F!40, F!40)),
% 0.62/0.76 inference(unit_resolution,[status(thm)],[448, 441])).
% 0.62/0.76 tff(450,plain,
% 0.62/0.76 (tptp_fun_X_22(A!39, A!39, F!40, F!40) = tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40)),
% 0.62/0.76 inference(symmetry,[status(thm)],[449])).
% 0.62/0.76 tff(451,plain,
% 0.62/0.76 (tptp_fun_X_22(A!39, A!39, F!40, F!40) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)),
% 0.62/0.76 inference(transitivity,[status(thm)],[450, 403])).
% 0.62/0.76 tff(452,plain,
% 0.62/0.76 (((~![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_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~((~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)))))) | (~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))))))))))) <=> ((~![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_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~((~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)))))) | (~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))))))))))),
% 0.62/0.76 inference(rewrite,[status(thm)],[])).
% 0.62/0.76 tff(453,plain,
% 0.62/0.76 (((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~((~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)))))) | (~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)))))))))) <=> ((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~((~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)))))) | (~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))))))))))),
% 0.62/0.77 inference(rewrite,[status(thm)],[])).
% 0.62/0.77 tff(454,plain,
% 0.62/0.77 ((~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)))))))) <=> (~((~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)))))) | (~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)))))))))),
% 0.62/0.77 inference(rewrite,[status(thm)],[])).
% 0.62/0.77 tff(455,plain,
% 0.62/0.77 (((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))))))))) <=> ((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~((~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)))))) | (~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))))))))))),
% 0.62/0.77 inference(monotonicity,[status(thm)],[454])).
% 0.62/0.77 tff(456,plain,
% 0.62/0.77 (((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))))))))) <=> ((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~((~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)))))) | (~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))))))))))),
% 0.62/0.77 inference(transitivity,[status(thm)],[455, 453])).
% 0.62/0.77 tff(457,plain,
% 0.62/0.77 (((~![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_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)))))))))) <=> ((~![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_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~((~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)))))) | (~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)))))))))))),
% 0.62/0.78 inference(monotonicity,[status(thm)],[456])).
% 0.62/0.78 tff(458,plain,
% 0.62/0.78 (((~![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_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)))))))))) <=> ((~![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_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~((~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)))))) | (~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))))))))))),
% 0.62/0.78 inference(transitivity,[status(thm)],[457, 452])).
% 0.62/0.78 tff(459,plain,
% 0.62/0.78 ((~![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_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)))))))))),
% 0.62/0.78 inference(quant_inst,[status(thm)],[])).
% 0.62/0.78 tff(460,plain,
% 0.62/0.78 ((~![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_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~((~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)))))) | (~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)))))))))),
% 0.62/0.78 inference(modus_ponens,[status(thm)],[459, 458])).
% 0.62/0.78 tff(461,plain,
% 0.62/0.78 (~((~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)))))) | (~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))))))))),
% 0.62/0.78 inference(unit_resolution,[status(thm)],[460, 134, 396])).
% 0.62/0.78 tff(462,plain,
% 0.62/0.78 (((~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)))))) | (~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)))))))) | ((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))))))),
% 0.62/0.79 inference(tautology,[status(thm)],[])).
% 0.62/0.79 tff(463,plain,
% 0.62/0.79 ((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)))))),
% 0.62/0.79 inference(unit_resolution,[status(thm)],[462, 461])).
% 0.62/0.79 tff(464,plain,
% 0.62/0.79 (((~![X: $i] : ((~member(X, A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), X, X))) | ((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)))) <=> ((~![X: $i] : ((~member(X, A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), X, X))) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)))),
% 0.62/0.79 inference(rewrite,[status(thm)],[])).
% 0.62/0.79 tff(465,plain,
% 0.62/0.79 ((~![X: $i] : ((~member(X, A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), X, X))) | ((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)))),
% 0.62/0.79 inference(quant_inst,[status(thm)],[])).
% 0.62/0.79 tff(466,plain,
% 0.62/0.79 ((~![X: $i] : ((~member(X, A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), X, X))) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))),
% 0.62/0.79 inference(modus_ponens,[status(thm)],[465, 464])).
% 0.62/0.79 tff(467,plain,
% 0.62/0.79 (apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))),
% 0.62/0.79 inference(unit_resolution,[status(thm)],[466, 235, 396])).
% 0.62/0.79 tff(468,plain,
% 0.62/0.79 ((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))))))) | (~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)))))),
% 0.62/0.79 inference(tautology,[status(thm)],[])).
% 0.62/0.79 tff(469,plain,
% 0.62/0.79 ((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))))))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)))))),
% 0.62/0.79 inference(unit_resolution,[status(thm)],[468, 467])).
% 0.62/0.79 tff(470,plain,
% 0.62/0.79 (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))))),
% 0.62/0.79 inference(unit_resolution,[status(thm)],[469, 463])).
% 0.62/0.79 tff(471,plain,
% 0.62/0.79 (((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)))) | apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))),
% 0.62/0.79 inference(tautology,[status(thm)],[])).
% 0.62/0.79 tff(472,plain,
% 0.62/0.79 (apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))),
% 0.62/0.79 inference(unit_resolution,[status(thm)],[471, 470])).
% 0.62/0.79 tff(473,plain,
% 0.62/0.79 (((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)))) | member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)),
% 0.62/0.79 inference(tautology,[status(thm)],[])).
% 0.62/0.79 tff(474,plain,
% 0.62/0.79 (member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)),
% 0.62/0.80 inference(unit_resolution,[status(thm)],[473, 470])).
% 0.62/0.80 tff(475,plain,
% 0.62/0.80 (((~![X: $i] : ((~member(X, A!39)) | (~((~member(tptp_fun_Y_3(X, A!39, F!40), A!39)) | (~apply(F!40, X, tptp_fun_Y_3(X, A!39, F!40))))))) | ((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40))))))) <=> ((~![X: $i] : ((~member(X, A!39)) | (~((~member(tptp_fun_Y_3(X, A!39, F!40), A!39)) | (~apply(F!40, X, tptp_fun_Y_3(X, A!39, F!40))))))) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40))))))),
% 0.62/0.80 inference(rewrite,[status(thm)],[])).
% 0.62/0.80 tff(476,plain,
% 0.62/0.80 ((~![X: $i] : ((~member(X, A!39)) | (~((~member(tptp_fun_Y_3(X, A!39, F!40), A!39)) | (~apply(F!40, X, tptp_fun_Y_3(X, A!39, F!40))))))) | ((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40))))))),
% 0.62/0.80 inference(quant_inst,[status(thm)],[])).
% 0.62/0.80 tff(477,plain,
% 0.62/0.80 ((~![X: $i] : ((~member(X, A!39)) | (~((~member(tptp_fun_Y_3(X, A!39, F!40), A!39)) | (~apply(F!40, X, tptp_fun_Y_3(X, A!39, F!40))))))) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40)))))),
% 0.62/0.80 inference(modus_ponens,[status(thm)],[476, 475])).
% 0.62/0.80 tff(478,plain,
% 0.62/0.80 (~((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40))))),
% 0.62/0.80 inference(unit_resolution,[status(thm)],[477, 112, 396])).
% 0.62/0.80 tff(479,plain,
% 0.62/0.80 (((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40)))) | apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40))),
% 0.62/0.80 inference(tautology,[status(thm)],[])).
% 0.62/0.80 tff(480,plain,
% 0.62/0.80 (apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40))),
% 0.62/0.80 inference(unit_resolution,[status(thm)],[479, 478])).
% 0.62/0.80 tff(481,plain,
% 0.62/0.80 (((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40)))) | member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40), A!39)),
% 0.62/0.80 inference(tautology,[status(thm)],[])).
% 0.62/0.80 tff(482,plain,
% 0.62/0.80 (member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40), A!39)),
% 0.62/0.80 inference(unit_resolution,[status(thm)],[481, 478])).
% 0.62/0.80 tff(483,plain,
% 0.62/0.80 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | ((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40))) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40))) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40)))),
% 0.62/0.80 inference(rewrite,[status(thm)],[])).
% 0.62/0.80 tff(484,plain,
% 0.62/0.80 (((tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40))) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39))) <=> ((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40))) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40)))),
% 0.62/0.80 inference(rewrite,[status(thm)],[])).
% 0.62/0.80 tff(485,plain,
% 0.62/0.80 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | ((tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40))) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | ((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40))) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40))))),
% 0.62/0.81 inference(monotonicity,[status(thm)],[484])).
% 0.62/0.81 tff(486,plain,
% 0.62/0.81 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | ((tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40))) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40))) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40)))),
% 0.62/0.81 inference(transitivity,[status(thm)],[485, 483])).
% 0.62/0.81 tff(487,plain,
% 0.62/0.81 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | ((tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40))) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)))),
% 0.62/0.81 inference(quant_inst,[status(thm)],[])).
% 0.62/0.81 tff(488,plain,
% 0.62/0.81 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40))) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40))),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[487, 486])).
% 0.62/0.81 tff(489,plain,
% 0.62/0.81 (tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40)),
% 0.62/0.81 inference(unit_resolution,[status(thm)],[488, 256, 396, 482, 480, 474, 472])).
% 0.62/0.81 tff(490,plain,
% 0.62/0.81 (tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40) = tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40)),
% 0.62/0.81 inference(symmetry,[status(thm)],[489])).
% 0.62/0.81 tff(491,plain,
% 0.62/0.81 (tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40) = tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40, F!40)),
% 0.62/0.81 inference(symmetry,[status(thm)],[403])).
% 0.62/0.81 tff(492,plain,
% 0.62/0.81 (tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40) = tptp_fun_X_22(A!39, A!39, F!40, F!40)),
% 0.62/0.81 inference(transitivity,[status(thm)],[491, 449])).
% 0.62/0.81 tff(493,plain,
% 0.62/0.81 (tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40) = tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40)),
% 0.62/0.81 inference(monotonicity,[status(thm)],[492])).
% 0.62/0.81 tff(494,plain,
% 0.62/0.81 (tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40) = tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40)),
% 0.62/0.81 inference(symmetry,[status(thm)],[493])).
% 0.62/0.81 tff(495,assumption,(~(apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40)) <=> apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40)))), introduced(assumption)).
% 0.62/0.81 tff(496,assumption,(~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))), introduced(assumption)).
% 0.62/0.81 tff(497,plain,
% 0.62/0.81 ((apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40)) <=> apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))) | apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40)) | apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))),
% 0.62/0.81 inference(tautology,[status(thm)],[])).
% 0.62/0.81 tff(498,plain,
% 0.62/0.81 (apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40))),
% 0.62/0.81 inference(unit_resolution,[status(thm)],[497, 496, 495])).
% 0.62/0.81 tff(499,assumption,(member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)), introduced(assumption)).
% 0.62/0.81 tff(500,plain,
% 0.62/0.81 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | ((~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40))) | (~member(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))) | (tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40) = tptp_fun_Y_21(A!39, A!39, F!40, F!40)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | (~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40))) | (~member(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))) | (tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40) = tptp_fun_Y_21(A!39, A!39, F!40, F!40)))),
% 0.62/0.81 inference(rewrite,[status(thm)],[])).
% 0.62/0.81 tff(501,plain,
% 0.62/0.81 (((tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40) = tptp_fun_Y_21(A!39, A!39, F!40, F!40)) | (~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40))) | (~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39))) <=> ((~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40))) | (~member(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))) | (tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40) = tptp_fun_Y_21(A!39, A!39, F!40, F!40)))),
% 0.62/0.81 inference(rewrite,[status(thm)],[])).
% 0.62/0.81 tff(502,plain,
% 0.62/0.81 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | ((tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40) = tptp_fun_Y_21(A!39, A!39, F!40, F!40)) | (~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40))) | (~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | ((~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40))) | (~member(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))) | (tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40) = tptp_fun_Y_21(A!39, A!39, F!40, F!40))))),
% 0.62/0.81 inference(monotonicity,[status(thm)],[501])).
% 0.62/0.81 tff(503,plain,
% 0.62/0.81 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | ((tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40) = tptp_fun_Y_21(A!39, A!39, F!40, F!40)) | (~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40))) | (~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | (~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40))) | (~member(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))) | (tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40) = tptp_fun_Y_21(A!39, A!39, F!40, F!40)))),
% 0.62/0.81 inference(transitivity,[status(thm)],[502, 500])).
% 0.62/0.82 tff(504,plain,
% 0.62/0.82 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | ((tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40) = tptp_fun_Y_21(A!39, A!39, F!40, F!40)) | (~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40))) | (~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)))),
% 0.62/0.82 inference(quant_inst,[status(thm)],[])).
% 0.62/0.82 tff(505,plain,
% 0.62/0.82 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | (~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40))) | (~member(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40))) | (tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40) = tptp_fun_Y_21(A!39, A!39, F!40, F!40))),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[504, 503])).
% 0.62/0.82 tff(506,plain,
% 0.62/0.82 ((~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40))) | (tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40) = tptp_fun_Y_21(A!39, A!39, F!40, F!40))),
% 0.62/0.82 inference(unit_resolution,[status(thm)],[505, 256, 499, 359, 365, 428])).
% 0.62/0.82 tff(507,plain,
% 0.62/0.82 (tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40) = tptp_fun_Y_21(A!39, A!39, F!40, F!40)),
% 0.62/0.82 inference(unit_resolution,[status(thm)],[506, 498])).
% 0.62/0.82 tff(508,plain,
% 0.62/0.82 (tptp_fun_Y_21(A!39, A!39, F!40, F!40) = tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40)),
% 0.62/0.82 inference(symmetry,[status(thm)],[507])).
% 0.62/0.82 tff(509,plain,
% 0.62/0.82 (tptp_fun_Y_21(A!39, A!39, F!40, F!40) = tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40)),
% 0.62/0.82 inference(transitivity,[status(thm)],[508, 494, 490])).
% 0.62/0.82 tff(510,plain,
% 0.62/0.82 (apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40)) <=> apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))),
% 0.62/0.82 inference(monotonicity,[status(thm)],[509, 451])).
% 0.62/0.82 tff(511,plain,
% 0.62/0.82 (apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)) <=> apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))),
% 0.62/0.82 inference(symmetry,[status(thm)],[510])).
% 0.62/0.82 tff(512,plain,
% 0.62/0.82 (((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)))) | apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))),
% 0.62/0.82 inference(tautology,[status(thm)],[])).
% 0.62/0.82 tff(513,plain,
% 0.62/0.82 (apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))),
% 0.62/0.82 inference(unit_resolution,[status(thm)],[512, 470])).
% 0.62/0.82 tff(514,plain,
% 0.62/0.82 (apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[513, 511])).
% 0.62/0.82 tff(515,plain,
% 0.62/0.82 ($false),
% 0.62/0.82 inference(unit_resolution,[status(thm)],[496, 514])).
% 0.62/0.82 tff(516,plain,(apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40)) | (~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40)) <=> apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40)))), inference(lemma,lemma(discharge,[]))).
% 0.62/0.82 tff(517,plain,
% 0.62/0.82 (apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))),
% 0.62/0.82 inference(unit_resolution,[status(thm)],[516, 67, 358, 356])).
% 0.62/0.82 tff(518,plain,
% 0.62/0.82 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | ((~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))) | (~member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))) | (tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40) = tptp_fun_X_22(A!39, A!39, F!40, F!40)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | (~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))) | (~member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))) | (tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40) = tptp_fun_X_22(A!39, A!39, F!40, F!40)))),
% 0.62/0.82 inference(rewrite,[status(thm)],[])).
% 0.62/0.82 tff(519,plain,
% 0.62/0.82 (((tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40) = tptp_fun_X_22(A!39, A!39, F!40, F!40)) | (~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))) | (~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39))) <=> ((~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))) | (~member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))) | (tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40) = tptp_fun_X_22(A!39, A!39, F!40, F!40)))),
% 0.68/0.82 inference(rewrite,[status(thm)],[])).
% 0.68/0.82 tff(520,plain,
% 0.68/0.82 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | ((tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40) = tptp_fun_X_22(A!39, A!39, F!40, F!40)) | (~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))) | (~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | ((~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))) | (~member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))) | (tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40) = tptp_fun_X_22(A!39, A!39, F!40, F!40))))),
% 0.68/0.82 inference(monotonicity,[status(thm)],[519])).
% 0.68/0.82 tff(521,plain,
% 0.68/0.82 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | ((tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40) = tptp_fun_X_22(A!39, A!39, F!40, F!40)) | (~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))) | (~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | (~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))) | (~member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))) | (tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40) = tptp_fun_X_22(A!39, A!39, F!40, F!40)))),
% 0.68/0.82 inference(transitivity,[status(thm)],[520, 518])).
% 0.68/0.82 tff(522,plain,
% 0.68/0.82 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | ((tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40) = tptp_fun_X_22(A!39, A!39, F!40, F!40)) | (~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))) | (~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)))),
% 0.68/0.82 inference(quant_inst,[status(thm)],[])).
% 0.68/0.82 tff(523,plain,
% 0.68/0.82 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | (~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | (~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))) | (~member(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40))) | (tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40) = tptp_fun_X_22(A!39, A!39, F!40, F!40))),
% 0.68/0.83 inference(modus_ponens,[status(thm)],[522, 521])).
% 0.68/0.83 tff(524,plain,
% 0.68/0.83 ((~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))) | (tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40) = tptp_fun_X_22(A!39, A!39, F!40, F!40))),
% 0.68/0.83 inference(unit_resolution,[status(thm)],[523, 256, 67, 358, 118, 288])).
% 0.68/0.83 tff(525,plain,
% 0.68/0.83 (tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40) = tptp_fun_X_22(A!39, A!39, F!40, F!40)),
% 0.68/0.83 inference(unit_resolution,[status(thm)],[524, 517])).
% 0.68/0.83 tff(526,plain,
% 0.68/0.83 (tptp_fun_X_22(A!39, A!39, F!40, F!40) = tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40)),
% 0.68/0.83 inference(symmetry,[status(thm)],[525])).
% 0.68/0.83 tff(527,plain,
% 0.68/0.83 (tptp_fun_X_22(A!39, A!39, F!40, F!40) = tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40)),
% 0.68/0.83 inference(transitivity,[status(thm)],[526, 354, 350])).
% 0.68/0.83 tff(528,plain,
% 0.68/0.83 (apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40)) <=> apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))),
% 0.68/0.83 inference(monotonicity,[status(thm)],[527, 311])).
% 0.68/0.83 tff(529,plain,
% 0.68/0.83 (apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)) <=> apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40))),
% 0.68/0.83 inference(symmetry,[status(thm)],[528])).
% 0.68/0.83 tff(530,plain,
% 0.68/0.83 (((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40)))) | apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))),
% 0.68/0.83 inference(tautology,[status(thm)],[])).
% 0.68/0.83 tff(531,plain,
% 0.68/0.83 (apply(F!40, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39, F!40), A!39, F!40))),
% 0.68/0.83 inference(unit_resolution,[status(thm)],[530, 330])).
% 0.68/0.83 tff(532,plain,
% 0.68/0.83 (apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40))),
% 0.68/0.83 inference(modus_ponens,[status(thm)],[531, 529])).
% 0.68/0.83 tff(533,plain,
% 0.68/0.83 ((apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40)) <=> apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40)))),
% 0.68/0.83 inference(tautology,[status(thm)],[])).
% 0.68/0.83 tff(534,plain,
% 0.68/0.83 (~apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40))),
% 0.68/0.83 inference(unit_resolution,[status(thm)],[533, 517, 356])).
% 0.68/0.83 tff(535,plain,
% 0.68/0.83 ($false),
% 0.68/0.83 inference(unit_resolution,[status(thm)],[534, 532])).
% 0.68/0.83 tff(536,plain,((~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | (apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40)) <=> apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))) | (~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39))), inference(lemma,lemma(discharge,[]))).
% 0.68/0.83 tff(537,plain,
% 0.68/0.83 ((~(inverse_predicate(F!40, F!40, A!39, A!39) | (~((~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | (apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40)) <=> apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))) | (~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)))))) | inverse_predicate(F!40, F!40, A!39, A!39) | (~((~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | (apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40)) <=> apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))) | (~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39))))),
% 0.68/0.83 inference(tautology,[status(thm)],[])).
% 0.68/0.83 tff(538,plain,
% 0.68/0.83 ((~(inverse_predicate(F!40, F!40, A!39, A!39) | (~((~member(tptp_fun_Y_21(A!39, A!39, F!40, F!40), A!39)) | (apply(F!40, tptp_fun_X_22(A!39, A!39, F!40, F!40), tptp_fun_Y_21(A!39, A!39, F!40, F!40)) <=> apply(F!40, tptp_fun_Y_21(A!39, A!39, F!40, F!40), tptp_fun_X_22(A!39, A!39, F!40, F!40))) | (~member(tptp_fun_X_22(A!39, A!39, F!40, F!40), A!39)))))) | inverse_predicate(F!40, F!40, A!39, A!39)),
% 0.68/0.83 inference(unit_resolution,[status(thm)],[537, 536])).
% 0.68/0.83 tff(539,plain,
% 0.68/0.83 (inverse_predicate(F!40, F!40, A!39, A!39)),
% 0.68/0.83 inference(unit_resolution,[status(thm)],[538, 64])).
% 0.68/0.83 tff(540,plain,
% 0.68/0.83 (((~one_to_one(F!40, A!39, A!39)) | (~inverse_predicate(F!40, F!40, A!39, A!39))) | (~identity(compose_function(F!40, F!40, A!39, A!39, A!39), A!39)) | (~(((~one_to_one(F!40, A!39, A!39)) | (~inverse_predicate(F!40, F!40, A!39, A!39))) <=> identity(compose_function(F!40, F!40, A!39, A!39, A!39), A!39)))),
% 0.68/0.83 inference(tautology,[status(thm)],[])).
% 0.68/0.83 tff(541,plain,
% 0.68/0.83 (((~one_to_one(F!40, A!39, A!39)) | (~inverse_predicate(F!40, F!40, A!39, A!39))) | (~identity(compose_function(F!40, F!40, A!39, A!39, A!39), A!39))),
% 0.68/0.83 inference(unit_resolution,[status(thm)],[540, 217])).
% 0.68/0.83 tff(542,plain,
% 0.68/0.83 ((~one_to_one(F!40, A!39, A!39)) | (~inverse_predicate(F!40, F!40, A!39, A!39))),
% 0.68/0.83 inference(unit_resolution,[status(thm)],[541, 230])).
% 0.68/0.83 tff(543,plain,
% 0.68/0.83 ((~((~one_to_one(F!40, A!39, A!39)) | (~inverse_predicate(F!40, F!40, A!39, A!39)))) | (~one_to_one(F!40, A!39, A!39)) | (~inverse_predicate(F!40, F!40, A!39, A!39))),
% 0.68/0.83 inference(tautology,[status(thm)],[])).
% 0.68/0.83 tff(544,plain,
% 0.68/0.83 ((~one_to_one(F!40, A!39, A!39)) | (~inverse_predicate(F!40, F!40, A!39, A!39))),
% 0.68/0.83 inference(unit_resolution,[status(thm)],[543, 542])).
% 0.68/0.83 tff(545,plain,
% 0.68/0.83 (~one_to_one(F!40, A!39, A!39)),
% 0.68/0.83 inference(unit_resolution,[status(thm)],[544, 539])).
% 0.68/0.83 tff(546,plain,
% 0.68/0.83 ((((~injective(F!40, A!39, A!39)) | (~surjective(F!40, A!39, A!39))) <=> one_to_one(F!40, A!39, A!39)) | ((~injective(F!40, A!39, A!39)) | (~surjective(F!40, A!39, A!39))) | one_to_one(F!40, A!39, A!39)),
% 0.68/0.83 inference(tautology,[status(thm)],[])).
% 0.68/0.83 tff(547,plain,
% 0.68/0.83 ((((~injective(F!40, A!39, A!39)) | (~surjective(F!40, A!39, A!39))) <=> one_to_one(F!40, A!39, A!39)) | ((~injective(F!40, A!39, A!39)) | (~surjective(F!40, A!39, A!39)))),
% 0.68/0.83 inference(unit_resolution,[status(thm)],[546, 545])).
% 0.68/0.83 tff(548,plain,
% 0.68/0.83 ((~injective(F!40, A!39, A!39)) | (~surjective(F!40, A!39, A!39))),
% 0.68/0.83 inference(unit_resolution,[status(thm)],[547, 37])).
% 0.68/0.83 tff(549,assumption,((~((~surjective(F!40, A!39, A!39)) | ![Y: $i] : ((~member(Y, A!39)) | (~((~member(tptp_fun_E_19(Y, A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_E_19(Y, A!39, F!40), Y))))))) | (~(surjective(F!40, A!39, A!39) | (~((~member(tptp_fun_Y_20(A!39, A!39, F!40), A!39)) | (~![E: $i] : ((~member(E, A!39)) | (~apply(F!40, E, tptp_fun_Y_20(A!39, A!39, F!40)))))))))), introduced(assumption)).
% 0.68/0.83 tff(550,plain,
% 0.68/0.83 (^[F: $i, A: $i, B: $i] : refl((~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))))))) <=> (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))))))))),
% 0.68/0.83 inference(bind,[status(th)],[])).
% 0.68/0.83 tff(551,plain,
% 0.68/0.83 (![F: $i, A: $i, B: $i] : (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))))))),
% 0.68/0.83 inference(quant_intro,[status(thm)],[550])).
% 0.68/0.83 tff(552,plain,
% 0.68/0.83 (^[F: $i, A: $i, B: $i] : rewrite((~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))))))) <=> (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))))))))),
% 0.68/0.83 inference(bind,[status(th)],[])).
% 0.68/0.83 tff(553,plain,
% 0.68/0.83 (![F: $i, A: $i, B: $i] : (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))))))),
% 0.68/0.83 inference(quant_intro,[status(thm)],[552])).
% 0.68/0.83 tff(554,plain,
% 0.68/0.83 (![F: $i, A: $i, B: $i] : (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))))))),
% 0.68/0.83 inference(transitivity,[status(thm)],[553, 551])).
% 0.68/0.83 tff(555,plain,
% 0.68/0.83 (^[F: $i, A: $i, B: $i] : trans(monotonicity(rewrite(((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (member(tptp_fun_E_19(Y, A, F), A) & apply(F, tptp_fun_E_19(Y, A, F), Y)))) <=> ((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))), trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[E: $i] : trans(monotonicity(rewrite((member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F))) <=> (~((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))), ((~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F)))) <=> (~(~((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))), rewrite((~(~((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))) <=> ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))), ((~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F)))) <=> ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))), (![E: $i] : (~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F)))) <=> ![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))), ((member(tptp_fun_Y_20(B, A, F), B) & ![E: $i] : (~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F))))) <=> (member(tptp_fun_Y_20(B, A, F), B) & ![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))), rewrite((member(tptp_fun_Y_20(B, A, F), B) & ![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))) <=> (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))), ((member(tptp_fun_Y_20(B, A, F), B) & ![E: $i] : (~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F))))) <=> (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))))), ((surjective(F, A, B) | (member(tptp_fun_Y_20(B, A, F), B) & ![E: $i] : (~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F)))))) <=> (surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))))), rewrite((surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))) <=> (surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))))), ((surjective(F, A, B) | (member(tptp_fun_Y_20(B, A, F), B) & ![E: $i] : (~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F)))))) <=> (surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))))), ((((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (member(tptp_fun_E_19(Y, A, F), A) & apply(F, tptp_fun_E_19(Y, A, F), Y)))) & (surjective(F, A, B) | (member(tptp_fun_Y_20(B, A, F), B) & ![E: $i] : (~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F))))))) <=> (((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y)))))) & (surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))))))), rewrite((((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y)))))) & (surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))))) <=> (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))))))), ((((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (member(tptp_fun_E_19(Y, A, F), A) & apply(F, tptp_fun_E_19(Y, A, F), Y)))) & (surjective(F, A, B) | (member(tptp_fun_Y_20(B, A, F), B) & ![E: $i] : (~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F))))))) <=> (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))))))))),
% 0.68/0.83 inference(bind,[status(th)],[])).
% 0.68/0.83 tff(556,plain,
% 0.68/0.83 (![F: $i, A: $i, B: $i] : (((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (member(tptp_fun_E_19(Y, A, F), A) & apply(F, tptp_fun_E_19(Y, A, F), Y)))) & (surjective(F, A, B) | (member(tptp_fun_Y_20(B, A, F), B) & ![E: $i] : (~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))))))),
% 0.68/0.83 inference(quant_intro,[status(thm)],[555])).
% 0.68/0.83 tff(557,plain,
% 0.68/0.83 (![F: $i, A: $i, B: $i] : (surjective(F, A, B) <=> ![Y: $i] : ((~member(Y, B)) | ?[E: $i] : (member(E, A) & apply(F, E, Y)))) <=> ![F: $i, A: $i, B: $i] : (surjective(F, A, B) <=> ![Y: $i] : ((~member(Y, B)) | ?[E: $i] : (member(E, A) & apply(F, E, Y))))),
% 0.68/0.83 inference(rewrite,[status(thm)],[])).
% 0.68/0.83 tff(558,plain,
% 0.68/0.83 (^[F: $i, A: $i, B: $i] : rewrite((surjective(F, A, B) <=> ![Y: $i] : (member(Y, B) => ?[E: $i] : (member(E, A) & apply(F, E, Y)))) <=> (surjective(F, A, B) <=> ![Y: $i] : ((~member(Y, B)) | ?[E: $i] : (member(E, A) & apply(F, E, Y)))))),
% 0.68/0.83 inference(bind,[status(th)],[])).
% 0.68/0.83 tff(559,plain,
% 0.68/0.83 (![F: $i, A: $i, B: $i] : (surjective(F, A, B) <=> ![Y: $i] : (member(Y, B) => ?[E: $i] : (member(E, A) & apply(F, E, Y)))) <=> ![F: $i, A: $i, B: $i] : (surjective(F, A, B) <=> ![Y: $i] : ((~member(Y, B)) | ?[E: $i] : (member(E, A) & apply(F, E, Y))))),
% 0.68/0.83 inference(quant_intro,[status(thm)],[558])).
% 0.68/0.83 tff(560,axiom,(![F: $i, A: $i, B: $i] : (surjective(F, A, B) <=> ![Y: $i] : (member(Y, B) => ?[E: $i] : (member(E, A) & apply(F, E, Y))))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+1.ax','surjective')).
% 0.68/0.83 tff(561,plain,
% 0.68/0.83 (![F: $i, A: $i, B: $i] : (surjective(F, A, B) <=> ![Y: $i] : ((~member(Y, B)) | ?[E: $i] : (member(E, A) & apply(F, E, Y))))),
% 0.68/0.83 inference(modus_ponens,[status(thm)],[560, 559])).
% 0.68/0.83 tff(562,plain,
% 0.68/0.83 (![F: $i, A: $i, B: $i] : (surjective(F, A, B) <=> ![Y: $i] : ((~member(Y, B)) | ?[E: $i] : (member(E, A) & apply(F, E, Y))))),
% 0.68/0.83 inference(modus_ponens,[status(thm)],[561, 557])).
% 0.68/0.83 tff(563,plain,(
% 0.68/0.83 ![F: $i, A: $i, B: $i] : (((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (member(tptp_fun_E_19(Y, A, F), A) & apply(F, tptp_fun_E_19(Y, A, F), Y)))) & (surjective(F, A, B) | (member(tptp_fun_Y_20(B, A, F), B) & ![E: $i] : (~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F)))))))),
% 0.68/0.83 inference(skolemize,[status(sab)],[562])).
% 0.68/0.83 tff(564,plain,
% 0.68/0.83 (![F: $i, A: $i, B: $i] : (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))))))),
% 0.68/0.83 inference(modus_ponens,[status(thm)],[563, 556])).
% 0.68/0.83 tff(565,plain,
% 0.68/0.83 (![F: $i, A: $i, B: $i] : (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))))))),
% 0.68/0.83 inference(modus_ponens,[status(thm)],[564, 554])).
% 0.68/0.83 tff(566,plain,
% 0.68/0.83 ((~![F: $i, A: $i, B: $i] : (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))))))) | (~((~((~surjective(F!40, A!39, A!39)) | ![Y: $i] : ((~member(Y, A!39)) | (~((~member(tptp_fun_E_19(Y, A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_E_19(Y, A!39, F!40), Y))))))) | (~(surjective(F!40, A!39, A!39) | (~((~member(tptp_fun_Y_20(A!39, A!39, F!40), A!39)) | (~![E: $i] : ((~member(E, A!39)) | (~apply(F!40, E, tptp_fun_Y_20(A!39, A!39, F!40)))))))))))),
% 0.68/0.83 inference(quant_inst,[status(thm)],[])).
% 0.68/0.83 tff(567,plain,
% 0.68/0.83 ($false),
% 0.68/0.83 inference(unit_resolution,[status(thm)],[566, 565, 549])).
% 0.68/0.83 tff(568,plain,(~((~((~surjective(F!40, A!39, A!39)) | ![Y: $i] : ((~member(Y, A!39)) | (~((~member(tptp_fun_E_19(Y, A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_E_19(Y, A!39, F!40), Y))))))) | (~(surjective(F!40, A!39, A!39) | (~((~member(tptp_fun_Y_20(A!39, A!39, F!40), A!39)) | (~![E: $i] : ((~member(E, A!39)) | (~apply(F!40, E, tptp_fun_Y_20(A!39, A!39, F!40))))))))))), inference(lemma,lemma(discharge,[]))).
% 0.68/0.83 tff(569,plain,
% 0.68/0.83 (((~((~surjective(F!40, A!39, A!39)) | ![Y: $i] : ((~member(Y, A!39)) | (~((~member(tptp_fun_E_19(Y, A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_E_19(Y, A!39, F!40), Y))))))) | (~(surjective(F!40, A!39, A!39) | (~((~member(tptp_fun_Y_20(A!39, A!39, F!40), A!39)) | (~![E: $i] : ((~member(E, A!39)) | (~apply(F!40, E, tptp_fun_Y_20(A!39, A!39, F!40)))))))))) | (surjective(F!40, A!39, A!39) | (~((~member(tptp_fun_Y_20(A!39, A!39, F!40), A!39)) | (~![E: $i] : ((~member(E, A!39)) | (~apply(F!40, E, tptp_fun_Y_20(A!39, A!39, F!40))))))))),
% 0.68/0.83 inference(tautology,[status(thm)],[])).
% 0.68/0.83 tff(570,plain,
% 0.68/0.83 (surjective(F!40, A!39, A!39) | (~((~member(tptp_fun_Y_20(A!39, A!39, F!40), A!39)) | (~![E: $i] : ((~member(E, A!39)) | (~apply(F!40, E, tptp_fun_Y_20(A!39, A!39, F!40)))))))),
% 0.68/0.83 inference(unit_resolution,[status(thm)],[569, 568])).
% 0.68/0.83 tff(571,assumption,(~((~member(tptp_fun_Y_20(A!39, A!39, F!40), A!39)) | (~![E: $i] : ((~member(E, A!39)) | (~apply(F!40, E, tptp_fun_Y_20(A!39, A!39, F!40))))))), introduced(assumption)).
% 0.68/0.83 tff(572,plain,
% 0.68/0.83 (((~member(tptp_fun_Y_20(A!39, A!39, F!40), A!39)) | (~![E: $i] : ((~member(E, A!39)) | (~apply(F!40, E, tptp_fun_Y_20(A!39, A!39, F!40)))))) | member(tptp_fun_Y_20(A!39, A!39, F!40), A!39)),
% 0.68/0.83 inference(tautology,[status(thm)],[])).
% 0.68/0.83 tff(573,plain,
% 0.68/0.83 (member(tptp_fun_Y_20(A!39, A!39, F!40), A!39)),
% 0.68/0.83 inference(unit_resolution,[status(thm)],[572, 571])).
% 0.68/0.83 tff(574,plain,
% 0.68/0.83 (((~![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!39, A!39, F!40), A!39)) | (~((~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_20(A!39, A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_20(A!39, A!39, F!40)))))) | (~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_20(A!39, A!39, F!40))))))))))) <=> ((~![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!39, A!39, F!40), A!39)) | (~((~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_20(A!39, A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_20(A!39, A!39, F!40)))))) | (~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_20(A!39, A!39, F!40))))))))))),
% 0.68/0.84 inference(rewrite,[status(thm)],[])).
% 0.68/0.84 tff(575,plain,
% 0.68/0.84 (((~member(tptp_fun_Y_20(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_Y_20(A!39, A!39, F!40), A!39)) | (~((~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_20(A!39, A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_20(A!39, A!39, F!40)))))) | (~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_20(A!39, A!39, F!40)))))))))) <=> ((~member(tptp_fun_Y_20(A!39, A!39, F!40), A!39)) | (~((~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_20(A!39, A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_20(A!39, A!39, F!40)))))) | (~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_20(A!39, A!39, F!40))))))))))),
% 0.68/0.84 inference(rewrite,[status(thm)],[])).
% 0.68/0.84 tff(576,plain,
% 0.68/0.84 ((~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_20(A!39, A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_20(A!39, A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_20(A!39, A!39, F!40)))))))) <=> (~((~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_20(A!39, A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_20(A!39, A!39, F!40)))))) | (~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_20(A!39, A!39, F!40)))))))))),
% 0.68/0.84 inference(rewrite,[status(thm)],[])).
% 0.68/0.84 tff(577,plain,
% 0.68/0.84 (((~member(tptp_fun_Y_20(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_Y_20(A!39, A!39, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_20(A!39, A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_20(A!39, A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_20(A!39, A!39, F!40))))))))) <=> ((~member(tptp_fun_Y_20(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_Y_20(A!39, A!39, F!40), A!39)) | (~((~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_20(A!39, A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_20(A!39, A!39, F!40)))))) | (~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_20(A!39, A!39, F!40))))))))))),
% 0.68/0.84 inference(monotonicity,[status(thm)],[576])).
% 0.68/0.84 tff(578,plain,
% 0.68/0.84 (((~member(tptp_fun_Y_20(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_Y_20(A!39, A!39, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_20(A!39, A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_20(A!39, A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_20(A!39, A!39, F!40))))))))) <=> ((~member(tptp_fun_Y_20(A!39, A!39, F!40), A!39)) | (~((~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_20(A!39, A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_20(A!39, A!39, F!40)))))) | (~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_20(A!39, A!39, F!40))))))))))),
% 0.68/0.84 inference(transitivity,[status(thm)],[577, 575])).
% 0.68/0.84 tff(579,plain,
% 0.68/0.84 (((~![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!39, A!39, F!40), A!39)) | (~member(tptp_fun_Y_20(A!39, A!39, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_20(A!39, A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_20(A!39, A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_20(A!39, A!39, F!40)))))))))) <=> ((~![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!39, A!39, F!40), A!39)) | (~((~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_20(A!39, A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_20(A!39, A!39, F!40)))))) | (~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_20(A!39, A!39, F!40)))))))))))),
% 0.68/0.84 inference(monotonicity,[status(thm)],[578])).
% 0.68/0.84 tff(580,plain,
% 0.68/0.84 (((~![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!39, A!39, F!40), A!39)) | (~member(tptp_fun_Y_20(A!39, A!39, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_20(A!39, A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_20(A!39, A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_20(A!39, A!39, F!40)))))))))) <=> ((~![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!39, A!39, F!40), A!39)) | (~((~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_20(A!39, A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_20(A!39, A!39, F!40)))))) | (~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_20(A!39, A!39, F!40))))))))))),
% 0.68/0.85 inference(transitivity,[status(thm)],[579, 574])).
% 0.68/0.85 tff(581,plain,
% 0.68/0.85 ((~![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!39, A!39, F!40), A!39)) | (~member(tptp_fun_Y_20(A!39, A!39, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_20(A!39, A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_20(A!39, A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_20(A!39, A!39, F!40)))))))))),
% 0.68/0.85 inference(quant_inst,[status(thm)],[])).
% 0.68/0.85 tff(582,plain,
% 0.68/0.85 ((~![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!39, A!39, F!40), A!39)) | (~((~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_20(A!39, A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_20(A!39, A!39, F!40)))))) | (~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_20(A!39, A!39, F!40)))))))))),
% 0.68/0.85 inference(modus_ponens,[status(thm)],[581, 580])).
% 0.68/0.85 tff(583,plain,
% 0.68/0.85 (~((~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_20(A!39, A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_20(A!39, A!39, F!40)))))) | (~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_20(A!39, A!39, F!40))))))))),
% 0.68/0.85 inference(unit_resolution,[status(thm)],[582, 134, 573])).
% 0.68/0.85 tff(584,plain,
% 0.68/0.85 (((~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_Y_20(A!39, A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_Y_20(A!39, A!39, F!40)))))) | (~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_20(A!39, A!39, F!40)))))))) | ((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_20(A!39, A!39, F!40))))))),
% 0.68/0.85 inference(tautology,[status(thm)],[])).
% 0.68/0.85 tff(585,plain,
% 0.68/0.85 ((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_20(A!39, A!39, F!40)))))),
% 0.68/0.85 inference(unit_resolution,[status(thm)],[584, 583])).
% 0.68/0.85 tff(586,plain,
% 0.68/0.85 (((~![X: $i] : ((~member(X, A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), X, X))) | ((~member(tptp_fun_Y_20(A!39, A!39, F!40), A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40)))) <=> ((~![X: $i] : ((~member(X, A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), X, X))) | (~member(tptp_fun_Y_20(A!39, A!39, F!40), A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40)))),
% 0.68/0.85 inference(rewrite,[status(thm)],[])).
% 0.68/0.85 tff(587,plain,
% 0.68/0.85 ((~![X: $i] : ((~member(X, A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), X, X))) | ((~member(tptp_fun_Y_20(A!39, A!39, F!40), A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40)))),
% 0.68/0.85 inference(quant_inst,[status(thm)],[])).
% 0.68/0.85 tff(588,plain,
% 0.68/0.85 ((~![X: $i] : ((~member(X, A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), X, X))) | (~member(tptp_fun_Y_20(A!39, A!39, F!40), A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40))),
% 0.68/0.85 inference(modus_ponens,[status(thm)],[587, 586])).
% 0.68/0.85 tff(589,plain,
% 0.68/0.85 (apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40))),
% 0.68/0.85 inference(unit_resolution,[status(thm)],[588, 235, 573])).
% 0.68/0.85 tff(590,plain,
% 0.68/0.85 ((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_20(A!39, A!39, F!40))))))) | (~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_20(A!39, A!39, F!40)))))),
% 0.68/0.85 inference(tautology,[status(thm)],[])).
% 0.68/0.85 tff(591,plain,
% 0.68/0.85 ((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_20(A!39, A!39, F!40))))))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_20(A!39, A!39, F!40)))))),
% 0.68/0.85 inference(unit_resolution,[status(thm)],[590, 589])).
% 0.68/0.85 tff(592,plain,
% 0.68/0.85 (~((~member(tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_20(A!39, A!39, F!40))))),
% 0.68/0.85 inference(unit_resolution,[status(thm)],[591, 585])).
% 0.68/0.85 tff(593,plain,
% 0.68/0.85 (((~member(tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_20(A!39, A!39, F!40)))) | apply(F!40, tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_20(A!39, A!39, F!40))),
% 0.68/0.85 inference(tautology,[status(thm)],[])).
% 0.68/0.85 tff(594,plain,
% 0.68/0.85 (apply(F!40, tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_20(A!39, A!39, F!40))),
% 0.68/0.85 inference(unit_resolution,[status(thm)],[593, 592])).
% 0.68/0.85 tff(595,plain,
% 0.68/0.85 (((~member(tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_20(A!39, A!39, F!40)))) | member(tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40), A!39)),
% 0.68/0.85 inference(tautology,[status(thm)],[])).
% 0.68/0.85 tff(596,plain,
% 0.68/0.85 (member(tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40), A!39)),
% 0.68/0.85 inference(unit_resolution,[status(thm)],[595, 592])).
% 0.68/0.85 tff(597,plain,
% 0.68/0.85 (((~member(tptp_fun_Y_20(A!39, A!39, F!40), A!39)) | (~![E: $i] : ((~member(E, A!39)) | (~apply(F!40, E, tptp_fun_Y_20(A!39, A!39, F!40)))))) | ![E: $i] : ((~member(E, A!39)) | (~apply(F!40, E, tptp_fun_Y_20(A!39, A!39, F!40))))),
% 0.68/0.85 inference(tautology,[status(thm)],[])).
% 0.68/0.85 tff(598,plain,
% 0.68/0.85 (![E: $i] : ((~member(E, A!39)) | (~apply(F!40, E, tptp_fun_Y_20(A!39, A!39, F!40))))),
% 0.68/0.85 inference(unit_resolution,[status(thm)],[597, 571])).
% 0.68/0.85 tff(599,plain,
% 0.68/0.85 (((~![E: $i] : ((~member(E, A!39)) | (~apply(F!40, E, tptp_fun_Y_20(A!39, A!39, F!40))))) | ((~member(tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_20(A!39, A!39, F!40))))) <=> ((~![E: $i] : ((~member(E, A!39)) | (~apply(F!40, E, tptp_fun_Y_20(A!39, A!39, F!40))))) | (~member(tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_20(A!39, A!39, F!40))))),
% 0.68/0.85 inference(rewrite,[status(thm)],[])).
% 0.68/0.85 tff(600,plain,
% 0.68/0.85 ((~![E: $i] : ((~member(E, A!39)) | (~apply(F!40, E, tptp_fun_Y_20(A!39, A!39, F!40))))) | ((~member(tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_20(A!39, A!39, F!40))))),
% 0.68/0.85 inference(quant_inst,[status(thm)],[])).
% 0.68/0.85 tff(601,plain,
% 0.68/0.85 ((~![E: $i] : ((~member(E, A!39)) | (~apply(F!40, E, tptp_fun_Y_20(A!39, A!39, F!40))))) | (~member(tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_Y_20(A!39, A!39, F!40), tptp_fun_Y_20(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_Y_20(A!39, A!39, F!40)))),
% 0.68/0.85 inference(modus_ponens,[status(thm)],[600, 599])).
% 0.68/0.85 tff(602,plain,
% 0.68/0.85 ($false),
% 0.68/0.85 inference(unit_resolution,[status(thm)],[601, 598, 596, 594])).
% 0.68/0.85 tff(603,plain,((~member(tptp_fun_Y_20(A!39, A!39, F!40), A!39)) | (~![E: $i] : ((~member(E, A!39)) | (~apply(F!40, E, tptp_fun_Y_20(A!39, A!39, F!40)))))), inference(lemma,lemma(discharge,[]))).
% 0.68/0.85 tff(604,plain,
% 0.68/0.85 ((~(surjective(F!40, A!39, A!39) | (~((~member(tptp_fun_Y_20(A!39, A!39, F!40), A!39)) | (~![E: $i] : ((~member(E, A!39)) | (~apply(F!40, E, tptp_fun_Y_20(A!39, A!39, F!40))))))))) | surjective(F!40, A!39, A!39) | (~((~member(tptp_fun_Y_20(A!39, A!39, F!40), A!39)) | (~![E: $i] : ((~member(E, A!39)) | (~apply(F!40, E, tptp_fun_Y_20(A!39, A!39, F!40)))))))),
% 0.68/0.85 inference(tautology,[status(thm)],[])).
% 0.68/0.85 tff(605,plain,
% 0.68/0.85 ((~(surjective(F!40, A!39, A!39) | (~((~member(tptp_fun_Y_20(A!39, A!39, F!40), A!39)) | (~![E: $i] : ((~member(E, A!39)) | (~apply(F!40, E, tptp_fun_Y_20(A!39, A!39, F!40))))))))) | surjective(F!40, A!39, A!39)),
% 0.68/0.85 inference(unit_resolution,[status(thm)],[604, 603])).
% 0.68/0.85 tff(606,plain,
% 0.68/0.85 (surjective(F!40, A!39, A!39)),
% 0.68/0.86 inference(unit_resolution,[status(thm)],[605, 570])).
% 0.68/0.86 tff(607,plain,
% 0.68/0.86 ((~((~injective(F!40, A!39, A!39)) | (~surjective(F!40, A!39, A!39)))) | (~injective(F!40, A!39, A!39)) | (~surjective(F!40, A!39, A!39))),
% 0.68/0.86 inference(tautology,[status(thm)],[])).
% 0.68/0.86 tff(608,plain,
% 0.68/0.86 (~injective(F!40, A!39, A!39)),
% 0.68/0.86 inference(unit_resolution,[status(thm)],[607, 606, 548])).
% 0.68/0.86 tff(609,plain,
% 0.68/0.86 ((~(injective(F!40, A!39, A!39) | (~((~member(tptp_fun_Y_16(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_X1_18(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_X2_17(A!39, A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))) | (tptp_fun_X1_18(A!39, A!39, F!40) = tptp_fun_X2_17(A!39, A!39, F!40)))))) | injective(F!40, A!39, A!39) | (~((~member(tptp_fun_Y_16(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_X1_18(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_X2_17(A!39, A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))) | (tptp_fun_X1_18(A!39, A!39, F!40) = tptp_fun_X2_17(A!39, A!39, F!40))))),
% 0.68/0.86 inference(tautology,[status(thm)],[])).
% 0.68/0.86 tff(610,plain,
% 0.68/0.86 ((~(injective(F!40, A!39, A!39) | (~((~member(tptp_fun_Y_16(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_X1_18(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_X2_17(A!39, A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))) | (tptp_fun_X1_18(A!39, A!39, F!40) = tptp_fun_X2_17(A!39, A!39, F!40)))))) | (~((~member(tptp_fun_Y_16(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_X1_18(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_X2_17(A!39, A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))) | (tptp_fun_X1_18(A!39, A!39, F!40) = tptp_fun_X2_17(A!39, A!39, F!40))))),
% 0.68/0.86 inference(unit_resolution,[status(thm)],[609, 608])).
% 0.68/0.86 tff(611,plain,
% 0.68/0.86 (~((~member(tptp_fun_Y_16(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_X1_18(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_X2_17(A!39, A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))) | (tptp_fun_X1_18(A!39, A!39, F!40) = tptp_fun_X2_17(A!39, A!39, F!40)))),
% 0.68/0.86 inference(unit_resolution,[status(thm)],[610, 25])).
% 0.68/0.86 tff(612,plain,
% 0.68/0.86 (((~member(tptp_fun_Y_16(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_X1_18(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_X2_17(A!39, A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))) | (tptp_fun_X1_18(A!39, A!39, F!40) = tptp_fun_X2_17(A!39, A!39, F!40))) | member(tptp_fun_X1_18(A!39, A!39, F!40), A!39)),
% 0.68/0.86 inference(tautology,[status(thm)],[])).
% 0.68/0.86 tff(613,plain,
% 0.68/0.86 (member(tptp_fun_X1_18(A!39, A!39, F!40), A!39)),
% 0.68/0.86 inference(unit_resolution,[status(thm)],[612, 611])).
% 0.68/0.86 tff(614,plain,
% 0.68/0.86 (((~![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!39, A!39, F!40), A!39)) | (~((~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_X1_18(A!39, A!39, F!40)))))) | (~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_X1_18(A!39, A!39, F!40))))))))))) <=> ((~![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!39, A!39, F!40), A!39)) | (~((~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_X1_18(A!39, A!39, F!40)))))) | (~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_X1_18(A!39, A!39, F!40))))))))))),
% 0.68/0.86 inference(rewrite,[status(thm)],[])).
% 0.68/0.86 tff(615,plain,
% 0.68/0.86 (((~member(tptp_fun_X1_18(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_X1_18(A!39, A!39, F!40), A!39)) | (~((~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_X1_18(A!39, A!39, F!40)))))) | (~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_X1_18(A!39, A!39, F!40)))))))))) <=> ((~member(tptp_fun_X1_18(A!39, A!39, F!40), A!39)) | (~((~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_X1_18(A!39, A!39, F!40)))))) | (~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_X1_18(A!39, A!39, F!40))))))))))),
% 0.68/0.86 inference(rewrite,[status(thm)],[])).
% 0.68/0.86 tff(616,plain,
% 0.68/0.86 ((~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_X1_18(A!39, A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_X1_18(A!39, A!39, F!40)))))))) <=> (~((~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_X1_18(A!39, A!39, F!40)))))) | (~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_X1_18(A!39, A!39, F!40)))))))))),
% 0.72/0.86 inference(rewrite,[status(thm)],[])).
% 0.72/0.86 tff(617,plain,
% 0.72/0.86 (((~member(tptp_fun_X1_18(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_X1_18(A!39, A!39, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_X1_18(A!39, A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_X1_18(A!39, A!39, F!40))))))))) <=> ((~member(tptp_fun_X1_18(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_X1_18(A!39, A!39, F!40), A!39)) | (~((~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_X1_18(A!39, A!39, F!40)))))) | (~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_X1_18(A!39, A!39, F!40))))))))))),
% 0.72/0.86 inference(monotonicity,[status(thm)],[616])).
% 0.72/0.86 tff(618,plain,
% 0.72/0.86 (((~member(tptp_fun_X1_18(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_X1_18(A!39, A!39, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_X1_18(A!39, A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_X1_18(A!39, A!39, F!40))))))))) <=> ((~member(tptp_fun_X1_18(A!39, A!39, F!40), A!39)) | (~((~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_X1_18(A!39, A!39, F!40)))))) | (~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_X1_18(A!39, A!39, F!40))))))))))),
% 0.72/0.86 inference(transitivity,[status(thm)],[617, 615])).
% 0.72/0.86 tff(619,plain,
% 0.72/0.86 (((~![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!39, A!39, F!40), A!39)) | (~member(tptp_fun_X1_18(A!39, A!39, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_X1_18(A!39, A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_X1_18(A!39, A!39, F!40)))))))))) <=> ((~![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!39, A!39, F!40), A!39)) | (~((~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_X1_18(A!39, A!39, F!40)))))) | (~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_X1_18(A!39, A!39, F!40)))))))))))),
% 0.72/0.86 inference(monotonicity,[status(thm)],[618])).
% 0.72/0.86 tff(620,plain,
% 0.72/0.86 (((~![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!39, A!39, F!40), A!39)) | (~member(tptp_fun_X1_18(A!39, A!39, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_X1_18(A!39, A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_X1_18(A!39, A!39, F!40)))))))))) <=> ((~![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!39, A!39, F!40), A!39)) | (~((~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_X1_18(A!39, A!39, F!40)))))) | (~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_X1_18(A!39, A!39, F!40))))))))))),
% 0.72/0.87 inference(transitivity,[status(thm)],[619, 614])).
% 0.72/0.87 tff(621,plain,
% 0.72/0.87 ((~![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!39, A!39, F!40), A!39)) | (~member(tptp_fun_X1_18(A!39, A!39, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_X1_18(A!39, A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_X1_18(A!39, A!39, F!40)))))))))),
% 0.72/0.87 inference(quant_inst,[status(thm)],[])).
% 0.72/0.87 tff(622,plain,
% 0.72/0.87 ((~![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!39, A!39, F!40), A!39)) | (~((~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_X1_18(A!39, A!39, F!40)))))) | (~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_X1_18(A!39, A!39, F!40)))))))))),
% 0.72/0.87 inference(modus_ponens,[status(thm)],[621, 620])).
% 0.72/0.87 tff(623,plain,
% 0.72/0.87 (~((~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_X1_18(A!39, A!39, F!40)))))) | (~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_X1_18(A!39, A!39, F!40))))))))),
% 0.72/0.87 inference(unit_resolution,[status(thm)],[622, 134, 613])).
% 0.72/0.87 tff(624,plain,
% 0.72/0.87 (((~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_X1_18(A!39, A!39, F!40)))))) | (~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_X1_18(A!39, A!39, F!40)))))))) | ((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_X1_18(A!39, A!39, F!40))))))),
% 0.72/0.87 inference(tautology,[status(thm)],[])).
% 0.72/0.87 tff(625,plain,
% 0.72/0.87 ((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_X1_18(A!39, A!39, F!40)))))),
% 0.72/0.87 inference(unit_resolution,[status(thm)],[624, 623])).
% 0.72/0.87 tff(626,plain,
% 0.72/0.87 (((~![X: $i] : ((~member(X, A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), X, X))) | ((~member(tptp_fun_X1_18(A!39, A!39, F!40), A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40)))) <=> ((~![X: $i] : ((~member(X, A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), X, X))) | (~member(tptp_fun_X1_18(A!39, A!39, F!40), A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40)))),
% 0.72/0.87 inference(rewrite,[status(thm)],[])).
% 0.72/0.87 tff(627,plain,
% 0.72/0.87 ((~![X: $i] : ((~member(X, A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), X, X))) | ((~member(tptp_fun_X1_18(A!39, A!39, F!40), A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40)))),
% 0.72/0.87 inference(quant_inst,[status(thm)],[])).
% 0.72/0.87 tff(628,plain,
% 0.72/0.87 ((~![X: $i] : ((~member(X, A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), X, X))) | (~member(tptp_fun_X1_18(A!39, A!39, F!40), A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40))),
% 0.72/0.87 inference(modus_ponens,[status(thm)],[627, 626])).
% 0.72/0.87 tff(629,plain,
% 0.72/0.87 (apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40))),
% 0.72/0.87 inference(unit_resolution,[status(thm)],[628, 235, 613])).
% 0.72/0.87 tff(630,plain,
% 0.72/0.87 ((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_X1_18(A!39, A!39, F!40))))))) | (~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_X1_18(A!39, A!39, F!40)))))),
% 0.72/0.87 inference(tautology,[status(thm)],[])).
% 0.72/0.87 tff(631,plain,
% 0.72/0.87 ((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_X1_18(A!39, A!39, F!40))))))) | (~((~member(tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_X1_18(A!39, A!39, F!40)))))),
% 0.72/0.87 inference(unit_resolution,[status(thm)],[630, 629])).
% 0.72/0.87 tff(632,plain,
% 0.72/0.87 (~((~member(tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_X1_18(A!39, A!39, F!40))))),
% 0.72/0.88 inference(unit_resolution,[status(thm)],[631, 625])).
% 0.72/0.88 tff(633,plain,
% 0.72/0.88 (((~member(tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_X1_18(A!39, A!39, F!40)))) | apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40))),
% 0.72/0.88 inference(tautology,[status(thm)],[])).
% 0.72/0.88 tff(634,plain,
% 0.72/0.88 (apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40))),
% 0.72/0.88 inference(unit_resolution,[status(thm)],[633, 632])).
% 0.72/0.88 tff(635,plain,
% 0.72/0.88 (((~member(tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_X1_18(A!39, A!39, F!40)))) | member(tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40), A!39)),
% 0.72/0.88 inference(tautology,[status(thm)],[])).
% 0.72/0.88 tff(636,plain,
% 0.72/0.88 (member(tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40), A!39)),
% 0.72/0.88 inference(unit_resolution,[status(thm)],[635, 632])).
% 0.72/0.88 tff(637,plain,
% 0.72/0.88 (((~member(tptp_fun_Y_16(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_X1_18(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_X2_17(A!39, A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))) | (tptp_fun_X1_18(A!39, A!39, F!40) = tptp_fun_X2_17(A!39, A!39, F!40))) | apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))),
% 0.72/0.88 inference(tautology,[status(thm)],[])).
% 0.72/0.88 tff(638,plain,
% 0.72/0.88 (apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))),
% 0.72/0.88 inference(unit_resolution,[status(thm)],[637, 611])).
% 0.72/0.88 tff(639,plain,
% 0.72/0.88 (((~member(tptp_fun_Y_16(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_X1_18(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_X2_17(A!39, A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))) | (tptp_fun_X1_18(A!39, A!39, F!40) = tptp_fun_X2_17(A!39, A!39, F!40))) | member(tptp_fun_Y_16(A!39, A!39, F!40), A!39)),
% 0.72/0.88 inference(tautology,[status(thm)],[])).
% 0.72/0.88 tff(640,plain,
% 0.72/0.88 (member(tptp_fun_Y_16(A!39, A!39, F!40), A!39)),
% 0.72/0.88 inference(unit_resolution,[status(thm)],[639, 611])).
% 0.72/0.88 tff(641,plain,
% 0.72/0.88 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | ((~member(tptp_fun_Y_16(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_X1_18(A!39, A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40))) | (~member(tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_16(A!39, A!39, F!40)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | (~member(tptp_fun_Y_16(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_X1_18(A!39, A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40))) | (~member(tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_16(A!39, A!39, F!40)))),
% 0.72/0.88 inference(rewrite,[status(thm)],[])).
% 0.72/0.88 tff(642,plain,
% 0.72/0.88 (((tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_16(A!39, A!39, F!40)) | (~member(tptp_fun_Y_16(A!39, A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))) | (~member(tptp_fun_X1_18(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40), A!39))) <=> ((~member(tptp_fun_Y_16(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_X1_18(A!39, A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40))) | (~member(tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_16(A!39, A!39, F!40)))),
% 0.72/0.88 inference(rewrite,[status(thm)],[])).
% 0.72/0.88 tff(643,plain,
% 0.72/0.88 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | ((tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_16(A!39, A!39, F!40)) | (~member(tptp_fun_Y_16(A!39, A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))) | (~member(tptp_fun_X1_18(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40), A!39)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | ((~member(tptp_fun_Y_16(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_X1_18(A!39, A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40))) | (~member(tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_16(A!39, A!39, F!40))))),
% 0.72/0.88 inference(monotonicity,[status(thm)],[642])).
% 0.72/0.88 tff(644,plain,
% 0.72/0.88 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | ((tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_16(A!39, A!39, F!40)) | (~member(tptp_fun_Y_16(A!39, A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))) | (~member(tptp_fun_X1_18(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40), A!39)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | (~member(tptp_fun_Y_16(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_X1_18(A!39, A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40))) | (~member(tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_16(A!39, A!39, F!40)))),
% 0.72/0.88 inference(transitivity,[status(thm)],[643, 641])).
% 0.72/0.88 tff(645,plain,
% 0.72/0.88 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | ((tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_16(A!39, A!39, F!40)) | (~member(tptp_fun_Y_16(A!39, A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))) | (~member(tptp_fun_X1_18(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40), A!39)))),
% 0.72/0.88 inference(quant_inst,[status(thm)],[])).
% 0.72/0.88 tff(646,plain,
% 0.72/0.88 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | (~member(tptp_fun_Y_16(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_X1_18(A!39, A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40))) | (~member(tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_16(A!39, A!39, F!40))),
% 0.72/0.88 inference(modus_ponens,[status(thm)],[645, 644])).
% 0.72/0.88 tff(647,plain,
% 0.72/0.88 (tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_16(A!39, A!39, F!40)),
% 0.72/0.88 inference(unit_resolution,[status(thm)],[646, 256, 640, 613, 638, 636, 634])).
% 0.72/0.88 tff(648,plain,
% 0.72/0.88 (tptp_fun_Y_16(A!39, A!39, F!40) = tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40)),
% 0.72/0.88 inference(symmetry,[status(thm)],[647])).
% 0.72/0.88 tff(649,plain,
% 0.72/0.88 (apply(F!40, tptp_fun_Y_16(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40)) <=> apply(F!40, tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_X1_18(A!39, A!39, F!40))),
% 0.72/0.88 inference(monotonicity,[status(thm)],[648])).
% 0.72/0.88 tff(650,plain,
% 0.72/0.88 (apply(F!40, tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_X1_18(A!39, A!39, F!40)) <=> apply(F!40, tptp_fun_Y_16(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40))),
% 0.72/0.88 inference(symmetry,[status(thm)],[649])).
% 0.72/0.88 tff(651,plain,
% 0.72/0.88 (((~member(tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_X1_18(A!39, A!39, F!40)))) | apply(F!40, tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_X1_18(A!39, A!39, F!40))),
% 0.72/0.88 inference(tautology,[status(thm)],[])).
% 0.72/0.88 tff(652,plain,
% 0.72/0.88 (apply(F!40, tptp_fun_Y_8(tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_X1_18(A!39, A!39, F!40))),
% 0.72/0.88 inference(unit_resolution,[status(thm)],[651, 632])).
% 0.72/0.88 tff(653,plain,
% 0.72/0.88 (apply(F!40, tptp_fun_Y_16(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40))),
% 0.72/0.88 inference(modus_ponens,[status(thm)],[652, 650])).
% 0.72/0.88 tff(654,plain,
% 0.72/0.88 (((~member(tptp_fun_Y_16(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_X1_18(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_X2_17(A!39, A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))) | (tptp_fun_X1_18(A!39, A!39, F!40) = tptp_fun_X2_17(A!39, A!39, F!40))) | member(tptp_fun_X2_17(A!39, A!39, F!40), A!39)),
% 0.72/0.88 inference(tautology,[status(thm)],[])).
% 0.72/0.88 tff(655,plain,
% 0.72/0.88 (member(tptp_fun_X2_17(A!39, A!39, F!40), A!39)),
% 0.72/0.88 inference(unit_resolution,[status(thm)],[654, 611])).
% 0.72/0.88 tff(656,plain,
% 0.72/0.88 (((~![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!39, A!39, F!40), A!39)) | (~((~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_X2_17(A!39, A!39, F!40)))))) | (~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_X2_17(A!39, A!39, F!40))))))))))) <=> ((~![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!39, A!39, F!40), A!39)) | (~((~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_X2_17(A!39, A!39, F!40)))))) | (~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_X2_17(A!39, A!39, F!40))))))))))),
% 0.72/0.88 inference(rewrite,[status(thm)],[])).
% 0.72/0.88 tff(657,plain,
% 0.72/0.88 (((~member(tptp_fun_X2_17(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_X2_17(A!39, A!39, F!40), A!39)) | (~((~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_X2_17(A!39, A!39, F!40)))))) | (~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_X2_17(A!39, A!39, F!40)))))))))) <=> ((~member(tptp_fun_X2_17(A!39, A!39, F!40), A!39)) | (~((~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_X2_17(A!39, A!39, F!40)))))) | (~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_X2_17(A!39, A!39, F!40))))))))))),
% 0.72/0.89 inference(rewrite,[status(thm)],[])).
% 0.72/0.89 tff(658,plain,
% 0.72/0.89 ((~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_X2_17(A!39, A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_X2_17(A!39, A!39, F!40)))))))) <=> (~((~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_X2_17(A!39, A!39, F!40)))))) | (~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_X2_17(A!39, A!39, F!40)))))))))),
% 0.72/0.89 inference(rewrite,[status(thm)],[])).
% 0.72/0.89 tff(659,plain,
% 0.72/0.89 (((~member(tptp_fun_X2_17(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_X2_17(A!39, A!39, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_X2_17(A!39, A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_X2_17(A!39, A!39, F!40))))))))) <=> ((~member(tptp_fun_X2_17(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_X2_17(A!39, A!39, F!40), A!39)) | (~((~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_X2_17(A!39, A!39, F!40)))))) | (~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_X2_17(A!39, A!39, F!40))))))))))),
% 0.72/0.89 inference(monotonicity,[status(thm)],[658])).
% 0.72/0.89 tff(660,plain,
% 0.72/0.89 (((~member(tptp_fun_X2_17(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_X2_17(A!39, A!39, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_X2_17(A!39, A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_X2_17(A!39, A!39, F!40))))))))) <=> ((~member(tptp_fun_X2_17(A!39, A!39, F!40), A!39)) | (~((~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_X2_17(A!39, A!39, F!40)))))) | (~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_X2_17(A!39, A!39, F!40))))))))))),
% 0.72/0.89 inference(transitivity,[status(thm)],[659, 657])).
% 0.72/0.89 tff(661,plain,
% 0.72/0.89 (((~![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!39, A!39, F!40), A!39)) | (~member(tptp_fun_X2_17(A!39, A!39, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_X2_17(A!39, A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_X2_17(A!39, A!39, F!40)))))))))) <=> ((~![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!39, A!39, F!40), A!39)) | (~((~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_X2_17(A!39, A!39, F!40)))))) | (~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_X2_17(A!39, A!39, F!40)))))))))))),
% 0.72/0.89 inference(monotonicity,[status(thm)],[660])).
% 0.72/0.89 tff(662,plain,
% 0.72/0.89 (((~![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!39, A!39, F!40), A!39)) | (~member(tptp_fun_X2_17(A!39, A!39, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_X2_17(A!39, A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_X2_17(A!39, A!39, F!40)))))))))) <=> ((~![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!39, A!39, F!40), A!39)) | (~((~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_X2_17(A!39, A!39, F!40)))))) | (~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_X2_17(A!39, A!39, F!40))))))))))),
% 0.72/0.89 inference(transitivity,[status(thm)],[661, 656])).
% 0.72/0.89 tff(663,plain,
% 0.72/0.89 ((~![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!39, A!39, F!40), A!39)) | (~member(tptp_fun_X2_17(A!39, A!39, F!40), A!39)) | (~((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_X2_17(A!39, A!39, F!40))))))) | (~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_X2_17(A!39, A!39, F!40)))))))))),
% 0.72/0.89 inference(quant_inst,[status(thm)],[])).
% 0.72/0.89 tff(664,plain,
% 0.72/0.89 ((~![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!39, A!39, F!40), A!39)) | (~((~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_X2_17(A!39, A!39, F!40)))))) | (~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_X2_17(A!39, A!39, F!40)))))))))),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[663, 662])).
% 0.72/0.89 tff(665,plain,
% 0.72/0.89 (~((~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_X2_17(A!39, A!39, F!40)))))) | (~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_X2_17(A!39, A!39, F!40))))))))),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[664, 134, 655])).
% 0.72/0.90 tff(666,plain,
% 0.72/0.90 (((~(apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40)) | ![Y: $i] : ((~member(Y, A!39)) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), Y)) | (~apply(F!40, Y, tptp_fun_X2_17(A!39, A!39, F!40)))))) | (~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_X2_17(A!39, A!39, F!40)))))))) | ((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_X2_17(A!39, A!39, F!40))))))),
% 0.72/0.90 inference(tautology,[status(thm)],[])).
% 0.72/0.90 tff(667,plain,
% 0.72/0.90 ((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_X2_17(A!39, A!39, F!40)))))),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[666, 665])).
% 0.72/0.90 tff(668,plain,
% 0.72/0.90 (((~![X: $i] : ((~member(X, A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), X, X))) | ((~member(tptp_fun_X2_17(A!39, A!39, F!40), A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40)))) <=> ((~![X: $i] : ((~member(X, A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), X, X))) | (~member(tptp_fun_X2_17(A!39, A!39, F!40), A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40)))),
% 0.72/0.90 inference(rewrite,[status(thm)],[])).
% 0.72/0.90 tff(669,plain,
% 0.72/0.90 ((~![X: $i] : ((~member(X, A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), X, X))) | ((~member(tptp_fun_X2_17(A!39, A!39, F!40), A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40)))),
% 0.72/0.90 inference(quant_inst,[status(thm)],[])).
% 0.72/0.90 tff(670,plain,
% 0.72/0.90 ((~![X: $i] : ((~member(X, A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), X, X))) | (~member(tptp_fun_X2_17(A!39, A!39, F!40), A!39)) | apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40))),
% 0.72/0.90 inference(modus_ponens,[status(thm)],[669, 668])).
% 0.72/0.90 tff(671,plain,
% 0.72/0.90 (apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40))),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[670, 235, 655])).
% 0.72/0.90 tff(672,plain,
% 0.72/0.90 ((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_X2_17(A!39, A!39, F!40))))))) | (~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_X2_17(A!39, A!39, F!40)))))),
% 0.72/0.90 inference(tautology,[status(thm)],[])).
% 0.72/0.90 tff(673,plain,
% 0.72/0.90 ((~((~apply(compose_function(F!40, F!40, A!39, A!39, A!39), tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40))) | (~((~member(tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_X2_17(A!39, A!39, F!40))))))) | (~((~member(tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_X2_17(A!39, A!39, F!40)))))),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[672, 671])).
% 0.72/0.90 tff(674,plain,
% 0.72/0.90 (~((~member(tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_X2_17(A!39, A!39, F!40))))),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[673, 667])).
% 0.72/0.90 tff(675,plain,
% 0.72/0.90 (((~member(tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_X2_17(A!39, A!39, F!40)))) | apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40))),
% 0.72/0.90 inference(tautology,[status(thm)],[])).
% 0.72/0.90 tff(676,plain,
% 0.72/0.90 (apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40))),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[675, 674])).
% 0.72/0.90 tff(677,plain,
% 0.72/0.90 (((~member(tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_X2_17(A!39, A!39, F!40)))) | member(tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40), A!39)),
% 0.72/0.90 inference(tautology,[status(thm)],[])).
% 0.72/0.90 tff(678,plain,
% 0.72/0.90 (member(tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40), A!39)),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[677, 674])).
% 0.72/0.90 tff(679,plain,
% 0.72/0.90 (((~member(tptp_fun_Y_16(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_X1_18(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_X2_17(A!39, A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))) | (tptp_fun_X1_18(A!39, A!39, F!40) = tptp_fun_X2_17(A!39, A!39, F!40))) | apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))),
% 0.72/0.90 inference(tautology,[status(thm)],[])).
% 0.72/0.90 tff(680,plain,
% 0.72/0.90 (apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[679, 611])).
% 0.72/0.90 tff(681,plain,
% 0.72/0.90 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | ((~member(tptp_fun_Y_16(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_X2_17(A!39, A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40))) | (~member(tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_16(A!39, A!39, F!40)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | (~member(tptp_fun_Y_16(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_X2_17(A!39, A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40))) | (~member(tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_16(A!39, A!39, F!40)))),
% 0.72/0.90 inference(rewrite,[status(thm)],[])).
% 0.72/0.90 tff(682,plain,
% 0.72/0.90 (((tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_16(A!39, A!39, F!40)) | (~member(tptp_fun_Y_16(A!39, A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))) | (~member(tptp_fun_X2_17(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40), A!39))) <=> ((~member(tptp_fun_Y_16(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_X2_17(A!39, A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40))) | (~member(tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_16(A!39, A!39, F!40)))),
% 0.72/0.90 inference(rewrite,[status(thm)],[])).
% 0.72/0.90 tff(683,plain,
% 0.72/0.90 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | ((tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_16(A!39, A!39, F!40)) | (~member(tptp_fun_Y_16(A!39, A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))) | (~member(tptp_fun_X2_17(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40), A!39)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | ((~member(tptp_fun_Y_16(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_X2_17(A!39, A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40))) | (~member(tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_16(A!39, A!39, F!40))))),
% 0.72/0.91 inference(monotonicity,[status(thm)],[682])).
% 0.72/0.91 tff(684,plain,
% 0.72/0.91 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | ((tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_16(A!39, A!39, F!40)) | (~member(tptp_fun_Y_16(A!39, A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))) | (~member(tptp_fun_X2_17(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40), A!39)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | (~member(tptp_fun_Y_16(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_X2_17(A!39, A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40))) | (~member(tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_16(A!39, A!39, F!40)))),
% 0.72/0.91 inference(transitivity,[status(thm)],[683, 681])).
% 0.72/0.91 tff(685,plain,
% 0.72/0.91 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | ((tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_16(A!39, A!39, F!40)) | (~member(tptp_fun_Y_16(A!39, A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))) | (~member(tptp_fun_X2_17(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40), A!39)))),
% 0.72/0.91 inference(quant_inst,[status(thm)],[])).
% 0.72/0.91 tff(686,plain,
% 0.72/0.91 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | (~member(tptp_fun_Y_16(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_X2_17(A!39, A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40))) | (~member(tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_16(A!39, A!39, F!40))),
% 0.72/0.91 inference(modus_ponens,[status(thm)],[685, 684])).
% 0.72/0.91 tff(687,plain,
% 0.72/0.91 (tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40) = tptp_fun_Y_16(A!39, A!39, F!40)),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[686, 256, 640, 655, 680, 678, 676])).
% 0.72/0.91 tff(688,plain,
% 0.72/0.91 (tptp_fun_Y_16(A!39, A!39, F!40) = tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40)),
% 0.72/0.91 inference(symmetry,[status(thm)],[687])).
% 0.72/0.91 tff(689,plain,
% 0.72/0.91 (apply(F!40, tptp_fun_Y_16(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40)) <=> apply(F!40, tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_X2_17(A!39, A!39, F!40))),
% 0.72/0.91 inference(monotonicity,[status(thm)],[688])).
% 0.72/0.91 tff(690,plain,
% 0.72/0.91 (apply(F!40, tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_X2_17(A!39, A!39, F!40)) <=> apply(F!40, tptp_fun_Y_16(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40))),
% 0.72/0.91 inference(symmetry,[status(thm)],[689])).
% 0.72/0.91 tff(691,plain,
% 0.72/0.91 (((~member(tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40), A!39)) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40))) | (~apply(F!40, tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_X2_17(A!39, A!39, F!40)))) | apply(F!40, tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_X2_17(A!39, A!39, F!40))),
% 0.72/0.91 inference(tautology,[status(thm)],[])).
% 0.72/0.91 tff(692,plain,
% 0.72/0.91 (apply(F!40, tptp_fun_Y_8(tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40), A!39, F!40, F!40), tptp_fun_X2_17(A!39, A!39, F!40))),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[691, 674])).
% 0.72/0.91 tff(693,plain,
% 0.72/0.91 (apply(F!40, tptp_fun_Y_16(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40))),
% 0.72/0.91 inference(modus_ponens,[status(thm)],[692, 690])).
% 0.72/0.91 tff(694,plain,
% 0.72/0.91 ((tptp_fun_X2_17(A!39, A!39, F!40) = tptp_fun_X1_18(A!39, A!39, F!40)) <=> (tptp_fun_X1_18(A!39, A!39, F!40) = tptp_fun_X2_17(A!39, A!39, F!40))),
% 0.72/0.91 inference(commutativity,[status(thm)],[])).
% 0.72/0.91 tff(695,plain,
% 0.72/0.91 ((tptp_fun_X1_18(A!39, A!39, F!40) = tptp_fun_X2_17(A!39, A!39, F!40)) <=> (tptp_fun_X2_17(A!39, A!39, F!40) = tptp_fun_X1_18(A!39, A!39, F!40))),
% 0.72/0.91 inference(symmetry,[status(thm)],[694])).
% 0.72/0.91 tff(696,plain,
% 0.72/0.91 ((~(tptp_fun_X1_18(A!39, A!39, F!40) = tptp_fun_X2_17(A!39, A!39, F!40))) <=> (~(tptp_fun_X2_17(A!39, A!39, F!40) = tptp_fun_X1_18(A!39, A!39, F!40)))),
% 0.72/0.91 inference(monotonicity,[status(thm)],[695])).
% 0.72/0.91 tff(697,plain,
% 0.72/0.91 (((~member(tptp_fun_Y_16(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_X1_18(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_X2_17(A!39, A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_X2_17(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))) | (~apply(F!40, tptp_fun_X1_18(A!39, A!39, F!40), tptp_fun_Y_16(A!39, A!39, F!40))) | (tptp_fun_X1_18(A!39, A!39, F!40) = tptp_fun_X2_17(A!39, A!39, F!40))) | (~(tptp_fun_X1_18(A!39, A!39, F!40) = tptp_fun_X2_17(A!39, A!39, F!40)))),
% 0.72/0.91 inference(tautology,[status(thm)],[])).
% 0.72/0.91 tff(698,plain,
% 0.72/0.91 (~(tptp_fun_X1_18(A!39, A!39, F!40) = tptp_fun_X2_17(A!39, A!39, F!40))),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[697, 611])).
% 0.72/0.91 tff(699,plain,
% 0.72/0.91 (~(tptp_fun_X2_17(A!39, A!39, F!40) = tptp_fun_X1_18(A!39, A!39, F!40))),
% 0.72/0.91 inference(modus_ponens,[status(thm)],[698, 696])).
% 0.72/0.91 tff(700,plain,
% 0.72/0.91 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | ((~member(tptp_fun_Y_16(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_X1_18(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_X2_17(A!39, A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_16(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40))) | (tptp_fun_X2_17(A!39, A!39, F!40) = tptp_fun_X1_18(A!39, A!39, F!40)) | (~apply(F!40, tptp_fun_Y_16(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40))))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | (~member(tptp_fun_Y_16(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_X1_18(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_X2_17(A!39, A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_16(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40))) | (tptp_fun_X2_17(A!39, A!39, F!40) = tptp_fun_X1_18(A!39, A!39, F!40)) | (~apply(F!40, tptp_fun_Y_16(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40))))),
% 0.72/0.91 inference(rewrite,[status(thm)],[])).
% 0.72/0.91 tff(701,plain,
% 0.72/0.91 (((tptp_fun_X2_17(A!39, A!39, F!40) = tptp_fun_X1_18(A!39, A!39, F!40)) | (~member(tptp_fun_X1_18(A!39, A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_16(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40))) | (~apply(F!40, tptp_fun_Y_16(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40))) | (~member(tptp_fun_Y_16(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_X2_17(A!39, A!39, F!40), A!39))) <=> ((~member(tptp_fun_Y_16(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_X1_18(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_X2_17(A!39, A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_16(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40))) | (tptp_fun_X2_17(A!39, A!39, F!40) = tptp_fun_X1_18(A!39, A!39, F!40)) | (~apply(F!40, tptp_fun_Y_16(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40))))),
% 0.72/0.91 inference(rewrite,[status(thm)],[])).
% 0.72/0.91 tff(702,plain,
% 0.72/0.91 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | ((tptp_fun_X2_17(A!39, A!39, F!40) = tptp_fun_X1_18(A!39, A!39, F!40)) | (~member(tptp_fun_X1_18(A!39, A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_16(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40))) | (~apply(F!40, tptp_fun_Y_16(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40))) | (~member(tptp_fun_Y_16(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_X2_17(A!39, A!39, F!40), A!39)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | ((~member(tptp_fun_Y_16(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_X1_18(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_X2_17(A!39, A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_16(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40))) | (tptp_fun_X2_17(A!39, A!39, F!40) = tptp_fun_X1_18(A!39, A!39, F!40)) | (~apply(F!40, tptp_fun_Y_16(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40)))))),
% 0.72/0.91 inference(monotonicity,[status(thm)],[701])).
% 0.72/0.91 tff(703,plain,
% 0.72/0.91 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | ((tptp_fun_X2_17(A!39, A!39, F!40) = tptp_fun_X1_18(A!39, A!39, F!40)) | (~member(tptp_fun_X1_18(A!39, A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_16(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40))) | (~apply(F!40, tptp_fun_Y_16(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40))) | (~member(tptp_fun_Y_16(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_X2_17(A!39, A!39, F!40), A!39)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | (~member(tptp_fun_Y_16(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_X1_18(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_X2_17(A!39, A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_16(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40))) | (tptp_fun_X2_17(A!39, A!39, F!40) = tptp_fun_X1_18(A!39, A!39, F!40)) | (~apply(F!40, tptp_fun_Y_16(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40))))),
% 0.72/0.91 inference(transitivity,[status(thm)],[702, 700])).
% 0.72/0.91 tff(704,plain,
% 0.72/0.91 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | ((tptp_fun_X2_17(A!39, A!39, F!40) = tptp_fun_X1_18(A!39, A!39, F!40)) | (~member(tptp_fun_X1_18(A!39, A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_16(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40))) | (~apply(F!40, tptp_fun_Y_16(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40))) | (~member(tptp_fun_Y_16(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_X2_17(A!39, A!39, F!40), A!39)))),
% 0.72/0.91 inference(quant_inst,[status(thm)],[])).
% 0.72/0.91 tff(705,plain,
% 0.72/0.91 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!39)) | (~apply(F!40, X, Y1)) | (~apply(F!40, X, Y2)) | (~member(X, A!39)) | (~member(Y1, A!39)))) | (~member(tptp_fun_Y_16(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_X1_18(A!39, A!39, F!40), A!39)) | (~member(tptp_fun_X2_17(A!39, A!39, F!40), A!39)) | (~apply(F!40, tptp_fun_Y_16(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40))) | (tptp_fun_X2_17(A!39, A!39, F!40) = tptp_fun_X1_18(A!39, A!39, F!40)) | (~apply(F!40, tptp_fun_Y_16(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40)))),
% 0.72/0.91 inference(modus_ponens,[status(thm)],[704, 703])).
% 0.72/0.91 tff(706,plain,
% 0.72/0.91 ((~apply(F!40, tptp_fun_Y_16(A!39, A!39, F!40), tptp_fun_X2_17(A!39, A!39, F!40))) | (tptp_fun_X2_17(A!39, A!39, F!40) = tptp_fun_X1_18(A!39, A!39, F!40)) | (~apply(F!40, tptp_fun_Y_16(A!39, A!39, F!40), tptp_fun_X1_18(A!39, A!39, F!40)))),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[705, 256, 640, 613, 655])).
% 0.72/0.91 tff(707,plain,
% 0.72/0.91 ($false),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[706, 699, 693, 653])).
% 0.72/0.91 % SZS output end Proof
% 0.72/0.91 % E exiting
%------------------------------------------------------------------------------