%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET710+4 : TPTP v9.0.0. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:26:11 AM UTC 2025
% Result : Theorem 0.20s 0.40s
% Output : Proof 0.89s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET710+4 : TPTP v9.0.0. Bugfixed v2.2.1.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n003.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 05:38:54 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.20/0.40 % SZS status Theorem
% 0.20/0.40 % SZS output start Proof
% 0.20/0.40 tff(tptp_fun_Y2_12_type, type, (
% 0.20/0.40 tptp_fun_Y2_12: ( $i * $i * $i * $i ) > $i)).
% 0.20/0.40 tff(compose_function_type, type, (
% 0.20/0.40 compose_function: ( $i * $i * $i * $i * $i ) > $i)).
% 0.20/0.40 tff(tptp_fun_D_39_type, type, (
% 0.20/0.40 tptp_fun_D_39: $i)).
% 0.20/0.40 tff(tptp_fun_C_40_type, type, (
% 0.20/0.40 tptp_fun_C_40: $i)).
% 0.20/0.40 tff(tptp_fun_A_42_type, type, (
% 0.20/0.40 tptp_fun_A_42: $i)).
% 0.20/0.40 tff(tptp_fun_B_41_type, type, (
% 0.20/0.40 tptp_fun_B_41: $i)).
% 0.20/0.40 tff(tptp_fun_F_45_type, type, (
% 0.20/0.40 tptp_fun_F_45: $i)).
% 0.20/0.40 tff(tptp_fun_G_44_type, type, (
% 0.20/0.40 tptp_fun_G_44: $i)).
% 0.20/0.40 tff(tptp_fun_H_43_type, type, (
% 0.20/0.40 tptp_fun_H_43: $i)).
% 0.20/0.40 tff(tptp_fun_Y1_13_type, type, (
% 0.20/0.40 tptp_fun_Y1_13: ( $i * $i * $i * $i ) > $i)).
% 0.20/0.40 tff(tptp_fun_Y_3_type, type, (
% 0.20/0.40 tptp_fun_Y_3: ( $i * $i * $i ) > $i)).
% 0.20/0.40 tff(tptp_fun_Y_8_type, type, (
% 0.20/0.40 tptp_fun_Y_8: ( $i * $i * $i * $i * $i ) > $i)).
% 0.20/0.40 tff(tptp_fun_X_14_type, type, (
% 0.20/0.40 tptp_fun_X_14: ( $i * $i * $i * $i ) > $i)).
% 0.20/0.40 tff(apply_type, type, (
% 0.20/0.40 apply: ( $i * $i * $i ) > $o)).
% 0.20/0.40 tff(member_type, type, (
% 0.20/0.40 member: ( $i * $i ) > $o)).
% 0.20/0.40 tff(equal_maps_type, type, (
% 0.20/0.40 equal_maps: ( $i * $i * $i * $i ) > $o)).
% 0.20/0.40 tff(maps_type, type, (
% 0.20/0.40 maps: ( $i * $i * $i ) > $o)).
% 0.20/0.40 tff(tptp_fun_Y2_5_type, type, (
% 0.20/0.40 tptp_fun_Y2_5: ( $i * $i * $i ) > $i)).
% 0.20/0.40 tff(tptp_fun_Y1_6_type, type, (
% 0.20/0.40 tptp_fun_Y1_6: ( $i * $i * $i ) > $i)).
% 0.20/0.40 tff(tptp_fun_X_7_type, type, (
% 0.20/0.40 tptp_fun_X_7: ( $i * $i * $i ) > $i)).
% 0.20/0.40 tff(tptp_fun_X_4_type, type, (
% 0.20/0.40 tptp_fun_X_4: ( $i * $i * $i ) > $i)).
% 0.20/0.40 tff(1,plain,
% 0.20/0.40 (^[F: $i, G: $i, A: $i, B: $i] : refl((~((~((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1))))) | (~(equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F))))))))) <=> (~((~((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1))))) | (~(equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F))))))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(2,plain,
% 0.20/0.40 (![F: $i, G: $i, A: $i, B: $i] : (~((~((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1))))) | (~(equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F))))))))) <=> ![F: $i, G: $i, A: $i, B: $i] : (~((~((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1))))) | (~(equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F)))))))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.40 tff(3,plain,
% 0.20/0.40 (^[F: $i, G: $i, A: $i, B: $i] : rewrite((~((~((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1))))) | (~(equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F))))))))) <=> (~((~((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1))))) | (~(equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F))))))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(4,plain,
% 0.20/0.40 (![F: $i, G: $i, A: $i, B: $i] : (~((~((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1))))) | (~(equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F))))))))) <=> ![F: $i, G: $i, A: $i, B: $i] : (~((~((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1))))) | (~(equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F)))))))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[3])).
% 0.20/0.40 tff(5,plain,
% 0.20/0.40 (![F: $i, G: $i, A: $i, B: $i] : (~((~((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1))))) | (~(equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F))))))))) <=> ![F: $i, G: $i, A: $i, B: $i] : (~((~((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1))))) | (~(equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F)))))))))),
% 0.20/0.40 inference(transitivity,[status(thm)],[4, 2])).
% 0.20/0.40 tff(6,plain,
% 0.20/0.40 (^[F: $i, G: $i, A: $i, B: $i] : trans(monotonicity(rewrite(((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(member(X, A) & member(Y1, B) & member(Y2, B))) | (~(apply(F, X, Y1) & apply(G, X, Y2))))) <=> ((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1))))), trans(monotonicity(rewrite((~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~(member(tptp_fun_X_14(B, A, G, F), A) & member(tptp_fun_Y1_13(B, A, G, F), B) & member(tptp_fun_Y2_12(B, A, G, F), B))) | (~(apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F)) & apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F)))))) <=> (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F)))))), ((equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~(member(tptp_fun_X_14(B, A, G, F), A) & member(tptp_fun_Y1_13(B, A, G, F), B) & member(tptp_fun_Y2_12(B, A, G, F), B))) | (~(apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F)) & apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F))))))) <=> (equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F)))))))), rewrite((equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F)))))) <=> (equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F))))))), ((equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~(member(tptp_fun_X_14(B, A, G, F), A) & member(tptp_fun_Y1_13(B, A, G, F), B) & member(tptp_fun_Y2_12(B, A, G, F), B))) | (~(apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F)) & apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F))))))) <=> (equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F)))))))), ((((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(member(X, A) & member(Y1, B) & member(Y2, B))) | (~(apply(F, X, Y1) & apply(G, X, Y2))))) & (equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~(member(tptp_fun_X_14(B, A, G, F), A) & member(tptp_fun_Y1_13(B, A, G, F), B) & member(tptp_fun_Y2_12(B, A, G, F), B))) | (~(apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F)) & apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F)))))))) <=> (((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1)))) & (equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F))))))))), rewrite((((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1)))) & (equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F))))))) <=> (~((~((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1))))) | (~(equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F)))))))))), ((((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(member(X, A) & member(Y1, B) & member(Y2, B))) | (~(apply(F, X, Y1) & apply(G, X, Y2))))) & (equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~(member(tptp_fun_X_14(B, A, G, F), A) & member(tptp_fun_Y1_13(B, A, G, F), B) & member(tptp_fun_Y2_12(B, A, G, F), B))) | (~(apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F)) & apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F)))))))) <=> (~((~((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1))))) | (~(equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F)))))))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(7,plain,
% 0.20/0.40 (![F: $i, G: $i, A: $i, B: $i] : (((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(member(X, A) & member(Y1, B) & member(Y2, B))) | (~(apply(F, X, Y1) & apply(G, X, Y2))))) & (equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~(member(tptp_fun_X_14(B, A, G, F), A) & member(tptp_fun_Y1_13(B, A, G, F), B) & member(tptp_fun_Y2_12(B, A, G, F), B))) | (~(apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F)) & apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F)))))))) <=> ![F: $i, G: $i, A: $i, B: $i] : (~((~((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1))))) | (~(equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F)))))))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[6])).
% 0.20/0.40 tff(8,plain,
% 0.20/0.40 (![F: $i, G: $i, A: $i, B: $i] : (equal_maps(F, G, A, B) <=> ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(member(X, A) & member(Y1, B) & member(Y2, B))) | (~(apply(F, X, Y1) & apply(G, X, Y2))))) <=> ![F: $i, G: $i, A: $i, B: $i] : (equal_maps(F, G, A, B) <=> ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(member(X, A) & member(Y1, B) & member(Y2, B))) | (~(apply(F, X, Y1) & apply(G, X, Y2)))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(9,plain,
% 0.20/0.40 (^[F: $i, G: $i, A: $i, B: $i] : rewrite((equal_maps(F, G, A, B) <=> ![X: $i, Y1: $i, Y2: $i] : (((member(X, A) & member(Y1, B)) & member(Y2, B)) => ((apply(F, X, Y1) & apply(G, X, Y2)) => (Y1 = Y2)))) <=> (equal_maps(F, G, A, B) <=> ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(member(X, A) & member(Y1, B) & member(Y2, B))) | (~(apply(F, X, Y1) & apply(G, X, Y2))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(10,plain,
% 0.20/0.40 (![F: $i, G: $i, A: $i, B: $i] : (equal_maps(F, G, A, B) <=> ![X: $i, Y1: $i, Y2: $i] : (((member(X, A) & member(Y1, B)) & member(Y2, B)) => ((apply(F, X, Y1) & apply(G, X, Y2)) => (Y1 = Y2)))) <=> ![F: $i, G: $i, A: $i, B: $i] : (equal_maps(F, G, A, B) <=> ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(member(X, A) & member(Y1, B) & member(Y2, B))) | (~(apply(F, X, Y1) & apply(G, X, Y2)))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[9])).
% 0.20/0.40 tff(11,axiom,(![F: $i, G: $i, A: $i, B: $i] : (equal_maps(F, G, A, B) <=> ![X: $i, Y1: $i, Y2: $i] : (((member(X, A) & member(Y1, B)) & member(Y2, B)) => ((apply(F, X, Y1) & apply(G, X, Y2)) => (Y1 = Y2))))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+1.ax','equal_maps')).
% 0.20/0.40 tff(12,plain,
% 0.20/0.40 (![F: $i, G: $i, A: $i, B: $i] : (equal_maps(F, G, A, B) <=> ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(member(X, A) & member(Y1, B) & member(Y2, B))) | (~(apply(F, X, Y1) & apply(G, X, Y2)))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.20/0.40 tff(13,plain,
% 0.20/0.40 (![F: $i, G: $i, A: $i, B: $i] : (equal_maps(F, G, A, B) <=> ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(member(X, A) & member(Y1, B) & member(Y2, B))) | (~(apply(F, X, Y1) & apply(G, X, Y2)))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[12, 8])).
% 0.20/0.40 tff(14,plain,(
% 0.20/0.40 ![F: $i, G: $i, A: $i, B: $i] : (((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(member(X, A) & member(Y1, B) & member(Y2, B))) | (~(apply(F, X, Y1) & apply(G, X, Y2))))) & (equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~(member(tptp_fun_X_14(B, A, G, F), A) & member(tptp_fun_Y1_13(B, A, G, F), B) & member(tptp_fun_Y2_12(B, A, G, F), B))) | (~(apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F)) & apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F))))))))),
% 0.20/0.40 inference(skolemize,[status(sab)],[13])).
% 0.20/0.40 tff(15,plain,
% 0.20/0.40 (![F: $i, G: $i, A: $i, B: $i] : (~((~((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1))))) | (~(equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F)))))))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[14, 7])).
% 0.20/0.40 tff(16,plain,
% 0.20/0.40 (![F: $i, G: $i, A: $i, B: $i] : (~((~((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1))))) | (~(equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F)))))))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[15, 5])).
% 0.20/0.40 tff(17,plain,
% 0.20/0.40 (((~![F: $i, G: $i, A: $i, B: $i] : (~((~((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1))))) | (~(equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F)))))))))) | (~((~((~equal_maps(compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39), compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), A!42, D!39)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(X, A!42)) | (~member(Y2, D!39)) | (~member(Y1, D!39)) | (~apply(compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), X, Y2)) | (~apply(compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39), X, Y1))))) | (~(equal_maps(compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39), compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), A!42, D!39) | (~((~apply(compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), tptp_fun_Y2_12(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)))) | (~apply(compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39), tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), tptp_fun_Y1_13(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)))) | (~member(tptp_fun_Y2_12(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), D!39)) | (~member(tptp_fun_Y1_13(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), D!39)) | (~member(tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), A!42)) | (tptp_fun_Y1_13(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)) = tptp_fun_Y2_12(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)))))))))) <=> ((~![F: $i, G: $i, A: $i, B: $i] : (~((~((~equal_maps(F, G, A, B)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)) | (~apply(F, X, Y1))))) | (~(equal_maps(F, G, A, B) | (~((tptp_fun_Y1_13(B, A, G, F) = tptp_fun_Y2_12(B, A, G, F)) | (~member(tptp_fun_X_14(B, A, G, F), A)) | (~member(tptp_fun_Y1_13(B, A, G, F), B)) | (~member(tptp_fun_Y2_12(B, A, G, F), B)) | (~apply(F, tptp_fun_X_14(B, A, G, F), tptp_fun_Y1_13(B, A, G, 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% 0.20/0.42 inference(rewrite,[status(thm)],[])).
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% 0.20/0.46 inference(rewrite,[status(thm)],[])).
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% 0.20/0.46 inference(rewrite,[status(thm)],[])).
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% 0.20/0.47 inference(modus_ponens,[status(thm)],[29, 26])).
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% 0.20/0.47 inference(unit_resolution,[status(thm)],[35, 34])).
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% 0.20/0.48 inference(unit_resolution,[status(thm)],[36, 25])).
% 0.20/0.48 tff(38,plain,
% 0.20/0.48 (((~apply(compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), tptp_fun_Y2_12(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)))) | (~apply(compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39), tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), tptp_fun_Y1_13(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)))) | (~member(tptp_fun_Y2_12(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), D!39)) | (~member(tptp_fun_Y1_13(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), D!39)) | (~member(tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), A!42)) | (tptp_fun_Y1_13(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)) = tptp_fun_Y2_12(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)))) | member(tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), A!42)),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(39,plain,
% 0.20/0.48 (member(tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), A!42)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[38, 37])).
% 0.20/0.48 tff(40,plain,
% 0.20/0.48 (((~apply(compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), tptp_fun_Y2_12(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)))) | (~apply(compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39), tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), tptp_fun_Y1_13(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)))) | (~member(tptp_fun_Y2_12(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), D!39)) | (~member(tptp_fun_Y1_13(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), D!39)) | (~member(tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), A!42)) | (tptp_fun_Y1_13(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)) = tptp_fun_Y2_12(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)))) | member(tptp_fun_Y2_12(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), D!39)),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(41,plain,
% 0.20/0.48 (member(tptp_fun_Y2_12(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), D!39)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[40, 37])).
% 0.20/0.48 tff(42,plain,
% 0.20/0.48 (^[G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : refl(((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z)))))))) <=> ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z)))))))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(43,plain,
% 0.20/0.48 (![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z)))))))) <=> ![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[42])).
% 0.20/0.48 tff(44,plain,
% 0.20/0.48 (^[G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : rewrite(((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z)))))))) <=> ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z)))))))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(45,plain,
% 0.20/0.48 (![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z)))))))) <=> ![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[44])).
% 0.20/0.48 tff(46,plain,
% 0.20/0.48 (![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z)))))))) <=> ![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))),
% 0.20/0.48 inference(transitivity,[status(thm)],[45, 43])).
% 0.20/0.48 tff(47,plain,
% 0.20/0.48 (^[G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : trans(monotonicity(trans(monotonicity(rewrite((member(X, A) & member(Z, C)) <=> (~((~member(Z, C)) | (~member(X, A))))), ((~(member(X, A) & member(Z, C))) <=> (~(~((~member(Z, C)) | (~member(X, A))))))), rewrite((~(~((~member(Z, C)) | (~member(X, A))))) <=> ((~member(Z, C)) | (~member(X, A)))), ((~(member(X, A) & member(Z, C))) <=> ((~member(Z, C)) | (~member(X, A))))), trans(monotonicity(rewrite(((~apply(compose_function(G, F, A, B, C), X, Z)) | (member(tptp_fun_Y_8(Z, X, B, F, G), B) & apply(F, X, tptp_fun_Y_8(Z, X, B, F, G)) & apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z))) <=> ((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))), rewrite((apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y) & apply(G, Y, Z)))) <=> (apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))), ((((~apply(compose_function(G, F, A, B, C), X, Z)) | (member(tptp_fun_Y_8(Z, X, B, F, G), B) & apply(F, X, tptp_fun_Y_8(Z, X, B, F, G)) & apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z))) & (apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y) & apply(G, Y, Z))))) <=> (((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z))))) & (apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))), rewrite((((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z))))) & (apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))) <=> (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z)))))))), ((((~apply(compose_function(G, F, A, B, C), X, Z)) | (member(tptp_fun_Y_8(Z, X, B, F, G), B) & apply(F, X, tptp_fun_Y_8(Z, X, B, F, G)) & apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z))) & (apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y) & apply(G, Y, Z))))) <=> (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))), (((~(member(X, A) & member(Z, C))) | (((~apply(compose_function(G, F, A, B, C), X, Z)) | (member(tptp_fun_Y_8(Z, X, B, F, G), B) & apply(F, X, tptp_fun_Y_8(Z, X, B, F, G)) & apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z))) & (apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y) & apply(G, Y, Z)))))) <=> (((~member(Z, C)) | (~member(X, A))) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z)))))))))), rewrite((((~member(Z, C)) | (~member(X, A))) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z)))))))) <=> ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))), (((~(member(X, A) & member(Z, C))) | (((~apply(compose_function(G, F, A, B, C), X, Z)) | (member(tptp_fun_Y_8(Z, X, B, F, G), B) & apply(F, X, tptp_fun_Y_8(Z, X, B, F, G)) & apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z))) & (apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y) & apply(G, Y, Z)))))) <=> ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(48,plain,
% 0.20/0.48 (![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~(member(X, A) & member(Z, C))) | (((~apply(compose_function(G, F, A, B, C), X, Z)) | (member(tptp_fun_Y_8(Z, X, B, F, G), B) & apply(F, X, tptp_fun_Y_8(Z, X, B, F, G)) & apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z))) & (apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y) & apply(G, Y, Z)))))) <=> ![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[47])).
% 0.20/0.48 tff(49,plain,
% 0.20/0.48 (![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~(member(X, A) & member(Z, C))) | (apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : (member(Y, B) & apply(F, X, Y) & apply(G, Y, Z)))) <=> ![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~(member(X, A) & member(Z, C))) | (apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : (member(Y, B) & apply(F, X, Y) & apply(G, Y, Z))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(50,plain,
% 0.20/0.48 (^[G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : trans(monotonicity(rewrite((apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : ((member(Y, B) & apply(F, X, Y)) & apply(G, Y, Z))) <=> (apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : (member(Y, B) & apply(F, X, Y) & apply(G, Y, Z)))), (((member(X, A) & member(Z, C)) => (apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : ((member(Y, B) & apply(F, X, Y)) & apply(G, Y, Z)))) <=> ((member(X, A) & member(Z, C)) => (apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : (member(Y, B) & apply(F, X, Y) & apply(G, Y, Z)))))), rewrite(((member(X, A) & member(Z, C)) => (apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : (member(Y, B) & apply(F, X, Y) & apply(G, Y, Z)))) <=> ((~(member(X, A) & member(Z, C))) | (apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : (member(Y, B) & apply(F, X, Y) & apply(G, Y, Z))))), (((member(X, A) & member(Z, C)) => (apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : ((member(Y, B) & apply(F, X, Y)) & apply(G, Y, Z)))) <=> ((~(member(X, A) & member(Z, C))) | (apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : (member(Y, B) & apply(F, X, Y) & apply(G, Y, Z))))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(51,plain,
% 0.20/0.48 (![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((member(X, A) & member(Z, C)) => (apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : ((member(Y, B) & apply(F, X, Y)) & apply(G, Y, Z)))) <=> ![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~(member(X, A) & member(Z, C))) | (apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : (member(Y, B) & apply(F, X, Y) & apply(G, Y, Z))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[50])).
% 0.20/0.48 tff(52,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')).
% 0.20/0.48 tff(53,plain,
% 0.20/0.48 (![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~(member(X, A) & member(Z, C))) | (apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : (member(Y, B) & apply(F, X, Y) & apply(G, Y, Z))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.20/0.48 tff(54,plain,
% 0.20/0.48 (![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~(member(X, A) & member(Z, C))) | (apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : (member(Y, B) & apply(F, X, Y) & apply(G, Y, Z))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[53, 49])).
% 0.20/0.48 tff(55,plain,(
% 0.20/0.48 ![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~(member(X, A) & member(Z, C))) | (((~apply(compose_function(G, F, A, B, C), X, Z)) | (member(tptp_fun_Y_8(Z, X, B, F, G), B) & apply(F, X, tptp_fun_Y_8(Z, X, B, F, G)) & apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z))) & (apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y) & apply(G, Y, Z))))))),
% 0.20/0.48 inference(skolemize,[status(sab)],[54])).
% 0.20/0.48 tff(56,plain,
% 0.20/0.48 (![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[55, 48])).
% 0.20/0.49 tff(57,plain,
% 0.20/0.49 (![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[56, 46])).
% 0.20/0.49 tff(58,plain,
% 0.20/0.49 (((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_Y2_12(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), D!39)) | (~member(tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), A!42)) | (~((~(apply(compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), tptp_fun_Y2_12(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39))) | ![Y: $i] : ((~member(Y, B!41)) | (~apply(F!45, tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), Y)) | (~apply(compose_function(H!43, G!44, B!41, C!40, D!39), Y, tptp_fun_Y2_12(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39))))))) | (~((~apply(compose_function(compose_function(H!43, 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% 0.38/0.56 inference(unit_resolution,[status(thm)],[75, 74])).
% 0.38/0.56 tff(77,plain,
% 0.38/0.56 (^[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)))))))))))),
% 0.38/0.56 inference(bind,[status(th)],[])).
% 0.38/0.56 tff(78,plain,
% 0.38/0.56 (![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))))))))))),
% 0.38/0.56 inference(quant_intro,[status(thm)],[77])).
% 0.38/0.56 tff(79,plain,
% 0.38/0.56 (^[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)))))))))),
% 0.38/0.56 inference(bind,[status(th)],[])).
% 0.38/0.56 tff(80,plain,
% 0.38/0.56 (![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))))))))),
% 0.38/0.56 inference(quant_intro,[status(thm)],[79])).
% 0.38/0.56 tff(81,plain,
% 0.38/0.56 (^[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)))))))))),
% 0.38/0.56 inference(bind,[status(th)],[])).
% 0.38/0.56 tff(82,plain,
% 0.38/0.56 (![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))))))))),
% 0.38/0.56 inference(quant_intro,[status(thm)],[81])).
% 0.38/0.56 tff(83,plain,
% 0.38/0.56 (![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))))))))),
% 0.38/0.56 inference(transitivity,[status(thm)],[82, 80])).
% 0.38/0.56 tff(84,plain,
% 0.38/0.56 (^[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))))))))))),
% 0.38/0.57 inference(bind,[status(th)],[])).
% 0.38/0.57 tff(85,plain,
% 0.38/0.57 (![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))))))))),
% 0.38/0.57 inference(quant_intro,[status(thm)],[84])).
% 0.38/0.57 tff(86,plain,
% 0.38/0.57 (^[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))))))))),
% 0.38/0.57 inference(bind,[status(th)],[])).
% 0.38/0.57 tff(87,plain,
% 0.38/0.57 (![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)))))))),
% 0.38/0.57 inference(quant_intro,[status(thm)],[86])).
% 0.38/0.57 tff(88,plain,
% 0.38/0.57 (![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))))))),
% 0.38/0.57 inference(rewrite,[status(thm)],[])).
% 0.38/0.57 tff(89,plain,
% 0.38/0.57 (^[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)))))))),
% 0.38/0.57 inference(bind,[status(th)],[])).
% 0.38/0.57 tff(90,plain,
% 0.38/0.57 (![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))))))),
% 0.38/0.57 inference(quant_intro,[status(thm)],[89])).
% 0.38/0.57 tff(91,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')).
% 0.38/0.57 tff(92,plain,
% 0.38/0.57 (![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))))))),
% 0.38/0.57 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.38/0.57 tff(93,plain,
% 0.38/0.57 (![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))))))),
% 0.38/0.57 inference(modus_ponens,[status(thm)],[92, 88])).
% 0.38/0.57 tff(94,plain,(
% 0.38/0.57 ![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))))))))),
% 0.38/0.57 inference(skolemize,[status(sab)],[93])).
% 0.38/0.57 tff(95,plain,
% 0.38/0.57 (![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)))))))),
% 0.38/0.57 inference(modus_ponens,[status(thm)],[94, 87])).
% 0.38/0.57 tff(96,plain,
% 0.38/0.57 (![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))))))))),
% 0.38/0.57 inference(modus_ponens,[status(thm)],[95, 85])).
% 0.38/0.57 tff(97,plain,
% 0.38/0.57 (![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))))))))),
% 0.38/0.57 inference(modus_ponens,[status(thm)],[96, 83])).
% 0.38/0.57 tff(98,plain,
% 0.38/0.57 (![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))))))))))),
% 0.38/0.57 inference(modus_ponens,[status(thm)],[97, 78])).
% 0.38/0.57 tff(99,plain,
% 0.38/0.57 (((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(G!44, B!41, C!40)) | (~((~![X: $i] : ((~member(X, B!41)) | (~((~member(tptp_fun_Y_3(X, C!40, G!44), C!40)) | (~apply(G!44, X, tptp_fun_Y_3(X, C!40, G!44))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, C!40)) | (~apply(G!44, X, Y1)) | (~apply(G!44, X, Y2)) | (~member(X, B!41)) | (~member(Y1, C!40)))))))) | (~(maps(G!44, B!41, C!40) | (~((~member(tptp_fun_X_4(C!40, B!41, G!44), B!41)) | (~![Y: $i] : ((~member(Y, C!40)) | (~apply(G!44, tptp_fun_X_4(C!40, B!41, G!44), Y)))))) | (~((~member(tptp_fun_Y2_5(C!40, B!41, G!44), C!40)) | (~member(tptp_fun_Y1_6(C!40, B!41, G!44), C!40)) | (~member(tptp_fun_X_7(C!40, B!41, G!44), B!41)) | (~apply(G!44, tptp_fun_X_7(C!40, B!41, G!44), tptp_fun_Y2_5(C!40, B!41, G!44))) | (~apply(G!44, tptp_fun_X_7(C!40, B!41, G!44), tptp_fun_Y1_6(C!40, B!41, G!44))) | (tptp_fun_Y1_6(C!40, B!41, G!44) = tptp_fun_Y2_5(C!40, B!41, G!44))))))))) <=> ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(G!44, B!41, C!40)) | (~((~![X: $i] : ((~member(X, B!41)) | (~((~member(tptp_fun_Y_3(X, C!40, G!44), C!40)) | (~apply(G!44, X, tptp_fun_Y_3(X, C!40, G!44))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, C!40)) | (~apply(G!44, X, Y1)) | (~apply(G!44, X, Y2)) | (~member(X, B!41)) | (~member(Y1, C!40)))))))) | (~(maps(G!44, B!41, C!40) | (~((~member(tptp_fun_X_4(C!40, B!41, G!44), B!41)) | (~![Y: $i] : ((~member(Y, C!40)) | (~apply(G!44, tptp_fun_X_4(C!40, B!41, G!44), Y)))))) | (~((~member(tptp_fun_Y2_5(C!40, B!41, G!44), C!40)) | (~member(tptp_fun_Y1_6(C!40, B!41, G!44), C!40)) | (~member(tptp_fun_X_7(C!40, B!41, G!44), B!41)) | (~apply(G!44, tptp_fun_X_7(C!40, B!41, G!44), tptp_fun_Y2_5(C!40, B!41, G!44))) | (~apply(G!44, tptp_fun_X_7(C!40, B!41, G!44), tptp_fun_Y1_6(C!40, B!41, G!44))) | (tptp_fun_Y1_6(C!40, B!41, G!44) = tptp_fun_Y2_5(C!40, B!41, G!44)))))))))),
% 0.38/0.57 inference(rewrite,[status(thm)],[])).
% 0.38/0.57 tff(100,plain,
% 0.38/0.57 ((~((~((~maps(G!44, B!41, C!40)) | (~((~![X: $i] : ((~member(X, B!41)) | (~((~member(tptp_fun_Y_3(X, C!40, G!44), C!40)) | (~apply(G!44, X, tptp_fun_Y_3(X, C!40, G!44))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G!44, X, Y1)) | (~apply(G!44, X, Y2)) | (~member(X, B!41)) | (~member(Y1, C!40)) | (~member(Y2, C!40)))))))) | (~(maps(G!44, B!41, C!40) | (~((tptp_fun_Y1_6(C!40, B!41, G!44) = tptp_fun_Y2_5(C!40, B!41, G!44)) | (~apply(G!44, tptp_fun_X_7(C!40, B!41, G!44), tptp_fun_Y1_6(C!40, B!41, G!44))) | (~apply(G!44, tptp_fun_X_7(C!40, B!41, G!44), tptp_fun_Y2_5(C!40, B!41, G!44))) | (~member(tptp_fun_X_7(C!40, B!41, G!44), B!41)) | (~member(tptp_fun_Y1_6(C!40, B!41, G!44), C!40)) | (~member(tptp_fun_Y2_5(C!40, B!41, G!44), C!40)))) | (~((~member(tptp_fun_X_4(C!40, B!41, G!44), B!41)) | (~![Y: $i] : ((~member(Y, C!40)) | (~apply(G!44, tptp_fun_X_4(C!40, B!41, G!44), Y)))))))))) <=> (~((~((~maps(G!44, B!41, C!40)) | (~((~![X: $i] : ((~member(X, B!41)) | (~((~member(tptp_fun_Y_3(X, C!40, G!44), C!40)) | (~apply(G!44, X, tptp_fun_Y_3(X, C!40, G!44))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, C!40)) | (~apply(G!44, X, Y1)) | (~apply(G!44, X, Y2)) | (~member(X, B!41)) | (~member(Y1, C!40)))))))) | (~(maps(G!44, B!41, C!40) | (~((~member(tptp_fun_X_4(C!40, B!41, G!44), B!41)) | (~![Y: $i] : ((~member(Y, C!40)) | (~apply(G!44, tptp_fun_X_4(C!40, B!41, G!44), Y)))))) | (~((~member(tptp_fun_Y2_5(C!40, B!41, G!44), C!40)) | (~member(tptp_fun_Y1_6(C!40, B!41, G!44), C!40)) | (~member(tptp_fun_X_7(C!40, B!41, G!44), B!41)) | (~apply(G!44, tptp_fun_X_7(C!40, B!41, G!44), tptp_fun_Y2_5(C!40, B!41, G!44))) | (~apply(G!44, tptp_fun_X_7(C!40, B!41, G!44), tptp_fun_Y1_6(C!40, B!41, G!44))) | (tptp_fun_Y1_6(C!40, B!41, G!44) = tptp_fun_Y2_5(C!40, B!41, G!44))))))))),
% 0.38/0.57 inference(rewrite,[status(thm)],[])).
% 0.38/0.57 tff(101,plain,
% 0.38/0.57 (((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(G!44, B!41, C!40)) | (~((~![X: $i] : ((~member(X, B!41)) | (~((~member(tptp_fun_Y_3(X, C!40, G!44), C!40)) | (~apply(G!44, X, tptp_fun_Y_3(X, C!40, G!44))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G!44, X, Y1)) | (~apply(G!44, X, Y2)) | (~member(X, B!41)) | (~member(Y1, C!40)) | (~member(Y2, C!40)))))))) | (~(maps(G!44, B!41, C!40) | (~((tptp_fun_Y1_6(C!40, B!41, G!44) = tptp_fun_Y2_5(C!40, B!41, G!44)) | (~apply(G!44, tptp_fun_X_7(C!40, B!41, G!44), tptp_fun_Y1_6(C!40, B!41, G!44))) | (~apply(G!44, tptp_fun_X_7(C!40, B!41, G!44), tptp_fun_Y2_5(C!40, B!41, G!44))) | (~member(tptp_fun_X_7(C!40, B!41, G!44), B!41)) | (~member(tptp_fun_Y1_6(C!40, B!41, G!44), C!40)) | (~member(tptp_fun_Y2_5(C!40, B!41, G!44), C!40)))) | (~((~member(tptp_fun_X_4(C!40, B!41, G!44), B!41)) | (~![Y: $i] : ((~member(Y, C!40)) | (~apply(G!44, tptp_fun_X_4(C!40, B!41, G!44), Y))))))))))) <=> ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(G!44, B!41, C!40)) | (~((~![X: $i] : ((~member(X, B!41)) | (~((~member(tptp_fun_Y_3(X, C!40, G!44), C!40)) | (~apply(G!44, X, tptp_fun_Y_3(X, C!40, G!44))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, C!40)) | (~apply(G!44, X, Y1)) | (~apply(G!44, X, Y2)) | (~member(X, B!41)) | (~member(Y1, C!40)))))))) | (~(maps(G!44, B!41, C!40) | (~((~member(tptp_fun_X_4(C!40, B!41, G!44), B!41)) | (~![Y: $i] : ((~member(Y, C!40)) | (~apply(G!44, tptp_fun_X_4(C!40, B!41, G!44), Y)))))) | (~((~member(tptp_fun_Y2_5(C!40, B!41, G!44), C!40)) | (~member(tptp_fun_Y1_6(C!40, B!41, G!44), C!40)) | (~member(tptp_fun_X_7(C!40, B!41, G!44), B!41)) | (~apply(G!44, tptp_fun_X_7(C!40, B!41, G!44), tptp_fun_Y2_5(C!40, B!41, G!44))) | (~apply(G!44, tptp_fun_X_7(C!40, B!41, G!44), tptp_fun_Y1_6(C!40, B!41, G!44))) | (tptp_fun_Y1_6(C!40, B!41, G!44) = tptp_fun_Y2_5(C!40, B!41, G!44)))))))))),
% 0.38/0.58 inference(monotonicity,[status(thm)],[100])).
% 0.38/0.58 tff(102,plain,
% 0.38/0.58 (((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(G!44, B!41, C!40)) | (~((~![X: $i] : ((~member(X, B!41)) | (~((~member(tptp_fun_Y_3(X, C!40, G!44), C!40)) | (~apply(G!44, X, tptp_fun_Y_3(X, C!40, G!44))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G!44, X, Y1)) | (~apply(G!44, X, Y2)) | (~member(X, B!41)) | (~member(Y1, C!40)) | (~member(Y2, C!40)))))))) | (~(maps(G!44, B!41, C!40) | (~((tptp_fun_Y1_6(C!40, B!41, G!44) = tptp_fun_Y2_5(C!40, B!41, G!44)) | (~apply(G!44, tptp_fun_X_7(C!40, B!41, G!44), tptp_fun_Y1_6(C!40, B!41, G!44))) | (~apply(G!44, tptp_fun_X_7(C!40, B!41, G!44), tptp_fun_Y2_5(C!40, B!41, G!44))) | (~member(tptp_fun_X_7(C!40, B!41, G!44), B!41)) | (~member(tptp_fun_Y1_6(C!40, B!41, G!44), C!40)) | (~member(tptp_fun_Y2_5(C!40, B!41, G!44), C!40)))) | (~((~member(tptp_fun_X_4(C!40, B!41, G!44), B!41)) | (~![Y: $i] : ((~member(Y, C!40)) | (~apply(G!44, tptp_fun_X_4(C!40, B!41, G!44), Y))))))))))) <=> ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(G!44, B!41, C!40)) | (~((~![X: $i] : ((~member(X, B!41)) | (~((~member(tptp_fun_Y_3(X, C!40, G!44), C!40)) | (~apply(G!44, X, tptp_fun_Y_3(X, C!40, G!44))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, C!40)) | (~apply(G!44, X, Y1)) | (~apply(G!44, X, Y2)) | (~member(X, B!41)) | (~member(Y1, C!40)))))))) | (~(maps(G!44, B!41, C!40) | (~((~member(tptp_fun_X_4(C!40, B!41, G!44), B!41)) | (~![Y: $i] : ((~member(Y, C!40)) | (~apply(G!44, tptp_fun_X_4(C!40, B!41, G!44), Y)))))) | (~((~member(tptp_fun_Y2_5(C!40, B!41, G!44), C!40)) | (~member(tptp_fun_Y1_6(C!40, B!41, G!44), C!40)) | (~member(tptp_fun_X_7(C!40, B!41, G!44), B!41)) | (~apply(G!44, tptp_fun_X_7(C!40, B!41, G!44), tptp_fun_Y2_5(C!40, B!41, G!44))) | (~apply(G!44, tptp_fun_X_7(C!40, B!41, G!44), tptp_fun_Y1_6(C!40, B!41, G!44))) | (tptp_fun_Y1_6(C!40, B!41, G!44) = tptp_fun_Y2_5(C!40, B!41, G!44)))))))))),
% 0.38/0.58 inference(transitivity,[status(thm)],[101, 99])).
% 0.38/0.58 tff(103,plain,
% 0.38/0.58 ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(G!44, B!41, C!40)) | (~((~![X: $i] : ((~member(X, B!41)) | (~((~member(tptp_fun_Y_3(X, C!40, G!44), C!40)) | (~apply(G!44, X, tptp_fun_Y_3(X, C!40, G!44))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G!44, X, Y1)) | (~apply(G!44, X, Y2)) | (~member(X, B!41)) | (~member(Y1, C!40)) | (~member(Y2, C!40)))))))) | (~(maps(G!44, B!41, C!40) | (~((tptp_fun_Y1_6(C!40, B!41, G!44) = tptp_fun_Y2_5(C!40, B!41, G!44)) | (~apply(G!44, tptp_fun_X_7(C!40, B!41, G!44), tptp_fun_Y1_6(C!40, B!41, G!44))) | (~apply(G!44, tptp_fun_X_7(C!40, B!41, G!44), tptp_fun_Y2_5(C!40, B!41, G!44))) | (~member(tptp_fun_X_7(C!40, B!41, G!44), B!41)) | (~member(tptp_fun_Y1_6(C!40, B!41, G!44), C!40)) | (~member(tptp_fun_Y2_5(C!40, B!41, G!44), C!40)))) | (~((~member(tptp_fun_X_4(C!40, B!41, G!44), B!41)) | (~![Y: $i] : ((~member(Y, C!40)) | (~apply(G!44, tptp_fun_X_4(C!40, B!41, G!44), Y))))))))))),
% 0.38/0.58 inference(quant_inst,[status(thm)],[])).
% 0.38/0.58 tff(104,plain,
% 0.38/0.58 ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(G!44, B!41, C!40)) | (~((~![X: $i] : ((~member(X, B!41)) | (~((~member(tptp_fun_Y_3(X, C!40, G!44), C!40)) | (~apply(G!44, X, tptp_fun_Y_3(X, C!40, G!44))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, C!40)) | (~apply(G!44, X, Y1)) | (~apply(G!44, X, Y2)) | (~member(X, B!41)) | (~member(Y1, C!40)))))))) | (~(maps(G!44, B!41, C!40) | (~((~member(tptp_fun_X_4(C!40, B!41, G!44), B!41)) | (~![Y: $i] : ((~member(Y, C!40)) | (~apply(G!44, tptp_fun_X_4(C!40, B!41, G!44), Y)))))) | (~((~member(tptp_fun_Y2_5(C!40, B!41, G!44), C!40)) | (~member(tptp_fun_Y1_6(C!40, B!41, G!44), C!40)) | (~member(tptp_fun_X_7(C!40, B!41, G!44), B!41)) | (~apply(G!44, tptp_fun_X_7(C!40, B!41, G!44), tptp_fun_Y2_5(C!40, B!41, G!44))) | (~apply(G!44, tptp_fun_X_7(C!40, B!41, G!44), tptp_fun_Y1_6(C!40, B!41, G!44))) | (tptp_fun_Y1_6(C!40, B!41, G!44) = tptp_fun_Y2_5(C!40, B!41, G!44))))))))),
% 0.38/0.58 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.38/0.58 tff(105,plain,
% 0.38/0.58 (~((~((~maps(G!44, B!41, C!40)) | (~((~![X: $i] : ((~member(X, B!41)) | (~((~member(tptp_fun_Y_3(X, C!40, G!44), C!40)) | (~apply(G!44, X, tptp_fun_Y_3(X, C!40, G!44))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, C!40)) | (~apply(G!44, X, Y1)) | (~apply(G!44, X, Y2)) | (~member(X, B!41)) | (~member(Y1, C!40)))))))) | (~(maps(G!44, B!41, C!40) | (~((~member(tptp_fun_X_4(C!40, B!41, G!44), B!41)) | (~![Y: $i] : ((~member(Y, C!40)) | (~apply(G!44, tptp_fun_X_4(C!40, B!41, G!44), Y)))))) | (~((~member(tptp_fun_Y2_5(C!40, B!41, G!44), C!40)) | (~member(tptp_fun_Y1_6(C!40, B!41, G!44), C!40)) | (~member(tptp_fun_X_7(C!40, B!41, G!44), B!41)) | (~apply(G!44, tptp_fun_X_7(C!40, B!41, G!44), tptp_fun_Y2_5(C!40, B!41, G!44))) | (~apply(G!44, tptp_fun_X_7(C!40, B!41, G!44), tptp_fun_Y1_6(C!40, B!41, G!44))) | (tptp_fun_Y1_6(C!40, B!41, G!44) = tptp_fun_Y2_5(C!40, B!41, G!44)))))))),
% 0.38/0.58 inference(unit_resolution,[status(thm)],[104, 98])).
% 0.38/0.58 tff(106,plain,
% 0.38/0.58 (((~((~maps(G!44, B!41, C!40)) | (~((~![X: $i] : ((~member(X, B!41)) | (~((~member(tptp_fun_Y_3(X, C!40, G!44), C!40)) | (~apply(G!44, X, tptp_fun_Y_3(X, C!40, G!44))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, C!40)) | (~apply(G!44, X, Y1)) | (~apply(G!44, X, Y2)) | (~member(X, B!41)) | (~member(Y1, C!40)))))))) | (~(maps(G!44, B!41, C!40) | (~((~member(tptp_fun_X_4(C!40, B!41, G!44), B!41)) | (~![Y: $i] : ((~member(Y, C!40)) | (~apply(G!44, tptp_fun_X_4(C!40, B!41, G!44), Y)))))) | (~((~member(tptp_fun_Y2_5(C!40, B!41, G!44), C!40)) | (~member(tptp_fun_Y1_6(C!40, B!41, G!44), C!40)) | (~member(tptp_fun_X_7(C!40, B!41, G!44), B!41)) | (~apply(G!44, tptp_fun_X_7(C!40, B!41, G!44), tptp_fun_Y2_5(C!40, B!41, G!44))) | (~apply(G!44, tptp_fun_X_7(C!40, B!41, G!44), tptp_fun_Y1_6(C!40, B!41, G!44))) | (tptp_fun_Y1_6(C!40, B!41, G!44) = tptp_fun_Y2_5(C!40, B!41, G!44))))))) | ((~maps(G!44, B!41, C!40)) | (~((~![X: $i] : ((~member(X, B!41)) | (~((~member(tptp_fun_Y_3(X, C!40, G!44), C!40)) | (~apply(G!44, X, tptp_fun_Y_3(X, C!40, G!44))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, C!40)) | (~apply(G!44, X, Y1)) | (~apply(G!44, X, Y2)) | (~member(X, B!41)) | (~member(Y1, C!40)))))))),
% 0.38/0.58 inference(tautology,[status(thm)],[])).
% 0.38/0.58 tff(107,plain,
% 0.38/0.58 ((~maps(G!44, B!41, C!40)) | (~((~![X: $i] : ((~member(X, B!41)) | (~((~member(tptp_fun_Y_3(X, C!40, G!44), C!40)) | (~apply(G!44, X, tptp_fun_Y_3(X, C!40, G!44))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, C!40)) | (~apply(G!44, X, Y1)) | (~apply(G!44, X, Y2)) | (~member(X, B!41)) | (~member(Y1, C!40))))))),
% 0.38/0.58 inference(unit_resolution,[status(thm)],[106, 105])).
% 0.38/0.58 tff(108,plain,
% 0.38/0.58 (maps(F!45, A!42, B!41) & maps(G!44, B!41, C!40) & maps(H!43, C!40, D!39)),
% 0.38/0.58 inference(or_elim,[status(thm)],[33])).
% 0.38/0.58 tff(109,plain,
% 0.38/0.58 (maps(G!44, B!41, C!40)),
% 0.38/0.58 inference(and_elim,[status(thm)],[108])).
% 0.38/0.58 tff(110,plain,
% 0.38/0.58 ((~((~maps(G!44, B!41, C!40)) | (~((~![X: $i] : ((~member(X, B!41)) | (~((~member(tptp_fun_Y_3(X, C!40, G!44), C!40)) | (~apply(G!44, X, tptp_fun_Y_3(X, C!40, G!44))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, C!40)) | (~apply(G!44, X, Y1)) | (~apply(G!44, X, Y2)) | (~member(X, B!41)) | (~member(Y1, C!40)))))))) | (~maps(G!44, B!41, C!40)) | (~((~![X: $i] : ((~member(X, B!41)) | (~((~member(tptp_fun_Y_3(X, C!40, G!44), C!40)) | (~apply(G!44, X, tptp_fun_Y_3(X, C!40, G!44))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, C!40)) | (~apply(G!44, X, Y1)) | (~apply(G!44, X, Y2)) | (~member(X, B!41)) | (~member(Y1, C!40))))))),
% 0.38/0.58 inference(tautology,[status(thm)],[])).
% 0.38/0.58 tff(111,plain,
% 0.38/0.58 ((~((~maps(G!44, B!41, C!40)) | (~((~![X: $i] : ((~member(X, B!41)) | (~((~member(tptp_fun_Y_3(X, C!40, G!44), C!40)) | (~apply(G!44, X, tptp_fun_Y_3(X, C!40, G!44))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, C!40)) | (~apply(G!44, X, Y1)) | (~apply(G!44, X, Y2)) | (~member(X, B!41)) | (~member(Y1, C!40)))))))) | (~((~![X: $i] : ((~member(X, B!41)) | (~((~member(tptp_fun_Y_3(X, C!40, G!44), C!40)) | (~apply(G!44, X, tptp_fun_Y_3(X, C!40, G!44))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, C!40)) | (~apply(G!44, X, Y1)) | (~apply(G!44, X, Y2)) | (~member(X, B!41)) | (~member(Y1, C!40))))))),
% 0.38/0.58 inference(unit_resolution,[status(thm)],[110, 109])).
% 0.38/0.58 tff(112,plain,
% 0.38/0.58 (~((~![X: $i] : ((~member(X, B!41)) | (~((~member(tptp_fun_Y_3(X, C!40, G!44), C!40)) | (~apply(G!44, X, tptp_fun_Y_3(X, C!40, G!44))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, C!40)) | (~apply(G!44, X, Y1)) | (~apply(G!44, X, Y2)) | (~member(X, B!41)) | (~member(Y1, C!40)))))),
% 0.38/0.58 inference(unit_resolution,[status(thm)],[111, 107])).
% 0.38/0.58 tff(113,plain,
% 0.38/0.58 (((~![X: $i] : ((~member(X, B!41)) | (~((~member(tptp_fun_Y_3(X, C!40, G!44), C!40)) | (~apply(G!44, X, tptp_fun_Y_3(X, C!40, G!44))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, C!40)) | (~apply(G!44, X, Y1)) | (~apply(G!44, X, Y2)) | (~member(X, B!41)) | (~member(Y1, C!40))))) | ![X: $i] : ((~member(X, B!41)) | (~((~member(tptp_fun_Y_3(X, C!40, G!44), C!40)) | (~apply(G!44, X, tptp_fun_Y_3(X, C!40, G!44))))))),
% 0.38/0.58 inference(tautology,[status(thm)],[])).
% 0.38/0.58 tff(114,plain,
% 0.38/0.58 (![X: $i] : ((~member(X, B!41)) | (~((~member(tptp_fun_Y_3(X, C!40, G!44), C!40)) | (~apply(G!44, X, tptp_fun_Y_3(X, C!40, G!44))))))),
% 0.38/0.58 inference(unit_resolution,[status(thm)],[113, 112])).
% 0.38/0.58 tff(115,plain,
% 0.38/0.58 (((~![X: $i] : ((~member(X, B!41)) | (~((~member(tptp_fun_Y_3(X, C!40, G!44), C!40)) | (~apply(G!44, X, tptp_fun_Y_3(X, C!40, G!44))))))) | ((~member(tptp_fun_Y_8(tptp_fun_Y2_12(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), B!41, F!45, compose_function(H!43, G!44, B!41, C!40, D!39)), B!41)) | (~((~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y2_12(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), B!41, F!45, compose_function(H!43, G!44, B!41, C!40, D!39)), C!40, G!44), C!40)) | (~apply(G!44, tptp_fun_Y_8(tptp_fun_Y2_12(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), B!41, F!45, compose_function(H!43, G!44, B!41, C!40, D!39)), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y2_12(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), B!41, F!45, compose_function(H!43, G!44, B!41, C!40, D!39)), C!40, G!44))))))) <=> ((~![X: $i] : ((~member(X, B!41)) | (~((~member(tptp_fun_Y_3(X, C!40, G!44), C!40)) | (~apply(G!44, X, tptp_fun_Y_3(X, C!40, G!44))))))) | (~member(tptp_fun_Y_8(tptp_fun_Y2_12(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), B!41, F!45, compose_function(H!43, G!44, B!41, C!40, D!39)), B!41)) | (~((~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y2_12(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), B!41, F!45, compose_function(H!43, G!44, B!41, C!40, D!39)), C!40, G!44), C!40)) | (~apply(G!44, tptp_fun_Y_8(tptp_fun_Y2_12(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), B!41, F!45, compose_function(H!43, G!44, B!41, C!40, D!39)), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y2_12(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), B!41, F!45, compose_function(H!43, G!44, B!41, C!40, D!39)), C!40, G!44))))))),
% 0.38/0.59 inference(rewrite,[status(thm)],[])).
% 0.38/0.59 tff(116,plain,
% 0.38/0.59 ((~![X: $i] : ((~member(X, B!41)) | (~((~member(tptp_fun_Y_3(X, C!40, G!44), C!40)) | (~apply(G!44, X, tptp_fun_Y_3(X, C!40, G!44))))))) | ((~member(tptp_fun_Y_8(tptp_fun_Y2_12(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), B!41, F!45, compose_function(H!43, G!44, B!41, C!40, D!39)), B!41)) | (~((~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y2_12(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), B!41, F!45, compose_function(H!43, G!44, B!41, C!40, D!39)), C!40, G!44), C!40)) | (~apply(G!44, tptp_fun_Y_8(tptp_fun_Y2_12(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), B!41, F!45, compose_function(H!43, G!44, B!41, C!40, D!39)), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y2_12(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), B!41, F!45, compose_function(H!43, G!44, B!41, C!40, D!39)), C!40, G!44))))))),
% 0.38/0.59 inference(quant_inst,[status(thm)],[])).
% 0.38/0.59 tff(117,plain,
% 0.38/0.59 ((~![X: $i] : ((~member(X, B!41)) | (~((~member(tptp_fun_Y_3(X, C!40, G!44), C!40)) | (~apply(G!44, X, tptp_fun_Y_3(X, C!40, G!44))))))) | (~member(tptp_fun_Y_8(tptp_fun_Y2_12(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), B!41, F!45, compose_function(H!43, G!44, B!41, C!40, D!39)), B!41)) | (~((~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y2_12(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), B!41, F!45, compose_function(H!43, G!44, B!41, C!40, D!39)), C!40, G!44), C!40)) | (~apply(G!44, tptp_fun_Y_8(tptp_fun_Y2_12(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), B!41, F!45, compose_function(H!43, G!44, B!41, C!40, D!39)), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y2_12(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), B!41, F!45, compose_function(H!43, G!44, B!41, C!40, D!39)), C!40, G!44)))))),
% 0.38/0.59 inference(modus_ponens,[status(thm)],[116, 115])).
% 0.38/0.59 tff(118,plain,
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% 0.38/0.59 inference(unit_resolution,[status(thm)],[117, 114, 76])).
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% 0.38/0.60 inference(tautology,[status(thm)],[])).
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% 0.38/0.60 inference(unit_resolution,[status(thm)],[119, 118])).
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% 0.38/0.60 inference(tautology,[status(thm)],[])).
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% 0.38/0.60 inference(unit_resolution,[status(thm)],[121, 118])).
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% 0.53/0.73 inference(modus_ponens,[status(thm)],[147, 146])).
% 0.53/0.73 tff(149,plain,
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% 0.53/0.73 inference(unit_resolution,[status(thm)],[148, 142, 76, 140, 138, 122, 120])).
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% 0.53/0.73 inference(monotonicity,[status(thm)],[149])).
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% 0.53/0.74 inference(symmetry,[status(thm)],[150])).
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% 0.53/0.74 inference(tautology,[status(thm)],[])).
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% 0.53/0.74 inference(unit_resolution,[status(thm)],[152, 136])).
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% 0.53/0.74 inference(modus_ponens,[status(thm)],[153, 151])).
% 0.53/0.74 tff(155,plain,
% 0.53/0.74 (((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(H!43, C!40, D!39)) | (~((~![X: $i] : ((~member(X, C!40)) | (~((~member(tptp_fun_Y_3(X, D!39, H!43), D!39)) | (~apply(H!43, X, tptp_fun_Y_3(X, D!39, H!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, D!39)) | (~apply(H!43, X, Y1)) | (~apply(H!43, X, Y2)) | (~member(X, C!40)) | (~member(Y1, D!39)))))))) | (~(maps(H!43, C!40, D!39) | (~((~member(tptp_fun_X_4(D!39, C!40, H!43), C!40)) | (~![Y: $i] : ((~member(Y, D!39)) | (~apply(H!43, tptp_fun_X_4(D!39, C!40, H!43), Y)))))) | (~((~member(tptp_fun_Y2_5(D!39, C!40, H!43), D!39)) | (~member(tptp_fun_Y1_6(D!39, C!40, H!43), D!39)) | (~member(tptp_fun_X_7(D!39, C!40, H!43), C!40)) | (~apply(H!43, tptp_fun_X_7(D!39, C!40, H!43), tptp_fun_Y2_5(D!39, C!40, H!43))) | (~apply(H!43, tptp_fun_X_7(D!39, C!40, H!43), tptp_fun_Y1_6(D!39, C!40, H!43))) | (tptp_fun_Y1_6(D!39, C!40, H!43) = tptp_fun_Y2_5(D!39, C!40, H!43))))))))) <=> ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(H!43, C!40, D!39)) | (~((~![X: $i] : ((~member(X, C!40)) | (~((~member(tptp_fun_Y_3(X, D!39, H!43), D!39)) | (~apply(H!43, X, tptp_fun_Y_3(X, D!39, H!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, D!39)) | (~apply(H!43, X, Y1)) | (~apply(H!43, X, Y2)) | (~member(X, C!40)) | (~member(Y1, D!39)))))))) | (~(maps(H!43, C!40, D!39) | (~((~member(tptp_fun_X_4(D!39, C!40, H!43), C!40)) | (~![Y: $i] : ((~member(Y, D!39)) | (~apply(H!43, tptp_fun_X_4(D!39, C!40, H!43), Y)))))) | (~((~member(tptp_fun_Y2_5(D!39, C!40, H!43), D!39)) | (~member(tptp_fun_Y1_6(D!39, C!40, H!43), D!39)) | (~member(tptp_fun_X_7(D!39, C!40, H!43), C!40)) | (~apply(H!43, tptp_fun_X_7(D!39, C!40, H!43), tptp_fun_Y2_5(D!39, C!40, H!43))) | (~apply(H!43, tptp_fun_X_7(D!39, C!40, H!43), tptp_fun_Y1_6(D!39, C!40, H!43))) | (tptp_fun_Y1_6(D!39, C!40, H!43) = tptp_fun_Y2_5(D!39, C!40, H!43)))))))))),
% 0.53/0.74 inference(rewrite,[status(thm)],[])).
% 0.53/0.74 tff(156,plain,
% 0.53/0.74 ((~((~((~maps(H!43, C!40, D!39)) | (~((~![X: $i] : ((~member(X, C!40)) | (~((~member(tptp_fun_Y_3(X, D!39, H!43), D!39)) | (~apply(H!43, X, tptp_fun_Y_3(X, D!39, H!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(H!43, X, Y1)) | (~apply(H!43, X, Y2)) | (~member(X, C!40)) | (~member(Y1, D!39)) | (~member(Y2, D!39)))))))) | (~(maps(H!43, C!40, D!39) | (~((tptp_fun_Y1_6(D!39, C!40, H!43) = tptp_fun_Y2_5(D!39, C!40, H!43)) | (~apply(H!43, tptp_fun_X_7(D!39, C!40, H!43), tptp_fun_Y1_6(D!39, C!40, H!43))) | (~apply(H!43, tptp_fun_X_7(D!39, C!40, H!43), tptp_fun_Y2_5(D!39, C!40, H!43))) | (~member(tptp_fun_X_7(D!39, C!40, H!43), C!40)) | (~member(tptp_fun_Y1_6(D!39, C!40, H!43), D!39)) | (~member(tptp_fun_Y2_5(D!39, C!40, H!43), D!39)))) | (~((~member(tptp_fun_X_4(D!39, C!40, H!43), C!40)) | (~![Y: $i] : ((~member(Y, D!39)) | (~apply(H!43, tptp_fun_X_4(D!39, C!40, H!43), Y)))))))))) <=> (~((~((~maps(H!43, C!40, D!39)) | (~((~![X: $i] : ((~member(X, C!40)) | (~((~member(tptp_fun_Y_3(X, D!39, H!43), D!39)) | (~apply(H!43, X, tptp_fun_Y_3(X, D!39, H!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, D!39)) | (~apply(H!43, X, Y1)) | (~apply(H!43, X, Y2)) | (~member(X, C!40)) | (~member(Y1, D!39)))))))) | (~(maps(H!43, C!40, D!39) | (~((~member(tptp_fun_X_4(D!39, C!40, H!43), C!40)) | (~![Y: $i] : ((~member(Y, D!39)) | (~apply(H!43, tptp_fun_X_4(D!39, C!40, H!43), Y)))))) | (~((~member(tptp_fun_Y2_5(D!39, C!40, H!43), D!39)) | (~member(tptp_fun_Y1_6(D!39, C!40, H!43), D!39)) | (~member(tptp_fun_X_7(D!39, C!40, H!43), C!40)) | (~apply(H!43, tptp_fun_X_7(D!39, C!40, H!43), tptp_fun_Y2_5(D!39, C!40, H!43))) | (~apply(H!43, tptp_fun_X_7(D!39, C!40, H!43), tptp_fun_Y1_6(D!39, C!40, H!43))) | (tptp_fun_Y1_6(D!39, C!40, H!43) = tptp_fun_Y2_5(D!39, C!40, H!43))))))))),
% 0.53/0.74 inference(rewrite,[status(thm)],[])).
% 0.53/0.74 tff(157,plain,
% 0.53/0.74 (((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(H!43, C!40, D!39)) | (~((~![X: $i] : ((~member(X, C!40)) | (~((~member(tptp_fun_Y_3(X, D!39, H!43), D!39)) | (~apply(H!43, X, tptp_fun_Y_3(X, D!39, H!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(H!43, X, Y1)) | (~apply(H!43, X, Y2)) | (~member(X, C!40)) | (~member(Y1, D!39)) | (~member(Y2, D!39)))))))) | (~(maps(H!43, C!40, D!39) | (~((tptp_fun_Y1_6(D!39, C!40, H!43) = tptp_fun_Y2_5(D!39, C!40, H!43)) | (~apply(H!43, tptp_fun_X_7(D!39, C!40, H!43), tptp_fun_Y1_6(D!39, C!40, H!43))) | (~apply(H!43, tptp_fun_X_7(D!39, C!40, H!43), tptp_fun_Y2_5(D!39, C!40, H!43))) | (~member(tptp_fun_X_7(D!39, C!40, H!43), C!40)) | (~member(tptp_fun_Y1_6(D!39, C!40, H!43), D!39)) | (~member(tptp_fun_Y2_5(D!39, C!40, H!43), D!39)))) | (~((~member(tptp_fun_X_4(D!39, C!40, H!43), C!40)) | (~![Y: $i] : ((~member(Y, D!39)) | (~apply(H!43, tptp_fun_X_4(D!39, C!40, H!43), Y))))))))))) <=> ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(H!43, C!40, D!39)) | (~((~![X: $i] : ((~member(X, C!40)) | (~((~member(tptp_fun_Y_3(X, D!39, H!43), D!39)) | (~apply(H!43, X, tptp_fun_Y_3(X, D!39, H!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, D!39)) | (~apply(H!43, X, Y1)) | (~apply(H!43, X, Y2)) | (~member(X, C!40)) | (~member(Y1, D!39)))))))) | (~(maps(H!43, C!40, D!39) | (~((~member(tptp_fun_X_4(D!39, C!40, H!43), C!40)) | (~![Y: $i] : ((~member(Y, D!39)) | (~apply(H!43, tptp_fun_X_4(D!39, C!40, H!43), Y)))))) | (~((~member(tptp_fun_Y2_5(D!39, C!40, H!43), D!39)) | (~member(tptp_fun_Y1_6(D!39, C!40, H!43), D!39)) | (~member(tptp_fun_X_7(D!39, C!40, H!43), C!40)) | (~apply(H!43, tptp_fun_X_7(D!39, C!40, H!43), tptp_fun_Y2_5(D!39, C!40, H!43))) | (~apply(H!43, tptp_fun_X_7(D!39, C!40, H!43), tptp_fun_Y1_6(D!39, C!40, H!43))) | (tptp_fun_Y1_6(D!39, C!40, H!43) = tptp_fun_Y2_5(D!39, C!40, H!43)))))))))),
% 0.53/0.74 inference(monotonicity,[status(thm)],[156])).
% 0.53/0.74 tff(158,plain,
% 0.53/0.74 (((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(H!43, C!40, D!39)) | (~((~![X: $i] : ((~member(X, C!40)) | (~((~member(tptp_fun_Y_3(X, D!39, H!43), D!39)) | (~apply(H!43, X, tptp_fun_Y_3(X, D!39, H!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(H!43, X, Y1)) | (~apply(H!43, X, Y2)) | (~member(X, C!40)) | (~member(Y1, D!39)) | (~member(Y2, D!39)))))))) | (~(maps(H!43, C!40, D!39) | (~((tptp_fun_Y1_6(D!39, C!40, H!43) = tptp_fun_Y2_5(D!39, C!40, H!43)) | (~apply(H!43, tptp_fun_X_7(D!39, C!40, H!43), tptp_fun_Y1_6(D!39, C!40, H!43))) | (~apply(H!43, tptp_fun_X_7(D!39, C!40, H!43), tptp_fun_Y2_5(D!39, C!40, H!43))) | (~member(tptp_fun_X_7(D!39, C!40, H!43), C!40)) | (~member(tptp_fun_Y1_6(D!39, C!40, H!43), D!39)) | (~member(tptp_fun_Y2_5(D!39, C!40, H!43), D!39)))) | (~((~member(tptp_fun_X_4(D!39, C!40, H!43), C!40)) | (~![Y: $i] : ((~member(Y, D!39)) | (~apply(H!43, tptp_fun_X_4(D!39, C!40, H!43), Y))))))))))) <=> ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(H!43, C!40, D!39)) | (~((~![X: $i] : ((~member(X, C!40)) | (~((~member(tptp_fun_Y_3(X, D!39, H!43), D!39)) | (~apply(H!43, X, tptp_fun_Y_3(X, D!39, H!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, D!39)) | (~apply(H!43, X, Y1)) | (~apply(H!43, X, Y2)) | (~member(X, C!40)) | (~member(Y1, D!39)))))))) | (~(maps(H!43, C!40, D!39) | (~((~member(tptp_fun_X_4(D!39, C!40, H!43), C!40)) | (~![Y: $i] : ((~member(Y, D!39)) | (~apply(H!43, tptp_fun_X_4(D!39, C!40, H!43), Y)))))) | (~((~member(tptp_fun_Y2_5(D!39, C!40, H!43), D!39)) | (~member(tptp_fun_Y1_6(D!39, C!40, H!43), D!39)) | (~member(tptp_fun_X_7(D!39, C!40, H!43), C!40)) | (~apply(H!43, tptp_fun_X_7(D!39, C!40, H!43), tptp_fun_Y2_5(D!39, C!40, H!43))) | (~apply(H!43, tptp_fun_X_7(D!39, C!40, H!43), tptp_fun_Y1_6(D!39, C!40, H!43))) | (tptp_fun_Y1_6(D!39, C!40, H!43) = tptp_fun_Y2_5(D!39, C!40, H!43)))))))))),
% 0.53/0.75 inference(transitivity,[status(thm)],[157, 155])).
% 0.53/0.75 tff(159,plain,
% 0.53/0.75 ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(H!43, C!40, D!39)) | (~((~![X: $i] : ((~member(X, C!40)) | (~((~member(tptp_fun_Y_3(X, D!39, H!43), D!39)) | (~apply(H!43, X, tptp_fun_Y_3(X, D!39, H!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(H!43, X, Y1)) | (~apply(H!43, X, Y2)) | (~member(X, C!40)) | (~member(Y1, D!39)) | (~member(Y2, D!39)))))))) | (~(maps(H!43, C!40, D!39) | (~((tptp_fun_Y1_6(D!39, C!40, H!43) = tptp_fun_Y2_5(D!39, C!40, H!43)) | (~apply(H!43, tptp_fun_X_7(D!39, C!40, H!43), tptp_fun_Y1_6(D!39, C!40, H!43))) | (~apply(H!43, tptp_fun_X_7(D!39, C!40, H!43), tptp_fun_Y2_5(D!39, C!40, H!43))) | (~member(tptp_fun_X_7(D!39, C!40, H!43), C!40)) | (~member(tptp_fun_Y1_6(D!39, C!40, H!43), D!39)) | (~member(tptp_fun_Y2_5(D!39, C!40, H!43), D!39)))) | (~((~member(tptp_fun_X_4(D!39, C!40, H!43), C!40)) | (~![Y: $i] : ((~member(Y, D!39)) | (~apply(H!43, tptp_fun_X_4(D!39, C!40, H!43), Y))))))))))),
% 0.53/0.75 inference(quant_inst,[status(thm)],[])).
% 0.53/0.75 tff(160,plain,
% 0.53/0.75 ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(H!43, C!40, D!39)) | (~((~![X: $i] : ((~member(X, C!40)) | (~((~member(tptp_fun_Y_3(X, D!39, H!43), D!39)) | (~apply(H!43, X, tptp_fun_Y_3(X, D!39, H!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, D!39)) | (~apply(H!43, X, Y1)) | (~apply(H!43, X, Y2)) | (~member(X, C!40)) | (~member(Y1, D!39)))))))) | (~(maps(H!43, C!40, D!39) | (~((~member(tptp_fun_X_4(D!39, C!40, H!43), C!40)) | (~![Y: $i] : ((~member(Y, D!39)) | (~apply(H!43, tptp_fun_X_4(D!39, C!40, H!43), Y)))))) | (~((~member(tptp_fun_Y2_5(D!39, C!40, H!43), D!39)) | (~member(tptp_fun_Y1_6(D!39, C!40, H!43), D!39)) | (~member(tptp_fun_X_7(D!39, C!40, H!43), C!40)) | (~apply(H!43, tptp_fun_X_7(D!39, C!40, H!43), tptp_fun_Y2_5(D!39, C!40, H!43))) | (~apply(H!43, tptp_fun_X_7(D!39, C!40, H!43), tptp_fun_Y1_6(D!39, C!40, H!43))) | (tptp_fun_Y1_6(D!39, C!40, H!43) = tptp_fun_Y2_5(D!39, C!40, H!43))))))))),
% 0.53/0.75 inference(modus_ponens,[status(thm)],[159, 158])).
% 0.53/0.75 tff(161,plain,
% 0.53/0.75 (~((~((~maps(H!43, C!40, D!39)) | (~((~![X: $i] : ((~member(X, C!40)) | (~((~member(tptp_fun_Y_3(X, D!39, H!43), D!39)) | (~apply(H!43, X, tptp_fun_Y_3(X, D!39, H!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, D!39)) | (~apply(H!43, X, Y1)) | (~apply(H!43, X, Y2)) | (~member(X, C!40)) | (~member(Y1, D!39)))))))) | (~(maps(H!43, C!40, D!39) | (~((~member(tptp_fun_X_4(D!39, C!40, H!43), C!40)) | (~![Y: $i] : ((~member(Y, D!39)) | (~apply(H!43, tptp_fun_X_4(D!39, C!40, H!43), Y)))))) | (~((~member(tptp_fun_Y2_5(D!39, C!40, H!43), D!39)) | (~member(tptp_fun_Y1_6(D!39, C!40, H!43), D!39)) | (~member(tptp_fun_X_7(D!39, C!40, H!43), C!40)) | (~apply(H!43, tptp_fun_X_7(D!39, C!40, H!43), tptp_fun_Y2_5(D!39, C!40, H!43))) | (~apply(H!43, tptp_fun_X_7(D!39, C!40, H!43), tptp_fun_Y1_6(D!39, C!40, H!43))) | (tptp_fun_Y1_6(D!39, C!40, H!43) = tptp_fun_Y2_5(D!39, C!40, H!43)))))))),
% 0.53/0.75 inference(unit_resolution,[status(thm)],[160, 98])).
% 0.53/0.75 tff(162,plain,
% 0.53/0.75 (((~((~maps(H!43, C!40, D!39)) | (~((~![X: $i] : ((~member(X, C!40)) | (~((~member(tptp_fun_Y_3(X, D!39, H!43), D!39)) | (~apply(H!43, X, tptp_fun_Y_3(X, D!39, H!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, D!39)) | (~apply(H!43, X, Y1)) | (~apply(H!43, X, Y2)) | (~member(X, C!40)) | (~member(Y1, D!39)))))))) | (~(maps(H!43, C!40, D!39) | (~((~member(tptp_fun_X_4(D!39, C!40, H!43), C!40)) | (~![Y: $i] : ((~member(Y, D!39)) | (~apply(H!43, tptp_fun_X_4(D!39, C!40, H!43), Y)))))) | (~((~member(tptp_fun_Y2_5(D!39, C!40, H!43), D!39)) | (~member(tptp_fun_Y1_6(D!39, C!40, H!43), D!39)) | (~member(tptp_fun_X_7(D!39, C!40, H!43), C!40)) | (~apply(H!43, tptp_fun_X_7(D!39, C!40, H!43), tptp_fun_Y2_5(D!39, C!40, H!43))) | (~apply(H!43, tptp_fun_X_7(D!39, C!40, H!43), tptp_fun_Y1_6(D!39, C!40, H!43))) | (tptp_fun_Y1_6(D!39, C!40, H!43) = tptp_fun_Y2_5(D!39, C!40, H!43))))))) | ((~maps(H!43, C!40, D!39)) | (~((~![X: $i] : ((~member(X, C!40)) | (~((~member(tptp_fun_Y_3(X, D!39, H!43), D!39)) | (~apply(H!43, X, tptp_fun_Y_3(X, D!39, H!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, D!39)) | (~apply(H!43, X, Y1)) | (~apply(H!43, X, Y2)) | (~member(X, C!40)) | (~member(Y1, D!39)))))))),
% 0.53/0.75 inference(tautology,[status(thm)],[])).
% 0.53/0.75 tff(163,plain,
% 0.53/0.75 ((~maps(H!43, C!40, D!39)) | (~((~![X: $i] : ((~member(X, C!40)) | (~((~member(tptp_fun_Y_3(X, D!39, H!43), D!39)) | (~apply(H!43, X, tptp_fun_Y_3(X, D!39, H!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, D!39)) | (~apply(H!43, X, Y1)) | (~apply(H!43, X, Y2)) | (~member(X, C!40)) | (~member(Y1, D!39))))))),
% 0.53/0.75 inference(unit_resolution,[status(thm)],[162, 161])).
% 0.53/0.75 tff(164,plain,
% 0.53/0.75 (maps(H!43, C!40, D!39)),
% 0.53/0.75 inference(and_elim,[status(thm)],[108])).
% 0.53/0.75 tff(165,plain,
% 0.53/0.75 ((~((~maps(H!43, C!40, D!39)) | (~((~![X: $i] : ((~member(X, C!40)) | (~((~member(tptp_fun_Y_3(X, D!39, H!43), D!39)) | (~apply(H!43, X, tptp_fun_Y_3(X, D!39, H!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, D!39)) | (~apply(H!43, X, Y1)) | (~apply(H!43, X, Y2)) | (~member(X, C!40)) | (~member(Y1, D!39)))))))) | (~maps(H!43, C!40, D!39)) | (~((~![X: $i] : ((~member(X, C!40)) | (~((~member(tptp_fun_Y_3(X, D!39, H!43), D!39)) | (~apply(H!43, X, tptp_fun_Y_3(X, D!39, H!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, D!39)) | (~apply(H!43, X, Y1)) | (~apply(H!43, X, Y2)) | (~member(X, C!40)) | (~member(Y1, D!39))))))),
% 0.53/0.75 inference(tautology,[status(thm)],[])).
% 0.53/0.75 tff(166,plain,
% 0.53/0.75 ((~((~maps(H!43, C!40, D!39)) | (~((~![X: $i] : ((~member(X, C!40)) | (~((~member(tptp_fun_Y_3(X, D!39, H!43), D!39)) | (~apply(H!43, X, tptp_fun_Y_3(X, D!39, H!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, D!39)) | (~apply(H!43, X, Y1)) | (~apply(H!43, X, Y2)) | (~member(X, C!40)) | (~member(Y1, D!39)))))))) | (~((~![X: $i] : ((~member(X, C!40)) | (~((~member(tptp_fun_Y_3(X, D!39, H!43), D!39)) | (~apply(H!43, X, tptp_fun_Y_3(X, D!39, H!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, D!39)) | (~apply(H!43, X, Y1)) | (~apply(H!43, X, Y2)) | (~member(X, C!40)) | (~member(Y1, D!39))))))),
% 0.53/0.75 inference(unit_resolution,[status(thm)],[165, 164])).
% 0.53/0.75 tff(167,plain,
% 0.53/0.75 (~((~![X: $i] : ((~member(X, C!40)) | (~((~member(tptp_fun_Y_3(X, D!39, H!43), D!39)) | (~apply(H!43, X, tptp_fun_Y_3(X, D!39, H!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, D!39)) | (~apply(H!43, X, Y1)) | (~apply(H!43, X, Y2)) | (~member(X, C!40)) | (~member(Y1, D!39)))))),
% 0.53/0.75 inference(unit_resolution,[status(thm)],[166, 163])).
% 0.53/0.75 tff(168,plain,
% 0.53/0.75 (((~![X: $i] : ((~member(X, C!40)) | (~((~member(tptp_fun_Y_3(X, D!39, H!43), D!39)) | (~apply(H!43, X, tptp_fun_Y_3(X, D!39, H!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, D!39)) | (~apply(H!43, X, Y1)) | (~apply(H!43, X, Y2)) | (~member(X, C!40)) | (~member(Y1, D!39))))) | ![X: $i] : ((~member(X, C!40)) | (~((~member(tptp_fun_Y_3(X, D!39, H!43), D!39)) | (~apply(H!43, X, tptp_fun_Y_3(X, D!39, H!43))))))),
% 0.53/0.75 inference(tautology,[status(thm)],[])).
% 0.53/0.75 tff(169,plain,
% 0.53/0.75 (![X: $i] : ((~member(X, C!40)) | (~((~member(tptp_fun_Y_3(X, D!39, H!43), D!39)) | (~apply(H!43, X, tptp_fun_Y_3(X, D!39, H!43))))))),
% 0.53/0.75 inference(unit_resolution,[status(thm)],[168, 167])).
% 0.53/0.75 tff(170,plain,
% 0.53/0.75 (((~![X: $i] : ((~member(X, C!40)) | (~((~member(tptp_fun_Y_3(X, D!39, H!43), D!39)) | (~apply(H!43, X, tptp_fun_Y_3(X, D!39, H!43))))))) | ((~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y2_12(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), B!41, F!45, compose_function(H!43, G!44, B!41, C!40, D!39)), C!40, G!44), C!40)) | (~((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y2_12(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), B!41, F!45, compose_function(H!43, G!44, B!41, C!40, D!39)), C!40, G!44), D!39, H!43), D!39)) | (~apply(H!43, tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y2_12(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), B!41, F!45, compose_function(H!43, G!44, B!41, C!40, D!39)), C!40, G!44), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y2_12(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), B!41, F!45, compose_function(H!43, G!44, B!41, C!40, D!39)), C!40, G!44), D!39, H!43))))))) <=> ((~![X: $i] : ((~member(X, C!40)) | (~((~member(tptp_fun_Y_3(X, D!39, H!43), D!39)) | (~apply(H!43, X, tptp_fun_Y_3(X, D!39, H!43))))))) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y2_12(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), B!41, F!45, compose_function(H!43, G!44, B!41, C!40, D!39)), C!40, G!44), C!40)) | (~((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y2_12(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), B!41, F!45, compose_function(H!43, G!44, B!41, C!40, D!39)), C!40, G!44), D!39, H!43), D!39)) | (~apply(H!43, tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y2_12(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), B!41, F!45, compose_function(H!43, G!44, B!41, C!40, D!39)), C!40, G!44), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y2_12(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), B!41, F!45, compose_function(H!43, G!44, B!41, C!40, D!39)), C!40, G!44), D!39, H!43))))))),
% 0.59/0.75 inference(rewrite,[status(thm)],[])).
% 0.59/0.75 tff(171,plain,
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% 0.59/0.76 inference(quant_inst,[status(thm)],[])).
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% 0.59/0.76 inference(modus_ponens,[status(thm)],[171, 170])).
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% 0.59/0.76 inference(unit_resolution,[status(thm)],[172, 169, 122])).
% 0.59/0.76 tff(174,plain,
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% 0.60/0.76 inference(tautology,[status(thm)],[])).
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% 0.60/0.76 inference(unit_resolution,[status(thm)],[174, 173])).
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% 0.60/0.77 inference(unit_resolution,[status(thm)],[176, 173])).
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% 0.60/0.77 inference(tautology,[status(thm)],[])).
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% 0.60/0.80 inference(modus_ponens,[status(thm)],[184, 183])).
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% 0.60/0.80 inference(unit_resolution,[status(thm)],[185, 179, 41, 122, 177, 175])).
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% 0.60/0.80 inference(unit_resolution,[status(thm)],[186, 154])).
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% 0.60/0.80 inference(tautology,[status(thm)],[])).
% 0.60/0.80 tff(189,plain,
% 0.60/0.80 (member(tptp_fun_Y1_13(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), D!39)),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[188, 37])).
% 0.60/0.80 tff(190,plain,
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% 0.64/0.81 inference(rewrite,[status(thm)],[])).
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% 0.77/0.95 (((~member(tptp_fun_Y_8(tptp_fun_Y_8(tptp_fun_Y1_13(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), C!40, compose_function(G!44, F!45, A!42, B!41, C!40), H!43), tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), B!41, F!45, G!44), B!41)) | (~apply(F!45, tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), tptp_fun_Y_8(tptp_fun_Y_8(tptp_fun_Y1_13(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), C!40, compose_function(G!44, F!45, A!42, B!41, C!40), H!43), tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), B!41, F!45, G!44))) | (~apply(G!44, tptp_fun_Y_8(tptp_fun_Y_8(tptp_fun_Y1_13(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), C!40, compose_function(G!44, F!45, A!42, B!41, C!40), H!43), tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), B!41, F!45, G!44), tptp_fun_Y_8(tptp_fun_Y1_13(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), C!40, compose_function(G!44, F!45, A!42, B!41, C!40), H!43)))) | member(tptp_fun_Y_8(tptp_fun_Y_8(tptp_fun_Y1_13(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), C!40, compose_function(G!44, F!45, A!42, B!41, C!40), H!43), tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), B!41, F!45, G!44), B!41)),
% 0.77/0.96 inference(tautology,[status(thm)],[])).
% 0.77/0.96 tff(229,plain,
% 0.77/0.96 (member(tptp_fun_Y_8(tptp_fun_Y_8(tptp_fun_Y1_13(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), C!40, compose_function(G!44, F!45, A!42, B!41, C!40), H!43), tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), B!41, F!45, G!44), B!41)),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[228, 225])).
% 0.77/0.96 tff(230,plain,
% 0.77/0.96 (((~member(tptp_fun_Y_8(tptp_fun_Y2_12(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), B!41, F!45, compose_function(H!43, G!44, B!41, C!40, D!39)), B!41)) | (~apply(F!45, tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), tptp_fun_Y_8(tptp_fun_Y2_12(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), B!41, F!45, compose_function(H!43, G!44, B!41, C!40, D!39)))) | (~apply(compose_function(H!43, G!44, B!41, C!40, D!39), tptp_fun_Y_8(tptp_fun_Y2_12(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), B!41, F!45, compose_function(H!43, G!44, B!41, C!40, D!39)), tptp_fun_Y2_12(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39))))) | apply(F!45, tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), tptp_fun_Y_8(tptp_fun_Y2_12(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), B!41, F!45, compose_function(H!43, G!44, B!41, C!40, D!39)))),
% 0.77/0.96 inference(tautology,[status(thm)],[])).
% 0.77/0.96 tff(231,plain,
% 0.77/0.96 (apply(F!45, tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), tptp_fun_Y_8(tptp_fun_Y2_12(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), B!41, F!45, compose_function(H!43, G!44, B!41, C!40, D!39)))),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[230, 74])).
% 0.77/0.96 tff(232,plain,
% 0.77/0.96 (((~![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!45, A!42, B!41)) | (~((~![X: $i] : ((~member(X, A!42)) | (~((~member(tptp_fun_Y_3(X, B!41, F!45), B!41)) | (~apply(F!45, X, tptp_fun_Y_3(X, B!41, F!45))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!41)) | (~apply(F!45, X, Y1)) | (~apply(F!45, X, Y2)) | (~member(X, A!42)) | (~member(Y1, B!41)))))))) | (~(maps(F!45, A!42, B!41) | (~((~member(tptp_fun_X_4(B!41, A!42, F!45), A!42)) | (~![Y: $i] : ((~member(Y, B!41)) | (~apply(F!45, tptp_fun_X_4(B!41, A!42, F!45), Y)))))) | (~((~member(tptp_fun_Y2_5(B!41, A!42, F!45), B!41)) | (~member(tptp_fun_Y1_6(B!41, A!42, F!45), B!41)) | (~member(tptp_fun_X_7(B!41, A!42, F!45), A!42)) | (~apply(F!45, tptp_fun_X_7(B!41, A!42, F!45), tptp_fun_Y2_5(B!41, A!42, F!45))) | (~apply(F!45, tptp_fun_X_7(B!41, A!42, F!45), tptp_fun_Y1_6(B!41, A!42, F!45))) | (tptp_fun_Y1_6(B!41, A!42, F!45) = tptp_fun_Y2_5(B!41, A!42, F!45))))))))) <=> ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(F!45, A!42, B!41)) | (~((~![X: $i] : ((~member(X, A!42)) | (~((~member(tptp_fun_Y_3(X, B!41, F!45), B!41)) | (~apply(F!45, X, tptp_fun_Y_3(X, B!41, F!45))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!41)) | (~apply(F!45, X, Y1)) | (~apply(F!45, X, Y2)) | (~member(X, A!42)) | (~member(Y1, B!41)))))))) | (~(maps(F!45, A!42, B!41) | (~((~member(tptp_fun_X_4(B!41, A!42, F!45), A!42)) | (~![Y: $i] : ((~member(Y, B!41)) | (~apply(F!45, tptp_fun_X_4(B!41, A!42, F!45), Y)))))) | (~((~member(tptp_fun_Y2_5(B!41, A!42, F!45), B!41)) | (~member(tptp_fun_Y1_6(B!41, A!42, F!45), B!41)) | (~member(tptp_fun_X_7(B!41, A!42, F!45), A!42)) | (~apply(F!45, tptp_fun_X_7(B!41, A!42, F!45), tptp_fun_Y2_5(B!41, A!42, F!45))) | (~apply(F!45, tptp_fun_X_7(B!41, A!42, F!45), tptp_fun_Y1_6(B!41, A!42, F!45))) | (tptp_fun_Y1_6(B!41, A!42, F!45) = tptp_fun_Y2_5(B!41, A!42, F!45)))))))))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(233,plain,
% 0.77/0.96 ((~((~((~maps(F!45, A!42, B!41)) | (~((~![X: $i] : ((~member(X, A!42)) | (~((~member(tptp_fun_Y_3(X, B!41, F!45), B!41)) | (~apply(F!45, X, tptp_fun_Y_3(X, B!41, F!45))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!45, X, Y1)) | (~apply(F!45, X, Y2)) | (~member(X, A!42)) | (~member(Y1, B!41)) | (~member(Y2, B!41)))))))) | (~(maps(F!45, A!42, B!41) | (~((tptp_fun_Y1_6(B!41, A!42, F!45) = tptp_fun_Y2_5(B!41, A!42, F!45)) | (~apply(F!45, tptp_fun_X_7(B!41, A!42, F!45), tptp_fun_Y1_6(B!41, A!42, F!45))) | (~apply(F!45, tptp_fun_X_7(B!41, A!42, F!45), tptp_fun_Y2_5(B!41, A!42, F!45))) | (~member(tptp_fun_X_7(B!41, A!42, F!45), A!42)) | (~member(tptp_fun_Y1_6(B!41, A!42, F!45), B!41)) | (~member(tptp_fun_Y2_5(B!41, A!42, F!45), B!41)))) | (~((~member(tptp_fun_X_4(B!41, A!42, F!45), A!42)) | (~![Y: $i] : ((~member(Y, B!41)) | (~apply(F!45, tptp_fun_X_4(B!41, A!42, F!45), Y)))))))))) <=> (~((~((~maps(F!45, A!42, B!41)) | (~((~![X: $i] : ((~member(X, A!42)) | (~((~member(tptp_fun_Y_3(X, B!41, F!45), B!41)) | (~apply(F!45, X, tptp_fun_Y_3(X, B!41, F!45))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!41)) | (~apply(F!45, X, Y1)) | (~apply(F!45, X, Y2)) | (~member(X, A!42)) | (~member(Y1, B!41)))))))) | (~(maps(F!45, A!42, B!41) | (~((~member(tptp_fun_X_4(B!41, A!42, F!45), A!42)) | (~![Y: $i] : ((~member(Y, B!41)) | (~apply(F!45, tptp_fun_X_4(B!41, A!42, F!45), Y)))))) | (~((~member(tptp_fun_Y2_5(B!41, A!42, F!45), B!41)) | (~member(tptp_fun_Y1_6(B!41, A!42, F!45), B!41)) | (~member(tptp_fun_X_7(B!41, A!42, F!45), A!42)) | (~apply(F!45, tptp_fun_X_7(B!41, A!42, F!45), tptp_fun_Y2_5(B!41, A!42, F!45))) | (~apply(F!45, tptp_fun_X_7(B!41, A!42, F!45), tptp_fun_Y1_6(B!41, A!42, F!45))) | (tptp_fun_Y1_6(B!41, A!42, F!45) = tptp_fun_Y2_5(B!41, A!42, F!45))))))))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(234,plain,
% 0.77/0.96 (((~![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!45, A!42, B!41)) | (~((~![X: $i] : ((~member(X, A!42)) | (~((~member(tptp_fun_Y_3(X, B!41, F!45), B!41)) | (~apply(F!45, X, tptp_fun_Y_3(X, B!41, F!45))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!45, X, Y1)) | (~apply(F!45, X, Y2)) | (~member(X, A!42)) | (~member(Y1, B!41)) | (~member(Y2, B!41)))))))) | (~(maps(F!45, A!42, B!41) | (~((tptp_fun_Y1_6(B!41, A!42, F!45) = tptp_fun_Y2_5(B!41, A!42, F!45)) | (~apply(F!45, tptp_fun_X_7(B!41, A!42, F!45), tptp_fun_Y1_6(B!41, A!42, F!45))) | (~apply(F!45, tptp_fun_X_7(B!41, A!42, F!45), tptp_fun_Y2_5(B!41, A!42, F!45))) | (~member(tptp_fun_X_7(B!41, A!42, F!45), A!42)) | (~member(tptp_fun_Y1_6(B!41, A!42, F!45), B!41)) | (~member(tptp_fun_Y2_5(B!41, A!42, F!45), B!41)))) | (~((~member(tptp_fun_X_4(B!41, A!42, F!45), A!42)) | (~![Y: $i] : ((~member(Y, B!41)) | (~apply(F!45, tptp_fun_X_4(B!41, A!42, F!45), 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!45, A!42, B!41)) | (~((~![X: $i] : ((~member(X, A!42)) | (~((~member(tptp_fun_Y_3(X, B!41, F!45), B!41)) | (~apply(F!45, X, tptp_fun_Y_3(X, B!41, F!45))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!41)) | (~apply(F!45, X, Y1)) | (~apply(F!45, X, Y2)) | (~member(X, A!42)) | (~member(Y1, B!41)))))))) | (~(maps(F!45, A!42, B!41) | (~((~member(tptp_fun_X_4(B!41, A!42, F!45), A!42)) | (~![Y: $i] : ((~member(Y, B!41)) | (~apply(F!45, tptp_fun_X_4(B!41, A!42, F!45), Y)))))) | (~((~member(tptp_fun_Y2_5(B!41, A!42, F!45), B!41)) | (~member(tptp_fun_Y1_6(B!41, A!42, F!45), B!41)) | (~member(tptp_fun_X_7(B!41, A!42, F!45), A!42)) | (~apply(F!45, tptp_fun_X_7(B!41, A!42, F!45), tptp_fun_Y2_5(B!41, A!42, F!45))) | (~apply(F!45, tptp_fun_X_7(B!41, A!42, F!45), tptp_fun_Y1_6(B!41, A!42, F!45))) | (tptp_fun_Y1_6(B!41, A!42, F!45) = tptp_fun_Y2_5(B!41, A!42, F!45)))))))))),
% 0.77/0.96 inference(monotonicity,[status(thm)],[233])).
% 0.77/0.96 tff(235,plain,
% 0.77/0.96 (((~![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!45, A!42, B!41)) | (~((~![X: $i] : ((~member(X, A!42)) | (~((~member(tptp_fun_Y_3(X, B!41, F!45), B!41)) | (~apply(F!45, X, tptp_fun_Y_3(X, B!41, F!45))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!45, X, Y1)) | (~apply(F!45, X, Y2)) | (~member(X, A!42)) | (~member(Y1, B!41)) | (~member(Y2, B!41)))))))) | (~(maps(F!45, A!42, B!41) | (~((tptp_fun_Y1_6(B!41, A!42, F!45) = tptp_fun_Y2_5(B!41, A!42, F!45)) | (~apply(F!45, tptp_fun_X_7(B!41, A!42, F!45), tptp_fun_Y1_6(B!41, A!42, F!45))) | (~apply(F!45, tptp_fun_X_7(B!41, A!42, F!45), tptp_fun_Y2_5(B!41, A!42, F!45))) | (~member(tptp_fun_X_7(B!41, A!42, F!45), A!42)) | (~member(tptp_fun_Y1_6(B!41, A!42, F!45), B!41)) | (~member(tptp_fun_Y2_5(B!41, A!42, F!45), B!41)))) | (~((~member(tptp_fun_X_4(B!41, A!42, F!45), A!42)) | (~![Y: $i] : ((~member(Y, B!41)) | (~apply(F!45, tptp_fun_X_4(B!41, A!42, F!45), 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!45, A!42, B!41)) | (~((~![X: $i] : ((~member(X, A!42)) | (~((~member(tptp_fun_Y_3(X, B!41, F!45), B!41)) | (~apply(F!45, X, tptp_fun_Y_3(X, B!41, F!45))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!41)) | (~apply(F!45, X, Y1)) | (~apply(F!45, X, Y2)) | (~member(X, A!42)) | (~member(Y1, B!41)))))))) | (~(maps(F!45, A!42, B!41) | (~((~member(tptp_fun_X_4(B!41, A!42, F!45), A!42)) | (~![Y: $i] : ((~member(Y, B!41)) | (~apply(F!45, tptp_fun_X_4(B!41, A!42, F!45), Y)))))) | (~((~member(tptp_fun_Y2_5(B!41, A!42, F!45), B!41)) | (~member(tptp_fun_Y1_6(B!41, A!42, F!45), B!41)) | (~member(tptp_fun_X_7(B!41, A!42, F!45), A!42)) | (~apply(F!45, tptp_fun_X_7(B!41, A!42, F!45), tptp_fun_Y2_5(B!41, A!42, F!45))) | (~apply(F!45, tptp_fun_X_7(B!41, A!42, F!45), tptp_fun_Y1_6(B!41, A!42, F!45))) | (tptp_fun_Y1_6(B!41, A!42, F!45) = tptp_fun_Y2_5(B!41, A!42, F!45)))))))))),
% 0.77/0.96 inference(transitivity,[status(thm)],[234, 232])).
% 0.77/0.96 tff(236,plain,
% 0.77/0.96 ((~![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!45, A!42, B!41)) | (~((~![X: $i] : ((~member(X, A!42)) | (~((~member(tptp_fun_Y_3(X, B!41, F!45), B!41)) | (~apply(F!45, X, tptp_fun_Y_3(X, B!41, F!45))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!45, X, Y1)) | (~apply(F!45, X, Y2)) | (~member(X, A!42)) | (~member(Y1, B!41)) | (~member(Y2, B!41)))))))) | (~(maps(F!45, A!42, B!41) | (~((tptp_fun_Y1_6(B!41, A!42, F!45) = tptp_fun_Y2_5(B!41, A!42, F!45)) | (~apply(F!45, tptp_fun_X_7(B!41, A!42, F!45), tptp_fun_Y1_6(B!41, A!42, F!45))) | (~apply(F!45, tptp_fun_X_7(B!41, A!42, F!45), tptp_fun_Y2_5(B!41, A!42, F!45))) | (~member(tptp_fun_X_7(B!41, A!42, F!45), A!42)) | (~member(tptp_fun_Y1_6(B!41, A!42, F!45), B!41)) | (~member(tptp_fun_Y2_5(B!41, A!42, F!45), B!41)))) | (~((~member(tptp_fun_X_4(B!41, A!42, F!45), A!42)) | (~![Y: $i] : ((~member(Y, B!41)) | (~apply(F!45, tptp_fun_X_4(B!41, A!42, F!45), Y))))))))))),
% 0.77/0.96 inference(quant_inst,[status(thm)],[])).
% 0.77/0.96 tff(237,plain,
% 0.77/0.96 ((~![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!45, A!42, B!41)) | (~((~![X: $i] : ((~member(X, A!42)) | (~((~member(tptp_fun_Y_3(X, B!41, F!45), B!41)) | (~apply(F!45, X, tptp_fun_Y_3(X, B!41, F!45))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!41)) | (~apply(F!45, X, Y1)) | (~apply(F!45, X, Y2)) | (~member(X, A!42)) | (~member(Y1, B!41)))))))) | (~(maps(F!45, A!42, B!41) | (~((~member(tptp_fun_X_4(B!41, A!42, F!45), A!42)) | (~![Y: $i] : ((~member(Y, B!41)) | (~apply(F!45, tptp_fun_X_4(B!41, A!42, F!45), Y)))))) | (~((~member(tptp_fun_Y2_5(B!41, A!42, F!45), B!41)) | (~member(tptp_fun_Y1_6(B!41, A!42, F!45), B!41)) | (~member(tptp_fun_X_7(B!41, A!42, F!45), A!42)) | (~apply(F!45, tptp_fun_X_7(B!41, A!42, F!45), tptp_fun_Y2_5(B!41, A!42, F!45))) | (~apply(F!45, tptp_fun_X_7(B!41, A!42, F!45), tptp_fun_Y1_6(B!41, A!42, F!45))) | (tptp_fun_Y1_6(B!41, A!42, F!45) = tptp_fun_Y2_5(B!41, A!42, F!45))))))))),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[236, 235])).
% 0.77/0.96 tff(238,plain,
% 0.77/0.96 (~((~((~maps(F!45, A!42, B!41)) | (~((~![X: $i] : ((~member(X, A!42)) | (~((~member(tptp_fun_Y_3(X, B!41, F!45), B!41)) | (~apply(F!45, X, tptp_fun_Y_3(X, B!41, F!45))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!41)) | (~apply(F!45, X, Y1)) | (~apply(F!45, X, Y2)) | (~member(X, A!42)) | (~member(Y1, B!41)))))))) | (~(maps(F!45, A!42, B!41) | (~((~member(tptp_fun_X_4(B!41, A!42, F!45), A!42)) | (~![Y: $i] : ((~member(Y, B!41)) | (~apply(F!45, tptp_fun_X_4(B!41, A!42, F!45), Y)))))) | (~((~member(tptp_fun_Y2_5(B!41, A!42, F!45), B!41)) | (~member(tptp_fun_Y1_6(B!41, A!42, F!45), B!41)) | (~member(tptp_fun_X_7(B!41, A!42, F!45), A!42)) | (~apply(F!45, tptp_fun_X_7(B!41, A!42, F!45), tptp_fun_Y2_5(B!41, A!42, F!45))) | (~apply(F!45, tptp_fun_X_7(B!41, A!42, F!45), tptp_fun_Y1_6(B!41, A!42, F!45))) | (tptp_fun_Y1_6(B!41, A!42, F!45) = tptp_fun_Y2_5(B!41, A!42, F!45)))))))),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[237, 98])).
% 0.77/0.96 tff(239,plain,
% 0.77/0.96 (((~((~maps(F!45, A!42, B!41)) | (~((~![X: $i] : ((~member(X, A!42)) | (~((~member(tptp_fun_Y_3(X, B!41, F!45), B!41)) | (~apply(F!45, X, tptp_fun_Y_3(X, B!41, F!45))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!41)) | (~apply(F!45, X, Y1)) | (~apply(F!45, X, Y2)) | (~member(X, A!42)) | (~member(Y1, B!41)))))))) | (~(maps(F!45, A!42, B!41) | (~((~member(tptp_fun_X_4(B!41, A!42, F!45), A!42)) | (~![Y: $i] : ((~member(Y, B!41)) | (~apply(F!45, tptp_fun_X_4(B!41, A!42, F!45), Y)))))) | (~((~member(tptp_fun_Y2_5(B!41, A!42, F!45), B!41)) | (~member(tptp_fun_Y1_6(B!41, A!42, F!45), B!41)) | (~member(tptp_fun_X_7(B!41, A!42, F!45), A!42)) | (~apply(F!45, tptp_fun_X_7(B!41, A!42, F!45), tptp_fun_Y2_5(B!41, A!42, F!45))) | (~apply(F!45, tptp_fun_X_7(B!41, A!42, F!45), tptp_fun_Y1_6(B!41, A!42, F!45))) | (tptp_fun_Y1_6(B!41, A!42, F!45) = tptp_fun_Y2_5(B!41, A!42, F!45))))))) | ((~maps(F!45, A!42, B!41)) | (~((~![X: $i] : ((~member(X, A!42)) | (~((~member(tptp_fun_Y_3(X, B!41, F!45), B!41)) | (~apply(F!45, X, tptp_fun_Y_3(X, B!41, F!45))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!41)) | (~apply(F!45, X, Y1)) | (~apply(F!45, X, Y2)) | (~member(X, A!42)) | (~member(Y1, B!41)))))))),
% 0.77/0.97 inference(tautology,[status(thm)],[])).
% 0.77/0.97 tff(240,plain,
% 0.77/0.97 ((~maps(F!45, A!42, B!41)) | (~((~![X: $i] : ((~member(X, A!42)) | (~((~member(tptp_fun_Y_3(X, B!41, F!45), B!41)) | (~apply(F!45, X, tptp_fun_Y_3(X, B!41, F!45))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!41)) | (~apply(F!45, X, Y1)) | (~apply(F!45, X, Y2)) | (~member(X, A!42)) | (~member(Y1, B!41))))))),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[239, 238])).
% 0.77/0.97 tff(241,plain,
% 0.77/0.97 (maps(F!45, A!42, B!41)),
% 0.77/0.97 inference(and_elim,[status(thm)],[108])).
% 0.77/0.97 tff(242,plain,
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% 0.83/0.99 inference(quant_inst,[status(thm)],[])).
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% 0.83/0.99 inference(modus_ponens,[status(thm)],[251, 250])).
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% 0.83/0.99 inference(unit_resolution,[status(thm)],[252, 246, 39, 76, 231, 229, 227])).
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% 0.83/0.99 inference(symmetry,[status(thm)],[253])).
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% 0.83/1.00 inference(monotonicity,[status(thm)],[254])).
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% 0.83/1.00 inference(symmetry,[status(thm)],[255])).
% 0.83/1.00 tff(257,plain,
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% 0.83/1.00 inference(tautology,[status(thm)],[])).
% 0.83/1.00 tff(258,plain,
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% 0.83/1.00 inference(unit_resolution,[status(thm)],[257, 225])).
% 0.83/1.00 tff(259,plain,
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% 0.83/1.00 inference(modus_ponens,[status(thm)],[258, 256])).
% 0.83/1.00 tff(260,plain,
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% 0.83/1.02 inference(monotonicity,[status(thm)],[261])).
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% 0.83/1.03 inference(quant_inst,[status(thm)],[])).
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% 0.83/1.03 inference(modus_ponens,[status(thm)],[264, 263])).
% 0.83/1.03 tff(266,plain,
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% 0.83/1.03 inference(unit_resolution,[status(thm)],[265, 142, 208, 76, 122, 120])).
% 0.83/1.03 tff(267,plain,
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% 0.83/1.03 inference(unit_resolution,[status(thm)],[266, 259])).
% 0.83/1.03 tff(268,plain,
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% 0.83/1.03 inference(monotonicity,[status(thm)],[267])).
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% 0.83/1.03 inference(rewrite,[status(thm)],[])).
% 0.83/1.03 tff(270,plain,
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% 0.83/1.03 inference(quant_inst,[status(thm)],[])).
% 0.83/1.03 tff(271,plain,
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% 0.83/1.04 inference(modus_ponens,[status(thm)],[270, 269])).
% 0.83/1.04 tff(272,plain,
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% 0.83/1.04 inference(unit_resolution,[status(thm)],[271, 169, 208])).
% 0.83/1.04 tff(273,plain,
% 0.83/1.04 (((~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y1_13(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), C!40, compose_function(G!44, F!45, A!42, B!41, C!40), H!43), D!39, H!43), D!39)) | (~apply(H!43, tptp_fun_Y_8(tptp_fun_Y1_13(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), C!40, compose_function(G!44, F!45, A!42, B!41, C!40), H!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y1_13(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), C!40, compose_function(G!44, F!45, A!42, B!41, C!40), H!43), D!39, H!43)))) | apply(H!43, tptp_fun_Y_8(tptp_fun_Y1_13(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), C!40, compose_function(G!44, F!45, A!42, B!41, C!40), H!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y1_13(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), C!40, compose_function(G!44, F!45, A!42, B!41, C!40), H!43), D!39, H!43))),
% 0.83/1.04 inference(tautology,[status(thm)],[])).
% 0.83/1.04 tff(274,plain,
% 0.83/1.04 (apply(H!43, tptp_fun_Y_8(tptp_fun_Y1_13(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), C!40, compose_function(G!44, F!45, A!42, B!41, C!40), H!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y1_13(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), C!40, compose_function(G!44, F!45, A!42, B!41, C!40), H!43), D!39, H!43))),
% 0.83/1.04 inference(unit_resolution,[status(thm)],[273, 272])).
% 0.83/1.04 tff(275,plain,
% 0.83/1.04 (((~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y1_13(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), C!40, compose_function(G!44, F!45, A!42, B!41, C!40), H!43), D!39, H!43), D!39)) | (~apply(H!43, tptp_fun_Y_8(tptp_fun_Y1_13(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), C!40, compose_function(G!44, F!45, A!42, B!41, C!40), H!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y1_13(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), C!40, compose_function(G!44, F!45, A!42, B!41, C!40), H!43), D!39, H!43)))) | member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y1_13(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), C!40, compose_function(G!44, F!45, A!42, B!41, C!40), H!43), D!39, H!43), D!39)),
% 0.83/1.04 inference(tautology,[status(thm)],[])).
% 0.83/1.04 tff(276,plain,
% 0.83/1.04 (member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y1_13(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), C!40, compose_function(G!44, F!45, A!42, B!41, C!40), H!43), D!39, H!43), D!39)),
% 0.83/1.04 inference(unit_resolution,[status(thm)],[275, 272])).
% 0.83/1.04 tff(277,plain,
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% 0.83/1.05 inference(rewrite,[status(thm)],[])).
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% 0.89/1.06 inference(quant_inst,[status(thm)],[])).
% 0.89/1.06 tff(284,plain,
% 0.89/1.06 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, D!39)) | (~apply(H!43, X, Y1)) | (~apply(H!43, X, Y2)) | (~member(X, C!40)) | (~member(Y1, D!39)))) | (~member(tptp_fun_Y1_13(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), D!39)) | (~apply(H!43, tptp_fun_Y_8(tptp_fun_Y1_13(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), C!40, compose_function(G!44, F!45, A!42, B!41, C!40), H!43), tptp_fun_Y1_13(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)))) | (~member(tptp_fun_Y_8(tptp_fun_Y1_13(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), C!40, compose_function(G!44, F!45, A!42, B!41, C!40), H!43), C!40)) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y1_13(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), C!40, compose_function(G!44, F!45, A!42, B!41, C!40), H!43), D!39, H!43), D!39)) | (~apply(H!43, tptp_fun_Y_8(tptp_fun_Y1_13(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), C!40, compose_function(G!44, F!45, A!42, B!41, C!40), H!43), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y1_13(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), C!40, compose_function(G!44, F!45, A!42, B!41, C!40), H!43), D!39, H!43))) | (tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y1_13(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), C!40, compose_function(G!44, F!45, A!42, B!41, C!40), H!43), D!39, H!43) = tptp_fun_Y1_13(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)))),
% 0.89/1.07 inference(modus_ponens,[status(thm)],[283, 282])).
% 0.89/1.07 tff(285,plain,
% 0.89/1.07 (tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y1_13(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), C!40, compose_function(G!44, F!45, A!42, B!41, C!40), H!43), D!39, H!43) = tptp_fun_Y1_13(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39))),
% 0.89/1.07 inference(unit_resolution,[status(thm)],[284, 179, 189, 278, 208, 276, 274])).
% 0.89/1.07 tff(286,plain,
% 0.89/1.07 (tptp_fun_Y1_13(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)) = tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y1_13(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), C!40, compose_function(G!44, F!45, A!42, B!41, C!40), H!43), D!39, H!43)),
% 0.89/1.07 inference(symmetry,[status(thm)],[285])).
% 0.89/1.07 tff(287,plain,
% 0.89/1.07 (tptp_fun_Y1_13(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)) = tptp_fun_Y2_12(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39))),
% 0.89/1.07 inference(transitivity,[status(thm)],[286, 268, 187])).
% 0.89/1.07 tff(288,plain,
% 0.89/1.07 (((~apply(compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), tptp_fun_Y2_12(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)))) | (~apply(compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39), tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), tptp_fun_Y1_13(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)))) | (~member(tptp_fun_Y2_12(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), D!39)) | (~member(tptp_fun_Y1_13(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), D!39)) | (~member(tptp_fun_X_14(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)), A!42)) | (tptp_fun_Y1_13(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)) = tptp_fun_Y2_12(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)))) | (~(tptp_fun_Y1_13(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)) = tptp_fun_Y2_12(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39))))),
% 0.89/1.07 inference(tautology,[status(thm)],[])).
% 0.89/1.07 tff(289,plain,
% 0.89/1.07 (~(tptp_fun_Y1_13(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)) = tptp_fun_Y2_12(D!39, A!42, compose_function(compose_function(H!43, G!44, B!41, C!40, D!39), F!45, A!42, B!41, D!39), compose_function(H!43, compose_function(G!44, F!45, A!42, B!41, C!40), A!42, C!40, D!39)))),
% 0.89/1.07 inference(unit_resolution,[status(thm)],[288, 37])).
% 0.89/1.07 tff(290,plain,
% 0.89/1.07 ($false),
% 0.89/1.07 inference(unit_resolution,[status(thm)],[289, 287])).
% 0.89/1.07 % SZS output end Proof
% 0.89/1.07 % E exiting
%------------------------------------------------------------------------------