%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET708+4 : TPTP v9.0.0. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n014.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 0.18s 0.39s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SET708+4 : TPTP v9.0.0. Bugfixed v2.2.1.
% 0.03/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n014.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Jun 20 05:38:39 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.18/0.39 % SZS status Theorem
% 0.18/0.39 % SZS output start Proof
% 0.18/0.39 tff(apply_type, type, (
% 0.18/0.39 apply: ( $i * $i * $i ) > $o)).
% 0.18/0.39 tff(tptp_fun_Y2_12_type, type, (
% 0.18/0.39 tptp_fun_Y2_12: ( $i * $i * $i * $i ) > $i)).
% 0.18/0.39 tff(tptp_fun_H1_43_type, type, (
% 0.18/0.39 tptp_fun_H1_43: $i)).
% 0.18/0.39 tff(tptp_fun_H2_42_type, type, (
% 0.18/0.39 tptp_fun_H2_42: $i)).
% 0.18/0.39 tff(tptp_fun_A_41_type, type, (
% 0.18/0.39 tptp_fun_A_41: $i)).
% 0.18/0.39 tff(tptp_fun_C_39_type, type, (
% 0.18/0.39 tptp_fun_C_39: $i)).
% 0.18/0.39 tff(tptp_fun_Y_8_type, type, (
% 0.18/0.39 tptp_fun_Y_8: ( $i * $i * $i * $i * $i ) > $i)).
% 0.18/0.39 tff(tptp_fun_G_44_type, type, (
% 0.18/0.39 tptp_fun_G_44: $i)).
% 0.18/0.39 tff(tptp_fun_F_45_type, type, (
% 0.18/0.39 tptp_fun_F_45: $i)).
% 0.18/0.39 tff(tptp_fun_B_40_type, type, (
% 0.18/0.39 tptp_fun_B_40: $i)).
% 0.18/0.39 tff(tptp_fun_X_14_type, type, (
% 0.18/0.39 tptp_fun_X_14: ( $i * $i * $i * $i ) > $i)).
% 0.18/0.39 tff(tptp_fun_Y1_13_type, type, (
% 0.18/0.39 tptp_fun_Y1_13: ( $i * $i * $i * $i ) > $i)).
% 0.18/0.39 tff(tptp_fun_Y_3_type, type, (
% 0.18/0.39 tptp_fun_Y_3: ( $i * $i * $i ) > $i)).
% 0.18/0.39 tff(member_type, type, (
% 0.18/0.39 member: ( $i * $i ) > $o)).
% 0.18/0.39 tff(equal_maps_type, type, (
% 0.18/0.39 equal_maps: ( $i * $i * $i * $i ) > $o)).
% 0.18/0.39 tff(compose_predicate_type, type, (
% 0.18/0.39 compose_predicate: ( $i * $i * $i * $i * $i * $i ) > $o)).
% 0.18/0.39 tff(maps_type, type, (
% 0.18/0.39 maps: ( $i * $i * $i ) > $o)).
% 0.18/0.39 tff(tptp_fun_X_10_type, type, (
% 0.18/0.39 tptp_fun_X_10: ( $i * $i * $i * $i * $i * $i ) > $i)).
% 0.18/0.39 tff(tptp_fun_Z_9_type, type, (
% 0.18/0.39 tptp_fun_Z_9: ( $i * $i * $i * $i * $i * $i ) > $i)).
% 0.18/0.39 tff(tptp_fun_Y_11_type, type, (
% 0.18/0.39 tptp_fun_Y_11: ( $i * $i * $i * $i * $i * $i ) > $i)).
% 0.18/0.39 tff(tptp_fun_Y2_5_type, type, (
% 0.18/0.39 tptp_fun_Y2_5: ( $i * $i * $i ) > $i)).
% 0.18/0.39 tff(tptp_fun_Y1_6_type, type, (
% 0.18/0.39 tptp_fun_Y1_6: ( $i * $i * $i ) > $i)).
% 0.18/0.39 tff(tptp_fun_X_7_type, type, (
% 0.18/0.39 tptp_fun_X_7: ( $i * $i * $i ) > $i)).
% 0.18/0.39 tff(tptp_fun_X_4_type, type, (
% 0.18/0.39 tptp_fun_X_4: ( $i * $i * $i ) > $i)).
% 0.18/0.39 tff(1,plain,
% 0.18/0.39 (^[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))))))))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(2,plain,
% 0.18/0.39 (![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, 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)))))))))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[1])).
% 0.18/0.39 tff(3,plain,
% 0.18/0.39 (^[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))))))))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(4,plain,
% 0.18/0.39 (![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, 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)))))))))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[3])).
% 0.18/0.39 tff(5,plain,
% 0.18/0.39 (![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, 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)))))))))),
% 0.18/0.39 inference(transitivity,[status(thm)],[4, 2])).
% 0.18/0.39 tff(6,plain,
% 0.18/0.39 (^[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)))))))))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(7,plain,
% 0.18/0.39 (![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)))))))))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[6])).
% 0.18/0.39 tff(8,plain,
% 0.18/0.39 (![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)))))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(9,plain,
% 0.18/0.39 (^[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))))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(10,plain,
% 0.18/0.39 (![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)))))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[9])).
% 0.18/0.39 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')).
% 0.18/0.39 tff(12,plain,
% 0.18/0.39 (![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)))))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.18/0.39 tff(13,plain,
% 0.18/0.39 (![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)))))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[12, 8])).
% 0.18/0.39 tff(14,plain,(
% 0.18/0.39 ![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))))))))),
% 0.18/0.39 inference(skolemize,[status(sab)],[13])).
% 0.18/0.39 tff(15,plain,
% 0.18/0.39 (![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, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F)))))))))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[14, 7])).
% 0.18/0.39 tff(16,plain,
% 0.18/0.39 (![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, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F)))))))))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[15, 5])).
% 0.18/0.39 tff(17,plain,
% 0.18/0.39 (((~![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, F))) | (~apply(G, tptp_fun_X_14(B, A, G, F), tptp_fun_Y2_12(B, A, G, F)))))))))) | (~((~((~equal_maps(H1!43, H2!42, A!41, C!39)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(X, A!41)) | (~member(Y2, C!39)) | (~member(Y1, C!39)) | (~apply(H1!43, X, Y1)) | (~apply(H2!42, X, Y2))))) | (~(equal_maps(H1!43, H2!42, A!41, C!39) | (~((~apply(H2!42, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43))) | (~apply(H1!43, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43))) | (~member(tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43), C!39)) | (~member(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), C!39)) | (~member(tptp_fun_X_14(C!39, A!41, H2!42, H1!43), A!41)) | (tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43) = tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43))))))))) <=> ((~![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(H1!43, H2!42, A!41, C!39)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(X, A!41)) | (~member(Y2, C!39)) | (~member(Y1, C!39)) | (~apply(H1!43, X, Y1)) | (~apply(H2!42, X, Y2))))) | (~(equal_maps(H1!43, H2!42, A!41, C!39) | (~((~apply(H2!42, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43))) | (~apply(H1!43, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43))) | (~member(tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43), C!39)) | (~member(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), C!39)) | (~member(tptp_fun_X_14(C!39, A!41, H2!42, H1!43), A!41)) | (tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43) = tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43)))))))))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(18,plain,
% 0.18/0.40 ((~((~((~equal_maps(H1!43, H2!42, A!41, C!39)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(H2!42, X, Y2)) | (~member(X, A!41)) | (~member(Y1, C!39)) | (~member(Y2, C!39)) | (~apply(H1!43, X, Y1))))) | (~(equal_maps(H1!43, H2!42, A!41, C!39) | (~((tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43) = tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43)) | (~member(tptp_fun_X_14(C!39, A!41, H2!42, H1!43), A!41)) | (~member(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), C!39)) | (~member(tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43), C!39)) | (~apply(H1!43, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43))) | (~apply(H2!42, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43))))))))) <=> (~((~((~equal_maps(H1!43, H2!42, A!41, C!39)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(X, A!41)) | (~member(Y2, C!39)) | (~member(Y1, C!39)) | (~apply(H1!43, X, Y1)) | (~apply(H2!42, X, Y2))))) | (~(equal_maps(H1!43, H2!42, A!41, C!39) | (~((~apply(H2!42, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43))) | (~apply(H1!43, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43))) | (~member(tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43), C!39)) | (~member(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), C!39)) | (~member(tptp_fun_X_14(C!39, A!41, H2!42, H1!43), A!41)) | (tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43) = tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43))))))))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(19,plain,
% 0.18/0.40 (((~![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(H1!43, H2!42, A!41, C!39)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(H2!42, X, Y2)) | (~member(X, A!41)) | (~member(Y1, C!39)) | (~member(Y2, C!39)) | (~apply(H1!43, X, Y1))))) | (~(equal_maps(H1!43, H2!42, A!41, C!39) | (~((tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43) = tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43)) | (~member(tptp_fun_X_14(C!39, A!41, H2!42, H1!43), A!41)) | (~member(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), C!39)) | (~member(tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43), C!39)) | (~apply(H1!43, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43))) | (~apply(H2!42, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43)))))))))) <=> ((~![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(H1!43, H2!42, A!41, C!39)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(X, A!41)) | (~member(Y2, C!39)) | (~member(Y1, C!39)) | (~apply(H1!43, X, Y1)) | (~apply(H2!42, X, Y2))))) | (~(equal_maps(H1!43, H2!42, A!41, C!39) | (~((~apply(H2!42, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43))) | (~apply(H1!43, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43))) | (~member(tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43), C!39)) | (~member(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), C!39)) | (~member(tptp_fun_X_14(C!39, A!41, H2!42, H1!43), A!41)) | (tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43) = tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43)))))))))),
% 0.18/0.40 inference(monotonicity,[status(thm)],[18])).
% 0.18/0.40 tff(20,plain,
% 0.18/0.40 (((~![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(H1!43, H2!42, A!41, C!39)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(H2!42, X, Y2)) | (~member(X, A!41)) | (~member(Y1, C!39)) | (~member(Y2, C!39)) | (~apply(H1!43, X, Y1))))) | (~(equal_maps(H1!43, H2!42, A!41, C!39) | (~((tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43) = tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43)) | (~member(tptp_fun_X_14(C!39, A!41, H2!42, H1!43), A!41)) | (~member(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), C!39)) | (~member(tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43), C!39)) | (~apply(H1!43, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43))) | (~apply(H2!42, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43)))))))))) <=> ((~![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(H1!43, H2!42, A!41, C!39)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(X, A!41)) | (~member(Y2, C!39)) | (~member(Y1, C!39)) | (~apply(H1!43, X, Y1)) | (~apply(H2!42, X, Y2))))) | (~(equal_maps(H1!43, H2!42, A!41, C!39) | (~((~apply(H2!42, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43))) | (~apply(H1!43, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43))) | (~member(tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43), C!39)) | (~member(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), C!39)) | (~member(tptp_fun_X_14(C!39, A!41, H2!42, H1!43), A!41)) | (tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43) = tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43)))))))))),
% 0.18/0.40 inference(transitivity,[status(thm)],[19, 17])).
% 0.18/0.40 tff(21,plain,
% 0.18/0.40 ((~![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(H1!43, H2!42, A!41, C!39)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(H2!42, X, Y2)) | (~member(X, A!41)) | (~member(Y1, C!39)) | (~member(Y2, C!39)) | (~apply(H1!43, X, Y1))))) | (~(equal_maps(H1!43, H2!42, A!41, C!39) | (~((tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43) = tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43)) | (~member(tptp_fun_X_14(C!39, A!41, H2!42, H1!43), A!41)) | (~member(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), C!39)) | (~member(tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43), C!39)) | (~apply(H1!43, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43))) | (~apply(H2!42, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43)))))))))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(22,plain,
% 0.18/0.40 ((~![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(H1!43, H2!42, A!41, C!39)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(X, A!41)) | (~member(Y2, C!39)) | (~member(Y1, C!39)) | (~apply(H1!43, X, Y1)) | (~apply(H2!42, X, Y2))))) | (~(equal_maps(H1!43, H2!42, A!41, C!39) | (~((~apply(H2!42, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43))) | (~apply(H1!43, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43))) | (~member(tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43), C!39)) | (~member(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), C!39)) | (~member(tptp_fun_X_14(C!39, A!41, H2!42, H1!43), A!41)) | (tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43) = tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43))))))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.18/0.40 tff(23,plain,
% 0.18/0.40 (~((~((~equal_maps(H1!43, H2!42, A!41, C!39)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(X, A!41)) | (~member(Y2, C!39)) | (~member(Y1, C!39)) | (~apply(H1!43, X, Y1)) | (~apply(H2!42, X, Y2))))) | (~(equal_maps(H1!43, H2!42, A!41, C!39) | (~((~apply(H2!42, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43))) | (~apply(H1!43, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43))) | (~member(tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43), C!39)) | (~member(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), C!39)) | (~member(tptp_fun_X_14(C!39, A!41, H2!42, H1!43), A!41)) | (tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43) = tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43)))))))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[22, 16])).
% 0.18/0.40 tff(24,plain,
% 0.18/0.40 (((~((~equal_maps(H1!43, H2!42, A!41, C!39)) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(X, A!41)) | (~member(Y2, C!39)) | (~member(Y1, C!39)) | (~apply(H1!43, X, Y1)) | (~apply(H2!42, X, Y2))))) | (~(equal_maps(H1!43, H2!42, A!41, C!39) | (~((~apply(H2!42, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43))) | (~apply(H1!43, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43))) | (~member(tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43), C!39)) | (~member(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), C!39)) | (~member(tptp_fun_X_14(C!39, A!41, H2!42, H1!43), A!41)) | (tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43) = tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43))))))) | (equal_maps(H1!43, H2!42, A!41, C!39) | (~((~apply(H2!42, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43))) | (~apply(H1!43, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43))) | (~member(tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43), C!39)) | (~member(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), C!39)) | (~member(tptp_fun_X_14(C!39, A!41, H2!42, H1!43), A!41)) | (tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43) = tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43)))))),
% 0.18/0.41 inference(tautology,[status(thm)],[])).
% 0.18/0.41 tff(25,plain,
% 0.18/0.41 (equal_maps(H1!43, H2!42, A!41, C!39) | (~((~apply(H2!42, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43))) | (~apply(H1!43, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43))) | (~member(tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43), C!39)) | (~member(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), C!39)) | (~member(tptp_fun_X_14(C!39, A!41, H2!42, H1!43), A!41)) | (tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43) = tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43))))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[24, 23])).
% 0.18/0.41 tff(26,plain,
% 0.18/0.41 ((~![F: $i, G: $i, H1: $i, H2: $i, A: $i, B: $i, C: $i] : ((~(maps(F, A, B) & maps(G, B, C) & compose_predicate(H1, G, F, A, B, C) & compose_predicate(H2, G, F, A, B, C))) | equal_maps(H1, H2, A, C))) <=> (~![F: $i, G: $i, H1: $i, H2: $i, A: $i, B: $i, C: $i] : ((~(maps(F, A, B) & maps(G, B, C) & compose_predicate(H1, G, F, A, B, C) & compose_predicate(H2, G, F, A, B, C))) | equal_maps(H1, H2, A, C)))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(27,plain,
% 0.18/0.41 ((~![F: $i, G: $i, H1: $i, H2: $i, A: $i, B: $i, C: $i] : ((((maps(F, A, B) & maps(G, B, C)) & compose_predicate(H1, G, F, A, B, C)) & compose_predicate(H2, G, F, A, B, C)) => equal_maps(H1, H2, A, C))) <=> (~![F: $i, G: $i, H1: $i, H2: $i, A: $i, B: $i, C: $i] : ((~(maps(F, A, B) & maps(G, B, C) & compose_predicate(H1, G, F, A, B, C) & compose_predicate(H2, G, F, A, B, C))) | equal_maps(H1, H2, A, C)))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(28,axiom,(~![F: $i, G: $i, H1: $i, H2: $i, A: $i, B: $i, C: $i] : ((((maps(F, A, B) & maps(G, B, C)) & compose_predicate(H1, G, F, A, B, C)) & compose_predicate(H2, G, F, A, B, C)) => equal_maps(H1, H2, A, C))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thII01a')).
% 0.18/0.41 tff(29,plain,
% 0.18/0.41 (~![F: $i, G: $i, H1: $i, H2: $i, A: $i, B: $i, C: $i] : ((~(maps(F, A, B) & maps(G, B, C) & compose_predicate(H1, G, F, A, B, C) & compose_predicate(H2, G, F, A, B, C))) | equal_maps(H1, H2, A, C))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.18/0.41 tff(30,plain,
% 0.18/0.41 (~![F: $i, G: $i, H1: $i, H2: $i, A: $i, B: $i, C: $i] : ((~(maps(F, A, B) & maps(G, B, C) & compose_predicate(H1, G, F, A, B, C) & compose_predicate(H2, G, F, A, B, C))) | equal_maps(H1, H2, A, C))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[29, 26])).
% 0.18/0.41 tff(31,plain,
% 0.18/0.41 (~![F: $i, G: $i, H1: $i, H2: $i, A: $i, B: $i, C: $i] : ((~(maps(F, A, B) & maps(G, B, C) & compose_predicate(H1, G, F, A, B, C) & compose_predicate(H2, G, F, A, B, C))) | equal_maps(H1, H2, A, C))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[30, 26])).
% 0.18/0.41 tff(32,plain,
% 0.18/0.41 (~![F: $i, G: $i, H1: $i, H2: $i, A: $i, B: $i, C: $i] : ((~(maps(F, A, B) & maps(G, B, C) & compose_predicate(H1, G, F, A, B, C) & compose_predicate(H2, G, F, A, B, C))) | equal_maps(H1, H2, A, C))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[31, 26])).
% 0.18/0.41 tff(33,plain,(
% 0.18/0.41 ~((~(maps(F!45, A!41, B!40) & maps(G!44, B!40, C!39) & compose_predicate(H1!43, G!44, F!45, A!41, B!40, C!39) & compose_predicate(H2!42, G!44, F!45, A!41, B!40, C!39))) | equal_maps(H1!43, H2!42, A!41, C!39))),
% 0.18/0.41 inference(skolemize,[status(sab)],[32])).
% 0.18/0.41 tff(34,plain,
% 0.18/0.41 (~equal_maps(H1!43, H2!42, A!41, C!39)),
% 0.18/0.41 inference(or_elim,[status(thm)],[33])).
% 0.18/0.41 tff(35,plain,
% 0.18/0.41 ((~(equal_maps(H1!43, H2!42, A!41, C!39) | (~((~apply(H2!42, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43))) | (~apply(H1!43, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43))) | (~member(tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43), C!39)) | (~member(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), C!39)) | (~member(tptp_fun_X_14(C!39, A!41, H2!42, H1!43), A!41)) | (tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43) = tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43)))))) | equal_maps(H1!43, H2!42, A!41, C!39) | (~((~apply(H2!42, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43))) | (~apply(H1!43, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43))) | (~member(tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43), C!39)) | (~member(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), C!39)) | (~member(tptp_fun_X_14(C!39, A!41, H2!42, H1!43), A!41)) | (tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43) = tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43))))),
% 0.18/0.41 inference(tautology,[status(thm)],[])).
% 0.18/0.41 tff(36,plain,
% 0.18/0.41 ((~(equal_maps(H1!43, H2!42, A!41, C!39) | (~((~apply(H2!42, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43))) | (~apply(H1!43, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43))) | (~member(tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43), C!39)) | (~member(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), C!39)) | (~member(tptp_fun_X_14(C!39, A!41, H2!42, H1!43), A!41)) | (tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43) = tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43)))))) | (~((~apply(H2!42, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43))) | (~apply(H1!43, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43))) | (~member(tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43), C!39)) | (~member(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), C!39)) | (~member(tptp_fun_X_14(C!39, A!41, H2!42, H1!43), A!41)) | (tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43) = tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43))))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[35, 34])).
% 0.18/0.41 tff(37,plain,
% 0.18/0.41 (~((~apply(H2!42, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43))) | (~apply(H1!43, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43))) | (~member(tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43), C!39)) | (~member(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), C!39)) | (~member(tptp_fun_X_14(C!39, A!41, H2!42, H1!43), A!41)) | (tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43) = tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43)))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[36, 25])).
% 0.18/0.41 tff(38,plain,
% 0.18/0.41 (((~apply(H2!42, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43))) | (~apply(H1!43, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43))) | (~member(tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43), C!39)) | (~member(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), C!39)) | (~member(tptp_fun_X_14(C!39, A!41, H2!42, H1!43), A!41)) | (tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43) = tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43))) | member(tptp_fun_X_14(C!39, A!41, H2!42, H1!43), A!41)),
% 0.18/0.41 inference(tautology,[status(thm)],[])).
% 0.18/0.41 tff(39,plain,
% 0.18/0.41 (member(tptp_fun_X_14(C!39, A!41, H2!42, H1!43), A!41)),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[38, 37])).
% 0.18/0.41 tff(40,plain,
% 0.18/0.41 (((~apply(H2!42, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43))) | (~apply(H1!43, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43))) | (~member(tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43), C!39)) | (~member(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), C!39)) | (~member(tptp_fun_X_14(C!39, A!41, H2!42, H1!43), A!41)) | (tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43) = tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43))) | member(tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43), C!39)),
% 0.18/0.42 inference(tautology,[status(thm)],[])).
% 0.18/0.42 tff(41,plain,
% 0.18/0.42 (member(tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43), C!39)),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[40, 37])).
% 0.18/0.42 tff(42,plain,
% 0.18/0.42 (^[H: $i, G: $i, F: $i, A: $i, B: $i, C: $i] : refl((~((~((~compose_predicate(H, G, F, A, B, C)) | ![X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(H, X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(H, X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z)))))))))) | (~(compose_predicate(H, G, F, A, B, C) | (~((~member(tptp_fun_X_10(C, B, A, F, G, H), A)) | (~member(tptp_fun_Z_9(C, B, A, F, G, H), C)) | (~(apply(H, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H)) | (~((~member(tptp_fun_Y_11(C, B, A, F, G, H), B)) | (~apply(F, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Y_11(C, B, A, F, G, H))) | (~apply(G, tptp_fun_Y_11(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H))))))) | (~((~apply(H, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H))) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_10(C, B, A, F, G, H), Y)) | (~apply(G, Y, tptp_fun_Z_9(C, B, A, F, G, H)))))))))))) <=> (~((~((~compose_predicate(H, G, F, A, B, C)) | ![X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(H, X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(H, X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z)))))))))) | (~(compose_predicate(H, G, F, A, B, C) | (~((~member(tptp_fun_X_10(C, B, A, F, G, H), A)) | (~member(tptp_fun_Z_9(C, B, A, F, G, H), C)) | (~(apply(H, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H)) | (~((~member(tptp_fun_Y_11(C, B, A, F, G, H), B)) | (~apply(F, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Y_11(C, B, A, F, G, H))) | (~apply(G, tptp_fun_Y_11(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H))))))) | (~((~apply(H, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H))) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_10(C, B, A, F, G, H), Y)) | (~apply(G, Y, tptp_fun_Z_9(C, B, A, F, G, H)))))))))))))),
% 0.18/0.42 inference(bind,[status(th)],[])).
% 0.18/0.42 tff(43,plain,
% 0.18/0.42 (![H: $i, G: $i, F: $i, A: $i, B: $i, C: $i] : (~((~((~compose_predicate(H, G, F, A, B, C)) | ![X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(H, X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(H, X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z)))))))))) | (~(compose_predicate(H, G, F, A, B, C) | (~((~member(tptp_fun_X_10(C, B, A, F, G, H), A)) | (~member(tptp_fun_Z_9(C, B, A, F, G, H), C)) | (~(apply(H, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H)) | (~((~member(tptp_fun_Y_11(C, B, A, F, G, H), B)) | (~apply(F, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Y_11(C, B, A, F, G, H))) | (~apply(G, tptp_fun_Y_11(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H))))))) | (~((~apply(H, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H))) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_10(C, B, A, F, G, H), Y)) | (~apply(G, Y, tptp_fun_Z_9(C, B, A, F, G, H)))))))))))) <=> ![H: $i, G: $i, F: $i, A: $i, B: $i, C: $i] : (~((~((~compose_predicate(H, G, F, A, B, C)) | ![X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(H, X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(H, X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z)))))))))) | (~(compose_predicate(H, G, F, A, B, C) | (~((~member(tptp_fun_X_10(C, B, A, F, G, H), A)) | (~member(tptp_fun_Z_9(C, B, A, F, G, H), C)) | (~(apply(H, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H)) | (~((~member(tptp_fun_Y_11(C, B, A, F, G, H), B)) | (~apply(F, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Y_11(C, B, A, F, G, H))) | (~apply(G, tptp_fun_Y_11(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H))))))) | (~((~apply(H, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H))) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_10(C, B, A, F, G, H), Y)) | (~apply(G, Y, tptp_fun_Z_9(C, B, A, F, G, H))))))))))))),
% 0.18/0.42 inference(quant_intro,[status(thm)],[42])).
% 0.18/0.42 tff(44,plain,
% 0.18/0.42 (^[H: $i, G: $i, F: $i, A: $i, B: $i, C: $i] : rewrite((~((~((~compose_predicate(H, G, F, A, B, C)) | ![X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(H, X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(H, X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z)))))))))) | (~(compose_predicate(H, G, F, A, B, C) | (~((~member(tptp_fun_X_10(C, B, A, F, G, H), A)) | (~member(tptp_fun_Z_9(C, B, A, F, G, H), C)) | (~(apply(H, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H)) | (~((~member(tptp_fun_Y_11(C, B, A, F, G, H), B)) | (~apply(F, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Y_11(C, B, A, F, G, H))) | (~apply(G, tptp_fun_Y_11(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H))))))) | (~((~apply(H, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H))) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_10(C, B, A, F, G, H), Y)) | (~apply(G, Y, tptp_fun_Z_9(C, B, A, F, G, H)))))))))))) <=> (~((~((~compose_predicate(H, G, F, A, B, C)) | ![X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(H, X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(H, X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z)))))))))) | (~(compose_predicate(H, G, F, A, B, C) | (~((~member(tptp_fun_X_10(C, B, A, F, G, H), A)) | (~member(tptp_fun_Z_9(C, B, A, F, G, H), C)) | (~(apply(H, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H)) | (~((~member(tptp_fun_Y_11(C, B, A, F, G, H), B)) | (~apply(F, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Y_11(C, B, A, F, G, H))) | (~apply(G, tptp_fun_Y_11(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H))))))) | (~((~apply(H, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H))) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_10(C, B, A, F, G, H), Y)) | (~apply(G, Y, tptp_fun_Z_9(C, B, A, F, G, H)))))))))))))),
% 0.18/0.42 inference(bind,[status(th)],[])).
% 0.18/0.42 tff(45,plain,
% 0.18/0.42 (![H: $i, G: $i, F: $i, A: $i, B: $i, C: $i] : (~((~((~compose_predicate(H, G, F, A, B, C)) | ![X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(H, X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(H, X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z)))))))))) | (~(compose_predicate(H, G, F, A, B, C) | (~((~member(tptp_fun_X_10(C, B, A, F, G, H), A)) | (~member(tptp_fun_Z_9(C, B, A, F, G, H), C)) | (~(apply(H, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H)) | (~((~member(tptp_fun_Y_11(C, B, A, F, G, H), B)) | (~apply(F, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Y_11(C, B, A, F, G, H))) | (~apply(G, tptp_fun_Y_11(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H))))))) | (~((~apply(H, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H))) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_10(C, B, A, F, G, H), Y)) | (~apply(G, Y, tptp_fun_Z_9(C, B, A, F, G, H)))))))))))) <=> ![H: $i, G: $i, F: $i, A: $i, B: $i, C: $i] : (~((~((~compose_predicate(H, G, F, A, B, C)) | ![X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(H, X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(H, X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z)))))))))) | (~(compose_predicate(H, G, F, A, B, C) | (~((~member(tptp_fun_X_10(C, B, A, F, G, H), A)) | (~member(tptp_fun_Z_9(C, B, A, F, G, H), C)) | (~(apply(H, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H)) | (~((~member(tptp_fun_Y_11(C, B, A, F, G, H), B)) | (~apply(F, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Y_11(C, B, A, F, G, H))) | (~apply(G, tptp_fun_Y_11(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H))))))) | (~((~apply(H, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H))) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_10(C, B, A, F, G, H), Y)) | (~apply(G, Y, tptp_fun_Z_9(C, B, A, F, G, H))))))))))))),
% 0.18/0.42 inference(quant_intro,[status(thm)],[44])).
% 0.18/0.42 tff(46,plain,
% 0.18/0.42 (![H: $i, G: $i, F: $i, A: $i, B: $i, C: $i] : (~((~((~compose_predicate(H, G, F, A, B, C)) | ![X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(H, X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(H, X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z)))))))))) | (~(compose_predicate(H, G, F, A, B, C) | (~((~member(tptp_fun_X_10(C, B, A, F, G, H), A)) | (~member(tptp_fun_Z_9(C, B, A, F, G, H), C)) | (~(apply(H, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H)) | (~((~member(tptp_fun_Y_11(C, B, A, F, G, H), B)) | (~apply(F, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Y_11(C, B, A, F, G, H))) | (~apply(G, tptp_fun_Y_11(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H))))))) | (~((~apply(H, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H))) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_10(C, B, A, F, G, H), Y)) | (~apply(G, Y, tptp_fun_Z_9(C, B, A, F, G, H)))))))))))) <=> ![H: $i, G: $i, F: $i, A: $i, B: $i, C: $i] : (~((~((~compose_predicate(H, G, F, A, B, C)) | ![X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(H, X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(H, X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z)))))))))) | (~(compose_predicate(H, G, F, A, B, C) | (~((~member(tptp_fun_X_10(C, B, A, F, G, H), A)) | (~member(tptp_fun_Z_9(C, B, A, F, G, H), C)) | (~(apply(H, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H)) | (~((~member(tptp_fun_Y_11(C, B, A, F, G, H), B)) | (~apply(F, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Y_11(C, B, A, F, G, H))) | (~apply(G, tptp_fun_Y_11(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H))))))) | (~((~apply(H, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H))) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_10(C, B, A, F, G, H), Y)) | (~apply(G, Y, tptp_fun_Z_9(C, B, A, F, G, H))))))))))))),
% 0.18/0.42 inference(transitivity,[status(thm)],[45, 43])).
% 0.18/0.42 tff(47,plain,
% 0.18/0.42 (^[H: $i, G: $i, F: $i, A: $i, B: $i, C: $i] : trans(monotonicity(rewrite(((~compose_predicate(H, G, F, A, B, C)) | ![X: $i, Z: $i] : ((~(member(X, A) & member(Z, C))) | (((~apply(H, X, Z)) | (member(tptp_fun_Y_8(Z, X, B, F, G), B) & apply(F, X, tptp_fun_Y_8(Z, X, B, F, G)) & apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z))) & (apply(H, X, Z) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y) & apply(G, Y, Z))))))) <=> ((~compose_predicate(H, G, F, A, B, C)) | ![X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(H, X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(H, X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z)))))))))), trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((member(tptp_fun_Y_11(C, B, A, F, G, H), B) & apply(F, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Y_11(C, B, A, F, G, H)) & apply(G, tptp_fun_Y_11(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H))) <=> (~((~member(tptp_fun_Y_11(C, B, A, F, G, H), B)) | (~apply(F, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Y_11(C, B, A, F, G, H))) | (~apply(G, tptp_fun_Y_11(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H)))))), ((apply(H, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H)) | (member(tptp_fun_Y_11(C, B, A, F, G, H), B) & apply(F, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Y_11(C, B, A, F, G, H)) & apply(G, tptp_fun_Y_11(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H)))) <=> (apply(H, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H)) | (~((~member(tptp_fun_Y_11(C, B, A, F, G, H), B)) | (~apply(F, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Y_11(C, B, A, F, G, H))) | (~apply(G, tptp_fun_Y_11(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H)))))))), rewrite((apply(H, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H)) | (~((~member(tptp_fun_Y_11(C, B, A, F, G, H), B)) | (~apply(F, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Y_11(C, B, A, F, G, H))) | (~apply(G, tptp_fun_Y_11(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H)))))) <=> (apply(H, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H)) | (~((~member(tptp_fun_Y_11(C, B, A, F, G, H), B)) | (~apply(F, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Y_11(C, B, A, F, G, H))) | (~apply(G, tptp_fun_Y_11(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H))))))), ((apply(H, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H)) | (member(tptp_fun_Y_11(C, B, A, F, G, H), B) & apply(F, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Y_11(C, B, A, F, G, H)) & apply(G, tptp_fun_Y_11(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H)))) <=> (apply(H, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H)) | (~((~member(tptp_fun_Y_11(C, B, A, F, G, H), B)) | (~apply(F, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Y_11(C, B, A, F, G, H))) | (~apply(G, tptp_fun_Y_11(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H)))))))), rewrite(((~apply(H, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H))) | ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_10(C, B, A, F, G, H), Y) & apply(G, Y, tptp_fun_Z_9(C, B, A, F, G, H))))) <=> ((~apply(H, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H))) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_10(C, B, A, F, G, H), Y)) | (~apply(G, Y, tptp_fun_Z_9(C, B, A, F, G, H)))))), ((member(tptp_fun_X_10(C, B, A, F, G, H), A) & member(tptp_fun_Z_9(C, B, A, F, G, H), C) & (apply(H, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H)) | (member(tptp_fun_Y_11(C, B, A, F, G, H), B) & apply(F, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Y_11(C, B, A, F, G, H)) & apply(G, tptp_fun_Y_11(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H)))) & ((~apply(H, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H))) | ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_10(C, B, A, F, G, H), Y) & apply(G, Y, tptp_fun_Z_9(C, B, A, F, G, H)))))) <=> (member(tptp_fun_X_10(C, B, A, F, G, H), A) & member(tptp_fun_Z_9(C, B, A, F, G, H), C) & (apply(H, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H)) | (~((~member(tptp_fun_Y_11(C, B, A, F, G, H), B)) | (~apply(F, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Y_11(C, B, A, F, G, H))) | (~apply(G, tptp_fun_Y_11(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H)))))) & ((~apply(H, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H))) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_10(C, B, A, F, G, H), Y)) | (~apply(G, Y, tptp_fun_Z_9(C, B, A, F, G, H)))))))), rewrite((member(tptp_fun_X_10(C, B, A, F, G, H), A) & member(tptp_fun_Z_9(C, B, A, F, G, H), C) & (apply(H, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H)) | (~((~member(tptp_fun_Y_11(C, B, A, F, G, H), B)) | (~apply(F, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Y_11(C, B, A, F, G, H))) | (~apply(G, tptp_fun_Y_11(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H)))))) & ((~apply(H, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H))) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_10(C, B, A, F, G, H), Y)) | (~apply(G, Y, tptp_fun_Z_9(C, B, A, F, G, H)))))) <=> (~((~member(tptp_fun_X_10(C, B, A, F, G, H), A)) | (~member(tptp_fun_Z_9(C, B, A, F, G, H), C)) | (~(apply(H, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H)) | (~((~member(tptp_fun_Y_11(C, B, A, F, G, H), B)) | (~apply(F, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Y_11(C, B, A, F, G, H))) | (~apply(G, tptp_fun_Y_11(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H))))))) | (~((~apply(H, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H))) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_10(C, B, A, F, G, H), Y)) | (~apply(G, Y, tptp_fun_Z_9(C, B, A, F, G, H))))))))), ((member(tptp_fun_X_10(C, B, A, F, G, H), A) & member(tptp_fun_Z_9(C, B, A, F, G, H), C) & (apply(H, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H)) | (member(tptp_fun_Y_11(C, B, A, F, G, H), B) & apply(F, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Y_11(C, B, A, F, G, H)) & apply(G, tptp_fun_Y_11(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H)))) & ((~apply(H, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H))) | ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_10(C, B, A, F, G, H), Y) & apply(G, Y, tptp_fun_Z_9(C, B, A, F, G, H)))))) <=> (~((~member(tptp_fun_X_10(C, B, A, F, G, H), A)) | (~member(tptp_fun_Z_9(C, B, A, F, G, H), C)) | (~(apply(H, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H)) | (~((~member(tptp_fun_Y_11(C, B, A, F, G, H), B)) | (~apply(F, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Y_11(C, B, A, F, G, H))) | (~apply(G, tptp_fun_Y_11(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H))))))) | (~((~apply(H, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H))) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_10(C, B, A, F, G, H), Y)) | (~apply(G, Y, tptp_fun_Z_9(C, B, A, F, G, H)))))))))), ((compose_predicate(H, G, F, A, B, C) | (member(tptp_fun_X_10(C, B, A, F, G, H), A) & member(tptp_fun_Z_9(C, B, A, F, G, H), C) & (apply(H, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H)) | (member(tptp_fun_Y_11(C, B, A, F, G, H), B) & apply(F, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Y_11(C, B, A, F, G, H)) & apply(G, tptp_fun_Y_11(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H)))) & ((~apply(H, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H))) | ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_10(C, B, A, F, G, H), Y) & apply(G, Y, tptp_fun_Z_9(C, B, A, F, G, H))))))) <=> (compose_predicate(H, G, F, A, B, C) | (~((~member(tptp_fun_X_10(C, B, A, F, G, H), A)) | (~member(tptp_fun_Z_9(C, B, A, F, G, H), C)) | (~(apply(H, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H)) | (~((~member(tptp_fun_Y_11(C, B, A, F, G, H), B)) | (~apply(F, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Y_11(C, B, A, F, G, H))) | (~apply(G, tptp_fun_Y_11(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H))))))) | (~((~apply(H, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H))) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_10(C, B, A, F, G, H), Y)) | (~apply(G, Y, tptp_fun_Z_9(C, B, A, F, G, H))))))))))), rewrite((compose_predicate(H, G, F, A, B, C) | (~((~member(tptp_fun_X_10(C, B, A, F, G, H), A)) | (~member(tptp_fun_Z_9(C, B, A, F, G, H), C)) | (~(apply(H, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H)) | (~((~member(tptp_fun_Y_11(C, B, A, F, G, H), B)) | (~apply(F, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Y_11(C, B, A, F, G, H))) | (~apply(G, tptp_fun_Y_11(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H))))))) | (~((~apply(H, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H))) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_10(C, B, A, F, G, H), Y)) | (~apply(G, Y, tptp_fun_Z_9(C, B, A, F, G, H))))))))) <=> (compose_predicate(H, G, F, A, B, C) | (~((~member(tptp_fun_X_10(C, B, A, F, G, H), A)) | (~member(tptp_fun_Z_9(C, B, A, F, G, H), C)) | (~(apply(H, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H)) | (~((~member(tptp_fun_Y_11(C, B, A, F, G, H), B)) | (~apply(F, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Y_11(C, B, A, F, G, H))) | (~apply(G, tptp_fun_Y_11(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H))))))) | (~((~apply(H, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H))) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_10(C, B, A, F, G, H), Y)) | (~apply(G, Y, tptp_fun_Z_9(C, B, A, F, G, H)))))))))), ((compose_predicate(H, G, F, A, B, C) | (member(tptp_fun_X_10(C, B, A, F, G, H), A) & member(tptp_fun_Z_9(C, B, A, F, G, H), C) & (apply(H, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H)) | (member(tptp_fun_Y_11(C, B, A, F, G, H), B) & apply(F, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Y_11(C, B, A, F, G, H)) & apply(G, tptp_fun_Y_11(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H)))) & ((~apply(H, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H))) | ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_10(C, B, A, F, G, H), Y) & apply(G, Y, tptp_fun_Z_9(C, B, A, F, G, H))))))) <=> (compose_predicate(H, G, F, A, B, C) | (~((~member(tptp_fun_X_10(C, B, A, F, G, H), A)) | (~member(tptp_fun_Z_9(C, B, A, F, G, H), C)) | (~(apply(H, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H)) | (~((~member(tptp_fun_Y_11(C, B, A, F, G, H), B)) | (~apply(F, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Y_11(C, B, A, F, G, H))) | (~apply(G, tptp_fun_Y_11(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H))))))) | (~((~apply(H, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H))) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_10(C, B, A, F, G, H), Y)) | (~apply(G, Y, tptp_fun_Z_9(C, B, A, F, G, H))))))))))), ((((~compose_predicate(H, G, F, A, B, C)) | ![X: $i, Z: $i] : ((~(member(X, A) & member(Z, C))) | (((~apply(H, X, Z)) | (member(tptp_fun_Y_8(Z, X, B, F, G), B) & apply(F, X, tptp_fun_Y_8(Z, X, B, F, G)) & apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z))) & (apply(H, X, Z) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y) & apply(G, Y, Z))))))) & (compose_predicate(H, G, F, A, B, C) | (member(tptp_fun_X_10(C, B, A, F, G, H), A) & member(tptp_fun_Z_9(C, B, A, F, G, H), C) & (apply(H, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H)) | (member(tptp_fun_Y_11(C, B, A, F, G, H), B) & apply(F, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Y_11(C, B, A, F, G, H)) & apply(G, tptp_fun_Y_11(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H)))) & ((~apply(H, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H))) | ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_10(C, B, A, F, G, H), Y) & apply(G, Y, tptp_fun_Z_9(C, B, A, F, G, H)))))))) <=> (((~compose_predicate(H, G, F, A, B, C)) | ![X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(H, X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(H, X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) & (compose_predicate(H, G, F, A, B, C) | (~((~member(tptp_fun_X_10(C, B, A, F, G, H), A)) | (~member(tptp_fun_Z_9(C, B, A, F, G, H), C)) | (~(apply(H, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H)) | (~((~member(tptp_fun_Y_11(C, B, A, F, G, H), B)) | (~apply(F, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Y_11(C, B, A, F, G, H))) | (~apply(G, tptp_fun_Y_11(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H))))))) | (~((~apply(H, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H))) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_10(C, B, A, F, G, H), Y)) | (~apply(G, Y, tptp_fun_Z_9(C, B, A, F, G, H)))))))))))), rewrite((((~compose_predicate(H, G, F, A, B, C)) | ![X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(H, X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(H, X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) & (compose_predicate(H, G, F, A, B, C) | (~((~member(tptp_fun_X_10(C, B, A, F, G, H), A)) | (~member(tptp_fun_Z_9(C, B, A, F, G, H), C)) | (~(apply(H, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H)) | (~((~member(tptp_fun_Y_11(C, B, A, F, G, H), B)) | (~apply(F, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Y_11(C, B, A, F, G, H))) | (~apply(G, tptp_fun_Y_11(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H))))))) | (~((~apply(H, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H))) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_10(C, B, A, F, G, H), Y)) | (~apply(G, Y, tptp_fun_Z_9(C, B, A, F, G, H)))))))))) <=> (~((~((~compose_predicate(H, G, F, A, B, C)) | ![X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(H, X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(H, X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z)))))))))) | (~(compose_predicate(H, G, F, A, B, C) | (~((~member(tptp_fun_X_10(C, B, A, F, G, H), A)) | (~member(tptp_fun_Z_9(C, B, A, F, G, H), C)) | (~(apply(H, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H)) | (~((~member(tptp_fun_Y_11(C, B, A, F, G, H), B)) | (~apply(F, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Y_11(C, B, A, F, G, H))) | (~apply(G, tptp_fun_Y_11(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H))))))) | (~((~apply(H, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H))) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_10(C, B, A, F, G, H), Y)) | (~apply(G, Y, tptp_fun_Z_9(C, B, A, F, G, H))))))))))))), ((((~compose_predicate(H, G, F, A, B, C)) | ![X: $i, Z: $i] : ((~(member(X, A) & member(Z, C))) | (((~apply(H, X, Z)) | (member(tptp_fun_Y_8(Z, X, B, F, G), B) & apply(F, X, tptp_fun_Y_8(Z, X, B, F, G)) & apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z))) & (apply(H, X, Z) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y) & apply(G, Y, Z))))))) & (compose_predicate(H, G, F, A, B, C) | (member(tptp_fun_X_10(C, B, A, F, G, H), A) & member(tptp_fun_Z_9(C, B, A, F, G, H), C) & (apply(H, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H)) | (member(tptp_fun_Y_11(C, B, A, F, G, H), B) & apply(F, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Y_11(C, B, A, F, G, H)) & apply(G, tptp_fun_Y_11(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H)))) & ((~apply(H, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H))) | ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_10(C, B, A, F, G, H), Y) & apply(G, Y, tptp_fun_Z_9(C, B, A, F, G, H)))))))) <=> (~((~((~compose_predicate(H, G, F, A, B, C)) | ![X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(H, X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(H, X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z)))))))))) | (~(compose_predicate(H, G, F, A, B, C) | (~((~member(tptp_fun_X_10(C, B, A, F, G, H), A)) | (~member(tptp_fun_Z_9(C, B, A, F, G, H), C)) | (~(apply(H, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H)) | (~((~member(tptp_fun_Y_11(C, B, A, F, G, H), B)) | (~apply(F, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Y_11(C, B, A, F, G, H))) | (~apply(G, tptp_fun_Y_11(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H))))))) | (~((~apply(H, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H))) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_10(C, B, A, F, G, H), Y)) | (~apply(G, Y, tptp_fun_Z_9(C, B, A, F, G, H))))))))))))))),
% 0.18/0.42 inference(bind,[status(th)],[])).
% 0.18/0.42 tff(48,plain,
% 0.18/0.42 (![H: $i, G: $i, F: $i, A: $i, B: $i, C: $i] : (((~compose_predicate(H, G, F, A, B, C)) | ![X: $i, Z: $i] : ((~(member(X, A) & member(Z, C))) | (((~apply(H, X, Z)) | (member(tptp_fun_Y_8(Z, X, B, F, G), B) & apply(F, X, tptp_fun_Y_8(Z, X, B, F, G)) & apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z))) & (apply(H, X, Z) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y) & apply(G, Y, Z))))))) & (compose_predicate(H, G, F, A, B, C) | (member(tptp_fun_X_10(C, B, A, F, G, H), A) & member(tptp_fun_Z_9(C, B, A, F, G, H), C) & (apply(H, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H)) | (member(tptp_fun_Y_11(C, B, A, F, G, H), B) & apply(F, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Y_11(C, B, A, F, G, H)) & apply(G, tptp_fun_Y_11(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H)))) & ((~apply(H, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H))) | ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_10(C, B, A, F, G, H), Y) & apply(G, Y, tptp_fun_Z_9(C, B, A, F, G, H)))))))) <=> ![H: $i, G: $i, F: $i, A: $i, B: $i, C: $i] : (~((~((~compose_predicate(H, G, F, A, B, C)) | ![X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(H, X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(H, X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z)))))))))) | (~(compose_predicate(H, G, F, A, B, C) | (~((~member(tptp_fun_X_10(C, B, A, F, G, H), A)) | (~member(tptp_fun_Z_9(C, B, A, F, G, H), C)) | (~(apply(H, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H)) | (~((~member(tptp_fun_Y_11(C, B, A, F, G, H), B)) | (~apply(F, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Y_11(C, B, A, F, G, H))) | (~apply(G, tptp_fun_Y_11(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H))))))) | (~((~apply(H, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H))) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_10(C, B, A, F, G, H), Y)) | (~apply(G, Y, tptp_fun_Z_9(C, B, A, F, G, H))))))))))))),
% 0.18/0.42 inference(quant_intro,[status(thm)],[47])).
% 0.18/0.42 tff(49,plain,
% 0.18/0.42 (^[H: $i, G: $i, F: $i, A: $i, B: $i, C: $i] : rewrite((((~compose_predicate(H, G, F, A, B, C)) | ![X: $i, Z: $i] : ((~(member(X, A) & member(Z, C))) | (((~apply(H, X, Z)) | (member(tptp_fun_Y_8(Z, X, B, F, G), B) & apply(F, X, tptp_fun_Y_8(Z, X, B, F, G)) & apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z))) & (apply(H, X, Z) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y) & apply(G, Y, Z))))))) & (compose_predicate(H, G, F, A, B, C) | ((member(tptp_fun_X_10(C, B, A, F, G, H), A) & member(tptp_fun_Z_9(C, B, A, F, G, H), C)) & ((apply(H, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H)) | (member(tptp_fun_Y_11(C, B, A, F, G, H), B) & apply(F, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Y_11(C, B, A, F, G, H)) & apply(G, tptp_fun_Y_11(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H)))) & ((~apply(H, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H))) | ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_10(C, B, A, F, G, H), Y) & apply(G, Y, tptp_fun_Z_9(C, B, A, F, G, H))))))))) <=> (((~compose_predicate(H, G, F, A, B, C)) | ![X: $i, Z: $i] : ((~(member(X, A) & member(Z, C))) | (((~apply(H, X, Z)) | (member(tptp_fun_Y_8(Z, X, B, F, G), B) & apply(F, X, tptp_fun_Y_8(Z, X, B, F, G)) & apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z))) & (apply(H, X, Z) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y) & apply(G, Y, Z))))))) & (compose_predicate(H, G, F, A, B, C) | (member(tptp_fun_X_10(C, B, A, F, G, H), A) & member(tptp_fun_Z_9(C, B, A, F, G, H), C) & (apply(H, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H)) | (member(tptp_fun_Y_11(C, B, A, F, G, H), B) & apply(F, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Y_11(C, B, A, F, G, H)) & apply(G, tptp_fun_Y_11(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H)))) & ((~apply(H, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H))) | ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_10(C, B, A, F, G, H), Y) & apply(G, Y, tptp_fun_Z_9(C, B, A, F, G, H)))))))))),
% 0.18/0.42 inference(bind,[status(th)],[])).
% 0.18/0.42 tff(50,plain,
% 0.18/0.42 (![H: $i, G: $i, F: $i, A: $i, B: $i, C: $i] : (((~compose_predicate(H, G, F, A, B, C)) | ![X: $i, Z: $i] : ((~(member(X, A) & member(Z, C))) | (((~apply(H, X, Z)) | (member(tptp_fun_Y_8(Z, X, B, F, G), B) & apply(F, X, tptp_fun_Y_8(Z, X, B, F, G)) & apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z))) & (apply(H, X, Z) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y) & apply(G, Y, Z))))))) & (compose_predicate(H, G, F, A, B, C) | ((member(tptp_fun_X_10(C, B, A, F, G, H), A) & member(tptp_fun_Z_9(C, B, A, F, G, H), C)) & ((apply(H, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H)) | (member(tptp_fun_Y_11(C, B, A, F, G, H), B) & apply(F, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Y_11(C, B, A, F, G, H)) & apply(G, tptp_fun_Y_11(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H)))) & ((~apply(H, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H))) | ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_10(C, B, A, F, G, H), Y) & apply(G, Y, tptp_fun_Z_9(C, B, A, F, G, H))))))))) <=> ![H: $i, G: $i, F: $i, A: $i, B: $i, C: $i] : (((~compose_predicate(H, G, F, A, B, C)) | ![X: $i, Z: $i] : ((~(member(X, A) & member(Z, C))) | (((~apply(H, X, Z)) | (member(tptp_fun_Y_8(Z, X, B, F, G), B) & apply(F, X, tptp_fun_Y_8(Z, X, B, F, G)) & apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z))) & (apply(H, X, Z) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y) & apply(G, Y, Z))))))) & (compose_predicate(H, G, F, A, B, C) | (member(tptp_fun_X_10(C, B, A, F, G, H), A) & member(tptp_fun_Z_9(C, B, A, F, G, H), C) & (apply(H, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H)) | (member(tptp_fun_Y_11(C, B, A, F, G, H), B) & apply(F, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Y_11(C, B, A, F, G, H)) & apply(G, tptp_fun_Y_11(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H)))) & ((~apply(H, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H))) | ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_10(C, B, A, F, G, H), Y) & apply(G, Y, tptp_fun_Z_9(C, B, A, F, G, H))))))))),
% 0.18/0.43 inference(quant_intro,[status(thm)],[49])).
% 0.18/0.43 tff(51,plain,
% 0.18/0.43 (![H: $i, G: $i, F: $i, A: $i, B: $i, C: $i] : (compose_predicate(H, G, F, A, B, C) <=> ![X: $i, Z: $i] : ((~(member(X, A) & member(Z, C))) | (apply(H, X, Z) <=> ?[Y: $i] : (member(Y, B) & apply(F, X, Y) & apply(G, Y, Z))))) <=> ![H: $i, G: $i, F: $i, A: $i, B: $i, C: $i] : (compose_predicate(H, G, F, A, B, C) <=> ![X: $i, Z: $i] : ((~(member(X, A) & member(Z, C))) | (apply(H, X, Z) <=> ?[Y: $i] : (member(Y, B) & apply(F, X, Y) & apply(G, Y, Z)))))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(52,plain,
% 0.18/0.43 (^[H: $i, G: $i, F: $i, A: $i, B: $i, C: $i] : rewrite((compose_predicate(H, G, F, A, B, C) <=> ![X: $i, Z: $i] : ((member(X, A) & member(Z, C)) => (apply(H, X, Z) <=> ?[Y: $i] : ((member(Y, B) & apply(F, X, Y)) & apply(G, Y, Z))))) <=> (compose_predicate(H, G, F, A, B, C) <=> ![X: $i, Z: $i] : ((~(member(X, A) & member(Z, C))) | (apply(H, X, Z) <=> ?[Y: $i] : (member(Y, B) & apply(F, X, Y) & apply(G, Y, Z))))))),
% 0.18/0.43 inference(bind,[status(th)],[])).
% 0.18/0.43 tff(53,plain,
% 0.18/0.43 (![H: $i, G: $i, F: $i, A: $i, B: $i, C: $i] : (compose_predicate(H, G, F, A, B, C) <=> ![X: $i, Z: $i] : ((member(X, A) & member(Z, C)) => (apply(H, X, Z) <=> ?[Y: $i] : ((member(Y, B) & apply(F, X, Y)) & apply(G, Y, Z))))) <=> ![H: $i, G: $i, F: $i, A: $i, B: $i, C: $i] : (compose_predicate(H, G, F, A, B, C) <=> ![X: $i, Z: $i] : ((~(member(X, A) & member(Z, C))) | (apply(H, X, Z) <=> ?[Y: $i] : (member(Y, B) & apply(F, X, Y) & apply(G, Y, Z)))))),
% 0.18/0.43 inference(quant_intro,[status(thm)],[52])).
% 0.18/0.43 tff(54,axiom,(![H: $i, G: $i, F: $i, A: $i, B: $i, C: $i] : (compose_predicate(H, G, F, A, B, C) <=> ![X: $i, Z: $i] : ((member(X, A) & member(Z, C)) => (apply(H, 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_predicate')).
% 0.18/0.43 tff(55,plain,
% 0.18/0.43 (![H: $i, G: $i, F: $i, A: $i, B: $i, C: $i] : (compose_predicate(H, G, F, A, B, C) <=> ![X: $i, Z: $i] : ((~(member(X, A) & member(Z, C))) | (apply(H, X, Z) <=> ?[Y: $i] : (member(Y, B) & apply(F, X, Y) & apply(G, Y, Z)))))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.18/0.43 tff(56,plain,
% 0.18/0.43 (![H: $i, G: $i, F: $i, A: $i, B: $i, C: $i] : (compose_predicate(H, G, F, A, B, C) <=> ![X: $i, Z: $i] : ((~(member(X, A) & member(Z, C))) | (apply(H, X, Z) <=> ?[Y: $i] : (member(Y, B) & apply(F, X, Y) & apply(G, Y, Z)))))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[55, 51])).
% 0.18/0.43 tff(57,plain,(
% 0.18/0.43 ![H: $i, G: $i, F: $i, A: $i, B: $i, C: $i] : (((~compose_predicate(H, G, F, A, B, C)) | ![X: $i, Z: $i] : ((~(member(X, A) & member(Z, C))) | (((~apply(H, X, Z)) | (member(tptp_fun_Y_8(Z, X, B, F, G), B) & apply(F, X, tptp_fun_Y_8(Z, X, B, F, G)) & apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z))) & (apply(H, X, Z) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y) & apply(G, Y, Z))))))) & (compose_predicate(H, G, F, A, B, C) | ((member(tptp_fun_X_10(C, B, A, F, G, H), A) & member(tptp_fun_Z_9(C, B, A, F, G, H), C)) & ((apply(H, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H)) | (member(tptp_fun_Y_11(C, B, A, F, G, H), B) & apply(F, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Y_11(C, B, A, F, G, H)) & apply(G, tptp_fun_Y_11(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H)))) & ((~apply(H, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H))) | ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_10(C, B, A, F, G, H), Y) & apply(G, Y, tptp_fun_Z_9(C, B, A, F, G, H)))))))))),
% 0.18/0.43 inference(skolemize,[status(sab)],[56])).
% 0.18/0.43 tff(58,plain,
% 0.18/0.43 (![H: $i, G: $i, F: $i, A: $i, B: $i, C: $i] : (((~compose_predicate(H, G, F, A, B, C)) | ![X: $i, Z: $i] : ((~(member(X, A) & member(Z, C))) | (((~apply(H, X, Z)) | (member(tptp_fun_Y_8(Z, X, B, F, G), B) & apply(F, X, tptp_fun_Y_8(Z, X, B, F, G)) & apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z))) & (apply(H, X, Z) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y) & apply(G, Y, Z))))))) & (compose_predicate(H, G, F, A, B, C) | (member(tptp_fun_X_10(C, B, A, F, G, H), A) & member(tptp_fun_Z_9(C, B, A, F, G, H), C) & (apply(H, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H)) | (member(tptp_fun_Y_11(C, B, A, F, G, H), B) & apply(F, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Y_11(C, B, A, F, G, H)) & apply(G, tptp_fun_Y_11(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H)))) & ((~apply(H, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H))) | ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_10(C, B, A, F, G, H), Y) & apply(G, Y, tptp_fun_Z_9(C, B, A, F, G, H))))))))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[57, 50])).
% 0.18/0.43 tff(59,plain,
% 0.18/0.43 (![H: $i, G: $i, F: $i, A: $i, B: $i, C: $i] : (~((~((~compose_predicate(H, G, F, A, B, C)) | ![X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(H, X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(H, X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z)))))))))) | (~(compose_predicate(H, G, F, A, B, C) | (~((~member(tptp_fun_X_10(C, B, A, F, G, H), A)) | (~member(tptp_fun_Z_9(C, B, A, F, G, H), C)) | (~(apply(H, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H)) | (~((~member(tptp_fun_Y_11(C, B, A, F, G, H), B)) | (~apply(F, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Y_11(C, B, A, F, G, H))) | (~apply(G, tptp_fun_Y_11(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H))))))) | (~((~apply(H, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H))) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_10(C, B, A, F, G, H), Y)) | (~apply(G, Y, tptp_fun_Z_9(C, B, A, F, G, H))))))))))))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[58, 48])).
% 0.18/0.43 tff(60,plain,
% 0.18/0.43 (![H: $i, G: $i, F: $i, A: $i, B: $i, C: $i] : (~((~((~compose_predicate(H, G, F, A, B, C)) | ![X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(H, X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(H, X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z)))))))))) | (~(compose_predicate(H, G, F, A, B, C) | (~((~member(tptp_fun_X_10(C, B, A, F, G, H), A)) | (~member(tptp_fun_Z_9(C, B, A, F, G, H), C)) | (~(apply(H, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H)) | (~((~member(tptp_fun_Y_11(C, B, A, F, G, H), B)) | (~apply(F, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Y_11(C, B, A, F, G, H))) | (~apply(G, tptp_fun_Y_11(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H))))))) | (~((~apply(H, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H))) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_10(C, B, A, F, G, H), Y)) | (~apply(G, Y, tptp_fun_Z_9(C, B, A, F, G, H))))))))))))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[59, 46])).
% 0.18/0.43 tff(61,plain,
% 0.18/0.43 (((~![H: $i, G: $i, F: $i, A: $i, B: $i, C: $i] : (~((~((~compose_predicate(H, G, F, A, B, C)) | ![X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(H, X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(H, X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z)))))))))) | (~(compose_predicate(H, G, F, A, B, C) | (~((~member(tptp_fun_X_10(C, B, A, F, G, H), A)) | (~member(tptp_fun_Z_9(C, B, A, F, G, H), C)) | (~(apply(H, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H)) | (~((~member(tptp_fun_Y_11(C, B, A, F, G, H), B)) | (~apply(F, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Y_11(C, B, A, F, G, H))) | (~apply(G, tptp_fun_Y_11(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H))))))) | (~((~apply(H, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H))) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_10(C, B, A, F, G, H), Y)) | (~apply(G, Y, tptp_fun_Z_9(C, B, A, F, G, H))))))))))))) | (~((~((~compose_predicate(H2!42, G!44, F!45, A!41, B!40, C!39)) | ![X: $i, Z: $i] : ((~member(Z, C!39)) | (~member(X, A!41)) | (~((~(apply(H2!42, X, Z) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!45, X, Y)) | (~apply(G!44, Y, Z))))) | (~((~apply(H2!42, X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B!40, F!45, G!44), B!40)) | (~apply(F!45, X, tptp_fun_Y_8(Z, X, B!40, F!45, G!44))) | (~apply(G!44, tptp_fun_Y_8(Z, X, B!40, F!45, G!44), Z))))))))))) | (~(compose_predicate(H2!42, G!44, F!45, A!41, B!40, C!39) | (~((~((~apply(H2!42, tptp_fun_X_10(C!39, B!40, A!41, F!45, G!44, H2!42), tptp_fun_Z_9(C!39, B!40, A!41, F!45, G!44, H2!42))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!45, tptp_fun_X_10(C!39, B!40, A!41, F!45, G!44, H2!42), Y)) | (~apply(G!44, Y, tptp_fun_Z_9(C!39, B!40, A!41, F!45, G!44, H2!42)))))) | (~(apply(H2!42, tptp_fun_X_10(C!39, B!40, A!41, F!45, G!44, H2!42), tptp_fun_Z_9(C!39, B!40, A!41, F!45, G!44, H2!42)) | (~((~member(tptp_fun_Y_11(C!39, B!40, A!41, F!45, G!44, H2!42), B!40)) | (~apply(F!45, tptp_fun_X_10(C!39, B!40, A!41, F!45, G!44, H2!42), tptp_fun_Y_11(C!39, B!40, A!41, F!45, G!44, H2!42))) | (~apply(G!44, tptp_fun_Y_11(C!39, B!40, A!41, F!45, G!44, H2!42), tptp_fun_Z_9(C!39, B!40, A!41, F!45, G!44, H2!42))))))) | (~member(tptp_fun_Z_9(C!39, B!40, A!41, F!45, G!44, H2!42), C!39)) | (~member(tptp_fun_X_10(C!39, B!40, A!41, F!45, G!44, H2!42), A!41))))))))) <=> ((~![H: $i, G: $i, F: $i, A: $i, B: $i, C: $i] : (~((~((~compose_predicate(H, G, F, A, B, C)) | ![X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(H, X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(H, X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z)))))))))) | (~(compose_predicate(H, G, F, A, B, C) | (~((~member(tptp_fun_X_10(C, B, A, F, G, H), A)) | (~member(tptp_fun_Z_9(C, B, A, F, G, H), C)) | (~(apply(H, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H)) | (~((~member(tptp_fun_Y_11(C, B, A, F, G, H), B)) | (~apply(F, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Y_11(C, B, A, F, G, H))) | (~apply(G, tptp_fun_Y_11(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H))))))) | (~((~apply(H, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H))) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_10(C, B, A, F, G, H), Y)) | (~apply(G, Y, tptp_fun_Z_9(C, B, A, F, G, H))))))))))))) | (~((~((~compose_predicate(H2!42, G!44, F!45, A!41, B!40, C!39)) | ![X: $i, Z: $i] : ((~member(Z, C!39)) | (~member(X, A!41)) | (~((~(apply(H2!42, X, Z) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!45, X, Y)) | (~apply(G!44, Y, Z))))) | (~((~apply(H2!42, X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B!40, F!45, G!44), B!40)) | (~apply(F!45, X, tptp_fun_Y_8(Z, X, B!40, F!45, G!44))) | (~apply(G!44, tptp_fun_Y_8(Z, X, B!40, F!45, G!44), Z))))))))))) | (~(compose_predicate(H2!42, G!44, F!45, A!41, B!40, C!39) | (~((~((~apply(H2!42, tptp_fun_X_10(C!39, B!40, A!41, F!45, G!44, H2!42), tptp_fun_Z_9(C!39, B!40, A!41, F!45, G!44, H2!42))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!45, tptp_fun_X_10(C!39, B!40, A!41, F!45, G!44, H2!42), Y)) | (~apply(G!44, Y, tptp_fun_Z_9(C!39, B!40, A!41, F!45, G!44, H2!42)))))) | (~(apply(H2!42, tptp_fun_X_10(C!39, B!40, A!41, F!45, G!44, H2!42), tptp_fun_Z_9(C!39, B!40, A!41, F!45, G!44, H2!42)) | (~((~member(tptp_fun_Y_11(C!39, B!40, A!41, F!45, G!44, H2!42), B!40)) | (~apply(F!45, tptp_fun_X_10(C!39, B!40, A!41, F!45, G!44, H2!42), tptp_fun_Y_11(C!39, B!40, A!41, F!45, G!44, H2!42))) | (~apply(G!44, tptp_fun_Y_11(C!39, B!40, A!41, F!45, G!44, H2!42), tptp_fun_Z_9(C!39, B!40, A!41, F!45, G!44, H2!42))))))) | (~member(tptp_fun_Z_9(C!39, B!40, A!41, F!45, G!44, H2!42), C!39)) | (~member(tptp_fun_X_10(C!39, B!40, A!41, F!45, G!44, H2!42), A!41)))))))))),
% 0.18/0.44 inference(rewrite,[status(thm)],[])).
% 0.18/0.44 tff(62,plain,
% 0.18/0.44 ((~((~((~compose_predicate(H2!42, G!44, F!45, A!41, B!40, C!39)) | ![X: $i, Z: $i] : ((~member(Z, C!39)) | (~member(X, A!41)) | (~((~((~apply(H2!42, X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B!40, F!45, G!44), B!40)) | (~apply(F!45, X, tptp_fun_Y_8(Z, X, B!40, F!45, G!44))) | (~apply(G!44, tptp_fun_Y_8(Z, X, B!40, F!45, G!44), Z)))))) | (~(apply(H2!42, X, Z) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!45, X, Y)) | (~apply(G!44, Y, Z)))))))))) | (~(compose_predicate(H2!42, G!44, F!45, A!41, B!40, C!39) | (~((~member(tptp_fun_X_10(C!39, B!40, A!41, F!45, G!44, H2!42), A!41)) | (~member(tptp_fun_Z_9(C!39, B!40, A!41, F!45, G!44, H2!42), C!39)) | (~(apply(H2!42, tptp_fun_X_10(C!39, B!40, A!41, F!45, G!44, H2!42), tptp_fun_Z_9(C!39, B!40, A!41, F!45, G!44, H2!42)) | (~((~member(tptp_fun_Y_11(C!39, B!40, A!41, F!45, G!44, H2!42), B!40)) | (~apply(F!45, tptp_fun_X_10(C!39, B!40, A!41, F!45, G!44, H2!42), tptp_fun_Y_11(C!39, B!40, A!41, F!45, G!44, H2!42))) | (~apply(G!44, tptp_fun_Y_11(C!39, B!40, A!41, F!45, G!44, H2!42), tptp_fun_Z_9(C!39, B!40, A!41, F!45, G!44, H2!42))))))) | (~((~apply(H2!42, tptp_fun_X_10(C!39, B!40, A!41, F!45, G!44, H2!42), tptp_fun_Z_9(C!39, B!40, A!41, F!45, G!44, H2!42))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!45, tptp_fun_X_10(C!39, B!40, A!41, F!45, G!44, H2!42), Y)) | (~apply(G!44, Y, tptp_fun_Z_9(C!39, B!40, A!41, F!45, G!44, H2!42)))))))))))) <=> (~((~((~compose_predicate(H2!42, G!44, F!45, A!41, B!40, C!39)) | ![X: $i, Z: $i] : ((~member(Z, C!39)) | (~member(X, A!41)) | (~((~(apply(H2!42, X, Z) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!45, X, Y)) | (~apply(G!44, Y, Z))))) | (~((~apply(H2!42, X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B!40, F!45, G!44), B!40)) | (~apply(F!45, X, tptp_fun_Y_8(Z, X, B!40, F!45, G!44))) | (~apply(G!44, tptp_fun_Y_8(Z, X, B!40, F!45, G!44), Z))))))))))) | (~(compose_predicate(H2!42, G!44, F!45, A!41, B!40, C!39) | (~((~((~apply(H2!42, tptp_fun_X_10(C!39, B!40, A!41, F!45, G!44, H2!42), tptp_fun_Z_9(C!39, B!40, A!41, F!45, G!44, H2!42))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!45, tptp_fun_X_10(C!39, B!40, A!41, F!45, G!44, H2!42), Y)) | (~apply(G!44, Y, tptp_fun_Z_9(C!39, B!40, A!41, F!45, G!44, H2!42)))))) | (~(apply(H2!42, tptp_fun_X_10(C!39, B!40, A!41, F!45, G!44, H2!42), tptp_fun_Z_9(C!39, B!40, A!41, F!45, G!44, H2!42)) | (~((~member(tptp_fun_Y_11(C!39, B!40, A!41, F!45, G!44, H2!42), B!40)) | (~apply(F!45, tptp_fun_X_10(C!39, B!40, A!41, F!45, G!44, H2!42), tptp_fun_Y_11(C!39, B!40, A!41, F!45, G!44, H2!42))) | (~apply(G!44, tptp_fun_Y_11(C!39, B!40, A!41, F!45, G!44, H2!42), tptp_fun_Z_9(C!39, B!40, A!41, F!45, G!44, H2!42))))))) | (~member(tptp_fun_Z_9(C!39, B!40, A!41, F!45, G!44, H2!42), C!39)) | (~member(tptp_fun_X_10(C!39, B!40, A!41, F!45, G!44, H2!42), A!41))))))))),
% 0.18/0.44 inference(rewrite,[status(thm)],[])).
% 0.18/0.44 tff(63,plain,
% 0.18/0.44 (((~![H: $i, G: $i, F: $i, A: $i, B: $i, C: $i] : (~((~((~compose_predicate(H, G, F, A, B, C)) | ![X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(H, X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(H, X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z)))))))))) | (~(compose_predicate(H, G, F, A, B, C) | (~((~member(tptp_fun_X_10(C, B, A, F, G, H), A)) | (~member(tptp_fun_Z_9(C, B, A, F, G, H), C)) | (~(apply(H, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H)) | (~((~member(tptp_fun_Y_11(C, B, A, F, G, H), B)) | (~apply(F, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Y_11(C, B, A, F, G, H))) | (~apply(G, tptp_fun_Y_11(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H))))))) | (~((~apply(H, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H))) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_10(C, B, A, F, G, H), Y)) | (~apply(G, Y, tptp_fun_Z_9(C, B, A, F, G, H))))))))))))) | (~((~((~compose_predicate(H2!42, G!44, F!45, A!41, B!40, C!39)) | ![X: $i, Z: $i] : ((~member(Z, C!39)) | (~member(X, A!41)) | (~((~((~apply(H2!42, X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B!40, F!45, G!44), B!40)) | (~apply(F!45, X, tptp_fun_Y_8(Z, X, B!40, F!45, G!44))) | (~apply(G!44, tptp_fun_Y_8(Z, X, B!40, F!45, G!44), Z)))))) | (~(apply(H2!42, X, Z) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!45, X, Y)) | (~apply(G!44, Y, Z)))))))))) | (~(compose_predicate(H2!42, G!44, F!45, A!41, B!40, C!39) | (~((~member(tptp_fun_X_10(C!39, B!40, A!41, F!45, G!44, H2!42), A!41)) | (~member(tptp_fun_Z_9(C!39, B!40, A!41, F!45, G!44, H2!42), C!39)) | (~(apply(H2!42, tptp_fun_X_10(C!39, B!40, A!41, F!45, G!44, H2!42), tptp_fun_Z_9(C!39, B!40, A!41, F!45, G!44, H2!42)) | (~((~member(tptp_fun_Y_11(C!39, B!40, A!41, F!45, G!44, H2!42), B!40)) | (~apply(F!45, tptp_fun_X_10(C!39, B!40, A!41, F!45, G!44, H2!42), tptp_fun_Y_11(C!39, B!40, A!41, F!45, G!44, H2!42))) | (~apply(G!44, tptp_fun_Y_11(C!39, B!40, A!41, F!45, G!44, H2!42), tptp_fun_Z_9(C!39, B!40, A!41, F!45, G!44, H2!42))))))) | (~((~apply(H2!42, tptp_fun_X_10(C!39, B!40, A!41, F!45, G!44, H2!42), tptp_fun_Z_9(C!39, B!40, A!41, F!45, G!44, H2!42))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!45, tptp_fun_X_10(C!39, B!40, A!41, F!45, G!44, H2!42), Y)) | (~apply(G!44, Y, tptp_fun_Z_9(C!39, B!40, A!41, F!45, G!44, H2!42))))))))))))) <=> ((~![H: $i, G: $i, F: $i, A: $i, B: $i, C: $i] : (~((~((~compose_predicate(H, G, F, A, B, C)) | ![X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(H, X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(H, X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z)))))))))) | (~(compose_predicate(H, G, F, A, B, C) | (~((~member(tptp_fun_X_10(C, B, A, F, G, H), A)) | (~member(tptp_fun_Z_9(C, B, A, F, G, H), C)) | (~(apply(H, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H)) | (~((~member(tptp_fun_Y_11(C, B, A, F, G, H), B)) | (~apply(F, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Y_11(C, B, A, F, G, H))) | (~apply(G, tptp_fun_Y_11(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H))))))) | (~((~apply(H, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H))) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_10(C, B, A, F, G, H), Y)) | (~apply(G, Y, tptp_fun_Z_9(C, B, A, F, G, H))))))))))))) | (~((~((~compose_predicate(H2!42, G!44, F!45, A!41, B!40, C!39)) | ![X: $i, Z: $i] : ((~member(Z, C!39)) | (~member(X, A!41)) | (~((~(apply(H2!42, X, Z) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!45, X, Y)) | (~apply(G!44, Y, Z))))) | (~((~apply(H2!42, X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B!40, F!45, G!44), B!40)) | (~apply(F!45, X, tptp_fun_Y_8(Z, X, B!40, F!45, G!44))) | (~apply(G!44, tptp_fun_Y_8(Z, X, B!40, F!45, G!44), Z))))))))))) | (~(compose_predicate(H2!42, G!44, F!45, A!41, B!40, C!39) | (~((~((~apply(H2!42, tptp_fun_X_10(C!39, B!40, A!41, F!45, G!44, H2!42), tptp_fun_Z_9(C!39, B!40, A!41, F!45, G!44, H2!42))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!45, tptp_fun_X_10(C!39, B!40, A!41, F!45, G!44, H2!42), Y)) | (~apply(G!44, Y, tptp_fun_Z_9(C!39, B!40, A!41, F!45, G!44, H2!42)))))) | (~(apply(H2!42, tptp_fun_X_10(C!39, B!40, A!41, F!45, G!44, H2!42), tptp_fun_Z_9(C!39, B!40, A!41, F!45, G!44, H2!42)) | (~((~member(tptp_fun_Y_11(C!39, B!40, A!41, F!45, G!44, H2!42), B!40)) | (~apply(F!45, tptp_fun_X_10(C!39, B!40, A!41, F!45, G!44, H2!42), tptp_fun_Y_11(C!39, B!40, A!41, F!45, G!44, H2!42))) | (~apply(G!44, tptp_fun_Y_11(C!39, B!40, A!41, F!45, G!44, H2!42), tptp_fun_Z_9(C!39, B!40, A!41, F!45, G!44, H2!42))))))) | (~member(tptp_fun_Z_9(C!39, B!40, A!41, F!45, G!44, H2!42), C!39)) | (~member(tptp_fun_X_10(C!39, B!40, A!41, F!45, G!44, H2!42), A!41)))))))))),
% 0.18/0.45 inference(monotonicity,[status(thm)],[62])).
% 0.18/0.45 tff(64,plain,
% 0.18/0.45 (((~![H: $i, G: $i, F: $i, A: $i, B: $i, C: $i] : (~((~((~compose_predicate(H, G, F, A, B, C)) | ![X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(H, X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(H, X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z)))))))))) | (~(compose_predicate(H, G, F, A, B, C) | (~((~member(tptp_fun_X_10(C, B, A, F, G, H), A)) | (~member(tptp_fun_Z_9(C, B, A, F, G, H), C)) | (~(apply(H, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H)) | (~((~member(tptp_fun_Y_11(C, B, A, F, G, H), B)) | (~apply(F, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Y_11(C, B, A, F, G, H))) | (~apply(G, tptp_fun_Y_11(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H))))))) | (~((~apply(H, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H))) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_10(C, B, A, F, G, H), Y)) | (~apply(G, Y, tptp_fun_Z_9(C, B, A, F, G, H))))))))))))) | (~((~((~compose_predicate(H2!42, G!44, F!45, A!41, B!40, C!39)) | ![X: $i, Z: $i] : ((~member(Z, C!39)) | (~member(X, A!41)) | (~((~((~apply(H2!42, X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B!40, F!45, G!44), B!40)) | (~apply(F!45, X, tptp_fun_Y_8(Z, X, B!40, F!45, G!44))) | (~apply(G!44, tptp_fun_Y_8(Z, X, B!40, F!45, G!44), Z)))))) | (~(apply(H2!42, X, Z) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!45, X, Y)) | (~apply(G!44, Y, Z)))))))))) | (~(compose_predicate(H2!42, G!44, F!45, A!41, B!40, C!39) | (~((~member(tptp_fun_X_10(C!39, B!40, A!41, F!45, G!44, H2!42), A!41)) | (~member(tptp_fun_Z_9(C!39, B!40, A!41, F!45, G!44, H2!42), C!39)) | (~(apply(H2!42, tptp_fun_X_10(C!39, B!40, A!41, F!45, G!44, H2!42), tptp_fun_Z_9(C!39, B!40, A!41, F!45, G!44, H2!42)) | (~((~member(tptp_fun_Y_11(C!39, B!40, A!41, F!45, G!44, H2!42), B!40)) | (~apply(F!45, tptp_fun_X_10(C!39, B!40, A!41, F!45, G!44, H2!42), tptp_fun_Y_11(C!39, B!40, A!41, F!45, G!44, H2!42))) | (~apply(G!44, tptp_fun_Y_11(C!39, B!40, A!41, F!45, G!44, H2!42), tptp_fun_Z_9(C!39, B!40, A!41, F!45, G!44, H2!42))))))) | (~((~apply(H2!42, tptp_fun_X_10(C!39, B!40, A!41, F!45, G!44, H2!42), tptp_fun_Z_9(C!39, B!40, A!41, F!45, G!44, H2!42))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!45, tptp_fun_X_10(C!39, B!40, A!41, F!45, G!44, H2!42), Y)) | (~apply(G!44, Y, tptp_fun_Z_9(C!39, B!40, A!41, F!45, G!44, H2!42))))))))))))) <=> ((~![H: $i, G: $i, F: $i, A: $i, B: $i, C: $i] : (~((~((~compose_predicate(H, G, F, A, B, C)) | ![X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(H, X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(H, X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z)))))))))) | (~(compose_predicate(H, G, F, A, B, C) | (~((~member(tptp_fun_X_10(C, B, A, F, G, H), A)) | (~member(tptp_fun_Z_9(C, B, A, F, G, H), C)) | (~(apply(H, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H)) | (~((~member(tptp_fun_Y_11(C, B, A, F, G, H), B)) | (~apply(F, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Y_11(C, B, A, F, G, H))) | (~apply(G, tptp_fun_Y_11(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H))))))) | (~((~apply(H, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H))) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_10(C, B, A, F, G, H), Y)) | (~apply(G, Y, tptp_fun_Z_9(C, B, A, F, G, H))))))))))))) | (~((~((~compose_predicate(H2!42, G!44, F!45, A!41, B!40, C!39)) | ![X: $i, Z: $i] : ((~member(Z, C!39)) | (~member(X, A!41)) | (~((~(apply(H2!42, X, Z) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!45, X, Y)) | (~apply(G!44, Y, Z))))) | (~((~apply(H2!42, X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B!40, F!45, G!44), B!40)) | (~apply(F!45, X, tptp_fun_Y_8(Z, X, B!40, F!45, G!44))) | (~apply(G!44, tptp_fun_Y_8(Z, X, B!40, F!45, G!44), Z))))))))))) | (~(compose_predicate(H2!42, G!44, F!45, A!41, B!40, C!39) | (~((~((~apply(H2!42, tptp_fun_X_10(C!39, B!40, A!41, F!45, G!44, H2!42), tptp_fun_Z_9(C!39, B!40, A!41, F!45, G!44, H2!42))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!45, tptp_fun_X_10(C!39, B!40, A!41, F!45, G!44, H2!42), Y)) | (~apply(G!44, Y, tptp_fun_Z_9(C!39, B!40, A!41, F!45, G!44, H2!42)))))) | (~(apply(H2!42, tptp_fun_X_10(C!39, B!40, A!41, F!45, G!44, H2!42), tptp_fun_Z_9(C!39, B!40, A!41, F!45, G!44, H2!42)) | (~((~member(tptp_fun_Y_11(C!39, B!40, A!41, F!45, G!44, H2!42), B!40)) | (~apply(F!45, tptp_fun_X_10(C!39, B!40, A!41, F!45, G!44, H2!42), tptp_fun_Y_11(C!39, B!40, A!41, F!45, G!44, H2!42))) | (~apply(G!44, tptp_fun_Y_11(C!39, B!40, A!41, F!45, G!44, H2!42), tptp_fun_Z_9(C!39, B!40, A!41, F!45, G!44, H2!42))))))) | (~member(tptp_fun_Z_9(C!39, B!40, A!41, F!45, G!44, H2!42), C!39)) | (~member(tptp_fun_X_10(C!39, B!40, A!41, F!45, G!44, H2!42), A!41)))))))))),
% 0.18/0.45 inference(transitivity,[status(thm)],[63, 61])).
% 0.18/0.45 tff(65,plain,
% 0.18/0.45 ((~![H: $i, G: $i, F: $i, A: $i, B: $i, C: $i] : (~((~((~compose_predicate(H, G, F, A, B, C)) | ![X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(H, X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(H, X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z)))))))))) | (~(compose_predicate(H, G, F, A, B, C) | (~((~member(tptp_fun_X_10(C, B, A, F, G, H), A)) | (~member(tptp_fun_Z_9(C, B, A, F, G, H), C)) | (~(apply(H, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H)) | (~((~member(tptp_fun_Y_11(C, B, A, F, G, H), B)) | (~apply(F, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Y_11(C, B, A, F, G, H))) | (~apply(G, tptp_fun_Y_11(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H))))))) | (~((~apply(H, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H))) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_10(C, B, A, F, G, H), Y)) | (~apply(G, Y, tptp_fun_Z_9(C, B, A, F, G, H))))))))))))) | (~((~((~compose_predicate(H2!42, G!44, F!45, A!41, B!40, C!39)) | ![X: $i, Z: $i] : ((~member(Z, C!39)) | (~member(X, A!41)) | (~((~((~apply(H2!42, X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B!40, F!45, G!44), B!40)) | (~apply(F!45, X, tptp_fun_Y_8(Z, X, B!40, F!45, G!44))) | (~apply(G!44, tptp_fun_Y_8(Z, X, B!40, F!45, G!44), Z)))))) | (~(apply(H2!42, X, Z) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!45, X, Y)) | (~apply(G!44, Y, Z)))))))))) | (~(compose_predicate(H2!42, G!44, F!45, A!41, B!40, C!39) | (~((~member(tptp_fun_X_10(C!39, B!40, A!41, F!45, G!44, H2!42), A!41)) | (~member(tptp_fun_Z_9(C!39, B!40, A!41, F!45, G!44, H2!42), C!39)) | (~(apply(H2!42, tptp_fun_X_10(C!39, B!40, A!41, F!45, G!44, H2!42), tptp_fun_Z_9(C!39, B!40, A!41, F!45, G!44, H2!42)) | (~((~member(tptp_fun_Y_11(C!39, B!40, A!41, F!45, G!44, H2!42), B!40)) | (~apply(F!45, tptp_fun_X_10(C!39, B!40, A!41, F!45, G!44, H2!42), tptp_fun_Y_11(C!39, B!40, A!41, F!45, G!44, H2!42))) | (~apply(G!44, tptp_fun_Y_11(C!39, B!40, A!41, F!45, G!44, H2!42), tptp_fun_Z_9(C!39, B!40, A!41, F!45, G!44, H2!42))))))) | (~((~apply(H2!42, tptp_fun_X_10(C!39, B!40, A!41, F!45, G!44, H2!42), tptp_fun_Z_9(C!39, B!40, A!41, F!45, G!44, H2!42))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!45, tptp_fun_X_10(C!39, B!40, A!41, F!45, G!44, H2!42), Y)) | (~apply(G!44, Y, tptp_fun_Z_9(C!39, B!40, A!41, F!45, G!44, H2!42))))))))))))),
% 0.18/0.45 inference(quant_inst,[status(thm)],[])).
% 0.18/0.45 tff(66,plain,
% 0.18/0.45 ((~![H: $i, G: $i, F: $i, A: $i, B: $i, C: $i] : (~((~((~compose_predicate(H, G, F, A, B, C)) | ![X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(H, X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(H, X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z)))))))))) | (~(compose_predicate(H, G, F, A, B, C) | (~((~member(tptp_fun_X_10(C, B, A, F, G, H), A)) | (~member(tptp_fun_Z_9(C, B, A, F, G, H), C)) | (~(apply(H, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H)) | (~((~member(tptp_fun_Y_11(C, B, A, F, G, H), B)) | (~apply(F, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Y_11(C, B, A, F, G, H))) | (~apply(G, tptp_fun_Y_11(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H))))))) | (~((~apply(H, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H))) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_10(C, B, A, F, G, H), Y)) | (~apply(G, Y, tptp_fun_Z_9(C, B, A, F, G, H))))))))))))) | (~((~((~compose_predicate(H2!42, G!44, F!45, A!41, B!40, C!39)) | ![X: $i, Z: $i] : ((~member(Z, C!39)) | (~member(X, A!41)) | (~((~(apply(H2!42, X, Z) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!45, X, Y)) | (~apply(G!44, Y, Z))))) | (~((~apply(H2!42, X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B!40, F!45, G!44), B!40)) | (~apply(F!45, X, tptp_fun_Y_8(Z, X, B!40, F!45, G!44))) | (~apply(G!44, tptp_fun_Y_8(Z, X, B!40, F!45, G!44), Z))))))))))) | (~(compose_predicate(H2!42, G!44, F!45, A!41, B!40, C!39) | (~((~((~apply(H2!42, tptp_fun_X_10(C!39, B!40, A!41, F!45, G!44, H2!42), tptp_fun_Z_9(C!39, B!40, A!41, F!45, G!44, H2!42))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!45, tptp_fun_X_10(C!39, B!40, A!41, F!45, G!44, H2!42), Y)) | (~apply(G!44, Y, tptp_fun_Z_9(C!39, B!40, A!41, F!45, G!44, H2!42)))))) | (~(apply(H2!42, tptp_fun_X_10(C!39, B!40, A!41, F!45, G!44, H2!42), tptp_fun_Z_9(C!39, B!40, A!41, F!45, G!44, H2!42)) | (~((~member(tptp_fun_Y_11(C!39, B!40, A!41, F!45, G!44, H2!42), B!40)) | (~apply(F!45, tptp_fun_X_10(C!39, B!40, A!41, F!45, G!44, H2!42), tptp_fun_Y_11(C!39, B!40, A!41, F!45, G!44, H2!42))) | (~apply(G!44, tptp_fun_Y_11(C!39, B!40, A!41, F!45, G!44, H2!42), tptp_fun_Z_9(C!39, B!40, A!41, F!45, G!44, H2!42))))))) | (~member(tptp_fun_Z_9(C!39, B!40, A!41, F!45, G!44, H2!42), C!39)) | (~member(tptp_fun_X_10(C!39, B!40, A!41, F!45, G!44, H2!42), A!41))))))))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.18/0.45 tff(67,plain,
% 0.18/0.45 (~((~((~compose_predicate(H2!42, G!44, F!45, A!41, B!40, C!39)) | ![X: $i, Z: $i] : ((~member(Z, C!39)) | (~member(X, A!41)) | (~((~(apply(H2!42, X, Z) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!45, X, Y)) | (~apply(G!44, Y, Z))))) | (~((~apply(H2!42, X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B!40, F!45, G!44), B!40)) | (~apply(F!45, X, tptp_fun_Y_8(Z, X, B!40, F!45, G!44))) | (~apply(G!44, tptp_fun_Y_8(Z, X, B!40, F!45, G!44), Z))))))))))) | (~(compose_predicate(H2!42, G!44, F!45, A!41, B!40, C!39) | (~((~((~apply(H2!42, tptp_fun_X_10(C!39, B!40, A!41, F!45, G!44, H2!42), tptp_fun_Z_9(C!39, B!40, A!41, F!45, G!44, H2!42))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!45, tptp_fun_X_10(C!39, B!40, A!41, F!45, G!44, H2!42), Y)) | (~apply(G!44, Y, tptp_fun_Z_9(C!39, B!40, A!41, F!45, G!44, H2!42)))))) | (~(apply(H2!42, tptp_fun_X_10(C!39, B!40, A!41, F!45, G!44, H2!42), tptp_fun_Z_9(C!39, B!40, A!41, F!45, G!44, H2!42)) | (~((~member(tptp_fun_Y_11(C!39, B!40, A!41, F!45, G!44, H2!42), B!40)) | (~apply(F!45, tptp_fun_X_10(C!39, B!40, A!41, F!45, G!44, H2!42), tptp_fun_Y_11(C!39, B!40, A!41, F!45, G!44, H2!42))) | (~apply(G!44, tptp_fun_Y_11(C!39, B!40, A!41, F!45, G!44, H2!42), tptp_fun_Z_9(C!39, B!40, A!41, F!45, G!44, H2!42))))))) | (~member(tptp_fun_Z_9(C!39, B!40, A!41, F!45, G!44, H2!42), C!39)) | (~member(tptp_fun_X_10(C!39, B!40, A!41, F!45, G!44, H2!42), A!41)))))))),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[66, 60])).
% 0.18/0.46 tff(68,plain,
% 0.18/0.46 (((~((~compose_predicate(H2!42, G!44, F!45, A!41, B!40, C!39)) | ![X: $i, Z: $i] : ((~member(Z, C!39)) | (~member(X, A!41)) | (~((~(apply(H2!42, X, Z) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!45, X, Y)) | (~apply(G!44, Y, Z))))) | (~((~apply(H2!42, X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B!40, F!45, G!44), B!40)) | (~apply(F!45, X, tptp_fun_Y_8(Z, X, B!40, F!45, G!44))) | (~apply(G!44, tptp_fun_Y_8(Z, X, B!40, F!45, G!44), Z))))))))))) | (~(compose_predicate(H2!42, G!44, F!45, A!41, B!40, C!39) | (~((~((~apply(H2!42, tptp_fun_X_10(C!39, B!40, A!41, F!45, G!44, H2!42), tptp_fun_Z_9(C!39, B!40, A!41, F!45, G!44, H2!42))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!45, tptp_fun_X_10(C!39, B!40, A!41, F!45, G!44, H2!42), Y)) | (~apply(G!44, Y, tptp_fun_Z_9(C!39, B!40, A!41, F!45, G!44, H2!42)))))) | (~(apply(H2!42, tptp_fun_X_10(C!39, B!40, A!41, F!45, G!44, H2!42), tptp_fun_Z_9(C!39, B!40, A!41, F!45, G!44, H2!42)) | (~((~member(tptp_fun_Y_11(C!39, B!40, A!41, F!45, G!44, H2!42), B!40)) | (~apply(F!45, tptp_fun_X_10(C!39, B!40, A!41, F!45, G!44, H2!42), tptp_fun_Y_11(C!39, B!40, A!41, F!45, G!44, H2!42))) | (~apply(G!44, tptp_fun_Y_11(C!39, B!40, A!41, F!45, G!44, H2!42), tptp_fun_Z_9(C!39, B!40, A!41, F!45, G!44, H2!42))))))) | (~member(tptp_fun_Z_9(C!39, B!40, A!41, F!45, G!44, H2!42), C!39)) | (~member(tptp_fun_X_10(C!39, B!40, A!41, F!45, G!44, H2!42), A!41))))))) | ((~compose_predicate(H2!42, G!44, F!45, A!41, B!40, C!39)) | ![X: $i, Z: $i] : ((~member(Z, C!39)) | (~member(X, A!41)) | (~((~(apply(H2!42, X, Z) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!45, X, Y)) | (~apply(G!44, Y, Z))))) | (~((~apply(H2!42, X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B!40, F!45, G!44), B!40)) | (~apply(F!45, X, tptp_fun_Y_8(Z, X, B!40, F!45, G!44))) | (~apply(G!44, tptp_fun_Y_8(Z, X, B!40, F!45, G!44), Z))))))))))),
% 0.18/0.46 inference(tautology,[status(thm)],[])).
% 0.18/0.46 tff(69,plain,
% 0.18/0.46 ((~compose_predicate(H2!42, G!44, F!45, A!41, B!40, C!39)) | ![X: $i, Z: $i] : ((~member(Z, C!39)) | (~member(X, A!41)) | (~((~(apply(H2!42, X, Z) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!45, X, Y)) | (~apply(G!44, Y, Z))))) | (~((~apply(H2!42, X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B!40, F!45, G!44), B!40)) | (~apply(F!45, X, tptp_fun_Y_8(Z, X, B!40, F!45, G!44))) | (~apply(G!44, tptp_fun_Y_8(Z, X, B!40, F!45, G!44), Z)))))))))),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[68, 67])).
% 0.18/0.46 tff(70,plain,
% 0.18/0.46 (maps(F!45, A!41, B!40) & maps(G!44, B!40, C!39) & compose_predicate(H1!43, G!44, F!45, A!41, B!40, C!39) & compose_predicate(H2!42, G!44, F!45, A!41, B!40, C!39)),
% 0.18/0.46 inference(or_elim,[status(thm)],[33])).
% 0.18/0.46 tff(71,plain,
% 0.18/0.46 (compose_predicate(H2!42, G!44, F!45, A!41, B!40, C!39)),
% 0.18/0.46 inference(and_elim,[status(thm)],[70])).
% 0.18/0.46 tff(72,plain,
% 0.18/0.46 ((~((~compose_predicate(H2!42, G!44, F!45, A!41, B!40, C!39)) | ![X: $i, Z: $i] : ((~member(Z, C!39)) | (~member(X, A!41)) | (~((~(apply(H2!42, X, Z) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!45, X, Y)) | (~apply(G!44, Y, Z))))) | (~((~apply(H2!42, X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B!40, F!45, G!44), B!40)) | (~apply(F!45, X, tptp_fun_Y_8(Z, X, B!40, F!45, G!44))) | (~apply(G!44, tptp_fun_Y_8(Z, X, B!40, F!45, G!44), Z))))))))))) | (~compose_predicate(H2!42, G!44, F!45, A!41, B!40, C!39)) | ![X: $i, Z: $i] : ((~member(Z, C!39)) | (~member(X, A!41)) | (~((~(apply(H2!42, X, Z) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!45, X, Y)) | (~apply(G!44, Y, Z))))) | (~((~apply(H2!42, X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B!40, F!45, G!44), B!40)) | (~apply(F!45, X, tptp_fun_Y_8(Z, X, B!40, F!45, G!44))) | (~apply(G!44, tptp_fun_Y_8(Z, X, B!40, F!45, G!44), Z)))))))))),
% 0.18/0.46 inference(tautology,[status(thm)],[])).
% 0.18/0.46 tff(73,plain,
% 0.18/0.46 ((~((~compose_predicate(H2!42, G!44, F!45, A!41, B!40, C!39)) | ![X: $i, Z: $i] : ((~member(Z, C!39)) | (~member(X, A!41)) | (~((~(apply(H2!42, X, Z) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!45, X, Y)) | (~apply(G!44, Y, Z))))) | (~((~apply(H2!42, X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B!40, F!45, G!44), B!40)) | (~apply(F!45, X, tptp_fun_Y_8(Z, X, B!40, F!45, G!44))) | (~apply(G!44, tptp_fun_Y_8(Z, X, B!40, F!45, G!44), Z))))))))))) | ![X: $i, Z: $i] : ((~member(Z, C!39)) | (~member(X, A!41)) | (~((~(apply(H2!42, X, Z) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!45, X, Y)) | (~apply(G!44, Y, Z))))) | (~((~apply(H2!42, X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B!40, F!45, G!44), B!40)) | (~apply(F!45, X, tptp_fun_Y_8(Z, X, B!40, F!45, G!44))) | (~apply(G!44, tptp_fun_Y_8(Z, X, B!40, F!45, G!44), Z)))))))))),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[72, 71])).
% 0.18/0.46 tff(74,plain,
% 0.18/0.46 (![X: $i, Z: $i] : ((~member(Z, C!39)) | (~member(X, A!41)) | (~((~(apply(H2!42, X, Z) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!45, X, Y)) | (~apply(G!44, Y, Z))))) | (~((~apply(H2!42, X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B!40, F!45, G!44), B!40)) | (~apply(F!45, X, tptp_fun_Y_8(Z, X, B!40, F!45, G!44))) | (~apply(G!44, tptp_fun_Y_8(Z, X, B!40, F!45, G!44), Z)))))))))),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[73, 69])).
% 0.18/0.46 tff(75,plain,
% 0.18/0.46 (((~![X: $i, Z: $i] : ((~member(Z, C!39)) | (~member(X, A!41)) | (~((~(apply(H2!42, X, Z) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!45, X, Y)) | (~apply(G!44, Y, Z))))) | (~((~apply(H2!42, X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B!40, F!45, G!44), B!40)) | (~apply(F!45, X, tptp_fun_Y_8(Z, X, B!40, F!45, G!44))) | (~apply(G!44, tptp_fun_Y_8(Z, X, B!40, F!45, G!44), Z)))))))))) | ((~member(tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43), C!39)) | (~member(tptp_fun_X_14(C!39, A!41, H2!42, H1!43), A!41)) | (~((~(apply(H2!42, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43)) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!45, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), Y)) | (~apply(G!44, Y, tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43)))))) | (~((~apply(H2!42, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44), B!40)) | (~apply(F!45, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y_8(tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44))) | (~apply(G!44, tptp_fun_Y_8(tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44), tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43))))))))))) <=> ((~![X: $i, Z: $i] : ((~member(Z, C!39)) | (~member(X, A!41)) | (~((~(apply(H2!42, X, Z) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!45, X, Y)) | (~apply(G!44, Y, Z))))) | (~((~apply(H2!42, X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B!40, F!45, G!44), B!40)) | (~apply(F!45, X, tptp_fun_Y_8(Z, X, B!40, F!45, G!44))) | (~apply(G!44, tptp_fun_Y_8(Z, X, B!40, F!45, G!44), Z)))))))))) | (~member(tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43), C!39)) | (~member(tptp_fun_X_14(C!39, A!41, H2!42, H1!43), A!41)) | (~((~(apply(H2!42, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43)) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!45, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), Y)) | (~apply(G!44, Y, tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43)))))) | (~((~apply(H2!42, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44), B!40)) | (~apply(F!45, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y_8(tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44))) | (~apply(G!44, tptp_fun_Y_8(tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44), tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43))))))))))),
% 0.18/0.46 inference(rewrite,[status(thm)],[])).
% 0.18/0.46 tff(76,plain,
% 0.18/0.46 ((~![X: $i, Z: $i] : ((~member(Z, C!39)) | (~member(X, A!41)) | (~((~(apply(H2!42, X, Z) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!45, X, Y)) | (~apply(G!44, Y, Z))))) | (~((~apply(H2!42, X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B!40, F!45, G!44), B!40)) | (~apply(F!45, X, tptp_fun_Y_8(Z, X, B!40, F!45, G!44))) | (~apply(G!44, tptp_fun_Y_8(Z, X, B!40, F!45, G!44), Z)))))))))) | ((~member(tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43), C!39)) | (~member(tptp_fun_X_14(C!39, A!41, H2!42, H1!43), A!41)) | (~((~(apply(H2!42, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43)) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!45, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), Y)) | (~apply(G!44, Y, tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43)))))) | (~((~apply(H2!42, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44), B!40)) | (~apply(F!45, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y_8(tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44))) | (~apply(G!44, tptp_fun_Y_8(tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44), tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43))))))))))),
% 0.18/0.46 inference(quant_inst,[status(thm)],[])).
% 0.18/0.46 tff(77,plain,
% 0.18/0.46 ((~![X: $i, Z: $i] : ((~member(Z, C!39)) | (~member(X, A!41)) | (~((~(apply(H2!42, X, Z) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!45, X, Y)) | (~apply(G!44, Y, Z))))) | (~((~apply(H2!42, X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B!40, F!45, G!44), B!40)) | (~apply(F!45, X, tptp_fun_Y_8(Z, X, B!40, F!45, G!44))) | (~apply(G!44, tptp_fun_Y_8(Z, X, B!40, F!45, G!44), Z)))))))))) | (~member(tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43), C!39)) | (~member(tptp_fun_X_14(C!39, A!41, H2!42, H1!43), A!41)) | (~((~(apply(H2!42, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43)) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!45, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), Y)) | (~apply(G!44, Y, tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43)))))) | (~((~apply(H2!42, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44), B!40)) | (~apply(F!45, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y_8(tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44))) | (~apply(G!44, tptp_fun_Y_8(tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44), tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43)))))))))),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.18/0.46 tff(78,plain,
% 0.18/0.46 (~((~(apply(H2!42, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43)) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!45, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), Y)) | (~apply(G!44, Y, tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43)))))) | (~((~apply(H2!42, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44), B!40)) | (~apply(F!45, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y_8(tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44))) | (~apply(G!44, tptp_fun_Y_8(tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44), tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43))))))))),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[77, 74, 41, 39])).
% 0.18/0.46 tff(79,plain,
% 0.18/0.46 (((~(apply(H2!42, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43)) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!45, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), Y)) | (~apply(G!44, Y, tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43)))))) | (~((~apply(H2!42, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44), B!40)) | (~apply(F!45, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y_8(tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44))) | (~apply(G!44, tptp_fun_Y_8(tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44), tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43)))))))) | ((~apply(H2!42, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44), B!40)) | (~apply(F!45, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y_8(tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44))) | (~apply(G!44, tptp_fun_Y_8(tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44), tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43))))))),
% 0.18/0.46 inference(tautology,[status(thm)],[])).
% 0.18/0.46 tff(80,plain,
% 0.18/0.46 ((~apply(H2!42, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44), B!40)) | (~apply(F!45, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y_8(tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44))) | (~apply(G!44, tptp_fun_Y_8(tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44), tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43)))))),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[79, 78])).
% 0.18/0.46 tff(81,plain,
% 0.18/0.46 (((~apply(H2!42, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43))) | (~apply(H1!43, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43))) | (~member(tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43), C!39)) | (~member(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), C!39)) | (~member(tptp_fun_X_14(C!39, A!41, H2!42, H1!43), A!41)) | (tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43) = tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43))) | apply(H2!42, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43))),
% 0.18/0.46 inference(tautology,[status(thm)],[])).
% 0.18/0.46 tff(82,plain,
% 0.18/0.46 (apply(H2!42, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43))),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[81, 37])).
% 0.18/0.46 tff(83,plain,
% 0.18/0.46 ((~((~apply(H2!42, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44), B!40)) | (~apply(F!45, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y_8(tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44))) | (~apply(G!44, tptp_fun_Y_8(tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44), tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43))))))) | (~apply(H2!42, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44), B!40)) | (~apply(F!45, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y_8(tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44))) | (~apply(G!44, tptp_fun_Y_8(tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44), tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43)))))),
% 0.18/0.46 inference(tautology,[status(thm)],[])).
% 0.18/0.46 tff(84,plain,
% 0.18/0.46 ((~((~apply(H2!42, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44), B!40)) | (~apply(F!45, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y_8(tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44))) | (~apply(G!44, tptp_fun_Y_8(tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44), tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43))))))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44), B!40)) | (~apply(F!45, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y_8(tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44))) | (~apply(G!44, tptp_fun_Y_8(tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44), tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43)))))),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[83, 82])).
% 0.18/0.47 tff(85,plain,
% 0.18/0.47 (~((~member(tptp_fun_Y_8(tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44), B!40)) | (~apply(F!45, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y_8(tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44))) | (~apply(G!44, tptp_fun_Y_8(tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44), tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43))))),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[84, 80])).
% 0.18/0.47 tff(86,plain,
% 0.18/0.47 (((~member(tptp_fun_Y_8(tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44), B!40)) | (~apply(F!45, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y_8(tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44))) | (~apply(G!44, tptp_fun_Y_8(tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44), tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43)))) | apply(F!45, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y_8(tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44))),
% 0.18/0.47 inference(tautology,[status(thm)],[])).
% 0.18/0.47 tff(87,plain,
% 0.18/0.47 (apply(F!45, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y_8(tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44))),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[86, 85])).
% 0.18/0.47 tff(88,plain,
% 0.18/0.47 (((~member(tptp_fun_Y_8(tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44), B!40)) | (~apply(F!45, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y_8(tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44))) | (~apply(G!44, tptp_fun_Y_8(tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44), tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43)))) | member(tptp_fun_Y_8(tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44), B!40)),
% 0.18/0.47 inference(tautology,[status(thm)],[])).
% 0.18/0.47 tff(89,plain,
% 0.18/0.47 (member(tptp_fun_Y_8(tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44), B!40)),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[88, 85])).
% 0.18/0.47 tff(90,plain,
% 0.18/0.47 (^[F: $i, A: $i, B: $i] : rewrite((~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))) <=> (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))))))))),
% 0.18/0.47 inference(bind,[status(th)],[])).
% 0.18/0.47 tff(91,plain,
% 0.18/0.47 (![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))),
% 0.18/0.47 inference(quant_intro,[status(thm)],[90])).
% 0.18/0.47 tff(92,plain,
% 0.18/0.47 (^[F: $i, A: $i, B: $i] : refl((~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))) <=> (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))))),
% 0.18/0.47 inference(bind,[status(th)],[])).
% 0.18/0.47 tff(93,plain,
% 0.18/0.47 (![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))))))),
% 0.18/0.47 inference(quant_intro,[status(thm)],[92])).
% 0.18/0.47 tff(94,plain,
% 0.18/0.47 (^[F: $i, A: $i, B: $i] : rewrite((~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))) <=> (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))))),
% 0.18/0.47 inference(bind,[status(th)],[])).
% 0.18/0.47 tff(95,plain,
% 0.18/0.47 (![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))))))),
% 0.18/0.47 inference(quant_intro,[status(thm)],[94])).
% 0.18/0.47 tff(96,plain,
% 0.18/0.47 (![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))))))),
% 0.18/0.47 inference(transitivity,[status(thm)],[95, 93])).
% 0.18/0.47 tff(97,plain,
% 0.18/0.47 (^[F: $i, A: $i, B: $i] : trans(monotonicity(rewrite(((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) <=> ((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))), trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[Y: $i] : trans(monotonicity(rewrite((member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)) <=> (~((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))), ((~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y))) <=> (~(~((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))), rewrite((~(~((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))) <=> ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))), ((~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y))) <=> ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))), (![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y))) <=> ![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))), ((member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) <=> (member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))), rewrite((member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))) <=> (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))), ((member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) <=> (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))))), rewrite((~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B))))) <=> (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))), ((maps(F, A, B) | (member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B)))))) <=> (maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))))), rewrite((maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))) <=> (maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))), ((maps(F, A, B) | (member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B)))))) <=> (maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))))), ((((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) & (maps(F, A, B) | (member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B))))))) <=> (((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B))))))) & (maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))), rewrite((((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B))))))) & (maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))) <=> (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))))))), ((((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) & (maps(F, A, B) | (member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B))))))) <=> (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))))))))),
% 0.18/0.47 inference(bind,[status(th)],[])).
% 0.18/0.47 tff(98,plain,
% 0.18/0.47 (![F: $i, A: $i, B: $i] : (((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) & (maps(F, A, B) | (member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))))))),
% 0.18/0.47 inference(quant_intro,[status(thm)],[97])).
% 0.18/0.47 tff(99,plain,
% 0.18/0.47 (^[F: $i, A: $i, B: $i] : rewrite((((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) & (maps(F, A, B) | ((member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B)))))))) <=> (((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) & (maps(F, A, B) | (member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B))))))))),
% 0.18/0.47 inference(bind,[status(th)],[])).
% 0.18/0.47 tff(100,plain,
% 0.18/0.47 (![F: $i, A: $i, B: $i] : (((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) & (maps(F, A, B) | ((member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B)))))))) <=> ![F: $i, A: $i, B: $i] : (((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) & (maps(F, A, B) | (member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B)))))))),
% 0.18/0.47 inference(quant_intro,[status(thm)],[99])).
% 0.18/0.47 tff(101,plain,
% 0.18/0.47 (![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))))))),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(102,plain,
% 0.18/0.47 (^[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)))))))),
% 0.18/0.47 inference(bind,[status(th)],[])).
% 0.18/0.47 tff(103,plain,
% 0.18/0.47 (![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))))))),
% 0.18/0.47 inference(quant_intro,[status(thm)],[102])).
% 0.18/0.47 tff(104,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')).
% 0.18/0.47 tff(105,plain,
% 0.18/0.47 (![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))))))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[104, 103])).
% 0.18/0.47 tff(106,plain,
% 0.18/0.47 (![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))))))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[105, 101])).
% 0.18/0.47 tff(107,plain,(
% 0.18/0.47 ![F: $i, A: $i, B: $i] : (((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) & (maps(F, A, B) | ((member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B))))))))),
% 0.18/0.47 inference(skolemize,[status(sab)],[106])).
% 0.18/0.47 tff(108,plain,
% 0.18/0.47 (![F: $i, A: $i, B: $i] : (((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) & (maps(F, A, B) | (member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B)))))))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[107, 100])).
% 0.18/0.47 tff(109,plain,
% 0.18/0.47 (![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))))))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[108, 98])).
% 0.18/0.48 tff(110,plain,
% 0.18/0.48 (![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))))))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[109, 96])).
% 0.18/0.48 tff(111,plain,
% 0.18/0.48 (![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[110, 91])).
% 0.18/0.48 tff(112,plain,
% 0.18/0.48 (((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(F!45, A!41, B!40)) | (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!45), B!40)) | (~apply(F!45, X, tptp_fun_Y_3(X, B!40, F!45))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!45, X, Y1)) | (~apply(F!45, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)))))))) | (~(maps(F!45, A!41, B!40) | (~((~member(tptp_fun_X_4(B!40, A!41, F!45), A!41)) | (~![Y: $i] : ((~member(Y, B!40)) | (~apply(F!45, tptp_fun_X_4(B!40, A!41, F!45), Y)))))) | (~((~member(tptp_fun_Y2_5(B!40, A!41, F!45), B!40)) | (~member(tptp_fun_Y1_6(B!40, A!41, F!45), B!40)) | (~member(tptp_fun_X_7(B!40, A!41, F!45), A!41)) | (~apply(F!45, tptp_fun_X_7(B!40, A!41, F!45), tptp_fun_Y2_5(B!40, A!41, F!45))) | (~apply(F!45, tptp_fun_X_7(B!40, A!41, F!45), tptp_fun_Y1_6(B!40, A!41, F!45))) | (tptp_fun_Y1_6(B!40, A!41, F!45) = tptp_fun_Y2_5(B!40, A!41, 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!41, B!40)) | (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!45), B!40)) | (~apply(F!45, X, tptp_fun_Y_3(X, B!40, F!45))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!45, X, Y1)) | (~apply(F!45, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)))))))) | (~(maps(F!45, A!41, B!40) | (~((~member(tptp_fun_X_4(B!40, A!41, F!45), A!41)) | (~![Y: $i] : ((~member(Y, B!40)) | (~apply(F!45, tptp_fun_X_4(B!40, A!41, F!45), Y)))))) | (~((~member(tptp_fun_Y2_5(B!40, A!41, F!45), B!40)) | (~member(tptp_fun_Y1_6(B!40, A!41, F!45), B!40)) | (~member(tptp_fun_X_7(B!40, A!41, F!45), A!41)) | (~apply(F!45, tptp_fun_X_7(B!40, A!41, F!45), tptp_fun_Y2_5(B!40, A!41, F!45))) | (~apply(F!45, tptp_fun_X_7(B!40, A!41, F!45), tptp_fun_Y1_6(B!40, A!41, F!45))) | (tptp_fun_Y1_6(B!40, A!41, F!45) = tptp_fun_Y2_5(B!40, A!41, F!45)))))))))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(113,plain,
% 0.18/0.48 ((~((~((~maps(F!45, A!41, B!40)) | (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!45), B!40)) | (~apply(F!45, X, tptp_fun_Y_3(X, B!40, F!45))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!45, X, Y1)) | (~apply(F!45, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)) | (~member(Y2, B!40)))))))) | (~(maps(F!45, A!41, B!40) | (~((tptp_fun_Y1_6(B!40, A!41, F!45) = tptp_fun_Y2_5(B!40, A!41, F!45)) | (~apply(F!45, tptp_fun_X_7(B!40, A!41, F!45), tptp_fun_Y1_6(B!40, A!41, F!45))) | (~apply(F!45, tptp_fun_X_7(B!40, A!41, F!45), tptp_fun_Y2_5(B!40, A!41, F!45))) | (~member(tptp_fun_X_7(B!40, A!41, F!45), A!41)) | (~member(tptp_fun_Y1_6(B!40, A!41, F!45), B!40)) | (~member(tptp_fun_Y2_5(B!40, A!41, F!45), B!40)))) | (~((~member(tptp_fun_X_4(B!40, A!41, F!45), A!41)) | (~![Y: $i] : ((~member(Y, B!40)) | (~apply(F!45, tptp_fun_X_4(B!40, A!41, F!45), Y)))))))))) <=> (~((~((~maps(F!45, A!41, B!40)) | (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!45), B!40)) | (~apply(F!45, X, tptp_fun_Y_3(X, B!40, F!45))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!45, X, Y1)) | (~apply(F!45, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)))))))) | (~(maps(F!45, A!41, B!40) | (~((~member(tptp_fun_X_4(B!40, A!41, F!45), A!41)) | (~![Y: $i] : ((~member(Y, B!40)) | (~apply(F!45, tptp_fun_X_4(B!40, A!41, F!45), Y)))))) | (~((~member(tptp_fun_Y2_5(B!40, A!41, F!45), B!40)) | (~member(tptp_fun_Y1_6(B!40, A!41, F!45), B!40)) | (~member(tptp_fun_X_7(B!40, A!41, F!45), A!41)) | (~apply(F!45, tptp_fun_X_7(B!40, A!41, F!45), tptp_fun_Y2_5(B!40, A!41, F!45))) | (~apply(F!45, tptp_fun_X_7(B!40, A!41, F!45), tptp_fun_Y1_6(B!40, A!41, F!45))) | (tptp_fun_Y1_6(B!40, A!41, F!45) = tptp_fun_Y2_5(B!40, A!41, F!45))))))))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(114,plain,
% 0.18/0.48 (((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(F!45, A!41, B!40)) | (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!45), B!40)) | (~apply(F!45, X, tptp_fun_Y_3(X, B!40, F!45))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!45, X, Y1)) | (~apply(F!45, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)) | (~member(Y2, B!40)))))))) | (~(maps(F!45, A!41, B!40) | (~((tptp_fun_Y1_6(B!40, A!41, F!45) = tptp_fun_Y2_5(B!40, A!41, F!45)) | (~apply(F!45, tptp_fun_X_7(B!40, A!41, F!45), tptp_fun_Y1_6(B!40, A!41, F!45))) | (~apply(F!45, tptp_fun_X_7(B!40, A!41, F!45), tptp_fun_Y2_5(B!40, A!41, F!45))) | (~member(tptp_fun_X_7(B!40, A!41, F!45), A!41)) | (~member(tptp_fun_Y1_6(B!40, A!41, F!45), B!40)) | (~member(tptp_fun_Y2_5(B!40, A!41, F!45), B!40)))) | (~((~member(tptp_fun_X_4(B!40, A!41, F!45), A!41)) | (~![Y: $i] : ((~member(Y, B!40)) | (~apply(F!45, tptp_fun_X_4(B!40, A!41, 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!41, B!40)) | (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!45), B!40)) | (~apply(F!45, X, tptp_fun_Y_3(X, B!40, F!45))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!45, X, Y1)) | (~apply(F!45, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)))))))) | (~(maps(F!45, A!41, B!40) | (~((~member(tptp_fun_X_4(B!40, A!41, F!45), A!41)) | (~![Y: $i] : ((~member(Y, B!40)) | (~apply(F!45, tptp_fun_X_4(B!40, A!41, F!45), Y)))))) | (~((~member(tptp_fun_Y2_5(B!40, A!41, F!45), B!40)) | (~member(tptp_fun_Y1_6(B!40, A!41, F!45), B!40)) | (~member(tptp_fun_X_7(B!40, A!41, F!45), A!41)) | (~apply(F!45, tptp_fun_X_7(B!40, A!41, F!45), tptp_fun_Y2_5(B!40, A!41, F!45))) | (~apply(F!45, tptp_fun_X_7(B!40, A!41, F!45), tptp_fun_Y1_6(B!40, A!41, F!45))) | (tptp_fun_Y1_6(B!40, A!41, F!45) = tptp_fun_Y2_5(B!40, A!41, F!45)))))))))),
% 0.18/0.48 inference(monotonicity,[status(thm)],[113])).
% 0.18/0.48 tff(115,plain,
% 0.18/0.48 (((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(F!45, A!41, B!40)) | (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!45), B!40)) | (~apply(F!45, X, tptp_fun_Y_3(X, B!40, F!45))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!45, X, Y1)) | (~apply(F!45, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)) | (~member(Y2, B!40)))))))) | (~(maps(F!45, A!41, B!40) | (~((tptp_fun_Y1_6(B!40, A!41, F!45) = tptp_fun_Y2_5(B!40, A!41, F!45)) | (~apply(F!45, tptp_fun_X_7(B!40, A!41, F!45), tptp_fun_Y1_6(B!40, A!41, F!45))) | (~apply(F!45, tptp_fun_X_7(B!40, A!41, F!45), tptp_fun_Y2_5(B!40, A!41, F!45))) | (~member(tptp_fun_X_7(B!40, A!41, F!45), A!41)) | (~member(tptp_fun_Y1_6(B!40, A!41, F!45), B!40)) | (~member(tptp_fun_Y2_5(B!40, A!41, F!45), B!40)))) | (~((~member(tptp_fun_X_4(B!40, A!41, F!45), A!41)) | (~![Y: $i] : ((~member(Y, B!40)) | (~apply(F!45, tptp_fun_X_4(B!40, A!41, 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!41, B!40)) | (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!45), B!40)) | (~apply(F!45, X, tptp_fun_Y_3(X, B!40, F!45))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!45, X, Y1)) | (~apply(F!45, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)))))))) | (~(maps(F!45, A!41, B!40) | (~((~member(tptp_fun_X_4(B!40, A!41, F!45), A!41)) | (~![Y: $i] : ((~member(Y, B!40)) | (~apply(F!45, tptp_fun_X_4(B!40, A!41, F!45), Y)))))) | (~((~member(tptp_fun_Y2_5(B!40, A!41, F!45), B!40)) | (~member(tptp_fun_Y1_6(B!40, A!41, F!45), B!40)) | (~member(tptp_fun_X_7(B!40, A!41, F!45), A!41)) | (~apply(F!45, tptp_fun_X_7(B!40, A!41, F!45), tptp_fun_Y2_5(B!40, A!41, F!45))) | (~apply(F!45, tptp_fun_X_7(B!40, A!41, F!45), tptp_fun_Y1_6(B!40, A!41, F!45))) | (tptp_fun_Y1_6(B!40, A!41, F!45) = tptp_fun_Y2_5(B!40, A!41, F!45)))))))))),
% 0.18/0.48 inference(transitivity,[status(thm)],[114, 112])).
% 0.18/0.48 tff(116,plain,
% 0.18/0.48 ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(F!45, A!41, B!40)) | (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!45), B!40)) | (~apply(F!45, X, tptp_fun_Y_3(X, B!40, F!45))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!45, X, Y1)) | (~apply(F!45, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)) | (~member(Y2, B!40)))))))) | (~(maps(F!45, A!41, B!40) | (~((tptp_fun_Y1_6(B!40, A!41, F!45) = tptp_fun_Y2_5(B!40, A!41, F!45)) | (~apply(F!45, tptp_fun_X_7(B!40, A!41, F!45), tptp_fun_Y1_6(B!40, A!41, F!45))) | (~apply(F!45, tptp_fun_X_7(B!40, A!41, F!45), tptp_fun_Y2_5(B!40, A!41, F!45))) | (~member(tptp_fun_X_7(B!40, A!41, F!45), A!41)) | (~member(tptp_fun_Y1_6(B!40, A!41, F!45), B!40)) | (~member(tptp_fun_Y2_5(B!40, A!41, F!45), B!40)))) | (~((~member(tptp_fun_X_4(B!40, A!41, F!45), A!41)) | (~![Y: $i] : ((~member(Y, B!40)) | (~apply(F!45, tptp_fun_X_4(B!40, A!41, F!45), Y))))))))))),
% 0.18/0.48 inference(quant_inst,[status(thm)],[])).
% 0.18/0.48 tff(117,plain,
% 0.18/0.48 ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(F!45, A!41, B!40)) | (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!45), B!40)) | (~apply(F!45, X, tptp_fun_Y_3(X, B!40, F!45))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!45, X, Y1)) | (~apply(F!45, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)))))))) | (~(maps(F!45, A!41, B!40) | (~((~member(tptp_fun_X_4(B!40, A!41, F!45), A!41)) | (~![Y: $i] : ((~member(Y, B!40)) | (~apply(F!45, tptp_fun_X_4(B!40, A!41, F!45), Y)))))) | (~((~member(tptp_fun_Y2_5(B!40, A!41, F!45), B!40)) | (~member(tptp_fun_Y1_6(B!40, A!41, F!45), B!40)) | (~member(tptp_fun_X_7(B!40, A!41, F!45), A!41)) | (~apply(F!45, tptp_fun_X_7(B!40, A!41, F!45), tptp_fun_Y2_5(B!40, A!41, F!45))) | (~apply(F!45, tptp_fun_X_7(B!40, A!41, F!45), tptp_fun_Y1_6(B!40, A!41, F!45))) | (tptp_fun_Y1_6(B!40, A!41, F!45) = tptp_fun_Y2_5(B!40, A!41, F!45))))))))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[116, 115])).
% 0.18/0.48 tff(118,plain,
% 0.18/0.48 (~((~((~maps(F!45, A!41, B!40)) | (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!45), B!40)) | (~apply(F!45, X, tptp_fun_Y_3(X, B!40, F!45))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!45, X, Y1)) | (~apply(F!45, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)))))))) | (~(maps(F!45, A!41, B!40) | (~((~member(tptp_fun_X_4(B!40, A!41, F!45), A!41)) | (~![Y: $i] : ((~member(Y, B!40)) | (~apply(F!45, tptp_fun_X_4(B!40, A!41, F!45), Y)))))) | (~((~member(tptp_fun_Y2_5(B!40, A!41, F!45), B!40)) | (~member(tptp_fun_Y1_6(B!40, A!41, F!45), B!40)) | (~member(tptp_fun_X_7(B!40, A!41, F!45), A!41)) | (~apply(F!45, tptp_fun_X_7(B!40, A!41, F!45), tptp_fun_Y2_5(B!40, A!41, F!45))) | (~apply(F!45, tptp_fun_X_7(B!40, A!41, F!45), tptp_fun_Y1_6(B!40, A!41, F!45))) | (tptp_fun_Y1_6(B!40, A!41, F!45) = tptp_fun_Y2_5(B!40, A!41, F!45)))))))),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[117, 111])).
% 0.18/0.48 tff(119,plain,
% 0.18/0.48 (((~((~maps(F!45, A!41, B!40)) | (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!45), B!40)) | (~apply(F!45, X, tptp_fun_Y_3(X, B!40, F!45))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!45, X, Y1)) | (~apply(F!45, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)))))))) | (~(maps(F!45, A!41, B!40) | (~((~member(tptp_fun_X_4(B!40, A!41, F!45), A!41)) | (~![Y: $i] : ((~member(Y, B!40)) | (~apply(F!45, tptp_fun_X_4(B!40, A!41, F!45), Y)))))) | (~((~member(tptp_fun_Y2_5(B!40, A!41, F!45), B!40)) | (~member(tptp_fun_Y1_6(B!40, A!41, F!45), B!40)) | (~member(tptp_fun_X_7(B!40, A!41, F!45), A!41)) | (~apply(F!45, tptp_fun_X_7(B!40, A!41, F!45), tptp_fun_Y2_5(B!40, A!41, F!45))) | (~apply(F!45, tptp_fun_X_7(B!40, A!41, F!45), tptp_fun_Y1_6(B!40, A!41, F!45))) | (tptp_fun_Y1_6(B!40, A!41, F!45) = tptp_fun_Y2_5(B!40, A!41, F!45))))))) | ((~maps(F!45, A!41, B!40)) | (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!45), B!40)) | (~apply(F!45, X, tptp_fun_Y_3(X, B!40, F!45))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!45, X, Y1)) | (~apply(F!45, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)))))))),
% 0.18/0.48 inference(tautology,[status(thm)],[])).
% 0.18/0.48 tff(120,plain,
% 0.18/0.48 ((~maps(F!45, A!41, B!40)) | (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!45), B!40)) | (~apply(F!45, X, tptp_fun_Y_3(X, B!40, F!45))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!45, X, Y1)) | (~apply(F!45, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40))))))),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[119, 118])).
% 0.18/0.48 tff(121,plain,
% 0.18/0.48 (maps(F!45, A!41, B!40)),
% 0.18/0.48 inference(and_elim,[status(thm)],[70])).
% 0.18/0.48 tff(122,plain,
% 0.18/0.48 ((~((~maps(F!45, A!41, B!40)) | (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!45), B!40)) | (~apply(F!45, X, tptp_fun_Y_3(X, B!40, F!45))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!45, X, Y1)) | (~apply(F!45, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)))))))) | (~maps(F!45, A!41, B!40)) | (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!45), B!40)) | (~apply(F!45, X, tptp_fun_Y_3(X, B!40, F!45))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!45, X, Y1)) | (~apply(F!45, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40))))))),
% 0.18/0.49 inference(tautology,[status(thm)],[])).
% 0.18/0.49 tff(123,plain,
% 0.18/0.49 ((~((~maps(F!45, A!41, B!40)) | (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!45), B!40)) | (~apply(F!45, X, tptp_fun_Y_3(X, B!40, F!45))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!45, X, Y1)) | (~apply(F!45, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)))))))) | (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!45), B!40)) | (~apply(F!45, X, tptp_fun_Y_3(X, B!40, F!45))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!45, X, Y1)) | (~apply(F!45, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40))))))),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[122, 121])).
% 0.18/0.49 tff(124,plain,
% 0.18/0.49 (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!45), B!40)) | (~apply(F!45, X, tptp_fun_Y_3(X, B!40, F!45))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!45, X, Y1)) | (~apply(F!45, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)))))),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[123, 120])).
% 0.18/0.49 tff(125,plain,
% 0.18/0.49 (((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!45), B!40)) | (~apply(F!45, X, tptp_fun_Y_3(X, B!40, F!45))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!45, X, Y1)) | (~apply(F!45, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40))))) | ![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!45), B!40)) | (~apply(F!45, X, tptp_fun_Y_3(X, B!40, F!45))))))),
% 0.18/0.49 inference(tautology,[status(thm)],[])).
% 0.18/0.49 tff(126,plain,
% 0.18/0.49 (![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!45), B!40)) | (~apply(F!45, X, tptp_fun_Y_3(X, B!40, F!45))))))),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[125, 124])).
% 0.18/0.49 tff(127,plain,
% 0.18/0.49 (((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!45), B!40)) | (~apply(F!45, X, tptp_fun_Y_3(X, B!40, F!45))))))) | ((~member(tptp_fun_X_14(C!39, A!41, H2!42, H1!43), A!41)) | (~((~member(tptp_fun_Y_3(tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45), B!40)) | (~apply(F!45, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y_3(tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45))))))) <=> ((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!45), B!40)) | (~apply(F!45, X, tptp_fun_Y_3(X, B!40, F!45))))))) | (~member(tptp_fun_X_14(C!39, A!41, H2!42, H1!43), A!41)) | (~((~member(tptp_fun_Y_3(tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45), B!40)) | (~apply(F!45, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y_3(tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45))))))),
% 0.18/0.49 inference(rewrite,[status(thm)],[])).
% 0.18/0.49 tff(128,plain,
% 0.18/0.49 ((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!45), B!40)) | (~apply(F!45, X, tptp_fun_Y_3(X, B!40, F!45))))))) | ((~member(tptp_fun_X_14(C!39, A!41, H2!42, H1!43), A!41)) | (~((~member(tptp_fun_Y_3(tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45), B!40)) | (~apply(F!45, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y_3(tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45))))))),
% 0.18/0.49 inference(quant_inst,[status(thm)],[])).
% 0.18/0.49 tff(129,plain,
% 0.18/0.49 ((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!45), B!40)) | (~apply(F!45, X, tptp_fun_Y_3(X, B!40, F!45))))))) | (~member(tptp_fun_X_14(C!39, A!41, H2!42, H1!43), A!41)) | (~((~member(tptp_fun_Y_3(tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45), B!40)) | (~apply(F!45, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y_3(tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45)))))),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[128, 127])).
% 0.18/0.49 tff(130,plain,
% 0.18/0.49 (~((~member(tptp_fun_Y_3(tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45), B!40)) | (~apply(F!45, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y_3(tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45))))),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[129, 126, 39])).
% 0.18/0.49 tff(131,plain,
% 0.18/0.49 (((~member(tptp_fun_Y_3(tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45), B!40)) | (~apply(F!45, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y_3(tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45)))) | apply(F!45, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y_3(tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45))),
% 0.18/0.49 inference(tautology,[status(thm)],[])).
% 0.18/0.49 tff(132,plain,
% 0.18/0.49 (apply(F!45, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y_3(tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45))),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[131, 130])).
% 0.18/0.49 tff(133,plain,
% 0.18/0.49 (((~member(tptp_fun_Y_3(tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45), B!40)) | (~apply(F!45, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y_3(tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45)))) | member(tptp_fun_Y_3(tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45), B!40)),
% 0.18/0.49 inference(tautology,[status(thm)],[])).
% 0.18/0.49 tff(134,plain,
% 0.18/0.49 (member(tptp_fun_Y_3(tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45), B!40)),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[133, 130])).
% 0.18/0.49 tff(135,plain,
% 0.18/0.49 (((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!45), B!40)) | (~apply(F!45, X, tptp_fun_Y_3(X, B!40, F!45))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!45, X, Y1)) | (~apply(F!45, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40))))) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!45, X, Y1)) | (~apply(F!45, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)))),
% 0.18/0.49 inference(tautology,[status(thm)],[])).
% 0.18/0.49 tff(136,plain,
% 0.18/0.49 (![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!45, X, Y1)) | (~apply(F!45, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)))),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[135, 124])).
% 0.18/0.49 tff(137,plain,
% 0.18/0.49 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!45, X, Y1)) | (~apply(F!45, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)))) | ((~member(tptp_fun_X_14(C!39, A!41, H2!42, H1!43), A!41)) | (~member(tptp_fun_Y_3(tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45), B!40)) | (~apply(F!45, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y_3(tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45))) | (~apply(F!45, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y_8(tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44))) | (~member(tptp_fun_Y_8(tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44), B!40)) | (tptp_fun_Y_3(tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45) = tptp_fun_Y_8(tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!45, X, Y1)) | (~apply(F!45, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)))) | (~member(tptp_fun_X_14(C!39, A!41, H2!42, H1!43), A!41)) | (~member(tptp_fun_Y_3(tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45), B!40)) | (~apply(F!45, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y_3(tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45))) | (~apply(F!45, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y_8(tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44))) | (~member(tptp_fun_Y_8(tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44), B!40)) | (tptp_fun_Y_3(tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45) = tptp_fun_Y_8(tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44)))),
% 0.18/0.49 inference(rewrite,[status(thm)],[])).
% 0.18/0.49 tff(138,plain,
% 0.18/0.49 (((tptp_fun_Y_3(tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45) = tptp_fun_Y_8(tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44)) | (~member(tptp_fun_Y_8(tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44), B!40)) | (~apply(F!45, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y_3(tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45))) | (~apply(F!45, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y_8(tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44))) | (~member(tptp_fun_X_14(C!39, A!41, H2!42, H1!43), A!41)) | (~member(tptp_fun_Y_3(tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45), B!40))) <=> ((~member(tptp_fun_X_14(C!39, A!41, H2!42, H1!43), A!41)) | (~member(tptp_fun_Y_3(tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45), B!40)) | (~apply(F!45, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y_3(tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45))) | (~apply(F!45, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y_8(tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44))) | (~member(tptp_fun_Y_8(tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44), B!40)) | (tptp_fun_Y_3(tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45) = tptp_fun_Y_8(tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44)))),
% 0.18/0.49 inference(rewrite,[status(thm)],[])).
% 0.18/0.49 tff(139,plain,
% 0.18/0.49 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!45, X, Y1)) | (~apply(F!45, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)))) | ((tptp_fun_Y_3(tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45) = tptp_fun_Y_8(tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44)) | (~member(tptp_fun_Y_8(tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44), B!40)) | (~apply(F!45, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y_3(tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45))) | (~apply(F!45, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y_8(tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44))) | (~member(tptp_fun_X_14(C!39, A!41, H2!42, H1!43), A!41)) | (~member(tptp_fun_Y_3(tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45), B!40)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!45, X, Y1)) | (~apply(F!45, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)))) | ((~member(tptp_fun_X_14(C!39, A!41, H2!42, H1!43), A!41)) | (~member(tptp_fun_Y_3(tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45), B!40)) | (~apply(F!45, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y_3(tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45))) | (~apply(F!45, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y_8(tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44))) | (~member(tptp_fun_Y_8(tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44), B!40)) | (tptp_fun_Y_3(tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45) = tptp_fun_Y_8(tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44))))),
% 0.18/0.49 inference(monotonicity,[status(thm)],[138])).
% 0.18/0.49 tff(140,plain,
% 0.18/0.49 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!45, X, Y1)) | (~apply(F!45, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)))) | ((tptp_fun_Y_3(tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45) = tptp_fun_Y_8(tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44)) | (~member(tptp_fun_Y_8(tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44), B!40)) | (~apply(F!45, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y_3(tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45))) | (~apply(F!45, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y_8(tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44))) | (~member(tptp_fun_X_14(C!39, A!41, H2!42, H1!43), A!41)) | (~member(tptp_fun_Y_3(tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45), B!40)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!45, X, Y1)) | (~apply(F!45, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)))) | (~member(tptp_fun_X_14(C!39, A!41, H2!42, H1!43), A!41)) | (~member(tptp_fun_Y_3(tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45), B!40)) | (~apply(F!45, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y_3(tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45))) | (~apply(F!45, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y_8(tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44))) | (~member(tptp_fun_Y_8(tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44), B!40)) | (tptp_fun_Y_3(tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45) = tptp_fun_Y_8(tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44)))),
% 0.18/0.50 inference(transitivity,[status(thm)],[139, 137])).
% 0.18/0.50 tff(141,plain,
% 0.18/0.50 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!45, X, Y1)) | (~apply(F!45, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)))) | ((tptp_fun_Y_3(tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45) = tptp_fun_Y_8(tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44)) | (~member(tptp_fun_Y_8(tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44), B!40)) | (~apply(F!45, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y_3(tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45))) | (~apply(F!45, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y_8(tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44))) | (~member(tptp_fun_X_14(C!39, A!41, H2!42, H1!43), A!41)) | (~member(tptp_fun_Y_3(tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45), B!40)))),
% 0.18/0.50 inference(quant_inst,[status(thm)],[])).
% 0.18/0.50 tff(142,plain,
% 0.18/0.50 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!45, X, Y1)) | (~apply(F!45, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)))) | (~member(tptp_fun_X_14(C!39, A!41, H2!42, H1!43), A!41)) | (~member(tptp_fun_Y_3(tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45), B!40)) | (~apply(F!45, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y_3(tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45))) | (~apply(F!45, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y_8(tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44))) | (~member(tptp_fun_Y_8(tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44), B!40)) | (tptp_fun_Y_3(tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45) = tptp_fun_Y_8(tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[141, 140])).
% 0.18/0.50 tff(143,plain,
% 0.18/0.50 (tptp_fun_Y_3(tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45) = tptp_fun_Y_8(tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44)),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[142, 136, 39, 134, 132, 89, 87])).
% 0.18/0.50 tff(144,plain,
% 0.18/0.50 (((~apply(H2!42, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43))) | (~apply(H1!43, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43))) | (~member(tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43), C!39)) | (~member(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), C!39)) | (~member(tptp_fun_X_14(C!39, A!41, H2!42, H1!43), A!41)) | (tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43) = tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43))) | member(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), C!39)),
% 0.18/0.50 inference(tautology,[status(thm)],[])).
% 0.18/0.50 tff(145,plain,
% 0.18/0.50 (member(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), C!39)),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[144, 37])).
% 0.18/0.50 tff(146,plain,
% 0.18/0.50 (((~![H: $i, G: $i, F: $i, A: $i, B: $i, C: $i] : (~((~((~compose_predicate(H, G, F, A, B, C)) | ![X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(H, X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(H, X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z)))))))))) | (~(compose_predicate(H, G, F, A, B, C) | (~((~member(tptp_fun_X_10(C, B, A, F, G, H), A)) | (~member(tptp_fun_Z_9(C, B, A, F, G, H), C)) | (~(apply(H, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H)) | (~((~member(tptp_fun_Y_11(C, B, A, F, G, H), B)) | (~apply(F, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Y_11(C, B, A, F, G, H))) | (~apply(G, tptp_fun_Y_11(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H))))))) | (~((~apply(H, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H))) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_10(C, B, A, F, G, H), Y)) | (~apply(G, Y, tptp_fun_Z_9(C, B, A, F, G, H))))))))))))) | (~((~((~compose_predicate(H1!43, G!44, F!45, A!41, B!40, C!39)) | ![X: $i, Z: $i] : ((~member(Z, C!39)) | (~member(X, A!41)) | (~((~(apply(H1!43, X, Z) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!45, X, Y)) | (~apply(G!44, Y, Z))))) | (~((~apply(H1!43, X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B!40, F!45, G!44), B!40)) | (~apply(F!45, X, tptp_fun_Y_8(Z, X, B!40, F!45, G!44))) | (~apply(G!44, tptp_fun_Y_8(Z, X, B!40, F!45, G!44), Z))))))))))) | (~(compose_predicate(H1!43, G!44, F!45, A!41, B!40, C!39) | (~((~((~apply(H1!43, tptp_fun_X_10(C!39, B!40, A!41, F!45, G!44, H1!43), tptp_fun_Z_9(C!39, B!40, A!41, F!45, G!44, H1!43))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!45, tptp_fun_X_10(C!39, B!40, A!41, F!45, G!44, H1!43), Y)) | (~apply(G!44, Y, tptp_fun_Z_9(C!39, B!40, A!41, F!45, G!44, H1!43)))))) | (~(apply(H1!43, tptp_fun_X_10(C!39, B!40, A!41, F!45, G!44, H1!43), tptp_fun_Z_9(C!39, B!40, A!41, F!45, G!44, H1!43)) | (~((~member(tptp_fun_Y_11(C!39, B!40, A!41, F!45, G!44, H1!43), B!40)) | (~apply(F!45, tptp_fun_X_10(C!39, B!40, A!41, F!45, G!44, H1!43), tptp_fun_Y_11(C!39, B!40, A!41, F!45, G!44, H1!43))) | (~apply(G!44, tptp_fun_Y_11(C!39, B!40, A!41, F!45, G!44, H1!43), tptp_fun_Z_9(C!39, B!40, A!41, F!45, G!44, H1!43))))))) | (~member(tptp_fun_Z_9(C!39, B!40, A!41, F!45, G!44, H1!43), C!39)) | (~member(tptp_fun_X_10(C!39, B!40, A!41, F!45, G!44, H1!43), A!41))))))))) <=> ((~![H: $i, G: $i, F: $i, A: $i, B: $i, C: $i] : (~((~((~compose_predicate(H, G, F, A, B, C)) | ![X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(H, X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(H, X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z)))))))))) | (~(compose_predicate(H, G, F, A, B, C) | (~((~member(tptp_fun_X_10(C, B, A, F, G, H), A)) | (~member(tptp_fun_Z_9(C, B, A, F, G, H), C)) | (~(apply(H, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H)) | (~((~member(tptp_fun_Y_11(C, B, A, F, G, H), B)) | (~apply(F, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Y_11(C, B, A, F, G, H))) | (~apply(G, tptp_fun_Y_11(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H))))))) | (~((~apply(H, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H))) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_10(C, B, A, F, G, H), Y)) | (~apply(G, Y, tptp_fun_Z_9(C, B, A, F, G, H))))))))))))) | (~((~((~compose_predicate(H1!43, G!44, F!45, A!41, B!40, C!39)) | ![X: $i, Z: $i] : ((~member(Z, C!39)) | (~member(X, A!41)) | (~((~(apply(H1!43, X, Z) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!45, X, Y)) | (~apply(G!44, Y, Z))))) | (~((~apply(H1!43, X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B!40, F!45, G!44), B!40)) | (~apply(F!45, X, tptp_fun_Y_8(Z, X, B!40, F!45, G!44))) | (~apply(G!44, tptp_fun_Y_8(Z, X, B!40, F!45, G!44), Z))))))))))) | (~(compose_predicate(H1!43, G!44, F!45, A!41, B!40, C!39) | (~((~((~apply(H1!43, tptp_fun_X_10(C!39, B!40, A!41, F!45, G!44, H1!43), tptp_fun_Z_9(C!39, B!40, A!41, F!45, G!44, H1!43))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!45, tptp_fun_X_10(C!39, B!40, A!41, F!45, G!44, H1!43), Y)) | (~apply(G!44, Y, tptp_fun_Z_9(C!39, B!40, A!41, F!45, G!44, H1!43)))))) | (~(apply(H1!43, tptp_fun_X_10(C!39, B!40, A!41, F!45, G!44, H1!43), tptp_fun_Z_9(C!39, B!40, A!41, F!45, G!44, H1!43)) | (~((~member(tptp_fun_Y_11(C!39, B!40, A!41, F!45, G!44, H1!43), B!40)) | (~apply(F!45, tptp_fun_X_10(C!39, B!40, A!41, F!45, G!44, H1!43), tptp_fun_Y_11(C!39, B!40, A!41, F!45, G!44, H1!43))) | (~apply(G!44, tptp_fun_Y_11(C!39, B!40, A!41, F!45, G!44, H1!43), tptp_fun_Z_9(C!39, B!40, A!41, F!45, G!44, H1!43))))))) | (~member(tptp_fun_Z_9(C!39, B!40, A!41, F!45, G!44, H1!43), C!39)) | (~member(tptp_fun_X_10(C!39, B!40, A!41, F!45, G!44, H1!43), A!41)))))))))),
% 0.18/0.50 inference(rewrite,[status(thm)],[])).
% 0.18/0.50 tff(147,plain,
% 0.18/0.50 ((~((~((~compose_predicate(H1!43, G!44, F!45, A!41, B!40, C!39)) | ![X: $i, Z: $i] : ((~member(Z, C!39)) | (~member(X, A!41)) | (~((~((~apply(H1!43, X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B!40, F!45, G!44), B!40)) | (~apply(F!45, X, tptp_fun_Y_8(Z, X, B!40, F!45, G!44))) | (~apply(G!44, tptp_fun_Y_8(Z, X, B!40, F!45, G!44), Z)))))) | (~(apply(H1!43, X, Z) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!45, X, Y)) | (~apply(G!44, Y, Z)))))))))) | (~(compose_predicate(H1!43, G!44, F!45, A!41, B!40, C!39) | (~((~member(tptp_fun_X_10(C!39, B!40, A!41, F!45, G!44, H1!43), A!41)) | (~member(tptp_fun_Z_9(C!39, B!40, A!41, F!45, G!44, H1!43), C!39)) | (~(apply(H1!43, tptp_fun_X_10(C!39, B!40, A!41, F!45, G!44, H1!43), tptp_fun_Z_9(C!39, B!40, A!41, F!45, G!44, H1!43)) | (~((~member(tptp_fun_Y_11(C!39, B!40, A!41, F!45, G!44, H1!43), B!40)) | (~apply(F!45, tptp_fun_X_10(C!39, B!40, A!41, F!45, G!44, H1!43), tptp_fun_Y_11(C!39, B!40, A!41, F!45, G!44, H1!43))) | (~apply(G!44, tptp_fun_Y_11(C!39, B!40, A!41, F!45, G!44, H1!43), tptp_fun_Z_9(C!39, B!40, A!41, F!45, G!44, H1!43))))))) | (~((~apply(H1!43, tptp_fun_X_10(C!39, B!40, A!41, F!45, G!44, H1!43), tptp_fun_Z_9(C!39, B!40, A!41, F!45, G!44, H1!43))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!45, tptp_fun_X_10(C!39, B!40, A!41, F!45, G!44, H1!43), Y)) | (~apply(G!44, Y, tptp_fun_Z_9(C!39, B!40, A!41, F!45, G!44, H1!43)))))))))))) <=> (~((~((~compose_predicate(H1!43, G!44, F!45, A!41, B!40, C!39)) | ![X: $i, Z: $i] : ((~member(Z, C!39)) | (~member(X, A!41)) | (~((~(apply(H1!43, X, Z) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!45, X, Y)) | (~apply(G!44, Y, Z))))) | (~((~apply(H1!43, X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B!40, F!45, G!44), B!40)) | (~apply(F!45, X, tptp_fun_Y_8(Z, X, B!40, F!45, G!44))) | (~apply(G!44, tptp_fun_Y_8(Z, X, B!40, F!45, G!44), Z))))))))))) | (~(compose_predicate(H1!43, G!44, F!45, A!41, B!40, C!39) | (~((~((~apply(H1!43, tptp_fun_X_10(C!39, B!40, A!41, F!45, G!44, H1!43), tptp_fun_Z_9(C!39, B!40, A!41, F!45, G!44, H1!43))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!45, tptp_fun_X_10(C!39, B!40, A!41, F!45, G!44, H1!43), Y)) | (~apply(G!44, Y, tptp_fun_Z_9(C!39, B!40, A!41, F!45, G!44, H1!43)))))) | (~(apply(H1!43, tptp_fun_X_10(C!39, B!40, A!41, F!45, G!44, H1!43), tptp_fun_Z_9(C!39, B!40, A!41, F!45, G!44, H1!43)) | (~((~member(tptp_fun_Y_11(C!39, B!40, A!41, F!45, G!44, H1!43), B!40)) | (~apply(F!45, tptp_fun_X_10(C!39, B!40, A!41, F!45, G!44, H1!43), tptp_fun_Y_11(C!39, B!40, A!41, F!45, G!44, H1!43))) | (~apply(G!44, tptp_fun_Y_11(C!39, B!40, A!41, F!45, G!44, H1!43), tptp_fun_Z_9(C!39, B!40, A!41, F!45, G!44, H1!43))))))) | (~member(tptp_fun_Z_9(C!39, B!40, A!41, F!45, G!44, H1!43), C!39)) | (~member(tptp_fun_X_10(C!39, B!40, A!41, F!45, G!44, H1!43), A!41))))))))),
% 0.18/0.50 inference(rewrite,[status(thm)],[])).
% 0.18/0.50 tff(148,plain,
% 0.18/0.50 (((~![H: $i, G: $i, F: $i, A: $i, B: $i, C: $i] : (~((~((~compose_predicate(H, G, F, A, B, C)) | ![X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(H, X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(H, X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z)))))))))) | (~(compose_predicate(H, G, F, A, B, C) | (~((~member(tptp_fun_X_10(C, B, A, F, G, H), A)) | (~member(tptp_fun_Z_9(C, B, A, F, G, H), C)) | (~(apply(H, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H)) | (~((~member(tptp_fun_Y_11(C, B, A, F, G, H), B)) | (~apply(F, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Y_11(C, B, A, F, G, H))) | (~apply(G, tptp_fun_Y_11(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H))))))) | (~((~apply(H, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H))) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_10(C, B, A, F, G, H), Y)) | (~apply(G, Y, tptp_fun_Z_9(C, B, A, F, G, H))))))))))))) | (~((~((~compose_predicate(H1!43, G!44, F!45, A!41, B!40, C!39)) | ![X: $i, Z: $i] : ((~member(Z, C!39)) | (~member(X, A!41)) | (~((~((~apply(H1!43, X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B!40, F!45, G!44), B!40)) | (~apply(F!45, X, tptp_fun_Y_8(Z, X, B!40, F!45, G!44))) | (~apply(G!44, tptp_fun_Y_8(Z, X, B!40, F!45, G!44), Z)))))) | (~(apply(H1!43, X, Z) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!45, X, Y)) | (~apply(G!44, Y, Z)))))))))) | (~(compose_predicate(H1!43, G!44, F!45, A!41, B!40, C!39) | (~((~member(tptp_fun_X_10(C!39, B!40, A!41, F!45, G!44, H1!43), A!41)) | (~member(tptp_fun_Z_9(C!39, B!40, A!41, F!45, G!44, H1!43), C!39)) | (~(apply(H1!43, tptp_fun_X_10(C!39, B!40, A!41, F!45, G!44, H1!43), tptp_fun_Z_9(C!39, B!40, A!41, F!45, G!44, H1!43)) | (~((~member(tptp_fun_Y_11(C!39, B!40, A!41, F!45, G!44, H1!43), B!40)) | (~apply(F!45, tptp_fun_X_10(C!39, B!40, A!41, F!45, G!44, H1!43), tptp_fun_Y_11(C!39, B!40, A!41, F!45, G!44, H1!43))) | (~apply(G!44, tptp_fun_Y_11(C!39, B!40, A!41, F!45, G!44, H1!43), tptp_fun_Z_9(C!39, B!40, A!41, F!45, G!44, H1!43))))))) | (~((~apply(H1!43, tptp_fun_X_10(C!39, B!40, A!41, F!45, G!44, H1!43), tptp_fun_Z_9(C!39, B!40, A!41, F!45, G!44, H1!43))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!45, tptp_fun_X_10(C!39, B!40, A!41, F!45, G!44, H1!43), Y)) | (~apply(G!44, Y, tptp_fun_Z_9(C!39, B!40, A!41, F!45, G!44, H1!43))))))))))))) <=> ((~![H: $i, G: $i, F: $i, A: $i, B: $i, C: $i] : (~((~((~compose_predicate(H, G, F, A, B, C)) | ![X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(H, X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(H, X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z)))))))))) | (~(compose_predicate(H, G, F, A, B, C) | (~((~member(tptp_fun_X_10(C, B, A, F, G, H), A)) | (~member(tptp_fun_Z_9(C, B, A, F, G, H), C)) | (~(apply(H, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H)) | (~((~member(tptp_fun_Y_11(C, B, A, F, G, H), B)) | (~apply(F, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Y_11(C, B, A, F, G, H))) | (~apply(G, tptp_fun_Y_11(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H))))))) | (~((~apply(H, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H))) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_10(C, B, A, F, G, H), Y)) | (~apply(G, Y, tptp_fun_Z_9(C, B, A, F, G, H))))))))))))) | (~((~((~compose_predicate(H1!43, G!44, F!45, A!41, B!40, C!39)) | ![X: $i, Z: $i] : ((~member(Z, C!39)) | (~member(X, A!41)) | (~((~(apply(H1!43, X, Z) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!45, X, Y)) | (~apply(G!44, Y, Z))))) | (~((~apply(H1!43, X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B!40, F!45, G!44), B!40)) | (~apply(F!45, X, tptp_fun_Y_8(Z, X, B!40, F!45, G!44))) | (~apply(G!44, tptp_fun_Y_8(Z, X, B!40, F!45, G!44), Z))))))))))) | (~(compose_predicate(H1!43, G!44, F!45, A!41, B!40, C!39) | (~((~((~apply(H1!43, tptp_fun_X_10(C!39, B!40, A!41, F!45, G!44, H1!43), tptp_fun_Z_9(C!39, B!40, A!41, F!45, G!44, H1!43))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!45, tptp_fun_X_10(C!39, B!40, A!41, F!45, G!44, H1!43), Y)) | (~apply(G!44, Y, tptp_fun_Z_9(C!39, B!40, A!41, F!45, G!44, H1!43)))))) | (~(apply(H1!43, tptp_fun_X_10(C!39, B!40, A!41, F!45, G!44, H1!43), tptp_fun_Z_9(C!39, B!40, A!41, F!45, G!44, H1!43)) | (~((~member(tptp_fun_Y_11(C!39, B!40, A!41, F!45, G!44, H1!43), B!40)) | (~apply(F!45, tptp_fun_X_10(C!39, B!40, A!41, F!45, G!44, H1!43), tptp_fun_Y_11(C!39, B!40, A!41, F!45, G!44, H1!43))) | (~apply(G!44, tptp_fun_Y_11(C!39, B!40, A!41, F!45, G!44, H1!43), tptp_fun_Z_9(C!39, B!40, A!41, F!45, G!44, H1!43))))))) | (~member(tptp_fun_Z_9(C!39, B!40, A!41, F!45, G!44, H1!43), C!39)) | (~member(tptp_fun_X_10(C!39, B!40, A!41, F!45, G!44, H1!43), A!41)))))))))),
% 0.18/0.51 inference(monotonicity,[status(thm)],[147])).
% 0.18/0.51 tff(149,plain,
% 0.18/0.51 (((~![H: $i, G: $i, F: $i, A: $i, B: $i, C: $i] : (~((~((~compose_predicate(H, G, F, A, B, C)) | ![X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(H, X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(H, X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z)))))))))) | (~(compose_predicate(H, G, F, A, B, C) | (~((~member(tptp_fun_X_10(C, B, A, F, G, H), A)) | (~member(tptp_fun_Z_9(C, B, A, F, G, H), C)) | (~(apply(H, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H)) | (~((~member(tptp_fun_Y_11(C, B, A, F, G, H), B)) | (~apply(F, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Y_11(C, B, A, F, G, H))) | (~apply(G, tptp_fun_Y_11(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H))))))) | (~((~apply(H, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H))) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_10(C, B, A, F, G, H), Y)) | (~apply(G, Y, tptp_fun_Z_9(C, B, A, F, G, H))))))))))))) | (~((~((~compose_predicate(H1!43, G!44, F!45, A!41, B!40, C!39)) | ![X: $i, Z: $i] : ((~member(Z, C!39)) | (~member(X, A!41)) | (~((~((~apply(H1!43, X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B!40, F!45, G!44), B!40)) | (~apply(F!45, X, tptp_fun_Y_8(Z, X, B!40, F!45, G!44))) | (~apply(G!44, tptp_fun_Y_8(Z, X, B!40, F!45, G!44), Z)))))) | (~(apply(H1!43, X, Z) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!45, X, Y)) | (~apply(G!44, Y, Z)))))))))) | (~(compose_predicate(H1!43, G!44, F!45, A!41, B!40, C!39) | (~((~member(tptp_fun_X_10(C!39, B!40, A!41, F!45, G!44, H1!43), A!41)) | (~member(tptp_fun_Z_9(C!39, B!40, A!41, F!45, G!44, H1!43), C!39)) | (~(apply(H1!43, tptp_fun_X_10(C!39, B!40, A!41, F!45, G!44, H1!43), tptp_fun_Z_9(C!39, B!40, A!41, F!45, G!44, H1!43)) | (~((~member(tptp_fun_Y_11(C!39, B!40, A!41, F!45, G!44, H1!43), B!40)) | (~apply(F!45, tptp_fun_X_10(C!39, B!40, A!41, F!45, G!44, H1!43), tptp_fun_Y_11(C!39, B!40, A!41, F!45, G!44, H1!43))) | (~apply(G!44, tptp_fun_Y_11(C!39, B!40, A!41, F!45, G!44, H1!43), tptp_fun_Z_9(C!39, B!40, A!41, F!45, G!44, H1!43))))))) | (~((~apply(H1!43, tptp_fun_X_10(C!39, B!40, A!41, F!45, G!44, H1!43), tptp_fun_Z_9(C!39, B!40, A!41, F!45, G!44, H1!43))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!45, tptp_fun_X_10(C!39, B!40, A!41, F!45, G!44, H1!43), Y)) | (~apply(G!44, Y, tptp_fun_Z_9(C!39, B!40, A!41, F!45, G!44, H1!43))))))))))))) <=> ((~![H: $i, G: $i, F: $i, A: $i, B: $i, C: $i] : (~((~((~compose_predicate(H, G, F, A, B, C)) | ![X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(H, X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(H, X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z)))))))))) | (~(compose_predicate(H, G, F, A, B, C) | (~((~member(tptp_fun_X_10(C, B, A, F, G, H), A)) | (~member(tptp_fun_Z_9(C, B, A, F, G, H), C)) | (~(apply(H, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H)) | (~((~member(tptp_fun_Y_11(C, B, A, F, G, H), B)) | (~apply(F, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Y_11(C, B, A, F, G, H))) | (~apply(G, tptp_fun_Y_11(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H))))))) | (~((~apply(H, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H))) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_10(C, B, A, F, G, H), Y)) | (~apply(G, Y, tptp_fun_Z_9(C, B, A, F, G, H))))))))))))) | (~((~((~compose_predicate(H1!43, G!44, F!45, A!41, B!40, C!39)) | ![X: $i, Z: $i] : ((~member(Z, C!39)) | (~member(X, A!41)) | (~((~(apply(H1!43, X, Z) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!45, X, Y)) | (~apply(G!44, Y, Z))))) | (~((~apply(H1!43, X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B!40, F!45, G!44), B!40)) | (~apply(F!45, X, tptp_fun_Y_8(Z, X, B!40, F!45, G!44))) | (~apply(G!44, tptp_fun_Y_8(Z, X, B!40, F!45, G!44), Z))))))))))) | (~(compose_predicate(H1!43, G!44, F!45, A!41, B!40, C!39) | (~((~((~apply(H1!43, tptp_fun_X_10(C!39, B!40, A!41, F!45, G!44, H1!43), tptp_fun_Z_9(C!39, B!40, A!41, F!45, G!44, H1!43))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!45, tptp_fun_X_10(C!39, B!40, A!41, F!45, G!44, H1!43), Y)) | (~apply(G!44, Y, tptp_fun_Z_9(C!39, B!40, A!41, F!45, G!44, H1!43)))))) | (~(apply(H1!43, tptp_fun_X_10(C!39, B!40, A!41, F!45, G!44, H1!43), tptp_fun_Z_9(C!39, B!40, A!41, F!45, G!44, H1!43)) | (~((~member(tptp_fun_Y_11(C!39, B!40, A!41, F!45, G!44, H1!43), B!40)) | (~apply(F!45, tptp_fun_X_10(C!39, B!40, A!41, F!45, G!44, H1!43), tptp_fun_Y_11(C!39, B!40, A!41, F!45, G!44, H1!43))) | (~apply(G!44, tptp_fun_Y_11(C!39, B!40, A!41, F!45, G!44, H1!43), tptp_fun_Z_9(C!39, B!40, A!41, F!45, G!44, H1!43))))))) | (~member(tptp_fun_Z_9(C!39, B!40, A!41, F!45, G!44, H1!43), C!39)) | (~member(tptp_fun_X_10(C!39, B!40, A!41, F!45, G!44, H1!43), A!41)))))))))),
% 0.18/0.51 inference(transitivity,[status(thm)],[148, 146])).
% 0.18/0.51 tff(150,plain,
% 0.18/0.51 ((~![H: $i, G: $i, F: $i, A: $i, B: $i, C: $i] : (~((~((~compose_predicate(H, G, F, A, B, C)) | ![X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(H, X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(H, X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z)))))))))) | (~(compose_predicate(H, G, F, A, B, C) | (~((~member(tptp_fun_X_10(C, B, A, F, G, H), A)) | (~member(tptp_fun_Z_9(C, B, A, F, G, H), C)) | (~(apply(H, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H)) | (~((~member(tptp_fun_Y_11(C, B, A, F, G, H), B)) | (~apply(F, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Y_11(C, B, A, F, G, H))) | (~apply(G, tptp_fun_Y_11(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H))))))) | (~((~apply(H, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H))) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_10(C, B, A, F, G, H), Y)) | (~apply(G, Y, tptp_fun_Z_9(C, B, A, F, G, H))))))))))))) | (~((~((~compose_predicate(H1!43, G!44, F!45, A!41, B!40, C!39)) | ![X: $i, Z: $i] : ((~member(Z, C!39)) | (~member(X, A!41)) | (~((~((~apply(H1!43, X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B!40, F!45, G!44), B!40)) | (~apply(F!45, X, tptp_fun_Y_8(Z, X, B!40, F!45, G!44))) | (~apply(G!44, tptp_fun_Y_8(Z, X, B!40, F!45, G!44), Z)))))) | (~(apply(H1!43, X, Z) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!45, X, Y)) | (~apply(G!44, Y, Z)))))))))) | (~(compose_predicate(H1!43, G!44, F!45, A!41, B!40, C!39) | (~((~member(tptp_fun_X_10(C!39, B!40, A!41, F!45, G!44, H1!43), A!41)) | (~member(tptp_fun_Z_9(C!39, B!40, A!41, F!45, G!44, H1!43), C!39)) | (~(apply(H1!43, tptp_fun_X_10(C!39, B!40, A!41, F!45, G!44, H1!43), tptp_fun_Z_9(C!39, B!40, A!41, F!45, G!44, H1!43)) | (~((~member(tptp_fun_Y_11(C!39, B!40, A!41, F!45, G!44, H1!43), B!40)) | (~apply(F!45, tptp_fun_X_10(C!39, B!40, A!41, F!45, G!44, H1!43), tptp_fun_Y_11(C!39, B!40, A!41, F!45, G!44, H1!43))) | (~apply(G!44, tptp_fun_Y_11(C!39, B!40, A!41, F!45, G!44, H1!43), tptp_fun_Z_9(C!39, B!40, A!41, F!45, G!44, H1!43))))))) | (~((~apply(H1!43, tptp_fun_X_10(C!39, B!40, A!41, F!45, G!44, H1!43), tptp_fun_Z_9(C!39, B!40, A!41, F!45, G!44, H1!43))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!45, tptp_fun_X_10(C!39, B!40, A!41, F!45, G!44, H1!43), Y)) | (~apply(G!44, Y, tptp_fun_Z_9(C!39, B!40, A!41, F!45, G!44, H1!43))))))))))))),
% 0.18/0.51 inference(quant_inst,[status(thm)],[])).
% 0.18/0.51 tff(151,plain,
% 0.18/0.51 ((~![H: $i, G: $i, F: $i, A: $i, B: $i, C: $i] : (~((~((~compose_predicate(H, G, F, A, B, C)) | ![X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(H, X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(H, X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z)))))))))) | (~(compose_predicate(H, G, F, A, B, C) | (~((~member(tptp_fun_X_10(C, B, A, F, G, H), A)) | (~member(tptp_fun_Z_9(C, B, A, F, G, H), C)) | (~(apply(H, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H)) | (~((~member(tptp_fun_Y_11(C, B, A, F, G, H), B)) | (~apply(F, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Y_11(C, B, A, F, G, H))) | (~apply(G, tptp_fun_Y_11(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H))))))) | (~((~apply(H, tptp_fun_X_10(C, B, A, F, G, H), tptp_fun_Z_9(C, B, A, F, G, H))) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_10(C, B, A, F, G, H), Y)) | (~apply(G, Y, tptp_fun_Z_9(C, B, A, F, G, H))))))))))))) | (~((~((~compose_predicate(H1!43, G!44, F!45, A!41, B!40, C!39)) | ![X: $i, Z: $i] : ((~member(Z, C!39)) | (~member(X, A!41)) | (~((~(apply(H1!43, X, Z) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!45, X, Y)) | (~apply(G!44, Y, Z))))) | (~((~apply(H1!43, X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B!40, F!45, G!44), B!40)) | (~apply(F!45, X, tptp_fun_Y_8(Z, X, B!40, F!45, G!44))) | (~apply(G!44, tptp_fun_Y_8(Z, X, B!40, F!45, G!44), Z))))))))))) | (~(compose_predicate(H1!43, G!44, F!45, A!41, B!40, C!39) | (~((~((~apply(H1!43, tptp_fun_X_10(C!39, B!40, A!41, F!45, G!44, H1!43), tptp_fun_Z_9(C!39, B!40, A!41, F!45, G!44, H1!43))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!45, tptp_fun_X_10(C!39, B!40, A!41, F!45, G!44, H1!43), Y)) | (~apply(G!44, Y, tptp_fun_Z_9(C!39, B!40, A!41, F!45, G!44, H1!43)))))) | (~(apply(H1!43, tptp_fun_X_10(C!39, B!40, A!41, F!45, G!44, H1!43), tptp_fun_Z_9(C!39, B!40, A!41, F!45, G!44, H1!43)) | (~((~member(tptp_fun_Y_11(C!39, B!40, A!41, F!45, G!44, H1!43), B!40)) | (~apply(F!45, tptp_fun_X_10(C!39, B!40, A!41, F!45, G!44, H1!43), tptp_fun_Y_11(C!39, B!40, A!41, F!45, G!44, H1!43))) | (~apply(G!44, tptp_fun_Y_11(C!39, B!40, A!41, F!45, G!44, H1!43), tptp_fun_Z_9(C!39, B!40, A!41, F!45, G!44, H1!43))))))) | (~member(tptp_fun_Z_9(C!39, B!40, A!41, F!45, G!44, H1!43), C!39)) | (~member(tptp_fun_X_10(C!39, B!40, A!41, F!45, G!44, H1!43), A!41))))))))),
% 0.18/0.51 inference(modus_ponens,[status(thm)],[150, 149])).
% 0.18/0.51 tff(152,plain,
% 0.18/0.51 (~((~((~compose_predicate(H1!43, G!44, F!45, A!41, B!40, C!39)) | ![X: $i, Z: $i] : ((~member(Z, C!39)) | (~member(X, A!41)) | (~((~(apply(H1!43, X, Z) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!45, X, Y)) | (~apply(G!44, Y, Z))))) | (~((~apply(H1!43, X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B!40, F!45, G!44), B!40)) | (~apply(F!45, X, tptp_fun_Y_8(Z, X, B!40, F!45, G!44))) | (~apply(G!44, tptp_fun_Y_8(Z, X, B!40, F!45, G!44), Z))))))))))) | (~(compose_predicate(H1!43, G!44, F!45, A!41, B!40, C!39) | (~((~((~apply(H1!43, tptp_fun_X_10(C!39, B!40, A!41, F!45, G!44, H1!43), tptp_fun_Z_9(C!39, B!40, A!41, F!45, G!44, H1!43))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!45, tptp_fun_X_10(C!39, B!40, A!41, F!45, G!44, H1!43), Y)) | (~apply(G!44, Y, tptp_fun_Z_9(C!39, B!40, A!41, F!45, G!44, H1!43)))))) | (~(apply(H1!43, tptp_fun_X_10(C!39, B!40, A!41, F!45, G!44, H1!43), tptp_fun_Z_9(C!39, B!40, A!41, F!45, G!44, H1!43)) | (~((~member(tptp_fun_Y_11(C!39, B!40, A!41, F!45, G!44, H1!43), B!40)) | (~apply(F!45, tptp_fun_X_10(C!39, B!40, A!41, F!45, G!44, H1!43), tptp_fun_Y_11(C!39, B!40, A!41, F!45, G!44, H1!43))) | (~apply(G!44, tptp_fun_Y_11(C!39, B!40, A!41, F!45, G!44, H1!43), tptp_fun_Z_9(C!39, B!40, A!41, F!45, G!44, H1!43))))))) | (~member(tptp_fun_Z_9(C!39, B!40, A!41, F!45, G!44, H1!43), C!39)) | (~member(tptp_fun_X_10(C!39, B!40, A!41, F!45, G!44, H1!43), A!41)))))))),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[151, 60])).
% 0.18/0.51 tff(153,plain,
% 0.18/0.51 (((~((~compose_predicate(H1!43, G!44, F!45, A!41, B!40, C!39)) | ![X: $i, Z: $i] : ((~member(Z, C!39)) | (~member(X, A!41)) | (~((~(apply(H1!43, X, Z) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!45, X, Y)) | (~apply(G!44, Y, Z))))) | (~((~apply(H1!43, X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B!40, F!45, G!44), B!40)) | (~apply(F!45, X, tptp_fun_Y_8(Z, X, B!40, F!45, G!44))) | (~apply(G!44, tptp_fun_Y_8(Z, X, B!40, F!45, G!44), Z))))))))))) | (~(compose_predicate(H1!43, G!44, F!45, A!41, B!40, C!39) | (~((~((~apply(H1!43, tptp_fun_X_10(C!39, B!40, A!41, F!45, G!44, H1!43), tptp_fun_Z_9(C!39, B!40, A!41, F!45, G!44, H1!43))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!45, tptp_fun_X_10(C!39, B!40, A!41, F!45, G!44, H1!43), Y)) | (~apply(G!44, Y, tptp_fun_Z_9(C!39, B!40, A!41, F!45, G!44, H1!43)))))) | (~(apply(H1!43, tptp_fun_X_10(C!39, B!40, A!41, F!45, G!44, H1!43), tptp_fun_Z_9(C!39, B!40, A!41, F!45, G!44, H1!43)) | (~((~member(tptp_fun_Y_11(C!39, B!40, A!41, F!45, G!44, H1!43), B!40)) | (~apply(F!45, tptp_fun_X_10(C!39, B!40, A!41, F!45, G!44, H1!43), tptp_fun_Y_11(C!39, B!40, A!41, F!45, G!44, H1!43))) | (~apply(G!44, tptp_fun_Y_11(C!39, B!40, A!41, F!45, G!44, H1!43), tptp_fun_Z_9(C!39, B!40, A!41, F!45, G!44, H1!43))))))) | (~member(tptp_fun_Z_9(C!39, B!40, A!41, F!45, G!44, H1!43), C!39)) | (~member(tptp_fun_X_10(C!39, B!40, A!41, F!45, G!44, H1!43), A!41))))))) | ((~compose_predicate(H1!43, G!44, F!45, A!41, B!40, C!39)) | ![X: $i, Z: $i] : ((~member(Z, C!39)) | (~member(X, A!41)) | (~((~(apply(H1!43, X, Z) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!45, X, Y)) | (~apply(G!44, Y, Z))))) | (~((~apply(H1!43, X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B!40, F!45, G!44), B!40)) | (~apply(F!45, X, tptp_fun_Y_8(Z, X, B!40, F!45, G!44))) | (~apply(G!44, tptp_fun_Y_8(Z, X, B!40, F!45, G!44), Z))))))))))),
% 0.18/0.51 inference(tautology,[status(thm)],[])).
% 0.18/0.51 tff(154,plain,
% 0.18/0.51 ((~compose_predicate(H1!43, G!44, F!45, A!41, B!40, C!39)) | ![X: $i, Z: $i] : ((~member(Z, C!39)) | (~member(X, A!41)) | (~((~(apply(H1!43, X, Z) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!45, X, Y)) | (~apply(G!44, Y, Z))))) | (~((~apply(H1!43, X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B!40, F!45, G!44), B!40)) | (~apply(F!45, X, tptp_fun_Y_8(Z, X, B!40, F!45, G!44))) | (~apply(G!44, tptp_fun_Y_8(Z, X, B!40, F!45, G!44), Z)))))))))),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[153, 152])).
% 0.18/0.51 tff(155,plain,
% 0.18/0.51 (compose_predicate(H1!43, G!44, F!45, A!41, B!40, C!39)),
% 0.18/0.51 inference(and_elim,[status(thm)],[70])).
% 0.18/0.51 tff(156,plain,
% 0.18/0.51 ((~((~compose_predicate(H1!43, G!44, F!45, A!41, B!40, C!39)) | ![X: $i, Z: $i] : ((~member(Z, C!39)) | (~member(X, A!41)) | (~((~(apply(H1!43, X, Z) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!45, X, Y)) | (~apply(G!44, Y, Z))))) | (~((~apply(H1!43, X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B!40, F!45, G!44), B!40)) | (~apply(F!45, X, tptp_fun_Y_8(Z, X, B!40, F!45, G!44))) | (~apply(G!44, tptp_fun_Y_8(Z, X, B!40, F!45, G!44), Z))))))))))) | (~compose_predicate(H1!43, G!44, F!45, A!41, B!40, C!39)) | ![X: $i, Z: $i] : ((~member(Z, C!39)) | (~member(X, A!41)) | (~((~(apply(H1!43, X, Z) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!45, X, Y)) | (~apply(G!44, Y, Z))))) | (~((~apply(H1!43, X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B!40, F!45, G!44), B!40)) | (~apply(F!45, X, tptp_fun_Y_8(Z, X, B!40, F!45, G!44))) | (~apply(G!44, tptp_fun_Y_8(Z, X, B!40, F!45, G!44), Z)))))))))),
% 0.18/0.51 inference(tautology,[status(thm)],[])).
% 0.18/0.51 tff(157,plain,
% 0.18/0.51 ((~((~compose_predicate(H1!43, G!44, F!45, A!41, B!40, C!39)) | ![X: $i, Z: $i] : ((~member(Z, C!39)) | (~member(X, A!41)) | (~((~(apply(H1!43, X, Z) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!45, X, Y)) | (~apply(G!44, Y, Z))))) | (~((~apply(H1!43, X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B!40, F!45, G!44), B!40)) | (~apply(F!45, X, tptp_fun_Y_8(Z, X, B!40, F!45, G!44))) | (~apply(G!44, tptp_fun_Y_8(Z, X, B!40, F!45, G!44), Z))))))))))) | ![X: $i, Z: $i] : ((~member(Z, C!39)) | (~member(X, A!41)) | (~((~(apply(H1!43, X, Z) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!45, X, Y)) | (~apply(G!44, Y, Z))))) | (~((~apply(H1!43, X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B!40, F!45, G!44), B!40)) | (~apply(F!45, X, tptp_fun_Y_8(Z, X, B!40, F!45, G!44))) | (~apply(G!44, tptp_fun_Y_8(Z, X, B!40, F!45, G!44), Z)))))))))),
% 0.18/0.52 inference(unit_resolution,[status(thm)],[156, 155])).
% 0.18/0.52 tff(158,plain,
% 0.18/0.52 (![X: $i, Z: $i] : ((~member(Z, C!39)) | (~member(X, A!41)) | (~((~(apply(H1!43, X, Z) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!45, X, Y)) | (~apply(G!44, Y, Z))))) | (~((~apply(H1!43, X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B!40, F!45, G!44), B!40)) | (~apply(F!45, X, tptp_fun_Y_8(Z, X, B!40, F!45, G!44))) | (~apply(G!44, tptp_fun_Y_8(Z, X, B!40, F!45, G!44), Z)))))))))),
% 0.18/0.52 inference(unit_resolution,[status(thm)],[157, 154])).
% 0.18/0.52 tff(159,plain,
% 0.18/0.52 (((~![X: $i, Z: $i] : ((~member(Z, C!39)) | (~member(X, A!41)) | (~((~(apply(H1!43, X, Z) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!45, X, Y)) | (~apply(G!44, Y, Z))))) | (~((~apply(H1!43, X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B!40, F!45, G!44), B!40)) | (~apply(F!45, X, tptp_fun_Y_8(Z, X, B!40, F!45, G!44))) | (~apply(G!44, tptp_fun_Y_8(Z, X, B!40, F!45, G!44), Z)))))))))) | ((~member(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), C!39)) | (~member(tptp_fun_X_14(C!39, A!41, H2!42, H1!43), A!41)) | (~((~(apply(H1!43, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43)) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!45, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), Y)) | (~apply(G!44, Y, tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43)))))) | (~((~apply(H1!43, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44), B!40)) | (~apply(F!45, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y_8(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44))) | (~apply(G!44, tptp_fun_Y_8(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44), tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43))))))))))) <=> ((~![X: $i, Z: $i] : ((~member(Z, C!39)) | (~member(X, A!41)) | (~((~(apply(H1!43, X, Z) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!45, X, Y)) | (~apply(G!44, Y, Z))))) | (~((~apply(H1!43, X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B!40, F!45, G!44), B!40)) | (~apply(F!45, X, tptp_fun_Y_8(Z, X, B!40, F!45, G!44))) | (~apply(G!44, tptp_fun_Y_8(Z, X, B!40, F!45, G!44), Z)))))))))) | (~member(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), C!39)) | (~member(tptp_fun_X_14(C!39, A!41, H2!42, H1!43), A!41)) | (~((~(apply(H1!43, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43)) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!45, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), Y)) | (~apply(G!44, Y, tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43)))))) | (~((~apply(H1!43, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44), B!40)) | (~apply(F!45, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y_8(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44))) | (~apply(G!44, tptp_fun_Y_8(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44), tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43))))))))))),
% 0.18/0.52 inference(rewrite,[status(thm)],[])).
% 0.18/0.52 tff(160,plain,
% 0.18/0.52 ((~![X: $i, Z: $i] : ((~member(Z, C!39)) | (~member(X, A!41)) | (~((~(apply(H1!43, X, Z) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!45, X, Y)) | (~apply(G!44, Y, Z))))) | (~((~apply(H1!43, X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B!40, F!45, G!44), B!40)) | (~apply(F!45, X, tptp_fun_Y_8(Z, X, B!40, F!45, G!44))) | (~apply(G!44, tptp_fun_Y_8(Z, X, B!40, F!45, G!44), Z)))))))))) | ((~member(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), C!39)) | (~member(tptp_fun_X_14(C!39, A!41, H2!42, H1!43), A!41)) | (~((~(apply(H1!43, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43)) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!45, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), Y)) | (~apply(G!44, Y, tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43)))))) | (~((~apply(H1!43, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44), B!40)) | (~apply(F!45, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y_8(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44))) | (~apply(G!44, tptp_fun_Y_8(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44), tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43))))))))))),
% 0.18/0.52 inference(quant_inst,[status(thm)],[])).
% 0.18/0.52 tff(161,plain,
% 0.18/0.52 ((~![X: $i, Z: $i] : ((~member(Z, C!39)) | (~member(X, A!41)) | (~((~(apply(H1!43, X, Z) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!45, X, Y)) | (~apply(G!44, Y, Z))))) | (~((~apply(H1!43, X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B!40, F!45, G!44), B!40)) | (~apply(F!45, X, tptp_fun_Y_8(Z, X, B!40, F!45, G!44))) | (~apply(G!44, tptp_fun_Y_8(Z, X, B!40, F!45, G!44), Z)))))))))) | (~member(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), C!39)) | (~member(tptp_fun_X_14(C!39, A!41, H2!42, H1!43), A!41)) | (~((~(apply(H1!43, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43)) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!45, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), Y)) | (~apply(G!44, Y, tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43)))))) | (~((~apply(H1!43, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44), B!40)) | (~apply(F!45, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y_8(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44))) | (~apply(G!44, tptp_fun_Y_8(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44), tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43)))))))))),
% 0.18/0.52 inference(modus_ponens,[status(thm)],[160, 159])).
% 0.18/0.52 tff(162,plain,
% 0.18/0.52 (~((~(apply(H1!43, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43)) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!45, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), Y)) | (~apply(G!44, Y, tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43)))))) | (~((~apply(H1!43, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44), B!40)) | (~apply(F!45, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y_8(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44))) | (~apply(G!44, tptp_fun_Y_8(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44), tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43))))))))),
% 0.18/0.52 inference(unit_resolution,[status(thm)],[161, 158, 145, 39])).
% 0.18/0.52 tff(163,plain,
% 0.18/0.52 (((~(apply(H1!43, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43)) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!45, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), Y)) | (~apply(G!44, Y, tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43)))))) | (~((~apply(H1!43, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44), B!40)) | (~apply(F!45, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y_8(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44))) | (~apply(G!44, tptp_fun_Y_8(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44), tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43)))))))) | ((~apply(H1!43, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44), B!40)) | (~apply(F!45, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y_8(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44))) | (~apply(G!44, tptp_fun_Y_8(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44), tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43))))))),
% 0.18/0.52 inference(tautology,[status(thm)],[])).
% 0.18/0.52 tff(164,plain,
% 0.18/0.52 ((~apply(H1!43, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44), B!40)) | (~apply(F!45, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y_8(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44))) | (~apply(G!44, tptp_fun_Y_8(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44), tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43)))))),
% 0.18/0.52 inference(unit_resolution,[status(thm)],[163, 162])).
% 0.18/0.52 tff(165,plain,
% 0.18/0.52 (((~apply(H2!42, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43))) | (~apply(H1!43, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43))) | (~member(tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43), C!39)) | (~member(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), C!39)) | (~member(tptp_fun_X_14(C!39, A!41, H2!42, H1!43), A!41)) | (tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43) = tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43))) | apply(H1!43, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43))),
% 0.18/0.52 inference(tautology,[status(thm)],[])).
% 0.18/0.52 tff(166,plain,
% 0.18/0.52 (apply(H1!43, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43))),
% 0.18/0.52 inference(unit_resolution,[status(thm)],[165, 37])).
% 0.18/0.52 tff(167,plain,
% 0.18/0.52 ((~((~apply(H1!43, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44), B!40)) | (~apply(F!45, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y_8(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44))) | (~apply(G!44, tptp_fun_Y_8(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44), tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43))))))) | (~apply(H1!43, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44), B!40)) | (~apply(F!45, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y_8(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44))) | (~apply(G!44, tptp_fun_Y_8(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44), tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43)))))),
% 0.18/0.52 inference(tautology,[status(thm)],[])).
% 0.18/0.52 tff(168,plain,
% 0.18/0.52 ((~((~apply(H1!43, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44), B!40)) | (~apply(F!45, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y_8(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44))) | (~apply(G!44, tptp_fun_Y_8(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44), tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43))))))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44), B!40)) | (~apply(F!45, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y_8(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44))) | (~apply(G!44, tptp_fun_Y_8(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44), tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43)))))),
% 0.18/0.53 inference(unit_resolution,[status(thm)],[167, 166])).
% 0.18/0.53 tff(169,plain,
% 0.18/0.53 (~((~member(tptp_fun_Y_8(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44), B!40)) | (~apply(F!45, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y_8(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44))) | (~apply(G!44, tptp_fun_Y_8(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44), tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43))))),
% 0.18/0.53 inference(unit_resolution,[status(thm)],[168, 164])).
% 0.18/0.53 tff(170,plain,
% 0.18/0.53 (((~member(tptp_fun_Y_8(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44), B!40)) | (~apply(F!45, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y_8(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44))) | (~apply(G!44, tptp_fun_Y_8(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44), tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43)))) | apply(F!45, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y_8(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44))),
% 0.18/0.53 inference(tautology,[status(thm)],[])).
% 0.18/0.53 tff(171,plain,
% 0.18/0.53 (apply(F!45, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y_8(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44))),
% 0.18/0.53 inference(unit_resolution,[status(thm)],[170, 169])).
% 0.18/0.53 tff(172,plain,
% 0.18/0.53 (((~member(tptp_fun_Y_8(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44), B!40)) | (~apply(F!45, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y_8(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44))) | (~apply(G!44, tptp_fun_Y_8(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44), tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43)))) | member(tptp_fun_Y_8(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44), B!40)),
% 0.18/0.53 inference(tautology,[status(thm)],[])).
% 0.18/0.53 tff(173,plain,
% 0.18/0.53 (member(tptp_fun_Y_8(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44), B!40)),
% 0.18/0.53 inference(unit_resolution,[status(thm)],[172, 169])).
% 0.18/0.53 tff(174,plain,
% 0.18/0.53 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!45, X, Y1)) | (~apply(F!45, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)))) | ((~member(tptp_fun_X_14(C!39, A!41, H2!42, H1!43), A!41)) | (~member(tptp_fun_Y_3(tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45), B!40)) | (~apply(F!45, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y_3(tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45))) | (~apply(F!45, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y_8(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44))) | (~member(tptp_fun_Y_8(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44), B!40)) | (tptp_fun_Y_3(tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45) = tptp_fun_Y_8(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!45, X, Y1)) | (~apply(F!45, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)))) | (~member(tptp_fun_X_14(C!39, A!41, H2!42, H1!43), A!41)) | (~member(tptp_fun_Y_3(tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45), B!40)) | (~apply(F!45, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y_3(tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45))) | (~apply(F!45, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y_8(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44))) | (~member(tptp_fun_Y_8(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44), B!40)) | (tptp_fun_Y_3(tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45) = tptp_fun_Y_8(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44)))),
% 0.18/0.53 inference(rewrite,[status(thm)],[])).
% 0.18/0.53 tff(175,plain,
% 0.18/0.53 (((tptp_fun_Y_3(tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45) = tptp_fun_Y_8(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44)) | (~member(tptp_fun_Y_8(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44), B!40)) | (~apply(F!45, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y_3(tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45))) | (~apply(F!45, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y_8(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44))) | (~member(tptp_fun_X_14(C!39, A!41, H2!42, H1!43), A!41)) | (~member(tptp_fun_Y_3(tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45), B!40))) <=> ((~member(tptp_fun_X_14(C!39, A!41, H2!42, H1!43), A!41)) | (~member(tptp_fun_Y_3(tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45), B!40)) | (~apply(F!45, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y_3(tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45))) | (~apply(F!45, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y_8(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44))) | (~member(tptp_fun_Y_8(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44), B!40)) | (tptp_fun_Y_3(tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45) = tptp_fun_Y_8(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44)))),
% 0.18/0.53 inference(rewrite,[status(thm)],[])).
% 0.18/0.53 tff(176,plain,
% 0.18/0.53 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!45, X, Y1)) | (~apply(F!45, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)))) | ((tptp_fun_Y_3(tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45) = tptp_fun_Y_8(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44)) | (~member(tptp_fun_Y_8(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44), B!40)) | (~apply(F!45, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y_3(tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45))) | (~apply(F!45, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y_8(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44))) | (~member(tptp_fun_X_14(C!39, A!41, H2!42, H1!43), A!41)) | (~member(tptp_fun_Y_3(tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45), B!40)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!45, X, Y1)) | (~apply(F!45, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)))) | ((~member(tptp_fun_X_14(C!39, A!41, H2!42, H1!43), A!41)) | (~member(tptp_fun_Y_3(tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45), B!40)) | (~apply(F!45, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y_3(tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45))) | (~apply(F!45, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y_8(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44))) | (~member(tptp_fun_Y_8(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44), B!40)) | (tptp_fun_Y_3(tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45) = tptp_fun_Y_8(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44))))),
% 0.18/0.53 inference(monotonicity,[status(thm)],[175])).
% 0.18/0.53 tff(177,plain,
% 0.18/0.53 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!45, X, Y1)) | (~apply(F!45, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)))) | ((tptp_fun_Y_3(tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45) = tptp_fun_Y_8(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44)) | (~member(tptp_fun_Y_8(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44), B!40)) | (~apply(F!45, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y_3(tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45))) | (~apply(F!45, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y_8(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44))) | (~member(tptp_fun_X_14(C!39, A!41, H2!42, H1!43), A!41)) | (~member(tptp_fun_Y_3(tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45), B!40)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!45, X, Y1)) | (~apply(F!45, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)))) | (~member(tptp_fun_X_14(C!39, A!41, H2!42, H1!43), A!41)) | (~member(tptp_fun_Y_3(tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45), B!40)) | (~apply(F!45, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y_3(tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45))) | (~apply(F!45, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y_8(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44))) | (~member(tptp_fun_Y_8(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44), B!40)) | (tptp_fun_Y_3(tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45) = tptp_fun_Y_8(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44)))),
% 0.18/0.53 inference(transitivity,[status(thm)],[176, 174])).
% 0.18/0.53 tff(178,plain,
% 0.18/0.53 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!45, X, Y1)) | (~apply(F!45, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)))) | ((tptp_fun_Y_3(tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45) = tptp_fun_Y_8(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44)) | (~member(tptp_fun_Y_8(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44), B!40)) | (~apply(F!45, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y_3(tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45))) | (~apply(F!45, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y_8(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44))) | (~member(tptp_fun_X_14(C!39, A!41, H2!42, H1!43), A!41)) | (~member(tptp_fun_Y_3(tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45), B!40)))),
% 0.18/0.53 inference(quant_inst,[status(thm)],[])).
% 0.18/0.53 tff(179,plain,
% 0.18/0.53 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!45, X, Y1)) | (~apply(F!45, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)))) | (~member(tptp_fun_X_14(C!39, A!41, H2!42, H1!43), A!41)) | (~member(tptp_fun_Y_3(tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45), B!40)) | (~apply(F!45, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y_3(tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45))) | (~apply(F!45, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y_8(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44))) | (~member(tptp_fun_Y_8(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44), B!40)) | (tptp_fun_Y_3(tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45) = tptp_fun_Y_8(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44))),
% 0.18/0.53 inference(modus_ponens,[status(thm)],[178, 177])).
% 0.18/0.53 tff(180,plain,
% 0.18/0.53 (tptp_fun_Y_3(tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45) = tptp_fun_Y_8(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44)),
% 0.18/0.53 inference(unit_resolution,[status(thm)],[179, 136, 39, 134, 132, 173, 171])).
% 0.18/0.53 tff(181,plain,
% 0.18/0.53 (tptp_fun_Y_8(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44) = tptp_fun_Y_3(tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45)),
% 0.18/0.53 inference(symmetry,[status(thm)],[180])).
% 0.18/0.53 tff(182,plain,
% 0.18/0.53 (tptp_fun_Y_8(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44) = tptp_fun_Y_8(tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44)),
% 0.18/0.53 inference(transitivity,[status(thm)],[181, 143])).
% 0.18/0.53 tff(183,plain,
% 0.18/0.53 (apply(G!44, tptp_fun_Y_8(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44), tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43)) <=> apply(G!44, tptp_fun_Y_8(tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44), tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43))),
% 0.18/0.53 inference(monotonicity,[status(thm)],[182])).
% 0.18/0.53 tff(184,plain,
% 0.18/0.53 (apply(G!44, tptp_fun_Y_8(tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44), tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43)) <=> apply(G!44, tptp_fun_Y_8(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44), tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43))),
% 0.18/0.53 inference(symmetry,[status(thm)],[183])).
% 0.18/0.53 tff(185,plain,
% 0.18/0.53 (((~member(tptp_fun_Y_8(tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44), B!40)) | (~apply(F!45, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y_8(tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44))) | (~apply(G!44, tptp_fun_Y_8(tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44), tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43)))) | apply(G!44, tptp_fun_Y_8(tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44), tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43))),
% 0.18/0.53 inference(tautology,[status(thm)],[])).
% 0.18/0.53 tff(186,plain,
% 0.18/0.53 (apply(G!44, tptp_fun_Y_8(tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44), tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43))),
% 0.18/0.53 inference(unit_resolution,[status(thm)],[185, 85])).
% 0.18/0.53 tff(187,plain,
% 0.18/0.53 (apply(G!44, tptp_fun_Y_8(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44), tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43))),
% 0.18/0.53 inference(modus_ponens,[status(thm)],[186, 184])).
% 0.18/0.53 tff(188,plain,
% 0.18/0.53 (((~member(tptp_fun_Y_8(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44), B!40)) | (~apply(F!45, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y_8(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44))) | (~apply(G!44, tptp_fun_Y_8(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44), tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43)))) | apply(G!44, tptp_fun_Y_8(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44), tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43))),
% 0.18/0.53 inference(tautology,[status(thm)],[])).
% 0.18/0.53 tff(189,plain,
% 0.18/0.53 (apply(G!44, tptp_fun_Y_8(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44), tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43))),
% 0.18/0.53 inference(unit_resolution,[status(thm)],[188, 169])).
% 0.18/0.53 tff(190,plain,
% 0.18/0.53 (((~apply(H2!42, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43))) | (~apply(H1!43, tptp_fun_X_14(C!39, A!41, H2!42, H1!43), tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43))) | (~member(tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43), C!39)) | (~member(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), C!39)) | (~member(tptp_fun_X_14(C!39, A!41, H2!42, H1!43), A!41)) | (tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43) = tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43))) | (~(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43) = tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43)))),
% 0.18/0.54 inference(tautology,[status(thm)],[])).
% 0.18/0.54 tff(191,plain,
% 0.18/0.54 (~(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43) = tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43))),
% 0.18/0.54 inference(unit_resolution,[status(thm)],[190, 37])).
% 0.18/0.54 tff(192,plain,
% 0.18/0.54 (((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(G!44, B!40, C!39)) | (~((~![X: $i] : ((~member(X, B!40)) | (~((~member(tptp_fun_Y_3(X, C!39, G!44), C!39)) | (~apply(G!44, X, tptp_fun_Y_3(X, C!39, G!44))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, C!39)) | (~apply(G!44, X, Y1)) | (~apply(G!44, X, Y2)) | (~member(X, B!40)) | (~member(Y1, C!39)))))))) | (~(maps(G!44, B!40, C!39) | (~((~member(tptp_fun_X_4(C!39, B!40, G!44), B!40)) | (~![Y: $i] : ((~member(Y, C!39)) | (~apply(G!44, tptp_fun_X_4(C!39, B!40, G!44), Y)))))) | (~((~member(tptp_fun_Y2_5(C!39, B!40, G!44), C!39)) | (~member(tptp_fun_Y1_6(C!39, B!40, G!44), C!39)) | (~member(tptp_fun_X_7(C!39, B!40, G!44), B!40)) | (~apply(G!44, tptp_fun_X_7(C!39, B!40, G!44), tptp_fun_Y2_5(C!39, B!40, G!44))) | (~apply(G!44, tptp_fun_X_7(C!39, B!40, G!44), tptp_fun_Y1_6(C!39, B!40, G!44))) | (tptp_fun_Y1_6(C!39, B!40, G!44) = tptp_fun_Y2_5(C!39, B!40, 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!40, C!39)) | (~((~![X: $i] : ((~member(X, B!40)) | (~((~member(tptp_fun_Y_3(X, C!39, G!44), C!39)) | (~apply(G!44, X, tptp_fun_Y_3(X, C!39, G!44))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, C!39)) | (~apply(G!44, X, Y1)) | (~apply(G!44, X, Y2)) | (~member(X, B!40)) | (~member(Y1, C!39)))))))) | (~(maps(G!44, B!40, C!39) | (~((~member(tptp_fun_X_4(C!39, B!40, G!44), B!40)) | (~![Y: $i] : ((~member(Y, C!39)) | (~apply(G!44, tptp_fun_X_4(C!39, B!40, G!44), Y)))))) | (~((~member(tptp_fun_Y2_5(C!39, B!40, G!44), C!39)) | (~member(tptp_fun_Y1_6(C!39, B!40, G!44), C!39)) | (~member(tptp_fun_X_7(C!39, B!40, G!44), B!40)) | (~apply(G!44, tptp_fun_X_7(C!39, B!40, G!44), tptp_fun_Y2_5(C!39, B!40, G!44))) | (~apply(G!44, tptp_fun_X_7(C!39, B!40, G!44), tptp_fun_Y1_6(C!39, B!40, G!44))) | (tptp_fun_Y1_6(C!39, B!40, G!44) = tptp_fun_Y2_5(C!39, B!40, G!44)))))))))),
% 0.18/0.54 inference(rewrite,[status(thm)],[])).
% 0.18/0.54 tff(193,plain,
% 0.18/0.54 ((~((~((~maps(G!44, B!40, C!39)) | (~((~![X: $i] : ((~member(X, B!40)) | (~((~member(tptp_fun_Y_3(X, C!39, G!44), C!39)) | (~apply(G!44, X, tptp_fun_Y_3(X, C!39, G!44))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G!44, X, Y1)) | (~apply(G!44, X, Y2)) | (~member(X, B!40)) | (~member(Y1, C!39)) | (~member(Y2, C!39)))))))) | (~(maps(G!44, B!40, C!39) | (~((tptp_fun_Y1_6(C!39, B!40, G!44) = tptp_fun_Y2_5(C!39, B!40, G!44)) | (~apply(G!44, tptp_fun_X_7(C!39, B!40, G!44), tptp_fun_Y1_6(C!39, B!40, G!44))) | (~apply(G!44, tptp_fun_X_7(C!39, B!40, G!44), tptp_fun_Y2_5(C!39, B!40, G!44))) | (~member(tptp_fun_X_7(C!39, B!40, G!44), B!40)) | (~member(tptp_fun_Y1_6(C!39, B!40, G!44), C!39)) | (~member(tptp_fun_Y2_5(C!39, B!40, G!44), C!39)))) | (~((~member(tptp_fun_X_4(C!39, B!40, G!44), B!40)) | (~![Y: $i] : ((~member(Y, C!39)) | (~apply(G!44, tptp_fun_X_4(C!39, B!40, G!44), Y)))))))))) <=> (~((~((~maps(G!44, B!40, C!39)) | (~((~![X: $i] : ((~member(X, B!40)) | (~((~member(tptp_fun_Y_3(X, C!39, G!44), C!39)) | (~apply(G!44, X, tptp_fun_Y_3(X, C!39, G!44))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, C!39)) | (~apply(G!44, X, Y1)) | (~apply(G!44, X, Y2)) | (~member(X, B!40)) | (~member(Y1, C!39)))))))) | (~(maps(G!44, B!40, C!39) | (~((~member(tptp_fun_X_4(C!39, B!40, G!44), B!40)) | (~![Y: $i] : ((~member(Y, C!39)) | (~apply(G!44, tptp_fun_X_4(C!39, B!40, G!44), Y)))))) | (~((~member(tptp_fun_Y2_5(C!39, B!40, G!44), C!39)) | (~member(tptp_fun_Y1_6(C!39, B!40, G!44), C!39)) | (~member(tptp_fun_X_7(C!39, B!40, G!44), B!40)) | (~apply(G!44, tptp_fun_X_7(C!39, B!40, G!44), tptp_fun_Y2_5(C!39, B!40, G!44))) | (~apply(G!44, tptp_fun_X_7(C!39, B!40, G!44), tptp_fun_Y1_6(C!39, B!40, G!44))) | (tptp_fun_Y1_6(C!39, B!40, G!44) = tptp_fun_Y2_5(C!39, B!40, G!44))))))))),
% 0.18/0.54 inference(rewrite,[status(thm)],[])).
% 0.18/0.54 tff(194,plain,
% 0.18/0.54 (((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(G!44, B!40, C!39)) | (~((~![X: $i] : ((~member(X, B!40)) | (~((~member(tptp_fun_Y_3(X, C!39, G!44), C!39)) | (~apply(G!44, X, tptp_fun_Y_3(X, C!39, G!44))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G!44, X, Y1)) | (~apply(G!44, X, Y2)) | (~member(X, B!40)) | (~member(Y1, C!39)) | (~member(Y2, C!39)))))))) | (~(maps(G!44, B!40, C!39) | (~((tptp_fun_Y1_6(C!39, B!40, G!44) = tptp_fun_Y2_5(C!39, B!40, G!44)) | (~apply(G!44, tptp_fun_X_7(C!39, B!40, G!44), tptp_fun_Y1_6(C!39, B!40, G!44))) | (~apply(G!44, tptp_fun_X_7(C!39, B!40, G!44), tptp_fun_Y2_5(C!39, B!40, G!44))) | (~member(tptp_fun_X_7(C!39, B!40, G!44), B!40)) | (~member(tptp_fun_Y1_6(C!39, B!40, G!44), C!39)) | (~member(tptp_fun_Y2_5(C!39, B!40, G!44), C!39)))) | (~((~member(tptp_fun_X_4(C!39, B!40, G!44), B!40)) | (~![Y: $i] : ((~member(Y, C!39)) | (~apply(G!44, tptp_fun_X_4(C!39, B!40, 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!40, C!39)) | (~((~![X: $i] : ((~member(X, B!40)) | (~((~member(tptp_fun_Y_3(X, C!39, G!44), C!39)) | (~apply(G!44, X, tptp_fun_Y_3(X, C!39, G!44))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, C!39)) | (~apply(G!44, X, Y1)) | (~apply(G!44, X, Y2)) | (~member(X, B!40)) | (~member(Y1, C!39)))))))) | (~(maps(G!44, B!40, C!39) | (~((~member(tptp_fun_X_4(C!39, B!40, G!44), B!40)) | (~![Y: $i] : ((~member(Y, C!39)) | (~apply(G!44, tptp_fun_X_4(C!39, B!40, G!44), Y)))))) | (~((~member(tptp_fun_Y2_5(C!39, B!40, G!44), C!39)) | (~member(tptp_fun_Y1_6(C!39, B!40, G!44), C!39)) | (~member(tptp_fun_X_7(C!39, B!40, G!44), B!40)) | (~apply(G!44, tptp_fun_X_7(C!39, B!40, G!44), tptp_fun_Y2_5(C!39, B!40, G!44))) | (~apply(G!44, tptp_fun_X_7(C!39, B!40, G!44), tptp_fun_Y1_6(C!39, B!40, G!44))) | (tptp_fun_Y1_6(C!39, B!40, G!44) = tptp_fun_Y2_5(C!39, B!40, G!44)))))))))),
% 0.18/0.54 inference(monotonicity,[status(thm)],[193])).
% 0.18/0.54 tff(195,plain,
% 0.18/0.54 (((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(G!44, B!40, C!39)) | (~((~![X: $i] : ((~member(X, B!40)) | (~((~member(tptp_fun_Y_3(X, C!39, G!44), C!39)) | (~apply(G!44, X, tptp_fun_Y_3(X, C!39, G!44))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G!44, X, Y1)) | (~apply(G!44, X, Y2)) | (~member(X, B!40)) | (~member(Y1, C!39)) | (~member(Y2, C!39)))))))) | (~(maps(G!44, B!40, C!39) | (~((tptp_fun_Y1_6(C!39, B!40, G!44) = tptp_fun_Y2_5(C!39, B!40, G!44)) | (~apply(G!44, tptp_fun_X_7(C!39, B!40, G!44), tptp_fun_Y1_6(C!39, B!40, G!44))) | (~apply(G!44, tptp_fun_X_7(C!39, B!40, G!44), tptp_fun_Y2_5(C!39, B!40, G!44))) | (~member(tptp_fun_X_7(C!39, B!40, G!44), B!40)) | (~member(tptp_fun_Y1_6(C!39, B!40, G!44), C!39)) | (~member(tptp_fun_Y2_5(C!39, B!40, G!44), C!39)))) | (~((~member(tptp_fun_X_4(C!39, B!40, G!44), B!40)) | (~![Y: $i] : ((~member(Y, C!39)) | (~apply(G!44, tptp_fun_X_4(C!39, B!40, 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!40, C!39)) | (~((~![X: $i] : ((~member(X, B!40)) | (~((~member(tptp_fun_Y_3(X, C!39, G!44), C!39)) | (~apply(G!44, X, tptp_fun_Y_3(X, C!39, G!44))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, C!39)) | (~apply(G!44, X, Y1)) | (~apply(G!44, X, Y2)) | (~member(X, B!40)) | (~member(Y1, C!39)))))))) | (~(maps(G!44, B!40, C!39) | (~((~member(tptp_fun_X_4(C!39, B!40, G!44), B!40)) | (~![Y: $i] : ((~member(Y, C!39)) | (~apply(G!44, tptp_fun_X_4(C!39, B!40, G!44), Y)))))) | (~((~member(tptp_fun_Y2_5(C!39, B!40, G!44), C!39)) | (~member(tptp_fun_Y1_6(C!39, B!40, G!44), C!39)) | (~member(tptp_fun_X_7(C!39, B!40, G!44), B!40)) | (~apply(G!44, tptp_fun_X_7(C!39, B!40, G!44), tptp_fun_Y2_5(C!39, B!40, G!44))) | (~apply(G!44, tptp_fun_X_7(C!39, B!40, G!44), tptp_fun_Y1_6(C!39, B!40, G!44))) | (tptp_fun_Y1_6(C!39, B!40, G!44) = tptp_fun_Y2_5(C!39, B!40, G!44)))))))))),
% 0.18/0.54 inference(transitivity,[status(thm)],[194, 192])).
% 0.18/0.54 tff(196,plain,
% 0.18/0.54 ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(G!44, B!40, C!39)) | (~((~![X: $i] : ((~member(X, B!40)) | (~((~member(tptp_fun_Y_3(X, C!39, G!44), C!39)) | (~apply(G!44, X, tptp_fun_Y_3(X, C!39, G!44))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G!44, X, Y1)) | (~apply(G!44, X, Y2)) | (~member(X, B!40)) | (~member(Y1, C!39)) | (~member(Y2, C!39)))))))) | (~(maps(G!44, B!40, C!39) | (~((tptp_fun_Y1_6(C!39, B!40, G!44) = tptp_fun_Y2_5(C!39, B!40, G!44)) | (~apply(G!44, tptp_fun_X_7(C!39, B!40, G!44), tptp_fun_Y1_6(C!39, B!40, G!44))) | (~apply(G!44, tptp_fun_X_7(C!39, B!40, G!44), tptp_fun_Y2_5(C!39, B!40, G!44))) | (~member(tptp_fun_X_7(C!39, B!40, G!44), B!40)) | (~member(tptp_fun_Y1_6(C!39, B!40, G!44), C!39)) | (~member(tptp_fun_Y2_5(C!39, B!40, G!44), C!39)))) | (~((~member(tptp_fun_X_4(C!39, B!40, G!44), B!40)) | (~![Y: $i] : ((~member(Y, C!39)) | (~apply(G!44, tptp_fun_X_4(C!39, B!40, G!44), Y))))))))))),
% 0.18/0.54 inference(quant_inst,[status(thm)],[])).
% 0.18/0.54 tff(197,plain,
% 0.18/0.54 ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(G!44, B!40, C!39)) | (~((~![X: $i] : ((~member(X, B!40)) | (~((~member(tptp_fun_Y_3(X, C!39, G!44), C!39)) | (~apply(G!44, X, tptp_fun_Y_3(X, C!39, G!44))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, C!39)) | (~apply(G!44, X, Y1)) | (~apply(G!44, X, Y2)) | (~member(X, B!40)) | (~member(Y1, C!39)))))))) | (~(maps(G!44, B!40, C!39) | (~((~member(tptp_fun_X_4(C!39, B!40, G!44), B!40)) | (~![Y: $i] : ((~member(Y, C!39)) | (~apply(G!44, tptp_fun_X_4(C!39, B!40, G!44), Y)))))) | (~((~member(tptp_fun_Y2_5(C!39, B!40, G!44), C!39)) | (~member(tptp_fun_Y1_6(C!39, B!40, G!44), C!39)) | (~member(tptp_fun_X_7(C!39, B!40, G!44), B!40)) | (~apply(G!44, tptp_fun_X_7(C!39, B!40, G!44), tptp_fun_Y2_5(C!39, B!40, G!44))) | (~apply(G!44, tptp_fun_X_7(C!39, B!40, G!44), tptp_fun_Y1_6(C!39, B!40, G!44))) | (tptp_fun_Y1_6(C!39, B!40, G!44) = tptp_fun_Y2_5(C!39, B!40, G!44))))))))),
% 0.18/0.54 inference(modus_ponens,[status(thm)],[196, 195])).
% 0.18/0.54 tff(198,plain,
% 0.18/0.54 (~((~((~maps(G!44, B!40, C!39)) | (~((~![X: $i] : ((~member(X, B!40)) | (~((~member(tptp_fun_Y_3(X, C!39, G!44), C!39)) | (~apply(G!44, X, tptp_fun_Y_3(X, C!39, G!44))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, C!39)) | (~apply(G!44, X, Y1)) | (~apply(G!44, X, Y2)) | (~member(X, B!40)) | (~member(Y1, C!39)))))))) | (~(maps(G!44, B!40, C!39) | (~((~member(tptp_fun_X_4(C!39, B!40, G!44), B!40)) | (~![Y: $i] : ((~member(Y, C!39)) | (~apply(G!44, tptp_fun_X_4(C!39, B!40, G!44), Y)))))) | (~((~member(tptp_fun_Y2_5(C!39, B!40, G!44), C!39)) | (~member(tptp_fun_Y1_6(C!39, B!40, G!44), C!39)) | (~member(tptp_fun_X_7(C!39, B!40, G!44), B!40)) | (~apply(G!44, tptp_fun_X_7(C!39, B!40, G!44), tptp_fun_Y2_5(C!39, B!40, G!44))) | (~apply(G!44, tptp_fun_X_7(C!39, B!40, G!44), tptp_fun_Y1_6(C!39, B!40, G!44))) | (tptp_fun_Y1_6(C!39, B!40, G!44) = tptp_fun_Y2_5(C!39, B!40, G!44)))))))),
% 0.18/0.55 inference(unit_resolution,[status(thm)],[197, 111])).
% 0.18/0.55 tff(199,plain,
% 0.18/0.55 (((~((~maps(G!44, B!40, C!39)) | (~((~![X: $i] : ((~member(X, B!40)) | (~((~member(tptp_fun_Y_3(X, C!39, G!44), C!39)) | (~apply(G!44, X, tptp_fun_Y_3(X, C!39, G!44))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, C!39)) | (~apply(G!44, X, Y1)) | (~apply(G!44, X, Y2)) | (~member(X, B!40)) | (~member(Y1, C!39)))))))) | (~(maps(G!44, B!40, C!39) | (~((~member(tptp_fun_X_4(C!39, B!40, G!44), B!40)) | (~![Y: $i] : ((~member(Y, C!39)) | (~apply(G!44, tptp_fun_X_4(C!39, B!40, G!44), Y)))))) | (~((~member(tptp_fun_Y2_5(C!39, B!40, G!44), C!39)) | (~member(tptp_fun_Y1_6(C!39, B!40, G!44), C!39)) | (~member(tptp_fun_X_7(C!39, B!40, G!44), B!40)) | (~apply(G!44, tptp_fun_X_7(C!39, B!40, G!44), tptp_fun_Y2_5(C!39, B!40, G!44))) | (~apply(G!44, tptp_fun_X_7(C!39, B!40, G!44), tptp_fun_Y1_6(C!39, B!40, G!44))) | (tptp_fun_Y1_6(C!39, B!40, G!44) = tptp_fun_Y2_5(C!39, B!40, G!44))))))) | ((~maps(G!44, B!40, C!39)) | (~((~![X: $i] : ((~member(X, B!40)) | (~((~member(tptp_fun_Y_3(X, C!39, G!44), C!39)) | (~apply(G!44, X, tptp_fun_Y_3(X, C!39, G!44))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, C!39)) | (~apply(G!44, X, Y1)) | (~apply(G!44, X, Y2)) | (~member(X, B!40)) | (~member(Y1, C!39)))))))),
% 0.18/0.55 inference(tautology,[status(thm)],[])).
% 0.18/0.55 tff(200,plain,
% 0.18/0.55 ((~maps(G!44, B!40, C!39)) | (~((~![X: $i] : ((~member(X, B!40)) | (~((~member(tptp_fun_Y_3(X, C!39, G!44), C!39)) | (~apply(G!44, X, tptp_fun_Y_3(X, C!39, G!44))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, C!39)) | (~apply(G!44, X, Y1)) | (~apply(G!44, X, Y2)) | (~member(X, B!40)) | (~member(Y1, C!39))))))),
% 0.18/0.55 inference(unit_resolution,[status(thm)],[199, 198])).
% 0.18/0.55 tff(201,plain,
% 0.18/0.55 (maps(G!44, B!40, C!39)),
% 0.18/0.55 inference(and_elim,[status(thm)],[70])).
% 0.18/0.55 tff(202,plain,
% 0.18/0.55 ((~((~maps(G!44, B!40, C!39)) | (~((~![X: $i] : ((~member(X, B!40)) | (~((~member(tptp_fun_Y_3(X, C!39, G!44), C!39)) | (~apply(G!44, X, tptp_fun_Y_3(X, C!39, G!44))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, C!39)) | (~apply(G!44, X, Y1)) | (~apply(G!44, X, Y2)) | (~member(X, B!40)) | (~member(Y1, C!39)))))))) | (~maps(G!44, B!40, C!39)) | (~((~![X: $i] : ((~member(X, B!40)) | (~((~member(tptp_fun_Y_3(X, C!39, G!44), C!39)) | (~apply(G!44, X, tptp_fun_Y_3(X, C!39, G!44))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, C!39)) | (~apply(G!44, X, Y1)) | (~apply(G!44, X, Y2)) | (~member(X, B!40)) | (~member(Y1, C!39))))))),
% 0.18/0.55 inference(tautology,[status(thm)],[])).
% 0.18/0.55 tff(203,plain,
% 0.18/0.55 ((~((~maps(G!44, B!40, C!39)) | (~((~![X: $i] : ((~member(X, B!40)) | (~((~member(tptp_fun_Y_3(X, C!39, G!44), C!39)) | (~apply(G!44, X, tptp_fun_Y_3(X, C!39, G!44))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, C!39)) | (~apply(G!44, X, Y1)) | (~apply(G!44, X, Y2)) | (~member(X, B!40)) | (~member(Y1, C!39)))))))) | (~((~![X: $i] : ((~member(X, B!40)) | (~((~member(tptp_fun_Y_3(X, C!39, G!44), C!39)) | (~apply(G!44, X, tptp_fun_Y_3(X, C!39, G!44))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, C!39)) | (~apply(G!44, X, Y1)) | (~apply(G!44, X, Y2)) | (~member(X, B!40)) | (~member(Y1, C!39))))))),
% 0.18/0.55 inference(unit_resolution,[status(thm)],[202, 201])).
% 0.18/0.55 tff(204,plain,
% 0.18/0.55 (~((~![X: $i] : ((~member(X, B!40)) | (~((~member(tptp_fun_Y_3(X, C!39, G!44), C!39)) | (~apply(G!44, X, tptp_fun_Y_3(X, C!39, G!44))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, C!39)) | (~apply(G!44, X, Y1)) | (~apply(G!44, X, Y2)) | (~member(X, B!40)) | (~member(Y1, C!39)))))),
% 0.18/0.55 inference(unit_resolution,[status(thm)],[203, 200])).
% 0.18/0.55 tff(205,plain,
% 0.18/0.55 (((~![X: $i] : ((~member(X, B!40)) | (~((~member(tptp_fun_Y_3(X, C!39, G!44), C!39)) | (~apply(G!44, X, tptp_fun_Y_3(X, C!39, G!44))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, C!39)) | (~apply(G!44, X, Y1)) | (~apply(G!44, X, Y2)) | (~member(X, B!40)) | (~member(Y1, C!39))))) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, C!39)) | (~apply(G!44, X, Y1)) | (~apply(G!44, X, Y2)) | (~member(X, B!40)) | (~member(Y1, C!39)))),
% 0.18/0.55 inference(tautology,[status(thm)],[])).
% 0.18/0.55 tff(206,plain,
% 0.18/0.55 (![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, C!39)) | (~apply(G!44, X, Y1)) | (~apply(G!44, X, Y2)) | (~member(X, B!40)) | (~member(Y1, C!39)))),
% 0.18/0.55 inference(unit_resolution,[status(thm)],[205, 204])).
% 0.18/0.55 tff(207,plain,
% 0.18/0.55 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, C!39)) | (~apply(G!44, X, Y1)) | (~apply(G!44, X, Y2)) | (~member(X, B!40)) | (~member(Y1, C!39)))) | ((~member(tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43), C!39)) | (~member(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), C!39)) | (tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43) = tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43)) | (~apply(G!44, tptp_fun_Y_8(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44), tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43))) | (~member(tptp_fun_Y_8(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44), B!40)) | (~apply(G!44, tptp_fun_Y_8(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44), tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43))))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, C!39)) | (~apply(G!44, X, Y1)) | (~apply(G!44, X, Y2)) | (~member(X, B!40)) | (~member(Y1, C!39)))) | (~member(tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43), C!39)) | (~member(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), C!39)) | (tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43) = tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43)) | (~apply(G!44, tptp_fun_Y_8(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44), tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43))) | (~member(tptp_fun_Y_8(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44), B!40)) | (~apply(G!44, tptp_fun_Y_8(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44), tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43))))),
% 0.18/0.55 inference(rewrite,[status(thm)],[])).
% 0.18/0.55 tff(208,plain,
% 0.18/0.55 (((tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43) = tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43)) | (~member(tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43), C!39)) | (~apply(G!44, tptp_fun_Y_8(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44), tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43))) | (~apply(G!44, tptp_fun_Y_8(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44), tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43))) | (~member(tptp_fun_Y_8(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44), B!40)) | (~member(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), C!39))) <=> ((~member(tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43), C!39)) | (~member(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), C!39)) | (tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43) = tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43)) | (~apply(G!44, tptp_fun_Y_8(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44), tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43))) | (~member(tptp_fun_Y_8(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44), B!40)) | (~apply(G!44, tptp_fun_Y_8(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44), tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43))))),
% 0.18/0.55 inference(rewrite,[status(thm)],[])).
% 0.18/0.55 tff(209,plain,
% 0.18/0.55 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, C!39)) | (~apply(G!44, X, Y1)) | (~apply(G!44, X, Y2)) | (~member(X, B!40)) | (~member(Y1, C!39)))) | ((tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43) = tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43)) | (~member(tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43), C!39)) | (~apply(G!44, tptp_fun_Y_8(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44), tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43))) | (~apply(G!44, tptp_fun_Y_8(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44), tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43))) | (~member(tptp_fun_Y_8(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44), B!40)) | (~member(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), C!39)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, C!39)) | (~apply(G!44, X, Y1)) | (~apply(G!44, X, Y2)) | (~member(X, B!40)) | (~member(Y1, C!39)))) | ((~member(tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43), C!39)) | (~member(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), C!39)) | (tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43) = tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43)) | (~apply(G!44, tptp_fun_Y_8(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44), tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43))) | (~member(tptp_fun_Y_8(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44), B!40)) | (~apply(G!44, tptp_fun_Y_8(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44), tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43)))))),
% 0.18/0.55 inference(monotonicity,[status(thm)],[208])).
% 0.18/0.55 tff(210,plain,
% 0.18/0.55 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, C!39)) | (~apply(G!44, X, Y1)) | (~apply(G!44, X, Y2)) | (~member(X, B!40)) | (~member(Y1, C!39)))) | ((tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43) = tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43)) | (~member(tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43), C!39)) | (~apply(G!44, tptp_fun_Y_8(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44), tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43))) | (~apply(G!44, tptp_fun_Y_8(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44), tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43))) | (~member(tptp_fun_Y_8(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44), B!40)) | (~member(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), C!39)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, C!39)) | (~apply(G!44, X, Y1)) | (~apply(G!44, X, Y2)) | (~member(X, B!40)) | (~member(Y1, C!39)))) | (~member(tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43), C!39)) | (~member(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), C!39)) | (tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43) = tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43)) | (~apply(G!44, tptp_fun_Y_8(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44), tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43))) | (~member(tptp_fun_Y_8(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44), B!40)) | (~apply(G!44, tptp_fun_Y_8(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44), tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43))))),
% 0.18/0.55 inference(transitivity,[status(thm)],[209, 207])).
% 0.18/0.55 tff(211,plain,
% 0.18/0.55 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, C!39)) | (~apply(G!44, X, Y1)) | (~apply(G!44, X, Y2)) | (~member(X, B!40)) | (~member(Y1, C!39)))) | ((tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43) = tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43)) | (~member(tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43), C!39)) | (~apply(G!44, tptp_fun_Y_8(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44), tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43))) | (~apply(G!44, tptp_fun_Y_8(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44), tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43))) | (~member(tptp_fun_Y_8(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44), B!40)) | (~member(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), C!39)))),
% 0.18/0.55 inference(quant_inst,[status(thm)],[])).
% 0.18/0.55 tff(212,plain,
% 0.18/0.55 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, C!39)) | (~apply(G!44, X, Y1)) | (~apply(G!44, X, Y2)) | (~member(X, B!40)) | (~member(Y1, C!39)))) | (~member(tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43), C!39)) | (~member(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), C!39)) | (tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43) = tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43)) | (~apply(G!44, tptp_fun_Y_8(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44), tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43))) | (~member(tptp_fun_Y_8(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44), B!40)) | (~apply(G!44, tptp_fun_Y_8(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44), tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43)))),
% 0.18/0.55 inference(modus_ponens,[status(thm)],[211, 210])).
% 0.18/0.55 tff(213,plain,
% 0.18/0.55 (~apply(G!44, tptp_fun_Y_8(tptp_fun_Y1_13(C!39, A!41, H2!42, H1!43), tptp_fun_X_14(C!39, A!41, H2!42, H1!43), B!40, F!45, G!44), tptp_fun_Y2_12(C!39, A!41, H2!42, H1!43))),
% 0.18/0.55 inference(unit_resolution,[status(thm)],[212, 206, 41, 145, 191, 173, 189])).
% 0.18/0.55 tff(214,plain,
% 0.18/0.55 ($false),
% 0.18/0.55 inference(unit_resolution,[status(thm)],[213, 187])).
% 0.18/0.55 % SZS output end Proof
% 0.18/0.56 % E exiting
%------------------------------------------------------------------------------