%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET709+4 : TPTP v9.0.0. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n009.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 0.19s 0.39s
% Output : Proof 0.47s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.11 % Problem : SET709+4 : TPTP v9.0.0. Bugfixed v2.2.1.
% 0.02/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n009.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 05:38:18 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.19/0.39 % SZS status Theorem
% 0.19/0.39 % SZS output start Proof
% 0.19/0.39 tff(apply_type, type, (
% 0.19/0.39 apply: ( $i * $i * $i ) > $o)).
% 0.19/0.39 tff(tptp_fun_Y2_5_type, type, (
% 0.19/0.39 tptp_fun_Y2_5: ( $i * $i * $i ) > $i)).
% 0.19/0.39 tff(compose_function_type, type, (
% 0.19/0.39 compose_function: ( $i * $i * $i * $i * $i ) > $i)).
% 0.19/0.39 tff(tptp_fun_C_39_type, type, (
% 0.19/0.39 tptp_fun_C_39: $i)).
% 0.19/0.39 tff(tptp_fun_B_40_type, type, (
% 0.19/0.39 tptp_fun_B_40: $i)).
% 0.19/0.39 tff(tptp_fun_A_41_type, type, (
% 0.19/0.39 tptp_fun_A_41: $i)).
% 0.19/0.39 tff(tptp_fun_F_43_type, type, (
% 0.19/0.39 tptp_fun_F_43: $i)).
% 0.19/0.39 tff(tptp_fun_G_42_type, type, (
% 0.19/0.39 tptp_fun_G_42: $i)).
% 0.19/0.39 tff(tptp_fun_Y_8_type, type, (
% 0.19/0.39 tptp_fun_Y_8: ( $i * $i * $i * $i * $i ) > $i)).
% 0.19/0.39 tff(tptp_fun_X_7_type, type, (
% 0.19/0.39 tptp_fun_X_7: ( $i * $i * $i ) > $i)).
% 0.19/0.39 tff(tptp_fun_Y1_6_type, type, (
% 0.19/0.39 tptp_fun_Y1_6: ( $i * $i * $i ) > $i)).
% 0.19/0.39 tff(tptp_fun_Y_3_type, type, (
% 0.19/0.39 tptp_fun_Y_3: ( $i * $i * $i ) > $i)).
% 0.19/0.39 tff(member_type, type, (
% 0.19/0.39 member: ( $i * $i ) > $o)).
% 0.19/0.39 tff(tptp_fun_X_4_type, type, (
% 0.19/0.39 tptp_fun_X_4: ( $i * $i * $i ) > $i)).
% 0.19/0.39 tff(maps_type, type, (
% 0.19/0.39 maps: ( $i * $i * $i ) > $o)).
% 0.19/0.39 tff(1,assumption,(~((~member(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~![Y: $i] : ((~member(Y, C!39)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)))))), introduced(assumption)).
% 0.19/0.39 tff(2,plain,
% 0.19/0.39 (((~member(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~![Y: $i] : ((~member(Y, C!39)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y))))) | member(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(3,plain,
% 0.19/0.39 (member(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[2, 1])).
% 0.19/0.39 tff(4,plain,
% 0.19/0.39 (^[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)))))))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(5,plain,
% 0.19/0.39 (![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))))))))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[4])).
% 0.19/0.39 tff(6,plain,
% 0.19/0.39 (^[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)))))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(7,plain,
% 0.19/0.39 (![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))))))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[6])).
% 0.19/0.39 tff(8,plain,
% 0.19/0.39 (^[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)))))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(9,plain,
% 0.19/0.39 (![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))))))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[8])).
% 0.19/0.39 tff(10,plain,
% 0.19/0.39 (![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))))))))),
% 0.19/0.39 inference(transitivity,[status(thm)],[9, 7])).
% 0.19/0.39 tff(11,plain,
% 0.19/0.39 (^[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))))))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(12,plain,
% 0.19/0.39 (![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))))))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[11])).
% 0.19/0.39 tff(13,plain,
% 0.19/0.39 (^[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))))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(14,plain,
% 0.19/0.40 (![F: $i, A: $i, B: $i] : (((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) & (maps(F, A, B) | ((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)))))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[13])).
% 0.19/0.40 tff(15,plain,
% 0.19/0.40 (![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))))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(16,plain,
% 0.19/0.40 (^[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)))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(17,plain,
% 0.19/0.40 (![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))))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[16])).
% 0.19/0.40 tff(18,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')).
% 0.19/0.40 tff(19,plain,
% 0.19/0.40 (![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))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.19/0.40 tff(20,plain,
% 0.19/0.40 (![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))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.19/0.40 tff(21,plain,(
% 0.19/0.40 ![F: $i, A: $i, B: $i] : (((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) & (maps(F, A, B) | ((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))))))))),
% 0.19/0.40 inference(skolemize,[status(sab)],[20])).
% 0.19/0.40 tff(22,plain,
% 0.19/0.40 (![F: $i, A: $i, B: $i] : (((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) & (maps(F, A, B) | (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)))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[21, 14])).
% 0.19/0.40 tff(23,plain,
% 0.19/0.40 (![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~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))))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[22, 12])).
% 0.19/0.40 tff(24,plain,
% 0.19/0.40 (![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~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))))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[23, 10])).
% 0.19/0.40 tff(25,plain,
% 0.19/0.40 (![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[24, 5])).
% 0.19/0.40 tff(26,plain,
% 0.19/0.40 (((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(F!43, A!41, B!40)) | (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!43), B!40)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!40, F!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)))))))) | (~(maps(F!43, A!41, B!40) | (~((~member(tptp_fun_X_4(B!40, A!41, F!43), A!41)) | (~![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X_4(B!40, A!41, F!43), Y)))))) | (~((~member(tptp_fun_Y2_5(B!40, A!41, F!43), B!40)) | (~member(tptp_fun_Y1_6(B!40, A!41, F!43), B!40)) | (~member(tptp_fun_X_7(B!40, A!41, F!43), A!41)) | (~apply(F!43, tptp_fun_X_7(B!40, A!41, F!43), tptp_fun_Y2_5(B!40, A!41, F!43))) | (~apply(F!43, tptp_fun_X_7(B!40, A!41, F!43), tptp_fun_Y1_6(B!40, A!41, F!43))) | (tptp_fun_Y1_6(B!40, A!41, F!43) = tptp_fun_Y2_5(B!40, A!41, F!43))))))))) <=> ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(F!43, A!41, B!40)) | (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!43), B!40)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!40, F!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)))))))) | (~(maps(F!43, A!41, B!40) | (~((~member(tptp_fun_X_4(B!40, A!41, F!43), A!41)) | (~![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X_4(B!40, A!41, F!43), Y)))))) | (~((~member(tptp_fun_Y2_5(B!40, A!41, F!43), B!40)) | (~member(tptp_fun_Y1_6(B!40, A!41, F!43), B!40)) | (~member(tptp_fun_X_7(B!40, A!41, F!43), A!41)) | (~apply(F!43, tptp_fun_X_7(B!40, A!41, F!43), tptp_fun_Y2_5(B!40, A!41, F!43))) | (~apply(F!43, tptp_fun_X_7(B!40, A!41, F!43), tptp_fun_Y1_6(B!40, A!41, F!43))) | (tptp_fun_Y1_6(B!40, A!41, F!43) = tptp_fun_Y2_5(B!40, A!41, F!43)))))))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(27,plain,
% 0.19/0.41 ((~((~((~maps(F!43, A!41, B!40)) | (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!43), B!40)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!40, F!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)) | (~member(Y2, B!40)))))))) | (~(maps(F!43, A!41, B!40) | (~((tptp_fun_Y1_6(B!40, A!41, F!43) = tptp_fun_Y2_5(B!40, A!41, F!43)) | (~apply(F!43, tptp_fun_X_7(B!40, A!41, F!43), tptp_fun_Y1_6(B!40, A!41, F!43))) | (~apply(F!43, tptp_fun_X_7(B!40, A!41, F!43), tptp_fun_Y2_5(B!40, A!41, F!43))) | (~member(tptp_fun_X_7(B!40, A!41, F!43), A!41)) | (~member(tptp_fun_Y1_6(B!40, A!41, F!43), B!40)) | (~member(tptp_fun_Y2_5(B!40, A!41, F!43), B!40)))) | (~((~member(tptp_fun_X_4(B!40, A!41, F!43), A!41)) | (~![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X_4(B!40, A!41, F!43), Y)))))))))) <=> (~((~((~maps(F!43, A!41, B!40)) | (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!43), B!40)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!40, F!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)))))))) | (~(maps(F!43, A!41, B!40) | (~((~member(tptp_fun_X_4(B!40, A!41, F!43), A!41)) | (~![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X_4(B!40, A!41, F!43), Y)))))) | (~((~member(tptp_fun_Y2_5(B!40, A!41, F!43), B!40)) | (~member(tptp_fun_Y1_6(B!40, A!41, F!43), B!40)) | (~member(tptp_fun_X_7(B!40, A!41, F!43), A!41)) | (~apply(F!43, tptp_fun_X_7(B!40, A!41, F!43), tptp_fun_Y2_5(B!40, A!41, F!43))) | (~apply(F!43, tptp_fun_X_7(B!40, A!41, F!43), tptp_fun_Y1_6(B!40, A!41, F!43))) | (tptp_fun_Y1_6(B!40, A!41, F!43) = tptp_fun_Y2_5(B!40, A!41, F!43))))))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(28,plain,
% 0.19/0.41 (((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(F!43, A!41, B!40)) | (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!43), B!40)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!40, F!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)) | (~member(Y2, B!40)))))))) | (~(maps(F!43, A!41, B!40) | (~((tptp_fun_Y1_6(B!40, A!41, F!43) = tptp_fun_Y2_5(B!40, A!41, F!43)) | (~apply(F!43, tptp_fun_X_7(B!40, A!41, F!43), tptp_fun_Y1_6(B!40, A!41, F!43))) | (~apply(F!43, tptp_fun_X_7(B!40, A!41, F!43), tptp_fun_Y2_5(B!40, A!41, F!43))) | (~member(tptp_fun_X_7(B!40, A!41, F!43), A!41)) | (~member(tptp_fun_Y1_6(B!40, A!41, F!43), B!40)) | (~member(tptp_fun_Y2_5(B!40, A!41, F!43), B!40)))) | (~((~member(tptp_fun_X_4(B!40, A!41, F!43), A!41)) | (~![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X_4(B!40, A!41, F!43), Y))))))))))) <=> ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(F!43, A!41, B!40)) | (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!43), B!40)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!40, F!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)))))))) | (~(maps(F!43, A!41, B!40) | (~((~member(tptp_fun_X_4(B!40, A!41, F!43), A!41)) | (~![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X_4(B!40, A!41, F!43), Y)))))) | (~((~member(tptp_fun_Y2_5(B!40, A!41, F!43), B!40)) | (~member(tptp_fun_Y1_6(B!40, A!41, F!43), B!40)) | (~member(tptp_fun_X_7(B!40, A!41, F!43), A!41)) | (~apply(F!43, tptp_fun_X_7(B!40, A!41, F!43), tptp_fun_Y2_5(B!40, A!41, F!43))) | (~apply(F!43, tptp_fun_X_7(B!40, A!41, F!43), tptp_fun_Y1_6(B!40, A!41, F!43))) | (tptp_fun_Y1_6(B!40, A!41, F!43) = tptp_fun_Y2_5(B!40, A!41, F!43)))))))))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[27])).
% 0.19/0.41 tff(29,plain,
% 0.19/0.41 (((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(F!43, A!41, B!40)) | (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!43), B!40)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!40, F!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)) | (~member(Y2, B!40)))))))) | (~(maps(F!43, A!41, B!40) | (~((tptp_fun_Y1_6(B!40, A!41, F!43) = tptp_fun_Y2_5(B!40, A!41, F!43)) | (~apply(F!43, tptp_fun_X_7(B!40, A!41, F!43), tptp_fun_Y1_6(B!40, A!41, F!43))) | (~apply(F!43, tptp_fun_X_7(B!40, A!41, F!43), tptp_fun_Y2_5(B!40, A!41, F!43))) | (~member(tptp_fun_X_7(B!40, A!41, F!43), A!41)) | (~member(tptp_fun_Y1_6(B!40, A!41, F!43), B!40)) | (~member(tptp_fun_Y2_5(B!40, A!41, F!43), B!40)))) | (~((~member(tptp_fun_X_4(B!40, A!41, F!43), A!41)) | (~![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X_4(B!40, A!41, F!43), Y))))))))))) <=> ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(F!43, A!41, B!40)) | (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!43), B!40)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!40, F!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)))))))) | (~(maps(F!43, A!41, B!40) | (~((~member(tptp_fun_X_4(B!40, A!41, F!43), A!41)) | (~![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X_4(B!40, A!41, F!43), Y)))))) | (~((~member(tptp_fun_Y2_5(B!40, A!41, F!43), B!40)) | (~member(tptp_fun_Y1_6(B!40, A!41, F!43), B!40)) | (~member(tptp_fun_X_7(B!40, A!41, F!43), A!41)) | (~apply(F!43, tptp_fun_X_7(B!40, A!41, F!43), tptp_fun_Y2_5(B!40, A!41, F!43))) | (~apply(F!43, tptp_fun_X_7(B!40, A!41, F!43), tptp_fun_Y1_6(B!40, A!41, F!43))) | (tptp_fun_Y1_6(B!40, A!41, F!43) = tptp_fun_Y2_5(B!40, A!41, F!43)))))))))),
% 0.19/0.41 inference(transitivity,[status(thm)],[28, 26])).
% 0.19/0.41 tff(30,plain,
% 0.19/0.41 ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(F!43, A!41, B!40)) | (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!43), B!40)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!40, F!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)) | (~member(Y2, B!40)))))))) | (~(maps(F!43, A!41, B!40) | (~((tptp_fun_Y1_6(B!40, A!41, F!43) = tptp_fun_Y2_5(B!40, A!41, F!43)) | (~apply(F!43, tptp_fun_X_7(B!40, A!41, F!43), tptp_fun_Y1_6(B!40, A!41, F!43))) | (~apply(F!43, tptp_fun_X_7(B!40, A!41, F!43), tptp_fun_Y2_5(B!40, A!41, F!43))) | (~member(tptp_fun_X_7(B!40, A!41, F!43), A!41)) | (~member(tptp_fun_Y1_6(B!40, A!41, F!43), B!40)) | (~member(tptp_fun_Y2_5(B!40, A!41, F!43), B!40)))) | (~((~member(tptp_fun_X_4(B!40, A!41, F!43), A!41)) | (~![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X_4(B!40, A!41, F!43), Y))))))))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(31,plain,
% 0.19/0.41 ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(F!43, A!41, B!40)) | (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!43), B!40)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!40, F!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)))))))) | (~(maps(F!43, A!41, B!40) | (~((~member(tptp_fun_X_4(B!40, A!41, F!43), A!41)) | (~![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X_4(B!40, A!41, F!43), Y)))))) | (~((~member(tptp_fun_Y2_5(B!40, A!41, F!43), B!40)) | (~member(tptp_fun_Y1_6(B!40, A!41, F!43), B!40)) | (~member(tptp_fun_X_7(B!40, A!41, F!43), A!41)) | (~apply(F!43, tptp_fun_X_7(B!40, A!41, F!43), tptp_fun_Y2_5(B!40, A!41, F!43))) | (~apply(F!43, tptp_fun_X_7(B!40, A!41, F!43), tptp_fun_Y1_6(B!40, A!41, F!43))) | (tptp_fun_Y1_6(B!40, A!41, F!43) = tptp_fun_Y2_5(B!40, A!41, F!43))))))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.19/0.41 tff(32,plain,
% 0.19/0.41 (~((~((~maps(F!43, A!41, B!40)) | (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!43), B!40)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!40, F!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)))))))) | (~(maps(F!43, A!41, B!40) | (~((~member(tptp_fun_X_4(B!40, A!41, F!43), A!41)) | (~![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X_4(B!40, A!41, F!43), Y)))))) | (~((~member(tptp_fun_Y2_5(B!40, A!41, F!43), B!40)) | (~member(tptp_fun_Y1_6(B!40, A!41, F!43), B!40)) | (~member(tptp_fun_X_7(B!40, A!41, F!43), A!41)) | (~apply(F!43, tptp_fun_X_7(B!40, A!41, F!43), tptp_fun_Y2_5(B!40, A!41, F!43))) | (~apply(F!43, tptp_fun_X_7(B!40, A!41, F!43), tptp_fun_Y1_6(B!40, A!41, F!43))) | (tptp_fun_Y1_6(B!40, A!41, F!43) = tptp_fun_Y2_5(B!40, A!41, F!43)))))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[31, 25])).
% 0.19/0.42 tff(33,plain,
% 0.19/0.42 (((~((~maps(F!43, A!41, B!40)) | (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!43), B!40)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!40, F!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)))))))) | (~(maps(F!43, A!41, B!40) | (~((~member(tptp_fun_X_4(B!40, A!41, F!43), A!41)) | (~![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X_4(B!40, A!41, F!43), Y)))))) | (~((~member(tptp_fun_Y2_5(B!40, A!41, F!43), B!40)) | (~member(tptp_fun_Y1_6(B!40, A!41, F!43), B!40)) | (~member(tptp_fun_X_7(B!40, A!41, F!43), A!41)) | (~apply(F!43, tptp_fun_X_7(B!40, A!41, F!43), tptp_fun_Y2_5(B!40, A!41, F!43))) | (~apply(F!43, tptp_fun_X_7(B!40, A!41, F!43), tptp_fun_Y1_6(B!40, A!41, F!43))) | (tptp_fun_Y1_6(B!40, A!41, F!43) = tptp_fun_Y2_5(B!40, A!41, F!43))))))) | ((~maps(F!43, A!41, B!40)) | (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!43), B!40)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!40, F!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)))))))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(34,plain,
% 0.19/0.42 ((~maps(F!43, A!41, B!40)) | (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!43), B!40)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!40, F!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40))))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[33, 32])).
% 0.19/0.42 tff(35,plain,
% 0.19/0.42 ((~![F: $i, G: $i, A: $i, B: $i, C: $i] : ((~(maps(F, A, B) & maps(G, B, C))) | maps(compose_function(G, F, A, B, C), A, C))) <=> (~![F: $i, G: $i, A: $i, B: $i, C: $i] : ((~(maps(F, A, B) & maps(G, B, C))) | maps(compose_function(G, F, A, B, C), A, C)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(36,plain,
% 0.19/0.42 ((~![F: $i, G: $i, A: $i, B: $i, C: $i] : ((maps(F, A, B) & maps(G, B, C)) => maps(compose_function(G, F, A, B, C), A, C))) <=> (~![F: $i, G: $i, A: $i, B: $i, C: $i] : ((~(maps(F, A, B) & maps(G, B, C))) | maps(compose_function(G, F, A, B, C), A, C)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(37,axiom,(~![F: $i, G: $i, A: $i, B: $i, C: $i] : ((maps(F, A, B) & maps(G, B, C)) => maps(compose_function(G, F, A, B, C), A, C))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thII01')).
% 0.19/0.42 tff(38,plain,
% 0.19/0.42 (~![F: $i, G: $i, A: $i, B: $i, C: $i] : ((~(maps(F, A, B) & maps(G, B, C))) | maps(compose_function(G, F, A, B, C), A, C))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.19/0.42 tff(39,plain,
% 0.19/0.42 (~![F: $i, G: $i, A: $i, B: $i, C: $i] : ((~(maps(F, A, B) & maps(G, B, C))) | maps(compose_function(G, F, A, B, C), A, C))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[38, 35])).
% 0.19/0.42 tff(40,plain,
% 0.19/0.42 (~![F: $i, G: $i, A: $i, B: $i, C: $i] : ((~(maps(F, A, B) & maps(G, B, C))) | maps(compose_function(G, F, A, B, C), A, C))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[39, 35])).
% 0.19/0.42 tff(41,plain,
% 0.19/0.42 (~![F: $i, G: $i, A: $i, B: $i, C: $i] : ((~(maps(F, A, B) & maps(G, B, C))) | maps(compose_function(G, F, A, B, C), A, C))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[40, 35])).
% 0.19/0.42 tff(42,plain,(
% 0.19/0.42 ~((~(maps(F!43, A!41, B!40) & maps(G!42, B!40, C!39))) | maps(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39))),
% 0.19/0.42 inference(skolemize,[status(sab)],[41])).
% 0.19/0.42 tff(43,plain,
% 0.19/0.42 (maps(F!43, A!41, B!40) & maps(G!42, B!40, C!39)),
% 0.19/0.42 inference(or_elim,[status(thm)],[42])).
% 0.19/0.42 tff(44,plain,
% 0.19/0.42 (maps(F!43, A!41, B!40)),
% 0.19/0.42 inference(and_elim,[status(thm)],[43])).
% 0.19/0.42 tff(45,plain,
% 0.19/0.42 ((~((~maps(F!43, A!41, B!40)) | (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!43), B!40)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!40, F!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)))))))) | (~maps(F!43, A!41, B!40)) | (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!43), B!40)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!40, F!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40))))))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(46,plain,
% 0.19/0.42 ((~((~maps(F!43, A!41, B!40)) | (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!43), B!40)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!40, F!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!43, X, Y1)) | (~apply(F!43, 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!43), B!40)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!40, F!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40))))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[45, 44])).
% 0.19/0.42 tff(47,plain,
% 0.19/0.42 (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!43), B!40)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!40, F!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[46, 34])).
% 0.19/0.42 tff(48,plain,
% 0.19/0.42 (((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!43), B!40)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!40, F!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!43, X, Y1)) | (~apply(F!43, 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!43), B!40)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!40, F!43))))))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(49,plain,
% 0.19/0.42 (![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!43), B!40)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!40, F!43))))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[48, 47])).
% 0.19/0.42 tff(50,plain,
% 0.19/0.42 (((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!43), B!40)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!40, F!43))))))) | ((~member(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~((~member(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), B!40)) | (~apply(F!43, tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43))))))) <=> ((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!43), B!40)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!40, F!43))))))) | (~member(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~((~member(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), B!40)) | (~apply(F!43, tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43))))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(51,plain,
% 0.19/0.42 ((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!43), B!40)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!40, F!43))))))) | ((~member(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~((~member(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), B!40)) | (~apply(F!43, tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43))))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(52,plain,
% 0.19/0.42 ((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!43), B!40)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!40, F!43))))))) | (~member(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~((~member(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), B!40)) | (~apply(F!43, tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43)))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.19/0.42 tff(53,plain,
% 0.19/0.42 (~((~member(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), B!40)) | (~apply(F!43, tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[52, 49, 3])).
% 0.19/0.42 tff(54,plain,
% 0.19/0.42 (((~member(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), B!40)) | (~apply(F!43, tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43)))) | member(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), B!40)),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(55,plain,
% 0.19/0.42 (member(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), B!40)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[54, 53])).
% 0.19/0.42 tff(56,plain,
% 0.19/0.42 (((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(G!42, B!40, C!39)) | (~((~![X: $i] : ((~member(X, B!40)) | (~((~member(tptp_fun_Y_3(X, C!39, G!42), C!39)) | (~apply(G!42, X, tptp_fun_Y_3(X, C!39, G!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, C!39)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!40)) | (~member(Y1, C!39)))))))) | (~(maps(G!42, B!40, C!39) | (~((~member(tptp_fun_X_4(C!39, B!40, G!42), B!40)) | (~![Y: $i] : ((~member(Y, C!39)) | (~apply(G!42, tptp_fun_X_4(C!39, B!40, G!42), Y)))))) | (~((~member(tptp_fun_Y2_5(C!39, B!40, G!42), C!39)) | (~member(tptp_fun_Y1_6(C!39, B!40, G!42), C!39)) | (~member(tptp_fun_X_7(C!39, B!40, G!42), B!40)) | (~apply(G!42, tptp_fun_X_7(C!39, B!40, G!42), tptp_fun_Y2_5(C!39, B!40, G!42))) | (~apply(G!42, tptp_fun_X_7(C!39, B!40, G!42), tptp_fun_Y1_6(C!39, B!40, G!42))) | (tptp_fun_Y1_6(C!39, B!40, G!42) = tptp_fun_Y2_5(C!39, B!40, G!42))))))))) <=> ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(G!42, B!40, C!39)) | (~((~![X: $i] : ((~member(X, B!40)) | (~((~member(tptp_fun_Y_3(X, C!39, G!42), C!39)) | (~apply(G!42, X, tptp_fun_Y_3(X, C!39, G!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, C!39)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!40)) | (~member(Y1, C!39)))))))) | (~(maps(G!42, B!40, C!39) | (~((~member(tptp_fun_X_4(C!39, B!40, G!42), B!40)) | (~![Y: $i] : ((~member(Y, C!39)) | (~apply(G!42, tptp_fun_X_4(C!39, B!40, G!42), Y)))))) | (~((~member(tptp_fun_Y2_5(C!39, B!40, G!42), C!39)) | (~member(tptp_fun_Y1_6(C!39, B!40, G!42), C!39)) | (~member(tptp_fun_X_7(C!39, B!40, G!42), B!40)) | (~apply(G!42, tptp_fun_X_7(C!39, B!40, G!42), tptp_fun_Y2_5(C!39, B!40, G!42))) | (~apply(G!42, tptp_fun_X_7(C!39, B!40, G!42), tptp_fun_Y1_6(C!39, B!40, G!42))) | (tptp_fun_Y1_6(C!39, B!40, G!42) = tptp_fun_Y2_5(C!39, B!40, G!42)))))))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(57,plain,
% 0.19/0.43 ((~((~((~maps(G!42, B!40, C!39)) | (~((~![X: $i] : ((~member(X, B!40)) | (~((~member(tptp_fun_Y_3(X, C!39, G!42), C!39)) | (~apply(G!42, X, tptp_fun_Y_3(X, C!39, G!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!40)) | (~member(Y1, C!39)) | (~member(Y2, C!39)))))))) | (~(maps(G!42, B!40, C!39) | (~((tptp_fun_Y1_6(C!39, B!40, G!42) = tptp_fun_Y2_5(C!39, B!40, G!42)) | (~apply(G!42, tptp_fun_X_7(C!39, B!40, G!42), tptp_fun_Y1_6(C!39, B!40, G!42))) | (~apply(G!42, tptp_fun_X_7(C!39, B!40, G!42), tptp_fun_Y2_5(C!39, B!40, G!42))) | (~member(tptp_fun_X_7(C!39, B!40, G!42), B!40)) | (~member(tptp_fun_Y1_6(C!39, B!40, G!42), C!39)) | (~member(tptp_fun_Y2_5(C!39, B!40, G!42), C!39)))) | (~((~member(tptp_fun_X_4(C!39, B!40, G!42), B!40)) | (~![Y: $i] : ((~member(Y, C!39)) | (~apply(G!42, tptp_fun_X_4(C!39, B!40, G!42), Y)))))))))) <=> (~((~((~maps(G!42, B!40, C!39)) | (~((~![X: $i] : ((~member(X, B!40)) | (~((~member(tptp_fun_Y_3(X, C!39, G!42), C!39)) | (~apply(G!42, X, tptp_fun_Y_3(X, C!39, G!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, C!39)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!40)) | (~member(Y1, C!39)))))))) | (~(maps(G!42, B!40, C!39) | (~((~member(tptp_fun_X_4(C!39, B!40, G!42), B!40)) | (~![Y: $i] : ((~member(Y, C!39)) | (~apply(G!42, tptp_fun_X_4(C!39, B!40, G!42), Y)))))) | (~((~member(tptp_fun_Y2_5(C!39, B!40, G!42), C!39)) | (~member(tptp_fun_Y1_6(C!39, B!40, G!42), C!39)) | (~member(tptp_fun_X_7(C!39, B!40, G!42), B!40)) | (~apply(G!42, tptp_fun_X_7(C!39, B!40, G!42), tptp_fun_Y2_5(C!39, B!40, G!42))) | (~apply(G!42, tptp_fun_X_7(C!39, B!40, G!42), tptp_fun_Y1_6(C!39, B!40, G!42))) | (tptp_fun_Y1_6(C!39, B!40, G!42) = tptp_fun_Y2_5(C!39, B!40, G!42))))))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(58,plain,
% 0.19/0.43 (((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(G!42, B!40, C!39)) | (~((~![X: $i] : ((~member(X, B!40)) | (~((~member(tptp_fun_Y_3(X, C!39, G!42), C!39)) | (~apply(G!42, X, tptp_fun_Y_3(X, C!39, G!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!40)) | (~member(Y1, C!39)) | (~member(Y2, C!39)))))))) | (~(maps(G!42, B!40, C!39) | (~((tptp_fun_Y1_6(C!39, B!40, G!42) = tptp_fun_Y2_5(C!39, B!40, G!42)) | (~apply(G!42, tptp_fun_X_7(C!39, B!40, G!42), tptp_fun_Y1_6(C!39, B!40, G!42))) | (~apply(G!42, tptp_fun_X_7(C!39, B!40, G!42), tptp_fun_Y2_5(C!39, B!40, G!42))) | (~member(tptp_fun_X_7(C!39, B!40, G!42), B!40)) | (~member(tptp_fun_Y1_6(C!39, B!40, G!42), C!39)) | (~member(tptp_fun_Y2_5(C!39, B!40, G!42), C!39)))) | (~((~member(tptp_fun_X_4(C!39, B!40, G!42), B!40)) | (~![Y: $i] : ((~member(Y, C!39)) | (~apply(G!42, tptp_fun_X_4(C!39, B!40, G!42), Y))))))))))) <=> ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(G!42, B!40, C!39)) | (~((~![X: $i] : ((~member(X, B!40)) | (~((~member(tptp_fun_Y_3(X, C!39, G!42), C!39)) | (~apply(G!42, X, tptp_fun_Y_3(X, C!39, G!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, C!39)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!40)) | (~member(Y1, C!39)))))))) | (~(maps(G!42, B!40, C!39) | (~((~member(tptp_fun_X_4(C!39, B!40, G!42), B!40)) | (~![Y: $i] : ((~member(Y, C!39)) | (~apply(G!42, tptp_fun_X_4(C!39, B!40, G!42), Y)))))) | (~((~member(tptp_fun_Y2_5(C!39, B!40, G!42), C!39)) | (~member(tptp_fun_Y1_6(C!39, B!40, G!42), C!39)) | (~member(tptp_fun_X_7(C!39, B!40, G!42), B!40)) | (~apply(G!42, tptp_fun_X_7(C!39, B!40, G!42), tptp_fun_Y2_5(C!39, B!40, G!42))) | (~apply(G!42, tptp_fun_X_7(C!39, B!40, G!42), tptp_fun_Y1_6(C!39, B!40, G!42))) | (tptp_fun_Y1_6(C!39, B!40, G!42) = tptp_fun_Y2_5(C!39, B!40, G!42)))))))))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[57])).
% 0.19/0.43 tff(59,plain,
% 0.19/0.43 (((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(G!42, B!40, C!39)) | (~((~![X: $i] : ((~member(X, B!40)) | (~((~member(tptp_fun_Y_3(X, C!39, G!42), C!39)) | (~apply(G!42, X, tptp_fun_Y_3(X, C!39, G!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!40)) | (~member(Y1, C!39)) | (~member(Y2, C!39)))))))) | (~(maps(G!42, B!40, C!39) | (~((tptp_fun_Y1_6(C!39, B!40, G!42) = tptp_fun_Y2_5(C!39, B!40, G!42)) | (~apply(G!42, tptp_fun_X_7(C!39, B!40, G!42), tptp_fun_Y1_6(C!39, B!40, G!42))) | (~apply(G!42, tptp_fun_X_7(C!39, B!40, G!42), tptp_fun_Y2_5(C!39, B!40, G!42))) | (~member(tptp_fun_X_7(C!39, B!40, G!42), B!40)) | (~member(tptp_fun_Y1_6(C!39, B!40, G!42), C!39)) | (~member(tptp_fun_Y2_5(C!39, B!40, G!42), C!39)))) | (~((~member(tptp_fun_X_4(C!39, B!40, G!42), B!40)) | (~![Y: $i] : ((~member(Y, C!39)) | (~apply(G!42, tptp_fun_X_4(C!39, B!40, G!42), Y))))))))))) <=> ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(G!42, B!40, C!39)) | (~((~![X: $i] : ((~member(X, B!40)) | (~((~member(tptp_fun_Y_3(X, C!39, G!42), C!39)) | (~apply(G!42, X, tptp_fun_Y_3(X, C!39, G!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, C!39)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!40)) | (~member(Y1, C!39)))))))) | (~(maps(G!42, B!40, C!39) | (~((~member(tptp_fun_X_4(C!39, B!40, G!42), B!40)) | (~![Y: $i] : ((~member(Y, C!39)) | (~apply(G!42, tptp_fun_X_4(C!39, B!40, G!42), Y)))))) | (~((~member(tptp_fun_Y2_5(C!39, B!40, G!42), C!39)) | (~member(tptp_fun_Y1_6(C!39, B!40, G!42), C!39)) | (~member(tptp_fun_X_7(C!39, B!40, G!42), B!40)) | (~apply(G!42, tptp_fun_X_7(C!39, B!40, G!42), tptp_fun_Y2_5(C!39, B!40, G!42))) | (~apply(G!42, tptp_fun_X_7(C!39, B!40, G!42), tptp_fun_Y1_6(C!39, B!40, G!42))) | (tptp_fun_Y1_6(C!39, B!40, G!42) = tptp_fun_Y2_5(C!39, B!40, G!42)))))))))),
% 0.19/0.44 inference(transitivity,[status(thm)],[58, 56])).
% 0.19/0.44 tff(60,plain,
% 0.19/0.44 ((~![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!42, B!40, C!39)) | (~((~![X: $i] : ((~member(X, B!40)) | (~((~member(tptp_fun_Y_3(X, C!39, G!42), C!39)) | (~apply(G!42, X, tptp_fun_Y_3(X, C!39, G!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!40)) | (~member(Y1, C!39)) | (~member(Y2, C!39)))))))) | (~(maps(G!42, B!40, C!39) | (~((tptp_fun_Y1_6(C!39, B!40, G!42) = tptp_fun_Y2_5(C!39, B!40, G!42)) | (~apply(G!42, tptp_fun_X_7(C!39, B!40, G!42), tptp_fun_Y1_6(C!39, B!40, G!42))) | (~apply(G!42, tptp_fun_X_7(C!39, B!40, G!42), tptp_fun_Y2_5(C!39, B!40, G!42))) | (~member(tptp_fun_X_7(C!39, B!40, G!42), B!40)) | (~member(tptp_fun_Y1_6(C!39, B!40, G!42), C!39)) | (~member(tptp_fun_Y2_5(C!39, B!40, G!42), C!39)))) | (~((~member(tptp_fun_X_4(C!39, B!40, G!42), B!40)) | (~![Y: $i] : ((~member(Y, C!39)) | (~apply(G!42, tptp_fun_X_4(C!39, B!40, G!42), Y))))))))))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(61,plain,
% 0.19/0.44 ((~![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!42, B!40, C!39)) | (~((~![X: $i] : ((~member(X, B!40)) | (~((~member(tptp_fun_Y_3(X, C!39, G!42), C!39)) | (~apply(G!42, X, tptp_fun_Y_3(X, C!39, G!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, C!39)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!40)) | (~member(Y1, C!39)))))))) | (~(maps(G!42, B!40, C!39) | (~((~member(tptp_fun_X_4(C!39, B!40, G!42), B!40)) | (~![Y: $i] : ((~member(Y, C!39)) | (~apply(G!42, tptp_fun_X_4(C!39, B!40, G!42), Y)))))) | (~((~member(tptp_fun_Y2_5(C!39, B!40, G!42), C!39)) | (~member(tptp_fun_Y1_6(C!39, B!40, G!42), C!39)) | (~member(tptp_fun_X_7(C!39, B!40, G!42), B!40)) | (~apply(G!42, tptp_fun_X_7(C!39, B!40, G!42), tptp_fun_Y2_5(C!39, B!40, G!42))) | (~apply(G!42, tptp_fun_X_7(C!39, B!40, G!42), tptp_fun_Y1_6(C!39, B!40, G!42))) | (tptp_fun_Y1_6(C!39, B!40, G!42) = tptp_fun_Y2_5(C!39, B!40, G!42))))))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.19/0.44 tff(62,plain,
% 0.19/0.44 (~((~((~maps(G!42, B!40, C!39)) | (~((~![X: $i] : ((~member(X, B!40)) | (~((~member(tptp_fun_Y_3(X, C!39, G!42), C!39)) | (~apply(G!42, X, tptp_fun_Y_3(X, C!39, G!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, C!39)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!40)) | (~member(Y1, C!39)))))))) | (~(maps(G!42, B!40, C!39) | (~((~member(tptp_fun_X_4(C!39, B!40, G!42), B!40)) | (~![Y: $i] : ((~member(Y, C!39)) | (~apply(G!42, tptp_fun_X_4(C!39, B!40, G!42), Y)))))) | (~((~member(tptp_fun_Y2_5(C!39, B!40, G!42), C!39)) | (~member(tptp_fun_Y1_6(C!39, B!40, G!42), C!39)) | (~member(tptp_fun_X_7(C!39, B!40, G!42), B!40)) | (~apply(G!42, tptp_fun_X_7(C!39, B!40, G!42), tptp_fun_Y2_5(C!39, B!40, G!42))) | (~apply(G!42, tptp_fun_X_7(C!39, B!40, G!42), tptp_fun_Y1_6(C!39, B!40, G!42))) | (tptp_fun_Y1_6(C!39, B!40, G!42) = tptp_fun_Y2_5(C!39, B!40, G!42)))))))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[61, 25])).
% 0.19/0.44 tff(63,plain,
% 0.19/0.44 (((~((~maps(G!42, B!40, C!39)) | (~((~![X: $i] : ((~member(X, B!40)) | (~((~member(tptp_fun_Y_3(X, C!39, G!42), C!39)) | (~apply(G!42, X, tptp_fun_Y_3(X, C!39, G!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, C!39)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!40)) | (~member(Y1, C!39)))))))) | (~(maps(G!42, B!40, C!39) | (~((~member(tptp_fun_X_4(C!39, B!40, G!42), B!40)) | (~![Y: $i] : ((~member(Y, C!39)) | (~apply(G!42, tptp_fun_X_4(C!39, B!40, G!42), Y)))))) | (~((~member(tptp_fun_Y2_5(C!39, B!40, G!42), C!39)) | (~member(tptp_fun_Y1_6(C!39, B!40, G!42), C!39)) | (~member(tptp_fun_X_7(C!39, B!40, G!42), B!40)) | (~apply(G!42, tptp_fun_X_7(C!39, B!40, G!42), tptp_fun_Y2_5(C!39, B!40, G!42))) | (~apply(G!42, tptp_fun_X_7(C!39, B!40, G!42), tptp_fun_Y1_6(C!39, B!40, G!42))) | (tptp_fun_Y1_6(C!39, B!40, G!42) = tptp_fun_Y2_5(C!39, B!40, G!42))))))) | ((~maps(G!42, B!40, C!39)) | (~((~![X: $i] : ((~member(X, B!40)) | (~((~member(tptp_fun_Y_3(X, C!39, G!42), C!39)) | (~apply(G!42, X, tptp_fun_Y_3(X, C!39, G!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, C!39)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!40)) | (~member(Y1, C!39)))))))),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(64,plain,
% 0.19/0.44 ((~maps(G!42, B!40, C!39)) | (~((~![X: $i] : ((~member(X, B!40)) | (~((~member(tptp_fun_Y_3(X, C!39, G!42), C!39)) | (~apply(G!42, X, tptp_fun_Y_3(X, C!39, G!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, C!39)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!40)) | (~member(Y1, C!39))))))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[63, 62])).
% 0.19/0.44 tff(65,plain,
% 0.19/0.44 (maps(G!42, B!40, C!39)),
% 0.19/0.44 inference(and_elim,[status(thm)],[43])).
% 0.19/0.44 tff(66,plain,
% 0.19/0.44 ((~((~maps(G!42, B!40, C!39)) | (~((~![X: $i] : ((~member(X, B!40)) | (~((~member(tptp_fun_Y_3(X, C!39, G!42), C!39)) | (~apply(G!42, X, tptp_fun_Y_3(X, C!39, G!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, C!39)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!40)) | (~member(Y1, C!39)))))))) | (~maps(G!42, B!40, C!39)) | (~((~![X: $i] : ((~member(X, B!40)) | (~((~member(tptp_fun_Y_3(X, C!39, G!42), C!39)) | (~apply(G!42, X, tptp_fun_Y_3(X, C!39, G!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, C!39)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!40)) | (~member(Y1, C!39))))))),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(67,plain,
% 0.19/0.44 ((~((~maps(G!42, B!40, C!39)) | (~((~![X: $i] : ((~member(X, B!40)) | (~((~member(tptp_fun_Y_3(X, C!39, G!42), C!39)) | (~apply(G!42, X, tptp_fun_Y_3(X, C!39, G!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, C!39)) | (~apply(G!42, X, Y1)) | (~apply(G!42, 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!42), C!39)) | (~apply(G!42, X, tptp_fun_Y_3(X, C!39, G!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, C!39)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!40)) | (~member(Y1, C!39))))))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[66, 65])).
% 0.19/0.44 tff(68,plain,
% 0.19/0.44 (~((~![X: $i] : ((~member(X, B!40)) | (~((~member(tptp_fun_Y_3(X, C!39, G!42), C!39)) | (~apply(G!42, X, tptp_fun_Y_3(X, C!39, G!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, C!39)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!40)) | (~member(Y1, C!39)))))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[67, 64])).
% 0.19/0.44 tff(69,plain,
% 0.19/0.44 (((~![X: $i] : ((~member(X, B!40)) | (~((~member(tptp_fun_Y_3(X, C!39, G!42), C!39)) | (~apply(G!42, X, tptp_fun_Y_3(X, C!39, G!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, C!39)) | (~apply(G!42, X, Y1)) | (~apply(G!42, 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!42), C!39)) | (~apply(G!42, X, tptp_fun_Y_3(X, C!39, G!42))))))),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(70,plain,
% 0.19/0.44 (![X: $i] : ((~member(X, B!40)) | (~((~member(tptp_fun_Y_3(X, C!39, G!42), C!39)) | (~apply(G!42, X, tptp_fun_Y_3(X, C!39, G!42))))))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[69, 68])).
% 0.19/0.44 tff(71,plain,
% 0.19/0.44 (((~![X: $i] : ((~member(X, B!40)) | (~((~member(tptp_fun_Y_3(X, C!39, G!42), C!39)) | (~apply(G!42, X, tptp_fun_Y_3(X, C!39, G!42))))))) | ((~member(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), B!40)) | (~((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42), C!39)) | (~apply(G!42, tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42))))))) <=> ((~![X: $i] : ((~member(X, B!40)) | (~((~member(tptp_fun_Y_3(X, C!39, G!42), C!39)) | (~apply(G!42, X, tptp_fun_Y_3(X, C!39, G!42))))))) | (~member(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), B!40)) | (~((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42), C!39)) | (~apply(G!42, tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42))))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(72,plain,
% 0.19/0.44 ((~![X: $i] : ((~member(X, B!40)) | (~((~member(tptp_fun_Y_3(X, C!39, G!42), C!39)) | (~apply(G!42, X, tptp_fun_Y_3(X, C!39, G!42))))))) | ((~member(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), B!40)) | (~((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42), C!39)) | (~apply(G!42, tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42))))))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(73,plain,
% 0.19/0.45 ((~![X: $i] : ((~member(X, B!40)) | (~((~member(tptp_fun_Y_3(X, C!39, G!42), C!39)) | (~apply(G!42, X, tptp_fun_Y_3(X, C!39, G!42))))))) | (~member(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), B!40)) | (~((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42), C!39)) | (~apply(G!42, tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42)))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.19/0.45 tff(74,plain,
% 0.19/0.45 (~((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42), C!39)) | (~apply(G!42, tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42))))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[73, 70, 55])).
% 0.19/0.45 tff(75,plain,
% 0.19/0.45 (((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42), C!39)) | (~apply(G!42, tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42)))) | member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42), C!39)),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(76,plain,
% 0.19/0.45 (member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42), C!39)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[75, 74])).
% 0.19/0.45 tff(77,plain,
% 0.19/0.45 (^[G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : refl(((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z)))))))) <=> ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z)))))))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(78,plain,
% 0.19/0.45 (![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z)))))))) <=> ![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[77])).
% 0.19/0.45 tff(79,plain,
% 0.19/0.45 (^[G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : rewrite(((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z)))))))) <=> ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z)))))))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(80,plain,
% 0.19/0.45 (![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z)))))))) <=> ![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[79])).
% 0.19/0.45 tff(81,plain,
% 0.19/0.45 (![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z)))))))) <=> ![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))),
% 0.19/0.45 inference(transitivity,[status(thm)],[80, 78])).
% 0.19/0.45 tff(82,plain,
% 0.19/0.45 (^[G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : trans(monotonicity(trans(monotonicity(rewrite((member(X, A) & member(Z, C)) <=> (~((~member(Z, C)) | (~member(X, A))))), ((~(member(X, A) & member(Z, C))) <=> (~(~((~member(Z, C)) | (~member(X, A))))))), rewrite((~(~((~member(Z, C)) | (~member(X, A))))) <=> ((~member(Z, C)) | (~member(X, A)))), ((~(member(X, A) & member(Z, C))) <=> ((~member(Z, C)) | (~member(X, A))))), trans(monotonicity(rewrite(((~apply(compose_function(G, F, A, B, C), X, Z)) | (member(tptp_fun_Y_8(Z, X, B, F, G), B) & apply(F, X, tptp_fun_Y_8(Z, X, B, F, G)) & apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z))) <=> ((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))), rewrite((apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y) & apply(G, Y, Z)))) <=> (apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))), ((((~apply(compose_function(G, F, A, B, C), X, Z)) | (member(tptp_fun_Y_8(Z, X, B, F, G), B) & apply(F, X, tptp_fun_Y_8(Z, X, B, F, G)) & apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z))) & (apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y) & apply(G, Y, Z))))) <=> (((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z))))) & (apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))), rewrite((((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z))))) & (apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))) <=> (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z)))))))), ((((~apply(compose_function(G, F, A, B, C), X, Z)) | (member(tptp_fun_Y_8(Z, X, B, F, G), B) & apply(F, X, tptp_fun_Y_8(Z, X, B, F, G)) & apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z))) & (apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y) & apply(G, Y, Z))))) <=> (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))), (((~(member(X, A) & member(Z, C))) | (((~apply(compose_function(G, F, A, B, C), X, Z)) | (member(tptp_fun_Y_8(Z, X, B, F, G), B) & apply(F, X, tptp_fun_Y_8(Z, X, B, F, G)) & apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z))) & (apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y) & apply(G, Y, Z)))))) <=> (((~member(Z, C)) | (~member(X, A))) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z)))))))))), rewrite((((~member(Z, C)) | (~member(X, A))) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z)))))))) <=> ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))), (((~(member(X, A) & member(Z, C))) | (((~apply(compose_function(G, F, A, B, C), X, Z)) | (member(tptp_fun_Y_8(Z, X, B, F, G), B) & apply(F, X, tptp_fun_Y_8(Z, X, B, F, G)) & apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z))) & (apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y) & apply(G, Y, Z)))))) <=> ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(83,plain,
% 0.19/0.45 (![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~(member(X, A) & member(Z, C))) | (((~apply(compose_function(G, F, A, B, C), X, Z)) | (member(tptp_fun_Y_8(Z, X, B, F, G), B) & apply(F, X, tptp_fun_Y_8(Z, X, B, F, G)) & apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z))) & (apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y) & apply(G, Y, Z)))))) <=> ![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[82])).
% 0.19/0.45 tff(84,plain,
% 0.19/0.45 (![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~(member(X, A) & member(Z, C))) | (apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : (member(Y, B) & apply(F, X, Y) & apply(G, Y, Z)))) <=> ![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~(member(X, A) & member(Z, C))) | (apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : (member(Y, B) & apply(F, X, Y) & apply(G, Y, Z))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(85,plain,
% 0.19/0.45 (^[G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : trans(monotonicity(rewrite((apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : ((member(Y, B) & apply(F, X, Y)) & apply(G, Y, Z))) <=> (apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : (member(Y, B) & apply(F, X, Y) & apply(G, Y, Z)))), (((member(X, A) & member(Z, C)) => (apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : ((member(Y, B) & apply(F, X, Y)) & apply(G, Y, Z)))) <=> ((member(X, A) & member(Z, C)) => (apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : (member(Y, B) & apply(F, X, Y) & apply(G, Y, Z)))))), rewrite(((member(X, A) & member(Z, C)) => (apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : (member(Y, B) & apply(F, X, Y) & apply(G, Y, Z)))) <=> ((~(member(X, A) & member(Z, C))) | (apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : (member(Y, B) & apply(F, X, Y) & apply(G, Y, Z))))), (((member(X, A) & member(Z, C)) => (apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : ((member(Y, B) & apply(F, X, Y)) & apply(G, Y, Z)))) <=> ((~(member(X, A) & member(Z, C))) | (apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : (member(Y, B) & apply(F, X, Y) & apply(G, Y, Z))))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(86,plain,
% 0.19/0.45 (![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((member(X, A) & member(Z, C)) => (apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : ((member(Y, B) & apply(F, X, Y)) & apply(G, Y, Z)))) <=> ![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~(member(X, A) & member(Z, C))) | (apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : (member(Y, B) & apply(F, X, Y) & apply(G, Y, Z))))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[85])).
% 0.19/0.45 tff(87,axiom,(![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((member(X, A) & member(Z, C)) => (apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : ((member(Y, B) & apply(F, X, Y)) & apply(G, Y, Z))))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+1.ax','compose_function')).
% 0.19/0.45 tff(88,plain,
% 0.19/0.45 (![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~(member(X, A) & member(Z, C))) | (apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : (member(Y, B) & apply(F, X, Y) & apply(G, Y, Z))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.19/0.45 tff(89,plain,
% 0.19/0.45 (![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~(member(X, A) & member(Z, C))) | (apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : (member(Y, B) & apply(F, X, Y) & apply(G, Y, Z))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[88, 84])).
% 0.19/0.45 tff(90,plain,(
% 0.19/0.45 ![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~(member(X, A) & member(Z, C))) | (((~apply(compose_function(G, F, A, B, C), X, Z)) | (member(tptp_fun_Y_8(Z, X, B, F, G), B) & apply(F, X, tptp_fun_Y_8(Z, X, B, F, G)) & apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z))) & (apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y) & apply(G, Y, Z))))))),
% 0.19/0.46 inference(skolemize,[status(sab)],[89])).
% 0.19/0.46 tff(91,plain,
% 0.19/0.46 (![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[90, 83])).
% 0.19/0.46 tff(92,plain,
% 0.19/0.46 (![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[91, 81])).
% 0.19/0.46 tff(93,plain,
% 0.19/0.46 (((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42), C!39)) | (~((~(apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42)) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42)))))) | (~((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42), tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42), tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42), tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42))))))))))) <=> ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | (~member(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42), C!39)) | (~((~(apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42)) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42)))))) | (~((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42), tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42), tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42), tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42))))))))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(94,plain,
% 0.19/0.46 (((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42), C!39)) | (~member(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~((~(apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42)) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42)))))) | (~((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42), tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42), tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42), tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42)))))))))) <=> ((~member(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42), C!39)) | (~((~(apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42)) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42)))))) | (~((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42), tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42), tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42), tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42))))))))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(95,plain,
% 0.19/0.46 ((~((~((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42), tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42), tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42), tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42))))))) | (~(apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42)) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42)))))))) <=> (~((~(apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42)) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42)))))) | (~((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42), tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42), tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42), tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42)))))))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(96,plain,
% 0.19/0.47 (((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42), C!39)) | (~member(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~((~((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42), tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42), tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42), tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42))))))) | (~(apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42)) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42))))))))) <=> ((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42), C!39)) | (~member(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~((~(apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42)) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42)))))) | (~((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42), tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42), tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42), tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42))))))))))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[95])).
% 0.19/0.47 tff(97,plain,
% 0.19/0.47 (((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42), C!39)) | (~member(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~((~((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42), tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42), tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42), tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42))))))) | (~(apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42)) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42))))))))) <=> ((~member(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42), C!39)) | (~((~(apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42)) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42)))))) | (~((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42), tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42), tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42), tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42))))))))))),
% 0.19/0.47 inference(transitivity,[status(thm)],[96, 94])).
% 0.19/0.47 tff(98,plain,
% 0.19/0.47 (((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42), C!39)) | (~member(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~((~((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42), tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42), tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42), tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42))))))) | (~(apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42)) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42)))))))))) <=> ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42), C!39)) | (~((~(apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42)) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42)))))) | (~((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42), tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42), tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42), tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42)))))))))))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[97])).
% 0.19/0.48 tff(99,plain,
% 0.19/0.48 (((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42), C!39)) | (~member(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~((~((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42), tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42), tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42), tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42))))))) | (~(apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42)) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42)))))))))) <=> ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | (~member(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42), C!39)) | (~((~(apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42)) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42)))))) | (~((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42), tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42), tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42), tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42))))))))))),
% 0.19/0.48 inference(transitivity,[status(thm)],[98, 93])).
% 0.19/0.48 tff(100,plain,
% 0.19/0.48 ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42), C!39)) | (~member(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~((~((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42), tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42), tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42), tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42))))))) | (~(apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42)) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42)))))))))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(101,plain,
% 0.19/0.48 ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | (~member(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42), C!39)) | (~((~(apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42)) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42)))))) | (~((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42), tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42), tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42), tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42)))))))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[100, 99])).
% 0.19/0.48 tff(102,plain,
% 0.19/0.48 (~((~(apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42)) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42)))))) | (~((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42), tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42), tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42), tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42))))))))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[101, 92, 3, 76])).
% 0.19/0.49 tff(103,plain,
% 0.19/0.49 (((~(apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42)) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42)))))) | (~((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42), tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42), tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42), tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42)))))))) | (apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42)) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42)))))),
% 0.19/0.49 inference(tautology,[status(thm)],[])).
% 0.19/0.49 tff(104,plain,
% 0.19/0.49 (apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42)) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42))))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[103, 102])).
% 0.19/0.49 tff(105,plain,
% 0.19/0.49 (((~member(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~![Y: $i] : ((~member(Y, C!39)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y))))) | ![Y: $i] : ((~member(Y, C!39)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)))),
% 0.19/0.49 inference(tautology,[status(thm)],[])).
% 0.19/0.49 tff(106,plain,
% 0.19/0.49 (![Y: $i] : ((~member(Y, C!39)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[105, 1])).
% 0.19/0.49 tff(107,plain,
% 0.19/0.49 (((~![Y: $i] : ((~member(Y, C!39)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)))) | ((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42), C!39)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42))))) <=> ((~![Y: $i] : ((~member(Y, C!39)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)))) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42), C!39)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(108,plain,
% 0.19/0.49 ((~![Y: $i] : ((~member(Y, C!39)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)))) | ((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42), C!39)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42))))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(109,plain,
% 0.19/0.49 ((~![Y: $i] : ((~member(Y, C!39)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)))) | (~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42), C!39)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42)))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[108, 107])).
% 0.19/0.49 tff(110,plain,
% 0.19/0.49 (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[109, 106, 76])).
% 0.19/0.49 tff(111,plain,
% 0.19/0.49 ((~(apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42)) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42)))))) | apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42)) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42))))),
% 0.19/0.49 inference(tautology,[status(thm)],[])).
% 0.19/0.49 tff(112,plain,
% 0.19/0.49 ((~(apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42)) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42)))))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42))))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[111, 110])).
% 0.19/0.49 tff(113,plain,
% 0.19/0.49 (![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42))))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[112, 104])).
% 0.19/0.49 tff(114,plain,
% 0.19/0.49 (((~member(tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42), C!39)) | (~apply(G!42, tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42)))) | apply(G!42, tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42))),
% 0.19/0.49 inference(tautology,[status(thm)],[])).
% 0.19/0.49 tff(115,plain,
% 0.19/0.49 (apply(G!42, tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[114, 74])).
% 0.19/0.49 tff(116,plain,
% 0.19/0.49 (((~member(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), B!40)) | (~apply(F!43, tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43)))) | apply(F!43, tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43))),
% 0.19/0.49 inference(tautology,[status(thm)],[])).
% 0.19/0.49 tff(117,plain,
% 0.19/0.49 (apply(F!43, tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[116, 53])).
% 0.19/0.49 tff(118,plain,
% 0.19/0.49 (((~![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42))))) | ((~member(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), B!40)) | (~apply(F!43, tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43))) | (~apply(G!42, tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42))))) <=> ((~![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42))))) | (~member(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), B!40)) | (~apply(F!43, tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43))) | (~apply(G!42, tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(119,plain,
% 0.19/0.49 ((~![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42))))) | ((~member(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), B!40)) | (~apply(F!43, tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43))) | (~apply(G!42, tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42))))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(120,plain,
% 0.19/0.49 ((~![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42))))) | (~member(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), B!40)) | (~apply(F!43, tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43))) | (~apply(G!42, tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42)))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[119, 118])).
% 0.19/0.49 tff(121,plain,
% 0.19/0.49 ($false),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[120, 55, 117, 115, 113])).
% 0.19/0.49 tff(122,plain,((~member(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~![Y: $i] : ((~member(Y, C!39)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.49 tff(123,plain,
% 0.19/0.49 (((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)) | (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, C!39, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), X, tptp_fun_Y_3(X, C!39, compose_function(G!42, F!43, A!41, B!40, C!39)))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(X, A!41)) | (~member(Y2, C!39)) | (~member(Y1, C!39)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), X, Y1)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), X, Y2)))))))) | (~(maps(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39) | (~((~member(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~![Y: $i] : ((~member(Y, C!39)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)))))) | (~((~member(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)) = tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))))) <=> ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)) | (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, C!39, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), X, tptp_fun_Y_3(X, C!39, compose_function(G!42, F!43, A!41, B!40, C!39)))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(X, A!41)) | (~member(Y2, C!39)) | (~member(Y1, C!39)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), X, Y1)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), X, Y2)))))))) | (~(maps(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39) | (~((~member(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~![Y: $i] : ((~member(Y, C!39)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)))))) | (~((~member(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)) = tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(124,plain,
% 0.19/0.50 ((~((~((~maps(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)) | (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, C!39, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), X, tptp_fun_Y_3(X, C!39, compose_function(G!42, F!43, A!41, B!40, C!39)))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), X, Y1)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), X, Y2)) | (~member(X, A!41)) | (~member(Y1, C!39)) | (~member(Y2, C!39)))))))) | (~(maps(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39) | (~((tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)) = tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~member(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)))) | (~((~member(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~![Y: $i] : ((~member(Y, C!39)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)))))))))) <=> (~((~((~maps(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)) | (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, C!39, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), X, tptp_fun_Y_3(X, C!39, compose_function(G!42, F!43, A!41, B!40, C!39)))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(X, A!41)) | (~member(Y2, C!39)) | (~member(Y1, C!39)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), X, Y1)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), X, Y2)))))))) | (~(maps(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39) | (~((~member(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~![Y: $i] : ((~member(Y, C!39)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)))))) | (~((~member(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)) = tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(125,plain,
% 0.19/0.50 (((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)) | (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, C!39, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), X, tptp_fun_Y_3(X, C!39, compose_function(G!42, F!43, A!41, B!40, C!39)))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), X, Y1)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), X, Y2)) | (~member(X, A!41)) | (~member(Y1, C!39)) | (~member(Y2, C!39)))))))) | (~(maps(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39) | (~((tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)) = tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~member(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)))) | (~((~member(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~![Y: $i] : ((~member(Y, C!39)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y))))))))))) <=> ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)) | (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, C!39, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), X, tptp_fun_Y_3(X, C!39, compose_function(G!42, F!43, A!41, B!40, C!39)))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(X, A!41)) | (~member(Y2, C!39)) | (~member(Y1, C!39)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), X, Y1)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), X, Y2)))))))) | (~(maps(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39) | (~((~member(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~![Y: $i] : ((~member(Y, C!39)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)))))) | (~((~member(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)) = tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))))))),
% 0.19/0.51 inference(monotonicity,[status(thm)],[124])).
% 0.19/0.51 tff(126,plain,
% 0.19/0.51 (((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)) | (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, C!39, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), X, tptp_fun_Y_3(X, C!39, compose_function(G!42, F!43, A!41, B!40, C!39)))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), X, Y1)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), X, Y2)) | (~member(X, A!41)) | (~member(Y1, C!39)) | (~member(Y2, C!39)))))))) | (~(maps(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39) | (~((tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)) = tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~member(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)))) | (~((~member(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~![Y: $i] : ((~member(Y, C!39)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y))))))))))) <=> ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)) | (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, C!39, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), X, tptp_fun_Y_3(X, C!39, compose_function(G!42, F!43, A!41, B!40, C!39)))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(X, A!41)) | (~member(Y2, C!39)) | (~member(Y1, C!39)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), X, Y1)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), X, Y2)))))))) | (~(maps(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39) | (~((~member(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~![Y: $i] : ((~member(Y, C!39)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)))))) | (~((~member(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)) = tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))))))),
% 0.19/0.51 inference(transitivity,[status(thm)],[125, 123])).
% 0.19/0.51 tff(127,plain,
% 0.19/0.51 ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)) | (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, C!39, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), X, tptp_fun_Y_3(X, C!39, compose_function(G!42, F!43, A!41, B!40, C!39)))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), X, Y1)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), X, Y2)) | (~member(X, A!41)) | (~member(Y1, C!39)) | (~member(Y2, C!39)))))))) | (~(maps(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39) | (~((tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)) = tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~member(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)))) | (~((~member(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~![Y: $i] : ((~member(Y, C!39)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y))))))))))),
% 0.19/0.51 inference(quant_inst,[status(thm)],[])).
% 0.19/0.51 tff(128,plain,
% 0.19/0.51 ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)) | (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, C!39, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), X, tptp_fun_Y_3(X, C!39, compose_function(G!42, F!43, A!41, B!40, C!39)))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(X, A!41)) | (~member(Y2, C!39)) | (~member(Y1, C!39)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), X, Y1)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), X, Y2)))))))) | (~(maps(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39) | (~((~member(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~![Y: $i] : ((~member(Y, C!39)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)))))) | (~((~member(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)) = tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[127, 126])).
% 0.19/0.51 tff(129,plain,
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% 0.19/0.51 inference(unit_resolution,[status(thm)],[128, 25])).
% 0.19/0.51 tff(130,plain,
% 0.19/0.51 (((~((~maps(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)) | (~((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, C!39, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), X, tptp_fun_Y_3(X, C!39, compose_function(G!42, F!43, A!41, B!40, C!39)))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(X, A!41)) | (~member(Y2, C!39)) | (~member(Y1, C!39)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), X, Y1)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), X, Y2)))))))) | (~(maps(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39) | (~((~member(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~![Y: $i] : ((~member(Y, C!39)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)))))) | (~((~member(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)) = tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))) | (maps(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39) | (~((~member(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~![Y: $i] : ((~member(Y, C!39)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)))))) | (~((~member(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)) = tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))),
% 0.19/0.52 inference(tautology,[status(thm)],[])).
% 0.19/0.52 tff(131,plain,
% 0.19/0.52 (maps(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39) | (~((~member(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~![Y: $i] : ((~member(Y, C!39)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)))))) | (~((~member(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)) = tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[130, 129])).
% 0.19/0.52 tff(132,plain,
% 0.19/0.52 (~maps(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)),
% 0.19/0.52 inference(or_elim,[status(thm)],[42])).
% 0.19/0.52 tff(133,plain,
% 0.19/0.52 ((~(maps(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39) | (~((~member(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~![Y: $i] : ((~member(Y, C!39)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)))))) | (~((~member(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)) = tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))) | maps(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39) | (~((~member(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~![Y: $i] : ((~member(Y, C!39)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)))))) | (~((~member(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)) = tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))),
% 0.19/0.52 inference(tautology,[status(thm)],[])).
% 0.19/0.52 tff(134,plain,
% 0.19/0.52 ((~(maps(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39) | (~((~member(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~![Y: $i] : ((~member(Y, C!39)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)))))) | (~((~member(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)) = tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))) | (~((~member(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~![Y: $i] : ((~member(Y, C!39)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)))))) | (~((~member(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)) = tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[133, 132])).
% 0.19/0.52 tff(135,plain,
% 0.19/0.52 ((~((~member(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~![Y: $i] : ((~member(Y, C!39)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)))))) | (~((~member(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)) = tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[134, 131])).
% 0.19/0.52 tff(136,plain,
% 0.19/0.52 (~((~member(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)) = tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[135, 122])).
% 0.19/0.52 tff(137,plain,
% 0.19/0.52 (((~member(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)) = tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | member(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)),
% 0.19/0.52 inference(tautology,[status(thm)],[])).
% 0.19/0.52 tff(138,plain,
% 0.19/0.52 (member(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[137, 136])).
% 0.19/0.52 tff(139,plain,
% 0.19/0.52 (((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!43), B!40)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!40, F!43))))))) | ((~member(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~((~member(tptp_fun_Y_3(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), B!40)) | (~apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43))))))) <=> ((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!43), B!40)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!40, F!43))))))) | (~member(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~((~member(tptp_fun_Y_3(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), B!40)) | (~apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43))))))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(140,plain,
% 0.19/0.52 ((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!43), B!40)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!40, F!43))))))) | ((~member(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~((~member(tptp_fun_Y_3(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), B!40)) | (~apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43))))))),
% 0.19/0.52 inference(quant_inst,[status(thm)],[])).
% 0.19/0.52 tff(141,plain,
% 0.19/0.52 ((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!43), B!40)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!40, F!43))))))) | (~member(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~((~member(tptp_fun_Y_3(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), B!40)) | (~apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43)))))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[140, 139])).
% 0.19/0.52 tff(142,plain,
% 0.19/0.53 (~((~member(tptp_fun_Y_3(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), B!40)) | (~apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43))))),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[141, 49, 138])).
% 0.19/0.53 tff(143,plain,
% 0.19/0.53 (((~member(tptp_fun_Y_3(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), B!40)) | (~apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43)))) | apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43))),
% 0.19/0.53 inference(tautology,[status(thm)],[])).
% 0.19/0.53 tff(144,plain,
% 0.19/0.53 (apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43))),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[143, 142])).
% 0.19/0.53 tff(145,plain,
% 0.19/0.53 (((~member(tptp_fun_Y_3(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), B!40)) | (~apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43)))) | member(tptp_fun_Y_3(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), B!40)),
% 0.19/0.53 inference(tautology,[status(thm)],[])).
% 0.19/0.53 tff(146,plain,
% 0.19/0.53 (member(tptp_fun_Y_3(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), B!40)),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[145, 142])).
% 0.19/0.53 tff(147,plain,
% 0.19/0.53 (((~member(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)) = tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | member(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)),
% 0.19/0.53 inference(tautology,[status(thm)],[])).
% 0.19/0.53 tff(148,plain,
% 0.19/0.53 (member(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[147, 136])).
% 0.19/0.53 tff(149,plain,
% 0.19/0.53 (((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~((~(apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))) | (~((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))))))) <=> ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | (~member(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~((~(apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))) | (~((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))))))),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(150,plain,
% 0.19/0.53 (((~member(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~((~(apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))) | (~((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))))))) <=> ((~member(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~((~(apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))) | (~((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))))))),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(151,plain,
% 0.19/0.53 ((~((~((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))) | (~(apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))))) <=> (~((~(apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))) | (~((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))))))),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(152,plain,
% 0.19/0.53 (((~member(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~((~((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))) | (~(apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))))) <=> ((~member(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~((~(apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))) | (~((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))))))),
% 0.19/0.54 inference(monotonicity,[status(thm)],[151])).
% 0.19/0.54 tff(153,plain,
% 0.19/0.54 (((~member(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~((~((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))) | (~(apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))))) <=> ((~member(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~((~(apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))) | (~((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))))))),
% 0.19/0.54 inference(transitivity,[status(thm)],[152, 150])).
% 0.19/0.54 tff(154,plain,
% 0.19/0.54 (((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~((~((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))) | (~(apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))))))) <=> ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~((~(apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))) | (~((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))))))))),
% 0.19/0.54 inference(monotonicity,[status(thm)],[153])).
% 0.19/0.54 tff(155,plain,
% 0.19/0.54 (((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~((~((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))) | (~(apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))))))) <=> ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | (~member(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~((~(apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))) | (~((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))))))),
% 0.19/0.54 inference(transitivity,[status(thm)],[154, 149])).
% 0.19/0.54 tff(156,plain,
% 0.19/0.54 ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~((~((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))) | (~(apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))))))),
% 0.19/0.55 inference(quant_inst,[status(thm)],[])).
% 0.19/0.55 tff(157,plain,
% 0.19/0.55 ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | (~member(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~((~(apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))) | (~((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))))))),
% 0.19/0.55 inference(modus_ponens,[status(thm)],[156, 155])).
% 0.19/0.55 tff(158,plain,
% 0.19/0.55 (~((~(apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))) | (~((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))))),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[157, 92, 148, 138])).
% 0.19/0.55 tff(159,plain,
% 0.19/0.55 (((~(apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))) | (~((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))))) | ((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))),
% 0.19/0.55 inference(tautology,[status(thm)],[])).
% 0.19/0.55 tff(160,plain,
% 0.19/0.55 ((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[159, 158])).
% 0.19/0.55 tff(161,plain,
% 0.19/0.55 (((~member(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)) = tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))),
% 0.19/0.55 inference(tautology,[status(thm)],[])).
% 0.19/0.55 tff(162,plain,
% 0.19/0.55 (apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[161, 136])).
% 0.19/0.55 tff(163,plain,
% 0.19/0.55 ((~((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))),
% 0.19/0.55 inference(tautology,[status(thm)],[])).
% 0.19/0.55 tff(164,plain,
% 0.19/0.55 ((~((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[163, 162])).
% 0.19/0.56 tff(165,plain,
% 0.19/0.56 (~((~member(tptp_fun_Y_8(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[164, 160])).
% 0.19/0.56 tff(166,plain,
% 0.19/0.56 (((~member(tptp_fun_Y_8(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))) | apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))),
% 0.19/0.56 inference(tautology,[status(thm)],[])).
% 0.19/0.56 tff(167,plain,
% 0.19/0.56 (apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[166, 165])).
% 0.19/0.56 tff(168,plain,
% 0.19/0.56 (((~member(tptp_fun_Y_8(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))) | member(tptp_fun_Y_8(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)),
% 0.40/0.56 inference(tautology,[status(thm)],[])).
% 0.40/0.56 tff(169,plain,
% 0.40/0.56 (member(tptp_fun_Y_8(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)),
% 0.40/0.56 inference(unit_resolution,[status(thm)],[168, 165])).
% 0.40/0.56 tff(170,plain,
% 0.40/0.56 (((~![X: $i] : ((~member(X, A!41)) | (~((~member(tptp_fun_Y_3(X, B!40, F!43), B!40)) | (~apply(F!43, X, tptp_fun_Y_3(X, B!40, F!43))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40))))) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)))),
% 0.40/0.56 inference(tautology,[status(thm)],[])).
% 0.40/0.56 tff(171,plain,
% 0.40/0.56 (![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)))),
% 0.40/0.56 inference(unit_resolution,[status(thm)],[170, 47])).
% 0.40/0.56 tff(172,plain,
% 0.40/0.56 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)))) | ((~member(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~member(tptp_fun_Y_8(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~member(tptp_fun_Y_3(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), B!40)) | (~apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43))) | (tptp_fun_Y_3(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43) = tptp_fun_Y_8(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)))) | (~member(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~member(tptp_fun_Y_8(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~member(tptp_fun_Y_3(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), B!40)) | (~apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43))) | (tptp_fun_Y_3(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43) = tptp_fun_Y_8(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42)))),
% 0.40/0.56 inference(rewrite,[status(thm)],[])).
% 0.40/0.56 tff(173,plain,
% 0.40/0.56 (((tptp_fun_Y_3(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43) = tptp_fun_Y_8(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42)) | (~member(tptp_fun_Y_8(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43))) | (~apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~member(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_Y_3(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), B!40))) <=> ((~member(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~member(tptp_fun_Y_8(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~member(tptp_fun_Y_3(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), B!40)) | (~apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43))) | (tptp_fun_Y_3(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43) = tptp_fun_Y_8(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42)))),
% 0.40/0.56 inference(rewrite,[status(thm)],[])).
% 0.40/0.56 tff(174,plain,
% 0.40/0.56 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)))) | ((tptp_fun_Y_3(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43) = tptp_fun_Y_8(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42)) | (~member(tptp_fun_Y_8(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43))) | (~apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~member(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_Y_3(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), B!40)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)))) | ((~member(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~member(tptp_fun_Y_8(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~member(tptp_fun_Y_3(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), B!40)) | (~apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43))) | (tptp_fun_Y_3(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43) = tptp_fun_Y_8(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))))),
% 0.40/0.57 inference(monotonicity,[status(thm)],[173])).
% 0.40/0.57 tff(175,plain,
% 0.40/0.57 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)))) | ((tptp_fun_Y_3(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43) = tptp_fun_Y_8(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42)) | (~member(tptp_fun_Y_8(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43))) | (~apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~member(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_Y_3(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), B!40)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)))) | (~member(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~member(tptp_fun_Y_8(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~member(tptp_fun_Y_3(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), B!40)) | (~apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43))) | (tptp_fun_Y_3(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43) = tptp_fun_Y_8(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42)))),
% 0.40/0.57 inference(transitivity,[status(thm)],[174, 172])).
% 0.40/0.57 tff(176,plain,
% 0.40/0.57 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)))) | ((tptp_fun_Y_3(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43) = tptp_fun_Y_8(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42)) | (~member(tptp_fun_Y_8(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43))) | (~apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~member(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_Y_3(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), B!40)))),
% 0.40/0.57 inference(quant_inst,[status(thm)],[])).
% 0.40/0.57 tff(177,plain,
% 0.40/0.57 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)))) | (~member(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~member(tptp_fun_Y_8(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~member(tptp_fun_Y_3(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), B!40)) | (~apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43))) | (tptp_fun_Y_3(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43) = tptp_fun_Y_8(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))),
% 0.40/0.57 inference(modus_ponens,[status(thm)],[176, 175])).
% 0.40/0.57 tff(178,plain,
% 0.40/0.57 (tptp_fun_Y_3(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43) = tptp_fun_Y_8(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42)),
% 0.40/0.57 inference(unit_resolution,[status(thm)],[177, 171, 138, 169, 167, 146, 144])).
% 0.40/0.57 tff(179,plain,
% 0.40/0.57 (((~member(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)) = tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | member(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)),
% 0.40/0.57 inference(tautology,[status(thm)],[])).
% 0.40/0.57 tff(180,plain,
% 0.40/0.57 (member(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)),
% 0.40/0.57 inference(unit_resolution,[status(thm)],[179, 136])).
% 0.40/0.57 tff(181,plain,
% 0.40/0.57 (((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~((~(apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))) | (~((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))))))) <=> ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | (~member(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~((~(apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))) | (~((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))))))),
% 0.40/0.57 inference(rewrite,[status(thm)],[])).
% 0.40/0.57 tff(182,plain,
% 0.40/0.57 (((~member(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~((~(apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))) | (~((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))))))) <=> ((~member(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~((~(apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))) | (~((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))))))),
% 0.42/0.57 inference(rewrite,[status(thm)],[])).
% 0.42/0.57 tff(183,plain,
% 0.42/0.57 ((~((~((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))) | (~(apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))))) <=> (~((~(apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))) | (~((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))))))),
% 0.42/0.58 inference(rewrite,[status(thm)],[])).
% 0.42/0.58 tff(184,plain,
% 0.42/0.58 (((~member(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~((~((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))) | (~(apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))))) <=> ((~member(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~((~(apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))) | (~((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))))))),
% 0.42/0.58 inference(monotonicity,[status(thm)],[183])).
% 0.42/0.58 tff(185,plain,
% 0.42/0.58 (((~member(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~((~((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))) | (~(apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))))) <=> ((~member(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~((~(apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))) | (~((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))))))),
% 0.42/0.58 inference(transitivity,[status(thm)],[184, 182])).
% 0.42/0.58 tff(186,plain,
% 0.42/0.58 (((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~((~((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))) | (~(apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))))))) <=> ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~((~(apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))) | (~((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))))))))),
% 0.42/0.59 inference(monotonicity,[status(thm)],[185])).
% 0.42/0.59 tff(187,plain,
% 0.42/0.59 (((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~((~((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))) | (~(apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))))))) <=> ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | (~member(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~((~(apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))) | (~((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))))))),
% 0.42/0.59 inference(transitivity,[status(thm)],[186, 181])).
% 0.42/0.59 tff(188,plain,
% 0.42/0.59 ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~((~((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))) | (~(apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))))))),
% 0.42/0.59 inference(quant_inst,[status(thm)],[])).
% 0.42/0.59 tff(189,plain,
% 0.42/0.59 ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | (~member(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~((~(apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))) | (~((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))))))),
% 0.42/0.59 inference(modus_ponens,[status(thm)],[188, 187])).
% 0.42/0.59 tff(190,plain,
% 0.42/0.59 (~((~(apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))) | (~((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))))),
% 0.42/0.59 inference(unit_resolution,[status(thm)],[189, 92, 180, 138])).
% 0.42/0.59 tff(191,plain,
% 0.42/0.59 (((~(apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))) | (~((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))))) | ((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))),
% 0.42/0.59 inference(tautology,[status(thm)],[])).
% 0.42/0.59 tff(192,plain,
% 0.42/0.59 ((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))),
% 0.42/0.60 inference(unit_resolution,[status(thm)],[191, 190])).
% 0.42/0.60 tff(193,plain,
% 0.42/0.60 (((~member(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)) = tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))),
% 0.42/0.60 inference(tautology,[status(thm)],[])).
% 0.42/0.60 tff(194,plain,
% 0.42/0.60 (apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))),
% 0.42/0.60 inference(unit_resolution,[status(thm)],[193, 136])).
% 0.42/0.60 tff(195,plain,
% 0.42/0.60 ((~((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))),
% 0.42/0.60 inference(tautology,[status(thm)],[])).
% 0.42/0.60 tff(196,plain,
% 0.42/0.60 ((~((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))),
% 0.42/0.60 inference(unit_resolution,[status(thm)],[195, 194])).
% 0.42/0.60 tff(197,plain,
% 0.42/0.60 (~((~member(tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))),
% 0.42/0.60 inference(unit_resolution,[status(thm)],[196, 192])).
% 0.42/0.60 tff(198,plain,
% 0.42/0.60 (((~member(tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))) | apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))),
% 0.42/0.60 inference(tautology,[status(thm)],[])).
% 0.42/0.60 tff(199,plain,
% 0.42/0.60 (apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))),
% 0.42/0.60 inference(unit_resolution,[status(thm)],[198, 197])).
% 0.42/0.60 tff(200,plain,
% 0.42/0.60 (((~member(tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))) | member(tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)),
% 0.42/0.60 inference(tautology,[status(thm)],[])).
% 0.42/0.60 tff(201,plain,
% 0.42/0.60 (member(tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)),
% 0.42/0.60 inference(unit_resolution,[status(thm)],[200, 197])).
% 0.42/0.60 tff(202,plain,
% 0.42/0.60 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)))) | ((~member(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~member(tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~member(tptp_fun_Y_3(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), B!40)) | (~apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43))) | (tptp_fun_Y_3(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43) = tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)))) | (~member(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~member(tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~member(tptp_fun_Y_3(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), B!40)) | (~apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43))) | (tptp_fun_Y_3(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43) = tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42)))),
% 0.42/0.60 inference(rewrite,[status(thm)],[])).
% 0.42/0.60 tff(203,plain,
% 0.42/0.60 (((tptp_fun_Y_3(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43) = tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42)) | (~member(tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43))) | (~apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~member(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_Y_3(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), B!40))) <=> ((~member(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~member(tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~member(tptp_fun_Y_3(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), B!40)) | (~apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43))) | (tptp_fun_Y_3(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43) = tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42)))),
% 0.42/0.61 inference(rewrite,[status(thm)],[])).
% 0.42/0.61 tff(204,plain,
% 0.42/0.61 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)))) | ((tptp_fun_Y_3(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43) = tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42)) | (~member(tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43))) | (~apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~member(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_Y_3(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), B!40)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)))) | ((~member(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~member(tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~member(tptp_fun_Y_3(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), B!40)) | (~apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43))) | (tptp_fun_Y_3(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43) = tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))))),
% 0.42/0.61 inference(monotonicity,[status(thm)],[203])).
% 0.42/0.61 tff(205,plain,
% 0.42/0.61 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)))) | ((tptp_fun_Y_3(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43) = tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42)) | (~member(tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43))) | (~apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~member(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_Y_3(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), B!40)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)))) | (~member(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~member(tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~member(tptp_fun_Y_3(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), B!40)) | (~apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43))) | (tptp_fun_Y_3(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43) = tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42)))),
% 0.42/0.61 inference(transitivity,[status(thm)],[204, 202])).
% 0.42/0.61 tff(206,plain,
% 0.42/0.61 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)))) | ((tptp_fun_Y_3(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43) = tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42)) | (~member(tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43))) | (~apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~member(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_Y_3(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), B!40)))),
% 0.42/0.61 inference(quant_inst,[status(thm)],[])).
% 0.42/0.61 tff(207,plain,
% 0.42/0.61 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, B!40)) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)))) | (~member(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~member(tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~member(tptp_fun_Y_3(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), B!40)) | (~apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43))) | (tptp_fun_Y_3(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43) = tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))),
% 0.42/0.61 inference(modus_ponens,[status(thm)],[206, 205])).
% 0.42/0.61 tff(208,plain,
% 0.42/0.61 (tptp_fun_Y_3(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43) = tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42)),
% 0.42/0.61 inference(unit_resolution,[status(thm)],[207, 171, 138, 201, 199, 146, 144])).
% 0.42/0.61 tff(209,plain,
% 0.42/0.61 (tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42) = tptp_fun_Y_3(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43)),
% 0.42/0.61 inference(symmetry,[status(thm)],[208])).
% 0.42/0.61 tff(210,plain,
% 0.42/0.61 (tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42) = tptp_fun_Y_8(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42)),
% 0.42/0.61 inference(transitivity,[status(thm)],[209, 178])).
% 0.42/0.61 tff(211,plain,
% 0.42/0.61 (apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) <=> apply(G!42, tptp_fun_Y_8(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))),
% 0.42/0.61 inference(monotonicity,[status(thm)],[210])).
% 0.42/0.61 tff(212,plain,
% 0.42/0.61 (apply(G!42, tptp_fun_Y_8(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) <=> apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))),
% 0.42/0.61 inference(symmetry,[status(thm)],[211])).
% 0.42/0.61 tff(213,plain,
% 0.42/0.61 (((~member(tptp_fun_Y_8(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))) | apply(G!42, tptp_fun_Y_8(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))),
% 0.42/0.61 inference(tautology,[status(thm)],[])).
% 0.42/0.61 tff(214,plain,
% 0.42/0.61 (apply(G!42, tptp_fun_Y_8(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))),
% 0.42/0.61 inference(unit_resolution,[status(thm)],[213, 165])).
% 0.42/0.61 tff(215,plain,
% 0.42/0.61 (apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))),
% 0.42/0.61 inference(modus_ponens,[status(thm)],[214, 212])).
% 0.42/0.61 tff(216,plain,
% 0.42/0.61 (((~member(tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))) | apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))),
% 0.42/0.61 inference(tautology,[status(thm)],[])).
% 0.42/0.61 tff(217,plain,
% 0.42/0.61 (apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))),
% 0.42/0.61 inference(unit_resolution,[status(thm)],[216, 197])).
% 0.42/0.61 tff(218,plain,
% 0.42/0.61 (((~member(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)) = tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)) = tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))),
% 0.42/0.62 inference(tautology,[status(thm)],[])).
% 0.42/0.62 tff(219,plain,
% 0.42/0.62 (~(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)) = tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))),
% 0.42/0.62 inference(unit_resolution,[status(thm)],[218, 136])).
% 0.42/0.62 tff(220,plain,
% 0.42/0.62 (((~![X: $i] : ((~member(X, B!40)) | (~((~member(tptp_fun_Y_3(X, C!39, G!42), C!39)) | (~apply(G!42, X, tptp_fun_Y_3(X, C!39, G!42))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, C!39)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!40)) | (~member(Y1, C!39))))) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, C!39)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!40)) | (~member(Y1, C!39)))),
% 0.42/0.62 inference(tautology,[status(thm)],[])).
% 0.42/0.62 tff(221,plain,
% 0.42/0.62 (![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, C!39)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!40)) | (~member(Y1, C!39)))),
% 0.42/0.62 inference(unit_resolution,[status(thm)],[220, 68])).
% 0.42/0.62 tff(222,plain,
% 0.42/0.62 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, C!39)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!40)) | (~member(Y1, C!39)))) | ((~member(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)) = tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~member(tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, C!39)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!40)) | (~member(Y1, C!39)))) | (~member(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)) = tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~member(tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))),
% 0.42/0.62 inference(rewrite,[status(thm)],[])).
% 0.42/0.62 tff(223,plain,
% 0.42/0.62 (((tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)) = tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | (~member(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~member(tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~member(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39))) <=> ((~member(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)) = tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~member(tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))),
% 0.42/0.62 inference(rewrite,[status(thm)],[])).
% 0.42/0.62 tff(224,plain,
% 0.42/0.62 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, C!39)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!40)) | (~member(Y1, C!39)))) | ((tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)) = tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | (~member(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~member(tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~member(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, C!39)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!40)) | (~member(Y1, C!39)))) | ((~member(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)) = tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~member(tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))),
% 0.42/0.62 inference(monotonicity,[status(thm)],[223])).
% 0.42/0.62 tff(225,plain,
% 0.42/0.62 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, C!39)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!40)) | (~member(Y1, C!39)))) | ((tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)) = tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | (~member(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~member(tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~member(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, C!39)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!40)) | (~member(Y1, C!39)))) | (~member(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)) = tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~member(tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))),
% 0.42/0.62 inference(transitivity,[status(thm)],[224, 222])).
% 0.42/0.62 tff(226,plain,
% 0.42/0.62 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, C!39)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!40)) | (~member(Y1, C!39)))) | ((tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)) = tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | (~member(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~member(tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~member(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)))),
% 0.47/0.63 inference(quant_inst,[status(thm)],[])).
% 0.47/0.63 tff(227,plain,
% 0.47/0.63 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, C!39)) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!40)) | (~member(Y1, C!39)))) | (~member(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)) = tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~member(tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))),
% 0.47/0.63 inference(modus_ponens,[status(thm)],[226, 225])).
% 0.47/0.63 tff(228,plain,
% 0.47/0.63 (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))),
% 0.47/0.63 inference(unit_resolution,[status(thm)],[227, 221, 148, 180, 219, 201, 217])).
% 0.47/0.63 tff(229,plain,
% 0.47/0.63 ($false),
% 0.47/0.63 inference(unit_resolution,[status(thm)],[228, 215])).
% 0.47/0.63 % SZS output end Proof
% 0.47/0.63 % E exiting
%------------------------------------------------------------------------------