TSTP Solution File: SET709+4 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET709+4 : TPTP v8.1.0. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n020.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 : Tue Sep 20 05:07:42 EDT 2022
% Result : Theorem 0.18s 0.40s
% Output : Proof 0.62s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SET709+4 : TPTP v8.1.0. Bugfixed v2.2.1.
% 0.03/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n020.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sat Sep 3 07:27:59 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.33 Usage: tptp [options] [-file:]file
% 0.12/0.33 -h, -? prints this message.
% 0.12/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.33 -m, -model generate model.
% 0.12/0.33 -p, -proof generate proof.
% 0.12/0.33 -c, -core generate unsat core of named formulas.
% 0.12/0.33 -st, -statistics display statistics.
% 0.12/0.33 -t:timeout set timeout (in second).
% 0.12/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.33 -<param>:<value> configuration parameter and value.
% 0.12/0.33 -o:<output-file> file to place output in.
% 0.18/0.40 % SZS status Theorem
% 0.18/0.40 % SZS output start Proof
% 0.18/0.40 tff(apply_type, type, (
% 0.18/0.40 apply: ( $i * $i * $i ) > $o)).
% 0.18/0.40 tff(tptp_fun_Y1_6_type, type, (
% 0.18/0.40 tptp_fun_Y1_6: ( $i * $i * $i ) > $i)).
% 0.18/0.40 tff(compose_function_type, type, (
% 0.18/0.40 compose_function: ( $i * $i * $i * $i * $i ) > $i)).
% 0.18/0.40 tff(tptp_fun_C_39_type, type, (
% 0.18/0.40 tptp_fun_C_39: $i)).
% 0.18/0.40 tff(tptp_fun_B_40_type, type, (
% 0.18/0.40 tptp_fun_B_40: $i)).
% 0.18/0.40 tff(tptp_fun_A_41_type, type, (
% 0.18/0.40 tptp_fun_A_41: $i)).
% 0.18/0.40 tff(tptp_fun_F_43_type, type, (
% 0.18/0.40 tptp_fun_F_43: $i)).
% 0.18/0.40 tff(tptp_fun_G_42_type, type, (
% 0.18/0.40 tptp_fun_G_42: $i)).
% 0.18/0.40 tff(tptp_fun_Y_8_type, type, (
% 0.18/0.40 tptp_fun_Y_8: ( $i * $i * $i * $i * $i ) > $i)).
% 0.18/0.40 tff(tptp_fun_X_7_type, type, (
% 0.18/0.40 tptp_fun_X_7: ( $i * $i * $i ) > $i)).
% 0.18/0.40 tff(tptp_fun_Y2_5_type, type, (
% 0.18/0.40 tptp_fun_Y2_5: ( $i * $i * $i ) > $i)).
% 0.18/0.40 tff(tptp_fun_Y_3_type, type, (
% 0.18/0.40 tptp_fun_Y_3: ( $i * $i * $i ) > $i)).
% 0.18/0.40 tff(member_type, type, (
% 0.18/0.40 member: ( $i * $i ) > $o)).
% 0.18/0.40 tff(tptp_fun_X_4_type, type, (
% 0.18/0.40 tptp_fun_X_4: ( $i * $i * $i ) > $i)).
% 0.18/0.40 tff(maps_type, type, (
% 0.18/0.40 maps: ( $i * $i * $i ) > $o)).
% 0.18/0.40 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)).
% 0.18/0.40 tff(2,plain,
% 0.18/0.40 (((~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)),
% 0.18/0.40 inference(tautology,[status(thm)],[])).
% 0.18/0.40 tff(3,plain,
% 0.18/0.40 (member(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[2, 1])).
% 0.18/0.40 tff(4,plain,
% 0.18/0.40 (^[F: $i, A: $i, B: $i] : rewrite((~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))) <=> (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))))))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(5,plain,
% 0.18/0.40 (![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) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[4])).
% 0.18/0.40 tff(6,plain,
% 0.18/0.40 (^[F: $i, A: $i, B: $i] : refl((~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))) <=> (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(7,plain,
% 0.18/0.40 (![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))))))))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[6])).
% 0.18/0.40 tff(8,plain,
% 0.18/0.40 (^[F: $i, A: $i, B: $i] : rewrite((~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))) <=> (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(9,plain,
% 0.18/0.40 (![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))))))))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[8])).
% 0.18/0.40 tff(10,plain,
% 0.18/0.40 (![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))))))))),
% 0.18/0.41 inference(transitivity,[status(thm)],[9, 7])).
% 0.18/0.41 tff(11,plain,
% 0.18/0.41 (^[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(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))))), 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)))))))), ((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, 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))))))))), rewrite((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, 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) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_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, 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)))))) <=> (((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $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) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_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, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))))))))),
% 0.18/0.41 inference(bind,[status(th)],[])).
% 0.18/0.41 tff(12,plain,
% 0.18/0.41 (![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)))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))))))),
% 0.18/0.41 inference(quant_intro,[status(thm)],[11])).
% 0.18/0.41 tff(13,plain,
% 0.18/0.41 (^[F: $i, A: $i, B: $i] : rewrite((((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) & (maps(F, A, B) | (((~(~member(tptp_fun_X_4(B, A, F), A))) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B)))))))) <=> (((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) & (maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B))))) | (member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))))))),
% 0.18/0.41 inference(bind,[status(th)],[])).
% 0.18/0.41 tff(14,plain,
% 0.18/0.41 (![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) | (((~(~member(tptp_fun_X_4(B, A, F), A))) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B)))))))) <=> ![F: $i, A: $i, B: $i] : (((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) & (maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B))))) | (member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y))))))),
% 0.18/0.41 inference(quant_intro,[status(thm)],[13])).
% 0.18/0.41 tff(15,plain,
% 0.18/0.41 (![F: $i, A: $i, B: $i] : (maps(F, A, B) <=> (![X: $i] : ((~member(X, A)) | ?[Y: $i] : (member(Y, B) & apply(F, X, Y))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) <=> ![F: $i, A: $i, B: $i] : (maps(F, A, B) <=> (![X: $i] : ((~member(X, A)) | ?[Y: $i] : (member(Y, B) & apply(F, X, Y))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B))))))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(16,plain,
% 0.18/0.41 (^[F: $i, A: $i, B: $i] : rewrite((maps(F, A, B) <=> (![X: $i] : (member(X, A) => ?[Y: $i] : (member(Y, B) & apply(F, X, Y))) & ![X: $i, Y1: $i, Y2: $i] : (((member(X, A) & member(Y1, B)) & member(Y2, B)) => ((apply(F, X, Y1) & apply(F, X, Y2)) => (Y1 = Y2))))) <=> (maps(F, A, B) <=> (![X: $i] : ((~member(X, A)) | ?[Y: $i] : (member(Y, B) & apply(F, X, Y))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))))),
% 0.18/0.41 inference(bind,[status(th)],[])).
% 0.18/0.41 tff(17,plain,
% 0.18/0.41 (![F: $i, A: $i, B: $i] : (maps(F, A, B) <=> (![X: $i] : (member(X, A) => ?[Y: $i] : (member(Y, B) & apply(F, X, Y))) & ![X: $i, Y1: $i, Y2: $i] : (((member(X, A) & member(Y1, B)) & member(Y2, B)) => ((apply(F, X, Y1) & apply(F, X, Y2)) => (Y1 = Y2))))) <=> ![F: $i, A: $i, B: $i] : (maps(F, A, B) <=> (![X: $i] : ((~member(X, A)) | ?[Y: $i] : (member(Y, B) & apply(F, X, Y))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B))))))),
% 0.18/0.41 inference(quant_intro,[status(thm)],[16])).
% 0.18/0.41 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/sandbox/benchmark/Axioms/SET006+1.ax','maps')).
% 0.18/0.41 tff(19,plain,
% 0.18/0.41 (![F: $i, A: $i, B: $i] : (maps(F, A, B) <=> (![X: $i] : ((~member(X, A)) | ?[Y: $i] : (member(Y, B) & apply(F, X, Y))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B))))))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.18/0.41 tff(20,plain,
% 0.18/0.41 (![F: $i, A: $i, B: $i] : (maps(F, A, B) <=> (![X: $i] : ((~member(X, A)) | ?[Y: $i] : (member(Y, B) & apply(F, X, Y))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B))))))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.18/0.41 tff(21,plain,(
% 0.18/0.41 ![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) | (((~(~member(tptp_fun_X_4(B, A, F), A))) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B))))))))),
% 0.18/0.41 inference(skolemize,[status(sab)],[20])).
% 0.18/0.41 tff(22,plain,
% 0.18/0.41 (![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))))))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[21, 14])).
% 0.18/0.41 tff(23,plain,
% 0.18/0.41 (![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) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))))))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[22, 12])).
% 0.18/0.41 tff(24,plain,
% 0.18/0.41 (![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) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))))))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[23, 10])).
% 0.18/0.41 tff(25,plain,
% 0.18/0.41 (![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))))))))))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[24, 5])).
% 0.18/0.42 tff(26,plain,
% 0.18/0.42 ((~![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(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))))))))))),
% 0.18/0.42 inference(quant_inst,[status(thm)],[])).
% 0.18/0.42 tff(27,plain,
% 0.18/0.42 (~((~((~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) | (~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)))))))))),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[26, 25])).
% 0.18/0.42 tff(28,plain,
% 0.18/0.42 (((~((~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) | (~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) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)) | (~member(Y2, B!40)))))))),
% 0.18/0.42 inference(tautology,[status(thm)],[])).
% 0.18/0.42 tff(29,plain,
% 0.18/0.42 ((~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) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)) | (~member(Y2, B!40))))))),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[28, 27])).
% 0.18/0.42 tff(30,plain,
% 0.18/0.42 ((~![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)))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(31,plain,
% 0.18/0.42 ((~![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)))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(32,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/sandbox/benchmark/theBenchmark.p','thII01')).
% 0.18/0.42 tff(33,plain,
% 0.18/0.42 (~![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))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.18/0.42 tff(34,plain,
% 0.18/0.42 (~![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))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[33, 30])).
% 0.18/0.42 tff(35,plain,
% 0.18/0.42 (~![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))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[34, 30])).
% 0.18/0.42 tff(36,plain,
% 0.18/0.42 (~![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))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[35, 30])).
% 0.18/0.42 tff(37,plain,
% 0.18/0.42 (~![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))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[36, 30])).
% 0.18/0.42 tff(38,plain,
% 0.18/0.42 (~![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))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[37, 30])).
% 0.18/0.42 tff(39,plain,
% 0.18/0.42 (~![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))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[38, 30])).
% 0.18/0.42 tff(40,plain,(
% 0.18/0.42 ~((~(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))),
% 0.18/0.42 inference(skolemize,[status(sab)],[39])).
% 0.18/0.42 tff(41,plain,
% 0.18/0.42 (maps(F!43, A!41, B!40) & maps(G!42, B!40, C!39)),
% 0.18/0.42 inference(or_elim,[status(thm)],[40])).
% 0.18/0.42 tff(42,plain,
% 0.18/0.42 (maps(F!43, A!41, B!40)),
% 0.18/0.42 inference(and_elim,[status(thm)],[41])).
% 0.18/0.42 tff(43,plain,
% 0.18/0.42 ((~((~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) | (~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)) | (~((~![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))))))),
% 0.18/0.43 inference(tautology,[status(thm)],[])).
% 0.18/0.43 tff(44,plain,
% 0.18/0.43 ((~((~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) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)) | (~member(Y2, 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))))))),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[43, 42])).
% 0.18/0.43 tff(45,plain,
% 0.18/0.43 (~((~![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))))))) | (~![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)))))),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[44, 29])).
% 0.18/0.43 tff(46,plain,
% 0.18/0.43 (((~![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))))))) | (~![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))))) | ![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))))))),
% 0.18/0.43 inference(tautology,[status(thm)],[])).
% 0.18/0.43 tff(47,plain,
% 0.18/0.43 (![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))))))),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[46, 45])).
% 0.18/0.43 tff(48,plain,
% 0.18/0.43 (((~![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))))))) <=> ((~![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))))))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(49,plain,
% 0.18/0.43 ((~![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))))))),
% 0.18/0.43 inference(quant_inst,[status(thm)],[])).
% 0.18/0.43 tff(50,plain,
% 0.18/0.43 ((~![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)))))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.18/0.43 tff(51,plain,
% 0.18/0.43 (~((~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)) | (~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))))),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[50, 47, 3])).
% 0.18/0.43 tff(52,plain,
% 0.18/0.43 (((~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)) | (~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)),
% 0.18/0.43 inference(tautology,[status(thm)],[])).
% 0.18/0.43 tff(53,plain,
% 0.18/0.43 (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)),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[52, 51])).
% 0.18/0.43 tff(54,plain,
% 0.18/0.43 ((~![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))))))))))),
% 0.18/0.43 inference(quant_inst,[status(thm)],[])).
% 0.18/0.43 tff(55,plain,
% 0.18/0.43 (~((~((~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)))))))))),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[54, 25])).
% 0.18/0.43 tff(56,plain,
% 0.18/0.43 (((~((~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) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!40)) | (~member(Y1, C!39)) | (~member(Y2, C!39)))))))),
% 0.18/0.43 inference(tautology,[status(thm)],[])).
% 0.18/0.43 tff(57,plain,
% 0.18/0.43 ((~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))))))),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[56, 55])).
% 0.18/0.43 tff(58,plain,
% 0.18/0.43 (maps(G!42, B!40, C!39)),
% 0.18/0.43 inference(and_elim,[status(thm)],[41])).
% 0.18/0.43 tff(59,plain,
% 0.18/0.43 ((~((~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)) | (~((~![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))))))),
% 0.18/0.43 inference(tautology,[status(thm)],[])).
% 0.18/0.43 tff(60,plain,
% 0.18/0.43 ((~((~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)))))))) | (~((~![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))))))),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[59, 58])).
% 0.18/0.43 tff(61,plain,
% 0.18/0.43 (~((~![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)))))),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[60, 57])).
% 0.18/0.43 tff(62,plain,
% 0.18/0.43 (((~![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))))) | ![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))))))),
% 0.18/0.43 inference(tautology,[status(thm)],[])).
% 0.18/0.44 tff(63,plain,
% 0.18/0.44 (![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))))))),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[62, 61])).
% 0.18/0.44 tff(64,plain,
% 0.18/0.44 (((~![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))))))),
% 0.18/0.44 inference(rewrite,[status(thm)],[])).
% 0.18/0.44 tff(65,plain,
% 0.18/0.44 ((~![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))))))),
% 0.18/0.44 inference(quant_inst,[status(thm)],[])).
% 0.18/0.44 tff(66,plain,
% 0.18/0.44 ((~![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)))))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.18/0.44 tff(67,plain,
% 0.18/0.44 (~((~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))))),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[66, 63, 53])).
% 0.18/0.44 tff(68,plain,
% 0.18/0.44 (((~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)),
% 0.18/0.44 inference(tautology,[status(thm)],[])).
% 0.18/0.44 tff(69,plain,
% 0.18/0.44 (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)),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[68, 67])).
% 0.18/0.44 tff(70,plain,
% 0.18/0.44 (^[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)))))))))),
% 0.18/0.44 inference(bind,[status(th)],[])).
% 0.18/0.44 tff(71,plain,
% 0.18/0.44 (![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))))))))),
% 0.18/0.44 inference(quant_intro,[status(thm)],[70])).
% 0.18/0.44 tff(72,plain,
% 0.18/0.44 (^[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)))))))))),
% 0.18/0.44 inference(bind,[status(th)],[])).
% 0.18/0.44 tff(73,plain,
% 0.18/0.44 (![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))))))))),
% 0.18/0.44 inference(quant_intro,[status(thm)],[72])).
% 0.18/0.44 tff(74,plain,
% 0.18/0.44 (![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))))))))),
% 0.18/0.44 inference(transitivity,[status(thm)],[73, 71])).
% 0.18/0.44 tff(75,plain,
% 0.18/0.44 (^[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))))))))))),
% 0.18/0.44 inference(bind,[status(th)],[])).
% 0.18/0.44 tff(76,plain,
% 0.18/0.44 (![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))))))))),
% 0.18/0.44 inference(quant_intro,[status(thm)],[75])).
% 0.18/0.44 tff(77,plain,
% 0.18/0.44 (![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))))),
% 0.18/0.44 inference(rewrite,[status(thm)],[])).
% 0.18/0.44 tff(78,plain,
% 0.18/0.44 (^[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))))))),
% 0.18/0.45 inference(bind,[status(th)],[])).
% 0.18/0.45 tff(79,plain,
% 0.18/0.45 (![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))))),
% 0.18/0.45 inference(quant_intro,[status(thm)],[78])).
% 0.18/0.45 tff(80,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/sandbox/benchmark/Axioms/SET006+1.ax','compose_function')).
% 0.18/0.45 tff(81,plain,
% 0.18/0.45 (![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))))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.18/0.45 tff(82,plain,
% 0.18/0.45 (![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))))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[81, 77])).
% 0.18/0.45 tff(83,plain,(
% 0.18/0.45 ![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))))))),
% 0.18/0.45 inference(skolemize,[status(sab)],[82])).
% 0.18/0.45 tff(84,plain,
% 0.18/0.45 (![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))))))))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[83, 76])).
% 0.18/0.45 tff(85,plain,
% 0.18/0.45 (![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))))))))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[84, 74])).
% 0.18/0.45 tff(86,plain,
% 0.18/0.45 (((~![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))))))))) | ((~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))) | (~((~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))) | (~((~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)))))))))),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(87,plain,
% 0.18/0.45 (((~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)) | (~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))) | (~((~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)))))))))),
% 0.18/0.46 inference(rewrite,[status(thm)],[])).
% 0.18/0.46 tff(88,plain,
% 0.18/0.46 ((~((~((~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))) | (~((~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))))))))),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(89,plain,
% 0.18/0.47 (((~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))) | (~((~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)))))))))),
% 0.18/0.47 inference(monotonicity,[status(thm)],[88])).
% 0.18/0.47 tff(90,plain,
% 0.18/0.47 (((~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))) | (~((~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)))))))))),
% 0.18/0.48 inference(transitivity,[status(thm)],[89, 87])).
% 0.18/0.48 tff(91,plain,
% 0.18/0.48 (((~![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))) | (~((~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))))))))))),
% 0.18/0.48 inference(monotonicity,[status(thm)],[90])).
% 0.18/0.48 tff(92,plain,
% 0.18/0.48 (((~![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))) | (~((~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)))))))))),
% 0.18/0.49 inference(transitivity,[status(thm)],[91, 86])).
% 0.18/0.49 tff(93,plain,
% 0.18/0.49 ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_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)))))))))),
% 0.18/0.49 inference(quant_inst,[status(thm)],[])).
% 0.18/0.49 tff(94,plain,
% 0.18/0.49 ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | (~member(tptp_fun_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))) | (~((~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))))))))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[93, 92])).
% 0.18/0.50 tff(95,plain,
% 0.18/0.50 (~((~((~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)))))))),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[94, 85, 3, 69])).
% 0.18/0.50 tff(96,plain,
% 0.18/0.50 (((~((~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)))))),
% 0.18/0.50 inference(tautology,[status(thm)],[])).
% 0.18/0.50 tff(97,plain,
% 0.18/0.50 (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))))),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[96, 95])).
% 0.18/0.50 tff(98,plain,
% 0.18/0.50 (((~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)))),
% 0.18/0.50 inference(tautology,[status(thm)],[])).
% 0.18/0.50 tff(99,plain,
% 0.18/0.50 (![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)))),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[98, 1])).
% 0.18/0.50 tff(100,plain,
% 0.18/0.50 (((~![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))))),
% 0.18/0.50 inference(rewrite,[status(thm)],[])).
% 0.18/0.50 tff(101,plain,
% 0.18/0.50 ((~![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))))),
% 0.18/0.51 inference(quant_inst,[status(thm)],[])).
% 0.18/0.51 tff(102,plain,
% 0.18/0.51 ((~![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)))),
% 0.18/0.51 inference(modus_ponens,[status(thm)],[101, 100])).
% 0.18/0.51 tff(103,plain,
% 0.18/0.51 (~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))),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[102, 99, 69])).
% 0.18/0.51 tff(104,plain,
% 0.18/0.51 ((~(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))))),
% 0.18/0.51 inference(tautology,[status(thm)],[])).
% 0.18/0.51 tff(105,plain,
% 0.18/0.51 ((~(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))))),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[104, 103])).
% 0.18/0.51 tff(106,plain,
% 0.18/0.51 (![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))))),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[105, 97])).
% 0.18/0.51 tff(107,plain,
% 0.18/0.51 (((~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))),
% 0.18/0.51 inference(tautology,[status(thm)],[])).
% 0.18/0.51 tff(108,plain,
% 0.18/0.51 (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))),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[107, 67])).
% 0.18/0.51 tff(109,plain,
% 0.18/0.51 (((~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))),
% 0.18/0.51 inference(tautology,[status(thm)],[])).
% 0.18/0.51 tff(110,plain,
% 0.18/0.51 (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))),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[109, 51])).
% 0.18/0.51 tff(111,plain,
% 0.18/0.51 (((~![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))))),
% 0.18/0.51 inference(rewrite,[status(thm)],[])).
% 0.18/0.51 tff(112,plain,
% 0.18/0.51 ((~![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))))),
% 0.18/0.52 inference(quant_inst,[status(thm)],[])).
% 0.18/0.52 tff(113,plain,
% 0.18/0.52 ((~![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42))))) | (~member(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), B!40)) | (~apply(F!43, tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43))) | (~apply(G!42, tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), tptp_fun_Y_3(tptp_fun_Y_3(tptp_fun_X_4(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43), C!39, G!42)))),
% 0.18/0.52 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.18/0.52 tff(114,plain,
% 0.18/0.52 ($false),
% 0.18/0.52 inference(unit_resolution,[status(thm)],[113, 53, 110, 108, 106])).
% 0.18/0.52 tff(115,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,[]))).
% 0.18/0.52 tff(116,plain,
% 0.18/0.52 (((~![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) | (~((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(Y1, C!39)) | (~member(Y2, 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))))))))))) <=> ((~![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) | (~((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(Y1, C!39)) | (~member(Y2, 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)))))))))))),
% 0.18/0.52 inference(rewrite,[status(thm)],[])).
% 0.18/0.52 tff(117,plain,
% 0.18/0.52 ((~((~((~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) | (~((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(Y1, C!39)) | (~member(Y2, 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))))))))))),
% 0.18/0.53 inference(rewrite,[status(thm)],[])).
% 0.18/0.53 tff(118,plain,
% 0.18/0.53 (((~![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) | (~((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(Y1, C!39)) | (~member(Y2, 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)))))))))))),
% 0.18/0.53 inference(monotonicity,[status(thm)],[117])).
% 0.18/0.53 tff(119,plain,
% 0.18/0.53 (((~![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) | (~((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(Y1, C!39)) | (~member(Y2, 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)))))))))))),
% 0.40/0.54 inference(transitivity,[status(thm)],[118, 116])).
% 0.40/0.54 tff(120,plain,
% 0.40/0.54 ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(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))))))))))),
% 0.40/0.54 inference(quant_inst,[status(thm)],[])).
% 0.40/0.54 tff(121,plain,
% 0.40/0.54 ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~(maps(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(Y1, C!39)) | (~member(Y2, 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))))))))))),
% 0.40/0.55 inference(modus_ponens,[status(thm)],[120, 119])).
% 0.40/0.55 tff(122,plain,
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% 0.40/0.55 inference(unit_resolution,[status(thm)],[121, 25])).
% 0.40/0.55 tff(123,plain,
% 0.40/0.55 (((~(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(Y1, C!39)) | (~member(Y2, 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) | (~((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)))))))),
% 0.40/0.55 inference(tautology,[status(thm)],[])).
% 0.40/0.55 tff(124,plain,
% 0.40/0.55 (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))))))),
% 0.40/0.55 inference(unit_resolution,[status(thm)],[123, 122])).
% 0.40/0.55 tff(125,plain,
% 0.40/0.55 (~maps(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)),
% 0.40/0.55 inference(or_elim,[status(thm)],[40])).
% 0.40/0.55 tff(126,plain,
% 0.40/0.55 ((~(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) | (~((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))))))),
% 0.41/0.56 inference(tautology,[status(thm)],[])).
% 0.41/0.56 tff(127,plain,
% 0.41/0.56 ((~(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)))))))) | (~((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))))))),
% 0.41/0.57 inference(unit_resolution,[status(thm)],[126, 125])).
% 0.41/0.57 tff(128,plain,
% 0.41/0.57 ((~((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))))))),
% 0.41/0.57 inference(unit_resolution,[status(thm)],[127, 124])).
% 0.41/0.57 tff(129,plain,
% 0.41/0.57 (~((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)))),
% 0.41/0.57 inference(unit_resolution,[status(thm)],[128, 115])).
% 0.41/0.57 tff(130,plain,
% 0.41/0.57 (((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_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)),
% 0.41/0.57 inference(tautology,[status(thm)],[])).
% 0.41/0.57 tff(131,plain,
% 0.41/0.57 (member(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)),
% 0.41/0.57 inference(unit_resolution,[status(thm)],[130, 129])).
% 0.41/0.57 tff(132,plain,
% 0.41/0.57 (((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_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)),
% 0.41/0.57 inference(tautology,[status(thm)],[])).
% 0.41/0.57 tff(133,plain,
% 0.41/0.57 (member(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)),
% 0.41/0.57 inference(unit_resolution,[status(thm)],[132, 129])).
% 0.41/0.57 tff(134,plain,
% 0.41/0.57 (((~![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_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)) | (~((~((~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_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)) | (~((~((~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))))))))))),
% 0.41/0.58 inference(rewrite,[status(thm)],[])).
% 0.41/0.58 tff(135,plain,
% 0.41/0.58 (((~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_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)) | (~((~((~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))))))))))),
% 0.41/0.58 inference(rewrite,[status(thm)],[])).
% 0.41/0.58 tff(136,plain,
% 0.41/0.58 ((~((~((~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)))) | (~((~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)))))))))),
% 0.41/0.58 inference(rewrite,[status(thm)],[])).
% 0.41/0.58 tff(137,plain,
% 0.41/0.58 (((~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)))) | (~((~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))))))))))),
% 0.41/0.59 inference(monotonicity,[status(thm)],[136])).
% 0.41/0.59 tff(138,plain,
% 0.41/0.59 (((~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_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)) | (~((~((~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))))))))))),
% 0.41/0.59 inference(transitivity,[status(thm)],[137, 135])).
% 0.41/0.59 tff(139,plain,
% 0.41/0.59 (((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_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_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)) | (~((~((~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)))))))))))),
% 0.41/0.60 inference(monotonicity,[status(thm)],[138])).
% 0.41/0.60 tff(140,plain,
% 0.41/0.60 (((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_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_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)) | (~((~((~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))))))))))),
% 0.41/0.60 inference(transitivity,[status(thm)],[139, 134])).
% 0.41/0.60 tff(141,plain,
% 0.41/0.60 ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_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))))))))))),
% 0.41/0.60 inference(quant_inst,[status(thm)],[])).
% 0.41/0.60 tff(142,plain,
% 0.41/0.60 ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | (~member(tptp_fun_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)) | (~((~((~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)))))))))),
% 0.41/0.61 inference(modus_ponens,[status(thm)],[141, 140])).
% 0.41/0.61 tff(143,plain,
% 0.41/0.61 (~((~((~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))))))))),
% 0.41/0.61 inference(unit_resolution,[status(thm)],[142, 85, 133, 131])).
% 0.41/0.61 tff(144,plain,
% 0.41/0.61 (((~((~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)))) | (~((~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)))))))),
% 0.41/0.62 inference(tautology,[status(thm)],[])).
% 0.41/0.62 tff(145,plain,
% 0.41/0.62 ((~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))))))),
% 0.41/0.62 inference(unit_resolution,[status(thm)],[144, 143])).
% 0.41/0.62 tff(146,plain,
% 0.41/0.62 (((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))) | (~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))) | 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)))),
% 0.41/0.62 inference(tautology,[status(thm)],[])).
% 0.41/0.62 tff(147,plain,
% 0.41/0.62 (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)))),
% 0.41/0.62 inference(unit_resolution,[status(thm)],[146, 129])).
% 0.41/0.62 tff(148,plain,
% 0.41/0.62 ((~((~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))))))),
% 0.41/0.62 inference(tautology,[status(thm)],[])).
% 0.41/0.62 tff(149,plain,
% 0.41/0.62 ((~((~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))))))),
% 0.41/0.62 inference(unit_resolution,[status(thm)],[148, 147])).
% 0.41/0.62 tff(150,plain,
% 0.41/0.62 (~((~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)))))),
% 0.41/0.62 inference(unit_resolution,[status(thm)],[149, 145])).
% 0.41/0.62 tff(151,plain,
% 0.41/0.62 (((~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))),
% 0.41/0.63 inference(tautology,[status(thm)],[])).
% 0.41/0.63 tff(152,plain,
% 0.41/0.63 (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))),
% 0.41/0.63 inference(unit_resolution,[status(thm)],[151, 150])).
% 0.41/0.63 tff(153,plain,
% 0.41/0.63 (((~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)),
% 0.41/0.63 inference(tautology,[status(thm)],[])).
% 0.41/0.63 tff(154,plain,
% 0.41/0.63 (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)),
% 0.41/0.63 inference(unit_resolution,[status(thm)],[153, 150])).
% 0.41/0.63 tff(155,plain,
% 0.41/0.63 (((~![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))))))),
% 0.41/0.63 inference(rewrite,[status(thm)],[])).
% 0.41/0.63 tff(156,plain,
% 0.41/0.63 ((~![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))))))),
% 0.41/0.63 inference(quant_inst,[status(thm)],[])).
% 0.41/0.63 tff(157,plain,
% 0.41/0.63 ((~![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)))))),
% 0.49/0.63 inference(modus_ponens,[status(thm)],[156, 155])).
% 0.49/0.63 tff(158,plain,
% 0.49/0.63 (~((~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))))),
% 0.49/0.63 inference(unit_resolution,[status(thm)],[157, 47, 133])).
% 0.49/0.63 tff(159,plain,
% 0.49/0.63 (((~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))),
% 0.49/0.63 inference(tautology,[status(thm)],[])).
% 0.49/0.63 tff(160,plain,
% 0.49/0.63 (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))),
% 0.49/0.63 inference(unit_resolution,[status(thm)],[159, 158])).
% 0.49/0.63 tff(161,plain,
% 0.49/0.63 (((~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)),
% 0.49/0.63 inference(tautology,[status(thm)],[])).
% 0.49/0.63 tff(162,plain,
% 0.49/0.63 (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)),
% 0.49/0.63 inference(unit_resolution,[status(thm)],[161, 158])).
% 0.49/0.63 tff(163,plain,
% 0.49/0.63 (((~![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))))) | ![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)))),
% 0.49/0.63 inference(tautology,[status(thm)],[])).
% 0.49/0.63 tff(164,plain,
% 0.49/0.63 (![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)))),
% 0.49/0.63 inference(unit_resolution,[status(thm)],[163, 45])).
% 0.49/0.63 tff(165,plain,
% 0.49/0.63 (((~![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)))) | ((~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))) | (~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))) | (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) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)) | (~member(Y2, 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)) | (~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_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))) | (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)))),
% 0.49/0.64 inference(rewrite,[status(thm)],[])).
% 0.49/0.64 tff(166,plain,
% 0.49/0.64 (((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)) | (~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_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_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))) | (~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))) | (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)))),
% 0.49/0.64 inference(rewrite,[status(thm)],[])).
% 0.49/0.64 tff(167,plain,
% 0.49/0.64 (((~![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)))) | ((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)) | (~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_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)))) <=> ((~![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)))) | ((~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))) | (~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))) | (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))))),
% 0.49/0.64 inference(monotonicity,[status(thm)],[166])).
% 0.49/0.64 tff(168,plain,
% 0.49/0.64 (((~![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)))) | ((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)) | (~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_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)))) <=> ((~![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)))) | (~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))) | (~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))) | (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)))),
% 0.49/0.65 inference(transitivity,[status(thm)],[167, 165])).
% 0.49/0.65 tff(169,plain,
% 0.49/0.65 ((~![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)))) | ((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)) | (~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_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)))),
% 0.49/0.65 inference(quant_inst,[status(thm)],[])).
% 0.49/0.65 tff(170,plain,
% 0.49/0.65 ((~![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)))) | (~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))) | (~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))) | (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))),
% 0.49/0.65 inference(modus_ponens,[status(thm)],[169, 168])).
% 0.49/0.65 tff(171,plain,
% 0.49/0.65 (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)),
% 0.49/0.65 inference(unit_resolution,[status(thm)],[170, 164, 133, 162, 160, 154, 152])).
% 0.49/0.65 tff(172,plain,
% 0.49/0.65 (((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_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)),
% 0.49/0.65 inference(tautology,[status(thm)],[])).
% 0.49/0.65 tff(173,plain,
% 0.49/0.65 (member(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)),
% 0.49/0.65 inference(unit_resolution,[status(thm)],[172, 129])).
% 0.49/0.65 tff(174,plain,
% 0.49/0.65 (((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_Y2_5(C!39, A!41, 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), 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_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_Y2_5(C!39, A!41, 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), 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))))))))))),
% 0.49/0.66 inference(rewrite,[status(thm)],[])).
% 0.49/0.66 tff(175,plain,
% 0.49/0.66 (((~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_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_Y2_5(C!39, A!41, 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), 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))))))))))),
% 0.49/0.67 inference(rewrite,[status(thm)],[])).
% 0.49/0.67 tff(176,plain,
% 0.49/0.67 ((~((~((~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)))) | (~((~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)))))))))),
% 0.49/0.67 inference(rewrite,[status(thm)],[])).
% 0.49/0.67 tff(177,plain,
% 0.49/0.67 (((~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)))) | (~((~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))))))))))),
% 0.52/0.67 inference(monotonicity,[status(thm)],[176])).
% 0.52/0.67 tff(178,plain,
% 0.52/0.67 (((~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_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_Y2_5(C!39, A!41, 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), 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))))))))))),
% 0.52/0.68 inference(transitivity,[status(thm)],[177, 175])).
% 0.52/0.68 tff(179,plain,
% 0.52/0.68 (((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_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_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_Y2_5(C!39, A!41, 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), 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)))))))))))),
% 0.52/0.68 inference(monotonicity,[status(thm)],[178])).
% 0.52/0.68 tff(180,plain,
% 0.52/0.68 (((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_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_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_Y2_5(C!39, A!41, 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), 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))))))))))),
% 0.52/0.69 inference(transitivity,[status(thm)],[179, 174])).
% 0.52/0.69 tff(181,plain,
% 0.52/0.69 ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_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))))))))))),
% 0.52/0.69 inference(quant_inst,[status(thm)],[])).
% 0.52/0.69 tff(182,plain,
% 0.52/0.69 ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | (~member(tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_Y2_5(C!39, A!41, 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), 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)))))))))),
% 0.52/0.69 inference(modus_ponens,[status(thm)],[181, 180])).
% 0.52/0.69 tff(183,plain,
% 0.52/0.69 (~((~((~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))))))))),
% 0.52/0.69 inference(unit_resolution,[status(thm)],[182, 85, 133, 173])).
% 0.52/0.69 tff(184,plain,
% 0.52/0.69 (((~((~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)))) | (~((~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)))))))),
% 0.52/0.70 inference(tautology,[status(thm)],[])).
% 0.52/0.70 tff(185,plain,
% 0.52/0.70 ((~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))))))),
% 0.52/0.70 inference(unit_resolution,[status(thm)],[184, 183])).
% 0.52/0.70 tff(186,plain,
% 0.52/0.70 (((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))) | 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)))),
% 0.52/0.70 inference(tautology,[status(thm)],[])).
% 0.52/0.70 tff(187,plain,
% 0.52/0.70 (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)))),
% 0.52/0.71 inference(unit_resolution,[status(thm)],[186, 129])).
% 0.52/0.71 tff(188,plain,
% 0.52/0.71 ((~((~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))))))),
% 0.52/0.71 inference(tautology,[status(thm)],[])).
% 0.52/0.71 tff(189,plain,
% 0.52/0.71 ((~((~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))))))),
% 0.52/0.71 inference(unit_resolution,[status(thm)],[188, 187])).
% 0.52/0.71 tff(190,plain,
% 0.52/0.71 (~((~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)))))),
% 0.52/0.71 inference(unit_resolution,[status(thm)],[189, 185])).
% 0.52/0.71 tff(191,plain,
% 0.52/0.71 (((~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))),
% 0.52/0.71 inference(tautology,[status(thm)],[])).
% 0.52/0.71 tff(192,plain,
% 0.52/0.71 (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))),
% 0.52/0.71 inference(unit_resolution,[status(thm)],[191, 190])).
% 0.52/0.71 tff(193,plain,
% 0.52/0.71 (((~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)),
% 0.52/0.71 inference(tautology,[status(thm)],[])).
% 0.52/0.71 tff(194,plain,
% 0.52/0.71 (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)),
% 0.52/0.71 inference(unit_resolution,[status(thm)],[193, 190])).
% 0.52/0.71 tff(195,plain,
% 0.52/0.71 (((~![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)))) | ((~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))) | (~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))) | (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) | (~apply(F!43, X, Y1)) | (~apply(F!43, X, Y2)) | (~member(X, A!41)) | (~member(Y1, B!40)) | (~member(Y2, 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)) | (~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_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))) | (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)))),
% 0.52/0.72 inference(rewrite,[status(thm)],[])).
% 0.52/0.72 tff(196,plain,
% 0.52/0.72 (((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)) | (~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_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_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))) | (~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))) | (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)))),
% 0.52/0.72 inference(rewrite,[status(thm)],[])).
% 0.52/0.72 tff(197,plain,
% 0.52/0.72 (((~![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)))) | ((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)) | (~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_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)))) <=> ((~![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)))) | ((~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))) | (~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))) | (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))))),
% 0.52/0.72 inference(monotonicity,[status(thm)],[196])).
% 0.52/0.72 tff(198,plain,
% 0.52/0.72 (((~![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)))) | ((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)) | (~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_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)))) <=> ((~![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)))) | (~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))) | (~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))) | (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)))),
% 0.52/0.73 inference(transitivity,[status(thm)],[197, 195])).
% 0.52/0.73 tff(199,plain,
% 0.52/0.73 ((~![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)))) | ((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)) | (~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_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)))),
% 0.52/0.73 inference(quant_inst,[status(thm)],[])).
% 0.52/0.73 tff(200,plain,
% 0.52/0.73 ((~![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)))) | (~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))) | (~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))) | (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))),
% 0.59/0.73 inference(modus_ponens,[status(thm)],[199, 198])).
% 0.59/0.73 tff(201,plain,
% 0.59/0.73 (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)),
% 0.59/0.73 inference(unit_resolution,[status(thm)],[200, 164, 133, 162, 160, 194, 192])).
% 0.59/0.73 tff(202,plain,
% 0.59/0.73 (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_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)),
% 0.59/0.73 inference(symmetry,[status(thm)],[201])).
% 0.59/0.73 tff(203,plain,
% 0.59/0.73 (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_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)),
% 0.59/0.73 inference(transitivity,[status(thm)],[202, 171])).
% 0.59/0.73 tff(204,plain,
% 0.59/0.73 (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_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)))),
% 0.59/0.73 inference(monotonicity,[status(thm)],[203])).
% 0.59/0.73 tff(205,plain,
% 0.59/0.73 (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_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_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))),
% 0.59/0.73 inference(symmetry,[status(thm)],[204])).
% 0.59/0.73 tff(206,plain,
% 0.59/0.73 (((~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)))),
% 0.59/0.73 inference(tautology,[status(thm)],[])).
% 0.59/0.73 tff(207,plain,
% 0.59/0.73 (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)))),
% 0.59/0.73 inference(unit_resolution,[status(thm)],[206, 150])).
% 0.59/0.73 tff(208,plain,
% 0.59/0.73 (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_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))),
% 0.59/0.74 inference(modus_ponens,[status(thm)],[207, 205])).
% 0.59/0.74 tff(209,plain,
% 0.59/0.74 (((~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)))),
% 0.59/0.74 inference(tautology,[status(thm)],[])).
% 0.59/0.74 tff(210,plain,
% 0.59/0.74 (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)))),
% 0.59/0.74 inference(unit_resolution,[status(thm)],[209, 190])).
% 0.59/0.74 tff(211,plain,
% 0.59/0.74 (((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))) | (~(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))))),
% 0.59/0.74 inference(tautology,[status(thm)],[])).
% 0.59/0.74 tff(212,plain,
% 0.59/0.74 (~(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)))),
% 0.59/0.74 inference(unit_resolution,[status(thm)],[211, 129])).
% 0.59/0.74 tff(213,plain,
% 0.59/0.74 (((~![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))))) | ![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)))),
% 0.59/0.74 inference(tautology,[status(thm)],[])).
% 0.59/0.74 tff(214,plain,
% 0.59/0.74 (![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)))),
% 0.59/0.74 inference(unit_resolution,[status(thm)],[213, 61])).
% 0.59/0.74 tff(215,plain,
% 0.59/0.74 (((~![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)))) | ((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)) | (~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_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(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_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))) <=> ((~![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)))) | (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)) | (~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_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(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_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))),
% 0.59/0.75 inference(rewrite,[status(thm)],[])).
% 0.59/0.75 tff(216,plain,
% 0.59/0.75 (((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_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_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_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)) | (~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))) <=> ((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)) | (~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_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(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_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))),
% 0.59/0.75 inference(rewrite,[status(thm)],[])).
% 0.59/0.75 tff(217,plain,
% 0.59/0.75 (((~![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)))) | ((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_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_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_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)) | (~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)))) <=> ((~![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)))) | ((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)) | (~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_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(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_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))),
% 0.59/0.75 inference(monotonicity,[status(thm)],[216])).
% 0.59/0.75 tff(218,plain,
% 0.59/0.75 (((~![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)))) | ((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_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_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_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)) | (~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)))) <=> ((~![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)))) | (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)) | (~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_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(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_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))),
% 0.59/0.76 inference(transitivity,[status(thm)],[217, 215])).
% 0.59/0.76 tff(219,plain,
% 0.59/0.76 ((~![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)))) | ((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_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_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_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)) | (~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)))),
% 0.59/0.76 inference(quant_inst,[status(thm)],[])).
% 0.59/0.76 tff(220,plain,
% 0.59/0.76 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G!42, X, Y1)) | (~apply(G!42, X, Y2)) | (~member(X, B!40)) | (~member(Y1, C!39)) | (~member(Y2, C!39)))) | (tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)) = tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | (~member(tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_Y_8(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))),
% 0.59/0.76 inference(modus_ponens,[status(thm)],[219, 218])).
% 0.59/0.76 tff(221,plain,
% 0.59/0.76 (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y2_5(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X_7(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y1_6(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))),
% 0.62/0.76 inference(unit_resolution,[status(thm)],[220, 214, 212, 131, 173, 194, 210])).
% 0.62/0.76 tff(222,plain,
% 0.62/0.76 ($false),
% 0.62/0.76 inference(unit_resolution,[status(thm)],[221, 208])).
% 0.62/0.76 % SZS output end Proof
%------------------------------------------------------------------------------