TSTP Solution File: SET749+4 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET749+4 : TPTP v8.1.0. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n013.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 05:07:51 EDT 2022
% Result : Theorem 0.22s 0.54s
% Output : Proof 0.73s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET749+4 : TPTP v8.1.0. Bugfixed v2.2.1.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.35 % Computer : n013.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sat Sep 3 07:39:17 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.35 Usage: tptp [options] [-file:]file
% 0.14/0.35 -h, -? prints this message.
% 0.14/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.35 -m, -model generate model.
% 0.14/0.35 -p, -proof generate proof.
% 0.14/0.35 -c, -core generate unsat core of named formulas.
% 0.14/0.35 -st, -statistics display statistics.
% 0.14/0.35 -t:timeout set timeout (in second).
% 0.14/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.35 -<param>:<value> configuration parameter and value.
% 0.14/0.35 -o:<output-file> file to place output in.
% 0.22/0.54 % SZS status Theorem
% 0.22/0.54 % SZS output start Proof
% 0.22/0.54 tff(apply_type, type, (
% 0.22/0.54 apply: ( $i * $i * $i ) > $o)).
% 0.22/0.54 tff(tptp_fun_Y_3_type, type, (
% 0.22/0.54 tptp_fun_Y_3: ( $i * $i * $i ) > $i)).
% 0.22/0.54 tff(tptp_fun_G_45_type, type, (
% 0.22/0.54 tptp_fun_G_45: $i)).
% 0.22/0.54 tff(tptp_fun_C_42_type, type, (
% 0.22/0.54 tptp_fun_C_42: $i)).
% 0.22/0.54 tff(tptp_fun_Y_8_type, type, (
% 0.22/0.54 tptp_fun_Y_8: ( $i * $i * $i * $i * $i ) > $i)).
% 0.22/0.54 tff(tptp_fun_F_46_type, type, (
% 0.22/0.54 tptp_fun_F_46: $i)).
% 0.22/0.54 tff(tptp_fun_B_43_type, type, (
% 0.22/0.54 tptp_fun_B_43: $i)).
% 0.22/0.54 tff(tptp_fun_X2_28_type, type, (
% 0.22/0.54 tptp_fun_X2_28: ( $i * $i * $i * $i * $i ) > $i)).
% 0.22/0.54 tff(compose_function_type, type, (
% 0.22/0.54 compose_function: ( $i * $i * $i * $i * $i ) > $i)).
% 0.22/0.54 tff(tptp_fun_A_44_type, type, (
% 0.22/0.54 tptp_fun_A_44: $i)).
% 0.22/0.54 tff(tptp_fun_R_41_type, type, (
% 0.22/0.54 tptp_fun_R_41: $i)).
% 0.22/0.54 tff(tptp_fun_T_39_type, type, (
% 0.22/0.54 tptp_fun_T_39: $i)).
% 0.22/0.54 tff(tptp_fun_Y2_27_type, type, (
% 0.22/0.54 tptp_fun_Y2_27: ( $i * $i * $i * $i * $i ) > $i)).
% 0.22/0.54 tff(tptp_fun_X1_30_type, type, (
% 0.22/0.54 tptp_fun_X1_30: ( $i * $i * $i * $i * $i ) > $i)).
% 0.22/0.54 tff(tptp_fun_Y1_29_type, type, (
% 0.22/0.54 tptp_fun_Y1_29: ( $i * $i * $i * $i * $i ) > $i)).
% 0.22/0.54 tff(member_type, type, (
% 0.22/0.54 member: ( $i * $i ) > $o)).
% 0.22/0.54 tff(increasing_type, type, (
% 0.22/0.54 increasing: ( $i * $i * $i * $i * $i ) > $o)).
% 0.22/0.54 tff(decreasing_type, type, (
% 0.22/0.54 decreasing: ( $i * $i * $i * $i * $i ) > $o)).
% 0.22/0.54 tff(tptp_fun_S_40_type, type, (
% 0.22/0.54 tptp_fun_S_40: $i)).
% 0.22/0.54 tff(maps_type, type, (
% 0.22/0.54 maps: ( $i * $i * $i ) > $o)).
% 0.22/0.54 tff(tptp_fun_X_4_type, type, (
% 0.22/0.54 tptp_fun_X_4: ( $i * $i * $i ) > $i)).
% 0.22/0.54 tff(tptp_fun_Y2_5_type, type, (
% 0.22/0.54 tptp_fun_Y2_5: ( $i * $i * $i ) > $i)).
% 0.22/0.54 tff(tptp_fun_Y1_6_type, type, (
% 0.22/0.54 tptp_fun_Y1_6: ( $i * $i * $i ) > $i)).
% 0.22/0.54 tff(tptp_fun_X_7_type, type, (
% 0.22/0.54 tptp_fun_X_7: ( $i * $i * $i ) > $i)).
% 0.22/0.54 tff(tptp_fun_Y2_31_type, type, (
% 0.22/0.54 tptp_fun_Y2_31: ( $i * $i * $i * $i * $i ) > $i)).
% 0.22/0.54 tff(tptp_fun_X2_32_type, type, (
% 0.22/0.54 tptp_fun_X2_32: ( $i * $i * $i * $i * $i ) > $i)).
% 0.22/0.54 tff(tptp_fun_Y1_33_type, type, (
% 0.22/0.54 tptp_fun_Y1_33: ( $i * $i * $i * $i * $i ) > $i)).
% 0.22/0.54 tff(tptp_fun_X1_34_type, type, (
% 0.22/0.54 tptp_fun_X1_34: ( $i * $i * $i * $i * $i ) > $i)).
% 0.22/0.54 tff(1,plain,
% 0.22/0.54 (^[F: $i, A: $i, R: $i, B: $i, S: $i] : refl((~((~((~increasing(F, A, R, B, S)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(S, Y1, Y2) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(R, X1, X2)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2))))) | (~(increasing(F, A, R, B, S) | (~(apply(S, tptp_fun_Y1_29(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)) | (~member(tptp_fun_X1_30(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_29(S, B, R, A, F), B)) | (~member(tptp_fun_X2_28(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_27(S, B, R, A, F), B)) | (~apply(R, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_X2_28(S, B, R, A, F))) | (~apply(F, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_Y1_29(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_28(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F))))))))) <=> (~((~((~increasing(F, A, R, B, S)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(S, Y1, Y2) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(R, X1, X2)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2))))) | (~(increasing(F, A, R, B, S) | (~(apply(S, tptp_fun_Y1_29(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)) | (~member(tptp_fun_X1_30(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_29(S, B, R, A, F), B)) | (~member(tptp_fun_X2_28(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_27(S, B, R, A, F), B)) | (~apply(R, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_X2_28(S, B, R, A, F))) | (~apply(F, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_Y1_29(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_28(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F))))))))))),
% 0.22/0.54 inference(bind,[status(th)],[])).
% 0.22/0.54 tff(2,plain,
% 0.22/0.54 (![F: $i, A: $i, R: $i, B: $i, S: $i] : (~((~((~increasing(F, A, R, B, S)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(S, Y1, Y2) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(R, X1, X2)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2))))) | (~(increasing(F, A, R, B, S) | (~(apply(S, tptp_fun_Y1_29(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)) | (~member(tptp_fun_X1_30(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_29(S, B, R, A, F), B)) | (~member(tptp_fun_X2_28(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_27(S, B, R, A, F), B)) | (~apply(R, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_X2_28(S, B, R, A, F))) | (~apply(F, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_Y1_29(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_28(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F))))))))) <=> ![F: $i, A: $i, R: $i, B: $i, S: $i] : (~((~((~increasing(F, A, R, B, S)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(S, Y1, Y2) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(R, X1, X2)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2))))) | (~(increasing(F, A, R, B, S) | (~(apply(S, tptp_fun_Y1_29(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)) | (~member(tptp_fun_X1_30(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_29(S, B, R, A, F), B)) | (~member(tptp_fun_X2_28(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_27(S, B, R, A, F), B)) | (~apply(R, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_X2_28(S, B, R, A, F))) | (~apply(F, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_Y1_29(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_28(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)))))))))),
% 0.22/0.54 inference(quant_intro,[status(thm)],[1])).
% 0.22/0.54 tff(3,plain,
% 0.22/0.54 (^[F: $i, A: $i, R: $i, B: $i, S: $i] : rewrite((~((~((~increasing(F, A, R, B, S)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(S, Y1, Y2) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(R, X1, X2)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2))))) | (~(increasing(F, A, R, B, S) | (~(apply(S, tptp_fun_Y1_29(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)) | (~member(tptp_fun_X1_30(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_29(S, B, R, A, F), B)) | (~member(tptp_fun_X2_28(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_27(S, B, R, A, F), B)) | (~apply(R, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_X2_28(S, B, R, A, F))) | (~apply(F, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_Y1_29(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_28(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F))))))))) <=> (~((~((~increasing(F, A, R, B, S)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(S, Y1, Y2) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(R, X1, X2)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2))))) | (~(increasing(F, A, R, B, S) | (~(apply(S, tptp_fun_Y1_29(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)) | (~member(tptp_fun_X1_30(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_29(S, B, R, A, F), B)) | (~member(tptp_fun_X2_28(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_27(S, B, R, A, F), B)) | (~apply(R, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_X2_28(S, B, R, A, F))) | (~apply(F, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_Y1_29(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_28(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F))))))))))),
% 0.22/0.54 inference(bind,[status(th)],[])).
% 0.22/0.54 tff(4,plain,
% 0.22/0.54 (![F: $i, A: $i, R: $i, B: $i, S: $i] : (~((~((~increasing(F, A, R, B, S)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(S, Y1, Y2) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(R, X1, X2)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2))))) | (~(increasing(F, A, R, B, S) | (~(apply(S, tptp_fun_Y1_29(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)) | (~member(tptp_fun_X1_30(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_29(S, B, R, A, F), B)) | (~member(tptp_fun_X2_28(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_27(S, B, R, A, F), B)) | (~apply(R, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_X2_28(S, B, R, A, F))) | (~apply(F, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_Y1_29(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_28(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F))))))))) <=> ![F: $i, A: $i, R: $i, B: $i, S: $i] : (~((~((~increasing(F, A, R, B, S)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(S, Y1, Y2) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(R, X1, X2)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2))))) | (~(increasing(F, A, R, B, S) | (~(apply(S, tptp_fun_Y1_29(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)) | (~member(tptp_fun_X1_30(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_29(S, B, R, A, F), B)) | (~member(tptp_fun_X2_28(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_27(S, B, R, A, F), B)) | (~apply(R, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_X2_28(S, B, R, A, F))) | (~apply(F, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_Y1_29(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_28(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)))))))))),
% 0.22/0.54 inference(quant_intro,[status(thm)],[3])).
% 0.22/0.54 tff(5,plain,
% 0.22/0.54 (![F: $i, A: $i, R: $i, B: $i, S: $i] : (~((~((~increasing(F, A, R, B, S)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(S, Y1, Y2) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(R, X1, X2)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2))))) | (~(increasing(F, A, R, B, S) | (~(apply(S, tptp_fun_Y1_29(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)) | (~member(tptp_fun_X1_30(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_29(S, B, R, A, F), B)) | (~member(tptp_fun_X2_28(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_27(S, B, R, A, F), B)) | (~apply(R, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_X2_28(S, B, R, A, F))) | (~apply(F, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_Y1_29(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_28(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F))))))))) <=> ![F: $i, A: $i, R: $i, B: $i, S: $i] : (~((~((~increasing(F, A, R, B, S)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(S, Y1, Y2) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(R, X1, X2)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2))))) | (~(increasing(F, A, R, B, S) | (~(apply(S, tptp_fun_Y1_29(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)) | (~member(tptp_fun_X1_30(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_29(S, B, R, A, F), B)) | (~member(tptp_fun_X2_28(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_27(S, B, R, A, F), B)) | (~apply(R, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_X2_28(S, B, R, A, F))) | (~apply(F, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_Y1_29(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_28(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)))))))))),
% 0.22/0.54 inference(transitivity,[status(thm)],[4, 2])).
% 0.22/0.54 tff(6,plain,
% 0.22/0.54 (^[F: $i, A: $i, R: $i, B: $i, S: $i] : trans(monotonicity(rewrite(((~increasing(F, A, R, B, S)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~(member(X1, A) & member(Y1, B) & member(X2, A) & member(Y2, B) & apply(R, X1, X2) & apply(F, X1, Y1) & apply(F, X2, Y2))) | apply(S, Y1, Y2))) <=> ((~increasing(F, A, R, B, S)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(S, Y1, Y2) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(R, X1, X2)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2))))), trans(monotonicity(rewrite((~((~(member(tptp_fun_X1_30(S, B, R, A, F), A) & member(tptp_fun_Y1_29(S, B, R, A, F), B) & member(tptp_fun_X2_28(S, B, R, A, F), A) & member(tptp_fun_Y2_27(S, B, R, A, F), B) & apply(R, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_X2_28(S, B, R, A, F)) & apply(F, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_Y1_29(S, B, R, A, F)) & apply(F, tptp_fun_X2_28(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)))) | apply(S, tptp_fun_Y1_29(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)))) <=> (~(apply(S, tptp_fun_Y1_29(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)) | (~member(tptp_fun_X1_30(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_29(S, B, R, A, F), B)) | (~member(tptp_fun_X2_28(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_27(S, B, R, A, F), B)) | (~apply(R, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_X2_28(S, B, R, A, F))) | (~apply(F, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_Y1_29(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_28(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)))))), ((increasing(F, A, R, B, S) | (~((~(member(tptp_fun_X1_30(S, B, R, A, F), A) & member(tptp_fun_Y1_29(S, B, R, A, F), B) & member(tptp_fun_X2_28(S, B, R, A, F), A) & member(tptp_fun_Y2_27(S, B, R, A, F), B) & apply(R, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_X2_28(S, B, R, A, F)) & apply(F, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_Y1_29(S, B, R, A, F)) & apply(F, tptp_fun_X2_28(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)))) | apply(S, tptp_fun_Y1_29(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F))))) <=> (increasing(F, A, R, B, S) | (~(apply(S, tptp_fun_Y1_29(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)) | (~member(tptp_fun_X1_30(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_29(S, B, R, A, F), B)) | (~member(tptp_fun_X2_28(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_27(S, B, R, A, F), B)) | (~apply(R, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_X2_28(S, B, R, A, F))) | (~apply(F, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_Y1_29(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_28(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)))))))), rewrite((increasing(F, A, R, B, S) | (~(apply(S, tptp_fun_Y1_29(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)) | (~member(tptp_fun_X1_30(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_29(S, B, R, A, F), B)) | (~member(tptp_fun_X2_28(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_27(S, B, R, A, F), B)) | (~apply(R, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_X2_28(S, B, R, A, F))) | (~apply(F, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_Y1_29(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_28(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)))))) <=> (increasing(F, A, R, B, S) | (~(apply(S, tptp_fun_Y1_29(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)) | (~member(tptp_fun_X1_30(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_29(S, B, R, A, F), B)) | (~member(tptp_fun_X2_28(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_27(S, B, R, A, F), B)) | (~apply(R, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_X2_28(S, B, R, A, F))) | (~apply(F, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_Y1_29(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_28(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F))))))), ((increasing(F, A, R, B, S) | (~((~(member(tptp_fun_X1_30(S, B, R, A, F), A) & member(tptp_fun_Y1_29(S, B, R, A, F), B) & member(tptp_fun_X2_28(S, B, R, A, F), A) & member(tptp_fun_Y2_27(S, B, R, A, F), B) & apply(R, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_X2_28(S, B, R, A, F)) & apply(F, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_Y1_29(S, B, R, A, F)) & apply(F, tptp_fun_X2_28(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)))) | apply(S, tptp_fun_Y1_29(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F))))) <=> (increasing(F, A, R, B, S) | (~(apply(S, tptp_fun_Y1_29(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)) | (~member(tptp_fun_X1_30(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_29(S, B, R, A, F), B)) | (~member(tptp_fun_X2_28(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_27(S, B, R, A, F), B)) | (~apply(R, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_X2_28(S, B, R, A, F))) | (~apply(F, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_Y1_29(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_28(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)))))))), ((((~increasing(F, A, R, B, S)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~(member(X1, A) & member(Y1, B) & member(X2, A) & member(Y2, B) & apply(R, X1, X2) & apply(F, X1, Y1) & apply(F, X2, Y2))) | apply(S, Y1, Y2))) & (increasing(F, A, R, B, S) | (~((~(member(tptp_fun_X1_30(S, B, R, A, F), A) & member(tptp_fun_Y1_29(S, B, R, A, F), B) & member(tptp_fun_X2_28(S, B, R, A, F), A) & member(tptp_fun_Y2_27(S, B, R, A, F), B) & apply(R, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_X2_28(S, B, R, A, F)) & apply(F, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_Y1_29(S, B, R, A, F)) & apply(F, tptp_fun_X2_28(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)))) | apply(S, tptp_fun_Y1_29(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)))))) <=> (((~increasing(F, A, R, B, S)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(S, Y1, Y2) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(R, X1, X2)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2)))) & (increasing(F, A, R, B, S) | (~(apply(S, tptp_fun_Y1_29(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)) | (~member(tptp_fun_X1_30(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_29(S, B, R, A, F), B)) | (~member(tptp_fun_X2_28(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_27(S, B, R, A, F), B)) | (~apply(R, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_X2_28(S, B, R, A, F))) | (~apply(F, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_Y1_29(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_28(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F))))))))), rewrite((((~increasing(F, A, R, B, S)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(S, Y1, Y2) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(R, X1, X2)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2)))) & (increasing(F, A, R, B, S) | (~(apply(S, tptp_fun_Y1_29(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)) | (~member(tptp_fun_X1_30(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_29(S, B, R, A, F), B)) | (~member(tptp_fun_X2_28(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_27(S, B, R, A, F), B)) | (~apply(R, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_X2_28(S, B, R, A, F))) | (~apply(F, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_Y1_29(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_28(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F))))))) <=> (~((~((~increasing(F, A, R, B, S)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(S, Y1, Y2) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(R, X1, X2)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2))))) | (~(increasing(F, A, R, B, S) | (~(apply(S, tptp_fun_Y1_29(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)) | (~member(tptp_fun_X1_30(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_29(S, B, R, A, F), B)) | (~member(tptp_fun_X2_28(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_27(S, B, R, A, F), B)) | (~apply(R, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_X2_28(S, B, R, A, F))) | (~apply(F, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_Y1_29(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_28(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)))))))))), ((((~increasing(F, A, R, B, S)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~(member(X1, A) & member(Y1, B) & member(X2, A) & member(Y2, B) & apply(R, X1, X2) & apply(F, X1, Y1) & apply(F, X2, Y2))) | apply(S, Y1, Y2))) & (increasing(F, A, R, B, S) | (~((~(member(tptp_fun_X1_30(S, B, R, A, F), A) & member(tptp_fun_Y1_29(S, B, R, A, F), B) & member(tptp_fun_X2_28(S, B, R, A, F), A) & member(tptp_fun_Y2_27(S, B, R, A, F), B) & apply(R, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_X2_28(S, B, R, A, F)) & apply(F, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_Y1_29(S, B, R, A, F)) & apply(F, tptp_fun_X2_28(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)))) | apply(S, tptp_fun_Y1_29(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)))))) <=> (~((~((~increasing(F, A, R, B, S)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(S, Y1, Y2) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(R, X1, X2)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2))))) | (~(increasing(F, A, R, B, S) | (~(apply(S, tptp_fun_Y1_29(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)) | (~member(tptp_fun_X1_30(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_29(S, B, R, A, F), B)) | (~member(tptp_fun_X2_28(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_27(S, B, R, A, F), B)) | (~apply(R, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_X2_28(S, B, R, A, F))) | (~apply(F, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_Y1_29(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_28(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)))))))))))),
% 0.22/0.54 inference(bind,[status(th)],[])).
% 0.22/0.54 tff(7,plain,
% 0.22/0.54 (![F: $i, A: $i, R: $i, B: $i, S: $i] : (((~increasing(F, A, R, B, S)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~(member(X1, A) & member(Y1, B) & member(X2, A) & member(Y2, B) & apply(R, X1, X2) & apply(F, X1, Y1) & apply(F, X2, Y2))) | apply(S, Y1, Y2))) & (increasing(F, A, R, B, S) | (~((~(member(tptp_fun_X1_30(S, B, R, A, F), A) & member(tptp_fun_Y1_29(S, B, R, A, F), B) & member(tptp_fun_X2_28(S, B, R, A, F), A) & member(tptp_fun_Y2_27(S, B, R, A, F), B) & apply(R, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_X2_28(S, B, R, A, F)) & apply(F, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_Y1_29(S, B, R, A, F)) & apply(F, tptp_fun_X2_28(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)))) | apply(S, tptp_fun_Y1_29(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)))))) <=> ![F: $i, A: $i, R: $i, B: $i, S: $i] : (~((~((~increasing(F, A, R, B, S)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(S, Y1, Y2) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(R, X1, X2)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2))))) | (~(increasing(F, A, R, B, S) | (~(apply(S, tptp_fun_Y1_29(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)) | (~member(tptp_fun_X1_30(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_29(S, B, R, A, F), B)) | (~member(tptp_fun_X2_28(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_27(S, B, R, A, F), B)) | (~apply(R, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_X2_28(S, B, R, A, F))) | (~apply(F, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_Y1_29(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_28(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)))))))))),
% 0.22/0.54 inference(quant_intro,[status(thm)],[6])).
% 0.22/0.54 tff(8,plain,
% 0.22/0.54 (![F: $i, A: $i, R: $i, B: $i, S: $i] : (increasing(F, A, R, B, S) <=> ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~(member(X1, A) & member(Y1, B) & member(X2, A) & member(Y2, B) & apply(R, X1, X2) & apply(F, X1, Y1) & apply(F, X2, Y2))) | apply(S, Y1, Y2))) <=> ![F: $i, A: $i, R: $i, B: $i, S: $i] : (increasing(F, A, R, B, S) <=> ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~(member(X1, A) & member(Y1, B) & member(X2, A) & member(Y2, B) & apply(R, X1, X2) & apply(F, X1, Y1) & apply(F, X2, Y2))) | apply(S, Y1, Y2)))),
% 0.22/0.54 inference(rewrite,[status(thm)],[])).
% 0.22/0.54 tff(9,plain,
% 0.22/0.54 (^[F: $i, A: $i, R: $i, B: $i, S: $i] : rewrite((increasing(F, A, R, B, S) <=> ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (((((((member(X1, A) & member(Y1, B)) & member(X2, A)) & member(Y2, B)) & apply(R, X1, X2)) & apply(F, X1, Y1)) & apply(F, X2, Y2)) => apply(S, Y1, Y2))) <=> (increasing(F, A, R, B, S) <=> ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~(member(X1, A) & member(Y1, B) & member(X2, A) & member(Y2, B) & apply(R, X1, X2) & apply(F, X1, Y1) & apply(F, X2, Y2))) | apply(S, Y1, Y2))))),
% 0.22/0.54 inference(bind,[status(th)],[])).
% 0.22/0.54 tff(10,plain,
% 0.22/0.54 (![F: $i, A: $i, R: $i, B: $i, S: $i] : (increasing(F, A, R, B, S) <=> ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (((((((member(X1, A) & member(Y1, B)) & member(X2, A)) & member(Y2, B)) & apply(R, X1, X2)) & apply(F, X1, Y1)) & apply(F, X2, Y2)) => apply(S, Y1, Y2))) <=> ![F: $i, A: $i, R: $i, B: $i, S: $i] : (increasing(F, A, R, B, S) <=> ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~(member(X1, A) & member(Y1, B) & member(X2, A) & member(Y2, B) & apply(R, X1, X2) & apply(F, X1, Y1) & apply(F, X2, Y2))) | apply(S, Y1, Y2)))),
% 0.22/0.54 inference(quant_intro,[status(thm)],[9])).
% 0.22/0.54 tff(11,axiom,(![F: $i, A: $i, R: $i, B: $i, S: $i] : (increasing(F, A, R, B, S) <=> ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (((((((member(X1, A) & member(Y1, B)) & member(X2, A)) & member(Y2, B)) & apply(R, X1, X2)) & apply(F, X1, Y1)) & apply(F, X2, Y2)) => apply(S, Y1, Y2)))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+1.ax','increasing_function')).
% 0.22/0.54 tff(12,plain,
% 0.22/0.54 (![F: $i, A: $i, R: $i, B: $i, S: $i] : (increasing(F, A, R, B, S) <=> ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~(member(X1, A) & member(Y1, B) & member(X2, A) & member(Y2, B) & apply(R, X1, X2) & apply(F, X1, Y1) & apply(F, X2, Y2))) | apply(S, Y1, Y2)))),
% 0.22/0.54 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.22/0.54 tff(13,plain,
% 0.22/0.54 (![F: $i, A: $i, R: $i, B: $i, S: $i] : (increasing(F, A, R, B, S) <=> ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~(member(X1, A) & member(Y1, B) & member(X2, A) & member(Y2, B) & apply(R, X1, X2) & apply(F, X1, Y1) & apply(F, X2, Y2))) | apply(S, Y1, Y2)))),
% 0.22/0.54 inference(modus_ponens,[status(thm)],[12, 8])).
% 0.22/0.54 tff(14,plain,(
% 0.22/0.54 ![F: $i, A: $i, R: $i, B: $i, S: $i] : (((~increasing(F, A, R, B, S)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~(member(X1, A) & member(Y1, B) & member(X2, A) & member(Y2, B) & apply(R, X1, X2) & apply(F, X1, Y1) & apply(F, X2, Y2))) | apply(S, Y1, Y2))) & (increasing(F, A, R, B, S) | (~((~(member(tptp_fun_X1_30(S, B, R, A, F), A) & member(tptp_fun_Y1_29(S, B, R, A, F), B) & member(tptp_fun_X2_28(S, B, R, A, F), A) & member(tptp_fun_Y2_27(S, B, R, A, F), B) & apply(R, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_X2_28(S, B, R, A, F)) & apply(F, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_Y1_29(S, B, R, A, F)) & apply(F, tptp_fun_X2_28(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)))) | apply(S, tptp_fun_Y1_29(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F))))))),
% 0.22/0.54 inference(skolemize,[status(sab)],[13])).
% 0.22/0.54 tff(15,plain,
% 0.22/0.54 (![F: $i, A: $i, R: $i, B: $i, S: $i] : (~((~((~increasing(F, A, R, B, S)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(S, Y1, Y2) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(R, X1, X2)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2))))) | (~(increasing(F, A, R, B, S) | (~(apply(S, tptp_fun_Y1_29(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)) | (~member(tptp_fun_X1_30(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_29(S, B, R, A, F), B)) | (~member(tptp_fun_X2_28(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_27(S, B, R, A, F), B)) | (~apply(R, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_X2_28(S, B, R, A, F))) | (~apply(F, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_Y1_29(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_28(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)))))))))),
% 0.22/0.54 inference(modus_ponens,[status(thm)],[14, 7])).
% 0.22/0.54 tff(16,plain,
% 0.22/0.54 (![F: $i, A: $i, R: $i, B: $i, S: $i] : (~((~((~increasing(F, A, R, B, S)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(S, Y1, Y2) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(R, X1, X2)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2))))) | (~(increasing(F, A, R, B, S) | (~(apply(S, tptp_fun_Y1_29(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)) | (~member(tptp_fun_X1_30(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_29(S, B, R, A, F), B)) | (~member(tptp_fun_X2_28(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_27(S, B, R, A, F), B)) | (~apply(R, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_X2_28(S, B, R, A, F))) | (~apply(F, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_Y1_29(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_28(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)))))))))),
% 0.22/0.54 inference(modus_ponens,[status(thm)],[15, 5])).
% 0.22/0.54 tff(17,plain,
% 0.22/0.54 (((~![F: $i, A: $i, R: $i, B: $i, S: $i] : (~((~((~increasing(F, A, R, B, S)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(S, Y1, Y2) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(R, X1, X2)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2))))) | (~(increasing(F, A, R, B, S) | (~(apply(S, tptp_fun_Y1_29(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)) | (~member(tptp_fun_X1_30(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_29(S, B, R, A, F), B)) | (~member(tptp_fun_X2_28(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_27(S, B, R, A, F), B)) | (~apply(R, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_X2_28(S, B, R, A, F))) | (~apply(F, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_Y1_29(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_28(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)))))))))) | (~((~((~increasing(compose_function(G!45, F!46, A!44, B!43, C!42), A!44, R!41, C!42, T!39)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, C!42)) | apply(T!39, Y1, Y2) | (~member(X1, A!44)) | (~member(Y1, C!42)) | (~member(X2, A!44)) | (~apply(R!41, X1, X2)) | (~apply(compose_function(G!45, F!46, A!44, B!43, C!42), X1, Y1)) | (~apply(compose_function(G!45, F!46, A!44, B!43, C!42), X2, Y2))))) | (~(increasing(compose_function(G!45, F!46, A!44, B!43, C!42), A!44, R!41, C!42, T!39) | (~(apply(T!39, tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42))) | (~member(tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), A!44)) | (~member(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), C!42)) | (~member(tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), A!44)) | (~member(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), C!42)) | (~apply(R!41, tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))) | (~apply(compose_function(G!45, F!46, A!44, B!43, C!42), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))) | (~apply(compose_function(G!45, F!46, A!44, B!43, C!42), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42))))))))))) <=> ((~![F: $i, A: $i, R: $i, B: $i, S: $i] : (~((~((~increasing(F, A, R, B, S)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(S, Y1, Y2) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(R, X1, X2)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2))))) | (~(increasing(F, A, R, B, S) | (~(apply(S, tptp_fun_Y1_29(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)) | (~member(tptp_fun_X1_30(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_29(S, B, R, A, F), B)) | (~member(tptp_fun_X2_28(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_27(S, B, R, A, F), B)) | (~apply(R, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_X2_28(S, B, R, A, F))) | (~apply(F, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_Y1_29(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_28(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)))))))))) | (~((~((~increasing(compose_function(G!45, F!46, A!44, B!43, C!42), A!44, R!41, C!42, T!39)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, C!42)) | apply(T!39, Y1, Y2) | (~member(X1, A!44)) | (~member(Y1, C!42)) | (~member(X2, A!44)) | (~apply(R!41, X1, X2)) | (~apply(compose_function(G!45, F!46, A!44, B!43, C!42), X1, Y1)) | (~apply(compose_function(G!45, F!46, A!44, B!43, C!42), X2, Y2))))) | (~(increasing(compose_function(G!45, F!46, A!44, B!43, C!42), A!44, R!41, C!42, T!39) | (~(apply(T!39, tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42))) | (~member(tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), A!44)) | (~member(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), C!42)) | (~member(tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), A!44)) | (~member(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), C!42)) | (~apply(R!41, tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))) | (~apply(compose_function(G!45, F!46, A!44, B!43, C!42), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))) | (~apply(compose_function(G!45, F!46, A!44, B!43, C!42), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))))))))))),
% 0.22/0.55 inference(rewrite,[status(thm)],[])).
% 0.22/0.55 tff(18,plain,
% 0.22/0.55 ((~((~((~increasing(compose_function(G!45, F!46, A!44, B!43, C!42), A!44, R!41, C!42, T!39)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(T!39, Y1, Y2) | (~member(X1, A!44)) | (~member(Y1, C!42)) | (~member(X2, A!44)) | (~member(Y2, C!42)) | (~apply(R!41, X1, X2)) | (~apply(compose_function(G!45, F!46, A!44, B!43, C!42), X1, Y1)) | (~apply(compose_function(G!45, F!46, A!44, B!43, C!42), X2, Y2))))) | (~(increasing(compose_function(G!45, F!46, A!44, B!43, C!42), A!44, R!41, C!42, T!39) | (~(apply(T!39, tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42))) | (~member(tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), A!44)) | (~member(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), C!42)) | (~member(tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), A!44)) | (~member(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), C!42)) | (~apply(R!41, tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))) | (~apply(compose_function(G!45, F!46, A!44, B!43, C!42), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))) | (~apply(compose_function(G!45, F!46, A!44, B!43, C!42), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))))))))) <=> (~((~((~increasing(compose_function(G!45, F!46, A!44, B!43, C!42), A!44, R!41, C!42, T!39)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, C!42)) | apply(T!39, Y1, Y2) | (~member(X1, A!44)) | (~member(Y1, C!42)) | (~member(X2, A!44)) | (~apply(R!41, X1, X2)) | (~apply(compose_function(G!45, F!46, A!44, B!43, C!42), X1, Y1)) | (~apply(compose_function(G!45, F!46, A!44, B!43, C!42), X2, Y2))))) | (~(increasing(compose_function(G!45, F!46, A!44, B!43, C!42), A!44, R!41, C!42, T!39) | (~(apply(T!39, tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42))) | (~member(tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), A!44)) | (~member(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), C!42)) | (~member(tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), A!44)) | (~member(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), C!42)) | (~apply(R!41, tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))) | (~apply(compose_function(G!45, F!46, A!44, B!43, C!42), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))) | (~apply(compose_function(G!45, F!46, A!44, B!43, C!42), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42))))))))))),
% 0.22/0.55 inference(rewrite,[status(thm)],[])).
% 0.22/0.55 tff(19,plain,
% 0.22/0.55 (((~![F: $i, A: $i, R: $i, B: $i, S: $i] : (~((~((~increasing(F, A, R, B, S)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(S, Y1, Y2) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(R, X1, X2)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2))))) | (~(increasing(F, A, R, B, S) | (~(apply(S, tptp_fun_Y1_29(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)) | (~member(tptp_fun_X1_30(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_29(S, B, R, A, F), B)) | (~member(tptp_fun_X2_28(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_27(S, B, R, A, F), B)) | (~apply(R, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_X2_28(S, B, R, A, F))) | (~apply(F, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_Y1_29(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_28(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)))))))))) | (~((~((~increasing(compose_function(G!45, F!46, A!44, B!43, C!42), A!44, R!41, C!42, T!39)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(T!39, Y1, Y2) | (~member(X1, A!44)) | (~member(Y1, C!42)) | (~member(X2, A!44)) | (~member(Y2, C!42)) | (~apply(R!41, X1, X2)) | (~apply(compose_function(G!45, F!46, A!44, B!43, C!42), X1, Y1)) | (~apply(compose_function(G!45, F!46, A!44, B!43, C!42), X2, Y2))))) | (~(increasing(compose_function(G!45, F!46, A!44, B!43, C!42), A!44, R!41, C!42, T!39) | (~(apply(T!39, tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42))) | (~member(tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), A!44)) | (~member(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), C!42)) | (~member(tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), A!44)) | (~member(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), C!42)) | (~apply(R!41, tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))) | (~apply(compose_function(G!45, F!46, A!44, B!43, C!42), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))) | (~apply(compose_function(G!45, F!46, A!44, B!43, C!42), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42))))))))))) <=> ((~![F: $i, A: $i, R: $i, B: $i, S: $i] : (~((~((~increasing(F, A, R, B, S)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(S, Y1, Y2) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(R, X1, X2)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2))))) | (~(increasing(F, A, R, B, S) | (~(apply(S, tptp_fun_Y1_29(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)) | (~member(tptp_fun_X1_30(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_29(S, B, R, A, F), B)) | (~member(tptp_fun_X2_28(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_27(S, B, R, A, F), B)) | (~apply(R, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_X2_28(S, B, R, A, F))) | (~apply(F, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_Y1_29(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_28(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)))))))))) | (~((~((~increasing(compose_function(G!45, F!46, A!44, B!43, C!42), A!44, R!41, C!42, T!39)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, C!42)) | apply(T!39, Y1, Y2) | (~member(X1, A!44)) | (~member(Y1, C!42)) | (~member(X2, A!44)) | (~apply(R!41, X1, X2)) | (~apply(compose_function(G!45, F!46, A!44, B!43, C!42), X1, Y1)) | (~apply(compose_function(G!45, F!46, A!44, B!43, C!42), X2, Y2))))) | (~(increasing(compose_function(G!45, F!46, A!44, B!43, C!42), A!44, R!41, C!42, T!39) | (~(apply(T!39, tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42))) | (~member(tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), A!44)) | (~member(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), C!42)) | (~member(tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), A!44)) | (~member(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), C!42)) | (~apply(R!41, tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))) | (~apply(compose_function(G!45, F!46, A!44, B!43, C!42), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))) | (~apply(compose_function(G!45, F!46, A!44, B!43, C!42), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))))))))))),
% 0.22/0.55 inference(monotonicity,[status(thm)],[18])).
% 0.22/0.55 tff(20,plain,
% 0.22/0.55 (((~![F: $i, A: $i, R: $i, B: $i, S: $i] : (~((~((~increasing(F, A, R, B, S)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(S, Y1, Y2) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(R, X1, X2)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2))))) | (~(increasing(F, A, R, B, S) | (~(apply(S, tptp_fun_Y1_29(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)) | (~member(tptp_fun_X1_30(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_29(S, B, R, A, F), B)) | (~member(tptp_fun_X2_28(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_27(S, B, R, A, F), B)) | (~apply(R, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_X2_28(S, B, R, A, F))) | (~apply(F, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_Y1_29(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_28(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)))))))))) | (~((~((~increasing(compose_function(G!45, F!46, A!44, B!43, C!42), A!44, R!41, C!42, T!39)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(T!39, Y1, Y2) | (~member(X1, A!44)) | (~member(Y1, C!42)) | (~member(X2, A!44)) | (~member(Y2, C!42)) | (~apply(R!41, X1, X2)) | (~apply(compose_function(G!45, F!46, A!44, B!43, C!42), X1, Y1)) | (~apply(compose_function(G!45, F!46, A!44, B!43, C!42), X2, Y2))))) | (~(increasing(compose_function(G!45, F!46, A!44, B!43, C!42), A!44, R!41, C!42, T!39) | (~(apply(T!39, tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42))) | (~member(tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), A!44)) | (~member(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), C!42)) | (~member(tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), A!44)) | (~member(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), C!42)) | (~apply(R!41, tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))) | (~apply(compose_function(G!45, F!46, A!44, B!43, C!42), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))) | (~apply(compose_function(G!45, F!46, A!44, B!43, C!42), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42))))))))))) <=> ((~![F: $i, A: $i, R: $i, B: $i, S: $i] : (~((~((~increasing(F, A, R, B, S)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(S, Y1, Y2) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(R, X1, X2)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2))))) | (~(increasing(F, A, R, B, S) | (~(apply(S, tptp_fun_Y1_29(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)) | (~member(tptp_fun_X1_30(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_29(S, B, R, A, F), B)) | (~member(tptp_fun_X2_28(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_27(S, B, R, A, F), B)) | (~apply(R, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_X2_28(S, B, R, A, F))) | (~apply(F, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_Y1_29(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_28(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)))))))))) | (~((~((~increasing(compose_function(G!45, F!46, A!44, B!43, C!42), A!44, R!41, C!42, T!39)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, C!42)) | apply(T!39, Y1, Y2) | (~member(X1, A!44)) | (~member(Y1, C!42)) | (~member(X2, A!44)) | (~apply(R!41, X1, X2)) | (~apply(compose_function(G!45, F!46, A!44, B!43, C!42), X1, Y1)) | (~apply(compose_function(G!45, F!46, A!44, B!43, C!42), X2, Y2))))) | (~(increasing(compose_function(G!45, F!46, A!44, B!43, C!42), A!44, R!41, C!42, T!39) | (~(apply(T!39, tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42))) | (~member(tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), A!44)) | (~member(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), C!42)) | (~member(tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), A!44)) | (~member(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), C!42)) | (~apply(R!41, tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))) | (~apply(compose_function(G!45, F!46, A!44, B!43, C!42), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))) | (~apply(compose_function(G!45, F!46, A!44, B!43, C!42), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))))))))))),
% 0.22/0.56 inference(transitivity,[status(thm)],[19, 17])).
% 0.22/0.56 tff(21,plain,
% 0.22/0.56 ((~![F: $i, A: $i, R: $i, B: $i, S: $i] : (~((~((~increasing(F, A, R, B, S)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(S, Y1, Y2) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(R, X1, X2)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2))))) | (~(increasing(F, A, R, B, S) | (~(apply(S, tptp_fun_Y1_29(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)) | (~member(tptp_fun_X1_30(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_29(S, B, R, A, F), B)) | (~member(tptp_fun_X2_28(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_27(S, B, R, A, F), B)) | (~apply(R, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_X2_28(S, B, R, A, F))) | (~apply(F, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_Y1_29(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_28(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)))))))))) | (~((~((~increasing(compose_function(G!45, F!46, A!44, B!43, C!42), A!44, R!41, C!42, T!39)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(T!39, Y1, Y2) | (~member(X1, A!44)) | (~member(Y1, C!42)) | (~member(X2, A!44)) | (~member(Y2, C!42)) | (~apply(R!41, X1, X2)) | (~apply(compose_function(G!45, F!46, A!44, B!43, C!42), X1, Y1)) | (~apply(compose_function(G!45, F!46, A!44, B!43, C!42), X2, Y2))))) | (~(increasing(compose_function(G!45, F!46, A!44, B!43, C!42), A!44, R!41, C!42, T!39) | (~(apply(T!39, tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42))) | (~member(tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), A!44)) | (~member(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), C!42)) | (~member(tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), A!44)) | (~member(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), C!42)) | (~apply(R!41, tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))) | (~apply(compose_function(G!45, F!46, A!44, B!43, C!42), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))) | (~apply(compose_function(G!45, F!46, A!44, B!43, C!42), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42))))))))))),
% 0.22/0.56 inference(quant_inst,[status(thm)],[])).
% 0.22/0.56 tff(22,plain,
% 0.22/0.56 ((~![F: $i, A: $i, R: $i, B: $i, S: $i] : (~((~((~increasing(F, A, R, B, S)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(S, Y1, Y2) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(R, X1, X2)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2))))) | (~(increasing(F, A, R, B, S) | (~(apply(S, tptp_fun_Y1_29(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)) | (~member(tptp_fun_X1_30(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_29(S, B, R, A, F), B)) | (~member(tptp_fun_X2_28(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_27(S, B, R, A, F), B)) | (~apply(R, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_X2_28(S, B, R, A, F))) | (~apply(F, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_Y1_29(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_28(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)))))))))) | (~((~((~increasing(compose_function(G!45, F!46, A!44, B!43, C!42), A!44, R!41, C!42, T!39)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, C!42)) | apply(T!39, Y1, Y2) | (~member(X1, A!44)) | (~member(Y1, C!42)) | (~member(X2, A!44)) | (~apply(R!41, X1, X2)) | (~apply(compose_function(G!45, F!46, A!44, B!43, C!42), X1, Y1)) | (~apply(compose_function(G!45, F!46, A!44, B!43, C!42), X2, Y2))))) | (~(increasing(compose_function(G!45, F!46, A!44, B!43, C!42), A!44, R!41, C!42, T!39) | (~(apply(T!39, tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42))) | (~member(tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), A!44)) | (~member(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), C!42)) | (~member(tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), A!44)) | (~member(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), C!42)) | (~apply(R!41, tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))) | (~apply(compose_function(G!45, F!46, A!44, B!43, C!42), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))) | (~apply(compose_function(G!45, F!46, A!44, B!43, C!42), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42))))))))))),
% 0.22/0.56 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.22/0.56 tff(23,plain,
% 0.22/0.56 (~((~((~increasing(compose_function(G!45, F!46, A!44, B!43, C!42), A!44, R!41, C!42, T!39)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, C!42)) | apply(T!39, Y1, Y2) | (~member(X1, A!44)) | (~member(Y1, C!42)) | (~member(X2, A!44)) | (~apply(R!41, X1, X2)) | (~apply(compose_function(G!45, F!46, A!44, B!43, C!42), X1, Y1)) | (~apply(compose_function(G!45, F!46, A!44, B!43, C!42), X2, Y2))))) | (~(increasing(compose_function(G!45, F!46, A!44, B!43, C!42), A!44, R!41, C!42, T!39) | (~(apply(T!39, tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42))) | (~member(tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), A!44)) | (~member(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), C!42)) | (~member(tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), A!44)) | (~member(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), C!42)) | (~apply(R!41, tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))) | (~apply(compose_function(G!45, F!46, A!44, B!43, C!42), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))) | (~apply(compose_function(G!45, F!46, A!44, B!43, C!42), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))))))))),
% 0.22/0.56 inference(unit_resolution,[status(thm)],[22, 16])).
% 0.22/0.56 tff(24,plain,
% 0.22/0.56 (((~((~increasing(compose_function(G!45, F!46, A!44, B!43, C!42), A!44, R!41, C!42, T!39)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, C!42)) | apply(T!39, Y1, Y2) | (~member(X1, A!44)) | (~member(Y1, C!42)) | (~member(X2, A!44)) | (~apply(R!41, X1, X2)) | (~apply(compose_function(G!45, F!46, A!44, B!43, C!42), X1, Y1)) | (~apply(compose_function(G!45, F!46, A!44, B!43, C!42), X2, Y2))))) | (~(increasing(compose_function(G!45, F!46, A!44, B!43, C!42), A!44, R!41, C!42, T!39) | (~(apply(T!39, tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42))) | (~member(tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), A!44)) | (~member(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), C!42)) | (~member(tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), A!44)) | (~member(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), C!42)) | (~apply(R!41, tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))) | (~apply(compose_function(G!45, F!46, A!44, B!43, C!42), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))) | (~apply(compose_function(G!45, F!46, A!44, B!43, C!42), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42))))))))) | (increasing(compose_function(G!45, F!46, A!44, B!43, C!42), A!44, R!41, C!42, T!39) | (~(apply(T!39, tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42))) | (~member(tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), A!44)) | (~member(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), C!42)) | (~member(tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), A!44)) | (~member(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), C!42)) | (~apply(R!41, tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))) | (~apply(compose_function(G!45, F!46, A!44, B!43, C!42), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))) | (~apply(compose_function(G!45, F!46, A!44, B!43, C!42), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))))))),
% 0.22/0.56 inference(tautology,[status(thm)],[])).
% 0.22/0.56 tff(25,plain,
% 0.22/0.56 (increasing(compose_function(G!45, F!46, A!44, B!43, C!42), A!44, R!41, C!42, T!39) | (~(apply(T!39, tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42))) | (~member(tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), A!44)) | (~member(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), C!42)) | (~member(tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), A!44)) | (~member(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), C!42)) | (~apply(R!41, tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))) | (~apply(compose_function(G!45, F!46, A!44, B!43, C!42), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))) | (~apply(compose_function(G!45, F!46, A!44, B!43, C!42), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42))))))),
% 0.22/0.57 inference(unit_resolution,[status(thm)],[24, 23])).
% 0.22/0.57 tff(26,plain,
% 0.22/0.57 ((~![F: $i, G: $i, A: $i, B: $i, C: $i, R: $i, S: $i, T: $i] : ((~(maps(F, A, B) & maps(G, B, C) & decreasing(F, A, R, B, S) & decreasing(G, B, S, C, T))) | increasing(compose_function(G, F, A, B, C), A, R, C, T))) <=> (~![F: $i, G: $i, A: $i, B: $i, C: $i, R: $i, S: $i, T: $i] : ((~(maps(F, A, B) & maps(G, B, C) & decreasing(F, A, R, B, S) & decreasing(G, B, S, C, T))) | increasing(compose_function(G, F, A, B, C), A, R, C, T)))),
% 0.22/0.57 inference(rewrite,[status(thm)],[])).
% 0.22/0.57 tff(27,plain,
% 0.22/0.57 ((~![F: $i, G: $i, A: $i, B: $i, C: $i, R: $i, S: $i, T: $i] : ((((maps(F, A, B) & maps(G, B, C)) & decreasing(F, A, R, B, S)) & decreasing(G, B, S, C, T)) => increasing(compose_function(G, F, A, B, C), A, R, C, T))) <=> (~![F: $i, G: $i, A: $i, B: $i, C: $i, R: $i, S: $i, T: $i] : ((~(maps(F, A, B) & maps(G, B, C) & decreasing(F, A, R, B, S) & decreasing(G, B, S, C, T))) | increasing(compose_function(G, F, A, B, C), A, R, C, T)))),
% 0.22/0.57 inference(rewrite,[status(thm)],[])).
% 0.22/0.57 tff(28,axiom,(~![F: $i, G: $i, A: $i, B: $i, C: $i, R: $i, S: $i, T: $i] : ((((maps(F, A, B) & maps(G, B, C)) & decreasing(F, A, R, B, S)) & decreasing(G, B, S, C, T)) => increasing(compose_function(G, F, A, B, C), A, R, C, T))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thII40')).
% 0.22/0.57 tff(29,plain,
% 0.22/0.57 (~![F: $i, G: $i, A: $i, B: $i, C: $i, R: $i, S: $i, T: $i] : ((~(maps(F, A, B) & maps(G, B, C) & decreasing(F, A, R, B, S) & decreasing(G, B, S, C, T))) | increasing(compose_function(G, F, A, B, C), A, R, C, T))),
% 0.22/0.57 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.22/0.57 tff(30,plain,
% 0.22/0.57 (~![F: $i, G: $i, A: $i, B: $i, C: $i, R: $i, S: $i, T: $i] : ((~(maps(F, A, B) & maps(G, B, C) & decreasing(F, A, R, B, S) & decreasing(G, B, S, C, T))) | increasing(compose_function(G, F, A, B, C), A, R, C, T))),
% 0.22/0.57 inference(modus_ponens,[status(thm)],[29, 26])).
% 0.22/0.57 tff(31,plain,
% 0.22/0.57 (~![F: $i, G: $i, A: $i, B: $i, C: $i, R: $i, S: $i, T: $i] : ((~(maps(F, A, B) & maps(G, B, C) & decreasing(F, A, R, B, S) & decreasing(G, B, S, C, T))) | increasing(compose_function(G, F, A, B, C), A, R, C, T))),
% 0.22/0.57 inference(modus_ponens,[status(thm)],[30, 26])).
% 0.22/0.57 tff(32,plain,
% 0.22/0.57 (~![F: $i, G: $i, A: $i, B: $i, C: $i, R: $i, S: $i, T: $i] : ((~(maps(F, A, B) & maps(G, B, C) & decreasing(F, A, R, B, S) & decreasing(G, B, S, C, T))) | increasing(compose_function(G, F, A, B, C), A, R, C, T))),
% 0.22/0.57 inference(modus_ponens,[status(thm)],[31, 26])).
% 0.22/0.57 tff(33,plain,
% 0.22/0.57 (~![F: $i, G: $i, A: $i, B: $i, C: $i, R: $i, S: $i, T: $i] : ((~(maps(F, A, B) & maps(G, B, C) & decreasing(F, A, R, B, S) & decreasing(G, B, S, C, T))) | increasing(compose_function(G, F, A, B, C), A, R, C, T))),
% 0.22/0.57 inference(modus_ponens,[status(thm)],[32, 26])).
% 0.22/0.57 tff(34,plain,
% 0.22/0.57 (~![F: $i, G: $i, A: $i, B: $i, C: $i, R: $i, S: $i, T: $i] : ((~(maps(F, A, B) & maps(G, B, C) & decreasing(F, A, R, B, S) & decreasing(G, B, S, C, T))) | increasing(compose_function(G, F, A, B, C), A, R, C, T))),
% 0.22/0.57 inference(modus_ponens,[status(thm)],[33, 26])).
% 0.22/0.57 tff(35,plain,
% 0.22/0.57 (~![F: $i, G: $i, A: $i, B: $i, C: $i, R: $i, S: $i, T: $i] : ((~(maps(F, A, B) & maps(G, B, C) & decreasing(F, A, R, B, S) & decreasing(G, B, S, C, T))) | increasing(compose_function(G, F, A, B, C), A, R, C, T))),
% 0.22/0.57 inference(modus_ponens,[status(thm)],[34, 26])).
% 0.22/0.57 tff(36,plain,(
% 0.22/0.57 ~((~(maps(F!46, A!44, B!43) & maps(G!45, B!43, C!42) & decreasing(F!46, A!44, R!41, B!43, S!40) & decreasing(G!45, B!43, S!40, C!42, T!39))) | increasing(compose_function(G!45, F!46, A!44, B!43, C!42), A!44, R!41, C!42, T!39))),
% 0.22/0.57 inference(skolemize,[status(sab)],[35])).
% 0.22/0.57 tff(37,plain,
% 0.22/0.57 (~increasing(compose_function(G!45, F!46, A!44, B!43, C!42), A!44, R!41, C!42, T!39)),
% 0.22/0.57 inference(or_elim,[status(thm)],[36])).
% 0.22/0.57 tff(38,plain,
% 0.22/0.57 ((~(increasing(compose_function(G!45, F!46, A!44, B!43, C!42), A!44, R!41, C!42, T!39) | (~(apply(T!39, tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42))) | (~member(tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), A!44)) | (~member(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), C!42)) | (~member(tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), A!44)) | (~member(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), C!42)) | (~apply(R!41, tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))) | (~apply(compose_function(G!45, F!46, A!44, B!43, C!42), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))) | (~apply(compose_function(G!45, F!46, A!44, B!43, C!42), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))))))) | increasing(compose_function(G!45, F!46, A!44, B!43, C!42), A!44, R!41, C!42, T!39) | (~(apply(T!39, tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42))) | (~member(tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), A!44)) | (~member(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), C!42)) | (~member(tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), A!44)) | (~member(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), C!42)) | (~apply(R!41, tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))) | (~apply(compose_function(G!45, F!46, A!44, B!43, C!42), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))) | (~apply(compose_function(G!45, F!46, A!44, B!43, C!42), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42))))))),
% 0.22/0.57 inference(tautology,[status(thm)],[])).
% 0.22/0.57 tff(39,plain,
% 0.22/0.57 ((~(increasing(compose_function(G!45, F!46, A!44, B!43, C!42), A!44, R!41, C!42, T!39) | (~(apply(T!39, tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42))) | (~member(tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), A!44)) | (~member(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), C!42)) | (~member(tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), A!44)) | (~member(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), C!42)) | (~apply(R!41, tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))) | (~apply(compose_function(G!45, F!46, A!44, B!43, C!42), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))) | (~apply(compose_function(G!45, F!46, A!44, B!43, C!42), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))))))) | (~(apply(T!39, tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42))) | (~member(tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), A!44)) | (~member(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), C!42)) | (~member(tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), A!44)) | (~member(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), C!42)) | (~apply(R!41, tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))) | (~apply(compose_function(G!45, F!46, A!44, B!43, C!42), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))) | (~apply(compose_function(G!45, F!46, A!44, B!43, C!42), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42))))))),
% 0.22/0.57 inference(unit_resolution,[status(thm)],[38, 37])).
% 0.22/0.57 tff(40,plain,
% 0.22/0.57 (~(apply(T!39, tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42))) | (~member(tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), A!44)) | (~member(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), C!42)) | (~member(tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), A!44)) | (~member(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), C!42)) | (~apply(R!41, tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))) | (~apply(compose_function(G!45, F!46, A!44, B!43, C!42), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))) | (~apply(compose_function(G!45, F!46, A!44, B!43, C!42), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))))),
% 0.22/0.57 inference(unit_resolution,[status(thm)],[39, 25])).
% 0.22/0.57 tff(41,plain,
% 0.22/0.57 ((apply(T!39, tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42))) | (~member(tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), A!44)) | (~member(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), C!42)) | (~member(tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), A!44)) | (~member(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), C!42)) | (~apply(R!41, tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))) | (~apply(compose_function(G!45, F!46, A!44, B!43, C!42), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))) | (~apply(compose_function(G!45, F!46, A!44, B!43, C!42), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42))))) | member(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), C!42)),
% 0.22/0.57 inference(tautology,[status(thm)],[])).
% 0.22/0.57 tff(42,plain,
% 0.22/0.57 (member(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), C!42)),
% 0.22/0.58 inference(unit_resolution,[status(thm)],[41, 40])).
% 0.22/0.58 tff(43,plain,
% 0.22/0.58 ((apply(T!39, tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42))) | (~member(tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), A!44)) | (~member(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), C!42)) | (~member(tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), A!44)) | (~member(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), C!42)) | (~apply(R!41, tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))) | (~apply(compose_function(G!45, F!46, A!44, B!43, C!42), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))) | (~apply(compose_function(G!45, F!46, A!44, B!43, C!42), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42))))) | member(tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), A!44)),
% 0.22/0.58 inference(tautology,[status(thm)],[])).
% 0.22/0.58 tff(44,plain,
% 0.22/0.58 (member(tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), A!44)),
% 0.22/0.58 inference(unit_resolution,[status(thm)],[43, 40])).
% 0.22/0.58 tff(45,plain,
% 0.22/0.58 (^[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)))))))))),
% 0.22/0.58 inference(bind,[status(th)],[])).
% 0.22/0.58 tff(46,plain,
% 0.22/0.58 (![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z)))))))) <=> ![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))))))))),
% 0.22/0.58 inference(quant_intro,[status(thm)],[45])).
% 0.22/0.58 tff(47,plain,
% 0.22/0.58 (^[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)))))))))),
% 0.22/0.58 inference(bind,[status(th)],[])).
% 0.22/0.58 tff(48,plain,
% 0.22/0.58 (![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z)))))))) <=> ![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))))))))),
% 0.22/0.58 inference(quant_intro,[status(thm)],[47])).
% 0.22/0.58 tff(49,plain,
% 0.22/0.58 (![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z)))))))) <=> ![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))))))))),
% 0.22/0.58 inference(transitivity,[status(thm)],[48, 46])).
% 0.22/0.58 tff(50,plain,
% 0.22/0.58 (^[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))))))))))),
% 0.22/0.58 inference(bind,[status(th)],[])).
% 0.22/0.58 tff(51,plain,
% 0.22/0.58 (![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))))))))),
% 0.22/0.58 inference(quant_intro,[status(thm)],[50])).
% 0.22/0.58 tff(52,plain,
% 0.22/0.58 (![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))))),
% 0.22/0.58 inference(rewrite,[status(thm)],[])).
% 0.22/0.58 tff(53,plain,
% 0.22/0.58 (^[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))))))),
% 0.22/0.58 inference(bind,[status(th)],[])).
% 0.22/0.58 tff(54,plain,
% 0.22/0.58 (![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))))),
% 0.22/0.58 inference(quant_intro,[status(thm)],[53])).
% 0.22/0.58 tff(55,axiom,(![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((member(X, A) & member(Z, C)) => (apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : ((member(Y, B) & apply(F, X, Y)) & apply(G, Y, Z))))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+1.ax','compose_function')).
% 0.22/0.58 tff(56,plain,
% 0.22/0.58 (![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))))),
% 0.22/0.58 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.22/0.58 tff(57,plain,
% 0.22/0.58 (![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))))),
% 0.22/0.58 inference(modus_ponens,[status(thm)],[56, 52])).
% 0.22/0.58 tff(58,plain,(
% 0.22/0.58 ![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))))))),
% 0.22/0.58 inference(skolemize,[status(sab)],[57])).
% 0.22/0.58 tff(59,plain,
% 0.22/0.58 (![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))),
% 0.22/0.58 inference(modus_ponens,[status(thm)],[58, 51])).
% 0.22/0.58 tff(60,plain,
% 0.22/0.58 (![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))),
% 0.22/0.58 inference(modus_ponens,[status(thm)],[59, 49])).
% 0.22/0.58 tff(61,plain,
% 0.22/0.58 (((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), A!44)) | (~member(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), C!42)) | (~((~((~apply(compose_function(G!45, F!46, A!44, B!43, C!42), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), B!43)) | (~apply(F!46, tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45))) | (~apply(G!45, tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))))))) | (~(apply(compose_function(G!45, F!46, A!44, B!43, C!42), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42))) | ![Y: $i] : ((~member(Y, B!43)) | (~apply(F!46, tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), Y)) | (~apply(G!45, Y, tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!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_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), A!44)) | (~member(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), C!42)) | (~((~((~apply(compose_function(G!45, F!46, A!44, B!43, C!42), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), B!43)) | (~apply(F!46, tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45))) | (~apply(G!45, tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))))))) | (~(apply(compose_function(G!45, F!46, A!44, B!43, C!42), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42))) | ![Y: $i] : ((~member(Y, B!43)) | (~apply(F!46, tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), Y)) | (~apply(G!45, Y, tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42))))))))))),
% 0.22/0.59 inference(rewrite,[status(thm)],[])).
% 0.22/0.59 tff(62,plain,
% 0.22/0.59 (((~member(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), C!42)) | (~member(tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), A!44)) | (~((~((~apply(compose_function(G!45, F!46, A!44, B!43, C!42), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), B!43)) | (~apply(F!46, tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45))) | (~apply(G!45, tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))))))) | (~(apply(compose_function(G!45, F!46, A!44, B!43, C!42), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42))) | ![Y: $i] : ((~member(Y, B!43)) | (~apply(F!46, tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), Y)) | (~apply(G!45, Y, tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))))))))) <=> ((~member(tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), A!44)) | (~member(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), C!42)) | (~((~((~apply(compose_function(G!45, F!46, A!44, B!43, C!42), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), B!43)) | (~apply(F!46, tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45))) | (~apply(G!45, tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))))))) | (~(apply(compose_function(G!45, F!46, A!44, B!43, C!42), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42))) | ![Y: $i] : ((~member(Y, B!43)) | (~apply(F!46, tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), Y)) | (~apply(G!45, Y, tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42))))))))))),
% 0.53/0.59 inference(rewrite,[status(thm)],[])).
% 0.53/0.59 tff(63,plain,
% 0.53/0.59 ((~((~((~apply(compose_function(G!45, F!46, A!44, B!43, C!42), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), B!43)) | (~apply(F!46, tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45))) | (~apply(G!45, tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))))))) | (~(apply(compose_function(G!45, F!46, A!44, B!43, C!42), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42))) | ![Y: $i] : ((~member(Y, B!43)) | (~apply(F!46, tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), Y)) | (~apply(G!45, Y, tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42))))))))) <=> (~((~((~apply(compose_function(G!45, F!46, A!44, B!43, C!42), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), B!43)) | (~apply(F!46, tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45))) | (~apply(G!45, tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))))))) | (~(apply(compose_function(G!45, F!46, A!44, B!43, C!42), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42))) | ![Y: $i] : ((~member(Y, B!43)) | (~apply(F!46, tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), Y)) | (~apply(G!45, Y, tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))))))))),
% 0.53/0.59 inference(rewrite,[status(thm)],[])).
% 0.53/0.59 tff(64,plain,
% 0.53/0.59 (((~member(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), C!42)) | (~member(tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), A!44)) | (~((~((~apply(compose_function(G!45, F!46, A!44, B!43, C!42), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), B!43)) | (~apply(F!46, tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45))) | (~apply(G!45, tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))))))) | (~(apply(compose_function(G!45, F!46, A!44, B!43, C!42), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42))) | ![Y: $i] : ((~member(Y, B!43)) | (~apply(F!46, tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), Y)) | (~apply(G!45, Y, tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))))))))) <=> ((~member(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), C!42)) | (~member(tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), A!44)) | (~((~((~apply(compose_function(G!45, F!46, A!44, B!43, C!42), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), B!43)) | (~apply(F!46, tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45))) | (~apply(G!45, tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))))))) | (~(apply(compose_function(G!45, F!46, A!44, B!43, C!42), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42))) | ![Y: $i] : ((~member(Y, B!43)) | (~apply(F!46, tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), Y)) | (~apply(G!45, Y, tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42))))))))))),
% 0.53/0.59 inference(monotonicity,[status(thm)],[63])).
% 0.53/0.59 tff(65,plain,
% 0.53/0.59 (((~member(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), C!42)) | (~member(tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), A!44)) | (~((~((~apply(compose_function(G!45, F!46, A!44, B!43, C!42), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), B!43)) | (~apply(F!46, tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45))) | (~apply(G!45, tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))))))) | (~(apply(compose_function(G!45, F!46, A!44, B!43, C!42), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42))) | ![Y: $i] : ((~member(Y, B!43)) | (~apply(F!46, tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), Y)) | (~apply(G!45, Y, tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))))))))) <=> ((~member(tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), A!44)) | (~member(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), C!42)) | (~((~((~apply(compose_function(G!45, F!46, A!44, B!43, C!42), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), B!43)) | (~apply(F!46, tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45))) | (~apply(G!45, tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))))))) | (~(apply(compose_function(G!45, F!46, A!44, B!43, C!42), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42))) | ![Y: $i] : ((~member(Y, B!43)) | (~apply(F!46, tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), Y)) | (~apply(G!45, Y, tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42))))))))))),
% 0.53/0.60 inference(transitivity,[status(thm)],[64, 62])).
% 0.53/0.60 tff(66,plain,
% 0.53/0.60 (((~![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_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), C!42)) | (~member(tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), A!44)) | (~((~((~apply(compose_function(G!45, F!46, A!44, B!43, C!42), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), B!43)) | (~apply(F!46, tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45))) | (~apply(G!45, tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))))))) | (~(apply(compose_function(G!45, F!46, A!44, B!43, C!42), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42))) | ![Y: $i] : ((~member(Y, B!43)) | (~apply(F!46, tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), Y)) | (~apply(G!45, Y, tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!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_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), A!44)) | (~member(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), C!42)) | (~((~((~apply(compose_function(G!45, F!46, A!44, B!43, C!42), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), B!43)) | (~apply(F!46, tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45))) | (~apply(G!45, tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))))))) | (~(apply(compose_function(G!45, F!46, A!44, B!43, C!42), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42))) | ![Y: $i] : ((~member(Y, B!43)) | (~apply(F!46, tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), Y)) | (~apply(G!45, Y, tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))))))))))),
% 0.53/0.60 inference(monotonicity,[status(thm)],[65])).
% 0.53/0.60 tff(67,plain,
% 0.53/0.60 (((~![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_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), C!42)) | (~member(tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), A!44)) | (~((~((~apply(compose_function(G!45, F!46, A!44, B!43, C!42), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), B!43)) | (~apply(F!46, tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45))) | (~apply(G!45, tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))))))) | (~(apply(compose_function(G!45, F!46, A!44, B!43, C!42), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42))) | ![Y: $i] : ((~member(Y, B!43)) | (~apply(F!46, tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), Y)) | (~apply(G!45, Y, tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!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_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), A!44)) | (~member(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), C!42)) | (~((~((~apply(compose_function(G!45, F!46, A!44, B!43, C!42), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), B!43)) | (~apply(F!46, tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45))) | (~apply(G!45, tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))))))) | (~(apply(compose_function(G!45, F!46, A!44, B!43, C!42), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42))) | ![Y: $i] : ((~member(Y, B!43)) | (~apply(F!46, tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), Y)) | (~apply(G!45, Y, tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42))))))))))),
% 0.53/0.60 inference(transitivity,[status(thm)],[66, 61])).
% 0.53/0.60 tff(68,plain,
% 0.53/0.60 ((~![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_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), C!42)) | (~member(tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), A!44)) | (~((~((~apply(compose_function(G!45, F!46, A!44, B!43, C!42), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), B!43)) | (~apply(F!46, tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45))) | (~apply(G!45, tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))))))) | (~(apply(compose_function(G!45, F!46, A!44, B!43, C!42), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42))) | ![Y: $i] : ((~member(Y, B!43)) | (~apply(F!46, tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), Y)) | (~apply(G!45, Y, tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42))))))))))),
% 0.55/0.61 inference(quant_inst,[status(thm)],[])).
% 0.55/0.61 tff(69,plain,
% 0.55/0.61 ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | (~member(tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), A!44)) | (~member(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), C!42)) | (~((~((~apply(compose_function(G!45, F!46, A!44, B!43, C!42), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), B!43)) | (~apply(F!46, tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45))) | (~apply(G!45, tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))))))) | (~(apply(compose_function(G!45, F!46, A!44, B!43, C!42), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42))) | ![Y: $i] : ((~member(Y, B!43)) | (~apply(F!46, tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), Y)) | (~apply(G!45, Y, tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))))))))),
% 0.55/0.61 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.55/0.61 tff(70,plain,
% 0.55/0.61 (~((~((~apply(compose_function(G!45, F!46, A!44, B!43, C!42), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), B!43)) | (~apply(F!46, tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45))) | (~apply(G!45, tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))))))) | (~(apply(compose_function(G!45, F!46, A!44, B!43, C!42), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42))) | ![Y: $i] : ((~member(Y, B!43)) | (~apply(F!46, tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), Y)) | (~apply(G!45, Y, tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42))))))))),
% 0.55/0.61 inference(unit_resolution,[status(thm)],[69, 60, 44, 42])).
% 0.55/0.61 tff(71,plain,
% 0.55/0.61 (((~((~apply(compose_function(G!45, F!46, A!44, B!43, C!42), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), B!43)) | (~apply(F!46, tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45))) | (~apply(G!45, tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))))))) | (~(apply(compose_function(G!45, F!46, A!44, B!43, C!42), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42))) | ![Y: $i] : ((~member(Y, B!43)) | (~apply(F!46, tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), Y)) | (~apply(G!45, Y, tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))))))) | ((~apply(compose_function(G!45, F!46, A!44, B!43, C!42), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), B!43)) | (~apply(F!46, tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45))) | (~apply(G!45, tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))))))),
% 0.55/0.61 inference(tautology,[status(thm)],[])).
% 0.55/0.61 tff(72,plain,
% 0.55/0.61 ((~apply(compose_function(G!45, F!46, A!44, B!43, C!42), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), B!43)) | (~apply(F!46, tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45))) | (~apply(G!45, tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42))))))),
% 0.55/0.61 inference(unit_resolution,[status(thm)],[71, 70])).
% 0.55/0.61 tff(73,plain,
% 0.55/0.61 ((apply(T!39, tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42))) | (~member(tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), A!44)) | (~member(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), C!42)) | (~member(tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), A!44)) | (~member(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), C!42)) | (~apply(R!41, tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))) | (~apply(compose_function(G!45, F!46, A!44, B!43, C!42), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))) | (~apply(compose_function(G!45, F!46, A!44, B!43, C!42), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42))))) | apply(compose_function(G!45, F!46, A!44, B!43, C!42), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))),
% 0.55/0.61 inference(tautology,[status(thm)],[])).
% 0.55/0.61 tff(74,plain,
% 0.55/0.61 (apply(compose_function(G!45, F!46, A!44, B!43, C!42), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))),
% 0.55/0.61 inference(unit_resolution,[status(thm)],[73, 40])).
% 0.55/0.61 tff(75,plain,
% 0.55/0.61 ((~((~apply(compose_function(G!45, F!46, A!44, B!43, C!42), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), B!43)) | (~apply(F!46, tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45))) | (~apply(G!45, tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))))))) | (~apply(compose_function(G!45, F!46, A!44, B!43, C!42), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), B!43)) | (~apply(F!46, tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45))) | (~apply(G!45, tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42))))))),
% 0.55/0.62 inference(tautology,[status(thm)],[])).
% 0.55/0.62 tff(76,plain,
% 0.55/0.62 ((~((~apply(compose_function(G!45, F!46, A!44, B!43, C!42), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), B!43)) | (~apply(F!46, tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45))) | (~apply(G!45, tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))))))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), B!43)) | (~apply(F!46, tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45))) | (~apply(G!45, tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42))))))),
% 0.55/0.62 inference(unit_resolution,[status(thm)],[75, 74])).
% 0.55/0.62 tff(77,plain,
% 0.55/0.62 (~((~member(tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), B!43)) | (~apply(F!46, tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45))) | (~apply(G!45, tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))))),
% 0.55/0.62 inference(unit_resolution,[status(thm)],[76, 72])).
% 0.55/0.62 tff(78,plain,
% 0.55/0.62 (((~member(tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), B!43)) | (~apply(F!46, tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45))) | (~apply(G!45, tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42))))) | member(tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), B!43)),
% 0.55/0.62 inference(tautology,[status(thm)],[])).
% 0.55/0.62 tff(79,plain,
% 0.55/0.62 (member(tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), B!43)),
% 0.55/0.62 inference(unit_resolution,[status(thm)],[78, 77])).
% 0.55/0.62 tff(80,plain,
% 0.55/0.62 (^[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)))))))))))),
% 0.55/0.62 inference(bind,[status(th)],[])).
% 0.55/0.62 tff(81,plain,
% 0.55/0.62 (![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))))))))))),
% 0.55/0.62 inference(quant_intro,[status(thm)],[80])).
% 0.55/0.62 tff(82,plain,
% 0.55/0.62 (^[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)))))))))),
% 0.55/0.62 inference(bind,[status(th)],[])).
% 0.55/0.62 tff(83,plain,
% 0.55/0.62 (![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))))))))),
% 0.55/0.62 inference(quant_intro,[status(thm)],[82])).
% 0.55/0.62 tff(84,plain,
% 0.55/0.62 (^[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)))))))))),
% 0.55/0.62 inference(bind,[status(th)],[])).
% 0.55/0.62 tff(85,plain,
% 0.55/0.62 (![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))))))))),
% 0.55/0.62 inference(quant_intro,[status(thm)],[84])).
% 0.55/0.62 tff(86,plain,
% 0.55/0.62 (![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))))))))),
% 0.55/0.62 inference(transitivity,[status(thm)],[85, 83])).
% 0.55/0.62 tff(87,plain,
% 0.55/0.62 (^[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))))))))))),
% 0.55/0.63 inference(bind,[status(th)],[])).
% 0.55/0.63 tff(88,plain,
% 0.55/0.63 (![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))))))))),
% 0.55/0.63 inference(quant_intro,[status(thm)],[87])).
% 0.55/0.63 tff(89,plain,
% 0.55/0.63 (^[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)))))))),
% 0.55/0.63 inference(bind,[status(th)],[])).
% 0.55/0.63 tff(90,plain,
% 0.55/0.63 (![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))))))),
% 0.55/0.63 inference(quant_intro,[status(thm)],[89])).
% 0.55/0.63 tff(91,plain,
% 0.55/0.63 (![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))))))),
% 0.55/0.63 inference(rewrite,[status(thm)],[])).
% 0.55/0.63 tff(92,plain,
% 0.55/0.63 (^[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)))))))),
% 0.55/0.63 inference(bind,[status(th)],[])).
% 0.55/0.63 tff(93,plain,
% 0.55/0.63 (![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))))))),
% 0.55/0.63 inference(quant_intro,[status(thm)],[92])).
% 0.55/0.63 tff(94,axiom,(![F: $i, A: $i, B: $i] : (maps(F, A, B) <=> (![X: $i] : (member(X, A) => ?[Y: $i] : (member(Y, B) & apply(F, X, Y))) & ![X: $i, Y1: $i, Y2: $i] : (((member(X, A) & member(Y1, B)) & member(Y2, B)) => ((apply(F, X, Y1) & apply(F, X, Y2)) => (Y1 = Y2)))))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+1.ax','maps')).
% 0.55/0.63 tff(95,plain,
% 0.55/0.63 (![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))))))),
% 0.55/0.63 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.55/0.63 tff(96,plain,
% 0.55/0.63 (![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))))))),
% 0.55/0.63 inference(modus_ponens,[status(thm)],[95, 91])).
% 0.55/0.63 tff(97,plain,(
% 0.55/0.63 ![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))))))))),
% 0.55/0.63 inference(skolemize,[status(sab)],[96])).
% 0.55/0.63 tff(98,plain,
% 0.55/0.63 (![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))))))),
% 0.55/0.63 inference(modus_ponens,[status(thm)],[97, 90])).
% 0.55/0.63 tff(99,plain,
% 0.55/0.63 (![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))))))))),
% 0.55/0.63 inference(modus_ponens,[status(thm)],[98, 88])).
% 0.55/0.63 tff(100,plain,
% 0.55/0.63 (![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))))))))),
% 0.55/0.63 inference(modus_ponens,[status(thm)],[99, 86])).
% 0.55/0.63 tff(101,plain,
% 0.55/0.63 (![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))))))))))),
% 0.55/0.63 inference(modus_ponens,[status(thm)],[100, 81])).
% 0.55/0.63 tff(102,plain,
% 0.55/0.63 ((~![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!45, B!43, C!42)) | (~((~![X: $i] : ((~member(X, B!43)) | (~((~member(tptp_fun_Y_3(X, C!42, G!45), C!42)) | (~apply(G!45, X, tptp_fun_Y_3(X, C!42, G!45))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G!45, X, Y1)) | (~apply(G!45, X, Y2)) | (~member(X, B!43)) | (~member(Y1, C!42)) | (~member(Y2, C!42)))))))) | (~(maps(G!45, B!43, C!42) | (~((tptp_fun_Y1_6(C!42, B!43, G!45) = tptp_fun_Y2_5(C!42, B!43, G!45)) | (~apply(G!45, tptp_fun_X_7(C!42, B!43, G!45), tptp_fun_Y1_6(C!42, B!43, G!45))) | (~apply(G!45, tptp_fun_X_7(C!42, B!43, G!45), tptp_fun_Y2_5(C!42, B!43, G!45))) | (~member(tptp_fun_X_7(C!42, B!43, G!45), B!43)) | (~member(tptp_fun_Y1_6(C!42, B!43, G!45), C!42)) | (~member(tptp_fun_Y2_5(C!42, B!43, G!45), C!42)))) | (~((~member(tptp_fun_X_4(C!42, B!43, G!45), B!43)) | (~![Y: $i] : ((~member(Y, C!42)) | (~apply(G!45, tptp_fun_X_4(C!42, B!43, G!45), Y))))))))))),
% 0.55/0.63 inference(quant_inst,[status(thm)],[])).
% 0.55/0.63 tff(103,plain,
% 0.55/0.63 (~((~((~maps(G!45, B!43, C!42)) | (~((~![X: $i] : ((~member(X, B!43)) | (~((~member(tptp_fun_Y_3(X, C!42, G!45), C!42)) | (~apply(G!45, X, tptp_fun_Y_3(X, C!42, G!45))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G!45, X, Y1)) | (~apply(G!45, X, Y2)) | (~member(X, B!43)) | (~member(Y1, C!42)) | (~member(Y2, C!42)))))))) | (~(maps(G!45, B!43, C!42) | (~((tptp_fun_Y1_6(C!42, B!43, G!45) = tptp_fun_Y2_5(C!42, B!43, G!45)) | (~apply(G!45, tptp_fun_X_7(C!42, B!43, G!45), tptp_fun_Y1_6(C!42, B!43, G!45))) | (~apply(G!45, tptp_fun_X_7(C!42, B!43, G!45), tptp_fun_Y2_5(C!42, B!43, G!45))) | (~member(tptp_fun_X_7(C!42, B!43, G!45), B!43)) | (~member(tptp_fun_Y1_6(C!42, B!43, G!45), C!42)) | (~member(tptp_fun_Y2_5(C!42, B!43, G!45), C!42)))) | (~((~member(tptp_fun_X_4(C!42, B!43, G!45), B!43)) | (~![Y: $i] : ((~member(Y, C!42)) | (~apply(G!45, tptp_fun_X_4(C!42, B!43, G!45), Y)))))))))),
% 0.55/0.63 inference(unit_resolution,[status(thm)],[102, 101])).
% 0.55/0.63 tff(104,plain,
% 0.55/0.63 (((~((~maps(G!45, B!43, C!42)) | (~((~![X: $i] : ((~member(X, B!43)) | (~((~member(tptp_fun_Y_3(X, C!42, G!45), C!42)) | (~apply(G!45, X, tptp_fun_Y_3(X, C!42, G!45))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G!45, X, Y1)) | (~apply(G!45, X, Y2)) | (~member(X, B!43)) | (~member(Y1, C!42)) | (~member(Y2, C!42)))))))) | (~(maps(G!45, B!43, C!42) | (~((tptp_fun_Y1_6(C!42, B!43, G!45) = tptp_fun_Y2_5(C!42, B!43, G!45)) | (~apply(G!45, tptp_fun_X_7(C!42, B!43, G!45), tptp_fun_Y1_6(C!42, B!43, G!45))) | (~apply(G!45, tptp_fun_X_7(C!42, B!43, G!45), tptp_fun_Y2_5(C!42, B!43, G!45))) | (~member(tptp_fun_X_7(C!42, B!43, G!45), B!43)) | (~member(tptp_fun_Y1_6(C!42, B!43, G!45), C!42)) | (~member(tptp_fun_Y2_5(C!42, B!43, G!45), C!42)))) | (~((~member(tptp_fun_X_4(C!42, B!43, G!45), B!43)) | (~![Y: $i] : ((~member(Y, C!42)) | (~apply(G!45, tptp_fun_X_4(C!42, B!43, G!45), Y))))))))) | ((~maps(G!45, B!43, C!42)) | (~((~![X: $i] : ((~member(X, B!43)) | (~((~member(tptp_fun_Y_3(X, C!42, G!45), C!42)) | (~apply(G!45, X, tptp_fun_Y_3(X, C!42, G!45))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G!45, X, Y1)) | (~apply(G!45, X, Y2)) | (~member(X, B!43)) | (~member(Y1, C!42)) | (~member(Y2, C!42)))))))),
% 0.55/0.63 inference(tautology,[status(thm)],[])).
% 0.55/0.63 tff(105,plain,
% 0.55/0.63 ((~maps(G!45, B!43, C!42)) | (~((~![X: $i] : ((~member(X, B!43)) | (~((~member(tptp_fun_Y_3(X, C!42, G!45), C!42)) | (~apply(G!45, X, tptp_fun_Y_3(X, C!42, G!45))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G!45, X, Y1)) | (~apply(G!45, X, Y2)) | (~member(X, B!43)) | (~member(Y1, C!42)) | (~member(Y2, C!42))))))),
% 0.55/0.63 inference(unit_resolution,[status(thm)],[104, 103])).
% 0.55/0.63 tff(106,plain,
% 0.55/0.63 (maps(F!46, A!44, B!43) & maps(G!45, B!43, C!42) & decreasing(F!46, A!44, R!41, B!43, S!40) & decreasing(G!45, B!43, S!40, C!42, T!39)),
% 0.55/0.63 inference(or_elim,[status(thm)],[36])).
% 0.55/0.63 tff(107,plain,
% 0.55/0.63 (maps(G!45, B!43, C!42)),
% 0.55/0.63 inference(and_elim,[status(thm)],[106])).
% 0.55/0.63 tff(108,plain,
% 0.55/0.63 ((~((~maps(G!45, B!43, C!42)) | (~((~![X: $i] : ((~member(X, B!43)) | (~((~member(tptp_fun_Y_3(X, C!42, G!45), C!42)) | (~apply(G!45, X, tptp_fun_Y_3(X, C!42, G!45))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G!45, X, Y1)) | (~apply(G!45, X, Y2)) | (~member(X, B!43)) | (~member(Y1, C!42)) | (~member(Y2, C!42)))))))) | (~maps(G!45, B!43, C!42)) | (~((~![X: $i] : ((~member(X, B!43)) | (~((~member(tptp_fun_Y_3(X, C!42, G!45), C!42)) | (~apply(G!45, X, tptp_fun_Y_3(X, C!42, G!45))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G!45, X, Y1)) | (~apply(G!45, X, Y2)) | (~member(X, B!43)) | (~member(Y1, C!42)) | (~member(Y2, C!42))))))),
% 0.55/0.63 inference(tautology,[status(thm)],[])).
% 0.55/0.63 tff(109,plain,
% 0.55/0.63 ((~((~maps(G!45, B!43, C!42)) | (~((~![X: $i] : ((~member(X, B!43)) | (~((~member(tptp_fun_Y_3(X, C!42, G!45), C!42)) | (~apply(G!45, X, tptp_fun_Y_3(X, C!42, G!45))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G!45, X, Y1)) | (~apply(G!45, X, Y2)) | (~member(X, B!43)) | (~member(Y1, C!42)) | (~member(Y2, C!42)))))))) | (~((~![X: $i] : ((~member(X, B!43)) | (~((~member(tptp_fun_Y_3(X, C!42, G!45), C!42)) | (~apply(G!45, X, tptp_fun_Y_3(X, C!42, G!45))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G!45, X, Y1)) | (~apply(G!45, X, Y2)) | (~member(X, B!43)) | (~member(Y1, C!42)) | (~member(Y2, C!42))))))),
% 0.55/0.63 inference(unit_resolution,[status(thm)],[108, 107])).
% 0.55/0.63 tff(110,plain,
% 0.55/0.63 (~((~![X: $i] : ((~member(X, B!43)) | (~((~member(tptp_fun_Y_3(X, C!42, G!45), C!42)) | (~apply(G!45, X, tptp_fun_Y_3(X, C!42, G!45))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G!45, X, Y1)) | (~apply(G!45, X, Y2)) | (~member(X, B!43)) | (~member(Y1, C!42)) | (~member(Y2, C!42)))))),
% 0.55/0.63 inference(unit_resolution,[status(thm)],[109, 105])).
% 0.55/0.63 tff(111,plain,
% 0.55/0.63 (((~![X: $i] : ((~member(X, B!43)) | (~((~member(tptp_fun_Y_3(X, C!42, G!45), C!42)) | (~apply(G!45, X, tptp_fun_Y_3(X, C!42, G!45))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G!45, X, Y1)) | (~apply(G!45, X, Y2)) | (~member(X, B!43)) | (~member(Y1, C!42)) | (~member(Y2, C!42))))) | ![X: $i] : ((~member(X, B!43)) | (~((~member(tptp_fun_Y_3(X, C!42, G!45), C!42)) | (~apply(G!45, X, tptp_fun_Y_3(X, C!42, G!45))))))),
% 0.55/0.63 inference(tautology,[status(thm)],[])).
% 0.55/0.63 tff(112,plain,
% 0.55/0.63 (![X: $i] : ((~member(X, B!43)) | (~((~member(tptp_fun_Y_3(X, C!42, G!45), C!42)) | (~apply(G!45, X, tptp_fun_Y_3(X, C!42, G!45))))))),
% 0.55/0.63 inference(unit_resolution,[status(thm)],[111, 110])).
% 0.55/0.63 tff(113,plain,
% 0.55/0.63 (((~![X: $i] : ((~member(X, B!43)) | (~((~member(tptp_fun_Y_3(X, C!42, G!45), C!42)) | (~apply(G!45, X, tptp_fun_Y_3(X, C!42, G!45))))))) | ((~member(tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), B!43)) | (~((~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), C!42, G!45), C!42)) | (~apply(G!45, tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), C!42, G!45))))))) <=> ((~![X: $i] : ((~member(X, B!43)) | (~((~member(tptp_fun_Y_3(X, C!42, G!45), C!42)) | (~apply(G!45, X, tptp_fun_Y_3(X, C!42, G!45))))))) | (~member(tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), B!43)) | (~((~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), C!42, G!45), C!42)) | (~apply(G!45, tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), C!42, G!45))))))),
% 0.58/0.64 inference(rewrite,[status(thm)],[])).
% 0.58/0.64 tff(114,plain,
% 0.58/0.64 ((~![X: $i] : ((~member(X, B!43)) | (~((~member(tptp_fun_Y_3(X, C!42, G!45), C!42)) | (~apply(G!45, X, tptp_fun_Y_3(X, C!42, G!45))))))) | ((~member(tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), B!43)) | (~((~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), C!42, G!45), C!42)) | (~apply(G!45, tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), C!42, G!45))))))),
% 0.58/0.64 inference(quant_inst,[status(thm)],[])).
% 0.58/0.64 tff(115,plain,
% 0.58/0.64 ((~![X: $i] : ((~member(X, B!43)) | (~((~member(tptp_fun_Y_3(X, C!42, G!45), C!42)) | (~apply(G!45, X, tptp_fun_Y_3(X, C!42, G!45))))))) | (~member(tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), B!43)) | (~((~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), C!42, G!45), C!42)) | (~apply(G!45, tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), C!42, G!45)))))),
% 0.58/0.64 inference(modus_ponens,[status(thm)],[114, 113])).
% 0.58/0.64 tff(116,plain,
% 0.58/0.64 (~((~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), C!42, G!45), C!42)) | (~apply(G!45, tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), C!42, G!45))))),
% 0.58/0.64 inference(unit_resolution,[status(thm)],[115, 112, 79])).
% 0.58/0.64 tff(117,plain,
% 0.58/0.64 (((~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), C!42, G!45), C!42)) | (~apply(G!45, tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), C!42, G!45)))) | apply(G!45, tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), C!42, G!45))),
% 0.58/0.64 inference(tautology,[status(thm)],[])).
% 0.58/0.64 tff(118,plain,
% 0.58/0.64 (apply(G!45, tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), C!42, G!45))),
% 0.58/0.64 inference(unit_resolution,[status(thm)],[117, 116])).
% 0.58/0.64 tff(119,plain,
% 0.58/0.64 (((~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), C!42, G!45), C!42)) | (~apply(G!45, tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), C!42, G!45)))) | member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), C!42, G!45), C!42)),
% 0.58/0.64 inference(tautology,[status(thm)],[])).
% 0.58/0.64 tff(120,plain,
% 0.58/0.64 (member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), C!42, G!45), C!42)),
% 0.58/0.64 inference(unit_resolution,[status(thm)],[119, 116])).
% 0.58/0.64 tff(121,plain,
% 0.58/0.64 (((~member(tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), B!43)) | (~apply(F!46, tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45))) | (~apply(G!45, tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42))))) | apply(G!45, tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))),
% 0.58/0.64 inference(tautology,[status(thm)],[])).
% 0.58/0.64 tff(122,plain,
% 0.58/0.64 (apply(G!45, tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))),
% 0.58/0.64 inference(unit_resolution,[status(thm)],[121, 77])).
% 0.58/0.64 tff(123,plain,
% 0.58/0.64 (((~![X: $i] : ((~member(X, B!43)) | (~((~member(tptp_fun_Y_3(X, C!42, G!45), C!42)) | (~apply(G!45, X, tptp_fun_Y_3(X, C!42, G!45))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G!45, X, Y1)) | (~apply(G!45, X, Y2)) | (~member(X, B!43)) | (~member(Y1, C!42)) | (~member(Y2, C!42))))) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G!45, X, Y1)) | (~apply(G!45, X, Y2)) | (~member(X, B!43)) | (~member(Y1, C!42)) | (~member(Y2, C!42)))),
% 0.58/0.64 inference(tautology,[status(thm)],[])).
% 0.58/0.64 tff(124,plain,
% 0.58/0.64 (![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G!45, X, Y1)) | (~apply(G!45, X, Y2)) | (~member(X, B!43)) | (~member(Y1, C!42)) | (~member(Y2, C!42)))),
% 0.58/0.64 inference(unit_resolution,[status(thm)],[123, 110])).
% 0.58/0.64 tff(125,plain,
% 0.58/0.64 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G!45, X, Y1)) | (~apply(G!45, X, Y2)) | (~member(X, B!43)) | (~member(Y1, C!42)) | (~member(Y2, C!42)))) | ((~member(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), C!42)) | (~member(tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), B!43)) | (~apply(G!45, tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), C!42, G!45), C!42)) | (~apply(G!45, tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), C!42, G!45))) | (tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), C!42, G!45) = tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42))))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G!45, X, Y1)) | (~apply(G!45, X, Y2)) | (~member(X, B!43)) | (~member(Y1, C!42)) | (~member(Y2, C!42)))) | (~member(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), C!42)) | (~member(tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), B!43)) | (~apply(G!45, tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), C!42, G!45), C!42)) | (~apply(G!45, tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), C!42, G!45))) | (tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), C!42, G!45) = tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42))))),
% 0.58/0.65 inference(rewrite,[status(thm)],[])).
% 0.58/0.65 tff(126,plain,
% 0.58/0.65 (((tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), C!42, G!45) = tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42))) | (~apply(G!45, tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), C!42, G!45))) | (~apply(G!45, tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))) | (~member(tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), B!43)) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), C!42, G!45), C!42)) | (~member(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), C!42))) <=> ((~member(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), C!42)) | (~member(tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), B!43)) | (~apply(G!45, tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), C!42, G!45), C!42)) | (~apply(G!45, tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), C!42, G!45))) | (tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), C!42, G!45) = tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42))))),
% 0.58/0.65 inference(rewrite,[status(thm)],[])).
% 0.58/0.65 tff(127,plain,
% 0.58/0.65 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G!45, X, Y1)) | (~apply(G!45, X, Y2)) | (~member(X, B!43)) | (~member(Y1, C!42)) | (~member(Y2, C!42)))) | ((tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), C!42, G!45) = tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42))) | (~apply(G!45, tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), C!42, G!45))) | (~apply(G!45, tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))) | (~member(tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), B!43)) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), C!42, G!45), C!42)) | (~member(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), C!42)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G!45, X, Y1)) | (~apply(G!45, X, Y2)) | (~member(X, B!43)) | (~member(Y1, C!42)) | (~member(Y2, C!42)))) | ((~member(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), C!42)) | (~member(tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), B!43)) | (~apply(G!45, tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), C!42, G!45), C!42)) | (~apply(G!45, tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), C!42, G!45))) | (tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), C!42, G!45) = tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))))),
% 0.58/0.65 inference(monotonicity,[status(thm)],[126])).
% 0.58/0.65 tff(128,plain,
% 0.58/0.65 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G!45, X, Y1)) | (~apply(G!45, X, Y2)) | (~member(X, B!43)) | (~member(Y1, C!42)) | (~member(Y2, C!42)))) | ((tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), C!42, G!45) = tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42))) | (~apply(G!45, tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), C!42, G!45))) | (~apply(G!45, tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))) | (~member(tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), B!43)) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), C!42, G!45), C!42)) | (~member(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), C!42)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G!45, X, Y1)) | (~apply(G!45, X, Y2)) | (~member(X, B!43)) | (~member(Y1, C!42)) | (~member(Y2, C!42)))) | (~member(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), C!42)) | (~member(tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), B!43)) | (~apply(G!45, tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), C!42, G!45), C!42)) | (~apply(G!45, tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), C!42, G!45))) | (tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), C!42, G!45) = tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42))))),
% 0.58/0.66 inference(transitivity,[status(thm)],[127, 125])).
% 0.58/0.66 tff(129,plain,
% 0.58/0.66 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G!45, X, Y1)) | (~apply(G!45, X, Y2)) | (~member(X, B!43)) | (~member(Y1, C!42)) | (~member(Y2, C!42)))) | ((tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), C!42, G!45) = tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42))) | (~apply(G!45, tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), C!42, G!45))) | (~apply(G!45, tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))) | (~member(tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), B!43)) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), C!42, G!45), C!42)) | (~member(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), C!42)))),
% 0.58/0.66 inference(quant_inst,[status(thm)],[])).
% 0.58/0.66 tff(130,plain,
% 0.58/0.66 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G!45, X, Y1)) | (~apply(G!45, X, Y2)) | (~member(X, B!43)) | (~member(Y1, C!42)) | (~member(Y2, C!42)))) | (~member(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), C!42)) | (~member(tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), B!43)) | (~apply(G!45, tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), C!42, G!45), C!42)) | (~apply(G!45, tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), C!42, G!45))) | (tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), C!42, G!45) = tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))),
% 0.58/0.66 inference(modus_ponens,[status(thm)],[129, 128])).
% 0.58/0.66 tff(131,plain,
% 0.58/0.66 (tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), C!42, G!45) = tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42))),
% 0.58/0.66 inference(unit_resolution,[status(thm)],[130, 124, 42, 79, 122, 120, 118])).
% 0.58/0.66 tff(132,plain,
% 0.58/0.66 ((apply(T!39, tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42))) | (~member(tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), A!44)) | (~member(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), C!42)) | (~member(tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), A!44)) | (~member(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), C!42)) | (~apply(R!41, tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))) | (~apply(compose_function(G!45, F!46, A!44, B!43, C!42), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))) | (~apply(compose_function(G!45, F!46, A!44, B!43, C!42), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42))))) | member(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), C!42)),
% 0.58/0.66 inference(tautology,[status(thm)],[])).
% 0.58/0.66 tff(133,plain,
% 0.58/0.66 (member(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), C!42)),
% 0.58/0.66 inference(unit_resolution,[status(thm)],[132, 40])).
% 0.58/0.66 tff(134,plain,
% 0.58/0.66 ((apply(T!39, tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42))) | (~member(tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), A!44)) | (~member(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), C!42)) | (~member(tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), A!44)) | (~member(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), C!42)) | (~apply(R!41, tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))) | (~apply(compose_function(G!45, F!46, A!44, B!43, C!42), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))) | (~apply(compose_function(G!45, F!46, A!44, B!43, C!42), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42))))) | member(tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), A!44)),
% 0.58/0.66 inference(tautology,[status(thm)],[])).
% 0.58/0.66 tff(135,plain,
% 0.58/0.66 (member(tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), A!44)),
% 0.58/0.66 inference(unit_resolution,[status(thm)],[134, 40])).
% 0.58/0.66 tff(136,plain,
% 0.58/0.66 (((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), A!44)) | (~member(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), C!42)) | (~((~((~apply(compose_function(G!45, F!46, A!44, B!43, C!42), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), B!43)) | (~apply(F!46, tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45))) | (~apply(G!45, tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))))))) | (~(apply(compose_function(G!45, F!46, A!44, B!43, C!42), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42))) | ![Y: $i] : ((~member(Y, B!43)) | (~apply(F!46, tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), Y)) | (~apply(G!45, Y, tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!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_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), A!44)) | (~member(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), C!42)) | (~((~((~apply(compose_function(G!45, F!46, A!44, B!43, C!42), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), B!43)) | (~apply(F!46, tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45))) | (~apply(G!45, tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))))))) | (~(apply(compose_function(G!45, F!46, A!44, B!43, C!42), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42))) | ![Y: $i] : ((~member(Y, B!43)) | (~apply(F!46, tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), Y)) | (~apply(G!45, Y, tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42))))))))))),
% 0.58/0.67 inference(rewrite,[status(thm)],[])).
% 0.58/0.67 tff(137,plain,
% 0.58/0.67 (((~member(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), C!42)) | (~member(tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), A!44)) | (~((~((~apply(compose_function(G!45, F!46, A!44, B!43, C!42), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), B!43)) | (~apply(F!46, tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45))) | (~apply(G!45, tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))))))) | (~(apply(compose_function(G!45, F!46, A!44, B!43, C!42), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42))) | ![Y: $i] : ((~member(Y, B!43)) | (~apply(F!46, tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), Y)) | (~apply(G!45, Y, tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))))))))) <=> ((~member(tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), A!44)) | (~member(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), C!42)) | (~((~((~apply(compose_function(G!45, F!46, A!44, B!43, C!42), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), B!43)) | (~apply(F!46, tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45))) | (~apply(G!45, tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))))))) | (~(apply(compose_function(G!45, F!46, A!44, B!43, C!42), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42))) | ![Y: $i] : ((~member(Y, B!43)) | (~apply(F!46, tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), Y)) | (~apply(G!45, Y, tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42))))))))))),
% 0.58/0.67 inference(rewrite,[status(thm)],[])).
% 0.58/0.67 tff(138,plain,
% 0.58/0.67 ((~((~((~apply(compose_function(G!45, F!46, A!44, B!43, C!42), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), B!43)) | (~apply(F!46, tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45))) | (~apply(G!45, tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))))))) | (~(apply(compose_function(G!45, F!46, A!44, B!43, C!42), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42))) | ![Y: $i] : ((~member(Y, B!43)) | (~apply(F!46, tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), Y)) | (~apply(G!45, Y, tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42))))))))) <=> (~((~((~apply(compose_function(G!45, F!46, A!44, B!43, C!42), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), B!43)) | (~apply(F!46, tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45))) | (~apply(G!45, tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))))))) | (~(apply(compose_function(G!45, F!46, A!44, B!43, C!42), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42))) | ![Y: $i] : ((~member(Y, B!43)) | (~apply(F!46, tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), Y)) | (~apply(G!45, Y, tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))))))))),
% 0.58/0.67 inference(rewrite,[status(thm)],[])).
% 0.58/0.67 tff(139,plain,
% 0.58/0.67 (((~member(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), C!42)) | (~member(tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), A!44)) | (~((~((~apply(compose_function(G!45, F!46, A!44, B!43, C!42), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), B!43)) | (~apply(F!46, tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45))) | (~apply(G!45, tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))))))) | (~(apply(compose_function(G!45, F!46, A!44, B!43, C!42), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42))) | ![Y: $i] : ((~member(Y, B!43)) | (~apply(F!46, tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), Y)) | (~apply(G!45, Y, tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))))))))) <=> ((~member(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), C!42)) | (~member(tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), A!44)) | (~((~((~apply(compose_function(G!45, F!46, A!44, B!43, C!42), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), B!43)) | (~apply(F!46, tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45))) | (~apply(G!45, tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))))))) | (~(apply(compose_function(G!45, F!46, A!44, B!43, C!42), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42))) | ![Y: $i] : ((~member(Y, B!43)) | (~apply(F!46, tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), Y)) | (~apply(G!45, Y, tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42))))))))))),
% 0.58/0.68 inference(monotonicity,[status(thm)],[138])).
% 0.58/0.68 tff(140,plain,
% 0.58/0.68 (((~member(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), C!42)) | (~member(tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), A!44)) | (~((~((~apply(compose_function(G!45, F!46, A!44, B!43, C!42), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), B!43)) | (~apply(F!46, tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45))) | (~apply(G!45, tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))))))) | (~(apply(compose_function(G!45, F!46, A!44, B!43, C!42), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42))) | ![Y: $i] : ((~member(Y, B!43)) | (~apply(F!46, tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), Y)) | (~apply(G!45, Y, tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))))))))) <=> ((~member(tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), A!44)) | (~member(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), C!42)) | (~((~((~apply(compose_function(G!45, F!46, A!44, B!43, C!42), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), B!43)) | (~apply(F!46, tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45))) | (~apply(G!45, tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))))))) | (~(apply(compose_function(G!45, F!46, A!44, B!43, C!42), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42))) | ![Y: $i] : ((~member(Y, B!43)) | (~apply(F!46, tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), Y)) | (~apply(G!45, Y, tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42))))))))))),
% 0.58/0.68 inference(transitivity,[status(thm)],[139, 137])).
% 0.58/0.68 tff(141,plain,
% 0.58/0.68 (((~![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_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), C!42)) | (~member(tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), A!44)) | (~((~((~apply(compose_function(G!45, F!46, A!44, B!43, C!42), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), B!43)) | (~apply(F!46, tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45))) | (~apply(G!45, tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))))))) | (~(apply(compose_function(G!45, F!46, A!44, B!43, C!42), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42))) | ![Y: $i] : ((~member(Y, B!43)) | (~apply(F!46, tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), Y)) | (~apply(G!45, Y, tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!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_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), A!44)) | (~member(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), C!42)) | (~((~((~apply(compose_function(G!45, F!46, A!44, B!43, C!42), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), B!43)) | (~apply(F!46, tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45))) | (~apply(G!45, tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))))))) | (~(apply(compose_function(G!45, F!46, A!44, B!43, C!42), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42))) | ![Y: $i] : ((~member(Y, B!43)) | (~apply(F!46, tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), Y)) | (~apply(G!45, Y, tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))))))))))),
% 0.58/0.68 inference(monotonicity,[status(thm)],[140])).
% 0.58/0.68 tff(142,plain,
% 0.58/0.68 (((~![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_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), C!42)) | (~member(tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), A!44)) | (~((~((~apply(compose_function(G!45, F!46, A!44, B!43, C!42), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), B!43)) | (~apply(F!46, tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45))) | (~apply(G!45, tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))))))) | (~(apply(compose_function(G!45, F!46, A!44, B!43, C!42), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42))) | ![Y: $i] : ((~member(Y, B!43)) | (~apply(F!46, tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), Y)) | (~apply(G!45, Y, tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!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_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), A!44)) | (~member(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), C!42)) | (~((~((~apply(compose_function(G!45, F!46, A!44, B!43, C!42), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), B!43)) | (~apply(F!46, tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45))) | (~apply(G!45, tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))))))) | (~(apply(compose_function(G!45, F!46, A!44, B!43, C!42), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42))) | ![Y: $i] : ((~member(Y, B!43)) | (~apply(F!46, tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), Y)) | (~apply(G!45, Y, tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42))))))))))),
% 0.58/0.69 inference(transitivity,[status(thm)],[141, 136])).
% 0.58/0.69 tff(143,plain,
% 0.58/0.69 ((~![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_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), C!42)) | (~member(tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), A!44)) | (~((~((~apply(compose_function(G!45, F!46, A!44, B!43, C!42), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), B!43)) | (~apply(F!46, tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45))) | (~apply(G!45, tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))))))) | (~(apply(compose_function(G!45, F!46, A!44, B!43, C!42), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42))) | ![Y: $i] : ((~member(Y, B!43)) | (~apply(F!46, tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), Y)) | (~apply(G!45, Y, tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42))))))))))),
% 0.58/0.69 inference(quant_inst,[status(thm)],[])).
% 0.58/0.69 tff(144,plain,
% 0.58/0.69 ((~![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_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), A!44)) | (~member(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), C!42)) | (~((~((~apply(compose_function(G!45, F!46, A!44, B!43, C!42), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), B!43)) | (~apply(F!46, tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45))) | (~apply(G!45, tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))))))) | (~(apply(compose_function(G!45, F!46, A!44, B!43, C!42), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42))) | ![Y: $i] : ((~member(Y, B!43)) | (~apply(F!46, tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), Y)) | (~apply(G!45, Y, tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))))))))),
% 0.58/0.69 inference(modus_ponens,[status(thm)],[143, 142])).
% 0.58/0.69 tff(145,plain,
% 0.58/0.69 (~((~((~apply(compose_function(G!45, F!46, A!44, B!43, C!42), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), B!43)) | (~apply(F!46, tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45))) | (~apply(G!45, tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))))))) | (~(apply(compose_function(G!45, F!46, A!44, B!43, C!42), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42))) | ![Y: $i] : ((~member(Y, B!43)) | (~apply(F!46, tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), Y)) | (~apply(G!45, Y, tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42))))))))),
% 0.58/0.69 inference(unit_resolution,[status(thm)],[144, 60, 135, 133])).
% 0.58/0.69 tff(146,plain,
% 0.58/0.69 (((~((~apply(compose_function(G!45, F!46, A!44, B!43, C!42), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), B!43)) | (~apply(F!46, tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45))) | (~apply(G!45, tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))))))) | (~(apply(compose_function(G!45, F!46, A!44, B!43, C!42), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42))) | ![Y: $i] : ((~member(Y, B!43)) | (~apply(F!46, tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), Y)) | (~apply(G!45, Y, tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))))))) | ((~apply(compose_function(G!45, F!46, A!44, B!43, C!42), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), B!43)) | (~apply(F!46, tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45))) | (~apply(G!45, tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))))))),
% 0.58/0.69 inference(tautology,[status(thm)],[])).
% 0.58/0.69 tff(147,plain,
% 0.58/0.69 ((~apply(compose_function(G!45, F!46, A!44, B!43, C!42), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), B!43)) | (~apply(F!46, tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45))) | (~apply(G!45, tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42))))))),
% 0.58/0.70 inference(unit_resolution,[status(thm)],[146, 145])).
% 0.58/0.70 tff(148,plain,
% 0.58/0.70 ((apply(T!39, tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42))) | (~member(tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), A!44)) | (~member(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), C!42)) | (~member(tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), A!44)) | (~member(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), C!42)) | (~apply(R!41, tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))) | (~apply(compose_function(G!45, F!46, A!44, B!43, C!42), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))) | (~apply(compose_function(G!45, F!46, A!44, B!43, C!42), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42))))) | apply(compose_function(G!45, F!46, A!44, B!43, C!42), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))),
% 0.58/0.70 inference(tautology,[status(thm)],[])).
% 0.58/0.70 tff(149,plain,
% 0.58/0.70 (apply(compose_function(G!45, F!46, A!44, B!43, C!42), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))),
% 0.58/0.70 inference(unit_resolution,[status(thm)],[148, 40])).
% 0.58/0.70 tff(150,plain,
% 0.58/0.70 ((~((~apply(compose_function(G!45, F!46, A!44, B!43, C!42), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), B!43)) | (~apply(F!46, tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45))) | (~apply(G!45, tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))))))) | (~apply(compose_function(G!45, F!46, A!44, B!43, C!42), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), B!43)) | (~apply(F!46, tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45))) | (~apply(G!45, tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42))))))),
% 0.58/0.70 inference(tautology,[status(thm)],[])).
% 0.58/0.70 tff(151,plain,
% 0.58/0.70 ((~((~apply(compose_function(G!45, F!46, A!44, B!43, C!42), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), B!43)) | (~apply(F!46, tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45))) | (~apply(G!45, tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))))))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), B!43)) | (~apply(F!46, tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45))) | (~apply(G!45, tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42))))))),
% 0.58/0.70 inference(unit_resolution,[status(thm)],[150, 149])).
% 0.58/0.70 tff(152,plain,
% 0.58/0.70 (~((~member(tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), B!43)) | (~apply(F!46, tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45))) | (~apply(G!45, tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))))),
% 0.58/0.70 inference(unit_resolution,[status(thm)],[151, 147])).
% 0.58/0.70 tff(153,plain,
% 0.58/0.70 (((~member(tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), B!43)) | (~apply(F!46, tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45))) | (~apply(G!45, tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42))))) | member(tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), B!43)),
% 0.58/0.70 inference(tautology,[status(thm)],[])).
% 0.58/0.70 tff(154,plain,
% 0.58/0.70 (member(tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), B!43)),
% 0.58/0.70 inference(unit_resolution,[status(thm)],[153, 152])).
% 0.58/0.70 tff(155,plain,
% 0.58/0.70 (((~![X: $i] : ((~member(X, B!43)) | (~((~member(tptp_fun_Y_3(X, C!42, G!45), C!42)) | (~apply(G!45, X, tptp_fun_Y_3(X, C!42, G!45))))))) | ((~member(tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), B!43)) | (~((~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), C!42, G!45), C!42)) | (~apply(G!45, tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), C!42, G!45))))))) <=> ((~![X: $i] : ((~member(X, B!43)) | (~((~member(tptp_fun_Y_3(X, C!42, G!45), C!42)) | (~apply(G!45, X, tptp_fun_Y_3(X, C!42, G!45))))))) | (~member(tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), B!43)) | (~((~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), C!42, G!45), C!42)) | (~apply(G!45, tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), C!42, G!45))))))),
% 0.58/0.70 inference(rewrite,[status(thm)],[])).
% 0.58/0.70 tff(156,plain,
% 0.58/0.70 ((~![X: $i] : ((~member(X, B!43)) | (~((~member(tptp_fun_Y_3(X, C!42, G!45), C!42)) | (~apply(G!45, X, tptp_fun_Y_3(X, C!42, G!45))))))) | ((~member(tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), B!43)) | (~((~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), C!42, G!45), C!42)) | (~apply(G!45, tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), C!42, G!45))))))),
% 0.58/0.71 inference(quant_inst,[status(thm)],[])).
% 0.58/0.71 tff(157,plain,
% 0.58/0.71 ((~![X: $i] : ((~member(X, B!43)) | (~((~member(tptp_fun_Y_3(X, C!42, G!45), C!42)) | (~apply(G!45, X, tptp_fun_Y_3(X, C!42, G!45))))))) | (~member(tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), B!43)) | (~((~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), C!42, G!45), C!42)) | (~apply(G!45, tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), C!42, G!45)))))),
% 0.58/0.71 inference(modus_ponens,[status(thm)],[156, 155])).
% 0.58/0.71 tff(158,plain,
% 0.58/0.71 (~((~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), C!42, G!45), C!42)) | (~apply(G!45, tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), C!42, G!45))))),
% 0.58/0.71 inference(unit_resolution,[status(thm)],[157, 112, 154])).
% 0.58/0.71 tff(159,plain,
% 0.58/0.71 (((~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), C!42, G!45), C!42)) | (~apply(G!45, tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), C!42, G!45)))) | apply(G!45, tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), C!42, G!45))),
% 0.58/0.71 inference(tautology,[status(thm)],[])).
% 0.58/0.71 tff(160,plain,
% 0.58/0.71 (apply(G!45, tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), C!42, G!45))),
% 0.58/0.71 inference(unit_resolution,[status(thm)],[159, 158])).
% 0.58/0.71 tff(161,plain,
% 0.58/0.71 (((~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), C!42, G!45), C!42)) | (~apply(G!45, tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), C!42, G!45)))) | member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), C!42, G!45), C!42)),
% 0.58/0.71 inference(tautology,[status(thm)],[])).
% 0.58/0.71 tff(162,plain,
% 0.58/0.71 (member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), C!42, G!45), C!42)),
% 0.58/0.71 inference(unit_resolution,[status(thm)],[161, 158])).
% 0.58/0.71 tff(163,plain,
% 0.58/0.71 (((~member(tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), B!43)) | (~apply(F!46, tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45))) | (~apply(G!45, tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42))))) | apply(G!45, tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))),
% 0.58/0.71 inference(tautology,[status(thm)],[])).
% 0.58/0.71 tff(164,plain,
% 0.58/0.71 (apply(G!45, tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))),
% 0.58/0.71 inference(unit_resolution,[status(thm)],[163, 152])).
% 0.58/0.71 tff(165,plain,
% 0.58/0.71 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G!45, X, Y1)) | (~apply(G!45, X, Y2)) | (~member(X, B!43)) | (~member(Y1, C!42)) | (~member(Y2, C!42)))) | ((~member(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), C!42)) | (~member(tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), B!43)) | (~apply(G!45, tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), C!42, G!45), C!42)) | (~apply(G!45, tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), C!42, G!45))) | (tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), C!42, G!45) = tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42))))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G!45, X, Y1)) | (~apply(G!45, X, Y2)) | (~member(X, B!43)) | (~member(Y1, C!42)) | (~member(Y2, C!42)))) | (~member(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), C!42)) | (~member(tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), B!43)) | (~apply(G!45, tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), C!42, G!45), C!42)) | (~apply(G!45, tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), C!42, G!45))) | (tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), C!42, G!45) = tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42))))),
% 0.58/0.72 inference(rewrite,[status(thm)],[])).
% 0.58/0.72 tff(166,plain,
% 0.58/0.72 (((tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), C!42, G!45) = tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42))) | (~apply(G!45, tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), C!42, G!45))) | (~apply(G!45, tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))) | (~member(tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), B!43)) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), C!42, G!45), C!42)) | (~member(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), C!42))) <=> ((~member(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), C!42)) | (~member(tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), B!43)) | (~apply(G!45, tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), C!42, G!45), C!42)) | (~apply(G!45, tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), C!42, G!45))) | (tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), C!42, G!45) = tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42))))),
% 0.58/0.72 inference(rewrite,[status(thm)],[])).
% 0.58/0.72 tff(167,plain,
% 0.58/0.72 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G!45, X, Y1)) | (~apply(G!45, X, Y2)) | (~member(X, B!43)) | (~member(Y1, C!42)) | (~member(Y2, C!42)))) | ((tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), C!42, G!45) = tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42))) | (~apply(G!45, tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), C!42, G!45))) | (~apply(G!45, tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))) | (~member(tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), B!43)) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), C!42, G!45), C!42)) | (~member(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), C!42)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G!45, X, Y1)) | (~apply(G!45, X, Y2)) | (~member(X, B!43)) | (~member(Y1, C!42)) | (~member(Y2, C!42)))) | ((~member(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), C!42)) | (~member(tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), B!43)) | (~apply(G!45, tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), C!42, G!45), C!42)) | (~apply(G!45, tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), C!42, G!45))) | (tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), C!42, G!45) = tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))))),
% 0.58/0.72 inference(monotonicity,[status(thm)],[166])).
% 0.58/0.72 tff(168,plain,
% 0.58/0.72 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G!45, X, Y1)) | (~apply(G!45, X, Y2)) | (~member(X, B!43)) | (~member(Y1, C!42)) | (~member(Y2, C!42)))) | ((tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), C!42, G!45) = tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42))) | (~apply(G!45, tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), C!42, G!45))) | (~apply(G!45, tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))) | (~member(tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), B!43)) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), C!42, G!45), C!42)) | (~member(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), C!42)))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G!45, X, Y1)) | (~apply(G!45, X, Y2)) | (~member(X, B!43)) | (~member(Y1, C!42)) | (~member(Y2, C!42)))) | (~member(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), C!42)) | (~member(tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), B!43)) | (~apply(G!45, tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), C!42, G!45), C!42)) | (~apply(G!45, tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), C!42, G!45))) | (tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), C!42, G!45) = tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42))))),
% 0.67/0.73 inference(transitivity,[status(thm)],[167, 165])).
% 0.67/0.73 tff(169,plain,
% 0.67/0.73 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G!45, X, Y1)) | (~apply(G!45, X, Y2)) | (~member(X, B!43)) | (~member(Y1, C!42)) | (~member(Y2, C!42)))) | ((tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), C!42, G!45) = tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42))) | (~apply(G!45, tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), C!42, G!45))) | (~apply(G!45, tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))) | (~member(tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), B!43)) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), C!42, G!45), C!42)) | (~member(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), C!42)))),
% 0.67/0.73 inference(quant_inst,[status(thm)],[])).
% 0.67/0.73 tff(170,plain,
% 0.67/0.73 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(G!45, X, Y1)) | (~apply(G!45, X, Y2)) | (~member(X, B!43)) | (~member(Y1, C!42)) | (~member(Y2, C!42)))) | (~member(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), C!42)) | (~member(tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), B!43)) | (~apply(G!45, tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), C!42, G!45), C!42)) | (~apply(G!45, tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), C!42, G!45))) | (tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), C!42, G!45) = tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))),
% 0.67/0.73 inference(modus_ponens,[status(thm)],[169, 168])).
% 0.67/0.73 tff(171,plain,
% 0.67/0.73 (tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), C!42, G!45) = tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42))),
% 0.67/0.73 inference(unit_resolution,[status(thm)],[170, 124, 133, 154, 164, 162, 160])).
% 0.67/0.73 tff(172,plain,
% 0.67/0.73 (apply(T!39, tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), C!42, G!45), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), C!42, G!45)) <=> apply(T!39, tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))),
% 0.67/0.73 inference(monotonicity,[status(thm)],[171, 131])).
% 0.67/0.73 tff(173,plain,
% 0.67/0.73 (apply(T!39, tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42))) <=> apply(T!39, tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), C!42, G!45), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), C!42, G!45))),
% 0.67/0.73 inference(symmetry,[status(thm)],[172])).
% 0.67/0.73 tff(174,plain,
% 0.67/0.73 ((~apply(T!39, tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))) <=> (~apply(T!39, tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), C!42, G!45), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), C!42, G!45)))),
% 0.67/0.73 inference(monotonicity,[status(thm)],[173])).
% 0.67/0.73 tff(175,plain,
% 0.67/0.73 ((apply(T!39, tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42))) | (~member(tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), A!44)) | (~member(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), C!42)) | (~member(tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), A!44)) | (~member(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), C!42)) | (~apply(R!41, tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))) | (~apply(compose_function(G!45, F!46, A!44, B!43, C!42), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))) | (~apply(compose_function(G!45, F!46, A!44, B!43, C!42), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42))))) | (~apply(T!39, tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42))))),
% 0.67/0.73 inference(tautology,[status(thm)],[])).
% 0.67/0.73 tff(176,plain,
% 0.67/0.73 (~apply(T!39, tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))),
% 0.67/0.73 inference(unit_resolution,[status(thm)],[175, 40])).
% 0.67/0.73 tff(177,plain,
% 0.67/0.73 (~apply(T!39, tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), C!42, G!45), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), C!42, G!45))),
% 0.67/0.73 inference(modus_ponens,[status(thm)],[176, 174])).
% 0.67/0.73 tff(178,plain,
% 0.67/0.73 (((~member(tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), B!43)) | (~apply(F!46, tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45))) | (~apply(G!45, tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42))))) | apply(F!46, tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45))),
% 0.67/0.73 inference(tautology,[status(thm)],[])).
% 0.67/0.73 tff(179,plain,
% 0.67/0.73 (apply(F!46, tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45))),
% 0.67/0.73 inference(unit_resolution,[status(thm)],[178, 152])).
% 0.67/0.73 tff(180,plain,
% 0.67/0.73 (((~member(tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), B!43)) | (~apply(F!46, tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45))) | (~apply(G!45, tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42))))) | apply(F!46, tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45))),
% 0.67/0.74 inference(tautology,[status(thm)],[])).
% 0.67/0.74 tff(181,plain,
% 0.67/0.74 (apply(F!46, tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45))),
% 0.67/0.74 inference(unit_resolution,[status(thm)],[180, 77])).
% 0.67/0.74 tff(182,plain,
% 0.67/0.74 (^[F: $i, A: $i, R: $i, B: $i, S: $i] : refl((~((~((~decreasing(F, A, R, B, S)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(S, Y2, Y1) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(R, X1, X2)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2))))) | (~(decreasing(F, A, R, B, S) | (~(apply(S, tptp_fun_Y2_31(S, B, R, A, F), tptp_fun_Y1_33(S, B, R, A, F)) | (~member(tptp_fun_X1_34(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_33(S, B, R, A, F), B)) | (~member(tptp_fun_X2_32(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_31(S, B, R, A, F), B)) | (~apply(R, tptp_fun_X1_34(S, B, R, A, F), tptp_fun_X2_32(S, B, R, A, F))) | (~apply(F, tptp_fun_X1_34(S, B, R, A, F), tptp_fun_Y1_33(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_32(S, B, R, A, F), tptp_fun_Y2_31(S, B, R, A, F))))))))) <=> (~((~((~decreasing(F, A, R, B, S)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(S, Y2, Y1) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(R, X1, X2)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2))))) | (~(decreasing(F, A, R, B, S) | (~(apply(S, tptp_fun_Y2_31(S, B, R, A, F), tptp_fun_Y1_33(S, B, R, A, F)) | (~member(tptp_fun_X1_34(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_33(S, B, R, A, F), B)) | (~member(tptp_fun_X2_32(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_31(S, B, R, A, F), B)) | (~apply(R, tptp_fun_X1_34(S, B, R, A, F), tptp_fun_X2_32(S, B, R, A, F))) | (~apply(F, tptp_fun_X1_34(S, B, R, A, F), tptp_fun_Y1_33(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_32(S, B, R, A, F), tptp_fun_Y2_31(S, B, R, A, F))))))))))),
% 0.67/0.74 inference(bind,[status(th)],[])).
% 0.67/0.74 tff(183,plain,
% 0.67/0.74 (![F: $i, A: $i, R: $i, B: $i, S: $i] : (~((~((~decreasing(F, A, R, B, S)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(S, Y2, Y1) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(R, X1, X2)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2))))) | (~(decreasing(F, A, R, B, S) | (~(apply(S, tptp_fun_Y2_31(S, B, R, A, F), tptp_fun_Y1_33(S, B, R, A, F)) | (~member(tptp_fun_X1_34(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_33(S, B, R, A, F), B)) | (~member(tptp_fun_X2_32(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_31(S, B, R, A, F), B)) | (~apply(R, tptp_fun_X1_34(S, B, R, A, F), tptp_fun_X2_32(S, B, R, A, F))) | (~apply(F, tptp_fun_X1_34(S, B, R, A, F), tptp_fun_Y1_33(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_32(S, B, R, A, F), tptp_fun_Y2_31(S, B, R, A, F))))))))) <=> ![F: $i, A: $i, R: $i, B: $i, S: $i] : (~((~((~decreasing(F, A, R, B, S)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(S, Y2, Y1) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(R, X1, X2)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2))))) | (~(decreasing(F, A, R, B, S) | (~(apply(S, tptp_fun_Y2_31(S, B, R, A, F), tptp_fun_Y1_33(S, B, R, A, F)) | (~member(tptp_fun_X1_34(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_33(S, B, R, A, F), B)) | (~member(tptp_fun_X2_32(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_31(S, B, R, A, F), B)) | (~apply(R, tptp_fun_X1_34(S, B, R, A, F), tptp_fun_X2_32(S, B, R, A, F))) | (~apply(F, tptp_fun_X1_34(S, B, R, A, F), tptp_fun_Y1_33(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_32(S, B, R, A, F), tptp_fun_Y2_31(S, B, R, A, F)))))))))),
% 0.67/0.74 inference(quant_intro,[status(thm)],[182])).
% 0.67/0.74 tff(184,plain,
% 0.67/0.74 (^[F: $i, A: $i, R: $i, B: $i, S: $i] : rewrite((~((~((~decreasing(F, A, R, B, S)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(S, Y2, Y1) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(R, X1, X2)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2))))) | (~(decreasing(F, A, R, B, S) | (~(apply(S, tptp_fun_Y2_31(S, B, R, A, F), tptp_fun_Y1_33(S, B, R, A, F)) | (~member(tptp_fun_X1_34(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_33(S, B, R, A, F), B)) | (~member(tptp_fun_X2_32(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_31(S, B, R, A, F), B)) | (~apply(R, tptp_fun_X1_34(S, B, R, A, F), tptp_fun_X2_32(S, B, R, A, F))) | (~apply(F, tptp_fun_X1_34(S, B, R, A, F), tptp_fun_Y1_33(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_32(S, B, R, A, F), tptp_fun_Y2_31(S, B, R, A, F))))))))) <=> (~((~((~decreasing(F, A, R, B, S)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(S, Y2, Y1) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(R, X1, X2)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2))))) | (~(decreasing(F, A, R, B, S) | (~(apply(S, tptp_fun_Y2_31(S, B, R, A, F), tptp_fun_Y1_33(S, B, R, A, F)) | (~member(tptp_fun_X1_34(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_33(S, B, R, A, F), B)) | (~member(tptp_fun_X2_32(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_31(S, B, R, A, F), B)) | (~apply(R, tptp_fun_X1_34(S, B, R, A, F), tptp_fun_X2_32(S, B, R, A, F))) | (~apply(F, tptp_fun_X1_34(S, B, R, A, F), tptp_fun_Y1_33(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_32(S, B, R, A, F), tptp_fun_Y2_31(S, B, R, A, F))))))))))),
% 0.67/0.74 inference(bind,[status(th)],[])).
% 0.67/0.74 tff(185,plain,
% 0.67/0.74 (![F: $i, A: $i, R: $i, B: $i, S: $i] : (~((~((~decreasing(F, A, R, B, S)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(S, Y2, Y1) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(R, X1, X2)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2))))) | (~(decreasing(F, A, R, B, S) | (~(apply(S, tptp_fun_Y2_31(S, B, R, A, F), tptp_fun_Y1_33(S, B, R, A, F)) | (~member(tptp_fun_X1_34(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_33(S, B, R, A, F), B)) | (~member(tptp_fun_X2_32(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_31(S, B, R, A, F), B)) | (~apply(R, tptp_fun_X1_34(S, B, R, A, F), tptp_fun_X2_32(S, B, R, A, F))) | (~apply(F, tptp_fun_X1_34(S, B, R, A, F), tptp_fun_Y1_33(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_32(S, B, R, A, F), tptp_fun_Y2_31(S, B, R, A, F))))))))) <=> ![F: $i, A: $i, R: $i, B: $i, S: $i] : (~((~((~decreasing(F, A, R, B, S)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(S, Y2, Y1) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(R, X1, X2)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2))))) | (~(decreasing(F, A, R, B, S) | (~(apply(S, tptp_fun_Y2_31(S, B, R, A, F), tptp_fun_Y1_33(S, B, R, A, F)) | (~member(tptp_fun_X1_34(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_33(S, B, R, A, F), B)) | (~member(tptp_fun_X2_32(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_31(S, B, R, A, F), B)) | (~apply(R, tptp_fun_X1_34(S, B, R, A, F), tptp_fun_X2_32(S, B, R, A, F))) | (~apply(F, tptp_fun_X1_34(S, B, R, A, F), tptp_fun_Y1_33(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_32(S, B, R, A, F), tptp_fun_Y2_31(S, B, R, A, F)))))))))),
% 0.67/0.74 inference(quant_intro,[status(thm)],[184])).
% 0.67/0.74 tff(186,plain,
% 0.67/0.74 (![F: $i, A: $i, R: $i, B: $i, S: $i] : (~((~((~decreasing(F, A, R, B, S)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(S, Y2, Y1) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(R, X1, X2)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2))))) | (~(decreasing(F, A, R, B, S) | (~(apply(S, tptp_fun_Y2_31(S, B, R, A, F), tptp_fun_Y1_33(S, B, R, A, F)) | (~member(tptp_fun_X1_34(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_33(S, B, R, A, F), B)) | (~member(tptp_fun_X2_32(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_31(S, B, R, A, F), B)) | (~apply(R, tptp_fun_X1_34(S, B, R, A, F), tptp_fun_X2_32(S, B, R, A, F))) | (~apply(F, tptp_fun_X1_34(S, B, R, A, F), tptp_fun_Y1_33(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_32(S, B, R, A, F), tptp_fun_Y2_31(S, B, R, A, F))))))))) <=> ![F: $i, A: $i, R: $i, B: $i, S: $i] : (~((~((~decreasing(F, A, R, B, S)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(S, Y2, Y1) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(R, X1, X2)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2))))) | (~(decreasing(F, A, R, B, S) | (~(apply(S, tptp_fun_Y2_31(S, B, R, A, F), tptp_fun_Y1_33(S, B, R, A, F)) | (~member(tptp_fun_X1_34(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_33(S, B, R, A, F), B)) | (~member(tptp_fun_X2_32(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_31(S, B, R, A, F), B)) | (~apply(R, tptp_fun_X1_34(S, B, R, A, F), tptp_fun_X2_32(S, B, R, A, F))) | (~apply(F, tptp_fun_X1_34(S, B, R, A, F), tptp_fun_Y1_33(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_32(S, B, R, A, F), tptp_fun_Y2_31(S, B, R, A, F)))))))))),
% 0.67/0.74 inference(transitivity,[status(thm)],[185, 183])).
% 0.67/0.74 tff(187,plain,
% 0.67/0.74 (^[F: $i, A: $i, R: $i, B: $i, S: $i] : trans(monotonicity(rewrite(((~decreasing(F, A, R, B, S)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~(member(X1, A) & member(Y1, B) & member(X2, A) & member(Y2, B) & apply(R, X1, X2) & apply(F, X1, Y1) & apply(F, X2, Y2))) | apply(S, Y2, Y1))) <=> ((~decreasing(F, A, R, B, S)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(S, Y2, Y1) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(R, X1, X2)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2))))), trans(monotonicity(rewrite((~((~(member(tptp_fun_X1_34(S, B, R, A, F), A) & member(tptp_fun_Y1_33(S, B, R, A, F), B) & member(tptp_fun_X2_32(S, B, R, A, F), A) & member(tptp_fun_Y2_31(S, B, R, A, F), B) & apply(R, tptp_fun_X1_34(S, B, R, A, F), tptp_fun_X2_32(S, B, R, A, F)) & apply(F, tptp_fun_X1_34(S, B, R, A, F), tptp_fun_Y1_33(S, B, R, A, F)) & apply(F, tptp_fun_X2_32(S, B, R, A, F), tptp_fun_Y2_31(S, B, R, A, F)))) | apply(S, tptp_fun_Y2_31(S, B, R, A, F), tptp_fun_Y1_33(S, B, R, A, F)))) <=> (~(apply(S, tptp_fun_Y2_31(S, B, R, A, F), tptp_fun_Y1_33(S, B, R, A, F)) | (~member(tptp_fun_X1_34(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_33(S, B, R, A, F), B)) | (~member(tptp_fun_X2_32(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_31(S, B, R, A, F), B)) | (~apply(R, tptp_fun_X1_34(S, B, R, A, F), tptp_fun_X2_32(S, B, R, A, F))) | (~apply(F, tptp_fun_X1_34(S, B, R, A, F), tptp_fun_Y1_33(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_32(S, B, R, A, F), tptp_fun_Y2_31(S, B, R, A, F)))))), ((decreasing(F, A, R, B, S) | (~((~(member(tptp_fun_X1_34(S, B, R, A, F), A) & member(tptp_fun_Y1_33(S, B, R, A, F), B) & member(tptp_fun_X2_32(S, B, R, A, F), A) & member(tptp_fun_Y2_31(S, B, R, A, F), B) & apply(R, tptp_fun_X1_34(S, B, R, A, F), tptp_fun_X2_32(S, B, R, A, F)) & apply(F, tptp_fun_X1_34(S, B, R, A, F), tptp_fun_Y1_33(S, B, R, A, F)) & apply(F, tptp_fun_X2_32(S, B, R, A, F), tptp_fun_Y2_31(S, B, R, A, F)))) | apply(S, tptp_fun_Y2_31(S, B, R, A, F), tptp_fun_Y1_33(S, B, R, A, F))))) <=> (decreasing(F, A, R, B, S) | (~(apply(S, tptp_fun_Y2_31(S, B, R, A, F), tptp_fun_Y1_33(S, B, R, A, F)) | (~member(tptp_fun_X1_34(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_33(S, B, R, A, F), B)) | (~member(tptp_fun_X2_32(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_31(S, B, R, A, F), B)) | (~apply(R, tptp_fun_X1_34(S, B, R, A, F), tptp_fun_X2_32(S, B, R, A, F))) | (~apply(F, tptp_fun_X1_34(S, B, R, A, F), tptp_fun_Y1_33(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_32(S, B, R, A, F), tptp_fun_Y2_31(S, B, R, A, F)))))))), rewrite((decreasing(F, A, R, B, S) | (~(apply(S, tptp_fun_Y2_31(S, B, R, A, F), tptp_fun_Y1_33(S, B, R, A, F)) | (~member(tptp_fun_X1_34(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_33(S, B, R, A, F), B)) | (~member(tptp_fun_X2_32(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_31(S, B, R, A, F), B)) | (~apply(R, tptp_fun_X1_34(S, B, R, A, F), tptp_fun_X2_32(S, B, R, A, F))) | (~apply(F, tptp_fun_X1_34(S, B, R, A, F), tptp_fun_Y1_33(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_32(S, B, R, A, F), tptp_fun_Y2_31(S, B, R, A, F)))))) <=> (decreasing(F, A, R, B, S) | (~(apply(S, tptp_fun_Y2_31(S, B, R, A, F), tptp_fun_Y1_33(S, B, R, A, F)) | (~member(tptp_fun_X1_34(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_33(S, B, R, A, F), B)) | (~member(tptp_fun_X2_32(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_31(S, B, R, A, F), B)) | (~apply(R, tptp_fun_X1_34(S, B, R, A, F), tptp_fun_X2_32(S, B, R, A, F))) | (~apply(F, tptp_fun_X1_34(S, B, R, A, F), tptp_fun_Y1_33(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_32(S, B, R, A, F), tptp_fun_Y2_31(S, B, R, A, F))))))), ((decreasing(F, A, R, B, S) | (~((~(member(tptp_fun_X1_34(S, B, R, A, F), A) & member(tptp_fun_Y1_33(S, B, R, A, F), B) & member(tptp_fun_X2_32(S, B, R, A, F), A) & member(tptp_fun_Y2_31(S, B, R, A, F), B) & apply(R, tptp_fun_X1_34(S, B, R, A, F), tptp_fun_X2_32(S, B, R, A, F)) & apply(F, tptp_fun_X1_34(S, B, R, A, F), tptp_fun_Y1_33(S, B, R, A, F)) & apply(F, tptp_fun_X2_32(S, B, R, A, F), tptp_fun_Y2_31(S, B, R, A, F)))) | apply(S, tptp_fun_Y2_31(S, B, R, A, F), tptp_fun_Y1_33(S, B, R, A, F))))) <=> (decreasing(F, A, R, B, S) | (~(apply(S, tptp_fun_Y2_31(S, B, R, A, F), tptp_fun_Y1_33(S, B, R, A, F)) | (~member(tptp_fun_X1_34(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_33(S, B, R, A, F), B)) | (~member(tptp_fun_X2_32(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_31(S, B, R, A, F), B)) | (~apply(R, tptp_fun_X1_34(S, B, R, A, F), tptp_fun_X2_32(S, B, R, A, F))) | (~apply(F, tptp_fun_X1_34(S, B, R, A, F), tptp_fun_Y1_33(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_32(S, B, R, A, F), tptp_fun_Y2_31(S, B, R, A, F)))))))), ((((~decreasing(F, A, R, B, S)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~(member(X1, A) & member(Y1, B) & member(X2, A) & member(Y2, B) & apply(R, X1, X2) & apply(F, X1, Y1) & apply(F, X2, Y2))) | apply(S, Y2, Y1))) & (decreasing(F, A, R, B, S) | (~((~(member(tptp_fun_X1_34(S, B, R, A, F), A) & member(tptp_fun_Y1_33(S, B, R, A, F), B) & member(tptp_fun_X2_32(S, B, R, A, F), A) & member(tptp_fun_Y2_31(S, B, R, A, F), B) & apply(R, tptp_fun_X1_34(S, B, R, A, F), tptp_fun_X2_32(S, B, R, A, F)) & apply(F, tptp_fun_X1_34(S, B, R, A, F), tptp_fun_Y1_33(S, B, R, A, F)) & apply(F, tptp_fun_X2_32(S, B, R, A, F), tptp_fun_Y2_31(S, B, R, A, F)))) | apply(S, tptp_fun_Y2_31(S, B, R, A, F), tptp_fun_Y1_33(S, B, R, A, F)))))) <=> (((~decreasing(F, A, R, B, S)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(S, Y2, Y1) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(R, X1, X2)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2)))) & (decreasing(F, A, R, B, S) | (~(apply(S, tptp_fun_Y2_31(S, B, R, A, F), tptp_fun_Y1_33(S, B, R, A, F)) | (~member(tptp_fun_X1_34(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_33(S, B, R, A, F), B)) | (~member(tptp_fun_X2_32(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_31(S, B, R, A, F), B)) | (~apply(R, tptp_fun_X1_34(S, B, R, A, F), tptp_fun_X2_32(S, B, R, A, F))) | (~apply(F, tptp_fun_X1_34(S, B, R, A, F), tptp_fun_Y1_33(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_32(S, B, R, A, F), tptp_fun_Y2_31(S, B, R, A, F))))))))), rewrite((((~decreasing(F, A, R, B, S)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(S, Y2, Y1) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(R, X1, X2)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2)))) & (decreasing(F, A, R, B, S) | (~(apply(S, tptp_fun_Y2_31(S, B, R, A, F), tptp_fun_Y1_33(S, B, R, A, F)) | (~member(tptp_fun_X1_34(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_33(S, B, R, A, F), B)) | (~member(tptp_fun_X2_32(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_31(S, B, R, A, F), B)) | (~apply(R, tptp_fun_X1_34(S, B, R, A, F), tptp_fun_X2_32(S, B, R, A, F))) | (~apply(F, tptp_fun_X1_34(S, B, R, A, F), tptp_fun_Y1_33(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_32(S, B, R, A, F), tptp_fun_Y2_31(S, B, R, A, F))))))) <=> (~((~((~decreasing(F, A, R, B, S)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(S, Y2, Y1) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(R, X1, X2)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2))))) | (~(decreasing(F, A, R, B, S) | (~(apply(S, tptp_fun_Y2_31(S, B, R, A, F), tptp_fun_Y1_33(S, B, R, A, F)) | (~member(tptp_fun_X1_34(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_33(S, B, R, A, F), B)) | (~member(tptp_fun_X2_32(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_31(S, B, R, A, F), B)) | (~apply(R, tptp_fun_X1_34(S, B, R, A, F), tptp_fun_X2_32(S, B, R, A, F))) | (~apply(F, tptp_fun_X1_34(S, B, R, A, F), tptp_fun_Y1_33(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_32(S, B, R, A, F), tptp_fun_Y2_31(S, B, R, A, F)))))))))), ((((~decreasing(F, A, R, B, S)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~(member(X1, A) & member(Y1, B) & member(X2, A) & member(Y2, B) & apply(R, X1, X2) & apply(F, X1, Y1) & apply(F, X2, Y2))) | apply(S, Y2, Y1))) & (decreasing(F, A, R, B, S) | (~((~(member(tptp_fun_X1_34(S, B, R, A, F), A) & member(tptp_fun_Y1_33(S, B, R, A, F), B) & member(tptp_fun_X2_32(S, B, R, A, F), A) & member(tptp_fun_Y2_31(S, B, R, A, F), B) & apply(R, tptp_fun_X1_34(S, B, R, A, F), tptp_fun_X2_32(S, B, R, A, F)) & apply(F, tptp_fun_X1_34(S, B, R, A, F), tptp_fun_Y1_33(S, B, R, A, F)) & apply(F, tptp_fun_X2_32(S, B, R, A, F), tptp_fun_Y2_31(S, B, R, A, F)))) | apply(S, tptp_fun_Y2_31(S, B, R, A, F), tptp_fun_Y1_33(S, B, R, A, F)))))) <=> (~((~((~decreasing(F, A, R, B, S)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(S, Y2, Y1) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(R, X1, X2)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2))))) | (~(decreasing(F, A, R, B, S) | (~(apply(S, tptp_fun_Y2_31(S, B, R, A, F), tptp_fun_Y1_33(S, B, R, A, F)) | (~member(tptp_fun_X1_34(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_33(S, B, R, A, F), B)) | (~member(tptp_fun_X2_32(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_31(S, B, R, A, F), B)) | (~apply(R, tptp_fun_X1_34(S, B, R, A, F), tptp_fun_X2_32(S, B, R, A, F))) | (~apply(F, tptp_fun_X1_34(S, B, R, A, F), tptp_fun_Y1_33(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_32(S, B, R, A, F), tptp_fun_Y2_31(S, B, R, A, F)))))))))))),
% 0.67/0.74 inference(bind,[status(th)],[])).
% 0.67/0.74 tff(188,plain,
% 0.67/0.74 (![F: $i, A: $i, R: $i, B: $i, S: $i] : (((~decreasing(F, A, R, B, S)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~(member(X1, A) & member(Y1, B) & member(X2, A) & member(Y2, B) & apply(R, X1, X2) & apply(F, X1, Y1) & apply(F, X2, Y2))) | apply(S, Y2, Y1))) & (decreasing(F, A, R, B, S) | (~((~(member(tptp_fun_X1_34(S, B, R, A, F), A) & member(tptp_fun_Y1_33(S, B, R, A, F), B) & member(tptp_fun_X2_32(S, B, R, A, F), A) & member(tptp_fun_Y2_31(S, B, R, A, F), B) & apply(R, tptp_fun_X1_34(S, B, R, A, F), tptp_fun_X2_32(S, B, R, A, F)) & apply(F, tptp_fun_X1_34(S, B, R, A, F), tptp_fun_Y1_33(S, B, R, A, F)) & apply(F, tptp_fun_X2_32(S, B, R, A, F), tptp_fun_Y2_31(S, B, R, A, F)))) | apply(S, tptp_fun_Y2_31(S, B, R, A, F), tptp_fun_Y1_33(S, B, R, A, F)))))) <=> ![F: $i, A: $i, R: $i, B: $i, S: $i] : (~((~((~decreasing(F, A, R, B, S)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(S, Y2, Y1) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(R, X1, X2)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2))))) | (~(decreasing(F, A, R, B, S) | (~(apply(S, tptp_fun_Y2_31(S, B, R, A, F), tptp_fun_Y1_33(S, B, R, A, F)) | (~member(tptp_fun_X1_34(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_33(S, B, R, A, F), B)) | (~member(tptp_fun_X2_32(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_31(S, B, R, A, F), B)) | (~apply(R, tptp_fun_X1_34(S, B, R, A, F), tptp_fun_X2_32(S, B, R, A, F))) | (~apply(F, tptp_fun_X1_34(S, B, R, A, F), tptp_fun_Y1_33(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_32(S, B, R, A, F), tptp_fun_Y2_31(S, B, R, A, F)))))))))),
% 0.67/0.74 inference(quant_intro,[status(thm)],[187])).
% 0.67/0.74 tff(189,plain,
% 0.67/0.74 (![F: $i, A: $i, R: $i, B: $i, S: $i] : (decreasing(F, A, R, B, S) <=> ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~(member(X1, A) & member(Y1, B) & member(X2, A) & member(Y2, B) & apply(R, X1, X2) & apply(F, X1, Y1) & apply(F, X2, Y2))) | apply(S, Y2, Y1))) <=> ![F: $i, A: $i, R: $i, B: $i, S: $i] : (decreasing(F, A, R, B, S) <=> ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~(member(X1, A) & member(Y1, B) & member(X2, A) & member(Y2, B) & apply(R, X1, X2) & apply(F, X1, Y1) & apply(F, X2, Y2))) | apply(S, Y2, Y1)))),
% 0.67/0.74 inference(rewrite,[status(thm)],[])).
% 0.67/0.74 tff(190,plain,
% 0.67/0.74 (^[F: $i, A: $i, R: $i, B: $i, S: $i] : rewrite((decreasing(F, A, R, B, S) <=> ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (((((((member(X1, A) & member(Y1, B)) & member(X2, A)) & member(Y2, B)) & apply(R, X1, X2)) & apply(F, X1, Y1)) & apply(F, X2, Y2)) => apply(S, Y2, Y1))) <=> (decreasing(F, A, R, B, S) <=> ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~(member(X1, A) & member(Y1, B) & member(X2, A) & member(Y2, B) & apply(R, X1, X2) & apply(F, X1, Y1) & apply(F, X2, Y2))) | apply(S, Y2, Y1))))),
% 0.67/0.74 inference(bind,[status(th)],[])).
% 0.67/0.74 tff(191,plain,
% 0.67/0.74 (![F: $i, A: $i, R: $i, B: $i, S: $i] : (decreasing(F, A, R, B, S) <=> ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (((((((member(X1, A) & member(Y1, B)) & member(X2, A)) & member(Y2, B)) & apply(R, X1, X2)) & apply(F, X1, Y1)) & apply(F, X2, Y2)) => apply(S, Y2, Y1))) <=> ![F: $i, A: $i, R: $i, B: $i, S: $i] : (decreasing(F, A, R, B, S) <=> ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~(member(X1, A) & member(Y1, B) & member(X2, A) & member(Y2, B) & apply(R, X1, X2) & apply(F, X1, Y1) & apply(F, X2, Y2))) | apply(S, Y2, Y1)))),
% 0.67/0.74 inference(quant_intro,[status(thm)],[190])).
% 0.67/0.74 tff(192,axiom,(![F: $i, A: $i, R: $i, B: $i, S: $i] : (decreasing(F, A, R, B, S) <=> ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (((((((member(X1, A) & member(Y1, B)) & member(X2, A)) & member(Y2, B)) & apply(R, X1, X2)) & apply(F, X1, Y1)) & apply(F, X2, Y2)) => apply(S, Y2, Y1)))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+1.ax','decreasing_function')).
% 0.67/0.74 tff(193,plain,
% 0.67/0.74 (![F: $i, A: $i, R: $i, B: $i, S: $i] : (decreasing(F, A, R, B, S) <=> ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~(member(X1, A) & member(Y1, B) & member(X2, A) & member(Y2, B) & apply(R, X1, X2) & apply(F, X1, Y1) & apply(F, X2, Y2))) | apply(S, Y2, Y1)))),
% 0.67/0.74 inference(modus_ponens,[status(thm)],[192, 191])).
% 0.67/0.74 tff(194,plain,
% 0.67/0.74 (![F: $i, A: $i, R: $i, B: $i, S: $i] : (decreasing(F, A, R, B, S) <=> ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~(member(X1, A) & member(Y1, B) & member(X2, A) & member(Y2, B) & apply(R, X1, X2) & apply(F, X1, Y1) & apply(F, X2, Y2))) | apply(S, Y2, Y1)))),
% 0.67/0.74 inference(modus_ponens,[status(thm)],[193, 189])).
% 0.67/0.74 tff(195,plain,(
% 0.67/0.74 ![F: $i, A: $i, R: $i, B: $i, S: $i] : (((~decreasing(F, A, R, B, S)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~(member(X1, A) & member(Y1, B) & member(X2, A) & member(Y2, B) & apply(R, X1, X2) & apply(F, X1, Y1) & apply(F, X2, Y2))) | apply(S, Y2, Y1))) & (decreasing(F, A, R, B, S) | (~((~(member(tptp_fun_X1_34(S, B, R, A, F), A) & member(tptp_fun_Y1_33(S, B, R, A, F), B) & member(tptp_fun_X2_32(S, B, R, A, F), A) & member(tptp_fun_Y2_31(S, B, R, A, F), B) & apply(R, tptp_fun_X1_34(S, B, R, A, F), tptp_fun_X2_32(S, B, R, A, F)) & apply(F, tptp_fun_X1_34(S, B, R, A, F), tptp_fun_Y1_33(S, B, R, A, F)) & apply(F, tptp_fun_X2_32(S, B, R, A, F), tptp_fun_Y2_31(S, B, R, A, F)))) | apply(S, tptp_fun_Y2_31(S, B, R, A, F), tptp_fun_Y1_33(S, B, R, A, F))))))),
% 0.67/0.74 inference(skolemize,[status(sab)],[194])).
% 0.67/0.74 tff(196,plain,
% 0.67/0.74 (![F: $i, A: $i, R: $i, B: $i, S: $i] : (~((~((~decreasing(F, A, R, B, S)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(S, Y2, Y1) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(R, X1, X2)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2))))) | (~(decreasing(F, A, R, B, S) | (~(apply(S, tptp_fun_Y2_31(S, B, R, A, F), tptp_fun_Y1_33(S, B, R, A, F)) | (~member(tptp_fun_X1_34(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_33(S, B, R, A, F), B)) | (~member(tptp_fun_X2_32(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_31(S, B, R, A, F), B)) | (~apply(R, tptp_fun_X1_34(S, B, R, A, F), tptp_fun_X2_32(S, B, R, A, F))) | (~apply(F, tptp_fun_X1_34(S, B, R, A, F), tptp_fun_Y1_33(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_32(S, B, R, A, F), tptp_fun_Y2_31(S, B, R, A, F)))))))))),
% 0.67/0.74 inference(modus_ponens,[status(thm)],[195, 188])).
% 0.67/0.74 tff(197,plain,
% 0.67/0.74 (![F: $i, A: $i, R: $i, B: $i, S: $i] : (~((~((~decreasing(F, A, R, B, S)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(S, Y2, Y1) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(R, X1, X2)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2))))) | (~(decreasing(F, A, R, B, S) | (~(apply(S, tptp_fun_Y2_31(S, B, R, A, F), tptp_fun_Y1_33(S, B, R, A, F)) | (~member(tptp_fun_X1_34(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_33(S, B, R, A, F), B)) | (~member(tptp_fun_X2_32(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_31(S, B, R, A, F), B)) | (~apply(R, tptp_fun_X1_34(S, B, R, A, F), tptp_fun_X2_32(S, B, R, A, F))) | (~apply(F, tptp_fun_X1_34(S, B, R, A, F), tptp_fun_Y1_33(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_32(S, B, R, A, F), tptp_fun_Y2_31(S, B, R, A, F)))))))))),
% 0.67/0.74 inference(modus_ponens,[status(thm)],[196, 186])).
% 0.67/0.74 tff(198,plain,
% 0.67/0.74 (((~![F: $i, A: $i, R: $i, B: $i, S: $i] : (~((~((~decreasing(F, A, R, B, S)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(S, Y2, Y1) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(R, X1, X2)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2))))) | (~(decreasing(F, A, R, B, S) | (~(apply(S, tptp_fun_Y2_31(S, B, R, A, F), tptp_fun_Y1_33(S, B, R, A, F)) | (~member(tptp_fun_X1_34(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_33(S, B, R, A, F), B)) | (~member(tptp_fun_X2_32(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_31(S, B, R, A, F), B)) | (~apply(R, tptp_fun_X1_34(S, B, R, A, F), tptp_fun_X2_32(S, B, R, A, F))) | (~apply(F, tptp_fun_X1_34(S, B, R, A, F), tptp_fun_Y1_33(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_32(S, B, R, A, F), tptp_fun_Y2_31(S, B, R, A, F)))))))))) | (~((~((~decreasing(F!46, A!44, R!41, B!43, S!40)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!43)) | (~member(Y1, B!43)) | (~member(X1, A!44)) | (~member(X2, A!44)) | (~apply(R!41, X1, X2)) | apply(S!40, Y2, Y1) | (~apply(F!46, X1, Y1)) | (~apply(F!46, X2, Y2))))) | (~(decreasing(F!46, A!44, R!41, B!43, S!40) | (~(apply(S!40, tptp_fun_Y2_31(S!40, B!43, R!41, A!44, F!46), tptp_fun_Y1_33(S!40, B!43, R!41, A!44, F!46)) | (~member(tptp_fun_X1_34(S!40, B!43, R!41, A!44, F!46), A!44)) | (~member(tptp_fun_Y1_33(S!40, B!43, R!41, A!44, F!46), B!43)) | (~member(tptp_fun_X2_32(S!40, B!43, R!41, A!44, F!46), A!44)) | (~member(tptp_fun_Y2_31(S!40, B!43, R!41, A!44, F!46), B!43)) | (~apply(R!41, tptp_fun_X1_34(S!40, B!43, R!41, A!44, F!46), tptp_fun_X2_32(S!40, B!43, R!41, A!44, F!46))) | (~apply(F!46, tptp_fun_X1_34(S!40, B!43, R!41, A!44, F!46), tptp_fun_Y1_33(S!40, B!43, R!41, A!44, F!46))) | (~apply(F!46, tptp_fun_X2_32(S!40, B!43, R!41, A!44, F!46), tptp_fun_Y2_31(S!40, B!43, R!41, A!44, F!46)))))))))) <=> ((~![F: $i, A: $i, R: $i, B: $i, S: $i] : (~((~((~decreasing(F, A, R, B, S)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(S, Y2, Y1) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(R, X1, X2)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2))))) | (~(decreasing(F, A, R, B, S) | (~(apply(S, tptp_fun_Y2_31(S, B, R, A, F), tptp_fun_Y1_33(S, B, R, A, F)) | (~member(tptp_fun_X1_34(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_33(S, B, R, A, F), B)) | (~member(tptp_fun_X2_32(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_31(S, B, R, A, F), B)) | (~apply(R, tptp_fun_X1_34(S, B, R, A, F), tptp_fun_X2_32(S, B, R, A, F))) | (~apply(F, tptp_fun_X1_34(S, B, R, A, F), tptp_fun_Y1_33(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_32(S, B, R, A, F), tptp_fun_Y2_31(S, B, R, A, F)))))))))) | (~((~((~decreasing(F!46, A!44, R!41, B!43, S!40)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!43)) | (~member(Y1, B!43)) | (~member(X1, A!44)) | (~member(X2, A!44)) | (~apply(R!41, X1, X2)) | apply(S!40, Y2, Y1) | (~apply(F!46, X1, Y1)) | (~apply(F!46, X2, Y2))))) | (~(decreasing(F!46, A!44, R!41, B!43, S!40) | (~(apply(S!40, tptp_fun_Y2_31(S!40, B!43, R!41, A!44, F!46), tptp_fun_Y1_33(S!40, B!43, R!41, A!44, F!46)) | (~member(tptp_fun_X1_34(S!40, B!43, R!41, A!44, F!46), A!44)) | (~member(tptp_fun_Y1_33(S!40, B!43, R!41, A!44, F!46), B!43)) | (~member(tptp_fun_X2_32(S!40, B!43, R!41, A!44, F!46), A!44)) | (~member(tptp_fun_Y2_31(S!40, B!43, R!41, A!44, F!46), B!43)) | (~apply(R!41, tptp_fun_X1_34(S!40, B!43, R!41, A!44, F!46), tptp_fun_X2_32(S!40, B!43, R!41, A!44, F!46))) | (~apply(F!46, tptp_fun_X1_34(S!40, B!43, R!41, A!44, F!46), tptp_fun_Y1_33(S!40, B!43, R!41, A!44, F!46))) | (~apply(F!46, tptp_fun_X2_32(S!40, B!43, R!41, A!44, F!46), tptp_fun_Y2_31(S!40, B!43, R!41, A!44, F!46))))))))))),
% 0.67/0.74 inference(rewrite,[status(thm)],[])).
% 0.67/0.74 tff(199,plain,
% 0.67/0.74 ((~((~((~decreasing(F!46, A!44, R!41, B!43, S!40)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(S!40, Y2, Y1) | (~member(X1, A!44)) | (~member(Y1, B!43)) | (~member(X2, A!44)) | (~member(Y2, B!43)) | (~apply(R!41, X1, X2)) | (~apply(F!46, X1, Y1)) | (~apply(F!46, X2, Y2))))) | (~(decreasing(F!46, A!44, R!41, B!43, S!40) | (~(apply(S!40, tptp_fun_Y2_31(S!40, B!43, R!41, A!44, F!46), tptp_fun_Y1_33(S!40, B!43, R!41, A!44, F!46)) | (~member(tptp_fun_X1_34(S!40, B!43, R!41, A!44, F!46), A!44)) | (~member(tptp_fun_Y1_33(S!40, B!43, R!41, A!44, F!46), B!43)) | (~member(tptp_fun_X2_32(S!40, B!43, R!41, A!44, F!46), A!44)) | (~member(tptp_fun_Y2_31(S!40, B!43, R!41, A!44, F!46), B!43)) | (~apply(R!41, tptp_fun_X1_34(S!40, B!43, R!41, A!44, F!46), tptp_fun_X2_32(S!40, B!43, R!41, A!44, F!46))) | (~apply(F!46, tptp_fun_X1_34(S!40, B!43, R!41, A!44, F!46), tptp_fun_Y1_33(S!40, B!43, R!41, A!44, F!46))) | (~apply(F!46, tptp_fun_X2_32(S!40, B!43, R!41, A!44, F!46), tptp_fun_Y2_31(S!40, B!43, R!41, A!44, F!46))))))))) <=> (~((~((~decreasing(F!46, A!44, R!41, B!43, S!40)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!43)) | (~member(Y1, B!43)) | (~member(X1, A!44)) | (~member(X2, A!44)) | (~apply(R!41, X1, X2)) | apply(S!40, Y2, Y1) | (~apply(F!46, X1, Y1)) | (~apply(F!46, X2, Y2))))) | (~(decreasing(F!46, A!44, R!41, B!43, S!40) | (~(apply(S!40, tptp_fun_Y2_31(S!40, B!43, R!41, A!44, F!46), tptp_fun_Y1_33(S!40, B!43, R!41, A!44, F!46)) | (~member(tptp_fun_X1_34(S!40, B!43, R!41, A!44, F!46), A!44)) | (~member(tptp_fun_Y1_33(S!40, B!43, R!41, A!44, F!46), B!43)) | (~member(tptp_fun_X2_32(S!40, B!43, R!41, A!44, F!46), A!44)) | (~member(tptp_fun_Y2_31(S!40, B!43, R!41, A!44, F!46), B!43)) | (~apply(R!41, tptp_fun_X1_34(S!40, B!43, R!41, A!44, F!46), tptp_fun_X2_32(S!40, B!43, R!41, A!44, F!46))) | (~apply(F!46, tptp_fun_X1_34(S!40, B!43, R!41, A!44, F!46), tptp_fun_Y1_33(S!40, B!43, R!41, A!44, F!46))) | (~apply(F!46, tptp_fun_X2_32(S!40, B!43, R!41, A!44, F!46), tptp_fun_Y2_31(S!40, B!43, R!41, A!44, F!46)))))))))),
% 0.67/0.74 inference(rewrite,[status(thm)],[])).
% 0.67/0.74 tff(200,plain,
% 0.67/0.74 (((~![F: $i, A: $i, R: $i, B: $i, S: $i] : (~((~((~decreasing(F, A, R, B, S)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(S, Y2, Y1) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(R, X1, X2)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2))))) | (~(decreasing(F, A, R, B, S) | (~(apply(S, tptp_fun_Y2_31(S, B, R, A, F), tptp_fun_Y1_33(S, B, R, A, F)) | (~member(tptp_fun_X1_34(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_33(S, B, R, A, F), B)) | (~member(tptp_fun_X2_32(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_31(S, B, R, A, F), B)) | (~apply(R, tptp_fun_X1_34(S, B, R, A, F), tptp_fun_X2_32(S, B, R, A, F))) | (~apply(F, tptp_fun_X1_34(S, B, R, A, F), tptp_fun_Y1_33(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_32(S, B, R, A, F), tptp_fun_Y2_31(S, B, R, A, F)))))))))) | (~((~((~decreasing(F!46, A!44, R!41, B!43, S!40)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(S!40, Y2, Y1) | (~member(X1, A!44)) | (~member(Y1, B!43)) | (~member(X2, A!44)) | (~member(Y2, B!43)) | (~apply(R!41, X1, X2)) | (~apply(F!46, X1, Y1)) | (~apply(F!46, X2, Y2))))) | (~(decreasing(F!46, A!44, R!41, B!43, S!40) | (~(apply(S!40, tptp_fun_Y2_31(S!40, B!43, R!41, A!44, F!46), tptp_fun_Y1_33(S!40, B!43, R!41, A!44, F!46)) | (~member(tptp_fun_X1_34(S!40, B!43, R!41, A!44, F!46), A!44)) | (~member(tptp_fun_Y1_33(S!40, B!43, R!41, A!44, F!46), B!43)) | (~member(tptp_fun_X2_32(S!40, B!43, R!41, A!44, F!46), A!44)) | (~member(tptp_fun_Y2_31(S!40, B!43, R!41, A!44, F!46), B!43)) | (~apply(R!41, tptp_fun_X1_34(S!40, B!43, R!41, A!44, F!46), tptp_fun_X2_32(S!40, B!43, R!41, A!44, F!46))) | (~apply(F!46, tptp_fun_X1_34(S!40, B!43, R!41, A!44, F!46), tptp_fun_Y1_33(S!40, B!43, R!41, A!44, F!46))) | (~apply(F!46, tptp_fun_X2_32(S!40, B!43, R!41, A!44, F!46), tptp_fun_Y2_31(S!40, B!43, R!41, A!44, F!46)))))))))) <=> ((~![F: $i, A: $i, R: $i, B: $i, S: $i] : (~((~((~decreasing(F, A, R, B, S)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(S, Y2, Y1) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(R, X1, X2)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2))))) | (~(decreasing(F, A, R, B, S) | (~(apply(S, tptp_fun_Y2_31(S, B, R, A, F), tptp_fun_Y1_33(S, B, R, A, F)) | (~member(tptp_fun_X1_34(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_33(S, B, R, A, F), B)) | (~member(tptp_fun_X2_32(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_31(S, B, R, A, F), B)) | (~apply(R, tptp_fun_X1_34(S, B, R, A, F), tptp_fun_X2_32(S, B, R, A, F))) | (~apply(F, tptp_fun_X1_34(S, B, R, A, F), tptp_fun_Y1_33(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_32(S, B, R, A, F), tptp_fun_Y2_31(S, B, R, A, F)))))))))) | (~((~((~decreasing(F!46, A!44, R!41, B!43, S!40)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!43)) | (~member(Y1, B!43)) | (~member(X1, A!44)) | (~member(X2, A!44)) | (~apply(R!41, X1, X2)) | apply(S!40, Y2, Y1) | (~apply(F!46, X1, Y1)) | (~apply(F!46, X2, Y2))))) | (~(decreasing(F!46, A!44, R!41, B!43, S!40) | (~(apply(S!40, tptp_fun_Y2_31(S!40, B!43, R!41, A!44, F!46), tptp_fun_Y1_33(S!40, B!43, R!41, A!44, F!46)) | (~member(tptp_fun_X1_34(S!40, B!43, R!41, A!44, F!46), A!44)) | (~member(tptp_fun_Y1_33(S!40, B!43, R!41, A!44, F!46), B!43)) | (~member(tptp_fun_X2_32(S!40, B!43, R!41, A!44, F!46), A!44)) | (~member(tptp_fun_Y2_31(S!40, B!43, R!41, A!44, F!46), B!43)) | (~apply(R!41, tptp_fun_X1_34(S!40, B!43, R!41, A!44, F!46), tptp_fun_X2_32(S!40, B!43, R!41, A!44, F!46))) | (~apply(F!46, tptp_fun_X1_34(S!40, B!43, R!41, A!44, F!46), tptp_fun_Y1_33(S!40, B!43, R!41, A!44, F!46))) | (~apply(F!46, tptp_fun_X2_32(S!40, B!43, R!41, A!44, F!46), tptp_fun_Y2_31(S!40, B!43, R!41, A!44, F!46))))))))))),
% 0.67/0.75 inference(monotonicity,[status(thm)],[199])).
% 0.67/0.75 tff(201,plain,
% 0.67/0.75 (((~![F: $i, A: $i, R: $i, B: $i, S: $i] : (~((~((~decreasing(F, A, R, B, S)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(S, Y2, Y1) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(R, X1, X2)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2))))) | (~(decreasing(F, A, R, B, S) | (~(apply(S, tptp_fun_Y2_31(S, B, R, A, F), tptp_fun_Y1_33(S, B, R, A, F)) | (~member(tptp_fun_X1_34(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_33(S, B, R, A, F), B)) | (~member(tptp_fun_X2_32(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_31(S, B, R, A, F), B)) | (~apply(R, tptp_fun_X1_34(S, B, R, A, F), tptp_fun_X2_32(S, B, R, A, F))) | (~apply(F, tptp_fun_X1_34(S, B, R, A, F), tptp_fun_Y1_33(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_32(S, B, R, A, F), tptp_fun_Y2_31(S, B, R, A, F)))))))))) | (~((~((~decreasing(F!46, A!44, R!41, B!43, S!40)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(S!40, Y2, Y1) | (~member(X1, A!44)) | (~member(Y1, B!43)) | (~member(X2, A!44)) | (~member(Y2, B!43)) | (~apply(R!41, X1, X2)) | (~apply(F!46, X1, Y1)) | (~apply(F!46, X2, Y2))))) | (~(decreasing(F!46, A!44, R!41, B!43, S!40) | (~(apply(S!40, tptp_fun_Y2_31(S!40, B!43, R!41, A!44, F!46), tptp_fun_Y1_33(S!40, B!43, R!41, A!44, F!46)) | (~member(tptp_fun_X1_34(S!40, B!43, R!41, A!44, F!46), A!44)) | (~member(tptp_fun_Y1_33(S!40, B!43, R!41, A!44, F!46), B!43)) | (~member(tptp_fun_X2_32(S!40, B!43, R!41, A!44, F!46), A!44)) | (~member(tptp_fun_Y2_31(S!40, B!43, R!41, A!44, F!46), B!43)) | (~apply(R!41, tptp_fun_X1_34(S!40, B!43, R!41, A!44, F!46), tptp_fun_X2_32(S!40, B!43, R!41, A!44, F!46))) | (~apply(F!46, tptp_fun_X1_34(S!40, B!43, R!41, A!44, F!46), tptp_fun_Y1_33(S!40, B!43, R!41, A!44, F!46))) | (~apply(F!46, tptp_fun_X2_32(S!40, B!43, R!41, A!44, F!46), tptp_fun_Y2_31(S!40, B!43, R!41, A!44, F!46)))))))))) <=> ((~![F: $i, A: $i, R: $i, B: $i, S: $i] : (~((~((~decreasing(F, A, R, B, S)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(S, Y2, Y1) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(R, X1, X2)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2))))) | (~(decreasing(F, A, R, B, S) | (~(apply(S, tptp_fun_Y2_31(S, B, R, A, F), tptp_fun_Y1_33(S, B, R, A, F)) | (~member(tptp_fun_X1_34(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_33(S, B, R, A, F), B)) | (~member(tptp_fun_X2_32(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_31(S, B, R, A, F), B)) | (~apply(R, tptp_fun_X1_34(S, B, R, A, F), tptp_fun_X2_32(S, B, R, A, F))) | (~apply(F, tptp_fun_X1_34(S, B, R, A, F), tptp_fun_Y1_33(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_32(S, B, R, A, F), tptp_fun_Y2_31(S, B, R, A, F)))))))))) | (~((~((~decreasing(F!46, A!44, R!41, B!43, S!40)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!43)) | (~member(Y1, B!43)) | (~member(X1, A!44)) | (~member(X2, A!44)) | (~apply(R!41, X1, X2)) | apply(S!40, Y2, Y1) | (~apply(F!46, X1, Y1)) | (~apply(F!46, X2, Y2))))) | (~(decreasing(F!46, A!44, R!41, B!43, S!40) | (~(apply(S!40, tptp_fun_Y2_31(S!40, B!43, R!41, A!44, F!46), tptp_fun_Y1_33(S!40, B!43, R!41, A!44, F!46)) | (~member(tptp_fun_X1_34(S!40, B!43, R!41, A!44, F!46), A!44)) | (~member(tptp_fun_Y1_33(S!40, B!43, R!41, A!44, F!46), B!43)) | (~member(tptp_fun_X2_32(S!40, B!43, R!41, A!44, F!46), A!44)) | (~member(tptp_fun_Y2_31(S!40, B!43, R!41, A!44, F!46), B!43)) | (~apply(R!41, tptp_fun_X1_34(S!40, B!43, R!41, A!44, F!46), tptp_fun_X2_32(S!40, B!43, R!41, A!44, F!46))) | (~apply(F!46, tptp_fun_X1_34(S!40, B!43, R!41, A!44, F!46), tptp_fun_Y1_33(S!40, B!43, R!41, A!44, F!46))) | (~apply(F!46, tptp_fun_X2_32(S!40, B!43, R!41, A!44, F!46), tptp_fun_Y2_31(S!40, B!43, R!41, A!44, F!46))))))))))),
% 0.67/0.75 inference(transitivity,[status(thm)],[200, 198])).
% 0.67/0.75 tff(202,plain,
% 0.67/0.75 ((~![F: $i, A: $i, R: $i, B: $i, S: $i] : (~((~((~decreasing(F, A, R, B, S)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(S, Y2, Y1) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(R, X1, X2)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2))))) | (~(decreasing(F, A, R, B, S) | (~(apply(S, tptp_fun_Y2_31(S, B, R, A, F), tptp_fun_Y1_33(S, B, R, A, F)) | (~member(tptp_fun_X1_34(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_33(S, B, R, A, F), B)) | (~member(tptp_fun_X2_32(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_31(S, B, R, A, F), B)) | (~apply(R, tptp_fun_X1_34(S, B, R, A, F), tptp_fun_X2_32(S, B, R, A, F))) | (~apply(F, tptp_fun_X1_34(S, B, R, A, F), tptp_fun_Y1_33(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_32(S, B, R, A, F), tptp_fun_Y2_31(S, B, R, A, F)))))))))) | (~((~((~decreasing(F!46, A!44, R!41, B!43, S!40)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(S!40, Y2, Y1) | (~member(X1, A!44)) | (~member(Y1, B!43)) | (~member(X2, A!44)) | (~member(Y2, B!43)) | (~apply(R!41, X1, X2)) | (~apply(F!46, X1, Y1)) | (~apply(F!46, X2, Y2))))) | (~(decreasing(F!46, A!44, R!41, B!43, S!40) | (~(apply(S!40, tptp_fun_Y2_31(S!40, B!43, R!41, A!44, F!46), tptp_fun_Y1_33(S!40, B!43, R!41, A!44, F!46)) | (~member(tptp_fun_X1_34(S!40, B!43, R!41, A!44, F!46), A!44)) | (~member(tptp_fun_Y1_33(S!40, B!43, R!41, A!44, F!46), B!43)) | (~member(tptp_fun_X2_32(S!40, B!43, R!41, A!44, F!46), A!44)) | (~member(tptp_fun_Y2_31(S!40, B!43, R!41, A!44, F!46), B!43)) | (~apply(R!41, tptp_fun_X1_34(S!40, B!43, R!41, A!44, F!46), tptp_fun_X2_32(S!40, B!43, R!41, A!44, F!46))) | (~apply(F!46, tptp_fun_X1_34(S!40, B!43, R!41, A!44, F!46), tptp_fun_Y1_33(S!40, B!43, R!41, A!44, F!46))) | (~apply(F!46, tptp_fun_X2_32(S!40, B!43, R!41, A!44, F!46), tptp_fun_Y2_31(S!40, B!43, R!41, A!44, F!46)))))))))),
% 0.67/0.75 inference(quant_inst,[status(thm)],[])).
% 0.67/0.75 tff(203,plain,
% 0.67/0.75 ((~![F: $i, A: $i, R: $i, B: $i, S: $i] : (~((~((~decreasing(F, A, R, B, S)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(S, Y2, Y1) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(R, X1, X2)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2))))) | (~(decreasing(F, A, R, B, S) | (~(apply(S, tptp_fun_Y2_31(S, B, R, A, F), tptp_fun_Y1_33(S, B, R, A, F)) | (~member(tptp_fun_X1_34(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_33(S, B, R, A, F), B)) | (~member(tptp_fun_X2_32(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_31(S, B, R, A, F), B)) | (~apply(R, tptp_fun_X1_34(S, B, R, A, F), tptp_fun_X2_32(S, B, R, A, F))) | (~apply(F, tptp_fun_X1_34(S, B, R, A, F), tptp_fun_Y1_33(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_32(S, B, R, A, F), tptp_fun_Y2_31(S, B, R, A, F)))))))))) | (~((~((~decreasing(F!46, A!44, R!41, B!43, S!40)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!43)) | (~member(Y1, B!43)) | (~member(X1, A!44)) | (~member(X2, A!44)) | (~apply(R!41, X1, X2)) | apply(S!40, Y2, Y1) | (~apply(F!46, X1, Y1)) | (~apply(F!46, X2, Y2))))) | (~(decreasing(F!46, A!44, R!41, B!43, S!40) | (~(apply(S!40, tptp_fun_Y2_31(S!40, B!43, R!41, A!44, F!46), tptp_fun_Y1_33(S!40, B!43, R!41, A!44, F!46)) | (~member(tptp_fun_X1_34(S!40, B!43, R!41, A!44, F!46), A!44)) | (~member(tptp_fun_Y1_33(S!40, B!43, R!41, A!44, F!46), B!43)) | (~member(tptp_fun_X2_32(S!40, B!43, R!41, A!44, F!46), A!44)) | (~member(tptp_fun_Y2_31(S!40, B!43, R!41, A!44, F!46), B!43)) | (~apply(R!41, tptp_fun_X1_34(S!40, B!43, R!41, A!44, F!46), tptp_fun_X2_32(S!40, B!43, R!41, A!44, F!46))) | (~apply(F!46, tptp_fun_X1_34(S!40, B!43, R!41, A!44, F!46), tptp_fun_Y1_33(S!40, B!43, R!41, A!44, F!46))) | (~apply(F!46, tptp_fun_X2_32(S!40, B!43, R!41, A!44, F!46), tptp_fun_Y2_31(S!40, B!43, R!41, A!44, F!46)))))))))),
% 0.67/0.75 inference(modus_ponens,[status(thm)],[202, 201])).
% 0.67/0.75 tff(204,plain,
% 0.67/0.75 (~((~((~decreasing(F!46, A!44, R!41, B!43, S!40)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!43)) | (~member(Y1, B!43)) | (~member(X1, A!44)) | (~member(X2, A!44)) | (~apply(R!41, X1, X2)) | apply(S!40, Y2, Y1) | (~apply(F!46, X1, Y1)) | (~apply(F!46, X2, Y2))))) | (~(decreasing(F!46, A!44, R!41, B!43, S!40) | (~(apply(S!40, tptp_fun_Y2_31(S!40, B!43, R!41, A!44, F!46), tptp_fun_Y1_33(S!40, B!43, R!41, A!44, F!46)) | (~member(tptp_fun_X1_34(S!40, B!43, R!41, A!44, F!46), A!44)) | (~member(tptp_fun_Y1_33(S!40, B!43, R!41, A!44, F!46), B!43)) | (~member(tptp_fun_X2_32(S!40, B!43, R!41, A!44, F!46), A!44)) | (~member(tptp_fun_Y2_31(S!40, B!43, R!41, A!44, F!46), B!43)) | (~apply(R!41, tptp_fun_X1_34(S!40, B!43, R!41, A!44, F!46), tptp_fun_X2_32(S!40, B!43, R!41, A!44, F!46))) | (~apply(F!46, tptp_fun_X1_34(S!40, B!43, R!41, A!44, F!46), tptp_fun_Y1_33(S!40, B!43, R!41, A!44, F!46))) | (~apply(F!46, tptp_fun_X2_32(S!40, B!43, R!41, A!44, F!46), tptp_fun_Y2_31(S!40, B!43, R!41, A!44, F!46))))))))),
% 0.67/0.75 inference(unit_resolution,[status(thm)],[203, 197])).
% 0.67/0.75 tff(205,plain,
% 0.67/0.75 (((~((~decreasing(F!46, A!44, R!41, B!43, S!40)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!43)) | (~member(Y1, B!43)) | (~member(X1, A!44)) | (~member(X2, A!44)) | (~apply(R!41, X1, X2)) | apply(S!40, Y2, Y1) | (~apply(F!46, X1, Y1)) | (~apply(F!46, X2, Y2))))) | (~(decreasing(F!46, A!44, R!41, B!43, S!40) | (~(apply(S!40, tptp_fun_Y2_31(S!40, B!43, R!41, A!44, F!46), tptp_fun_Y1_33(S!40, B!43, R!41, A!44, F!46)) | (~member(tptp_fun_X1_34(S!40, B!43, R!41, A!44, F!46), A!44)) | (~member(tptp_fun_Y1_33(S!40, B!43, R!41, A!44, F!46), B!43)) | (~member(tptp_fun_X2_32(S!40, B!43, R!41, A!44, F!46), A!44)) | (~member(tptp_fun_Y2_31(S!40, B!43, R!41, A!44, F!46), B!43)) | (~apply(R!41, tptp_fun_X1_34(S!40, B!43, R!41, A!44, F!46), tptp_fun_X2_32(S!40, B!43, R!41, A!44, F!46))) | (~apply(F!46, tptp_fun_X1_34(S!40, B!43, R!41, A!44, F!46), tptp_fun_Y1_33(S!40, B!43, R!41, A!44, F!46))) | (~apply(F!46, tptp_fun_X2_32(S!40, B!43, R!41, A!44, F!46), tptp_fun_Y2_31(S!40, B!43, R!41, A!44, F!46)))))))) | ((~decreasing(F!46, A!44, R!41, B!43, S!40)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!43)) | (~member(Y1, B!43)) | (~member(X1, A!44)) | (~member(X2, A!44)) | (~apply(R!41, X1, X2)) | apply(S!40, Y2, Y1) | (~apply(F!46, X1, Y1)) | (~apply(F!46, X2, Y2))))),
% 0.67/0.76 inference(tautology,[status(thm)],[])).
% 0.67/0.76 tff(206,plain,
% 0.67/0.76 ((~decreasing(F!46, A!44, R!41, B!43, S!40)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!43)) | (~member(Y1, B!43)) | (~member(X1, A!44)) | (~member(X2, A!44)) | (~apply(R!41, X1, X2)) | apply(S!40, Y2, Y1) | (~apply(F!46, X1, Y1)) | (~apply(F!46, X2, Y2)))),
% 0.67/0.76 inference(unit_resolution,[status(thm)],[205, 204])).
% 0.67/0.76 tff(207,plain,
% 0.67/0.76 (decreasing(F!46, A!44, R!41, B!43, S!40)),
% 0.67/0.76 inference(and_elim,[status(thm)],[106])).
% 0.67/0.76 tff(208,plain,
% 0.67/0.76 ((~((~decreasing(F!46, A!44, R!41, B!43, S!40)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!43)) | (~member(Y1, B!43)) | (~member(X1, A!44)) | (~member(X2, A!44)) | (~apply(R!41, X1, X2)) | apply(S!40, Y2, Y1) | (~apply(F!46, X1, Y1)) | (~apply(F!46, X2, Y2))))) | (~decreasing(F!46, A!44, R!41, B!43, S!40)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!43)) | (~member(Y1, B!43)) | (~member(X1, A!44)) | (~member(X2, A!44)) | (~apply(R!41, X1, X2)) | apply(S!40, Y2, Y1) | (~apply(F!46, X1, Y1)) | (~apply(F!46, X2, Y2)))),
% 0.67/0.76 inference(tautology,[status(thm)],[])).
% 0.67/0.76 tff(209,plain,
% 0.67/0.76 ((~((~decreasing(F!46, A!44, R!41, B!43, S!40)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!43)) | (~member(Y1, B!43)) | (~member(X1, A!44)) | (~member(X2, A!44)) | (~apply(R!41, X1, X2)) | apply(S!40, Y2, Y1) | (~apply(F!46, X1, Y1)) | (~apply(F!46, X2, Y2))))) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!43)) | (~member(Y1, B!43)) | (~member(X1, A!44)) | (~member(X2, A!44)) | (~apply(R!41, X1, X2)) | apply(S!40, Y2, Y1) | (~apply(F!46, X1, Y1)) | (~apply(F!46, X2, Y2)))),
% 0.67/0.76 inference(unit_resolution,[status(thm)],[208, 207])).
% 0.67/0.76 tff(210,plain,
% 0.67/0.76 (![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!43)) | (~member(Y1, B!43)) | (~member(X1, A!44)) | (~member(X2, A!44)) | (~apply(R!41, X1, X2)) | apply(S!40, Y2, Y1) | (~apply(F!46, X1, Y1)) | (~apply(F!46, X2, Y2)))),
% 0.67/0.76 inference(unit_resolution,[status(thm)],[209, 206])).
% 0.67/0.76 tff(211,plain,
% 0.67/0.76 ((apply(T!39, tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42))) | (~member(tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), A!44)) | (~member(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), C!42)) | (~member(tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), A!44)) | (~member(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), C!42)) | (~apply(R!41, tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))) | (~apply(compose_function(G!45, F!46, A!44, B!43, C!42), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))) | (~apply(compose_function(G!45, F!46, A!44, B!43, C!42), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42))))) | apply(R!41, tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))),
% 0.67/0.76 inference(tautology,[status(thm)],[])).
% 0.67/0.76 tff(212,plain,
% 0.67/0.76 (apply(R!41, tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))),
% 0.67/0.76 inference(unit_resolution,[status(thm)],[211, 40])).
% 0.67/0.76 tff(213,plain,
% 0.67/0.76 (((~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!43)) | (~member(Y1, B!43)) | (~member(X1, A!44)) | (~member(X2, A!44)) | (~apply(R!41, X1, X2)) | apply(S!40, Y2, Y1) | (~apply(F!46, X1, Y1)) | (~apply(F!46, X2, Y2)))) | ((~member(tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), A!44)) | (~member(tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), A!44)) | (~apply(R!41, tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))) | (~member(tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), B!43)) | (~apply(F!46, tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45))) | (~member(tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), B!43)) | (~apply(F!46, tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45))) | apply(S!40, tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45)))) <=> ((~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!43)) | (~member(Y1, B!43)) | (~member(X1, A!44)) | (~member(X2, A!44)) | (~apply(R!41, X1, X2)) | apply(S!40, Y2, Y1) | (~apply(F!46, X1, Y1)) | (~apply(F!46, X2, Y2)))) | (~member(tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), A!44)) | (~member(tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), A!44)) | (~apply(R!41, tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))) | (~member(tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), B!43)) | (~apply(F!46, tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45))) | (~member(tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), B!43)) | (~apply(F!46, tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45))) | apply(S!40, tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45)))),
% 0.67/0.76 inference(rewrite,[status(thm)],[])).
% 0.67/0.76 tff(214,plain,
% 0.67/0.76 (((~member(tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), B!43)) | (~member(tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), B!43)) | (~member(tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), A!44)) | (~member(tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), A!44)) | (~apply(R!41, tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))) | apply(S!40, tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45)) | (~apply(F!46, tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45))) | (~apply(F!46, tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45)))) <=> ((~member(tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), A!44)) | (~member(tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), A!44)) | (~apply(R!41, tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))) | (~member(tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), B!43)) | (~apply(F!46, tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45))) | (~member(tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), B!43)) | (~apply(F!46, tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45))) | apply(S!40, tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45)))),
% 0.67/0.76 inference(rewrite,[status(thm)],[])).
% 0.67/0.76 tff(215,plain,
% 0.67/0.76 (((~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!43)) | (~member(Y1, B!43)) | (~member(X1, A!44)) | (~member(X2, A!44)) | (~apply(R!41, X1, X2)) | apply(S!40, Y2, Y1) | (~apply(F!46, X1, Y1)) | (~apply(F!46, X2, Y2)))) | ((~member(tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), B!43)) | (~member(tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), B!43)) | (~member(tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), A!44)) | (~member(tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), A!44)) | (~apply(R!41, tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))) | apply(S!40, tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45)) | (~apply(F!46, tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45))) | (~apply(F!46, tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45))))) <=> ((~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!43)) | (~member(Y1, B!43)) | (~member(X1, A!44)) | (~member(X2, A!44)) | (~apply(R!41, X1, X2)) | apply(S!40, Y2, Y1) | (~apply(F!46, X1, Y1)) | (~apply(F!46, X2, Y2)))) | ((~member(tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), A!44)) | (~member(tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), A!44)) | (~apply(R!41, tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))) | (~member(tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), B!43)) | (~apply(F!46, tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45))) | (~member(tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), B!43)) | (~apply(F!46, tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45))) | apply(S!40, tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45))))),
% 0.67/0.77 inference(monotonicity,[status(thm)],[214])).
% 0.67/0.77 tff(216,plain,
% 0.67/0.77 (((~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!43)) | (~member(Y1, B!43)) | (~member(X1, A!44)) | (~member(X2, A!44)) | (~apply(R!41, X1, X2)) | apply(S!40, Y2, Y1) | (~apply(F!46, X1, Y1)) | (~apply(F!46, X2, Y2)))) | ((~member(tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), B!43)) | (~member(tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), B!43)) | (~member(tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), A!44)) | (~member(tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), A!44)) | (~apply(R!41, tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))) | apply(S!40, tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45)) | (~apply(F!46, tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45))) | (~apply(F!46, tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45))))) <=> ((~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!43)) | (~member(Y1, B!43)) | (~member(X1, A!44)) | (~member(X2, A!44)) | (~apply(R!41, X1, X2)) | apply(S!40, Y2, Y1) | (~apply(F!46, X1, Y1)) | (~apply(F!46, X2, Y2)))) | (~member(tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), A!44)) | (~member(tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), A!44)) | (~apply(R!41, tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))) | (~member(tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), B!43)) | (~apply(F!46, tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45))) | (~member(tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), B!43)) | (~apply(F!46, tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45))) | apply(S!40, tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45)))),
% 0.67/0.77 inference(transitivity,[status(thm)],[215, 213])).
% 0.67/0.77 tff(217,plain,
% 0.67/0.77 ((~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!43)) | (~member(Y1, B!43)) | (~member(X1, A!44)) | (~member(X2, A!44)) | (~apply(R!41, X1, X2)) | apply(S!40, Y2, Y1) | (~apply(F!46, X1, Y1)) | (~apply(F!46, X2, Y2)))) | ((~member(tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), B!43)) | (~member(tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), B!43)) | (~member(tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), A!44)) | (~member(tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), A!44)) | (~apply(R!41, tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))) | apply(S!40, tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45)) | (~apply(F!46, tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45))) | (~apply(F!46, tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45))))),
% 0.67/0.77 inference(quant_inst,[status(thm)],[])).
% 0.67/0.77 tff(218,plain,
% 0.67/0.77 ((~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!43)) | (~member(Y1, B!43)) | (~member(X1, A!44)) | (~member(X2, A!44)) | (~apply(R!41, X1, X2)) | apply(S!40, Y2, Y1) | (~apply(F!46, X1, Y1)) | (~apply(F!46, X2, Y2)))) | (~member(tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), A!44)) | (~member(tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), A!44)) | (~apply(R!41, tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)))) | (~member(tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), B!43)) | (~apply(F!46, tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45))) | (~member(tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), B!43)) | (~apply(F!46, tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45))) | apply(S!40, tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45))),
% 0.67/0.78 inference(modus_ponens,[status(thm)],[217, 216])).
% 0.67/0.78 tff(219,plain,
% 0.67/0.78 (apply(S!40, tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45))),
% 0.67/0.78 inference(unit_resolution,[status(thm)],[218, 135, 44, 212, 210, 79, 181, 154, 179])).
% 0.67/0.78 tff(220,plain,
% 0.67/0.78 (((~![F: $i, A: $i, R: $i, B: $i, S: $i] : (~((~((~decreasing(F, A, R, B, S)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(S, Y2, Y1) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(R, X1, X2)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2))))) | (~(decreasing(F, A, R, B, S) | (~(apply(S, tptp_fun_Y2_31(S, B, R, A, F), tptp_fun_Y1_33(S, B, R, A, F)) | (~member(tptp_fun_X1_34(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_33(S, B, R, A, F), B)) | (~member(tptp_fun_X2_32(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_31(S, B, R, A, F), B)) | (~apply(R, tptp_fun_X1_34(S, B, R, A, F), tptp_fun_X2_32(S, B, R, A, F))) | (~apply(F, tptp_fun_X1_34(S, B, R, A, F), tptp_fun_Y1_33(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_32(S, B, R, A, F), tptp_fun_Y2_31(S, B, R, A, F)))))))))) | (~((~((~decreasing(G!45, B!43, S!40, C!42, T!39)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(X2, B!43)) | (~member(Y2, C!42)) | (~member(Y1, C!42)) | apply(T!39, Y2, Y1) | (~member(X1, B!43)) | (~apply(S!40, X1, X2)) | (~apply(G!45, X1, Y1)) | (~apply(G!45, X2, Y2))))) | (~(decreasing(G!45, B!43, S!40, C!42, T!39) | (~(apply(T!39, tptp_fun_Y2_31(T!39, C!42, S!40, B!43, G!45), tptp_fun_Y1_33(T!39, C!42, S!40, B!43, G!45)) | (~member(tptp_fun_X1_34(T!39, C!42, S!40, B!43, G!45), B!43)) | (~member(tptp_fun_Y1_33(T!39, C!42, S!40, B!43, G!45), C!42)) | (~member(tptp_fun_X2_32(T!39, C!42, S!40, B!43, G!45), B!43)) | (~member(tptp_fun_Y2_31(T!39, C!42, S!40, B!43, G!45), C!42)) | (~apply(S!40, tptp_fun_X1_34(T!39, C!42, S!40, B!43, G!45), tptp_fun_X2_32(T!39, C!42, S!40, B!43, G!45))) | (~apply(G!45, tptp_fun_X1_34(T!39, C!42, S!40, B!43, G!45), tptp_fun_Y1_33(T!39, C!42, S!40, B!43, G!45))) | (~apply(G!45, tptp_fun_X2_32(T!39, C!42, S!40, B!43, G!45), tptp_fun_Y2_31(T!39, C!42, S!40, B!43, G!45)))))))))) <=> ((~![F: $i, A: $i, R: $i, B: $i, S: $i] : (~((~((~decreasing(F, A, R, B, S)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(S, Y2, Y1) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(R, X1, X2)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2))))) | (~(decreasing(F, A, R, B, S) | (~(apply(S, tptp_fun_Y2_31(S, B, R, A, F), tptp_fun_Y1_33(S, B, R, A, F)) | (~member(tptp_fun_X1_34(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_33(S, B, R, A, F), B)) | (~member(tptp_fun_X2_32(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_31(S, B, R, A, F), B)) | (~apply(R, tptp_fun_X1_34(S, B, R, A, F), tptp_fun_X2_32(S, B, R, A, F))) | (~apply(F, tptp_fun_X1_34(S, B, R, A, F), tptp_fun_Y1_33(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_32(S, B, R, A, F), tptp_fun_Y2_31(S, B, R, A, F)))))))))) | (~((~((~decreasing(G!45, B!43, S!40, C!42, T!39)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(X2, B!43)) | (~member(Y2, C!42)) | (~member(Y1, C!42)) | apply(T!39, Y2, Y1) | (~member(X1, B!43)) | (~apply(S!40, X1, X2)) | (~apply(G!45, X1, Y1)) | (~apply(G!45, X2, Y2))))) | (~(decreasing(G!45, B!43, S!40, C!42, T!39) | (~(apply(T!39, tptp_fun_Y2_31(T!39, C!42, S!40, B!43, G!45), tptp_fun_Y1_33(T!39, C!42, S!40, B!43, G!45)) | (~member(tptp_fun_X1_34(T!39, C!42, S!40, B!43, G!45), B!43)) | (~member(tptp_fun_Y1_33(T!39, C!42, S!40, B!43, G!45), C!42)) | (~member(tptp_fun_X2_32(T!39, C!42, S!40, B!43, G!45), B!43)) | (~member(tptp_fun_Y2_31(T!39, C!42, S!40, B!43, G!45), C!42)) | (~apply(S!40, tptp_fun_X1_34(T!39, C!42, S!40, B!43, G!45), tptp_fun_X2_32(T!39, C!42, S!40, B!43, G!45))) | (~apply(G!45, tptp_fun_X1_34(T!39, C!42, S!40, B!43, G!45), tptp_fun_Y1_33(T!39, C!42, S!40, B!43, G!45))) | (~apply(G!45, tptp_fun_X2_32(T!39, C!42, S!40, B!43, G!45), tptp_fun_Y2_31(T!39, C!42, S!40, B!43, G!45))))))))))),
% 0.67/0.78 inference(rewrite,[status(thm)],[])).
% 0.67/0.78 tff(221,plain,
% 0.67/0.78 ((~((~((~decreasing(G!45, B!43, S!40, C!42, T!39)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(T!39, Y2, Y1) | (~member(X1, B!43)) | (~member(Y1, C!42)) | (~member(X2, B!43)) | (~member(Y2, C!42)) | (~apply(S!40, X1, X2)) | (~apply(G!45, X1, Y1)) | (~apply(G!45, X2, Y2))))) | (~(decreasing(G!45, B!43, S!40, C!42, T!39) | (~(apply(T!39, tptp_fun_Y2_31(T!39, C!42, S!40, B!43, G!45), tptp_fun_Y1_33(T!39, C!42, S!40, B!43, G!45)) | (~member(tptp_fun_X1_34(T!39, C!42, S!40, B!43, G!45), B!43)) | (~member(tptp_fun_Y1_33(T!39, C!42, S!40, B!43, G!45), C!42)) | (~member(tptp_fun_X2_32(T!39, C!42, S!40, B!43, G!45), B!43)) | (~member(tptp_fun_Y2_31(T!39, C!42, S!40, B!43, G!45), C!42)) | (~apply(S!40, tptp_fun_X1_34(T!39, C!42, S!40, B!43, G!45), tptp_fun_X2_32(T!39, C!42, S!40, B!43, G!45))) | (~apply(G!45, tptp_fun_X1_34(T!39, C!42, S!40, B!43, G!45), tptp_fun_Y1_33(T!39, C!42, S!40, B!43, G!45))) | (~apply(G!45, tptp_fun_X2_32(T!39, C!42, S!40, B!43, G!45), tptp_fun_Y2_31(T!39, C!42, S!40, B!43, G!45))))))))) <=> (~((~((~decreasing(G!45, B!43, S!40, C!42, T!39)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(X2, B!43)) | (~member(Y2, C!42)) | (~member(Y1, C!42)) | apply(T!39, Y2, Y1) | (~member(X1, B!43)) | (~apply(S!40, X1, X2)) | (~apply(G!45, X1, Y1)) | (~apply(G!45, X2, Y2))))) | (~(decreasing(G!45, B!43, S!40, C!42, T!39) | (~(apply(T!39, tptp_fun_Y2_31(T!39, C!42, S!40, B!43, G!45), tptp_fun_Y1_33(T!39, C!42, S!40, B!43, G!45)) | (~member(tptp_fun_X1_34(T!39, C!42, S!40, B!43, G!45), B!43)) | (~member(tptp_fun_Y1_33(T!39, C!42, S!40, B!43, G!45), C!42)) | (~member(tptp_fun_X2_32(T!39, C!42, S!40, B!43, G!45), B!43)) | (~member(tptp_fun_Y2_31(T!39, C!42, S!40, B!43, G!45), C!42)) | (~apply(S!40, tptp_fun_X1_34(T!39, C!42, S!40, B!43, G!45), tptp_fun_X2_32(T!39, C!42, S!40, B!43, G!45))) | (~apply(G!45, tptp_fun_X1_34(T!39, C!42, S!40, B!43, G!45), tptp_fun_Y1_33(T!39, C!42, S!40, B!43, G!45))) | (~apply(G!45, tptp_fun_X2_32(T!39, C!42, S!40, B!43, G!45), tptp_fun_Y2_31(T!39, C!42, S!40, B!43, G!45)))))))))),
% 0.67/0.78 inference(rewrite,[status(thm)],[])).
% 0.67/0.78 tff(222,plain,
% 0.67/0.78 (((~![F: $i, A: $i, R: $i, B: $i, S: $i] : (~((~((~decreasing(F, A, R, B, S)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(S, Y2, Y1) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(R, X1, X2)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2))))) | (~(decreasing(F, A, R, B, S) | (~(apply(S, tptp_fun_Y2_31(S, B, R, A, F), tptp_fun_Y1_33(S, B, R, A, F)) | (~member(tptp_fun_X1_34(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_33(S, B, R, A, F), B)) | (~member(tptp_fun_X2_32(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_31(S, B, R, A, F), B)) | (~apply(R, tptp_fun_X1_34(S, B, R, A, F), tptp_fun_X2_32(S, B, R, A, F))) | (~apply(F, tptp_fun_X1_34(S, B, R, A, F), tptp_fun_Y1_33(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_32(S, B, R, A, F), tptp_fun_Y2_31(S, B, R, A, F)))))))))) | (~((~((~decreasing(G!45, B!43, S!40, C!42, T!39)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(T!39, Y2, Y1) | (~member(X1, B!43)) | (~member(Y1, C!42)) | (~member(X2, B!43)) | (~member(Y2, C!42)) | (~apply(S!40, X1, X2)) | (~apply(G!45, X1, Y1)) | (~apply(G!45, X2, Y2))))) | (~(decreasing(G!45, B!43, S!40, C!42, T!39) | (~(apply(T!39, tptp_fun_Y2_31(T!39, C!42, S!40, B!43, G!45), tptp_fun_Y1_33(T!39, C!42, S!40, B!43, G!45)) | (~member(tptp_fun_X1_34(T!39, C!42, S!40, B!43, G!45), B!43)) | (~member(tptp_fun_Y1_33(T!39, C!42, S!40, B!43, G!45), C!42)) | (~member(tptp_fun_X2_32(T!39, C!42, S!40, B!43, G!45), B!43)) | (~member(tptp_fun_Y2_31(T!39, C!42, S!40, B!43, G!45), C!42)) | (~apply(S!40, tptp_fun_X1_34(T!39, C!42, S!40, B!43, G!45), tptp_fun_X2_32(T!39, C!42, S!40, B!43, G!45))) | (~apply(G!45, tptp_fun_X1_34(T!39, C!42, S!40, B!43, G!45), tptp_fun_Y1_33(T!39, C!42, S!40, B!43, G!45))) | (~apply(G!45, tptp_fun_X2_32(T!39, C!42, S!40, B!43, G!45), tptp_fun_Y2_31(T!39, C!42, S!40, B!43, G!45)))))))))) <=> ((~![F: $i, A: $i, R: $i, B: $i, S: $i] : (~((~((~decreasing(F, A, R, B, S)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(S, Y2, Y1) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(R, X1, X2)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2))))) | (~(decreasing(F, A, R, B, S) | (~(apply(S, tptp_fun_Y2_31(S, B, R, A, F), tptp_fun_Y1_33(S, B, R, A, F)) | (~member(tptp_fun_X1_34(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_33(S, B, R, A, F), B)) | (~member(tptp_fun_X2_32(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_31(S, B, R, A, F), B)) | (~apply(R, tptp_fun_X1_34(S, B, R, A, F), tptp_fun_X2_32(S, B, R, A, F))) | (~apply(F, tptp_fun_X1_34(S, B, R, A, F), tptp_fun_Y1_33(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_32(S, B, R, A, F), tptp_fun_Y2_31(S, B, R, A, F)))))))))) | (~((~((~decreasing(G!45, B!43, S!40, C!42, T!39)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(X2, B!43)) | (~member(Y2, C!42)) | (~member(Y1, C!42)) | apply(T!39, Y2, Y1) | (~member(X1, B!43)) | (~apply(S!40, X1, X2)) | (~apply(G!45, X1, Y1)) | (~apply(G!45, X2, Y2))))) | (~(decreasing(G!45, B!43, S!40, C!42, T!39) | (~(apply(T!39, tptp_fun_Y2_31(T!39, C!42, S!40, B!43, G!45), tptp_fun_Y1_33(T!39, C!42, S!40, B!43, G!45)) | (~member(tptp_fun_X1_34(T!39, C!42, S!40, B!43, G!45), B!43)) | (~member(tptp_fun_Y1_33(T!39, C!42, S!40, B!43, G!45), C!42)) | (~member(tptp_fun_X2_32(T!39, C!42, S!40, B!43, G!45), B!43)) | (~member(tptp_fun_Y2_31(T!39, C!42, S!40, B!43, G!45), C!42)) | (~apply(S!40, tptp_fun_X1_34(T!39, C!42, S!40, B!43, G!45), tptp_fun_X2_32(T!39, C!42, S!40, B!43, G!45))) | (~apply(G!45, tptp_fun_X1_34(T!39, C!42, S!40, B!43, G!45), tptp_fun_Y1_33(T!39, C!42, S!40, B!43, G!45))) | (~apply(G!45, tptp_fun_X2_32(T!39, C!42, S!40, B!43, G!45), tptp_fun_Y2_31(T!39, C!42, S!40, B!43, G!45))))))))))),
% 0.67/0.78 inference(monotonicity,[status(thm)],[221])).
% 0.67/0.78 tff(223,plain,
% 0.67/0.78 (((~![F: $i, A: $i, R: $i, B: $i, S: $i] : (~((~((~decreasing(F, A, R, B, S)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(S, Y2, Y1) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(R, X1, X2)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2))))) | (~(decreasing(F, A, R, B, S) | (~(apply(S, tptp_fun_Y2_31(S, B, R, A, F), tptp_fun_Y1_33(S, B, R, A, F)) | (~member(tptp_fun_X1_34(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_33(S, B, R, A, F), B)) | (~member(tptp_fun_X2_32(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_31(S, B, R, A, F), B)) | (~apply(R, tptp_fun_X1_34(S, B, R, A, F), tptp_fun_X2_32(S, B, R, A, F))) | (~apply(F, tptp_fun_X1_34(S, B, R, A, F), tptp_fun_Y1_33(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_32(S, B, R, A, F), tptp_fun_Y2_31(S, B, R, A, F)))))))))) | (~((~((~decreasing(G!45, B!43, S!40, C!42, T!39)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(T!39, Y2, Y1) | (~member(X1, B!43)) | (~member(Y1, C!42)) | (~member(X2, B!43)) | (~member(Y2, C!42)) | (~apply(S!40, X1, X2)) | (~apply(G!45, X1, Y1)) | (~apply(G!45, X2, Y2))))) | (~(decreasing(G!45, B!43, S!40, C!42, T!39) | (~(apply(T!39, tptp_fun_Y2_31(T!39, C!42, S!40, B!43, G!45), tptp_fun_Y1_33(T!39, C!42, S!40, B!43, G!45)) | (~member(tptp_fun_X1_34(T!39, C!42, S!40, B!43, G!45), B!43)) | (~member(tptp_fun_Y1_33(T!39, C!42, S!40, B!43, G!45), C!42)) | (~member(tptp_fun_X2_32(T!39, C!42, S!40, B!43, G!45), B!43)) | (~member(tptp_fun_Y2_31(T!39, C!42, S!40, B!43, G!45), C!42)) | (~apply(S!40, tptp_fun_X1_34(T!39, C!42, S!40, B!43, G!45), tptp_fun_X2_32(T!39, C!42, S!40, B!43, G!45))) | (~apply(G!45, tptp_fun_X1_34(T!39, C!42, S!40, B!43, G!45), tptp_fun_Y1_33(T!39, C!42, S!40, B!43, G!45))) | (~apply(G!45, tptp_fun_X2_32(T!39, C!42, S!40, B!43, G!45), tptp_fun_Y2_31(T!39, C!42, S!40, B!43, G!45)))))))))) <=> ((~![F: $i, A: $i, R: $i, B: $i, S: $i] : (~((~((~decreasing(F, A, R, B, S)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(S, Y2, Y1) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(R, X1, X2)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2))))) | (~(decreasing(F, A, R, B, S) | (~(apply(S, tptp_fun_Y2_31(S, B, R, A, F), tptp_fun_Y1_33(S, B, R, A, F)) | (~member(tptp_fun_X1_34(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_33(S, B, R, A, F), B)) | (~member(tptp_fun_X2_32(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_31(S, B, R, A, F), B)) | (~apply(R, tptp_fun_X1_34(S, B, R, A, F), tptp_fun_X2_32(S, B, R, A, F))) | (~apply(F, tptp_fun_X1_34(S, B, R, A, F), tptp_fun_Y1_33(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_32(S, B, R, A, F), tptp_fun_Y2_31(S, B, R, A, F)))))))))) | (~((~((~decreasing(G!45, B!43, S!40, C!42, T!39)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(X2, B!43)) | (~member(Y2, C!42)) | (~member(Y1, C!42)) | apply(T!39, Y2, Y1) | (~member(X1, B!43)) | (~apply(S!40, X1, X2)) | (~apply(G!45, X1, Y1)) | (~apply(G!45, X2, Y2))))) | (~(decreasing(G!45, B!43, S!40, C!42, T!39) | (~(apply(T!39, tptp_fun_Y2_31(T!39, C!42, S!40, B!43, G!45), tptp_fun_Y1_33(T!39, C!42, S!40, B!43, G!45)) | (~member(tptp_fun_X1_34(T!39, C!42, S!40, B!43, G!45), B!43)) | (~member(tptp_fun_Y1_33(T!39, C!42, S!40, B!43, G!45), C!42)) | (~member(tptp_fun_X2_32(T!39, C!42, S!40, B!43, G!45), B!43)) | (~member(tptp_fun_Y2_31(T!39, C!42, S!40, B!43, G!45), C!42)) | (~apply(S!40, tptp_fun_X1_34(T!39, C!42, S!40, B!43, G!45), tptp_fun_X2_32(T!39, C!42, S!40, B!43, G!45))) | (~apply(G!45, tptp_fun_X1_34(T!39, C!42, S!40, B!43, G!45), tptp_fun_Y1_33(T!39, C!42, S!40, B!43, G!45))) | (~apply(G!45, tptp_fun_X2_32(T!39, C!42, S!40, B!43, G!45), tptp_fun_Y2_31(T!39, C!42, S!40, B!43, G!45))))))))))),
% 0.73/0.79 inference(transitivity,[status(thm)],[222, 220])).
% 0.73/0.79 tff(224,plain,
% 0.73/0.79 ((~![F: $i, A: $i, R: $i, B: $i, S: $i] : (~((~((~decreasing(F, A, R, B, S)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(S, Y2, Y1) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(R, X1, X2)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2))))) | (~(decreasing(F, A, R, B, S) | (~(apply(S, tptp_fun_Y2_31(S, B, R, A, F), tptp_fun_Y1_33(S, B, R, A, F)) | (~member(tptp_fun_X1_34(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_33(S, B, R, A, F), B)) | (~member(tptp_fun_X2_32(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_31(S, B, R, A, F), B)) | (~apply(R, tptp_fun_X1_34(S, B, R, A, F), tptp_fun_X2_32(S, B, R, A, F))) | (~apply(F, tptp_fun_X1_34(S, B, R, A, F), tptp_fun_Y1_33(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_32(S, B, R, A, F), tptp_fun_Y2_31(S, B, R, A, F)))))))))) | (~((~((~decreasing(G!45, B!43, S!40, C!42, T!39)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(T!39, Y2, Y1) | (~member(X1, B!43)) | (~member(Y1, C!42)) | (~member(X2, B!43)) | (~member(Y2, C!42)) | (~apply(S!40, X1, X2)) | (~apply(G!45, X1, Y1)) | (~apply(G!45, X2, Y2))))) | (~(decreasing(G!45, B!43, S!40, C!42, T!39) | (~(apply(T!39, tptp_fun_Y2_31(T!39, C!42, S!40, B!43, G!45), tptp_fun_Y1_33(T!39, C!42, S!40, B!43, G!45)) | (~member(tptp_fun_X1_34(T!39, C!42, S!40, B!43, G!45), B!43)) | (~member(tptp_fun_Y1_33(T!39, C!42, S!40, B!43, G!45), C!42)) | (~member(tptp_fun_X2_32(T!39, C!42, S!40, B!43, G!45), B!43)) | (~member(tptp_fun_Y2_31(T!39, C!42, S!40, B!43, G!45), C!42)) | (~apply(S!40, tptp_fun_X1_34(T!39, C!42, S!40, B!43, G!45), tptp_fun_X2_32(T!39, C!42, S!40, B!43, G!45))) | (~apply(G!45, tptp_fun_X1_34(T!39, C!42, S!40, B!43, G!45), tptp_fun_Y1_33(T!39, C!42, S!40, B!43, G!45))) | (~apply(G!45, tptp_fun_X2_32(T!39, C!42, S!40, B!43, G!45), tptp_fun_Y2_31(T!39, C!42, S!40, B!43, G!45)))))))))),
% 0.73/0.79 inference(quant_inst,[status(thm)],[])).
% 0.73/0.79 tff(225,plain,
% 0.73/0.79 ((~![F: $i, A: $i, R: $i, B: $i, S: $i] : (~((~((~decreasing(F, A, R, B, S)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(S, Y2, Y1) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(R, X1, X2)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2))))) | (~(decreasing(F, A, R, B, S) | (~(apply(S, tptp_fun_Y2_31(S, B, R, A, F), tptp_fun_Y1_33(S, B, R, A, F)) | (~member(tptp_fun_X1_34(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_33(S, B, R, A, F), B)) | (~member(tptp_fun_X2_32(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_31(S, B, R, A, F), B)) | (~apply(R, tptp_fun_X1_34(S, B, R, A, F), tptp_fun_X2_32(S, B, R, A, F))) | (~apply(F, tptp_fun_X1_34(S, B, R, A, F), tptp_fun_Y1_33(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_32(S, B, R, A, F), tptp_fun_Y2_31(S, B, R, A, F)))))))))) | (~((~((~decreasing(G!45, B!43, S!40, C!42, T!39)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(X2, B!43)) | (~member(Y2, C!42)) | (~member(Y1, C!42)) | apply(T!39, Y2, Y1) | (~member(X1, B!43)) | (~apply(S!40, X1, X2)) | (~apply(G!45, X1, Y1)) | (~apply(G!45, X2, Y2))))) | (~(decreasing(G!45, B!43, S!40, C!42, T!39) | (~(apply(T!39, tptp_fun_Y2_31(T!39, C!42, S!40, B!43, G!45), tptp_fun_Y1_33(T!39, C!42, S!40, B!43, G!45)) | (~member(tptp_fun_X1_34(T!39, C!42, S!40, B!43, G!45), B!43)) | (~member(tptp_fun_Y1_33(T!39, C!42, S!40, B!43, G!45), C!42)) | (~member(tptp_fun_X2_32(T!39, C!42, S!40, B!43, G!45), B!43)) | (~member(tptp_fun_Y2_31(T!39, C!42, S!40, B!43, G!45), C!42)) | (~apply(S!40, tptp_fun_X1_34(T!39, C!42, S!40, B!43, G!45), tptp_fun_X2_32(T!39, C!42, S!40, B!43, G!45))) | (~apply(G!45, tptp_fun_X1_34(T!39, C!42, S!40, B!43, G!45), tptp_fun_Y1_33(T!39, C!42, S!40, B!43, G!45))) | (~apply(G!45, tptp_fun_X2_32(T!39, C!42, S!40, B!43, G!45), tptp_fun_Y2_31(T!39, C!42, S!40, B!43, G!45)))))))))),
% 0.73/0.79 inference(modus_ponens,[status(thm)],[224, 223])).
% 0.73/0.79 tff(226,plain,
% 0.73/0.79 (~((~((~decreasing(G!45, B!43, S!40, C!42, T!39)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(X2, B!43)) | (~member(Y2, C!42)) | (~member(Y1, C!42)) | apply(T!39, Y2, Y1) | (~member(X1, B!43)) | (~apply(S!40, X1, X2)) | (~apply(G!45, X1, Y1)) | (~apply(G!45, X2, Y2))))) | (~(decreasing(G!45, B!43, S!40, C!42, T!39) | (~(apply(T!39, tptp_fun_Y2_31(T!39, C!42, S!40, B!43, G!45), tptp_fun_Y1_33(T!39, C!42, S!40, B!43, G!45)) | (~member(tptp_fun_X1_34(T!39, C!42, S!40, B!43, G!45), B!43)) | (~member(tptp_fun_Y1_33(T!39, C!42, S!40, B!43, G!45), C!42)) | (~member(tptp_fun_X2_32(T!39, C!42, S!40, B!43, G!45), B!43)) | (~member(tptp_fun_Y2_31(T!39, C!42, S!40, B!43, G!45), C!42)) | (~apply(S!40, tptp_fun_X1_34(T!39, C!42, S!40, B!43, G!45), tptp_fun_X2_32(T!39, C!42, S!40, B!43, G!45))) | (~apply(G!45, tptp_fun_X1_34(T!39, C!42, S!40, B!43, G!45), tptp_fun_Y1_33(T!39, C!42, S!40, B!43, G!45))) | (~apply(G!45, tptp_fun_X2_32(T!39, C!42, S!40, B!43, G!45), tptp_fun_Y2_31(T!39, C!42, S!40, B!43, G!45))))))))),
% 0.73/0.79 inference(unit_resolution,[status(thm)],[225, 197])).
% 0.73/0.79 tff(227,plain,
% 0.73/0.79 (((~((~decreasing(G!45, B!43, S!40, C!42, T!39)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(X2, B!43)) | (~member(Y2, C!42)) | (~member(Y1, C!42)) | apply(T!39, Y2, Y1) | (~member(X1, B!43)) | (~apply(S!40, X1, X2)) | (~apply(G!45, X1, Y1)) | (~apply(G!45, X2, Y2))))) | (~(decreasing(G!45, B!43, S!40, C!42, T!39) | (~(apply(T!39, tptp_fun_Y2_31(T!39, C!42, S!40, B!43, G!45), tptp_fun_Y1_33(T!39, C!42, S!40, B!43, G!45)) | (~member(tptp_fun_X1_34(T!39, C!42, S!40, B!43, G!45), B!43)) | (~member(tptp_fun_Y1_33(T!39, C!42, S!40, B!43, G!45), C!42)) | (~member(tptp_fun_X2_32(T!39, C!42, S!40, B!43, G!45), B!43)) | (~member(tptp_fun_Y2_31(T!39, C!42, S!40, B!43, G!45), C!42)) | (~apply(S!40, tptp_fun_X1_34(T!39, C!42, S!40, B!43, G!45), tptp_fun_X2_32(T!39, C!42, S!40, B!43, G!45))) | (~apply(G!45, tptp_fun_X1_34(T!39, C!42, S!40, B!43, G!45), tptp_fun_Y1_33(T!39, C!42, S!40, B!43, G!45))) | (~apply(G!45, tptp_fun_X2_32(T!39, C!42, S!40, B!43, G!45), tptp_fun_Y2_31(T!39, C!42, S!40, B!43, G!45)))))))) | ((~decreasing(G!45, B!43, S!40, C!42, T!39)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(X2, B!43)) | (~member(Y2, C!42)) | (~member(Y1, C!42)) | apply(T!39, Y2, Y1) | (~member(X1, B!43)) | (~apply(S!40, X1, X2)) | (~apply(G!45, X1, Y1)) | (~apply(G!45, X2, Y2))))),
% 0.73/0.79 inference(tautology,[status(thm)],[])).
% 0.73/0.79 tff(228,plain,
% 0.73/0.79 ((~decreasing(G!45, B!43, S!40, C!42, T!39)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(X2, B!43)) | (~member(Y2, C!42)) | (~member(Y1, C!42)) | apply(T!39, Y2, Y1) | (~member(X1, B!43)) | (~apply(S!40, X1, X2)) | (~apply(G!45, X1, Y1)) | (~apply(G!45, X2, Y2)))),
% 0.73/0.79 inference(unit_resolution,[status(thm)],[227, 226])).
% 0.73/0.79 tff(229,plain,
% 0.73/0.79 (decreasing(G!45, B!43, S!40, C!42, T!39)),
% 0.73/0.79 inference(and_elim,[status(thm)],[106])).
% 0.73/0.79 tff(230,plain,
% 0.73/0.79 ((~((~decreasing(G!45, B!43, S!40, C!42, T!39)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(X2, B!43)) | (~member(Y2, C!42)) | (~member(Y1, C!42)) | apply(T!39, Y2, Y1) | (~member(X1, B!43)) | (~apply(S!40, X1, X2)) | (~apply(G!45, X1, Y1)) | (~apply(G!45, X2, Y2))))) | (~decreasing(G!45, B!43, S!40, C!42, T!39)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(X2, B!43)) | (~member(Y2, C!42)) | (~member(Y1, C!42)) | apply(T!39, Y2, Y1) | (~member(X1, B!43)) | (~apply(S!40, X1, X2)) | (~apply(G!45, X1, Y1)) | (~apply(G!45, X2, Y2)))),
% 0.73/0.79 inference(tautology,[status(thm)],[])).
% 0.73/0.79 tff(231,plain,
% 0.73/0.79 ((~((~decreasing(G!45, B!43, S!40, C!42, T!39)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(X2, B!43)) | (~member(Y2, C!42)) | (~member(Y1, C!42)) | apply(T!39, Y2, Y1) | (~member(X1, B!43)) | (~apply(S!40, X1, X2)) | (~apply(G!45, X1, Y1)) | (~apply(G!45, X2, Y2))))) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(X2, B!43)) | (~member(Y2, C!42)) | (~member(Y1, C!42)) | apply(T!39, Y2, Y1) | (~member(X1, B!43)) | (~apply(S!40, X1, X2)) | (~apply(G!45, X1, Y1)) | (~apply(G!45, X2, Y2)))),
% 0.73/0.79 inference(unit_resolution,[status(thm)],[230, 229])).
% 0.73/0.79 tff(232,plain,
% 0.73/0.79 (![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(X2, B!43)) | (~member(Y2, C!42)) | (~member(Y1, C!42)) | apply(T!39, Y2, Y1) | (~member(X1, B!43)) | (~apply(S!40, X1, X2)) | (~apply(G!45, X1, Y1)) | (~apply(G!45, X2, Y2)))),
% 0.73/0.79 inference(unit_resolution,[status(thm)],[231, 228])).
% 0.73/0.79 tff(233,plain,
% 0.73/0.79 (((~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(X2, B!43)) | (~member(Y2, C!42)) | (~member(Y1, C!42)) | apply(T!39, Y2, Y1) | (~member(X1, B!43)) | (~apply(S!40, X1, X2)) | (~apply(G!45, X1, Y1)) | (~apply(G!45, X2, Y2)))) | ((~member(tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), B!43)) | (~member(tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), B!43)) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), C!42, G!45), C!42)) | (~apply(G!45, tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, 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% 0.73/0.80 inference(rewrite,[status(thm)],[])).
% 0.73/0.80 tff(234,plain,
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% 0.73/0.80 inference(rewrite,[status(thm)],[])).
% 0.73/0.80 tff(235,plain,
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% 0.73/0.81 inference(monotonicity,[status(thm)],[234])).
% 0.73/0.81 tff(236,plain,
% 0.73/0.81 (((~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(X2, B!43)) | (~member(Y2, C!42)) | (~member(Y1, C!42)) | apply(T!39, Y2, Y1) | (~member(X1, B!43)) | (~apply(S!40, X1, X2)) | (~apply(G!45, X1, Y1)) | (~apply(G!45, X2, Y2)))) | ((~member(tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), B!43)) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), C!42, G!45), C!42)) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), C!42, G!45), C!42)) | apply(T!39, 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% 0.73/0.81 inference(transitivity,[status(thm)],[235, 233])).
% 0.73/0.81 tff(237,plain,
% 0.73/0.81 ((~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(X2, B!43)) | (~member(Y2, C!42)) | (~member(Y1, C!42)) | apply(T!39, Y2, Y1) | (~member(X1, B!43)) | (~apply(S!40, X1, X2)) | (~apply(G!45, X1, Y1)) | (~apply(G!45, X2, Y2)))) | ((~member(tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), B!43)) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), C!42, G!45), C!42)) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), C!42, G!45), C!42)) | apply(T!39, tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), C!42, G!45), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), C!42, G!45)) | (~member(tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), B!43)) | (~apply(S!40, tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45))) | (~apply(G!45, tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), C!42, G!45))) | (~apply(G!45, tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), C!42, G!45))))),
% 0.73/0.81 inference(quant_inst,[status(thm)],[])).
% 0.73/0.81 tff(238,plain,
% 0.73/0.81 ((~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(X2, B!43)) | (~member(Y2, C!42)) | (~member(Y1, C!42)) | apply(T!39, Y2, Y1) | (~member(X1, B!43)) | (~apply(S!40, X1, X2)) | (~apply(G!45, X1, Y1)) | (~apply(G!45, X2, Y2)))) | (~member(tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), B!43)) | (~member(tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), B!43)) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), C!42, G!45), C!42)) | (~apply(G!45, tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), C!42, G!45))) | (~member(tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), C!42, G!45), C!42)) | (~apply(G!45, tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), C!42, G!45))) | apply(T!39, tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), C!42, G!45), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), C!42, G!45)) | (~apply(S!40, tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45)))),
% 0.73/0.81 inference(modus_ponens,[status(thm)],[237, 236])).
% 0.73/0.81 tff(239,plain,
% 0.73/0.81 (apply(T!39, tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y1_29(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X1_30(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), C!42, G!45), tptp_fun_Y_3(tptp_fun_Y_8(tptp_fun_Y2_27(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), tptp_fun_X2_28(T!39, C!42, R!41, A!44, compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), C!42, G!45))),
% 0.73/0.82 inference(unit_resolution,[status(thm)],[238, 232, 79, 154, 120, 118, 162, 160, 219])).
% 0.73/0.82 tff(240,plain,
% 0.73/0.82 ($false),
% 0.73/0.82 inference(unit_resolution,[status(thm)],[239, 177])).
% 0.73/0.82 % SZS output end Proof
%------------------------------------------------------------------------------