TSTP Solution File: SET746+4 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET746+4 : TPTP v8.1.0. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n019.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 05:07:50 EDT 2022
% Result : Theorem 1.78s 2.02s
% Output : Proof 2.24s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SET746+4 : TPTP v8.1.0. Bugfixed v2.2.1.
% 0.07/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.35 % Computer : n019.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 07:44:50 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.36 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.36 Usage: tptp [options] [-file:]file
% 0.14/0.36 -h, -? prints this message.
% 0.14/0.36 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.36 -m, -model generate model.
% 0.14/0.36 -p, -proof generate proof.
% 0.14/0.36 -c, -core generate unsat core of named formulas.
% 0.14/0.36 -st, -statistics display statistics.
% 0.14/0.36 -t:timeout set timeout (in second).
% 0.14/0.36 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.36 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.36 -<param>:<value> configuration parameter and value.
% 0.14/0.36 -o:<output-file> file to place output in.
% 1.78/2.02 % SZS status Theorem
% 1.78/2.02 % SZS output start Proof
% 1.78/2.02 tff(apply_type, type, (
% 1.78/2.02 apply: ( $i * $i * $i ) > $o)).
% 1.78/2.02 tff(tptp_fun_Y_3_type, type, (
% 1.78/2.02 tptp_fun_Y_3: ( $i * $i * $i ) > $i)).
% 1.78/2.02 tff(tptp_fun_G_45_type, type, (
% 1.78/2.02 tptp_fun_G_45: $i)).
% 1.78/2.02 tff(tptp_fun_C_42_type, type, (
% 1.78/2.02 tptp_fun_C_42: $i)).
% 1.78/2.02 tff(tptp_fun_Y_8_type, type, (
% 1.78/2.02 tptp_fun_Y_8: ( $i * $i * $i * $i * $i ) > $i)).
% 1.78/2.02 tff(tptp_fun_F_46_type, type, (
% 1.78/2.02 tptp_fun_F_46: $i)).
% 1.78/2.02 tff(tptp_fun_B_43_type, type, (
% 1.78/2.02 tptp_fun_B_43: $i)).
% 1.78/2.02 tff(tptp_fun_X2_28_type, type, (
% 1.78/2.02 tptp_fun_X2_28: ( $i * $i * $i * $i * $i ) > $i)).
% 1.78/2.02 tff(compose_function_type, type, (
% 1.78/2.02 compose_function: ( $i * $i * $i * $i * $i ) > $i)).
% 1.78/2.02 tff(tptp_fun_A_44_type, type, (
% 1.78/2.02 tptp_fun_A_44: $i)).
% 1.78/2.02 tff(tptp_fun_R_41_type, type, (
% 1.78/2.02 tptp_fun_R_41: $i)).
% 1.78/2.02 tff(tptp_fun_T_39_type, type, (
% 1.78/2.02 tptp_fun_T_39: $i)).
% 1.78/2.02 tff(tptp_fun_Y2_27_type, type, (
% 1.78/2.02 tptp_fun_Y2_27: ( $i * $i * $i * $i * $i ) > $i)).
% 1.78/2.02 tff(tptp_fun_X1_30_type, type, (
% 1.78/2.02 tptp_fun_X1_30: ( $i * $i * $i * $i * $i ) > $i)).
% 1.78/2.02 tff(tptp_fun_Y1_29_type, type, (
% 1.78/2.02 tptp_fun_Y1_29: ( $i * $i * $i * $i * $i ) > $i)).
% 1.78/2.02 tff(member_type, type, (
% 1.78/2.02 member: ( $i * $i ) > $o)).
% 1.78/2.02 tff(increasing_type, type, (
% 1.78/2.02 increasing: ( $i * $i * $i * $i * $i ) > $o)).
% 1.78/2.02 tff(tptp_fun_S_40_type, type, (
% 1.78/2.02 tptp_fun_S_40: $i)).
% 1.78/2.02 tff(maps_type, type, (
% 1.78/2.02 maps: ( $i * $i * $i ) > $o)).
% 1.78/2.02 tff(tptp_fun_X_4_type, type, (
% 1.78/2.02 tptp_fun_X_4: ( $i * $i * $i ) > $i)).
% 1.78/2.02 tff(tptp_fun_Y2_5_type, type, (
% 1.78/2.02 tptp_fun_Y2_5: ( $i * $i * $i ) > $i)).
% 1.78/2.02 tff(tptp_fun_Y1_6_type, type, (
% 1.78/2.02 tptp_fun_Y1_6: ( $i * $i * $i ) > $i)).
% 1.78/2.02 tff(tptp_fun_X_7_type, type, (
% 1.78/2.02 tptp_fun_X_7: ( $i * $i * $i ) > $i)).
% 1.78/2.02 tff(1,plain,
% 1.78/2.02 (^[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))))))))))),
% 1.78/2.02 inference(bind,[status(th)],[])).
% 1.78/2.02 tff(2,plain,
% 1.78/2.02 (![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)))))))))),
% 1.78/2.02 inference(quant_intro,[status(thm)],[1])).
% 1.78/2.02 tff(3,plain,
% 1.78/2.02 (^[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))))))))))),
% 1.78/2.02 inference(bind,[status(th)],[])).
% 1.78/2.02 tff(4,plain,
% 1.78/2.02 (![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)))))))))),
% 1.78/2.02 inference(quant_intro,[status(thm)],[3])).
% 1.78/2.02 tff(5,plain,
% 1.78/2.02 (![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)))))))))),
% 1.78/2.02 inference(transitivity,[status(thm)],[4, 2])).
% 1.78/2.02 tff(6,plain,
% 1.78/2.02 (^[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)))))))))))),
% 1.78/2.03 inference(bind,[status(th)],[])).
% 1.78/2.03 tff(7,plain,
% 1.78/2.03 (![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)))))))))),
% 1.78/2.03 inference(quant_intro,[status(thm)],[6])).
% 1.78/2.03 tff(8,plain,
% 1.78/2.03 (![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)))),
% 1.78/2.03 inference(rewrite,[status(thm)],[])).
% 1.78/2.03 tff(9,plain,
% 1.78/2.03 (^[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))))),
% 1.78/2.03 inference(bind,[status(th)],[])).
% 1.78/2.03 tff(10,plain,
% 1.78/2.03 (![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)))),
% 1.78/2.03 inference(quant_intro,[status(thm)],[9])).
% 1.78/2.03 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')).
% 1.78/2.03 tff(12,plain,
% 1.78/2.03 (![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)))),
% 1.78/2.03 inference(modus_ponens,[status(thm)],[11, 10])).
% 1.78/2.03 tff(13,plain,
% 1.78/2.03 (![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)))),
% 1.78/2.03 inference(modus_ponens,[status(thm)],[12, 8])).
% 1.78/2.03 tff(14,plain,(
% 1.78/2.03 ![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))))))),
% 1.78/2.03 inference(skolemize,[status(sab)],[13])).
% 1.78/2.03 tff(15,plain,
% 1.78/2.03 (![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)))))))))),
% 1.78/2.03 inference(modus_ponens,[status(thm)],[14, 7])).
% 1.78/2.03 tff(16,plain,
% 1.78/2.03 (![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)))))))))),
% 1.78/2.03 inference(modus_ponens,[status(thm)],[15, 5])).
% 1.78/2.03 tff(17,plain,
% 1.78/2.03 (((~![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)) | (~member(X1, A!44)) | (~member(X2, A!44)) | (~apply(R!41, X1, X2)) | apply(T!39, Y1, Y2) | (~member(Y1, C!42)) | (~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)) | (~member(X1, A!44)) | (~member(X2, A!44)) | (~apply(R!41, X1, X2)) | apply(T!39, Y1, Y2) | (~member(Y1, C!42)) | (~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)))))))))))),
% 1.78/2.04 inference(rewrite,[status(thm)],[])).
% 1.78/2.04 tff(18,plain,
% 1.78/2.04 ((~((~((~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)) | (~member(X1, A!44)) | (~member(X2, A!44)) | (~apply(R!41, X1, X2)) | apply(T!39, Y1, Y2) | (~member(Y1, C!42)) | (~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))))))))))),
% 1.78/2.04 inference(rewrite,[status(thm)],[])).
% 1.78/2.04 tff(19,plain,
% 1.78/2.04 (((~![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)) | (~member(X1, A!44)) | (~member(X2, A!44)) | (~apply(R!41, X1, X2)) | apply(T!39, Y1, Y2) | (~member(Y1, C!42)) | (~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)))))))))))),
% 1.78/2.05 inference(monotonicity,[status(thm)],[18])).
% 1.78/2.05 tff(20,plain,
% 1.78/2.05 (((~![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)) | (~member(X1, A!44)) | (~member(X2, A!44)) | (~apply(R!41, X1, X2)) | apply(T!39, Y1, Y2) | (~member(Y1, C!42)) | (~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)))))))))))),
% 1.78/2.06 inference(transitivity,[status(thm)],[19, 17])).
% 1.78/2.06 tff(21,plain,
% 1.78/2.06 ((~![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))))))))))),
% 1.78/2.06 inference(quant_inst,[status(thm)],[])).
% 1.78/2.06 tff(22,plain,
% 1.78/2.06 ((~![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)) | (~member(X1, A!44)) | (~member(X2, A!44)) | (~apply(R!41, X1, X2)) | apply(T!39, Y1, Y2) | (~member(Y1, C!42)) | (~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))))))))))),
% 1.78/2.06 inference(modus_ponens,[status(thm)],[21, 20])).
% 1.78/2.06 tff(23,plain,
% 1.78/2.06 (~((~((~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)) | (~member(X1, A!44)) | (~member(X2, A!44)) | (~apply(R!41, X1, X2)) | apply(T!39, Y1, Y2) | (~member(Y1, C!42)) | (~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)))))))))),
% 1.78/2.06 inference(unit_resolution,[status(thm)],[22, 16])).
% 1.78/2.06 tff(24,plain,
% 1.78/2.06 (((~((~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)) | (~member(X1, A!44)) | (~member(X2, A!44)) | (~apply(R!41, X1, X2)) | apply(T!39, Y1, Y2) | (~member(Y1, C!42)) | (~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)))))))),
% 1.78/2.07 inference(tautology,[status(thm)],[])).
% 1.78/2.07 tff(25,plain,
% 1.78/2.07 (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))))))),
% 1.78/2.07 inference(unit_resolution,[status(thm)],[24, 23])).
% 1.78/2.07 tff(26,plain,
% 1.78/2.07 ((~![F: $i, G: $i, A: $i, B: $i, C: $i, R: $i, S: $i, T: $i] : ((~(maps(F, A, B) & maps(G, B, C) & increasing(F, A, R, B, S) & increasing(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) & increasing(F, A, R, B, S) & increasing(G, B, S, C, T))) | increasing(compose_function(G, F, A, B, C), A, R, C, T)))),
% 1.78/2.07 inference(rewrite,[status(thm)],[])).
% 1.78/2.07 tff(27,plain,
% 1.78/2.07 ((~![F: $i, G: $i, A: $i, B: $i, C: $i, R: $i, S: $i, T: $i] : ((((maps(F, A, B) & maps(G, B, C)) & increasing(F, A, R, B, S)) & increasing(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) & increasing(F, A, R, B, S) & increasing(G, B, S, C, T))) | increasing(compose_function(G, F, A, B, C), A, R, C, T)))),
% 1.78/2.07 inference(rewrite,[status(thm)],[])).
% 1.78/2.07 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)) & increasing(F, A, R, B, S)) & increasing(G, B, S, C, T)) => increasing(compose_function(G, F, A, B, C), A, R, C, T))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thII37')).
% 1.78/2.07 tff(29,plain,
% 1.78/2.07 (~![F: $i, G: $i, A: $i, B: $i, C: $i, R: $i, S: $i, T: $i] : ((~(maps(F, A, B) & maps(G, B, C) & increasing(F, A, R, B, S) & increasing(G, B, S, C, T))) | increasing(compose_function(G, F, A, B, C), A, R, C, T))),
% 1.78/2.07 inference(modus_ponens,[status(thm)],[28, 27])).
% 1.78/2.07 tff(30,plain,
% 1.78/2.07 (~![F: $i, G: $i, A: $i, B: $i, C: $i, R: $i, S: $i, T: $i] : ((~(maps(F, A, B) & maps(G, B, C) & increasing(F, A, R, B, S) & increasing(G, B, S, C, T))) | increasing(compose_function(G, F, A, B, C), A, R, C, T))),
% 1.78/2.07 inference(modus_ponens,[status(thm)],[29, 26])).
% 1.78/2.07 tff(31,plain,
% 1.78/2.07 (~![F: $i, G: $i, A: $i, B: $i, C: $i, R: $i, S: $i, T: $i] : ((~(maps(F, A, B) & maps(G, B, C) & increasing(F, A, R, B, S) & increasing(G, B, S, C, T))) | increasing(compose_function(G, F, A, B, C), A, R, C, T))),
% 1.78/2.07 inference(modus_ponens,[status(thm)],[30, 26])).
% 1.78/2.07 tff(32,plain,
% 1.78/2.07 (~![F: $i, G: $i, A: $i, B: $i, C: $i, R: $i, S: $i, T: $i] : ((~(maps(F, A, B) & maps(G, B, C) & increasing(F, A, R, B, S) & increasing(G, B, S, C, T))) | increasing(compose_function(G, F, A, B, C), A, R, C, T))),
% 1.78/2.07 inference(modus_ponens,[status(thm)],[31, 26])).
% 1.78/2.07 tff(33,plain,
% 1.78/2.07 (~![F: $i, G: $i, A: $i, B: $i, C: $i, R: $i, S: $i, T: $i] : ((~(maps(F, A, B) & maps(G, B, C) & increasing(F, A, R, B, S) & increasing(G, B, S, C, T))) | increasing(compose_function(G, F, A, B, C), A, R, C, T))),
% 1.78/2.07 inference(modus_ponens,[status(thm)],[32, 26])).
% 1.78/2.07 tff(34,plain,
% 1.78/2.07 (~![F: $i, G: $i, A: $i, B: $i, C: $i, R: $i, S: $i, T: $i] : ((~(maps(F, A, B) & maps(G, B, C) & increasing(F, A, R, B, S) & increasing(G, B, S, C, T))) | increasing(compose_function(G, F, A, B, C), A, R, C, T))),
% 1.78/2.07 inference(modus_ponens,[status(thm)],[33, 26])).
% 1.78/2.07 tff(35,plain,
% 1.78/2.07 (~![F: $i, G: $i, A: $i, B: $i, C: $i, R: $i, S: $i, T: $i] : ((~(maps(F, A, B) & maps(G, B, C) & increasing(F, A, R, B, S) & increasing(G, B, S, C, T))) | increasing(compose_function(G, F, A, B, C), A, R, C, T))),
% 1.78/2.07 inference(modus_ponens,[status(thm)],[34, 26])).
% 1.78/2.07 tff(36,plain,(
% 1.78/2.07 ~((~(maps(F!46, A!44, B!43) & maps(G!45, B!43, C!42) & increasing(F!46, A!44, R!41, B!43, S!40) & increasing(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))),
% 1.78/2.07 inference(skolemize,[status(sab)],[35])).
% 1.78/2.07 tff(37,plain,
% 1.78/2.07 (~increasing(compose_function(G!45, F!46, A!44, B!43, C!42), A!44, R!41, C!42, T!39)),
% 1.78/2.07 inference(or_elim,[status(thm)],[36])).
% 1.78/2.07 tff(38,plain,
% 1.78/2.07 ((~(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))))))),
% 1.86/2.08 inference(tautology,[status(thm)],[])).
% 1.86/2.08 tff(39,plain,
% 1.86/2.08 ((~(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))))))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[38, 37])).
% 1.86/2.09 tff(40,plain,
% 1.86/2.09 (~(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)))))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[39, 25])).
% 1.86/2.09 tff(41,plain,
% 1.86/2.09 ((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)),
% 1.86/2.09 inference(tautology,[status(thm)],[])).
% 1.86/2.09 tff(42,plain,
% 1.86/2.09 (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)),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[41, 40])).
% 1.86/2.09 tff(43,plain,
% 1.86/2.09 ((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)),
% 1.86/2.09 inference(tautology,[status(thm)],[])).
% 1.86/2.09 tff(44,plain,
% 1.86/2.09 (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)),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[43, 40])).
% 1.86/2.09 tff(45,plain,
% 1.86/2.09 (^[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)))))))))),
% 1.86/2.09 inference(bind,[status(th)],[])).
% 1.86/2.09 tff(46,plain,
% 1.86/2.09 (![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))))))))),
% 1.86/2.09 inference(quant_intro,[status(thm)],[45])).
% 1.86/2.09 tff(47,plain,
% 1.86/2.09 (^[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)))))))))),
% 1.86/2.09 inference(bind,[status(th)],[])).
% 1.86/2.09 tff(48,plain,
% 1.86/2.09 (![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))))))))),
% 1.86/2.09 inference(quant_intro,[status(thm)],[47])).
% 1.86/2.09 tff(49,plain,
% 1.86/2.09 (![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))))))))),
% 1.86/2.09 inference(transitivity,[status(thm)],[48, 46])).
% 1.86/2.09 tff(50,plain,
% 1.86/2.09 (^[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))))))))))),
% 1.86/2.09 inference(bind,[status(th)],[])).
% 1.86/2.09 tff(51,plain,
% 1.86/2.09 (![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))))))))),
% 1.86/2.09 inference(quant_intro,[status(thm)],[50])).
% 1.86/2.09 tff(52,plain,
% 1.86/2.09 (![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))))),
% 1.86/2.09 inference(rewrite,[status(thm)],[])).
% 1.86/2.09 tff(53,plain,
% 1.86/2.09 (^[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))))))),
% 1.86/2.09 inference(bind,[status(th)],[])).
% 1.86/2.09 tff(54,plain,
% 1.86/2.09 (![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))))),
% 1.86/2.09 inference(quant_intro,[status(thm)],[53])).
% 1.86/2.09 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')).
% 1.86/2.09 tff(56,plain,
% 1.86/2.09 (![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))))),
% 1.86/2.09 inference(modus_ponens,[status(thm)],[55, 54])).
% 1.86/2.09 tff(57,plain,
% 1.86/2.09 (![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))))),
% 1.86/2.09 inference(modus_ponens,[status(thm)],[56, 52])).
% 1.86/2.09 tff(58,plain,(
% 1.86/2.09 ![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))))))),
% 1.86/2.09 inference(skolemize,[status(sab)],[57])).
% 1.86/2.09 tff(59,plain,
% 1.86/2.09 (![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))))))))),
% 1.86/2.09 inference(modus_ponens,[status(thm)],[58, 51])).
% 1.86/2.09 tff(60,plain,
% 1.86/2.09 (![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))))))))),
% 1.86/2.09 inference(modus_ponens,[status(thm)],[59, 49])).
% 1.86/2.09 tff(61,plain,
% 1.86/2.09 (((~![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))))))))))),
% 1.86/2.11 inference(rewrite,[status(thm)],[])).
% 1.86/2.11 tff(62,plain,
% 1.86/2.11 (((~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))))))))))),
% 1.86/2.11 inference(rewrite,[status(thm)],[])).
% 1.86/2.11 tff(63,plain,
% 1.86/2.11 ((~((~((~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)))))))))),
% 1.86/2.11 inference(rewrite,[status(thm)],[])).
% 1.86/2.11 tff(64,plain,
% 1.86/2.11 (((~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))))))))))),
% 1.86/2.12 inference(monotonicity,[status(thm)],[63])).
% 1.86/2.12 tff(65,plain,
% 1.86/2.12 (((~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))))))))))),
% 1.86/2.13 inference(transitivity,[status(thm)],[64, 62])).
% 1.86/2.13 tff(66,plain,
% 1.86/2.13 (((~![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)))))))))))),
% 1.86/2.13 inference(monotonicity,[status(thm)],[65])).
% 1.86/2.13 tff(67,plain,
% 1.86/2.13 (((~![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))))))))))),
% 1.86/2.14 inference(transitivity,[status(thm)],[66, 61])).
% 1.86/2.14 tff(68,plain,
% 1.86/2.14 ((~![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))))))))))),
% 1.86/2.14 inference(quant_inst,[status(thm)],[])).
% 1.86/2.14 tff(69,plain,
% 1.86/2.14 ((~![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)))))))))),
% 1.86/2.14 inference(modus_ponens,[status(thm)],[68, 67])).
% 1.86/2.14 tff(70,plain,
% 1.86/2.14 (~((~((~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))))))))),
% 1.86/2.15 inference(unit_resolution,[status(thm)],[69, 60, 44, 42])).
% 1.86/2.15 tff(71,plain,
% 1.86/2.15 (((~((~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)))))))),
% 1.86/2.15 inference(tautology,[status(thm)],[])).
% 1.86/2.15 tff(72,plain,
% 1.86/2.15 ((~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))))))),
% 1.86/2.16 inference(unit_resolution,[status(thm)],[71, 70])).
% 1.86/2.16 tff(73,plain,
% 1.86/2.16 ((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)))),
% 1.86/2.16 inference(tautology,[status(thm)],[])).
% 1.86/2.16 tff(74,plain,
% 1.86/2.16 (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)))),
% 1.86/2.16 inference(unit_resolution,[status(thm)],[73, 40])).
% 1.86/2.16 tff(75,plain,
% 1.86/2.16 ((~((~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))))))),
% 1.86/2.16 inference(tautology,[status(thm)],[])).
% 1.86/2.16 tff(76,plain,
% 1.86/2.16 ((~((~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))))))),
% 1.86/2.16 inference(unit_resolution,[status(thm)],[75, 74])).
% 1.86/2.16 tff(77,plain,
% 1.86/2.16 (~((~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)))))),
% 1.86/2.16 inference(unit_resolution,[status(thm)],[76, 72])).
% 1.86/2.16 tff(78,plain,
% 1.86/2.16 (((~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)),
% 1.86/2.17 inference(tautology,[status(thm)],[])).
% 1.86/2.17 tff(79,plain,
% 1.86/2.17 (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)),
% 1.86/2.17 inference(unit_resolution,[status(thm)],[78, 77])).
% 1.86/2.17 tff(80,plain,
% 1.86/2.17 (^[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)))))))))))),
% 1.86/2.17 inference(bind,[status(th)],[])).
% 1.86/2.17 tff(81,plain,
% 1.86/2.17 (![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))))))))))),
% 1.86/2.17 inference(quant_intro,[status(thm)],[80])).
% 1.86/2.17 tff(82,plain,
% 1.86/2.17 (^[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)))))))))),
% 1.86/2.17 inference(bind,[status(th)],[])).
% 1.86/2.17 tff(83,plain,
% 1.86/2.17 (![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))))))))),
% 1.86/2.17 inference(quant_intro,[status(thm)],[82])).
% 1.86/2.17 tff(84,plain,
% 1.86/2.17 (^[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)))))))))),
% 1.86/2.17 inference(bind,[status(th)],[])).
% 1.86/2.17 tff(85,plain,
% 1.86/2.17 (![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))))))))),
% 1.86/2.17 inference(quant_intro,[status(thm)],[84])).
% 1.86/2.17 tff(86,plain,
% 1.86/2.17 (![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))))))))),
% 1.86/2.17 inference(transitivity,[status(thm)],[85, 83])).
% 1.86/2.17 tff(87,plain,
% 1.86/2.17 (^[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))))))))))),
% 1.96/2.17 inference(bind,[status(th)],[])).
% 1.96/2.17 tff(88,plain,
% 1.96/2.17 (![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))))))))),
% 1.96/2.17 inference(quant_intro,[status(thm)],[87])).
% 1.96/2.17 tff(89,plain,
% 1.96/2.17 (^[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)))))))),
% 1.96/2.18 inference(bind,[status(th)],[])).
% 1.96/2.18 tff(90,plain,
% 1.96/2.18 (![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))))))),
% 1.96/2.18 inference(quant_intro,[status(thm)],[89])).
% 1.96/2.18 tff(91,plain,
% 1.96/2.18 (![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))))))),
% 1.96/2.18 inference(rewrite,[status(thm)],[])).
% 1.96/2.18 tff(92,plain,
% 1.96/2.18 (^[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)))))))),
% 1.96/2.18 inference(bind,[status(th)],[])).
% 1.96/2.18 tff(93,plain,
% 1.96/2.18 (![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))))))),
% 1.96/2.18 inference(quant_intro,[status(thm)],[92])).
% 1.96/2.18 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')).
% 1.96/2.18 tff(95,plain,
% 1.96/2.18 (![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))))))),
% 1.96/2.18 inference(modus_ponens,[status(thm)],[94, 93])).
% 1.96/2.18 tff(96,plain,
% 1.96/2.18 (![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))))))),
% 1.96/2.18 inference(modus_ponens,[status(thm)],[95, 91])).
% 1.96/2.18 tff(97,plain,(
% 1.96/2.18 ![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))))))))),
% 1.96/2.18 inference(skolemize,[status(sab)],[96])).
% 1.96/2.18 tff(98,plain,
% 1.96/2.18 (![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))))))),
% 1.96/2.18 inference(modus_ponens,[status(thm)],[97, 90])).
% 1.96/2.18 tff(99,plain,
% 1.96/2.18 (![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))))))))),
% 1.96/2.18 inference(modus_ponens,[status(thm)],[98, 88])).
% 1.96/2.18 tff(100,plain,
% 1.96/2.18 (![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))))))))),
% 1.96/2.18 inference(modus_ponens,[status(thm)],[99, 86])).
% 1.96/2.18 tff(101,plain,
% 1.96/2.18 (![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))))))))))),
% 1.96/2.18 inference(modus_ponens,[status(thm)],[100, 81])).
% 1.96/2.18 tff(102,plain,
% 1.96/2.18 ((~![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))))))))))),
% 1.96/2.18 inference(quant_inst,[status(thm)],[])).
% 1.96/2.18 tff(103,plain,
% 1.96/2.18 (~((~((~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)))))))))),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[102, 101])).
% 1.96/2.18 tff(104,plain,
% 1.96/2.18 (((~((~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)))))))),
% 1.96/2.19 inference(tautology,[status(thm)],[])).
% 1.96/2.19 tff(105,plain,
% 1.96/2.19 ((~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))))))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[104, 103])).
% 1.96/2.19 tff(106,plain,
% 1.96/2.19 (maps(F!46, A!44, B!43) & maps(G!45, B!43, C!42) & increasing(F!46, A!44, R!41, B!43, S!40) & increasing(G!45, B!43, S!40, C!42, T!39)),
% 1.96/2.19 inference(or_elim,[status(thm)],[36])).
% 1.96/2.19 tff(107,plain,
% 1.96/2.19 (maps(G!45, B!43, C!42)),
% 1.96/2.19 inference(and_elim,[status(thm)],[106])).
% 1.96/2.19 tff(108,plain,
% 1.96/2.19 ((~((~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))))))),
% 1.96/2.19 inference(tautology,[status(thm)],[])).
% 1.96/2.19 tff(109,plain,
% 1.96/2.19 ((~((~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))))))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[108, 107])).
% 1.96/2.19 tff(110,plain,
% 1.96/2.19 (~((~![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)))))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[109, 105])).
% 1.96/2.19 tff(111,plain,
% 1.96/2.19 (((~![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))))))),
% 1.96/2.19 inference(tautology,[status(thm)],[])).
% 1.96/2.19 tff(112,plain,
% 1.96/2.19 (![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))))))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[111, 110])).
% 1.96/2.19 tff(113,plain,
% 1.96/2.19 (((~![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))))))),
% 1.97/2.19 inference(rewrite,[status(thm)],[])).
% 1.97/2.19 tff(114,plain,
% 1.97/2.19 ((~![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))))))),
% 1.97/2.19 inference(quant_inst,[status(thm)],[])).
% 1.97/2.19 tff(115,plain,
% 1.97/2.19 ((~![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)))))),
% 1.97/2.19 inference(modus_ponens,[status(thm)],[114, 113])).
% 1.97/2.19 tff(116,plain,
% 1.97/2.19 (~((~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))))),
% 1.97/2.20 inference(unit_resolution,[status(thm)],[115, 112, 79])).
% 1.97/2.20 tff(117,plain,
% 1.97/2.20 (((~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))),
% 1.97/2.20 inference(tautology,[status(thm)],[])).
% 1.97/2.20 tff(118,plain,
% 1.97/2.20 (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))),
% 1.97/2.20 inference(unit_resolution,[status(thm)],[117, 116])).
% 1.97/2.20 tff(119,plain,
% 1.97/2.20 (((~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)),
% 1.97/2.20 inference(tautology,[status(thm)],[])).
% 1.97/2.20 tff(120,plain,
% 1.97/2.20 (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)),
% 1.97/2.20 inference(unit_resolution,[status(thm)],[119, 116])).
% 1.97/2.20 tff(121,plain,
% 1.97/2.20 (((~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)))),
% 1.97/2.21 inference(tautology,[status(thm)],[])).
% 1.97/2.21 tff(122,plain,
% 1.97/2.21 (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)))),
% 1.97/2.21 inference(unit_resolution,[status(thm)],[121, 77])).
% 1.97/2.21 tff(123,plain,
% 1.97/2.21 (((~![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)))),
% 1.97/2.21 inference(tautology,[status(thm)],[])).
% 1.97/2.21 tff(124,plain,
% 1.97/2.21 (![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)))),
% 1.97/2.21 inference(unit_resolution,[status(thm)],[123, 110])).
% 1.97/2.21 tff(125,plain,
% 1.97/2.21 (((~![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))))),
% 1.97/2.21 inference(rewrite,[status(thm)],[])).
% 1.97/2.21 tff(126,plain,
% 1.97/2.21 (((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))))),
% 2.00/2.22 inference(rewrite,[status(thm)],[])).
% 2.00/2.22 tff(127,plain,
% 2.00/2.22 (((~![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)))))),
% 2.01/2.24 inference(monotonicity,[status(thm)],[126])).
% 2.01/2.24 tff(128,plain,
% 2.01/2.24 (((~![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))))),
% 2.01/2.25 inference(transitivity,[status(thm)],[127, 125])).
% 2.01/2.25 tff(129,plain,
% 2.01/2.25 ((~![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)))),
% 2.01/2.25 inference(quant_inst,[status(thm)],[])).
% 2.01/2.25 tff(130,plain,
% 2.01/2.25 ((~![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)))),
% 2.01/2.25 inference(modus_ponens,[status(thm)],[129, 128])).
% 2.01/2.25 tff(131,plain,
% 2.01/2.25 (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))),
% 2.01/2.25 inference(unit_resolution,[status(thm)],[130, 124, 42, 79, 122, 120, 118])).
% 2.01/2.25 tff(132,plain,
% 2.01/2.25 ((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)),
% 2.01/2.25 inference(tautology,[status(thm)],[])).
% 2.01/2.25 tff(133,plain,
% 2.01/2.25 (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)),
% 2.01/2.25 inference(unit_resolution,[status(thm)],[132, 40])).
% 2.01/2.25 tff(134,plain,
% 2.01/2.25 ((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)),
% 2.01/2.25 inference(tautology,[status(thm)],[])).
% 2.01/2.25 tff(135,plain,
% 2.01/2.25 (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)),
% 2.01/2.25 inference(unit_resolution,[status(thm)],[134, 40])).
% 2.01/2.25 tff(136,plain,
% 2.01/2.25 (((~![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))))))))))),
% 2.01/2.26 inference(rewrite,[status(thm)],[])).
% 2.01/2.26 tff(137,plain,
% 2.01/2.26 (((~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))))))))))),
% 2.01/2.27 inference(rewrite,[status(thm)],[])).
% 2.01/2.27 tff(138,plain,
% 2.01/2.27 ((~((~((~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)))))))))),
% 2.01/2.27 inference(rewrite,[status(thm)],[])).
% 2.01/2.27 tff(139,plain,
% 2.01/2.27 (((~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))))))))))),
% 2.01/2.28 inference(monotonicity,[status(thm)],[138])).
% 2.01/2.28 tff(140,plain,
% 2.01/2.28 (((~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))))))))))),
% 2.01/2.28 inference(transitivity,[status(thm)],[139, 137])).
% 2.01/2.28 tff(141,plain,
% 2.01/2.28 (((~![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)))))))))))),
% 2.01/2.29 inference(monotonicity,[status(thm)],[140])).
% 2.01/2.29 tff(142,plain,
% 2.01/2.29 (((~![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))))))))))),
% 2.01/2.29 inference(transitivity,[status(thm)],[141, 136])).
% 2.01/2.29 tff(143,plain,
% 2.01/2.29 ((~![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))))))))))),
% 2.01/2.30 inference(quant_inst,[status(thm)],[])).
% 2.01/2.30 tff(144,plain,
% 2.01/2.30 ((~![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)))))))))),
% 2.01/2.30 inference(modus_ponens,[status(thm)],[143, 142])).
% 2.01/2.30 tff(145,plain,
% 2.01/2.30 (~((~((~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))))))))),
% 2.01/2.31 inference(unit_resolution,[status(thm)],[144, 60, 135, 133])).
% 2.01/2.31 tff(146,plain,
% 2.01/2.31 (((~((~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)))))))),
% 2.01/2.31 inference(tautology,[status(thm)],[])).
% 2.01/2.31 tff(147,plain,
% 2.01/2.31 ((~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))))))),
% 2.01/2.31 inference(unit_resolution,[status(thm)],[146, 145])).
% 2.01/2.31 tff(148,plain,
% 2.01/2.31 ((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)))),
% 2.01/2.31 inference(tautology,[status(thm)],[])).
% 2.01/2.31 tff(149,plain,
% 2.01/2.31 (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)))),
% 2.01/2.31 inference(unit_resolution,[status(thm)],[148, 40])).
% 2.01/2.31 tff(150,plain,
% 2.01/2.31 ((~((~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))))))),
% 2.01/2.32 inference(tautology,[status(thm)],[])).
% 2.01/2.32 tff(151,plain,
% 2.01/2.32 ((~((~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))))))),
% 2.01/2.32 inference(unit_resolution,[status(thm)],[150, 149])).
% 2.01/2.32 tff(152,plain,
% 2.01/2.32 (~((~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)))))),
% 2.01/2.32 inference(unit_resolution,[status(thm)],[151, 147])).
% 2.01/2.32 tff(153,plain,
% 2.01/2.32 (((~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)),
% 2.09/2.33 inference(tautology,[status(thm)],[])).
% 2.09/2.33 tff(154,plain,
% 2.09/2.33 (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)),
% 2.09/2.33 inference(unit_resolution,[status(thm)],[153, 152])).
% 2.09/2.33 tff(155,plain,
% 2.09/2.33 (((~![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))))))),
% 2.09/2.33 inference(rewrite,[status(thm)],[])).
% 2.09/2.33 tff(156,plain,
% 2.09/2.33 ((~![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))))))),
% 2.09/2.33 inference(quant_inst,[status(thm)],[])).
% 2.09/2.33 tff(157,plain,
% 2.09/2.33 ((~![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)))))),
% 2.09/2.33 inference(modus_ponens,[status(thm)],[156, 155])).
% 2.09/2.33 tff(158,plain,
% 2.09/2.33 (~((~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))))),
% 2.09/2.33 inference(unit_resolution,[status(thm)],[157, 112, 154])).
% 2.09/2.33 tff(159,plain,
% 2.09/2.33 (((~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))),
% 2.09/2.33 inference(tautology,[status(thm)],[])).
% 2.09/2.33 tff(160,plain,
% 2.09/2.33 (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))),
% 2.09/2.33 inference(unit_resolution,[status(thm)],[159, 158])).
% 2.09/2.33 tff(161,plain,
% 2.09/2.33 (((~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)),
% 2.09/2.34 inference(tautology,[status(thm)],[])).
% 2.09/2.34 tff(162,plain,
% 2.09/2.34 (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)),
% 2.09/2.34 inference(unit_resolution,[status(thm)],[161, 158])).
% 2.09/2.34 tff(163,plain,
% 2.09/2.34 (((~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)))),
% 2.09/2.34 inference(tautology,[status(thm)],[])).
% 2.09/2.34 tff(164,plain,
% 2.09/2.34 (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)))),
% 2.09/2.34 inference(unit_resolution,[status(thm)],[163, 152])).
% 2.09/2.34 tff(165,plain,
% 2.09/2.34 (((~![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))))),
% 2.09/2.35 inference(rewrite,[status(thm)],[])).
% 2.09/2.35 tff(166,plain,
% 2.09/2.35 (((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))))),
% 2.09/2.35 inference(rewrite,[status(thm)],[])).
% 2.09/2.35 tff(167,plain,
% 2.09/2.35 (((~![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)))))),
% 2.09/2.36 inference(monotonicity,[status(thm)],[166])).
% 2.09/2.36 tff(168,plain,
% 2.09/2.36 (((~![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))))),
% 2.09/2.36 inference(transitivity,[status(thm)],[167, 165])).
% 2.09/2.36 tff(169,plain,
% 2.09/2.36 ((~![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)))),
% 2.09/2.36 inference(quant_inst,[status(thm)],[])).
% 2.09/2.36 tff(170,plain,
% 2.09/2.36 ((~![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)))),
% 2.09/2.37 inference(modus_ponens,[status(thm)],[169, 168])).
% 2.09/2.37 tff(171,plain,
% 2.09/2.37 (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))),
% 2.09/2.37 inference(unit_resolution,[status(thm)],[170, 124, 133, 154, 164, 162, 160])).
% 2.09/2.37 tff(172,plain,
% 2.09/2.37 (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)))),
% 2.09/2.37 inference(monotonicity,[status(thm)],[171, 131])).
% 2.09/2.37 tff(173,plain,
% 2.09/2.37 (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))),
% 2.09/2.37 inference(symmetry,[status(thm)],[172])).
% 2.09/2.37 tff(174,plain,
% 2.09/2.37 ((~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)))),
% 2.09/2.37 inference(monotonicity,[status(thm)],[173])).
% 2.09/2.37 tff(175,plain,
% 2.09/2.37 ((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))))),
% 2.09/2.38 inference(tautology,[status(thm)],[])).
% 2.09/2.38 tff(176,plain,
% 2.09/2.38 (~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)))),
% 2.09/2.38 inference(unit_resolution,[status(thm)],[175, 40])).
% 2.09/2.38 tff(177,plain,
% 2.09/2.38 (~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))),
% 2.09/2.38 inference(modus_ponens,[status(thm)],[176, 174])).
% 2.09/2.38 tff(178,plain,
% 2.09/2.38 (((~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))),
% 2.09/2.38 inference(tautology,[status(thm)],[])).
% 2.09/2.38 tff(179,plain,
% 2.09/2.38 (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))),
% 2.09/2.38 inference(unit_resolution,[status(thm)],[178, 152])).
% 2.09/2.38 tff(180,plain,
% 2.09/2.38 (((~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))),
% 2.09/2.38 inference(tautology,[status(thm)],[])).
% 2.09/2.38 tff(181,plain,
% 2.09/2.38 (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))),
% 2.09/2.38 inference(unit_resolution,[status(thm)],[180, 77])).
% 2.09/2.38 tff(182,plain,
% 2.09/2.38 ((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)))),
% 2.09/2.38 inference(tautology,[status(thm)],[])).
% 2.09/2.38 tff(183,plain,
% 2.09/2.38 (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)))),
% 2.09/2.38 inference(unit_resolution,[status(thm)],[182, 40])).
% 2.09/2.38 tff(184,plain,
% 2.09/2.38 (((~![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(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)) | apply(S!40, Y1, Y2) | (~member(X1, A!44)) | (~member(X2, A!44)) | (~apply(R!41, X1, X2)) | (~apply(F!46, X1, Y1)) | (~apply(F!46, X2, Y2))))) | (~(increasing(F!46, A!44, R!41, B!43, S!40) | (~(apply(S!40, tptp_fun_Y1_29(S!40, B!43, R!41, A!44, F!46), tptp_fun_Y2_27(S!40, B!43, R!41, A!44, F!46)) | (~member(tptp_fun_X1_30(S!40, B!43, R!41, A!44, F!46), A!44)) | (~member(tptp_fun_Y1_29(S!40, B!43, R!41, A!44, F!46), B!43)) | (~member(tptp_fun_X2_28(S!40, B!43, R!41, A!44, F!46), A!44)) | (~member(tptp_fun_Y2_27(S!40, B!43, R!41, A!44, F!46), B!43)) | (~apply(R!41, tptp_fun_X1_30(S!40, B!43, R!41, A!44, F!46), tptp_fun_X2_28(S!40, B!43, R!41, A!44, F!46))) | (~apply(F!46, tptp_fun_X1_30(S!40, B!43, R!41, A!44, F!46), tptp_fun_Y1_29(S!40, B!43, R!41, A!44, F!46))) | (~apply(F!46, tptp_fun_X2_28(S!40, B!43, R!41, A!44, F!46), tptp_fun_Y2_27(S!40, B!43, R!41, A!44, F!46)))))))))) <=> ((~![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(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)) | apply(S!40, Y1, Y2) | (~member(X1, A!44)) | (~member(X2, A!44)) | (~apply(R!41, X1, X2)) | (~apply(F!46, X1, Y1)) | (~apply(F!46, X2, Y2))))) | (~(increasing(F!46, A!44, R!41, B!43, S!40) | (~(apply(S!40, tptp_fun_Y1_29(S!40, B!43, R!41, A!44, F!46), tptp_fun_Y2_27(S!40, B!43, R!41, A!44, F!46)) | (~member(tptp_fun_X1_30(S!40, B!43, R!41, A!44, F!46), A!44)) | (~member(tptp_fun_Y1_29(S!40, B!43, R!41, A!44, F!46), B!43)) | (~member(tptp_fun_X2_28(S!40, B!43, R!41, A!44, F!46), A!44)) | (~member(tptp_fun_Y2_27(S!40, B!43, R!41, A!44, F!46), B!43)) | (~apply(R!41, tptp_fun_X1_30(S!40, B!43, R!41, A!44, F!46), tptp_fun_X2_28(S!40, B!43, R!41, A!44, F!46))) | (~apply(F!46, tptp_fun_X1_30(S!40, B!43, R!41, A!44, F!46), tptp_fun_Y1_29(S!40, B!43, R!41, A!44, F!46))) | (~apply(F!46, tptp_fun_X2_28(S!40, B!43, R!41, A!44, F!46), tptp_fun_Y2_27(S!40, B!43, R!41, A!44, F!46))))))))))),
% 2.09/2.39 inference(rewrite,[status(thm)],[])).
% 2.09/2.39 tff(185,plain,
% 2.09/2.39 ((~((~((~increasing(F!46, A!44, R!41, B!43, S!40)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(S!40, Y1, Y2) | (~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))))) | (~(increasing(F!46, A!44, R!41, B!43, S!40) | (~(apply(S!40, tptp_fun_Y1_29(S!40, B!43, R!41, A!44, F!46), tptp_fun_Y2_27(S!40, B!43, R!41, A!44, F!46)) | (~member(tptp_fun_X1_30(S!40, B!43, R!41, A!44, F!46), A!44)) | (~member(tptp_fun_Y1_29(S!40, B!43, R!41, A!44, F!46), B!43)) | (~member(tptp_fun_X2_28(S!40, B!43, R!41, A!44, F!46), A!44)) | (~member(tptp_fun_Y2_27(S!40, B!43, R!41, A!44, F!46), B!43)) | (~apply(R!41, tptp_fun_X1_30(S!40, B!43, R!41, A!44, F!46), tptp_fun_X2_28(S!40, B!43, R!41, A!44, F!46))) | (~apply(F!46, tptp_fun_X1_30(S!40, B!43, R!41, A!44, F!46), tptp_fun_Y1_29(S!40, B!43, R!41, A!44, F!46))) | (~apply(F!46, tptp_fun_X2_28(S!40, B!43, R!41, A!44, F!46), tptp_fun_Y2_27(S!40, B!43, R!41, A!44, F!46))))))))) <=> (~((~((~increasing(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)) | apply(S!40, Y1, Y2) | (~member(X1, A!44)) | (~member(X2, A!44)) | (~apply(R!41, X1, X2)) | (~apply(F!46, X1, Y1)) | (~apply(F!46, X2, Y2))))) | (~(increasing(F!46, A!44, R!41, B!43, S!40) | (~(apply(S!40, tptp_fun_Y1_29(S!40, B!43, R!41, A!44, F!46), tptp_fun_Y2_27(S!40, B!43, R!41, A!44, F!46)) | (~member(tptp_fun_X1_30(S!40, B!43, R!41, A!44, F!46), A!44)) | (~member(tptp_fun_Y1_29(S!40, B!43, R!41, A!44, F!46), B!43)) | (~member(tptp_fun_X2_28(S!40, B!43, R!41, A!44, F!46), A!44)) | (~member(tptp_fun_Y2_27(S!40, B!43, R!41, A!44, F!46), B!43)) | (~apply(R!41, tptp_fun_X1_30(S!40, B!43, R!41, A!44, F!46), tptp_fun_X2_28(S!40, B!43, R!41, A!44, F!46))) | (~apply(F!46, tptp_fun_X1_30(S!40, B!43, R!41, A!44, F!46), tptp_fun_Y1_29(S!40, B!43, R!41, A!44, F!46))) | (~apply(F!46, tptp_fun_X2_28(S!40, B!43, R!41, A!44, F!46), tptp_fun_Y2_27(S!40, B!43, R!41, A!44, F!46)))))))))),
% 2.09/2.39 inference(rewrite,[status(thm)],[])).
% 2.09/2.39 tff(186,plain,
% 2.09/2.39 (((~![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(F!46, A!44, R!41, B!43, S!40)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(S!40, Y1, Y2) | (~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))))) | (~(increasing(F!46, A!44, R!41, B!43, S!40) | (~(apply(S!40, tptp_fun_Y1_29(S!40, B!43, R!41, A!44, F!46), tptp_fun_Y2_27(S!40, B!43, R!41, A!44, F!46)) | (~member(tptp_fun_X1_30(S!40, B!43, R!41, A!44, F!46), A!44)) | (~member(tptp_fun_Y1_29(S!40, B!43, R!41, A!44, F!46), B!43)) | (~member(tptp_fun_X2_28(S!40, B!43, R!41, A!44, F!46), A!44)) | (~member(tptp_fun_Y2_27(S!40, B!43, R!41, A!44, F!46), B!43)) | (~apply(R!41, tptp_fun_X1_30(S!40, B!43, R!41, A!44, F!46), tptp_fun_X2_28(S!40, B!43, R!41, A!44, F!46))) | (~apply(F!46, tptp_fun_X1_30(S!40, B!43, R!41, A!44, F!46), tptp_fun_Y1_29(S!40, B!43, R!41, A!44, F!46))) | (~apply(F!46, tptp_fun_X2_28(S!40, B!43, R!41, A!44, F!46), tptp_fun_Y2_27(S!40, B!43, R!41, A!44, F!46)))))))))) <=> ((~![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(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)) | apply(S!40, Y1, Y2) | (~member(X1, A!44)) | (~member(X2, A!44)) | (~apply(R!41, X1, X2)) | (~apply(F!46, X1, Y1)) | (~apply(F!46, X2, Y2))))) | (~(increasing(F!46, A!44, R!41, B!43, S!40) | (~(apply(S!40, tptp_fun_Y1_29(S!40, B!43, R!41, A!44, F!46), tptp_fun_Y2_27(S!40, B!43, R!41, A!44, F!46)) | (~member(tptp_fun_X1_30(S!40, B!43, R!41, A!44, F!46), A!44)) | (~member(tptp_fun_Y1_29(S!40, B!43, R!41, A!44, F!46), B!43)) | (~member(tptp_fun_X2_28(S!40, B!43, R!41, A!44, F!46), A!44)) | (~member(tptp_fun_Y2_27(S!40, B!43, R!41, A!44, F!46), B!43)) | (~apply(R!41, tptp_fun_X1_30(S!40, B!43, R!41, A!44, F!46), tptp_fun_X2_28(S!40, B!43, R!41, A!44, F!46))) | (~apply(F!46, tptp_fun_X1_30(S!40, B!43, R!41, A!44, F!46), tptp_fun_Y1_29(S!40, B!43, R!41, A!44, F!46))) | (~apply(F!46, tptp_fun_X2_28(S!40, B!43, R!41, A!44, F!46), tptp_fun_Y2_27(S!40, B!43, R!41, A!44, F!46))))))))))),
% 2.09/2.39 inference(monotonicity,[status(thm)],[185])).
% 2.09/2.39 tff(187,plain,
% 2.09/2.39 (((~![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(F!46, A!44, R!41, B!43, S!40)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(S!40, Y1, Y2) | (~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))))) | (~(increasing(F!46, A!44, R!41, B!43, S!40) | (~(apply(S!40, tptp_fun_Y1_29(S!40, B!43, R!41, A!44, F!46), tptp_fun_Y2_27(S!40, B!43, R!41, A!44, F!46)) | (~member(tptp_fun_X1_30(S!40, B!43, R!41, A!44, F!46), A!44)) | (~member(tptp_fun_Y1_29(S!40, B!43, R!41, A!44, F!46), B!43)) | (~member(tptp_fun_X2_28(S!40, B!43, R!41, A!44, F!46), A!44)) | (~member(tptp_fun_Y2_27(S!40, B!43, R!41, A!44, F!46), B!43)) | (~apply(R!41, tptp_fun_X1_30(S!40, B!43, R!41, A!44, F!46), tptp_fun_X2_28(S!40, B!43, R!41, A!44, F!46))) | (~apply(F!46, tptp_fun_X1_30(S!40, B!43, R!41, A!44, F!46), tptp_fun_Y1_29(S!40, B!43, R!41, A!44, F!46))) | (~apply(F!46, tptp_fun_X2_28(S!40, B!43, R!41, A!44, F!46), tptp_fun_Y2_27(S!40, B!43, R!41, A!44, F!46)))))))))) <=> ((~![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(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)) | apply(S!40, Y1, Y2) | (~member(X1, A!44)) | (~member(X2, A!44)) | (~apply(R!41, X1, X2)) | (~apply(F!46, X1, Y1)) | (~apply(F!46, X2, Y2))))) | (~(increasing(F!46, A!44, R!41, B!43, S!40) | (~(apply(S!40, tptp_fun_Y1_29(S!40, B!43, R!41, A!44, F!46), tptp_fun_Y2_27(S!40, B!43, R!41, A!44, F!46)) | (~member(tptp_fun_X1_30(S!40, B!43, R!41, A!44, F!46), A!44)) | (~member(tptp_fun_Y1_29(S!40, B!43, R!41, A!44, F!46), B!43)) | (~member(tptp_fun_X2_28(S!40, B!43, R!41, A!44, F!46), A!44)) | (~member(tptp_fun_Y2_27(S!40, B!43, R!41, A!44, F!46), B!43)) | (~apply(R!41, tptp_fun_X1_30(S!40, B!43, R!41, A!44, F!46), tptp_fun_X2_28(S!40, B!43, R!41, A!44, F!46))) | (~apply(F!46, tptp_fun_X1_30(S!40, B!43, R!41, A!44, F!46), tptp_fun_Y1_29(S!40, B!43, R!41, A!44, F!46))) | (~apply(F!46, tptp_fun_X2_28(S!40, B!43, R!41, A!44, F!46), tptp_fun_Y2_27(S!40, B!43, R!41, A!44, F!46))))))))))),
% 2.09/2.40 inference(transitivity,[status(thm)],[186, 184])).
% 2.09/2.40 tff(188,plain,
% 2.09/2.40 ((~![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(F!46, A!44, R!41, B!43, S!40)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(S!40, Y1, Y2) | (~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))))) | (~(increasing(F!46, A!44, R!41, B!43, S!40) | (~(apply(S!40, tptp_fun_Y1_29(S!40, B!43, R!41, A!44, F!46), tptp_fun_Y2_27(S!40, B!43, R!41, A!44, F!46)) | (~member(tptp_fun_X1_30(S!40, B!43, R!41, A!44, F!46), A!44)) | (~member(tptp_fun_Y1_29(S!40, B!43, R!41, A!44, F!46), B!43)) | (~member(tptp_fun_X2_28(S!40, B!43, R!41, A!44, F!46), A!44)) | (~member(tptp_fun_Y2_27(S!40, B!43, R!41, A!44, F!46), B!43)) | (~apply(R!41, tptp_fun_X1_30(S!40, B!43, R!41, A!44, F!46), tptp_fun_X2_28(S!40, B!43, R!41, A!44, F!46))) | (~apply(F!46, tptp_fun_X1_30(S!40, B!43, R!41, A!44, F!46), tptp_fun_Y1_29(S!40, B!43, R!41, A!44, F!46))) | (~apply(F!46, tptp_fun_X2_28(S!40, B!43, R!41, A!44, F!46), tptp_fun_Y2_27(S!40, B!43, R!41, A!44, F!46)))))))))),
% 2.17/2.40 inference(quant_inst,[status(thm)],[])).
% 2.17/2.40 tff(189,plain,
% 2.17/2.40 ((~![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(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)) | apply(S!40, Y1, Y2) | (~member(X1, A!44)) | (~member(X2, A!44)) | (~apply(R!41, X1, X2)) | (~apply(F!46, X1, Y1)) | (~apply(F!46, X2, Y2))))) | (~(increasing(F!46, A!44, R!41, B!43, S!40) | (~(apply(S!40, tptp_fun_Y1_29(S!40, B!43, R!41, A!44, F!46), tptp_fun_Y2_27(S!40, B!43, R!41, A!44, F!46)) | (~member(tptp_fun_X1_30(S!40, B!43, R!41, A!44, F!46), A!44)) | (~member(tptp_fun_Y1_29(S!40, B!43, R!41, A!44, F!46), B!43)) | (~member(tptp_fun_X2_28(S!40, B!43, R!41, A!44, F!46), A!44)) | (~member(tptp_fun_Y2_27(S!40, B!43, R!41, A!44, F!46), B!43)) | (~apply(R!41, tptp_fun_X1_30(S!40, B!43, R!41, A!44, F!46), tptp_fun_X2_28(S!40, B!43, R!41, A!44, F!46))) | (~apply(F!46, tptp_fun_X1_30(S!40, B!43, R!41, A!44, F!46), tptp_fun_Y1_29(S!40, B!43, R!41, A!44, F!46))) | (~apply(F!46, tptp_fun_X2_28(S!40, B!43, R!41, A!44, F!46), tptp_fun_Y2_27(S!40, B!43, R!41, A!44, F!46)))))))))),
% 2.17/2.40 inference(modus_ponens,[status(thm)],[188, 187])).
% 2.17/2.40 tff(190,plain,
% 2.17/2.40 (~((~((~increasing(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)) | apply(S!40, Y1, Y2) | (~member(X1, A!44)) | (~member(X2, A!44)) | (~apply(R!41, X1, X2)) | (~apply(F!46, X1, Y1)) | (~apply(F!46, X2, Y2))))) | (~(increasing(F!46, A!44, R!41, B!43, S!40) | (~(apply(S!40, tptp_fun_Y1_29(S!40, B!43, R!41, A!44, F!46), tptp_fun_Y2_27(S!40, B!43, R!41, A!44, F!46)) | (~member(tptp_fun_X1_30(S!40, B!43, R!41, A!44, F!46), A!44)) | (~member(tptp_fun_Y1_29(S!40, B!43, R!41, A!44, F!46), B!43)) | (~member(tptp_fun_X2_28(S!40, B!43, R!41, A!44, F!46), A!44)) | (~member(tptp_fun_Y2_27(S!40, B!43, R!41, A!44, F!46), B!43)) | (~apply(R!41, tptp_fun_X1_30(S!40, B!43, R!41, A!44, F!46), tptp_fun_X2_28(S!40, B!43, R!41, A!44, F!46))) | (~apply(F!46, tptp_fun_X1_30(S!40, B!43, R!41, A!44, F!46), tptp_fun_Y1_29(S!40, B!43, R!41, A!44, F!46))) | (~apply(F!46, tptp_fun_X2_28(S!40, B!43, R!41, A!44, F!46), tptp_fun_Y2_27(S!40, B!43, R!41, A!44, F!46))))))))),
% 2.17/2.40 inference(unit_resolution,[status(thm)],[189, 16])).
% 2.17/2.40 tff(191,plain,
% 2.17/2.40 (((~((~increasing(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)) | apply(S!40, Y1, Y2) | (~member(X1, A!44)) | (~member(X2, A!44)) | (~apply(R!41, X1, X2)) | (~apply(F!46, X1, Y1)) | (~apply(F!46, X2, Y2))))) | (~(increasing(F!46, A!44, R!41, B!43, S!40) | (~(apply(S!40, tptp_fun_Y1_29(S!40, B!43, R!41, A!44, F!46), tptp_fun_Y2_27(S!40, B!43, R!41, A!44, F!46)) | (~member(tptp_fun_X1_30(S!40, B!43, R!41, A!44, F!46), A!44)) | (~member(tptp_fun_Y1_29(S!40, B!43, R!41, A!44, F!46), B!43)) | (~member(tptp_fun_X2_28(S!40, B!43, R!41, A!44, F!46), A!44)) | (~member(tptp_fun_Y2_27(S!40, B!43, R!41, A!44, F!46), B!43)) | (~apply(R!41, tptp_fun_X1_30(S!40, B!43, R!41, A!44, F!46), tptp_fun_X2_28(S!40, B!43, R!41, A!44, F!46))) | (~apply(F!46, tptp_fun_X1_30(S!40, B!43, R!41, A!44, F!46), tptp_fun_Y1_29(S!40, B!43, R!41, A!44, F!46))) | (~apply(F!46, tptp_fun_X2_28(S!40, B!43, R!41, A!44, F!46), tptp_fun_Y2_27(S!40, B!43, R!41, A!44, F!46)))))))) | ((~increasing(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)) | apply(S!40, Y1, Y2) | (~member(X1, A!44)) | (~member(X2, A!44)) | (~apply(R!41, X1, X2)) | (~apply(F!46, X1, Y1)) | (~apply(F!46, X2, Y2))))),
% 2.17/2.40 inference(tautology,[status(thm)],[])).
% 2.17/2.40 tff(192,plain,
% 2.17/2.40 ((~increasing(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)) | apply(S!40, Y1, Y2) | (~member(X1, A!44)) | (~member(X2, A!44)) | (~apply(R!41, X1, X2)) | (~apply(F!46, X1, Y1)) | (~apply(F!46, X2, Y2)))),
% 2.17/2.40 inference(unit_resolution,[status(thm)],[191, 190])).
% 2.17/2.40 tff(193,plain,
% 2.17/2.40 (increasing(F!46, A!44, R!41, B!43, S!40)),
% 2.17/2.40 inference(and_elim,[status(thm)],[106])).
% 2.17/2.40 tff(194,plain,
% 2.17/2.40 ((~((~increasing(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)) | apply(S!40, Y1, Y2) | (~member(X1, A!44)) | (~member(X2, A!44)) | (~apply(R!41, X1, X2)) | (~apply(F!46, X1, Y1)) | (~apply(F!46, X2, Y2))))) | (~increasing(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)) | apply(S!40, Y1, Y2) | (~member(X1, A!44)) | (~member(X2, A!44)) | (~apply(R!41, X1, X2)) | (~apply(F!46, X1, Y1)) | (~apply(F!46, X2, Y2)))),
% 2.17/2.40 inference(tautology,[status(thm)],[])).
% 2.17/2.40 tff(195,plain,
% 2.17/2.40 ((~((~increasing(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)) | apply(S!40, Y1, Y2) | (~member(X1, A!44)) | (~member(X2, A!44)) | (~apply(R!41, X1, X2)) | (~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)) | apply(S!40, Y1, Y2) | (~member(X1, A!44)) | (~member(X2, A!44)) | (~apply(R!41, X1, X2)) | (~apply(F!46, X1, Y1)) | (~apply(F!46, X2, Y2)))),
% 2.17/2.41 inference(unit_resolution,[status(thm)],[194, 193])).
% 2.17/2.41 tff(196,plain,
% 2.17/2.41 (![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!43)) | (~member(Y1, B!43)) | apply(S!40, Y1, Y2) | (~member(X1, A!44)) | (~member(X2, A!44)) | (~apply(R!41, X1, X2)) | (~apply(F!46, X1, Y1)) | (~apply(F!46, X2, Y2)))),
% 2.17/2.41 inference(unit_resolution,[status(thm)],[195, 192])).
% 2.17/2.41 tff(197,plain,
% 2.17/2.41 (((~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!43)) | (~member(Y1, B!43)) | apply(S!40, Y1, Y2) | (~member(X1, A!44)) | (~member(X2, A!44)) | (~apply(R!41, X1, X2)) | (~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_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_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)) | apply(S!40, Y1, Y2) | (~member(X1, A!44)) | (~member(X2, A!44)) | (~apply(R!41, X1, X2)) | (~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_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_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)))),
% 2.17/2.41 inference(rewrite,[status(thm)],[])).
% 2.17/2.41 tff(198,plain,
% 2.17/2.41 (((~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)) | apply(S!40, 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_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)))) | (~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_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_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)))),
% 2.17/2.42 inference(rewrite,[status(thm)],[])).
% 2.17/2.42 tff(199,plain,
% 2.17/2.42 (((~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!43)) | (~member(Y1, B!43)) | apply(S!40, Y1, Y2) | (~member(X1, A!44)) | (~member(X2, A!44)) | (~apply(R!41, X1, X2)) | (~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)) | apply(S!40, 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_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)))) | (~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)) | apply(S!40, Y1, Y2) | (~member(X1, A!44)) | (~member(X2, A!44)) | (~apply(R!41, X1, X2)) | (~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_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_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))))),
% 2.17/2.42 inference(monotonicity,[status(thm)],[198])).
% 2.17/2.42 tff(200,plain,
% 2.17/2.42 (((~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!43)) | (~member(Y1, B!43)) | apply(S!40, Y1, Y2) | (~member(X1, A!44)) | (~member(X2, A!44)) | (~apply(R!41, X1, X2)) | (~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)) | apply(S!40, 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_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)))) | (~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)) | apply(S!40, Y1, Y2) | (~member(X1, A!44)) | (~member(X2, A!44)) | (~apply(R!41, X1, X2)) | (~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_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_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)))),
% 2.17/2.44 inference(transitivity,[status(thm)],[199, 197])).
% 2.17/2.44 tff(201,plain,
% 2.17/2.44 ((~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!43)) | (~member(Y1, B!43)) | apply(S!40, Y1, Y2) | (~member(X1, A!44)) | (~member(X2, A!44)) | (~apply(R!41, X1, X2)) | (~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)) | apply(S!40, 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_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)))) | (~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))))),
% 2.17/2.44 inference(quant_inst,[status(thm)],[])).
% 2.17/2.44 tff(202,plain,
% 2.17/2.44 ((~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!43)) | (~member(Y1, B!43)) | apply(S!40, Y1, Y2) | (~member(X1, A!44)) | (~member(X2, A!44)) | (~apply(R!41, X1, X2)) | (~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_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_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))),
% 2.17/2.44 inference(modus_ponens,[status(thm)],[201, 200])).
% 2.17/2.44 tff(203,plain,
% 2.17/2.44 (apply(S!40, 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_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))),
% 2.17/2.44 inference(unit_resolution,[status(thm)],[202, 196, 135, 44, 183, 79, 181, 154, 179])).
% 2.17/2.44 tff(204,plain,
% 2.17/2.44 (((~![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(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)) | apply(T!39, Y1, Y2) | (~member(X1, B!43)) | (~member(Y1, C!42)) | (~apply(S!40, X1, X2)) | (~apply(G!45, X1, Y1)) | (~apply(G!45, X2, Y2))))) | (~(increasing(G!45, B!43, S!40, C!42, T!39) | (~(apply(T!39, tptp_fun_Y1_29(T!39, C!42, S!40, B!43, G!45), tptp_fun_Y2_27(T!39, C!42, S!40, B!43, G!45)) | (~member(tptp_fun_X1_30(T!39, C!42, S!40, B!43, G!45), B!43)) | (~member(tptp_fun_Y1_29(T!39, C!42, S!40, B!43, G!45), C!42)) | (~member(tptp_fun_X2_28(T!39, C!42, S!40, B!43, G!45), B!43)) | (~member(tptp_fun_Y2_27(T!39, C!42, S!40, B!43, G!45), C!42)) | (~apply(S!40, tptp_fun_X1_30(T!39, C!42, S!40, B!43, G!45), tptp_fun_X2_28(T!39, C!42, S!40, B!43, G!45))) | (~apply(G!45, tptp_fun_X1_30(T!39, C!42, S!40, B!43, G!45), tptp_fun_Y1_29(T!39, C!42, S!40, B!43, G!45))) | (~apply(G!45, tptp_fun_X2_28(T!39, C!42, S!40, B!43, G!45), tptp_fun_Y2_27(T!39, C!42, S!40, B!43, G!45)))))))))) <=> ((~![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(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)) | apply(T!39, Y1, Y2) | (~member(X1, B!43)) | (~member(Y1, C!42)) | (~apply(S!40, X1, X2)) | (~apply(G!45, X1, Y1)) | (~apply(G!45, X2, Y2))))) | (~(increasing(G!45, B!43, S!40, C!42, T!39) | (~(apply(T!39, tptp_fun_Y1_29(T!39, C!42, S!40, B!43, G!45), tptp_fun_Y2_27(T!39, C!42, S!40, B!43, G!45)) | (~member(tptp_fun_X1_30(T!39, C!42, S!40, B!43, G!45), B!43)) | (~member(tptp_fun_Y1_29(T!39, C!42, S!40, B!43, G!45), C!42)) | (~member(tptp_fun_X2_28(T!39, C!42, S!40, B!43, G!45), B!43)) | (~member(tptp_fun_Y2_27(T!39, C!42, S!40, B!43, G!45), C!42)) | (~apply(S!40, tptp_fun_X1_30(T!39, C!42, S!40, B!43, G!45), tptp_fun_X2_28(T!39, C!42, S!40, B!43, G!45))) | (~apply(G!45, tptp_fun_X1_30(T!39, C!42, S!40, B!43, G!45), tptp_fun_Y1_29(T!39, C!42, S!40, B!43, G!45))) | (~apply(G!45, tptp_fun_X2_28(T!39, C!42, S!40, B!43, G!45), tptp_fun_Y2_27(T!39, C!42, S!40, B!43, G!45))))))))))),
% 2.17/2.45 inference(rewrite,[status(thm)],[])).
% 2.17/2.45 tff(205,plain,
% 2.17/2.45 ((~((~((~increasing(G!45, B!43, S!40, C!42, T!39)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(T!39, Y1, Y2) | (~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))))) | (~(increasing(G!45, B!43, S!40, C!42, T!39) | (~(apply(T!39, tptp_fun_Y1_29(T!39, C!42, S!40, B!43, G!45), tptp_fun_Y2_27(T!39, C!42, S!40, B!43, G!45)) | (~member(tptp_fun_X1_30(T!39, C!42, S!40, B!43, G!45), B!43)) | (~member(tptp_fun_Y1_29(T!39, C!42, S!40, B!43, G!45), C!42)) | (~member(tptp_fun_X2_28(T!39, C!42, S!40, B!43, G!45), B!43)) | (~member(tptp_fun_Y2_27(T!39, C!42, S!40, B!43, G!45), C!42)) | (~apply(S!40, tptp_fun_X1_30(T!39, C!42, S!40, B!43, G!45), tptp_fun_X2_28(T!39, C!42, S!40, B!43, G!45))) | (~apply(G!45, tptp_fun_X1_30(T!39, C!42, S!40, B!43, G!45), tptp_fun_Y1_29(T!39, C!42, S!40, B!43, G!45))) | (~apply(G!45, tptp_fun_X2_28(T!39, C!42, S!40, B!43, G!45), tptp_fun_Y2_27(T!39, C!42, S!40, B!43, G!45))))))))) <=> (~((~((~increasing(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)) | apply(T!39, Y1, Y2) | (~member(X1, B!43)) | (~member(Y1, C!42)) | (~apply(S!40, X1, X2)) | (~apply(G!45, X1, Y1)) | (~apply(G!45, X2, Y2))))) | (~(increasing(G!45, B!43, S!40, C!42, T!39) | (~(apply(T!39, tptp_fun_Y1_29(T!39, C!42, S!40, B!43, G!45), tptp_fun_Y2_27(T!39, C!42, S!40, B!43, G!45)) | (~member(tptp_fun_X1_30(T!39, C!42, S!40, B!43, G!45), B!43)) | (~member(tptp_fun_Y1_29(T!39, C!42, S!40, B!43, G!45), C!42)) | (~member(tptp_fun_X2_28(T!39, C!42, S!40, B!43, G!45), B!43)) | (~member(tptp_fun_Y2_27(T!39, C!42, S!40, B!43, G!45), C!42)) | (~apply(S!40, tptp_fun_X1_30(T!39, C!42, S!40, B!43, G!45), tptp_fun_X2_28(T!39, C!42, S!40, B!43, G!45))) | (~apply(G!45, tptp_fun_X1_30(T!39, C!42, S!40, B!43, G!45), tptp_fun_Y1_29(T!39, C!42, S!40, B!43, G!45))) | (~apply(G!45, tptp_fun_X2_28(T!39, C!42, S!40, B!43, G!45), tptp_fun_Y2_27(T!39, C!42, S!40, B!43, G!45)))))))))),
% 2.17/2.45 inference(rewrite,[status(thm)],[])).
% 2.17/2.45 tff(206,plain,
% 2.17/2.45 (((~![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(G!45, B!43, S!40, C!42, T!39)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(T!39, Y1, Y2) | (~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))))) | (~(increasing(G!45, B!43, S!40, C!42, T!39) | (~(apply(T!39, tptp_fun_Y1_29(T!39, C!42, S!40, B!43, G!45), tptp_fun_Y2_27(T!39, C!42, S!40, B!43, G!45)) | (~member(tptp_fun_X1_30(T!39, C!42, S!40, B!43, G!45), B!43)) | (~member(tptp_fun_Y1_29(T!39, C!42, S!40, B!43, G!45), C!42)) | (~member(tptp_fun_X2_28(T!39, C!42, S!40, B!43, G!45), B!43)) | (~member(tptp_fun_Y2_27(T!39, C!42, S!40, B!43, G!45), C!42)) | (~apply(S!40, tptp_fun_X1_30(T!39, C!42, S!40, B!43, G!45), tptp_fun_X2_28(T!39, C!42, S!40, B!43, G!45))) | (~apply(G!45, tptp_fun_X1_30(T!39, C!42, S!40, B!43, G!45), tptp_fun_Y1_29(T!39, C!42, S!40, B!43, G!45))) | (~apply(G!45, tptp_fun_X2_28(T!39, C!42, S!40, B!43, G!45), tptp_fun_Y2_27(T!39, C!42, S!40, B!43, G!45)))))))))) <=> ((~![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(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)) | apply(T!39, Y1, Y2) | (~member(X1, B!43)) | (~member(Y1, C!42)) | (~apply(S!40, X1, X2)) | (~apply(G!45, X1, Y1)) | (~apply(G!45, X2, Y2))))) | (~(increasing(G!45, B!43, S!40, C!42, T!39) | (~(apply(T!39, tptp_fun_Y1_29(T!39, C!42, S!40, B!43, G!45), tptp_fun_Y2_27(T!39, C!42, S!40, B!43, G!45)) | (~member(tptp_fun_X1_30(T!39, C!42, S!40, B!43, G!45), B!43)) | (~member(tptp_fun_Y1_29(T!39, C!42, S!40, B!43, G!45), C!42)) | (~member(tptp_fun_X2_28(T!39, C!42, S!40, B!43, G!45), B!43)) | (~member(tptp_fun_Y2_27(T!39, C!42, S!40, B!43, G!45), C!42)) | (~apply(S!40, tptp_fun_X1_30(T!39, C!42, S!40, B!43, G!45), tptp_fun_X2_28(T!39, C!42, S!40, B!43, G!45))) | (~apply(G!45, tptp_fun_X1_30(T!39, C!42, S!40, B!43, G!45), tptp_fun_Y1_29(T!39, C!42, S!40, B!43, G!45))) | (~apply(G!45, tptp_fun_X2_28(T!39, C!42, S!40, B!43, G!45), tptp_fun_Y2_27(T!39, C!42, S!40, B!43, G!45))))))))))),
% 2.17/2.45 inference(monotonicity,[status(thm)],[205])).
% 2.17/2.45 tff(207,plain,
% 2.17/2.45 (((~![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(G!45, B!43, S!40, C!42, T!39)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(T!39, Y1, Y2) | (~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))))) | (~(increasing(G!45, B!43, S!40, C!42, T!39) | (~(apply(T!39, tptp_fun_Y1_29(T!39, C!42, S!40, B!43, G!45), tptp_fun_Y2_27(T!39, C!42, S!40, B!43, G!45)) | (~member(tptp_fun_X1_30(T!39, C!42, S!40, B!43, G!45), B!43)) | (~member(tptp_fun_Y1_29(T!39, C!42, S!40, B!43, G!45), C!42)) | (~member(tptp_fun_X2_28(T!39, C!42, S!40, B!43, G!45), B!43)) | (~member(tptp_fun_Y2_27(T!39, C!42, S!40, B!43, G!45), C!42)) | (~apply(S!40, tptp_fun_X1_30(T!39, C!42, S!40, B!43, G!45), tptp_fun_X2_28(T!39, C!42, S!40, B!43, G!45))) | (~apply(G!45, tptp_fun_X1_30(T!39, C!42, S!40, B!43, G!45), tptp_fun_Y1_29(T!39, C!42, S!40, B!43, G!45))) | (~apply(G!45, tptp_fun_X2_28(T!39, C!42, S!40, B!43, G!45), tptp_fun_Y2_27(T!39, C!42, S!40, B!43, G!45)))))))))) <=> ((~![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(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)) | apply(T!39, Y1, Y2) | (~member(X1, B!43)) | (~member(Y1, C!42)) | (~apply(S!40, X1, X2)) | (~apply(G!45, X1, Y1)) | (~apply(G!45, X2, Y2))))) | (~(increasing(G!45, B!43, S!40, C!42, T!39) | (~(apply(T!39, tptp_fun_Y1_29(T!39, C!42, S!40, B!43, G!45), tptp_fun_Y2_27(T!39, C!42, S!40, B!43, G!45)) | (~member(tptp_fun_X1_30(T!39, C!42, S!40, B!43, G!45), B!43)) | (~member(tptp_fun_Y1_29(T!39, C!42, S!40, B!43, G!45), C!42)) | (~member(tptp_fun_X2_28(T!39, C!42, S!40, B!43, G!45), B!43)) | (~member(tptp_fun_Y2_27(T!39, C!42, S!40, B!43, G!45), C!42)) | (~apply(S!40, tptp_fun_X1_30(T!39, C!42, S!40, B!43, G!45), tptp_fun_X2_28(T!39, C!42, S!40, B!43, G!45))) | (~apply(G!45, tptp_fun_X1_30(T!39, C!42, S!40, B!43, G!45), tptp_fun_Y1_29(T!39, C!42, S!40, B!43, G!45))) | (~apply(G!45, tptp_fun_X2_28(T!39, C!42, S!40, B!43, G!45), tptp_fun_Y2_27(T!39, C!42, S!40, B!43, G!45))))))))))),
% 2.17/2.46 inference(transitivity,[status(thm)],[206, 204])).
% 2.17/2.46 tff(208,plain,
% 2.17/2.46 ((~![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(G!45, B!43, S!40, C!42, T!39)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(T!39, Y1, Y2) | (~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))))) | (~(increasing(G!45, B!43, S!40, C!42, T!39) | (~(apply(T!39, tptp_fun_Y1_29(T!39, C!42, S!40, B!43, G!45), tptp_fun_Y2_27(T!39, C!42, S!40, B!43, G!45)) | (~member(tptp_fun_X1_30(T!39, C!42, S!40, B!43, G!45), B!43)) | (~member(tptp_fun_Y1_29(T!39, C!42, S!40, B!43, G!45), C!42)) | (~member(tptp_fun_X2_28(T!39, C!42, S!40, B!43, G!45), B!43)) | (~member(tptp_fun_Y2_27(T!39, C!42, S!40, B!43, G!45), C!42)) | (~apply(S!40, tptp_fun_X1_30(T!39, C!42, S!40, B!43, G!45), tptp_fun_X2_28(T!39, C!42, S!40, B!43, G!45))) | (~apply(G!45, tptp_fun_X1_30(T!39, C!42, S!40, B!43, G!45), tptp_fun_Y1_29(T!39, C!42, S!40, B!43, G!45))) | (~apply(G!45, tptp_fun_X2_28(T!39, C!42, S!40, B!43, G!45), tptp_fun_Y2_27(T!39, C!42, S!40, B!43, G!45)))))))))),
% 2.17/2.46 inference(quant_inst,[status(thm)],[])).
% 2.17/2.46 tff(209,plain,
% 2.17/2.46 ((~![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(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)) | apply(T!39, Y1, Y2) | (~member(X1, B!43)) | (~member(Y1, C!42)) | (~apply(S!40, X1, X2)) | (~apply(G!45, X1, Y1)) | (~apply(G!45, X2, Y2))))) | (~(increasing(G!45, B!43, S!40, C!42, T!39) | (~(apply(T!39, tptp_fun_Y1_29(T!39, C!42, S!40, B!43, G!45), tptp_fun_Y2_27(T!39, C!42, S!40, B!43, G!45)) | (~member(tptp_fun_X1_30(T!39, C!42, S!40, B!43, G!45), B!43)) | (~member(tptp_fun_Y1_29(T!39, C!42, S!40, B!43, G!45), C!42)) | (~member(tptp_fun_X2_28(T!39, C!42, S!40, B!43, G!45), B!43)) | (~member(tptp_fun_Y2_27(T!39, C!42, S!40, B!43, G!45), C!42)) | (~apply(S!40, tptp_fun_X1_30(T!39, C!42, S!40, B!43, G!45), tptp_fun_X2_28(T!39, C!42, S!40, B!43, G!45))) | (~apply(G!45, tptp_fun_X1_30(T!39, C!42, S!40, B!43, G!45), tptp_fun_Y1_29(T!39, C!42, S!40, B!43, G!45))) | (~apply(G!45, tptp_fun_X2_28(T!39, C!42, S!40, B!43, G!45), tptp_fun_Y2_27(T!39, C!42, S!40, B!43, G!45)))))))))),
% 2.17/2.46 inference(modus_ponens,[status(thm)],[208, 207])).
% 2.17/2.46 tff(210,plain,
% 2.17/2.46 (~((~((~increasing(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)) | apply(T!39, Y1, Y2) | (~member(X1, B!43)) | (~member(Y1, C!42)) | (~apply(S!40, X1, X2)) | (~apply(G!45, X1, Y1)) | (~apply(G!45, X2, Y2))))) | (~(increasing(G!45, B!43, S!40, C!42, T!39) | (~(apply(T!39, tptp_fun_Y1_29(T!39, C!42, S!40, B!43, G!45), tptp_fun_Y2_27(T!39, C!42, S!40, B!43, G!45)) | (~member(tptp_fun_X1_30(T!39, C!42, S!40, B!43, G!45), B!43)) | (~member(tptp_fun_Y1_29(T!39, C!42, S!40, B!43, G!45), C!42)) | (~member(tptp_fun_X2_28(T!39, C!42, S!40, B!43, G!45), B!43)) | (~member(tptp_fun_Y2_27(T!39, C!42, S!40, B!43, G!45), C!42)) | (~apply(S!40, tptp_fun_X1_30(T!39, C!42, S!40, B!43, G!45), tptp_fun_X2_28(T!39, C!42, S!40, B!43, G!45))) | (~apply(G!45, tptp_fun_X1_30(T!39, C!42, S!40, B!43, G!45), tptp_fun_Y1_29(T!39, C!42, S!40, B!43, G!45))) | (~apply(G!45, tptp_fun_X2_28(T!39, C!42, S!40, B!43, G!45), tptp_fun_Y2_27(T!39, C!42, S!40, B!43, G!45))))))))),
% 2.17/2.46 inference(unit_resolution,[status(thm)],[209, 16])).
% 2.17/2.46 tff(211,plain,
% 2.17/2.46 (((~((~increasing(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)) | apply(T!39, Y1, Y2) | (~member(X1, B!43)) | (~member(Y1, C!42)) | (~apply(S!40, X1, X2)) | (~apply(G!45, X1, Y1)) | (~apply(G!45, X2, Y2))))) | (~(increasing(G!45, B!43, S!40, C!42, T!39) | (~(apply(T!39, tptp_fun_Y1_29(T!39, C!42, S!40, B!43, G!45), tptp_fun_Y2_27(T!39, C!42, S!40, B!43, G!45)) | (~member(tptp_fun_X1_30(T!39, C!42, S!40, B!43, G!45), B!43)) | (~member(tptp_fun_Y1_29(T!39, C!42, S!40, B!43, G!45), C!42)) | (~member(tptp_fun_X2_28(T!39, C!42, S!40, B!43, G!45), B!43)) | (~member(tptp_fun_Y2_27(T!39, C!42, S!40, B!43, G!45), C!42)) | (~apply(S!40, tptp_fun_X1_30(T!39, C!42, S!40, B!43, G!45), tptp_fun_X2_28(T!39, C!42, S!40, B!43, G!45))) | (~apply(G!45, tptp_fun_X1_30(T!39, C!42, S!40, B!43, G!45), tptp_fun_Y1_29(T!39, C!42, S!40, B!43, G!45))) | (~apply(G!45, tptp_fun_X2_28(T!39, C!42, S!40, B!43, G!45), tptp_fun_Y2_27(T!39, C!42, S!40, B!43, G!45)))))))) | ((~increasing(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)) | apply(T!39, Y1, Y2) | (~member(X1, B!43)) | (~member(Y1, C!42)) | (~apply(S!40, X1, X2)) | (~apply(G!45, X1, Y1)) | (~apply(G!45, X2, Y2))))),
% 2.17/2.47 inference(tautology,[status(thm)],[])).
% 2.17/2.47 tff(212,plain,
% 2.17/2.47 ((~increasing(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)) | apply(T!39, Y1, Y2) | (~member(X1, B!43)) | (~member(Y1, C!42)) | (~apply(S!40, X1, X2)) | (~apply(G!45, X1, Y1)) | (~apply(G!45, X2, Y2)))),
% 2.17/2.47 inference(unit_resolution,[status(thm)],[211, 210])).
% 2.17/2.47 tff(213,plain,
% 2.17/2.47 (increasing(G!45, B!43, S!40, C!42, T!39)),
% 2.17/2.47 inference(and_elim,[status(thm)],[106])).
% 2.17/2.47 tff(214,plain,
% 2.17/2.47 ((~((~increasing(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)) | apply(T!39, Y1, Y2) | (~member(X1, B!43)) | (~member(Y1, C!42)) | (~apply(S!40, X1, X2)) | (~apply(G!45, X1, Y1)) | (~apply(G!45, X2, Y2))))) | (~increasing(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)) | apply(T!39, Y1, Y2) | (~member(X1, B!43)) | (~member(Y1, C!42)) | (~apply(S!40, X1, X2)) | (~apply(G!45, X1, Y1)) | (~apply(G!45, X2, Y2)))),
% 2.17/2.47 inference(tautology,[status(thm)],[])).
% 2.17/2.47 tff(215,plain,
% 2.17/2.47 ((~((~increasing(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)) | apply(T!39, Y1, Y2) | (~member(X1, B!43)) | (~member(Y1, C!42)) | (~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)) | apply(T!39, Y1, Y2) | (~member(X1, B!43)) | (~member(Y1, C!42)) | (~apply(S!40, X1, X2)) | (~apply(G!45, X1, Y1)) | (~apply(G!45, X2, Y2)))),
% 2.17/2.47 inference(unit_resolution,[status(thm)],[214, 213])).
% 2.17/2.47 tff(216,plain,
% 2.17/2.47 (![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(X2, B!43)) | (~member(Y2, C!42)) | apply(T!39, Y1, Y2) | (~member(X1, B!43)) | (~member(Y1, C!42)) | (~apply(S!40, X1, X2)) | (~apply(G!45, X1, Y1)) | (~apply(G!45, X2, Y2)))),
% 2.17/2.47 inference(unit_resolution,[status(thm)],[215, 212])).
% 2.17/2.47 tff(217,plain,
% 2.17/2.47 (((~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(X2, B!43)) | (~member(Y2, C!42)) | apply(T!39, Y1, Y2) | (~member(X1, B!43)) | (~member(Y1, C!42)) | (~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(S!40, 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_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(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)))) <=> ((~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(X2, B!43)) | (~member(Y2, C!42)) | apply(T!39, Y1, Y2) | (~member(X1, B!43)) | (~member(Y1, C!42)) | (~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(S!40, 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_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(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)))),
% 2.24/2.47 inference(rewrite,[status(thm)],[])).
% 2.24/2.47 tff(218,plain,
% 2.24/2.47 (((~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(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_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(S!40, 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_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_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_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_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(S!40, 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_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(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)))),
% 2.24/2.49 inference(rewrite,[status(thm)],[])).
% 2.24/2.49 tff(219,plain,
% 2.24/2.49 (((~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(X2, B!43)) | (~member(Y2, C!42)) | apply(T!39, Y1, Y2) | (~member(X1, B!43)) | (~member(Y1, C!42)) | (~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_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), 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compose_function(G!45, F!46, A!44, B!43, C!42)), B!43, F!46, G!45), C!42, G!45))))) <=> ((~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(X2, B!43)) | (~member(Y2, C!42)) | apply(T!39, Y1, Y2) | (~member(X1, B!43)) | (~member(Y1, C!42)) | (~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(S!40, 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_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(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, 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% 2.24/2.49 inference(monotonicity,[status(thm)],[218])).
% 2.24/2.49 tff(220,plain,
% 2.24/2.49 (((~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(X2, B!43)) | (~member(Y2, C!42)) | apply(T!39, Y1, Y2) | (~member(X1, B!43)) | (~member(Y1, C!42)) | (~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_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_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(S!40, 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_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_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_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))))) <=> ((~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(X2, B!43)) | (~member(Y2, C!42)) | apply(T!39, Y1, Y2) | (~member(X1, B!43)) | (~member(Y1, C!42)) | (~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(S!40, 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_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(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)))),
% 2.24/2.50 inference(transitivity,[status(thm)],[219, 217])).
% 2.24/2.50 tff(221,plain,
% 2.24/2.50 ((~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(X2, B!43)) | (~member(Y2, C!42)) | apply(T!39, Y1, Y2) | (~member(X1, B!43)) | (~member(Y1, C!42)) | (~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_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_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(S!40, 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_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_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_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))))),
% 2.24/2.51 inference(quant_inst,[status(thm)],[])).
% 2.24/2.51 tff(222,plain,
% 2.24/2.51 ((~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(X2, B!43)) | (~member(Y2, C!42)) | apply(T!39, Y1, Y2) | (~member(X1, B!43)) | (~member(Y1, C!42)) | (~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(S!40, 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_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(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))),
% 2.24/2.51 inference(modus_ponens,[status(thm)],[221, 220])).
% 2.24/2.51 tff(223,plain,
% 2.24/2.51 (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))),
% 2.24/2.51 inference(unit_resolution,[status(thm)],[222, 216, 79, 154, 120, 118, 162, 160, 203])).
% 2.24/2.51 tff(224,plain,
% 2.24/2.51 ($false),
% 2.24/2.52 inference(unit_resolution,[status(thm)],[223, 177])).
% 2.24/2.52 % SZS output end Proof
%------------------------------------------------------------------------------