TSTP Solution File: SET750+4 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET750+4 : TPTP v8.1.0. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 20 05:07:51 EDT 2022
% Result : Theorem 0.20s 0.41s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SET750+4 : TPTP v8.1.0. Bugfixed v2.2.1.
% 0.10/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n002.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sat Sep 3 07:56:02 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.20/0.41 % SZS status Theorem
% 0.20/0.41 % SZS output start Proof
% 0.20/0.41 tff(apply_type, type, (
% 0.20/0.41 apply: ( $i * $i * $i ) > $o)).
% 0.20/0.41 tff(tptp_fun_X2_28_type, type, (
% 0.20/0.41 tptp_fun_X2_28: ( $i * $i * $i * $i * $i ) > $i)).
% 0.20/0.41 tff(inverse_function_type, type, (
% 0.20/0.41 inverse_function: ( $i * $i * $i ) > $i)).
% 0.20/0.41 tff(tptp_fun_B_41_type, type, (
% 0.20/0.41 tptp_fun_B_41: $i)).
% 0.20/0.41 tff(tptp_fun_A_42_type, type, (
% 0.20/0.41 tptp_fun_A_42: $i)).
% 0.20/0.41 tff(tptp_fun_F_43_type, type, (
% 0.20/0.41 tptp_fun_F_43: $i)).
% 0.20/0.41 tff(tptp_fun_S_39_type, type, (
% 0.20/0.41 tptp_fun_S_39: $i)).
% 0.20/0.41 tff(tptp_fun_R_40_type, type, (
% 0.20/0.41 tptp_fun_R_40: $i)).
% 0.20/0.41 tff(tptp_fun_Y2_27_type, type, (
% 0.20/0.41 tptp_fun_Y2_27: ( $i * $i * $i * $i * $i ) > $i)).
% 0.20/0.41 tff(member_type, type, (
% 0.20/0.41 member: ( $i * $i ) > $o)).
% 0.20/0.41 tff(tptp_fun_Y1_29_type, type, (
% 0.20/0.41 tptp_fun_Y1_29: ( $i * $i * $i * $i * $i ) > $i)).
% 0.20/0.41 tff(tptp_fun_X1_30_type, type, (
% 0.20/0.41 tptp_fun_X1_30: ( $i * $i * $i * $i * $i ) > $i)).
% 0.20/0.41 tff(increasing_type, type, (
% 0.20/0.41 increasing: ( $i * $i * $i * $i * $i ) > $o)).
% 0.20/0.41 tff(one_to_one_type, type, (
% 0.20/0.41 one_to_one: ( $i * $i * $i ) > $o)).
% 0.20/0.41 tff(maps_type, type, (
% 0.20/0.41 maps: ( $i * $i * $i ) > $o)).
% 0.20/0.41 tff(isomorphism_type, type, (
% 0.20/0.41 isomorphism: ( $i * $i * $i * $i * $i ) > $o)).
% 0.20/0.41 tff(tptp_fun_X2_36_type, type, (
% 0.20/0.41 tptp_fun_X2_36: ( $i * $i * $i * $i * $i ) > $i)).
% 0.20/0.41 tff(tptp_fun_Y2_35_type, type, (
% 0.20/0.41 tptp_fun_Y2_35: ( $i * $i * $i * $i * $i ) > $i)).
% 0.20/0.41 tff(tptp_fun_Y1_37_type, type, (
% 0.20/0.41 tptp_fun_Y1_37: ( $i * $i * $i * $i * $i ) > $i)).
% 0.20/0.41 tff(tptp_fun_X1_38_type, type, (
% 0.20/0.41 tptp_fun_X1_38: ( $i * $i * $i * $i * $i ) > $i)).
% 0.20/0.41 tff(tptp_fun_E_19_type, type, (
% 0.20/0.41 tptp_fun_E_19: ( $i * $i * $i ) > $i)).
% 0.20/0.41 tff(surjective_type, type, (
% 0.20/0.41 surjective: ( $i * $i * $i ) > $o)).
% 0.20/0.41 tff(tptp_fun_Y_20_type, type, (
% 0.20/0.41 tptp_fun_Y_20: ( $i * $i * $i ) > $i)).
% 0.20/0.41 tff(injective_type, type, (
% 0.20/0.41 injective: ( $i * $i * $i ) > $o)).
% 0.20/0.41 tff(tptp_fun_Y_16_type, type, (
% 0.20/0.41 tptp_fun_Y_16: ( $i * $i * $i ) > $i)).
% 0.20/0.41 tff(tptp_fun_X2_17_type, type, (
% 0.20/0.41 tptp_fun_X2_17: ( $i * $i * $i ) > $i)).
% 0.20/0.41 tff(tptp_fun_X1_18_type, type, (
% 0.20/0.41 tptp_fun_X1_18: ( $i * $i * $i ) > $i)).
% 0.20/0.41 tff(1,plain,
% 0.20/0.41 (^[F: $i, A: $i, R: $i, B: $i, S: $i] : refl((~((~((~increasing(F, A, R, B, S)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(S, Y1, Y2) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(R, X1, X2)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2))))) | (~(increasing(F, A, R, B, S) | (~(apply(S, tptp_fun_Y1_29(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)) | (~member(tptp_fun_X1_30(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_29(S, B, R, A, F), B)) | (~member(tptp_fun_X2_28(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_27(S, B, R, A, F), B)) | (~apply(R, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_X2_28(S, B, R, A, F))) | (~apply(F, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_Y1_29(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_28(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F))))))))) <=> (~((~((~increasing(F, A, R, B, S)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(S, Y1, Y2) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(R, X1, X2)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2))))) | (~(increasing(F, A, R, B, S) | (~(apply(S, tptp_fun_Y1_29(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)) | (~member(tptp_fun_X1_30(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_29(S, B, R, A, F), B)) | (~member(tptp_fun_X2_28(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_27(S, B, R, A, F), B)) | (~apply(R, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_X2_28(S, B, R, A, F))) | (~apply(F, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_Y1_29(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_28(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F))))))))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(2,plain,
% 0.20/0.41 (![F: $i, A: $i, R: $i, B: $i, S: $i] : (~((~((~increasing(F, A, R, B, S)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(S, Y1, Y2) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(R, X1, X2)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2))))) | (~(increasing(F, A, R, B, S) | (~(apply(S, tptp_fun_Y1_29(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)) | (~member(tptp_fun_X1_30(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_29(S, B, R, A, F), B)) | (~member(tptp_fun_X2_28(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_27(S, B, R, A, F), B)) | (~apply(R, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_X2_28(S, B, R, A, F))) | (~apply(F, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_Y1_29(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_28(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F))))))))) <=> ![F: $i, A: $i, R: $i, B: $i, S: $i] : (~((~((~increasing(F, A, R, B, S)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(S, Y1, Y2) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(R, X1, X2)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2))))) | (~(increasing(F, A, R, B, S) | (~(apply(S, tptp_fun_Y1_29(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)) | (~member(tptp_fun_X1_30(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_29(S, B, R, A, F), B)) | (~member(tptp_fun_X2_28(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_27(S, B, R, A, F), B)) | (~apply(R, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_X2_28(S, B, R, A, F))) | (~apply(F, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_Y1_29(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_28(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)))))))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.41 tff(3,plain,
% 0.20/0.41 (^[F: $i, A: $i, R: $i, B: $i, S: $i] : rewrite((~((~((~increasing(F, A, R, B, S)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(S, Y1, Y2) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(R, X1, X2)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2))))) | (~(increasing(F, A, R, B, S) | (~(apply(S, tptp_fun_Y1_29(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)) | (~member(tptp_fun_X1_30(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_29(S, B, R, A, F), B)) | (~member(tptp_fun_X2_28(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_27(S, B, R, A, F), B)) | (~apply(R, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_X2_28(S, B, R, A, F))) | (~apply(F, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_Y1_29(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_28(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F))))))))) <=> (~((~((~increasing(F, A, R, B, S)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(S, Y1, Y2) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(R, X1, X2)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2))))) | (~(increasing(F, A, R, B, S) | (~(apply(S, tptp_fun_Y1_29(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)) | (~member(tptp_fun_X1_30(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_29(S, B, R, A, F), B)) | (~member(tptp_fun_X2_28(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_27(S, B, R, A, F), B)) | (~apply(R, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_X2_28(S, B, R, A, F))) | (~apply(F, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_Y1_29(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_28(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F))))))))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(4,plain,
% 0.20/0.41 (![F: $i, A: $i, R: $i, B: $i, S: $i] : (~((~((~increasing(F, A, R, B, S)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(S, Y1, Y2) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(R, X1, X2)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2))))) | (~(increasing(F, A, R, B, S) | (~(apply(S, tptp_fun_Y1_29(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)) | (~member(tptp_fun_X1_30(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_29(S, B, R, A, F), B)) | (~member(tptp_fun_X2_28(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_27(S, B, R, A, F), B)) | (~apply(R, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_X2_28(S, B, R, A, F))) | (~apply(F, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_Y1_29(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_28(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F))))))))) <=> ![F: $i, A: $i, R: $i, B: $i, S: $i] : (~((~((~increasing(F, A, R, B, S)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(S, Y1, Y2) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(R, X1, X2)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2))))) | (~(increasing(F, A, R, B, S) | (~(apply(S, tptp_fun_Y1_29(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)) | (~member(tptp_fun_X1_30(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_29(S, B, R, A, F), B)) | (~member(tptp_fun_X2_28(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_27(S, B, R, A, F), B)) | (~apply(R, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_X2_28(S, B, R, A, F))) | (~apply(F, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_Y1_29(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_28(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)))))))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[3])).
% 0.20/0.41 tff(5,plain,
% 0.20/0.41 (![F: $i, A: $i, R: $i, B: $i, S: $i] : (~((~((~increasing(F, A, R, B, S)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(S, Y1, Y2) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(R, X1, X2)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2))))) | (~(increasing(F, A, R, B, S) | (~(apply(S, tptp_fun_Y1_29(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)) | (~member(tptp_fun_X1_30(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_29(S, B, R, A, F), B)) | (~member(tptp_fun_X2_28(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_27(S, B, R, A, F), B)) | (~apply(R, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_X2_28(S, B, R, A, F))) | (~apply(F, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_Y1_29(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_28(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F))))))))) <=> ![F: $i, A: $i, R: $i, B: $i, S: $i] : (~((~((~increasing(F, A, R, B, S)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(S, Y1, Y2) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(R, X1, X2)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2))))) | (~(increasing(F, A, R, B, S) | (~(apply(S, tptp_fun_Y1_29(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)) | (~member(tptp_fun_X1_30(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_29(S, B, R, A, F), B)) | (~member(tptp_fun_X2_28(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_27(S, B, R, A, F), B)) | (~apply(R, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_X2_28(S, B, R, A, F))) | (~apply(F, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_Y1_29(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_28(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)))))))))),
% 0.20/0.41 inference(transitivity,[status(thm)],[4, 2])).
% 0.20/0.41 tff(6,plain,
% 0.20/0.41 (^[F: $i, A: $i, R: $i, B: $i, S: $i] : trans(monotonicity(rewrite(((~increasing(F, A, R, B, S)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~(member(X1, A) & member(Y1, B) & member(X2, A) & member(Y2, B) & apply(R, X1, X2) & apply(F, X1, Y1) & apply(F, X2, Y2))) | apply(S, Y1, Y2))) <=> ((~increasing(F, A, R, B, S)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(S, Y1, Y2) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(R, X1, X2)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2))))), trans(monotonicity(rewrite((~((~(member(tptp_fun_X1_30(S, B, R, A, F), A) & member(tptp_fun_Y1_29(S, B, R, A, F), B) & member(tptp_fun_X2_28(S, B, R, A, F), A) & member(tptp_fun_Y2_27(S, B, R, A, F), B) & apply(R, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_X2_28(S, B, R, A, F)) & apply(F, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_Y1_29(S, B, R, A, F)) & apply(F, tptp_fun_X2_28(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)))) | apply(S, tptp_fun_Y1_29(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)))) <=> (~(apply(S, tptp_fun_Y1_29(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)) | (~member(tptp_fun_X1_30(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_29(S, B, R, A, F), B)) | (~member(tptp_fun_X2_28(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_27(S, B, R, A, F), B)) | (~apply(R, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_X2_28(S, B, R, A, F))) | (~apply(F, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_Y1_29(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_28(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)))))), ((increasing(F, A, R, B, S) | (~((~(member(tptp_fun_X1_30(S, B, R, A, F), A) & member(tptp_fun_Y1_29(S, B, R, A, F), B) & member(tptp_fun_X2_28(S, B, R, A, F), A) & member(tptp_fun_Y2_27(S, B, R, A, F), B) & apply(R, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_X2_28(S, B, R, A, F)) & apply(F, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_Y1_29(S, B, R, A, F)) & apply(F, tptp_fun_X2_28(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)))) | apply(S, tptp_fun_Y1_29(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F))))) <=> (increasing(F, A, R, B, S) | (~(apply(S, tptp_fun_Y1_29(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)) | (~member(tptp_fun_X1_30(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_29(S, B, R, A, F), B)) | (~member(tptp_fun_X2_28(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_27(S, B, R, A, F), B)) | (~apply(R, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_X2_28(S, B, R, A, F))) | (~apply(F, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_Y1_29(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_28(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)))))))), rewrite((increasing(F, A, R, B, S) | (~(apply(S, tptp_fun_Y1_29(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)) | (~member(tptp_fun_X1_30(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_29(S, B, R, A, F), B)) | (~member(tptp_fun_X2_28(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_27(S, B, R, A, F), B)) | (~apply(R, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_X2_28(S, B, R, A, F))) | (~apply(F, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_Y1_29(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_28(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)))))) <=> (increasing(F, A, R, B, S) | (~(apply(S, tptp_fun_Y1_29(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)) | (~member(tptp_fun_X1_30(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_29(S, B, R, A, F), B)) | (~member(tptp_fun_X2_28(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_27(S, B, R, A, F), B)) | (~apply(R, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_X2_28(S, B, R, A, F))) | (~apply(F, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_Y1_29(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_28(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F))))))), ((increasing(F, A, R, B, S) | (~((~(member(tptp_fun_X1_30(S, B, R, A, F), A) & member(tptp_fun_Y1_29(S, B, R, A, F), B) & member(tptp_fun_X2_28(S, B, R, A, F), A) & member(tptp_fun_Y2_27(S, B, R, A, F), B) & apply(R, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_X2_28(S, B, R, A, F)) & apply(F, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_Y1_29(S, B, R, A, F)) & apply(F, tptp_fun_X2_28(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)))) | apply(S, tptp_fun_Y1_29(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F))))) <=> (increasing(F, A, R, B, S) | (~(apply(S, tptp_fun_Y1_29(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)) | (~member(tptp_fun_X1_30(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_29(S, B, R, A, F), B)) | (~member(tptp_fun_X2_28(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_27(S, B, R, A, F), B)) | (~apply(R, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_X2_28(S, B, R, A, F))) | (~apply(F, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_Y1_29(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_28(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)))))))), ((((~increasing(F, A, R, B, S)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~(member(X1, A) & member(Y1, B) & member(X2, A) & member(Y2, B) & apply(R, X1, X2) & apply(F, X1, Y1) & apply(F, X2, Y2))) | apply(S, Y1, Y2))) & (increasing(F, A, R, B, S) | (~((~(member(tptp_fun_X1_30(S, B, R, A, F), A) & member(tptp_fun_Y1_29(S, B, R, A, F), B) & member(tptp_fun_X2_28(S, B, R, A, F), A) & member(tptp_fun_Y2_27(S, B, R, A, F), B) & apply(R, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_X2_28(S, B, R, A, F)) & apply(F, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_Y1_29(S, B, R, A, F)) & apply(F, tptp_fun_X2_28(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)))) | apply(S, tptp_fun_Y1_29(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)))))) <=> (((~increasing(F, A, R, B, S)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(S, Y1, Y2) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(R, X1, X2)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2)))) & (increasing(F, A, R, B, S) | (~(apply(S, tptp_fun_Y1_29(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)) | (~member(tptp_fun_X1_30(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_29(S, B, R, A, F), B)) | (~member(tptp_fun_X2_28(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_27(S, B, R, A, F), B)) | (~apply(R, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_X2_28(S, B, R, A, F))) | (~apply(F, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_Y1_29(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_28(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F))))))))), rewrite((((~increasing(F, A, R, B, S)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(S, Y1, Y2) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(R, X1, X2)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2)))) & (increasing(F, A, R, B, S) | (~(apply(S, tptp_fun_Y1_29(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)) | (~member(tptp_fun_X1_30(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_29(S, B, R, A, F), B)) | (~member(tptp_fun_X2_28(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_27(S, B, R, A, F), B)) | (~apply(R, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_X2_28(S, B, R, A, F))) | (~apply(F, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_Y1_29(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_28(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F))))))) <=> (~((~((~increasing(F, A, R, B, S)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(S, Y1, Y2) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(R, X1, X2)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2))))) | (~(increasing(F, A, R, B, S) | (~(apply(S, tptp_fun_Y1_29(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)) | (~member(tptp_fun_X1_30(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_29(S, B, R, A, F), B)) | (~member(tptp_fun_X2_28(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_27(S, B, R, A, F), B)) | (~apply(R, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_X2_28(S, B, R, A, F))) | (~apply(F, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_Y1_29(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_28(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)))))))))), ((((~increasing(F, A, R, B, S)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~(member(X1, A) & member(Y1, B) & member(X2, A) & member(Y2, B) & apply(R, X1, X2) & apply(F, X1, Y1) & apply(F, X2, Y2))) | apply(S, Y1, Y2))) & (increasing(F, A, R, B, S) | (~((~(member(tptp_fun_X1_30(S, B, R, A, F), A) & member(tptp_fun_Y1_29(S, B, R, A, F), B) & member(tptp_fun_X2_28(S, B, R, A, F), A) & member(tptp_fun_Y2_27(S, B, R, A, F), B) & apply(R, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_X2_28(S, B, R, A, F)) & apply(F, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_Y1_29(S, B, R, A, F)) & apply(F, tptp_fun_X2_28(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)))) | apply(S, tptp_fun_Y1_29(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)))))) <=> (~((~((~increasing(F, A, R, B, S)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(S, Y1, Y2) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(R, X1, X2)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2))))) | (~(increasing(F, A, R, B, S) | (~(apply(S, tptp_fun_Y1_29(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)) | (~member(tptp_fun_X1_30(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_29(S, B, R, A, F), B)) | (~member(tptp_fun_X2_28(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_27(S, B, R, A, F), B)) | (~apply(R, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_X2_28(S, B, R, A, F))) | (~apply(F, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_Y1_29(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_28(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)))))))))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(7,plain,
% 0.20/0.41 (![F: $i, A: $i, R: $i, B: $i, S: $i] : (((~increasing(F, A, R, B, S)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~(member(X1, A) & member(Y1, B) & member(X2, A) & member(Y2, B) & apply(R, X1, X2) & apply(F, X1, Y1) & apply(F, X2, Y2))) | apply(S, Y1, Y2))) & (increasing(F, A, R, B, S) | (~((~(member(tptp_fun_X1_30(S, B, R, A, F), A) & member(tptp_fun_Y1_29(S, B, R, A, F), B) & member(tptp_fun_X2_28(S, B, R, A, F), A) & member(tptp_fun_Y2_27(S, B, R, A, F), B) & apply(R, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_X2_28(S, B, R, A, F)) & apply(F, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_Y1_29(S, B, R, A, F)) & apply(F, tptp_fun_X2_28(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)))) | apply(S, tptp_fun_Y1_29(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)))))) <=> ![F: $i, A: $i, R: $i, B: $i, S: $i] : (~((~((~increasing(F, A, R, B, S)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(S, Y1, Y2) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(R, X1, X2)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2))))) | (~(increasing(F, A, R, B, S) | (~(apply(S, tptp_fun_Y1_29(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)) | (~member(tptp_fun_X1_30(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_29(S, B, R, A, F), B)) | (~member(tptp_fun_X2_28(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_27(S, B, R, A, F), B)) | (~apply(R, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_X2_28(S, B, R, A, F))) | (~apply(F, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_Y1_29(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_28(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)))))))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[6])).
% 0.20/0.42 tff(8,plain,
% 0.20/0.42 (![F: $i, A: $i, R: $i, B: $i, S: $i] : (increasing(F, A, R, B, S) <=> ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~(member(X1, A) & member(Y1, B) & member(X2, A) & member(Y2, B) & apply(R, X1, X2) & apply(F, X1, Y1) & apply(F, X2, Y2))) | apply(S, Y1, Y2))) <=> ![F: $i, A: $i, R: $i, B: $i, S: $i] : (increasing(F, A, R, B, S) <=> ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~(member(X1, A) & member(Y1, B) & member(X2, A) & member(Y2, B) & apply(R, X1, X2) & apply(F, X1, Y1) & apply(F, X2, Y2))) | apply(S, Y1, Y2)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(9,plain,
% 0.20/0.42 (^[F: $i, A: $i, R: $i, B: $i, S: $i] : rewrite((increasing(F, A, R, B, S) <=> ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (((((((member(X1, A) & member(Y1, B)) & member(X2, A)) & member(Y2, B)) & apply(R, X1, X2)) & apply(F, X1, Y1)) & apply(F, X2, Y2)) => apply(S, Y1, Y2))) <=> (increasing(F, A, R, B, S) <=> ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~(member(X1, A) & member(Y1, B) & member(X2, A) & member(Y2, B) & apply(R, X1, X2) & apply(F, X1, Y1) & apply(F, X2, Y2))) | apply(S, Y1, Y2))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(10,plain,
% 0.20/0.42 (![F: $i, A: $i, R: $i, B: $i, S: $i] : (increasing(F, A, R, B, S) <=> ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (((((((member(X1, A) & member(Y1, B)) & member(X2, A)) & member(Y2, B)) & apply(R, X1, X2)) & apply(F, X1, Y1)) & apply(F, X2, Y2)) => apply(S, Y1, Y2))) <=> ![F: $i, A: $i, R: $i, B: $i, S: $i] : (increasing(F, A, R, B, S) <=> ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~(member(X1, A) & member(Y1, B) & member(X2, A) & member(Y2, B) & apply(R, X1, X2) & apply(F, X1, Y1) & apply(F, X2, Y2))) | apply(S, Y1, Y2)))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[9])).
% 0.20/0.42 tff(11,axiom,(![F: $i, A: $i, R: $i, B: $i, S: $i] : (increasing(F, A, R, B, S) <=> ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (((((((member(X1, A) & member(Y1, B)) & member(X2, A)) & member(Y2, B)) & apply(R, X1, X2)) & apply(F, X1, Y1)) & apply(F, X2, Y2)) => apply(S, Y1, Y2)))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+1.ax','increasing_function')).
% 0.20/0.42 tff(12,plain,
% 0.20/0.42 (![F: $i, A: $i, R: $i, B: $i, S: $i] : (increasing(F, A, R, B, S) <=> ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~(member(X1, A) & member(Y1, B) & member(X2, A) & member(Y2, B) & apply(R, X1, X2) & apply(F, X1, Y1) & apply(F, X2, Y2))) | apply(S, Y1, Y2)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.20/0.42 tff(13,plain,
% 0.20/0.42 (![F: $i, A: $i, R: $i, B: $i, S: $i] : (increasing(F, A, R, B, S) <=> ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~(member(X1, A) & member(Y1, B) & member(X2, A) & member(Y2, B) & apply(R, X1, X2) & apply(F, X1, Y1) & apply(F, X2, Y2))) | apply(S, Y1, Y2)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[12, 8])).
% 0.20/0.42 tff(14,plain,(
% 0.20/0.42 ![F: $i, A: $i, R: $i, B: $i, S: $i] : (((~increasing(F, A, R, B, S)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~(member(X1, A) & member(Y1, B) & member(X2, A) & member(Y2, B) & apply(R, X1, X2) & apply(F, X1, Y1) & apply(F, X2, Y2))) | apply(S, Y1, Y2))) & (increasing(F, A, R, B, S) | (~((~(member(tptp_fun_X1_30(S, B, R, A, F), A) & member(tptp_fun_Y1_29(S, B, R, A, F), B) & member(tptp_fun_X2_28(S, B, R, A, F), A) & member(tptp_fun_Y2_27(S, B, R, A, F), B) & apply(R, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_X2_28(S, B, R, A, F)) & apply(F, tptp_fun_X1_30(S, B, R, A, F), tptp_fun_Y1_29(S, B, R, A, F)) & apply(F, tptp_fun_X2_28(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F)))) | apply(S, tptp_fun_Y1_29(S, B, R, A, F), tptp_fun_Y2_27(S, B, R, A, F))))))),
% 0.20/0.42 inference(skolemize,[status(sab)],[13])).
% 0.20/0.42 tff(15,plain,
% 0.20/0.42 (![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)))))))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[14, 7])).
% 0.20/0.42 tff(16,plain,
% 0.20/0.42 (![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)))))))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[15, 5])).
% 0.20/0.42 tff(17,plain,
% 0.20/0.42 (((~![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(inverse_function(F!43, A!42, B!41), B!41, S!39, A!42, R!40)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, A!42)) | (~member(Y1, A!42)) | (~member(X2, B!41)) | apply(R!40, Y1, Y2) | (~member(X1, B!41)) | (~apply(S!39, X1, X2)) | (~apply(inverse_function(F!43, A!42, B!41), X1, Y1)) | (~apply(inverse_function(F!43, A!42, B!41), X2, Y2))))) | (~(increasing(inverse_function(F!43, A!42, B!41), B!41, S!39, A!42, R!40) | (~(apply(R!40, tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))) | (~member(tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (~member(tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~member(tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (~member(tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~apply(S!39, tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))))))))))) <=> ((~![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(inverse_function(F!43, A!42, B!41), B!41, S!39, A!42, R!40)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, A!42)) | (~member(Y1, A!42)) | (~member(X2, B!41)) | apply(R!40, Y1, Y2) | (~member(X1, B!41)) | (~apply(S!39, X1, X2)) | (~apply(inverse_function(F!43, A!42, B!41), X1, Y1)) | (~apply(inverse_function(F!43, A!42, B!41), X2, Y2))))) | (~(increasing(inverse_function(F!43, A!42, B!41), B!41, S!39, A!42, R!40) | (~(apply(R!40, tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))) | (~member(tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (~member(tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~member(tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (~member(tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~apply(S!39, tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))))))))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(18,plain,
% 0.20/0.42 ((~((~((~increasing(inverse_function(F!43, A!42, B!41), B!41, S!39, A!42, R!40)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(R!40, Y1, Y2) | (~member(X1, B!41)) | (~member(Y1, A!42)) | (~member(X2, B!41)) | (~member(Y2, A!42)) | (~apply(S!39, X1, X2)) | (~apply(inverse_function(F!43, A!42, B!41), X1, Y1)) | (~apply(inverse_function(F!43, A!42, B!41), X2, Y2))))) | (~(increasing(inverse_function(F!43, A!42, B!41), B!41, S!39, A!42, R!40) | (~(apply(R!40, tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))) | (~member(tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (~member(tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~member(tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (~member(tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~apply(S!39, tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))))))))) <=> (~((~((~increasing(inverse_function(F!43, A!42, B!41), B!41, S!39, A!42, R!40)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, A!42)) | (~member(Y1, A!42)) | (~member(X2, B!41)) | apply(R!40, Y1, Y2) | (~member(X1, B!41)) | (~apply(S!39, X1, X2)) | (~apply(inverse_function(F!43, A!42, B!41), X1, Y1)) | (~apply(inverse_function(F!43, A!42, B!41), X2, Y2))))) | (~(increasing(inverse_function(F!43, A!42, B!41), B!41, S!39, A!42, R!40) | (~(apply(R!40, tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))) | (~member(tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (~member(tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~member(tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (~member(tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~apply(S!39, tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))))))))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(19,plain,
% 0.20/0.42 (((~![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(inverse_function(F!43, A!42, B!41), B!41, S!39, A!42, R!40)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(R!40, Y1, Y2) | (~member(X1, B!41)) | (~member(Y1, A!42)) | (~member(X2, B!41)) | (~member(Y2, A!42)) | (~apply(S!39, X1, X2)) | (~apply(inverse_function(F!43, A!42, B!41), X1, Y1)) | (~apply(inverse_function(F!43, A!42, B!41), X2, Y2))))) | (~(increasing(inverse_function(F!43, A!42, B!41), B!41, S!39, A!42, R!40) | (~(apply(R!40, tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))) | (~member(tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (~member(tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~member(tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (~member(tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~apply(S!39, tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))))))))))) <=> ((~![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(inverse_function(F!43, A!42, B!41), B!41, S!39, A!42, R!40)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, A!42)) | (~member(Y1, A!42)) | (~member(X2, B!41)) | apply(R!40, Y1, Y2) | (~member(X1, B!41)) | (~apply(S!39, X1, X2)) | (~apply(inverse_function(F!43, A!42, B!41), X1, Y1)) | (~apply(inverse_function(F!43, A!42, B!41), X2, Y2))))) | (~(increasing(inverse_function(F!43, A!42, B!41), B!41, S!39, A!42, R!40) | (~(apply(R!40, tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))) | (~member(tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (~member(tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~member(tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (~member(tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~apply(S!39, tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))))))))))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[18])).
% 0.20/0.42 tff(20,plain,
% 0.20/0.42 (((~![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(inverse_function(F!43, A!42, B!41), B!41, S!39, A!42, R!40)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(R!40, Y1, Y2) | (~member(X1, B!41)) | (~member(Y1, A!42)) | (~member(X2, B!41)) | (~member(Y2, A!42)) | (~apply(S!39, X1, X2)) | (~apply(inverse_function(F!43, A!42, B!41), X1, Y1)) | (~apply(inverse_function(F!43, A!42, B!41), X2, Y2))))) | (~(increasing(inverse_function(F!43, A!42, B!41), B!41, S!39, A!42, R!40) | (~(apply(R!40, tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))) | (~member(tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (~member(tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~member(tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (~member(tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~apply(S!39, tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))))))))))) <=> ((~![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(inverse_function(F!43, A!42, B!41), B!41, S!39, A!42, R!40)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, A!42)) | (~member(Y1, A!42)) | (~member(X2, B!41)) | apply(R!40, Y1, Y2) | (~member(X1, B!41)) | (~apply(S!39, X1, X2)) | (~apply(inverse_function(F!43, A!42, B!41), X1, Y1)) | (~apply(inverse_function(F!43, A!42, B!41), X2, Y2))))) | (~(increasing(inverse_function(F!43, A!42, B!41), B!41, S!39, A!42, R!40) | (~(apply(R!40, tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))) | (~member(tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (~member(tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~member(tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (~member(tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~apply(S!39, tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))))))))))),
% 0.20/0.43 inference(transitivity,[status(thm)],[19, 17])).
% 0.20/0.43 tff(21,plain,
% 0.20/0.43 ((~![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(inverse_function(F!43, A!42, B!41), B!41, S!39, A!42, R!40)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(R!40, Y1, Y2) | (~member(X1, B!41)) | (~member(Y1, A!42)) | (~member(X2, B!41)) | (~member(Y2, A!42)) | (~apply(S!39, X1, X2)) | (~apply(inverse_function(F!43, A!42, B!41), X1, Y1)) | (~apply(inverse_function(F!43, A!42, B!41), X2, Y2))))) | (~(increasing(inverse_function(F!43, A!42, B!41), B!41, S!39, A!42, R!40) | (~(apply(R!40, tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))) | (~member(tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (~member(tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~member(tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (~member(tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~apply(S!39, tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))))))))))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(22,plain,
% 0.20/0.43 ((~![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(inverse_function(F!43, A!42, B!41), B!41, S!39, A!42, R!40)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, A!42)) | (~member(Y1, A!42)) | (~member(X2, B!41)) | apply(R!40, Y1, Y2) | (~member(X1, B!41)) | (~apply(S!39, X1, X2)) | (~apply(inverse_function(F!43, A!42, B!41), X1, Y1)) | (~apply(inverse_function(F!43, A!42, B!41), X2, Y2))))) | (~(increasing(inverse_function(F!43, A!42, B!41), B!41, S!39, A!42, R!40) | (~(apply(R!40, tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))) | (~member(tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (~member(tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~member(tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (~member(tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~apply(S!39, tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))))))))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.20/0.43 tff(23,plain,
% 0.20/0.43 (~((~((~increasing(inverse_function(F!43, A!42, B!41), B!41, S!39, A!42, R!40)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, A!42)) | (~member(Y1, A!42)) | (~member(X2, B!41)) | apply(R!40, Y1, Y2) | (~member(X1, B!41)) | (~apply(S!39, X1, X2)) | (~apply(inverse_function(F!43, A!42, B!41), X1, Y1)) | (~apply(inverse_function(F!43, A!42, B!41), X2, Y2))))) | (~(increasing(inverse_function(F!43, A!42, B!41), B!41, S!39, A!42, R!40) | (~(apply(R!40, tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))) | (~member(tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (~member(tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~member(tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (~member(tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~apply(S!39, tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))))))))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[22, 16])).
% 0.20/0.43 tff(24,plain,
% 0.20/0.43 (((~((~increasing(inverse_function(F!43, A!42, B!41), B!41, S!39, A!42, R!40)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, A!42)) | (~member(Y1, A!42)) | (~member(X2, B!41)) | apply(R!40, Y1, Y2) | (~member(X1, B!41)) | (~apply(S!39, X1, X2)) | (~apply(inverse_function(F!43, A!42, B!41), X1, Y1)) | (~apply(inverse_function(F!43, A!42, B!41), X2, Y2))))) | (~(increasing(inverse_function(F!43, A!42, B!41), B!41, S!39, A!42, R!40) | (~(apply(R!40, tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))) | (~member(tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (~member(tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~member(tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (~member(tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~apply(S!39, tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))))))))) | (increasing(inverse_function(F!43, A!42, B!41), B!41, S!39, A!42, R!40) | (~(apply(R!40, tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))) | (~member(tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (~member(tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~member(tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (~member(tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~apply(S!39, tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))))))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(25,plain,
% 0.20/0.43 (increasing(inverse_function(F!43, A!42, B!41), B!41, S!39, A!42, R!40) | (~(apply(R!40, tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))) | (~member(tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (~member(tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~member(tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (~member(tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~apply(S!39, tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))))))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[24, 23])).
% 0.20/0.43 tff(26,assumption,((~((~increasing(F!43, A!42, R!40, B!41, S!39)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!41)) | apply(S!39, Y1, Y2) | (~member(X1, A!42)) | (~member(Y1, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X1, Y1)) | (~apply(F!43, X2, Y2)) | (~apply(R!40, X1, X2))))) | (~(increasing(F!43, A!42, R!40, B!41, S!39) | (~(apply(S!39, tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43)) | (~member(tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43), B!41)) | (~apply(R!40, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43)))))))), introduced(assumption)).
% 0.20/0.43 tff(27,plain,
% 0.20/0.43 (((~![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!43, A!42, R!40, B!41, S!39)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!41)) | apply(S!39, Y1, Y2) | (~member(X1, A!42)) | (~member(Y1, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X1, Y1)) | (~apply(F!43, X2, Y2)) | (~apply(R!40, X1, X2))))) | (~(increasing(F!43, A!42, R!40, B!41, S!39) | (~(apply(S!39, tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43)) | (~member(tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43), B!41)) | (~apply(R!40, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43)))))))))) <=> ((~![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!43, A!42, R!40, B!41, S!39)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!41)) | apply(S!39, Y1, Y2) | (~member(X1, A!42)) | (~member(Y1, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X1, Y1)) | (~apply(F!43, X2, Y2)) | (~apply(R!40, X1, X2))))) | (~(increasing(F!43, A!42, R!40, B!41, S!39) | (~(apply(S!39, tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43)) | (~member(tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43), B!41)) | (~apply(R!40, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43))))))))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(28,plain,
% 0.20/0.44 ((~((~((~increasing(F!43, A!42, R!40, B!41, S!39)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(S!39, Y1, Y2) | (~member(X1, A!42)) | (~member(Y1, B!41)) | (~member(X2, A!42)) | (~member(Y2, B!41)) | (~apply(R!40, X1, X2)) | (~apply(F!43, X1, Y1)) | (~apply(F!43, X2, Y2))))) | (~(increasing(F!43, A!42, R!40, B!41, S!39) | (~(apply(S!39, tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43)) | (~member(tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43), B!41)) | (~apply(R!40, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43))))))))) <=> (~((~((~increasing(F!43, A!42, R!40, B!41, S!39)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!41)) | apply(S!39, Y1, Y2) | (~member(X1, A!42)) | (~member(Y1, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X1, Y1)) | (~apply(F!43, X2, Y2)) | (~apply(R!40, X1, X2))))) | (~(increasing(F!43, A!42, R!40, B!41, S!39) | (~(apply(S!39, tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43)) | (~member(tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43), B!41)) | (~apply(R!40, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43)))))))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(29,plain,
% 0.20/0.44 (((~![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(F!43, A!42, R!40, B!41, S!39)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(S!39, Y1, Y2) | (~member(X1, A!42)) | (~member(Y1, B!41)) | (~member(X2, A!42)) | (~member(Y2, B!41)) | (~apply(R!40, X1, X2)) | (~apply(F!43, X1, Y1)) | (~apply(F!43, X2, Y2))))) | (~(increasing(F!43, A!42, R!40, B!41, S!39) | (~(apply(S!39, tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43)) | (~member(tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43), B!41)) | (~apply(R!40, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43)))))))))) <=> ((~![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!43, A!42, R!40, B!41, S!39)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!41)) | apply(S!39, Y1, Y2) | (~member(X1, A!42)) | (~member(Y1, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X1, Y1)) | (~apply(F!43, X2, Y2)) | (~apply(R!40, X1, X2))))) | (~(increasing(F!43, A!42, R!40, B!41, S!39) | (~(apply(S!39, tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43)) | (~member(tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43), B!41)) | (~apply(R!40, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43))))))))))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[28])).
% 0.20/0.44 tff(30,plain,
% 0.20/0.44 (((~![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(F!43, A!42, R!40, B!41, S!39)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(S!39, Y1, Y2) | (~member(X1, A!42)) | (~member(Y1, B!41)) | (~member(X2, A!42)) | (~member(Y2, B!41)) | (~apply(R!40, X1, X2)) | (~apply(F!43, X1, Y1)) | (~apply(F!43, X2, Y2))))) | (~(increasing(F!43, A!42, R!40, B!41, S!39) | (~(apply(S!39, tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43)) | (~member(tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43), B!41)) | (~apply(R!40, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43)))))))))) <=> ((~![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!43, A!42, R!40, B!41, S!39)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!41)) | apply(S!39, Y1, Y2) | (~member(X1, A!42)) | (~member(Y1, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X1, Y1)) | (~apply(F!43, X2, Y2)) | (~apply(R!40, X1, X2))))) | (~(increasing(F!43, A!42, R!40, B!41, S!39) | (~(apply(S!39, tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43)) | (~member(tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43), B!41)) | (~apply(R!40, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43))))))))))),
% 0.20/0.44 inference(transitivity,[status(thm)],[29, 27])).
% 0.20/0.44 tff(31,plain,
% 0.20/0.44 ((~![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(F!43, A!42, R!40, B!41, S!39)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : (apply(S!39, Y1, Y2) | (~member(X1, A!42)) | (~member(Y1, B!41)) | (~member(X2, A!42)) | (~member(Y2, B!41)) | (~apply(R!40, X1, X2)) | (~apply(F!43, X1, Y1)) | (~apply(F!43, X2, Y2))))) | (~(increasing(F!43, A!42, R!40, B!41, S!39) | (~(apply(S!39, tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43)) | (~member(tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43), B!41)) | (~apply(R!40, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43)))))))))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(32,plain,
% 0.20/0.44 ((~![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(F!43, A!42, R!40, B!41, S!39)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!41)) | apply(S!39, Y1, Y2) | (~member(X1, A!42)) | (~member(Y1, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X1, Y1)) | (~apply(F!43, X2, Y2)) | (~apply(R!40, X1, X2))))) | (~(increasing(F!43, A!42, R!40, B!41, S!39) | (~(apply(S!39, tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43)) | (~member(tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43), B!41)) | (~apply(R!40, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43)))))))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.20/0.44 tff(33,plain,
% 0.20/0.44 ($false),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[32, 16, 26])).
% 0.20/0.44 tff(34,plain,(~((~((~increasing(F!43, A!42, R!40, B!41, S!39)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!41)) | apply(S!39, Y1, Y2) | (~member(X1, A!42)) | (~member(Y1, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X1, Y1)) | (~apply(F!43, X2, Y2)) | (~apply(R!40, X1, X2))))) | (~(increasing(F!43, A!42, R!40, B!41, S!39) | (~(apply(S!39, tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43)) | (~member(tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43), B!41)) | (~apply(R!40, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43))))))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.44 tff(35,plain,
% 0.20/0.44 (((~((~increasing(F!43, A!42, R!40, B!41, S!39)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!41)) | apply(S!39, Y1, Y2) | (~member(X1, A!42)) | (~member(Y1, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X1, Y1)) | (~apply(F!43, X2, Y2)) | (~apply(R!40, X1, X2))))) | (~(increasing(F!43, A!42, R!40, B!41, S!39) | (~(apply(S!39, tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43)) | (~member(tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43), B!41)) | (~apply(R!40, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43)))))))) | (increasing(F!43, A!42, R!40, B!41, S!39) | (~(apply(S!39, tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43)) | (~member(tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43), B!41)) | (~apply(R!40, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43))))))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(36,plain,
% 0.20/0.44 (increasing(F!43, A!42, R!40, B!41, S!39) | (~(apply(S!39, tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43)) | (~member(tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43), B!41)) | (~apply(R!40, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43)))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[35, 34])).
% 0.20/0.44 tff(37,assumption,(~(apply(S!39, tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43)) | (~member(tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43), B!41)) | (~apply(R!40, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43))))), introduced(assumption)).
% 0.20/0.44 tff(38,plain,
% 0.20/0.44 ((apply(S!39, tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43)) | (~member(tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43), B!41)) | (~apply(R!40, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43)))) | apply(R!40, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(39,plain,
% 0.20/0.45 (apply(R!40, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[38, 37])).
% 0.20/0.45 tff(40,plain,
% 0.20/0.45 ((apply(S!39, tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43)) | (~member(tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43), B!41)) | (~apply(R!40, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43)))) | (~apply(S!39, tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43)))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(41,plain,
% 0.20/0.45 (~apply(S!39, tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[40, 37])).
% 0.20/0.45 tff(42,plain,
% 0.20/0.45 ((~(apply(R!40, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43)) <=> apply(S!39, tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43)))) | (~apply(R!40, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43))) | apply(S!39, tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(43,plain,
% 0.20/0.45 (~(apply(R!40, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43)) <=> apply(S!39, tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43)))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[42, 41, 39])).
% 0.20/0.45 tff(44,plain,
% 0.20/0.45 ((apply(S!39, tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43)) | (~member(tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43), B!41)) | (~apply(R!40, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43)))) | apply(F!43, tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(45,plain,
% 0.20/0.45 (apply(F!43, tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[44, 37])).
% 0.20/0.45 tff(46,plain,
% 0.20/0.45 ((apply(S!39, tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43)) | (~member(tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43), B!41)) | (~apply(R!40, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43)))) | apply(F!43, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(47,plain,
% 0.20/0.45 (apply(F!43, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[46, 37])).
% 0.20/0.45 tff(48,plain,
% 0.20/0.45 ((apply(S!39, tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43)) | (~member(tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43), B!41)) | (~apply(R!40, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43)))) | member(tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43), B!41)),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(49,plain,
% 0.20/0.45 (member(tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43), B!41)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[48, 37])).
% 0.20/0.45 tff(50,plain,
% 0.20/0.45 ((apply(S!39, tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43)) | (~member(tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43), B!41)) | (~apply(R!40, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43)))) | member(tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), A!42)),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(51,plain,
% 0.20/0.45 (member(tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), A!42)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[50, 37])).
% 0.20/0.45 tff(52,plain,
% 0.20/0.45 ((apply(S!39, tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43)) | (~member(tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43), B!41)) | (~apply(R!40, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43)))) | member(tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), B!41)),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(53,plain,
% 0.20/0.45 (member(tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), B!41)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[52, 37])).
% 0.20/0.45 tff(54,plain,
% 0.20/0.45 ((apply(S!39, tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43)) | (~member(tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43), B!41)) | (~apply(R!40, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43)))) | member(tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), A!42)),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(55,plain,
% 0.20/0.45 (member(tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), A!42)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[54, 37])).
% 0.20/0.45 tff(56,assumption,(~((~increasing(F!43, A!42, R!40, B!41, S!39)) | (~increasing(inverse_function(F!43, A!42, B!41), B!41, S!39, A!42, R!40)))), introduced(assumption)).
% 0.20/0.45 tff(57,plain,
% 0.20/0.45 ((~(isomorphism(F!43, A!42, R!40, B!41, S!39) <=> (~((~increasing(F!43, A!42, R!40, B!41, S!39)) | (~increasing(inverse_function(F!43, A!42, B!41), B!41, S!39, A!42, R!40)))))) <=> (isomorphism(F!43, A!42, R!40, B!41, S!39) <=> ((~increasing(F!43, A!42, R!40, B!41, S!39)) | (~increasing(inverse_function(F!43, A!42, B!41), B!41, S!39, A!42, R!40))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(58,plain,
% 0.20/0.45 ((isomorphism(F!43, A!42, R!40, B!41, S!39) <=> (increasing(F!43, A!42, R!40, B!41, S!39) & increasing(inverse_function(F!43, A!42, B!41), B!41, S!39, A!42, R!40))) <=> (isomorphism(F!43, A!42, R!40, B!41, S!39) <=> (~((~increasing(F!43, A!42, R!40, B!41, S!39)) | (~increasing(inverse_function(F!43, A!42, B!41), B!41, S!39, A!42, R!40)))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(59,plain,
% 0.20/0.45 ((~(isomorphism(F!43, A!42, R!40, B!41, S!39) <=> (increasing(F!43, A!42, R!40, B!41, S!39) & increasing(inverse_function(F!43, A!42, B!41), B!41, S!39, A!42, R!40)))) <=> (~(isomorphism(F!43, A!42, R!40, B!41, S!39) <=> (~((~increasing(F!43, A!42, R!40, B!41, S!39)) | (~increasing(inverse_function(F!43, A!42, B!41), B!41, S!39, A!42, R!40))))))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[58])).
% 0.20/0.45 tff(60,plain,
% 0.20/0.45 ((~(isomorphism(F!43, A!42, R!40, B!41, S!39) <=> (increasing(F!43, A!42, R!40, B!41, S!39) & increasing(inverse_function(F!43, A!42, B!41), B!41, S!39, A!42, R!40)))) <=> (isomorphism(F!43, A!42, R!40, B!41, S!39) <=> ((~increasing(F!43, A!42, R!40, B!41, S!39)) | (~increasing(inverse_function(F!43, A!42, B!41), B!41, S!39, A!42, R!40))))),
% 0.20/0.45 inference(transitivity,[status(thm)],[59, 57])).
% 0.20/0.45 tff(61,plain,
% 0.20/0.45 ((~![F: $i, A: $i, B: $i, R: $i, S: $i] : ((~(maps(F, A, B) & one_to_one(F, A, B))) | (isomorphism(F, A, R, B, S) <=> (increasing(F, A, R, B, S) & increasing(inverse_function(F, A, B), B, S, A, R))))) <=> (~![F: $i, A: $i, B: $i, R: $i, S: $i] : ((~(maps(F, A, B) & one_to_one(F, A, B))) | (isomorphism(F, A, R, B, S) <=> (increasing(F, A, R, B, S) & increasing(inverse_function(F, A, B), B, S, A, R)))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(62,plain,
% 0.20/0.45 ((~![F: $i, A: $i, B: $i, R: $i, S: $i] : ((maps(F, A, B) & one_to_one(F, A, B)) => (isomorphism(F, A, R, B, S) <=> (increasing(F, A, R, B, S) & increasing(inverse_function(F, A, B), B, S, A, R))))) <=> (~![F: $i, A: $i, B: $i, R: $i, S: $i] : ((~(maps(F, A, B) & one_to_one(F, A, B))) | (isomorphism(F, A, R, B, S) <=> (increasing(F, A, R, B, S) & increasing(inverse_function(F, A, B), B, S, A, R)))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(63,axiom,(~![F: $i, A: $i, B: $i, R: $i, S: $i] : ((maps(F, A, B) & one_to_one(F, A, B)) => (isomorphism(F, A, R, B, S) <=> (increasing(F, A, R, B, S) & increasing(inverse_function(F, A, B), B, S, A, R))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thII41')).
% 0.20/0.45 tff(64,plain,
% 0.20/0.45 (~![F: $i, A: $i, B: $i, R: $i, S: $i] : ((~(maps(F, A, B) & one_to_one(F, A, B))) | (isomorphism(F, A, R, B, S) <=> (increasing(F, A, R, B, S) & increasing(inverse_function(F, A, B), B, S, A, R))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.20/0.45 tff(65,plain,
% 0.20/0.45 (~![F: $i, A: $i, B: $i, R: $i, S: $i] : ((~(maps(F, A, B) & one_to_one(F, A, B))) | (isomorphism(F, A, R, B, S) <=> (increasing(F, A, R, B, S) & increasing(inverse_function(F, A, B), B, S, A, R))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[64, 61])).
% 0.20/0.45 tff(66,plain,
% 0.20/0.45 (~![F: $i, A: $i, B: $i, R: $i, S: $i] : ((~(maps(F, A, B) & one_to_one(F, A, B))) | (isomorphism(F, A, R, B, S) <=> (increasing(F, A, R, B, S) & increasing(inverse_function(F, A, B), B, S, A, R))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[65, 61])).
% 0.20/0.45 tff(67,plain,
% 0.20/0.45 (~![F: $i, A: $i, B: $i, R: $i, S: $i] : ((~(maps(F, A, B) & one_to_one(F, A, B))) | (isomorphism(F, A, R, B, S) <=> (increasing(F, A, R, B, S) & increasing(inverse_function(F, A, B), B, S, A, R))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[66, 61])).
% 0.20/0.45 tff(68,plain,
% 0.20/0.45 (~![F: $i, A: $i, B: $i, R: $i, S: $i] : ((~(maps(F, A, B) & one_to_one(F, A, B))) | (isomorphism(F, A, R, B, S) <=> (increasing(F, A, R, B, S) & increasing(inverse_function(F, A, B), B, S, A, R))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[67, 61])).
% 0.20/0.45 tff(69,plain,
% 0.20/0.45 (~![F: $i, A: $i, B: $i, R: $i, S: $i] : ((~(maps(F, A, B) & one_to_one(F, A, B))) | (isomorphism(F, A, R, B, S) <=> (increasing(F, A, R, B, S) & increasing(inverse_function(F, A, B), B, S, A, R))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[68, 61])).
% 0.20/0.45 tff(70,plain,
% 0.20/0.45 (~![F: $i, A: $i, B: $i, R: $i, S: $i] : ((~(maps(F, A, B) & one_to_one(F, A, B))) | (isomorphism(F, A, R, B, S) <=> (increasing(F, A, R, B, S) & increasing(inverse_function(F, A, B), B, S, A, R))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[69, 61])).
% 0.20/0.45 tff(71,plain,(
% 0.20/0.45 ~((~(maps(F!43, A!42, B!41) & one_to_one(F!43, A!42, B!41))) | (isomorphism(F!43, A!42, R!40, B!41, S!39) <=> (increasing(F!43, A!42, R!40, B!41, S!39) & increasing(inverse_function(F!43, A!42, B!41), B!41, S!39, A!42, R!40))))),
% 0.20/0.45 inference(skolemize,[status(sab)],[70])).
% 0.20/0.45 tff(72,plain,
% 0.20/0.45 (~(isomorphism(F!43, A!42, R!40, B!41, S!39) <=> (increasing(F!43, A!42, R!40, B!41, S!39) & increasing(inverse_function(F!43, A!42, B!41), B!41, S!39, A!42, R!40)))),
% 0.20/0.45 inference(or_elim,[status(thm)],[71])).
% 0.20/0.45 tff(73,plain,
% 0.20/0.45 (isomorphism(F!43, A!42, R!40, B!41, S!39) <=> ((~increasing(F!43, A!42, R!40, B!41, S!39)) | (~increasing(inverse_function(F!43, A!42, B!41), B!41, S!39, A!42, R!40)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[72, 60])).
% 0.20/0.45 tff(74,plain,
% 0.20/0.45 ((~isomorphism(F!43, A!42, R!40, B!41, S!39)) | ((~increasing(F!43, A!42, R!40, B!41, S!39)) | (~increasing(inverse_function(F!43, A!42, B!41), B!41, S!39, A!42, R!40))) | (~(isomorphism(F!43, A!42, R!40, B!41, S!39) <=> ((~increasing(F!43, A!42, R!40, B!41, S!39)) | (~increasing(inverse_function(F!43, A!42, B!41), B!41, S!39, A!42, R!40)))))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(75,plain,
% 0.20/0.45 ((~isomorphism(F!43, A!42, R!40, B!41, S!39)) | ((~increasing(F!43, A!42, R!40, B!41, S!39)) | (~increasing(inverse_function(F!43, A!42, B!41), B!41, S!39, A!42, R!40)))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[74, 73])).
% 0.20/0.45 tff(76,plain,
% 0.20/0.45 (~isomorphism(F!43, A!42, R!40, B!41, S!39)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[75, 56])).
% 0.20/0.45 tff(77,plain,
% 0.20/0.45 (^[F: $i, A: $i, R: $i, B: $i, S: $i] : rewrite((~((~((~isomorphism(F, A, R, B, S)) | (~((~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((apply(R, X1, X2) <=> apply(S, Y1, Y2)) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2)))))))) | (~(isomorphism(F, A, R, B, S) | (~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~((apply(R, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_X2_36(S, B, R, A, F)) <=> apply(S, tptp_fun_Y1_37(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F))) | (~member(tptp_fun_X1_38(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_37(S, B, R, A, F), B)) | (~member(tptp_fun_X2_36(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_35(S, B, R, A, F), B)) | (~apply(F, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_Y1_37(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_36(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F))))))))) <=> (~((~(isomorphism(F, A, R, B, S) | (~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~((apply(R, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_X2_36(S, B, R, A, F)) <=> apply(S, tptp_fun_Y1_37(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F))) | (~member(tptp_fun_X1_38(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_37(S, B, R, A, F), B)) | (~member(tptp_fun_X2_36(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_35(S, B, R, A, F), B)) | (~apply(F, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_Y1_37(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_36(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F))))))) | (~((~isomorphism(F, A, R, B, S)) | (~((~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((apply(R, X1, X2) <=> apply(S, Y1, Y2)) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2)))))))))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(78,plain,
% 0.20/0.45 (![F: $i, A: $i, R: $i, B: $i, S: $i] : (~((~((~isomorphism(F, A, R, B, S)) | (~((~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((apply(R, X1, X2) <=> apply(S, Y1, Y2)) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2)))))))) | (~(isomorphism(F, A, R, B, S) | (~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~((apply(R, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_X2_36(S, B, R, A, F)) <=> apply(S, tptp_fun_Y1_37(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F))) | (~member(tptp_fun_X1_38(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_37(S, B, R, A, F), B)) | (~member(tptp_fun_X2_36(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_35(S, B, R, A, F), B)) | (~apply(F, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_Y1_37(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_36(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F))))))))) <=> ![F: $i, A: $i, R: $i, B: $i, S: $i] : (~((~(isomorphism(F, A, R, B, S) | (~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~((apply(R, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_X2_36(S, B, R, A, F)) <=> apply(S, tptp_fun_Y1_37(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F))) | (~member(tptp_fun_X1_38(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_37(S, B, R, A, F), B)) | (~member(tptp_fun_X2_36(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_35(S, B, R, A, F), B)) | (~apply(F, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_Y1_37(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_36(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F))))))) | (~((~isomorphism(F, A, R, B, S)) | (~((~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((apply(R, X1, X2) <=> apply(S, Y1, Y2)) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2))))))))))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[77])).
% 0.20/0.45 tff(79,plain,
% 0.20/0.45 (^[F: $i, A: $i, R: $i, B: $i, S: $i] : refl((~((~((~isomorphism(F, A, R, B, S)) | (~((~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((apply(R, X1, X2) <=> apply(S, Y1, Y2)) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2)))))))) | (~(isomorphism(F, A, R, B, S) | (~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~((apply(R, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_X2_36(S, B, R, A, F)) <=> apply(S, tptp_fun_Y1_37(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F))) | (~member(tptp_fun_X1_38(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_37(S, B, R, A, F), B)) | (~member(tptp_fun_X2_36(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_35(S, B, R, A, F), B)) | (~apply(F, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_Y1_37(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_36(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F))))))))) <=> (~((~((~isomorphism(F, A, R, B, S)) | (~((~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((apply(R, X1, X2) <=> apply(S, Y1, Y2)) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2)))))))) | (~(isomorphism(F, A, R, B, S) | (~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~((apply(R, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_X2_36(S, B, R, A, F)) <=> apply(S, tptp_fun_Y1_37(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F))) | (~member(tptp_fun_X1_38(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_37(S, B, R, A, F), B)) | (~member(tptp_fun_X2_36(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_35(S, B, R, A, F), B)) | (~apply(F, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_Y1_37(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_36(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F))))))))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(80,plain,
% 0.20/0.45 (![F: $i, A: $i, R: $i, B: $i, S: $i] : (~((~((~isomorphism(F, A, R, B, S)) | (~((~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((apply(R, X1, X2) <=> apply(S, Y1, Y2)) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2)))))))) | (~(isomorphism(F, A, R, B, S) | (~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~((apply(R, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_X2_36(S, B, R, A, F)) <=> apply(S, tptp_fun_Y1_37(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F))) | (~member(tptp_fun_X1_38(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_37(S, B, R, A, F), B)) | (~member(tptp_fun_X2_36(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_35(S, B, R, A, F), B)) | (~apply(F, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_Y1_37(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_36(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F))))))))) <=> ![F: $i, A: $i, R: $i, B: $i, S: $i] : (~((~((~isomorphism(F, A, R, B, S)) | (~((~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((apply(R, X1, X2) <=> apply(S, Y1, Y2)) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2)))))))) | (~(isomorphism(F, A, R, B, S) | (~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~((apply(R, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_X2_36(S, B, R, A, F)) <=> apply(S, tptp_fun_Y1_37(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F))) | (~member(tptp_fun_X1_38(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_37(S, B, R, A, F), B)) | (~member(tptp_fun_X2_36(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_35(S, B, R, A, F), B)) | (~apply(F, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_Y1_37(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_36(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F)))))))))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[79])).
% 0.20/0.45 tff(81,plain,
% 0.20/0.45 (^[F: $i, A: $i, R: $i, B: $i, S: $i] : rewrite((~((~((~isomorphism(F, A, R, B, S)) | (~((~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((apply(R, X1, X2) <=> apply(S, Y1, Y2)) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2)))))))) | (~(isomorphism(F, A, R, B, S) | (~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~((apply(R, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_X2_36(S, B, R, A, F)) <=> apply(S, tptp_fun_Y1_37(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F))) | (~member(tptp_fun_X1_38(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_37(S, B, R, A, F), B)) | (~member(tptp_fun_X2_36(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_35(S, B, R, A, F), B)) | (~apply(F, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_Y1_37(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_36(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F))))))))) <=> (~((~((~isomorphism(F, A, R, B, S)) | (~((~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((apply(R, X1, X2) <=> apply(S, Y1, Y2)) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2)))))))) | (~(isomorphism(F, A, R, B, S) | (~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~((apply(R, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_X2_36(S, B, R, A, F)) <=> apply(S, tptp_fun_Y1_37(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F))) | (~member(tptp_fun_X1_38(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_37(S, B, R, A, F), B)) | (~member(tptp_fun_X2_36(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_35(S, B, R, A, F), B)) | (~apply(F, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_Y1_37(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_36(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F))))))))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(82,plain,
% 0.20/0.45 (![F: $i, A: $i, R: $i, B: $i, S: $i] : (~((~((~isomorphism(F, A, R, B, S)) | (~((~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((apply(R, X1, X2) <=> apply(S, Y1, Y2)) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2)))))))) | (~(isomorphism(F, A, R, B, S) | (~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~((apply(R, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_X2_36(S, B, R, A, F)) <=> apply(S, tptp_fun_Y1_37(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F))) | (~member(tptp_fun_X1_38(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_37(S, B, R, A, F), B)) | (~member(tptp_fun_X2_36(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_35(S, B, R, A, F), B)) | (~apply(F, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_Y1_37(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_36(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F))))))))) <=> ![F: $i, A: $i, R: $i, B: $i, S: $i] : (~((~((~isomorphism(F, A, R, B, S)) | (~((~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((apply(R, X1, X2) <=> apply(S, Y1, Y2)) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2)))))))) | (~(isomorphism(F, A, R, B, S) | (~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~((apply(R, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_X2_36(S, B, R, A, F)) <=> apply(S, tptp_fun_Y1_37(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F))) | (~member(tptp_fun_X1_38(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_37(S, B, R, A, F), B)) | (~member(tptp_fun_X2_36(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_35(S, B, R, A, F), B)) | (~apply(F, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_Y1_37(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_36(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F)))))))))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[81])).
% 0.20/0.45 tff(83,plain,
% 0.20/0.45 (![F: $i, A: $i, R: $i, B: $i, S: $i] : (~((~((~isomorphism(F, A, R, B, S)) | (~((~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((apply(R, X1, X2) <=> apply(S, Y1, Y2)) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2)))))))) | (~(isomorphism(F, A, R, B, S) | (~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~((apply(R, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_X2_36(S, B, R, A, F)) <=> apply(S, tptp_fun_Y1_37(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F))) | (~member(tptp_fun_X1_38(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_37(S, B, R, A, F), B)) | (~member(tptp_fun_X2_36(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_35(S, B, R, A, F), B)) | (~apply(F, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_Y1_37(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_36(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F))))))))) <=> ![F: $i, A: $i, R: $i, B: $i, S: $i] : (~((~((~isomorphism(F, A, R, B, S)) | (~((~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((apply(R, X1, X2) <=> apply(S, Y1, Y2)) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2)))))))) | (~(isomorphism(F, A, R, B, S) | (~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~((apply(R, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_X2_36(S, B, R, A, F)) <=> apply(S, tptp_fun_Y1_37(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F))) | (~member(tptp_fun_X1_38(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_37(S, B, R, A, F), B)) | (~member(tptp_fun_X2_36(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_35(S, B, R, A, F), B)) | (~apply(F, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_Y1_37(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_36(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F)))))))))),
% 0.20/0.45 inference(transitivity,[status(thm)],[82, 80])).
% 0.20/0.45 tff(84,plain,
% 0.20/0.45 (^[F: $i, A: $i, R: $i, B: $i, S: $i] : trans(monotonicity(rewrite(((~isomorphism(F, A, R, B, S)) | (maps(F, A, B) & one_to_one(F, A, B) & ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~(member(X1, A) & member(Y1, B) & member(X2, A) & member(Y2, B) & apply(F, X1, Y1) & apply(F, X2, Y2))) | (apply(R, X1, X2) <=> apply(S, Y1, Y2))))) <=> ((~isomorphism(F, A, R, B, S)) | (~((~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((apply(R, X1, X2) <=> apply(S, Y1, Y2)) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2)))))))), trans(monotonicity(rewrite((~((~(member(tptp_fun_X1_38(S, B, R, A, F), A) & member(tptp_fun_Y1_37(S, B, R, A, F), B) & member(tptp_fun_X2_36(S, B, R, A, F), A) & member(tptp_fun_Y2_35(S, B, R, A, F), B) & apply(F, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_Y1_37(S, B, R, A, F)) & apply(F, tptp_fun_X2_36(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F)))) | (apply(R, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_X2_36(S, B, R, A, F)) <=> apply(S, tptp_fun_Y1_37(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F))))) <=> (~((apply(R, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_X2_36(S, B, R, A, F)) <=> apply(S, tptp_fun_Y1_37(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F))) | (~member(tptp_fun_X1_38(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_37(S, B, R, A, F), B)) | (~member(tptp_fun_X2_36(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_35(S, B, R, A, F), B)) | (~apply(F, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_Y1_37(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_36(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F)))))), ((isomorphism(F, A, R, B, S) | (~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~((~(member(tptp_fun_X1_38(S, B, R, A, F), A) & member(tptp_fun_Y1_37(S, B, R, A, F), B) & member(tptp_fun_X2_36(S, B, R, A, F), A) & member(tptp_fun_Y2_35(S, B, R, A, F), B) & apply(F, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_Y1_37(S, B, R, A, F)) & apply(F, tptp_fun_X2_36(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F)))) | (apply(R, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_X2_36(S, B, R, A, F)) <=> apply(S, tptp_fun_Y1_37(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F)))))) <=> (isomorphism(F, A, R, B, S) | (~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~((apply(R, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_X2_36(S, B, R, A, F)) <=> apply(S, tptp_fun_Y1_37(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F))) | (~member(tptp_fun_X1_38(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_37(S, B, R, A, F), B)) | (~member(tptp_fun_X2_36(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_35(S, B, R, A, F), B)) | (~apply(F, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_Y1_37(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_36(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F)))))))), rewrite((isomorphism(F, A, R, B, S) | (~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~((apply(R, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_X2_36(S, B, R, A, F)) <=> apply(S, tptp_fun_Y1_37(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F))) | (~member(tptp_fun_X1_38(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_37(S, B, R, A, F), B)) | (~member(tptp_fun_X2_36(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_35(S, B, R, A, F), B)) | (~apply(F, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_Y1_37(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_36(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F)))))) <=> (isomorphism(F, A, R, B, S) | (~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~((apply(R, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_X2_36(S, B, R, A, F)) <=> apply(S, tptp_fun_Y1_37(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F))) | (~member(tptp_fun_X1_38(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_37(S, B, R, A, F), B)) | (~member(tptp_fun_X2_36(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_35(S, B, R, A, F), B)) | (~apply(F, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_Y1_37(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_36(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F))))))), ((isomorphism(F, A, R, B, S) | (~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~((~(member(tptp_fun_X1_38(S, B, R, A, F), A) & member(tptp_fun_Y1_37(S, B, R, A, F), B) & member(tptp_fun_X2_36(S, B, R, A, F), A) & member(tptp_fun_Y2_35(S, B, R, A, F), B) & apply(F, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_Y1_37(S, B, R, A, F)) & apply(F, tptp_fun_X2_36(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F)))) | (apply(R, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_X2_36(S, B, R, A, F)) <=> apply(S, tptp_fun_Y1_37(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F)))))) <=> (isomorphism(F, A, R, B, S) | (~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~((apply(R, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_X2_36(S, B, R, A, F)) <=> apply(S, tptp_fun_Y1_37(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F))) | (~member(tptp_fun_X1_38(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_37(S, B, R, A, F), B)) | (~member(tptp_fun_X2_36(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_35(S, B, R, A, F), B)) | (~apply(F, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_Y1_37(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_36(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F)))))))), ((((~isomorphism(F, A, R, B, S)) | (maps(F, A, B) & one_to_one(F, A, B) & ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~(member(X1, A) & member(Y1, B) & member(X2, A) & member(Y2, B) & apply(F, X1, Y1) & apply(F, X2, Y2))) | (apply(R, X1, X2) <=> apply(S, Y1, Y2))))) & (isomorphism(F, A, R, B, S) | (~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~((~(member(tptp_fun_X1_38(S, B, R, A, F), A) & member(tptp_fun_Y1_37(S, B, R, A, F), B) & member(tptp_fun_X2_36(S, B, R, A, F), A) & member(tptp_fun_Y2_35(S, B, R, A, F), B) & apply(F, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_Y1_37(S, B, R, A, F)) & apply(F, tptp_fun_X2_36(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F)))) | (apply(R, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_X2_36(S, B, R, A, F)) <=> apply(S, tptp_fun_Y1_37(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F))))))) <=> (((~isomorphism(F, A, R, B, S)) | (~((~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((apply(R, X1, X2) <=> apply(S, Y1, Y2)) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2))))))) & (isomorphism(F, A, R, B, S) | (~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~((apply(R, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_X2_36(S, B, R, A, F)) <=> apply(S, tptp_fun_Y1_37(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F))) | (~member(tptp_fun_X1_38(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_37(S, B, R, A, F), B)) | (~member(tptp_fun_X2_36(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_35(S, B, R, A, F), B)) | (~apply(F, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_Y1_37(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_36(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F))))))))), rewrite((((~isomorphism(F, A, R, B, S)) | (~((~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((apply(R, X1, X2) <=> apply(S, Y1, Y2)) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2))))))) & (isomorphism(F, A, R, B, S) | (~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~((apply(R, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_X2_36(S, B, R, A, F)) <=> apply(S, tptp_fun_Y1_37(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F))) | (~member(tptp_fun_X1_38(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_37(S, B, R, A, F), B)) | (~member(tptp_fun_X2_36(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_35(S, B, R, A, F), B)) | (~apply(F, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_Y1_37(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_36(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F))))))) <=> (~((~((~isomorphism(F, A, R, B, S)) | (~((~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((apply(R, X1, X2) <=> apply(S, Y1, Y2)) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2)))))))) | (~(isomorphism(F, A, R, B, S) | (~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~((apply(R, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_X2_36(S, B, R, A, F)) <=> apply(S, tptp_fun_Y1_37(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F))) | (~member(tptp_fun_X1_38(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_37(S, B, R, A, F), B)) | (~member(tptp_fun_X2_36(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_35(S, B, R, A, F), B)) | (~apply(F, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_Y1_37(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_36(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F)))))))))), ((((~isomorphism(F, A, R, B, S)) | (maps(F, A, B) & one_to_one(F, A, B) & ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~(member(X1, A) & member(Y1, B) & member(X2, A) & member(Y2, B) & apply(F, X1, Y1) & apply(F, X2, Y2))) | (apply(R, X1, X2) <=> apply(S, Y1, Y2))))) & (isomorphism(F, A, R, B, S) | (~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~((~(member(tptp_fun_X1_38(S, B, R, A, F), A) & member(tptp_fun_Y1_37(S, B, R, A, F), B) & member(tptp_fun_X2_36(S, B, R, A, F), A) & member(tptp_fun_Y2_35(S, B, R, A, F), B) & apply(F, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_Y1_37(S, B, R, A, F)) & apply(F, tptp_fun_X2_36(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F)))) | (apply(R, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_X2_36(S, B, R, A, F)) <=> apply(S, tptp_fun_Y1_37(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F))))))) <=> (~((~((~isomorphism(F, A, R, B, S)) | (~((~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((apply(R, X1, X2) <=> apply(S, Y1, Y2)) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2)))))))) | (~(isomorphism(F, A, R, B, S) | (~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~((apply(R, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_X2_36(S, B, R, A, F)) <=> apply(S, tptp_fun_Y1_37(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F))) | (~member(tptp_fun_X1_38(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_37(S, B, R, A, F), B)) | (~member(tptp_fun_X2_36(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_35(S, B, R, A, F), B)) | (~apply(F, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_Y1_37(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_36(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F)))))))))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(85,plain,
% 0.20/0.46 (![F: $i, A: $i, R: $i, B: $i, S: $i] : (((~isomorphism(F, A, R, B, S)) | (maps(F, A, B) & one_to_one(F, A, B) & ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~(member(X1, A) & member(Y1, B) & member(X2, A) & member(Y2, B) & apply(F, X1, Y1) & apply(F, X2, Y2))) | (apply(R, X1, X2) <=> apply(S, Y1, Y2))))) & (isomorphism(F, A, R, B, S) | (~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~((~(member(tptp_fun_X1_38(S, B, R, A, F), A) & member(tptp_fun_Y1_37(S, B, R, A, F), B) & member(tptp_fun_X2_36(S, B, R, A, F), A) & member(tptp_fun_Y2_35(S, B, R, A, F), B) & apply(F, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_Y1_37(S, B, R, A, F)) & apply(F, tptp_fun_X2_36(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F)))) | (apply(R, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_X2_36(S, B, R, A, F)) <=> apply(S, tptp_fun_Y1_37(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F))))))) <=> ![F: $i, A: $i, R: $i, B: $i, S: $i] : (~((~((~isomorphism(F, A, R, B, S)) | (~((~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((apply(R, X1, X2) <=> apply(S, Y1, Y2)) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2)))))))) | (~(isomorphism(F, A, R, B, S) | (~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~((apply(R, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_X2_36(S, B, R, A, F)) <=> apply(S, tptp_fun_Y1_37(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F))) | (~member(tptp_fun_X1_38(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_37(S, B, R, A, F), B)) | (~member(tptp_fun_X2_36(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_35(S, B, R, A, F), B)) | (~apply(F, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_Y1_37(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_36(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F)))))))))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[84])).
% 0.20/0.46 tff(86,plain,
% 0.20/0.46 (^[F: $i, A: $i, R: $i, B: $i, S: $i] : rewrite((((~isomorphism(F, A, R, B, S)) | (maps(F, A, B) & one_to_one(F, A, B) & ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~(member(X1, A) & member(Y1, B) & member(X2, A) & member(Y2, B) & apply(F, X1, Y1) & apply(F, X2, Y2))) | (apply(R, X1, X2) <=> apply(S, Y1, Y2))))) & (isomorphism(F, A, R, B, S) | ((~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~((~(member(tptp_fun_X1_38(S, B, R, A, F), A) & member(tptp_fun_Y1_37(S, B, R, A, F), B) & member(tptp_fun_X2_36(S, B, R, A, F), A) & member(tptp_fun_Y2_35(S, B, R, A, F), B) & apply(F, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_Y1_37(S, B, R, A, F)) & apply(F, tptp_fun_X2_36(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F)))) | (apply(R, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_X2_36(S, B, R, A, F)) <=> apply(S, tptp_fun_Y1_37(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F)))))))) <=> (((~isomorphism(F, A, R, B, S)) | (maps(F, A, B) & one_to_one(F, A, B) & ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~(member(X1, A) & member(Y1, B) & member(X2, A) & member(Y2, B) & apply(F, X1, Y1) & apply(F, X2, Y2))) | (apply(R, X1, X2) <=> apply(S, Y1, Y2))))) & (isomorphism(F, A, R, B, S) | (~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~((~(member(tptp_fun_X1_38(S, B, R, A, F), A) & member(tptp_fun_Y1_37(S, B, R, A, F), B) & member(tptp_fun_X2_36(S, B, R, A, F), A) & member(tptp_fun_Y2_35(S, B, R, A, F), B) & apply(F, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_Y1_37(S, B, R, A, F)) & apply(F, tptp_fun_X2_36(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F)))) | (apply(R, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_X2_36(S, B, R, A, F)) <=> apply(S, tptp_fun_Y1_37(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F))))))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(87,plain,
% 0.20/0.46 (![F: $i, A: $i, R: $i, B: $i, S: $i] : (((~isomorphism(F, A, R, B, S)) | (maps(F, A, B) & one_to_one(F, A, B) & ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~(member(X1, A) & member(Y1, B) & member(X2, A) & member(Y2, B) & apply(F, X1, Y1) & apply(F, X2, Y2))) | (apply(R, X1, X2) <=> apply(S, Y1, Y2))))) & (isomorphism(F, A, R, B, S) | ((~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~((~(member(tptp_fun_X1_38(S, B, R, A, F), A) & member(tptp_fun_Y1_37(S, B, R, A, F), B) & member(tptp_fun_X2_36(S, B, R, A, F), A) & member(tptp_fun_Y2_35(S, B, R, A, F), B) & apply(F, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_Y1_37(S, B, R, A, F)) & apply(F, tptp_fun_X2_36(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F)))) | (apply(R, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_X2_36(S, B, R, A, F)) <=> apply(S, tptp_fun_Y1_37(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F)))))))) <=> ![F: $i, A: $i, R: $i, B: $i, S: $i] : (((~isomorphism(F, A, R, B, S)) | (maps(F, A, B) & one_to_one(F, A, B) & ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~(member(X1, A) & member(Y1, B) & member(X2, A) & member(Y2, B) & apply(F, X1, Y1) & apply(F, X2, Y2))) | (apply(R, X1, X2) <=> apply(S, Y1, Y2))))) & (isomorphism(F, A, R, B, S) | (~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~((~(member(tptp_fun_X1_38(S, B, R, A, F), A) & member(tptp_fun_Y1_37(S, B, R, A, F), B) & member(tptp_fun_X2_36(S, B, R, A, F), A) & member(tptp_fun_Y2_35(S, B, R, A, F), B) & apply(F, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_Y1_37(S, B, R, A, F)) & apply(F, tptp_fun_X2_36(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F)))) | (apply(R, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_X2_36(S, B, R, A, F)) <=> apply(S, tptp_fun_Y1_37(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F)))))))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[86])).
% 0.20/0.46 tff(88,plain,
% 0.20/0.46 (![F: $i, A: $i, R: $i, B: $i, S: $i] : (isomorphism(F, A, R, B, S) <=> (maps(F, A, B) & one_to_one(F, A, B) & ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~(member(X1, A) & member(Y1, B) & member(X2, A) & member(Y2, B) & apply(F, X1, Y1) & apply(F, X2, Y2))) | (apply(R, X1, X2) <=> apply(S, Y1, Y2))))) <=> ![F: $i, A: $i, R: $i, B: $i, S: $i] : (isomorphism(F, A, R, B, S) <=> (maps(F, A, B) & one_to_one(F, A, B) & ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~(member(X1, A) & member(Y1, B) & member(X2, A) & member(Y2, B) & apply(F, X1, Y1) & apply(F, X2, Y2))) | (apply(R, X1, X2) <=> apply(S, Y1, Y2)))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(89,plain,
% 0.20/0.46 (^[F: $i, A: $i, R: $i, B: $i, S: $i] : rewrite((isomorphism(F, A, R, B, S) <=> ((maps(F, A, B) & one_to_one(F, A, B)) & ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((((((member(X1, A) & member(Y1, B)) & member(X2, A)) & member(Y2, B)) & apply(F, X1, Y1)) & apply(F, X2, Y2)) => (apply(R, X1, X2) <=> apply(S, Y1, Y2))))) <=> (isomorphism(F, A, R, B, S) <=> (maps(F, A, B) & one_to_one(F, A, B) & ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~(member(X1, A) & member(Y1, B) & member(X2, A) & member(Y2, B) & apply(F, X1, Y1) & apply(F, X2, Y2))) | (apply(R, X1, X2) <=> apply(S, Y1, Y2))))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(90,plain,
% 0.20/0.46 (![F: $i, A: $i, R: $i, B: $i, S: $i] : (isomorphism(F, A, R, B, S) <=> ((maps(F, A, B) & one_to_one(F, A, B)) & ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((((((member(X1, A) & member(Y1, B)) & member(X2, A)) & member(Y2, B)) & apply(F, X1, Y1)) & apply(F, X2, Y2)) => (apply(R, X1, X2) <=> apply(S, Y1, Y2))))) <=> ![F: $i, A: $i, R: $i, B: $i, S: $i] : (isomorphism(F, A, R, B, S) <=> (maps(F, A, B) & one_to_one(F, A, B) & ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~(member(X1, A) & member(Y1, B) & member(X2, A) & member(Y2, B) & apply(F, X1, Y1) & apply(F, X2, Y2))) | (apply(R, X1, X2) <=> apply(S, Y1, Y2)))))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[89])).
% 0.20/0.46 tff(91,axiom,(![F: $i, A: $i, R: $i, B: $i, S: $i] : (isomorphism(F, A, R, B, S) <=> ((maps(F, A, B) & one_to_one(F, A, B)) & ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((((((member(X1, A) & member(Y1, B)) & member(X2, A)) & member(Y2, B)) & apply(F, X1, Y1)) & apply(F, X2, Y2)) => (apply(R, X1, X2) <=> apply(S, Y1, Y2)))))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+1.ax','isomorphism')).
% 0.20/0.46 tff(92,plain,
% 0.20/0.46 (![F: $i, A: $i, R: $i, B: $i, S: $i] : (isomorphism(F, A, R, B, S) <=> (maps(F, A, B) & one_to_one(F, A, B) & ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~(member(X1, A) & member(Y1, B) & member(X2, A) & member(Y2, B) & apply(F, X1, Y1) & apply(F, X2, Y2))) | (apply(R, X1, X2) <=> apply(S, Y1, Y2)))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.20/0.46 tff(93,plain,
% 0.20/0.46 (![F: $i, A: $i, R: $i, B: $i, S: $i] : (isomorphism(F, A, R, B, S) <=> (maps(F, A, B) & one_to_one(F, A, B) & ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~(member(X1, A) & member(Y1, B) & member(X2, A) & member(Y2, B) & apply(F, X1, Y1) & apply(F, X2, Y2))) | (apply(R, X1, X2) <=> apply(S, Y1, Y2)))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[92, 88])).
% 0.20/0.46 tff(94,plain,(
% 0.20/0.46 ![F: $i, A: $i, R: $i, B: $i, S: $i] : (((~isomorphism(F, A, R, B, S)) | (maps(F, A, B) & one_to_one(F, A, B) & ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~(member(X1, A) & member(Y1, B) & member(X2, A) & member(Y2, B) & apply(F, X1, Y1) & apply(F, X2, Y2))) | (apply(R, X1, X2) <=> apply(S, Y1, Y2))))) & (isomorphism(F, A, R, B, S) | ((~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~((~(member(tptp_fun_X1_38(S, B, R, A, F), A) & member(tptp_fun_Y1_37(S, B, R, A, F), B) & member(tptp_fun_X2_36(S, B, R, A, F), A) & member(tptp_fun_Y2_35(S, B, R, A, F), B) & apply(F, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_Y1_37(S, B, R, A, F)) & apply(F, tptp_fun_X2_36(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F)))) | (apply(R, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_X2_36(S, B, R, A, F)) <=> apply(S, tptp_fun_Y1_37(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F))))))))),
% 0.20/0.46 inference(skolemize,[status(sab)],[93])).
% 0.20/0.46 tff(95,plain,
% 0.20/0.46 (![F: $i, A: $i, R: $i, B: $i, S: $i] : (((~isomorphism(F, A, R, B, S)) | (maps(F, A, B) & one_to_one(F, A, B) & ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~(member(X1, A) & member(Y1, B) & member(X2, A) & member(Y2, B) & apply(F, X1, Y1) & apply(F, X2, Y2))) | (apply(R, X1, X2) <=> apply(S, Y1, Y2))))) & (isomorphism(F, A, R, B, S) | (~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~((~(member(tptp_fun_X1_38(S, B, R, A, F), A) & member(tptp_fun_Y1_37(S, B, R, A, F), B) & member(tptp_fun_X2_36(S, B, R, A, F), A) & member(tptp_fun_Y2_35(S, B, R, A, F), B) & apply(F, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_Y1_37(S, B, R, A, F)) & apply(F, tptp_fun_X2_36(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F)))) | (apply(R, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_X2_36(S, B, R, A, F)) <=> apply(S, tptp_fun_Y1_37(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F)))))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[94, 87])).
% 0.20/0.46 tff(96,plain,
% 0.20/0.46 (![F: $i, A: $i, R: $i, B: $i, S: $i] : (~((~((~isomorphism(F, A, R, B, S)) | (~((~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((apply(R, X1, X2) <=> apply(S, Y1, Y2)) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2)))))))) | (~(isomorphism(F, A, R, B, S) | (~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~((apply(R, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_X2_36(S, B, R, A, F)) <=> apply(S, tptp_fun_Y1_37(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F))) | (~member(tptp_fun_X1_38(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_37(S, B, R, A, F), B)) | (~member(tptp_fun_X2_36(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_35(S, B, R, A, F), B)) | (~apply(F, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_Y1_37(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_36(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F)))))))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[95, 85])).
% 0.20/0.46 tff(97,plain,
% 0.20/0.46 (![F: $i, A: $i, R: $i, B: $i, S: $i] : (~((~((~isomorphism(F, A, R, B, S)) | (~((~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((apply(R, X1, X2) <=> apply(S, Y1, Y2)) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2)))))))) | (~(isomorphism(F, A, R, B, S) | (~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~((apply(R, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_X2_36(S, B, R, A, F)) <=> apply(S, tptp_fun_Y1_37(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F))) | (~member(tptp_fun_X1_38(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_37(S, B, R, A, F), B)) | (~member(tptp_fun_X2_36(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_35(S, B, R, A, F), B)) | (~apply(F, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_Y1_37(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_36(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F)))))))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[96, 83])).
% 0.20/0.46 tff(98,plain,
% 0.20/0.46 (![F: $i, A: $i, R: $i, B: $i, S: $i] : (~((~(isomorphism(F, A, R, B, S) | (~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~((apply(R, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_X2_36(S, B, R, A, F)) <=> apply(S, tptp_fun_Y1_37(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F))) | (~member(tptp_fun_X1_38(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_37(S, B, R, A, F), B)) | (~member(tptp_fun_X2_36(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_35(S, B, R, A, F), B)) | (~apply(F, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_Y1_37(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_36(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F))))))) | (~((~isomorphism(F, A, R, B, S)) | (~((~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((apply(R, X1, X2) <=> apply(S, Y1, Y2)) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2))))))))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[97, 78])).
% 0.20/0.46 tff(99,plain,
% 0.20/0.46 (((~![F: $i, A: $i, R: $i, B: $i, S: $i] : (~((~(isomorphism(F, A, R, B, S) | (~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~((apply(R, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_X2_36(S, B, R, A, F)) <=> apply(S, tptp_fun_Y1_37(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F))) | (~member(tptp_fun_X1_38(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_37(S, B, R, A, F), B)) | (~member(tptp_fun_X2_36(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_35(S, B, R, A, F), B)) | (~apply(F, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_Y1_37(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_36(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F))))))) | (~((~isomorphism(F, A, R, B, S)) | (~((~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((apply(R, X1, X2) <=> apply(S, Y1, Y2)) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2))))))))))) | (~((~(isomorphism(F!43, A!42, R!40, B!41, S!39) | (~maps(F!43, A!42, B!41)) | (~one_to_one(F!43, A!42, B!41)) | (~((apply(R!40, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43)) <=> apply(S!39, tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))) | (~member(tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | (~apply(F!43, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))))))) | (~((~isomorphism(F!43, A!42, R!40, B!41, S!39)) | (~((~maps(F!43, A!42, B!41)) | (~one_to_one(F!43, A!42, B!41)) | (~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!41)) | (apply(R!40, X1, X2) <=> apply(S!39, Y1, Y2)) | (~member(X1, A!42)) | (~member(Y1, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X1, Y1)) | (~apply(F!43, X2, Y2))))))))))) <=> ((~![F: $i, A: $i, R: $i, B: $i, S: $i] : (~((~(isomorphism(F, A, R, B, S) | (~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~((apply(R, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_X2_36(S, B, R, A, F)) <=> apply(S, tptp_fun_Y1_37(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F))) | (~member(tptp_fun_X1_38(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_37(S, B, R, A, F), B)) | (~member(tptp_fun_X2_36(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_35(S, B, R, A, F), B)) | (~apply(F, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_Y1_37(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_36(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F))))))) | (~((~isomorphism(F, A, R, B, S)) | (~((~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((apply(R, X1, X2) <=> apply(S, Y1, Y2)) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2))))))))))) | (~((~(isomorphism(F!43, A!42, R!40, B!41, S!39) | (~maps(F!43, A!42, B!41)) | (~one_to_one(F!43, A!42, B!41)) | (~((apply(R!40, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43)) <=> apply(S!39, tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))) | (~member(tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | (~apply(F!43, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))))))) | (~((~isomorphism(F!43, A!42, R!40, B!41, S!39)) | (~((~maps(F!43, A!42, B!41)) | (~one_to_one(F!43, A!42, B!41)) | (~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!41)) | (apply(R!40, X1, X2) <=> apply(S!39, Y1, Y2)) | (~member(X1, A!42)) | (~member(Y1, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X1, Y1)) | (~apply(F!43, X2, Y2)))))))))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(100,plain,
% 0.20/0.46 ((~((~(isomorphism(F!43, A!42, R!40, B!41, S!39) | (~maps(F!43, A!42, B!41)) | (~one_to_one(F!43, A!42, B!41)) | (~((apply(R!40, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43)) <=> apply(S!39, tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))) | (~member(tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | (~apply(F!43, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))))))) | (~((~isomorphism(F!43, A!42, R!40, B!41, S!39)) | (~((~maps(F!43, A!42, B!41)) | (~one_to_one(F!43, A!42, B!41)) | (~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((apply(R!40, X1, X2) <=> apply(S!39, Y1, Y2)) | (~member(X1, A!42)) | (~member(Y1, B!41)) | (~member(X2, A!42)) | (~member(Y2, B!41)) | (~apply(F!43, X1, Y1)) | (~apply(F!43, X2, Y2)))))))))) <=> (~((~(isomorphism(F!43, A!42, R!40, B!41, S!39) | (~maps(F!43, A!42, B!41)) | (~one_to_one(F!43, A!42, B!41)) | (~((apply(R!40, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43)) <=> apply(S!39, tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))) | (~member(tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | (~apply(F!43, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))))))) | (~((~isomorphism(F!43, A!42, R!40, B!41, S!39)) | (~((~maps(F!43, A!42, B!41)) | (~one_to_one(F!43, A!42, B!41)) | (~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!41)) | (apply(R!40, X1, X2) <=> apply(S!39, Y1, Y2)) | (~member(X1, A!42)) | (~member(Y1, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X1, Y1)) | (~apply(F!43, X2, Y2))))))))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(101,plain,
% 0.20/0.46 (((~![F: $i, A: $i, R: $i, B: $i, S: $i] : (~((~(isomorphism(F, A, R, B, S) | (~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~((apply(R, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_X2_36(S, B, R, A, F)) <=> apply(S, tptp_fun_Y1_37(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F))) | (~member(tptp_fun_X1_38(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_37(S, B, R, A, F), B)) | (~member(tptp_fun_X2_36(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_35(S, B, R, A, F), B)) | (~apply(F, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_Y1_37(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_36(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F))))))) | (~((~isomorphism(F, A, R, B, S)) | (~((~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((apply(R, X1, X2) <=> apply(S, Y1, Y2)) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2))))))))))) | (~((~(isomorphism(F!43, A!42, R!40, B!41, S!39) | (~maps(F!43, A!42, B!41)) | (~one_to_one(F!43, A!42, B!41)) | (~((apply(R!40, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43)) <=> apply(S!39, tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))) | (~member(tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | (~apply(F!43, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))))))) | (~((~isomorphism(F!43, A!42, R!40, B!41, S!39)) | (~((~maps(F!43, A!42, B!41)) | (~one_to_one(F!43, A!42, B!41)) | (~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((apply(R!40, X1, X2) <=> apply(S!39, Y1, Y2)) | (~member(X1, A!42)) | (~member(Y1, B!41)) | (~member(X2, A!42)) | (~member(Y2, B!41)) | (~apply(F!43, X1, Y1)) | (~apply(F!43, X2, Y2))))))))))) <=> ((~![F: $i, A: $i, R: $i, B: $i, S: $i] : (~((~(isomorphism(F, A, R, B, S) | (~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~((apply(R, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_X2_36(S, B, R, A, F)) <=> apply(S, tptp_fun_Y1_37(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F))) | (~member(tptp_fun_X1_38(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_37(S, B, R, A, F), B)) | (~member(tptp_fun_X2_36(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_35(S, B, R, A, F), B)) | (~apply(F, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_Y1_37(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_36(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F))))))) | (~((~isomorphism(F, A, R, B, S)) | (~((~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((apply(R, X1, X2) <=> apply(S, Y1, Y2)) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2))))))))))) | (~((~(isomorphism(F!43, A!42, R!40, B!41, S!39) | (~maps(F!43, A!42, B!41)) | (~one_to_one(F!43, A!42, B!41)) | (~((apply(R!40, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43)) <=> apply(S!39, tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))) | (~member(tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | (~apply(F!43, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))))))) | (~((~isomorphism(F!43, A!42, R!40, B!41, S!39)) | (~((~maps(F!43, A!42, B!41)) | (~one_to_one(F!43, A!42, B!41)) | (~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!41)) | (apply(R!40, X1, X2) <=> apply(S!39, Y1, Y2)) | (~member(X1, A!42)) | (~member(Y1, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X1, Y1)) | (~apply(F!43, X2, Y2)))))))))))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[100])).
% 0.20/0.46 tff(102,plain,
% 0.20/0.46 (((~![F: $i, A: $i, R: $i, B: $i, S: $i] : (~((~(isomorphism(F, A, R, B, S) | (~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~((apply(R, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_X2_36(S, B, R, A, F)) <=> apply(S, tptp_fun_Y1_37(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F))) | (~member(tptp_fun_X1_38(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_37(S, B, R, A, F), B)) | (~member(tptp_fun_X2_36(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_35(S, B, R, A, F), B)) | (~apply(F, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_Y1_37(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_36(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F))))))) | (~((~isomorphism(F, A, R, B, S)) | (~((~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((apply(R, X1, X2) <=> apply(S, Y1, Y2)) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2))))))))))) | (~((~(isomorphism(F!43, A!42, R!40, B!41, S!39) | (~maps(F!43, A!42, B!41)) | (~one_to_one(F!43, A!42, B!41)) | (~((apply(R!40, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43)) <=> apply(S!39, tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))) | (~member(tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | (~apply(F!43, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))))))) | (~((~isomorphism(F!43, A!42, R!40, B!41, S!39)) | (~((~maps(F!43, A!42, B!41)) | (~one_to_one(F!43, A!42, B!41)) | (~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((apply(R!40, X1, X2) <=> apply(S!39, Y1, Y2)) | (~member(X1, A!42)) | (~member(Y1, B!41)) | (~member(X2, A!42)) | (~member(Y2, B!41)) | (~apply(F!43, X1, Y1)) | (~apply(F!43, X2, Y2))))))))))) <=> ((~![F: $i, A: $i, R: $i, B: $i, S: $i] : (~((~(isomorphism(F, A, R, B, S) | (~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~((apply(R, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_X2_36(S, B, R, A, F)) <=> apply(S, tptp_fun_Y1_37(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F))) | (~member(tptp_fun_X1_38(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_37(S, B, R, A, F), B)) | (~member(tptp_fun_X2_36(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_35(S, B, R, A, F), B)) | (~apply(F, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_Y1_37(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_36(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F))))))) | (~((~isomorphism(F, A, R, B, S)) | (~((~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((apply(R, X1, X2) <=> apply(S, Y1, Y2)) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2))))))))))) | (~((~(isomorphism(F!43, A!42, R!40, B!41, S!39) | (~maps(F!43, A!42, B!41)) | (~one_to_one(F!43, A!42, B!41)) | (~((apply(R!40, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43)) <=> apply(S!39, tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))) | (~member(tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | (~apply(F!43, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))))))) | (~((~isomorphism(F!43, A!42, R!40, B!41, S!39)) | (~((~maps(F!43, A!42, B!41)) | (~one_to_one(F!43, A!42, B!41)) | (~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!41)) | (apply(R!40, X1, X2) <=> apply(S!39, Y1, Y2)) | (~member(X1, A!42)) | (~member(Y1, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X1, Y1)) | (~apply(F!43, X2, Y2)))))))))))),
% 0.20/0.47 inference(transitivity,[status(thm)],[101, 99])).
% 0.20/0.47 tff(103,plain,
% 0.20/0.47 ((~![F: $i, A: $i, R: $i, B: $i, S: $i] : (~((~(isomorphism(F, A, R, B, S) | (~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~((apply(R, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_X2_36(S, B, R, A, F)) <=> apply(S, tptp_fun_Y1_37(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F))) | (~member(tptp_fun_X1_38(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_37(S, B, R, A, F), B)) | (~member(tptp_fun_X2_36(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_35(S, B, R, A, F), B)) | (~apply(F, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_Y1_37(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_36(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F))))))) | (~((~isomorphism(F, A, R, B, S)) | (~((~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((apply(R, X1, X2) <=> apply(S, Y1, Y2)) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2))))))))))) | (~((~(isomorphism(F!43, A!42, R!40, B!41, S!39) | (~maps(F!43, A!42, B!41)) | (~one_to_one(F!43, A!42, B!41)) | (~((apply(R!40, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43)) <=> apply(S!39, tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))) | (~member(tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | (~apply(F!43, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))))))) | (~((~isomorphism(F!43, A!42, R!40, B!41, S!39)) | (~((~maps(F!43, A!42, B!41)) | (~one_to_one(F!43, A!42, B!41)) | (~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((apply(R!40, X1, X2) <=> apply(S!39, Y1, Y2)) | (~member(X1, A!42)) | (~member(Y1, B!41)) | (~member(X2, A!42)) | (~member(Y2, B!41)) | (~apply(F!43, X1, Y1)) | (~apply(F!43, X2, Y2))))))))))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(104,plain,
% 0.20/0.47 ((~![F: $i, A: $i, R: $i, B: $i, S: $i] : (~((~(isomorphism(F, A, R, B, S) | (~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~((apply(R, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_X2_36(S, B, R, A, F)) <=> apply(S, tptp_fun_Y1_37(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F))) | (~member(tptp_fun_X1_38(S, B, R, A, F), A)) | (~member(tptp_fun_Y1_37(S, B, R, A, F), B)) | (~member(tptp_fun_X2_36(S, B, R, A, F), A)) | (~member(tptp_fun_Y2_35(S, B, R, A, F), B)) | (~apply(F, tptp_fun_X1_38(S, B, R, A, F), tptp_fun_Y1_37(S, B, R, A, F))) | (~apply(F, tptp_fun_X2_36(S, B, R, A, F), tptp_fun_Y2_35(S, B, R, A, F))))))) | (~((~isomorphism(F, A, R, B, S)) | (~((~maps(F, A, B)) | (~one_to_one(F, A, B)) | (~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((apply(R, X1, X2) <=> apply(S, Y1, Y2)) | (~member(X1, A)) | (~member(Y1, B)) | (~member(X2, A)) | (~member(Y2, B)) | (~apply(F, X1, Y1)) | (~apply(F, X2, Y2))))))))))) | (~((~(isomorphism(F!43, A!42, R!40, B!41, S!39) | (~maps(F!43, A!42, B!41)) | (~one_to_one(F!43, A!42, B!41)) | (~((apply(R!40, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43)) <=> apply(S!39, tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))) | (~member(tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | (~apply(F!43, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))))))) | (~((~isomorphism(F!43, A!42, R!40, B!41, S!39)) | (~((~maps(F!43, A!42, B!41)) | (~one_to_one(F!43, A!42, B!41)) | (~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!41)) | (apply(R!40, X1, X2) <=> apply(S!39, Y1, Y2)) | (~member(X1, A!42)) | (~member(Y1, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X1, Y1)) | (~apply(F!43, X2, Y2))))))))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.20/0.47 tff(105,plain,
% 0.20/0.47 (~((~(isomorphism(F!43, A!42, R!40, B!41, S!39) | (~maps(F!43, A!42, B!41)) | (~one_to_one(F!43, A!42, B!41)) | (~((apply(R!40, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43)) <=> apply(S!39, tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))) | (~member(tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | (~apply(F!43, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))))))) | (~((~isomorphism(F!43, A!42, R!40, B!41, S!39)) | (~((~maps(F!43, A!42, B!41)) | (~one_to_one(F!43, A!42, B!41)) | (~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!41)) | (apply(R!40, X1, X2) <=> apply(S!39, Y1, Y2)) | (~member(X1, A!42)) | (~member(Y1, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X1, Y1)) | (~apply(F!43, X2, Y2)))))))))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[104, 98])).
% 0.20/0.47 tff(106,plain,
% 0.20/0.47 (((~(isomorphism(F!43, A!42, R!40, B!41, S!39) | (~maps(F!43, A!42, B!41)) | (~one_to_one(F!43, A!42, B!41)) | (~((apply(R!40, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43)) <=> apply(S!39, tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))) | (~member(tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | (~apply(F!43, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))))))) | (~((~isomorphism(F!43, A!42, R!40, B!41, S!39)) | (~((~maps(F!43, A!42, B!41)) | (~one_to_one(F!43, A!42, B!41)) | (~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!41)) | (apply(R!40, X1, X2) <=> apply(S!39, Y1, Y2)) | (~member(X1, A!42)) | (~member(Y1, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X1, Y1)) | (~apply(F!43, X2, Y2))))))))) | (isomorphism(F!43, A!42, R!40, B!41, S!39) | (~maps(F!43, A!42, B!41)) | (~one_to_one(F!43, A!42, B!41)) | (~((apply(R!40, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43)) <=> apply(S!39, tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))) | (~member(tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | (~apply(F!43, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))))))),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(107,plain,
% 0.20/0.47 (isomorphism(F!43, A!42, R!40, B!41, S!39) | (~maps(F!43, A!42, B!41)) | (~one_to_one(F!43, A!42, B!41)) | (~((apply(R!40, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43)) <=> apply(S!39, tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))) | (~member(tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | (~apply(F!43, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43)))))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[106, 105])).
% 0.20/0.47 tff(108,plain,
% 0.20/0.47 (maps(F!43, A!42, B!41) & one_to_one(F!43, A!42, B!41)),
% 0.20/0.47 inference(or_elim,[status(thm)],[71])).
% 0.20/0.47 tff(109,plain,
% 0.20/0.47 (one_to_one(F!43, A!42, B!41)),
% 0.20/0.47 inference(and_elim,[status(thm)],[108])).
% 0.20/0.47 tff(110,plain,
% 0.20/0.47 (maps(F!43, A!42, B!41)),
% 0.20/0.47 inference(and_elim,[status(thm)],[108])).
% 0.20/0.47 tff(111,plain,
% 0.20/0.47 ((~(isomorphism(F!43, A!42, R!40, B!41, S!39) | (~maps(F!43, A!42, B!41)) | (~one_to_one(F!43, A!42, B!41)) | (~((apply(R!40, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43)) <=> apply(S!39, tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))) | (~member(tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | (~apply(F!43, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))))))) | isomorphism(F!43, A!42, R!40, B!41, S!39) | (~maps(F!43, A!42, B!41)) | (~one_to_one(F!43, A!42, B!41)) | (~((apply(R!40, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43)) <=> apply(S!39, tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))) | (~member(tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | (~apply(F!43, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43)))))),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(112,plain,
% 0.20/0.47 ((~(isomorphism(F!43, A!42, R!40, B!41, S!39) | (~maps(F!43, A!42, B!41)) | (~one_to_one(F!43, A!42, B!41)) | (~((apply(R!40, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43)) <=> apply(S!39, tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))) | (~member(tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | (~apply(F!43, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))))))) | isomorphism(F!43, A!42, R!40, B!41, S!39) | (~((apply(R!40, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43)) <=> apply(S!39, tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))) | (~member(tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | (~apply(F!43, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43)))))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[111, 110, 109])).
% 0.20/0.47 tff(113,plain,
% 0.20/0.47 (isomorphism(F!43, A!42, R!40, B!41, S!39) | (~((apply(R!40, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43)) <=> apply(S!39, tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))) | (~member(tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | (~apply(F!43, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43)))))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[112, 107])).
% 0.20/0.47 tff(114,plain,
% 0.20/0.47 (~((apply(R!40, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43)) <=> apply(S!39, tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))) | (~member(tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | (~apply(F!43, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[113, 76])).
% 0.20/0.47 tff(115,plain,
% 0.20/0.47 (((apply(R!40, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43)) <=> apply(S!39, tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))) | (~member(tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | (~apply(F!43, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43)))) | member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(116,plain,
% 0.20/0.47 (member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[115, 114])).
% 0.20/0.47 tff(117,plain,
% 0.20/0.47 (^[F: $i, A: $i, B: $i] : refl((~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))))))) <=> (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))))))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(118,plain,
% 0.20/0.47 (![F: $i, A: $i, B: $i] : (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))))))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[117])).
% 0.20/0.47 tff(119,plain,
% 0.20/0.47 (^[F: $i, A: $i, B: $i] : rewrite((~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))))))) <=> (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))))))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(120,plain,
% 0.20/0.47 (![F: $i, A: $i, B: $i] : (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))))))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[119])).
% 0.20/0.47 tff(121,plain,
% 0.20/0.47 (![F: $i, A: $i, B: $i] : (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))))))),
% 0.20/0.47 inference(transitivity,[status(thm)],[120, 118])).
% 0.20/0.47 tff(122,plain,
% 0.20/0.47 (^[F: $i, A: $i, B: $i] : trans(monotonicity(rewrite(((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (member(tptp_fun_E_19(Y, A, F), A) & apply(F, tptp_fun_E_19(Y, A, F), Y)))) <=> ((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))), trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[E: $i] : trans(monotonicity(rewrite((member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F))) <=> (~((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))), ((~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F)))) <=> (~(~((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))), rewrite((~(~((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))) <=> ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))), ((~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F)))) <=> ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))), (![E: $i] : (~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F)))) <=> ![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))), ((member(tptp_fun_Y_20(B, A, F), B) & ![E: $i] : (~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F))))) <=> (member(tptp_fun_Y_20(B, A, F), B) & ![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))), rewrite((member(tptp_fun_Y_20(B, A, F), B) & ![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))) <=> (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))), ((member(tptp_fun_Y_20(B, A, F), B) & ![E: $i] : (~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F))))) <=> (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))))), ((surjective(F, A, B) | (member(tptp_fun_Y_20(B, A, F), B) & ![E: $i] : (~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F)))))) <=> (surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))))), rewrite((surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))) <=> (surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))))), ((surjective(F, A, B) | (member(tptp_fun_Y_20(B, A, F), B) & ![E: $i] : (~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F)))))) <=> (surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))))), ((((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (member(tptp_fun_E_19(Y, A, F), A) & apply(F, tptp_fun_E_19(Y, A, F), Y)))) & (surjective(F, A, B) | (member(tptp_fun_Y_20(B, A, F), B) & ![E: $i] : (~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F))))))) <=> (((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y)))))) & (surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))))))), rewrite((((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y)))))) & (surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))))) <=> (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))))))), ((((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (member(tptp_fun_E_19(Y, A, F), A) & apply(F, tptp_fun_E_19(Y, A, F), Y)))) & (surjective(F, A, B) | (member(tptp_fun_Y_20(B, A, F), B) & ![E: $i] : (~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F))))))) <=> (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))))))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(123,plain,
% 0.20/0.48 (![F: $i, A: $i, B: $i] : (((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (member(tptp_fun_E_19(Y, A, F), A) & apply(F, tptp_fun_E_19(Y, A, F), Y)))) & (surjective(F, A, B) | (member(tptp_fun_Y_20(B, A, F), B) & ![E: $i] : (~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[122])).
% 0.20/0.48 tff(124,plain,
% 0.20/0.48 (^[F: $i, A: $i, B: $i] : rewrite((((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (member(tptp_fun_E_19(Y, A, F), A) & apply(F, tptp_fun_E_19(Y, A, F), Y)))) & (surjective(F, A, B) | ((~(~member(tptp_fun_Y_20(B, A, F), B))) & ![E: $i] : (~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F))))))) <=> (((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (member(tptp_fun_E_19(Y, A, F), A) & apply(F, tptp_fun_E_19(Y, A, F), Y)))) & (surjective(F, A, B) | (member(tptp_fun_Y_20(B, A, F), B) & ![E: $i] : (~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F))))))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(125,plain,
% 0.20/0.48 (![F: $i, A: $i, B: $i] : (((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (member(tptp_fun_E_19(Y, A, F), A) & apply(F, tptp_fun_E_19(Y, A, F), Y)))) & (surjective(F, A, B) | ((~(~member(tptp_fun_Y_20(B, A, F), B))) & ![E: $i] : (~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F))))))) <=> ![F: $i, A: $i, B: $i] : (((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (member(tptp_fun_E_19(Y, A, F), A) & apply(F, tptp_fun_E_19(Y, A, F), Y)))) & (surjective(F, A, B) | (member(tptp_fun_Y_20(B, A, F), B) & ![E: $i] : (~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F)))))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[124])).
% 0.20/0.48 tff(126,plain,
% 0.20/0.48 (![F: $i, A: $i, B: $i] : (surjective(F, A, B) <=> ![Y: $i] : ((~member(Y, B)) | ?[E: $i] : (member(E, A) & apply(F, E, Y)))) <=> ![F: $i, A: $i, B: $i] : (surjective(F, A, B) <=> ![Y: $i] : ((~member(Y, B)) | ?[E: $i] : (member(E, A) & apply(F, E, Y))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(127,plain,
% 0.20/0.48 (^[F: $i, A: $i, B: $i] : rewrite((surjective(F, A, B) <=> ![Y: $i] : (member(Y, B) => ?[E: $i] : (member(E, A) & apply(F, E, Y)))) <=> (surjective(F, A, B) <=> ![Y: $i] : ((~member(Y, B)) | ?[E: $i] : (member(E, A) & apply(F, E, Y)))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(128,plain,
% 0.20/0.48 (![F: $i, A: $i, B: $i] : (surjective(F, A, B) <=> ![Y: $i] : (member(Y, B) => ?[E: $i] : (member(E, A) & apply(F, E, Y)))) <=> ![F: $i, A: $i, B: $i] : (surjective(F, A, B) <=> ![Y: $i] : ((~member(Y, B)) | ?[E: $i] : (member(E, A) & apply(F, E, Y))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[127])).
% 0.20/0.48 tff(129,axiom,(![F: $i, A: $i, B: $i] : (surjective(F, A, B) <=> ![Y: $i] : (member(Y, B) => ?[E: $i] : (member(E, A) & apply(F, E, Y))))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+1.ax','surjective')).
% 0.20/0.48 tff(130,plain,
% 0.20/0.48 (![F: $i, A: $i, B: $i] : (surjective(F, A, B) <=> ![Y: $i] : ((~member(Y, B)) | ?[E: $i] : (member(E, A) & apply(F, E, Y))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[129, 128])).
% 0.20/0.48 tff(131,plain,
% 0.20/0.48 (![F: $i, A: $i, B: $i] : (surjective(F, A, B) <=> ![Y: $i] : ((~member(Y, B)) | ?[E: $i] : (member(E, A) & apply(F, E, Y))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[130, 126])).
% 0.20/0.48 tff(132,plain,(
% 0.20/0.48 ![F: $i, A: $i, B: $i] : (((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (member(tptp_fun_E_19(Y, A, F), A) & apply(F, tptp_fun_E_19(Y, A, F), Y)))) & (surjective(F, A, B) | ((~(~member(tptp_fun_Y_20(B, A, F), B))) & ![E: $i] : (~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F)))))))),
% 0.20/0.48 inference(skolemize,[status(sab)],[131])).
% 0.20/0.48 tff(133,plain,
% 0.20/0.48 (![F: $i, A: $i, B: $i] : (((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (member(tptp_fun_E_19(Y, A, F), A) & apply(F, tptp_fun_E_19(Y, A, F), Y)))) & (surjective(F, A, B) | (member(tptp_fun_Y_20(B, A, F), B) & ![E: $i] : (~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F)))))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[132, 125])).
% 0.20/0.48 tff(134,plain,
% 0.20/0.48 (![F: $i, A: $i, B: $i] : (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[133, 123])).
% 0.20/0.48 tff(135,plain,
% 0.20/0.48 (![F: $i, A: $i, B: $i] : (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[134, 121])).
% 0.20/0.48 tff(136,plain,
% 0.20/0.48 ((~![F: $i, A: $i, B: $i] : (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))))))) | (~((~((~surjective(F!43, A!42, B!41)) | ![Y: $i] : ((~member(Y, B!41)) | (~((~member(tptp_fun_E_19(Y, A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_E_19(Y, A!42, F!43), Y))))))) | (~(surjective(F!43, A!42, B!41) | (~((~member(tptp_fun_Y_20(B!41, A!42, F!43), B!41)) | (~![E: $i] : ((~member(E, A!42)) | (~apply(F!43, E, tptp_fun_Y_20(B!41, A!42, F!43)))))))))))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(137,plain,
% 0.20/0.48 (~((~((~surjective(F!43, A!42, B!41)) | ![Y: $i] : ((~member(Y, B!41)) | (~((~member(tptp_fun_E_19(Y, A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_E_19(Y, A!42, F!43), Y))))))) | (~(surjective(F!43, A!42, B!41) | (~((~member(tptp_fun_Y_20(B!41, A!42, F!43), B!41)) | (~![E: $i] : ((~member(E, A!42)) | (~apply(F!43, E, tptp_fun_Y_20(B!41, A!42, F!43))))))))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[136, 135])).
% 0.20/0.48 tff(138,plain,
% 0.20/0.48 (((~((~surjective(F!43, A!42, B!41)) | ![Y: $i] : ((~member(Y, B!41)) | (~((~member(tptp_fun_E_19(Y, A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_E_19(Y, A!42, F!43), Y))))))) | (~(surjective(F!43, A!42, B!41) | (~((~member(tptp_fun_Y_20(B!41, A!42, F!43), B!41)) | (~![E: $i] : ((~member(E, A!42)) | (~apply(F!43, E, tptp_fun_Y_20(B!41, A!42, F!43)))))))))) | ((~surjective(F!43, A!42, B!41)) | ![Y: $i] : ((~member(Y, B!41)) | (~((~member(tptp_fun_E_19(Y, A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_E_19(Y, A!42, F!43), Y))))))),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(139,plain,
% 0.20/0.48 ((~surjective(F!43, A!42, B!41)) | ![Y: $i] : ((~member(Y, B!41)) | (~((~member(tptp_fun_E_19(Y, A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_E_19(Y, A!42, F!43), Y)))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[138, 137])).
% 0.20/0.48 tff(140,plain,
% 0.20/0.48 (^[F: $i, A: $i, B: $i] : refl((one_to_one(F, A, B) <=> (~((~injective(F, A, B)) | (~surjective(F, A, B))))) <=> (one_to_one(F, A, B) <=> (~((~injective(F, A, B)) | (~surjective(F, A, B))))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(141,plain,
% 0.20/0.48 (![F: $i, A: $i, B: $i] : (one_to_one(F, A, B) <=> (~((~injective(F, A, B)) | (~surjective(F, A, B))))) <=> ![F: $i, A: $i, B: $i] : (one_to_one(F, A, B) <=> (~((~injective(F, A, B)) | (~surjective(F, A, B)))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[140])).
% 0.20/0.48 tff(142,plain,
% 0.20/0.48 (^[F: $i, A: $i, B: $i] : rewrite((one_to_one(F, A, B) <=> (injective(F, A, B) & surjective(F, A, B))) <=> (one_to_one(F, A, B) <=> (~((~injective(F, A, B)) | (~surjective(F, A, B))))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(143,plain,
% 0.20/0.48 (![F: $i, A: $i, B: $i] : (one_to_one(F, A, B) <=> (injective(F, A, B) & surjective(F, A, B))) <=> ![F: $i, A: $i, B: $i] : (one_to_one(F, A, B) <=> (~((~injective(F, A, B)) | (~surjective(F, A, B)))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[142])).
% 0.20/0.48 tff(144,plain,
% 0.20/0.48 (![F: $i, A: $i, B: $i] : (one_to_one(F, A, B) <=> (injective(F, A, B) & surjective(F, A, B))) <=> ![F: $i, A: $i, B: $i] : (one_to_one(F, A, B) <=> (injective(F, A, B) & surjective(F, A, B)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(145,axiom,(![F: $i, A: $i, B: $i] : (one_to_one(F, A, B) <=> (injective(F, A, B) & surjective(F, A, B)))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+1.ax','one_to_one')).
% 0.20/0.48 tff(146,plain,
% 0.20/0.48 (![F: $i, A: $i, B: $i] : (one_to_one(F, A, B) <=> (injective(F, A, B) & surjective(F, A, B)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[145, 144])).
% 0.20/0.48 tff(147,plain,(
% 0.20/0.48 ![F: $i, A: $i, B: $i] : (one_to_one(F, A, B) <=> (injective(F, A, B) & surjective(F, A, B)))),
% 0.20/0.48 inference(skolemize,[status(sab)],[146])).
% 0.20/0.48 tff(148,plain,
% 0.20/0.48 (![F: $i, A: $i, B: $i] : (one_to_one(F, A, B) <=> (~((~injective(F, A, B)) | (~surjective(F, A, B)))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[147, 143])).
% 0.20/0.48 tff(149,plain,
% 0.20/0.48 (![F: $i, A: $i, B: $i] : (one_to_one(F, A, B) <=> (~((~injective(F, A, B)) | (~surjective(F, A, B)))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[148, 141])).
% 0.20/0.48 tff(150,plain,
% 0.20/0.48 ((~![F: $i, A: $i, B: $i] : (one_to_one(F, A, B) <=> (~((~injective(F, A, B)) | (~surjective(F, A, B)))))) | (one_to_one(F!43, A!42, B!41) <=> (~((~injective(F!43, A!42, B!41)) | (~surjective(F!43, A!42, B!41)))))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(151,plain,
% 0.20/0.48 (one_to_one(F!43, A!42, B!41) <=> (~((~injective(F!43, A!42, B!41)) | (~surjective(F!43, A!42, B!41))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[150, 149])).
% 0.20/0.48 tff(152,plain,
% 0.20/0.48 ((~(one_to_one(F!43, A!42, B!41) <=> (~((~injective(F!43, A!42, B!41)) | (~surjective(F!43, A!42, B!41)))))) | (~one_to_one(F!43, A!42, B!41)) | (~((~injective(F!43, A!42, B!41)) | (~surjective(F!43, A!42, B!41))))),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(153,plain,
% 0.20/0.48 ((~(one_to_one(F!43, A!42, B!41) <=> (~((~injective(F!43, A!42, B!41)) | (~surjective(F!43, A!42, B!41)))))) | (~((~injective(F!43, A!42, B!41)) | (~surjective(F!43, A!42, B!41))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[152, 109])).
% 0.20/0.48 tff(154,plain,
% 0.20/0.48 (~((~injective(F!43, A!42, B!41)) | (~surjective(F!43, A!42, B!41)))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[153, 151])).
% 0.20/0.48 tff(155,plain,
% 0.20/0.48 (((~injective(F!43, A!42, B!41)) | (~surjective(F!43, A!42, B!41))) | surjective(F!43, A!42, B!41)),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(156,plain,
% 0.20/0.48 (surjective(F!43, A!42, B!41)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[155, 154])).
% 0.20/0.48 tff(157,plain,
% 0.20/0.48 ((~((~surjective(F!43, A!42, B!41)) | ![Y: $i] : ((~member(Y, B!41)) | (~((~member(tptp_fun_E_19(Y, A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_E_19(Y, A!42, F!43), Y))))))) | (~surjective(F!43, A!42, B!41)) | ![Y: $i] : ((~member(Y, B!41)) | (~((~member(tptp_fun_E_19(Y, A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_E_19(Y, A!42, F!43), Y)))))),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(158,plain,
% 0.20/0.48 ((~((~surjective(F!43, A!42, B!41)) | ![Y: $i] : ((~member(Y, B!41)) | (~((~member(tptp_fun_E_19(Y, A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_E_19(Y, A!42, F!43), Y))))))) | ![Y: $i] : ((~member(Y, B!41)) | (~((~member(tptp_fun_E_19(Y, A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_E_19(Y, A!42, F!43), Y)))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[157, 156])).
% 0.20/0.48 tff(159,plain,
% 0.20/0.48 (![Y: $i] : ((~member(Y, B!41)) | (~((~member(tptp_fun_E_19(Y, A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_E_19(Y, A!42, F!43), Y)))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[158, 139])).
% 0.20/0.48 tff(160,plain,
% 0.20/0.48 (((~![Y: $i] : ((~member(Y, B!41)) | (~((~member(tptp_fun_E_19(Y, A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_E_19(Y, A!42, F!43), Y)))))) | ((~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | (~((~member(tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))))))) <=> ((~![Y: $i] : ((~member(Y, B!41)) | (~((~member(tptp_fun_E_19(Y, A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_E_19(Y, A!42, F!43), Y)))))) | (~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | (~((~member(tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(161,plain,
% 0.20/0.48 ((~![Y: $i] : ((~member(Y, B!41)) | (~((~member(tptp_fun_E_19(Y, A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_E_19(Y, A!42, F!43), Y)))))) | ((~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | (~((~member(tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))))))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(162,plain,
% 0.20/0.48 ((~![Y: $i] : ((~member(Y, B!41)) | (~((~member(tptp_fun_E_19(Y, A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_E_19(Y, A!42, F!43), Y)))))) | (~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | (~((~member(tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43)))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[161, 160])).
% 0.20/0.48 tff(163,plain,
% 0.20/0.48 (~((~member(tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[162, 116, 159])).
% 0.20/0.48 tff(164,plain,
% 0.20/0.48 (((~member(tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43)))) | apply(F!43, tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(165,plain,
% 0.20/0.48 (apply(F!43, tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[164, 163])).
% 0.20/0.48 tff(166,plain,
% 0.20/0.48 (((~member(tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43)))) | member(tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43), A!42)),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(167,plain,
% 0.20/0.48 (member(tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43), A!42)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[166, 163])).
% 0.20/0.48 tff(168,plain,
% 0.20/0.48 (^[F: $i, A: $i, B: $i] : refl((~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B)))))))) <=> (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B)))))))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(169,plain,
% 0.20/0.48 (![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B)))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[168])).
% 0.20/0.48 tff(170,plain,
% 0.20/0.48 (^[F: $i, A: $i, B: $i] : rewrite((~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B)))))))) <=> (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B)))))))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(171,plain,
% 0.20/0.48 (![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B)))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[170])).
% 0.20/0.48 tff(172,plain,
% 0.20/0.48 (![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B)))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))),
% 0.20/0.48 inference(transitivity,[status(thm)],[171, 169])).
% 0.20/0.48 tff(173,plain,
% 0.20/0.48 (^[F: $i, A: $i, B: $i] : trans(monotonicity(rewrite(((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~(apply(F, X1, Y) & apply(F, X2, Y))) | (~(member(X1, A) & member(X2, A) & member(Y, B))))) <=> ((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))), trans(monotonicity(rewrite((~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~(apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F)) & apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F)))) | (~(member(tptp_fun_X1_18(B, A, F), A) & member(tptp_fun_X2_17(B, A, F), A) & member(tptp_fun_Y_16(B, A, F), B))))) <=> (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))), ((injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~(apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F)) & apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F)))) | (~(member(tptp_fun_X1_18(B, A, F), A) & member(tptp_fun_X2_17(B, A, F), A) & member(tptp_fun_Y_16(B, A, F), B)))))) <=> (injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))), rewrite((injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))) <=> (injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B)))))), ((injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~(apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F)) & apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F)))) | (~(member(tptp_fun_X1_18(B, A, F), A) & member(tptp_fun_X2_17(B, A, F), A) & member(tptp_fun_Y_16(B, A, F), B)))))) <=> (injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))), ((((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~(apply(F, X1, Y) & apply(F, X2, Y))) | (~(member(X1, A) & member(X2, A) & member(Y, B))))) & (injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~(apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F)) & apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F)))) | (~(member(tptp_fun_X1_18(B, A, F), A) & member(tptp_fun_X2_17(B, A, F), A) & member(tptp_fun_Y_16(B, A, F), B))))))) <=> (((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y)))) & (injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B)))))))), rewrite((((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y)))) & (injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B)))))) <=> (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))), ((((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~(apply(F, X1, Y) & apply(F, X2, Y))) | (~(member(X1, A) & member(X2, A) & member(Y, B))))) & (injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~(apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F)) & apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F)))) | (~(member(tptp_fun_X1_18(B, A, F), A) & member(tptp_fun_X2_17(B, A, F), A) & member(tptp_fun_Y_16(B, A, F), B))))))) <=> (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(174,plain,
% 0.20/0.48 (![F: $i, A: $i, B: $i] : (((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~(apply(F, X1, Y) & apply(F, X2, Y))) | (~(member(X1, A) & member(X2, A) & member(Y, B))))) & (injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~(apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F)) & apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F)))) | (~(member(tptp_fun_X1_18(B, A, F), A) & member(tptp_fun_X2_17(B, A, F), A) & member(tptp_fun_Y_16(B, A, F), B))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[173])).
% 0.20/0.48 tff(175,plain,
% 0.20/0.48 (![F: $i, A: $i, B: $i] : (injective(F, A, B) <=> ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~(apply(F, X1, Y) & apply(F, X2, Y))) | (~(member(X1, A) & member(X2, A) & member(Y, B))))) <=> ![F: $i, A: $i, B: $i] : (injective(F, A, B) <=> ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~(apply(F, X1, Y) & apply(F, X2, Y))) | (~(member(X1, A) & member(X2, A) & member(Y, B)))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(176,plain,
% 0.20/0.48 (^[F: $i, A: $i, B: $i] : rewrite((injective(F, A, B) <=> ![X1: $i, X2: $i, Y: $i] : (((member(X1, A) & member(X2, A)) & member(Y, B)) => ((apply(F, X1, Y) & apply(F, X2, Y)) => (X1 = X2)))) <=> (injective(F, A, B) <=> ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~(apply(F, X1, Y) & apply(F, X2, Y))) | (~(member(X1, A) & member(X2, A) & member(Y, B))))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(177,plain,
% 0.20/0.48 (![F: $i, A: $i, B: $i] : (injective(F, A, B) <=> ![X1: $i, X2: $i, Y: $i] : (((member(X1, A) & member(X2, A)) & member(Y, B)) => ((apply(F, X1, Y) & apply(F, X2, Y)) => (X1 = X2)))) <=> ![F: $i, A: $i, B: $i] : (injective(F, A, B) <=> ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~(apply(F, X1, Y) & apply(F, X2, Y))) | (~(member(X1, A) & member(X2, A) & member(Y, B)))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[176])).
% 0.20/0.48 tff(178,axiom,(![F: $i, A: $i, B: $i] : (injective(F, A, B) <=> ![X1: $i, X2: $i, Y: $i] : (((member(X1, A) & member(X2, A)) & member(Y, B)) => ((apply(F, X1, Y) & apply(F, X2, Y)) => (X1 = X2))))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+1.ax','injective')).
% 0.20/0.48 tff(179,plain,
% 0.20/0.48 (![F: $i, A: $i, B: $i] : (injective(F, A, B) <=> ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~(apply(F, X1, Y) & apply(F, X2, Y))) | (~(member(X1, A) & member(X2, A) & member(Y, B)))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[178, 177])).
% 0.20/0.48 tff(180,plain,
% 0.20/0.48 (![F: $i, A: $i, B: $i] : (injective(F, A, B) <=> ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~(apply(F, X1, Y) & apply(F, X2, Y))) | (~(member(X1, A) & member(X2, A) & member(Y, B)))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[179, 175])).
% 0.20/0.48 tff(181,plain,(
% 0.20/0.48 ![F: $i, A: $i, B: $i] : (((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~(apply(F, X1, Y) & apply(F, X2, Y))) | (~(member(X1, A) & member(X2, A) & member(Y, B))))) & (injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~(apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F)) & apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F)))) | (~(member(tptp_fun_X1_18(B, A, F), A) & member(tptp_fun_X2_17(B, A, F), A) & member(tptp_fun_Y_16(B, A, F), B)))))))),
% 0.20/0.48 inference(skolemize,[status(sab)],[180])).
% 0.20/0.48 tff(182,plain,
% 0.20/0.48 (![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[181, 174])).
% 0.20/0.48 tff(183,plain,
% 0.20/0.48 (![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[182, 172])).
% 0.20/0.48 tff(184,plain,
% 0.20/0.48 (((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(F!43, A!42, B!41)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!43, X1, Y)) | (~member(X1, A!42)) | (~member(Y, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X2, Y))))) | (~(injective(F!43, A!42, B!41) | (~((tptp_fun_X1_18(B!41, A!42, F!43) = tptp_fun_X2_17(B!41, A!42, F!43)) | (~apply(F!43, tptp_fun_X1_18(B!41, A!42, F!43), tptp_fun_Y_16(B!41, A!42, F!43))) | (~apply(F!43, tptp_fun_X2_17(B!41, A!42, F!43), tptp_fun_Y_16(B!41, A!42, F!43))) | (~member(tptp_fun_X1_18(B!41, A!42, F!43), A!42)) | (~member(tptp_fun_X2_17(B!41, A!42, F!43), A!42)) | (~member(tptp_fun_Y_16(B!41, A!42, F!43), B!41))))))))) <=> ((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(F!43, A!42, B!41)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!43, X1, Y)) | (~member(X1, A!42)) | (~member(Y, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X2, Y))))) | (~(injective(F!43, A!42, B!41) | (~((tptp_fun_X1_18(B!41, A!42, F!43) = tptp_fun_X2_17(B!41, A!42, F!43)) | (~apply(F!43, tptp_fun_X1_18(B!41, A!42, F!43), tptp_fun_Y_16(B!41, A!42, F!43))) | (~apply(F!43, tptp_fun_X2_17(B!41, A!42, F!43), tptp_fun_Y_16(B!41, A!42, F!43))) | (~member(tptp_fun_X1_18(B!41, A!42, F!43), A!42)) | (~member(tptp_fun_X2_17(B!41, A!42, F!43), A!42)) | (~member(tptp_fun_Y_16(B!41, A!42, F!43), B!41)))))))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(185,plain,
% 0.20/0.48 ((~((~((~injective(F!43, A!42, B!41)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!43, X1, Y)) | (~member(X2, A!42)) | (~member(X1, A!42)) | (~member(Y, B!41)) | (~apply(F!43, X2, Y))))) | (~(injective(F!43, A!42, B!41) | (~((tptp_fun_X1_18(B!41, A!42, F!43) = tptp_fun_X2_17(B!41, A!42, F!43)) | (~apply(F!43, tptp_fun_X1_18(B!41, A!42, F!43), tptp_fun_Y_16(B!41, A!42, F!43))) | (~apply(F!43, tptp_fun_X2_17(B!41, A!42, F!43), tptp_fun_Y_16(B!41, A!42, F!43))) | (~member(tptp_fun_X1_18(B!41, A!42, F!43), A!42)) | (~member(tptp_fun_X2_17(B!41, A!42, F!43), A!42)) | (~member(tptp_fun_Y_16(B!41, A!42, F!43), B!41)))))))) <=> (~((~((~injective(F!43, A!42, B!41)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!43, X1, Y)) | (~member(X1, A!42)) | (~member(Y, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X2, Y))))) | (~(injective(F!43, A!42, B!41) | (~((tptp_fun_X1_18(B!41, A!42, F!43) = tptp_fun_X2_17(B!41, A!42, F!43)) | (~apply(F!43, tptp_fun_X1_18(B!41, A!42, F!43), tptp_fun_Y_16(B!41, A!42, F!43))) | (~apply(F!43, tptp_fun_X2_17(B!41, A!42, F!43), tptp_fun_Y_16(B!41, A!42, F!43))) | (~member(tptp_fun_X1_18(B!41, A!42, F!43), A!42)) | (~member(tptp_fun_X2_17(B!41, A!42, F!43), A!42)) | (~member(tptp_fun_Y_16(B!41, A!42, F!43), B!41))))))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(186,plain,
% 0.20/0.49 (((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(F!43, A!42, B!41)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!43, X1, Y)) | (~member(X2, A!42)) | (~member(X1, A!42)) | (~member(Y, B!41)) | (~apply(F!43, X2, Y))))) | (~(injective(F!43, A!42, B!41) | (~((tptp_fun_X1_18(B!41, A!42, F!43) = tptp_fun_X2_17(B!41, A!42, F!43)) | (~apply(F!43, tptp_fun_X1_18(B!41, A!42, F!43), tptp_fun_Y_16(B!41, A!42, F!43))) | (~apply(F!43, tptp_fun_X2_17(B!41, A!42, F!43), tptp_fun_Y_16(B!41, A!42, F!43))) | (~member(tptp_fun_X1_18(B!41, A!42, F!43), A!42)) | (~member(tptp_fun_X2_17(B!41, A!42, F!43), A!42)) | (~member(tptp_fun_Y_16(B!41, A!42, F!43), B!41))))))))) <=> ((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(F!43, A!42, B!41)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!43, X1, Y)) | (~member(X1, A!42)) | (~member(Y, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X2, Y))))) | (~(injective(F!43, A!42, B!41) | (~((tptp_fun_X1_18(B!41, A!42, F!43) = tptp_fun_X2_17(B!41, A!42, F!43)) | (~apply(F!43, tptp_fun_X1_18(B!41, A!42, F!43), tptp_fun_Y_16(B!41, A!42, F!43))) | (~apply(F!43, tptp_fun_X2_17(B!41, A!42, F!43), tptp_fun_Y_16(B!41, A!42, F!43))) | (~member(tptp_fun_X1_18(B!41, A!42, F!43), A!42)) | (~member(tptp_fun_X2_17(B!41, A!42, F!43), A!42)) | (~member(tptp_fun_Y_16(B!41, A!42, F!43), B!41)))))))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[185])).
% 0.20/0.49 tff(187,plain,
% 0.20/0.49 (((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(F!43, A!42, B!41)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!43, X1, Y)) | (~member(X2, A!42)) | (~member(X1, A!42)) | (~member(Y, B!41)) | (~apply(F!43, X2, Y))))) | (~(injective(F!43, A!42, B!41) | (~((tptp_fun_X1_18(B!41, A!42, F!43) = tptp_fun_X2_17(B!41, A!42, F!43)) | (~apply(F!43, tptp_fun_X1_18(B!41, A!42, F!43), tptp_fun_Y_16(B!41, A!42, F!43))) | (~apply(F!43, tptp_fun_X2_17(B!41, A!42, F!43), tptp_fun_Y_16(B!41, A!42, F!43))) | (~member(tptp_fun_X1_18(B!41, A!42, F!43), A!42)) | (~member(tptp_fun_X2_17(B!41, A!42, F!43), A!42)) | (~member(tptp_fun_Y_16(B!41, A!42, F!43), B!41))))))))) <=> ((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(F!43, A!42, B!41)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!43, X1, Y)) | (~member(X1, A!42)) | (~member(Y, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X2, Y))))) | (~(injective(F!43, A!42, B!41) | (~((tptp_fun_X1_18(B!41, A!42, F!43) = tptp_fun_X2_17(B!41, A!42, F!43)) | (~apply(F!43, tptp_fun_X1_18(B!41, A!42, F!43), tptp_fun_Y_16(B!41, A!42, F!43))) | (~apply(F!43, tptp_fun_X2_17(B!41, A!42, F!43), tptp_fun_Y_16(B!41, A!42, F!43))) | (~member(tptp_fun_X1_18(B!41, A!42, F!43), A!42)) | (~member(tptp_fun_X2_17(B!41, A!42, F!43), A!42)) | (~member(tptp_fun_Y_16(B!41, A!42, F!43), B!41)))))))))),
% 0.20/0.49 inference(transitivity,[status(thm)],[186, 184])).
% 0.20/0.49 tff(188,plain,
% 0.20/0.49 ((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(F!43, A!42, B!41)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!43, X1, Y)) | (~member(X2, A!42)) | (~member(X1, A!42)) | (~member(Y, B!41)) | (~apply(F!43, X2, Y))))) | (~(injective(F!43, A!42, B!41) | (~((tptp_fun_X1_18(B!41, A!42, F!43) = tptp_fun_X2_17(B!41, A!42, F!43)) | (~apply(F!43, tptp_fun_X1_18(B!41, A!42, F!43), tptp_fun_Y_16(B!41, A!42, F!43))) | (~apply(F!43, tptp_fun_X2_17(B!41, A!42, F!43), tptp_fun_Y_16(B!41, A!42, F!43))) | (~member(tptp_fun_X1_18(B!41, A!42, F!43), A!42)) | (~member(tptp_fun_X2_17(B!41, A!42, F!43), A!42)) | (~member(tptp_fun_Y_16(B!41, A!42, F!43), B!41))))))))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(189,plain,
% 0.20/0.49 ((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(F!43, A!42, B!41)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!43, X1, Y)) | (~member(X1, A!42)) | (~member(Y, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X2, Y))))) | (~(injective(F!43, A!42, B!41) | (~((tptp_fun_X1_18(B!41, A!42, F!43) = tptp_fun_X2_17(B!41, A!42, F!43)) | (~apply(F!43, tptp_fun_X1_18(B!41, A!42, F!43), tptp_fun_Y_16(B!41, A!42, F!43))) | (~apply(F!43, tptp_fun_X2_17(B!41, A!42, F!43), tptp_fun_Y_16(B!41, A!42, F!43))) | (~member(tptp_fun_X1_18(B!41, A!42, F!43), A!42)) | (~member(tptp_fun_X2_17(B!41, A!42, F!43), A!42)) | (~member(tptp_fun_Y_16(B!41, A!42, F!43), B!41))))))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[188, 187])).
% 0.20/0.49 tff(190,plain,
% 0.20/0.49 (~((~((~injective(F!43, A!42, B!41)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!43, X1, Y)) | (~member(X1, A!42)) | (~member(Y, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X2, Y))))) | (~(injective(F!43, A!42, B!41) | (~((tptp_fun_X1_18(B!41, A!42, F!43) = tptp_fun_X2_17(B!41, A!42, F!43)) | (~apply(F!43, tptp_fun_X1_18(B!41, A!42, F!43), tptp_fun_Y_16(B!41, A!42, F!43))) | (~apply(F!43, tptp_fun_X2_17(B!41, A!42, F!43), tptp_fun_Y_16(B!41, A!42, F!43))) | (~member(tptp_fun_X1_18(B!41, A!42, F!43), A!42)) | (~member(tptp_fun_X2_17(B!41, A!42, F!43), A!42)) | (~member(tptp_fun_Y_16(B!41, A!42, F!43), B!41)))))))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[189, 183])).
% 0.20/0.49 tff(191,plain,
% 0.20/0.49 (((~((~injective(F!43, A!42, B!41)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!43, X1, Y)) | (~member(X1, A!42)) | (~member(Y, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X2, Y))))) | (~(injective(F!43, A!42, B!41) | (~((tptp_fun_X1_18(B!41, A!42, F!43) = tptp_fun_X2_17(B!41, A!42, F!43)) | (~apply(F!43, tptp_fun_X1_18(B!41, A!42, F!43), tptp_fun_Y_16(B!41, A!42, F!43))) | (~apply(F!43, tptp_fun_X2_17(B!41, A!42, F!43), tptp_fun_Y_16(B!41, A!42, F!43))) | (~member(tptp_fun_X1_18(B!41, A!42, F!43), A!42)) | (~member(tptp_fun_X2_17(B!41, A!42, F!43), A!42)) | (~member(tptp_fun_Y_16(B!41, A!42, F!43), B!41))))))) | ((~injective(F!43, A!42, B!41)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!43, X1, Y)) | (~member(X1, A!42)) | (~member(Y, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X2, Y))))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(192,plain,
% 0.20/0.49 ((~injective(F!43, A!42, B!41)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!43, X1, Y)) | (~member(X1, A!42)) | (~member(Y, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X2, Y)))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[191, 190])).
% 0.20/0.49 tff(193,plain,
% 0.20/0.49 (((~injective(F!43, A!42, B!41)) | (~surjective(F!43, A!42, B!41))) | injective(F!43, A!42, B!41)),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(194,plain,
% 0.20/0.49 (injective(F!43, A!42, B!41)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[193, 154])).
% 0.20/0.49 tff(195,plain,
% 0.20/0.49 ((~((~injective(F!43, A!42, B!41)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!43, X1, Y)) | (~member(X1, A!42)) | (~member(Y, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X2, Y))))) | (~injective(F!43, A!42, B!41)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!43, X1, Y)) | (~member(X1, A!42)) | (~member(Y, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X2, Y)))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(196,plain,
% 0.20/0.49 ((~((~injective(F!43, A!42, B!41)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!43, X1, Y)) | (~member(X1, A!42)) | (~member(Y, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X2, Y))))) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!43, X1, Y)) | (~member(X1, A!42)) | (~member(Y, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X2, Y)))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[195, 194])).
% 0.20/0.49 tff(197,plain,
% 0.20/0.49 (![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!43, X1, Y)) | (~member(X1, A!42)) | (~member(Y, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X2, Y)))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[196, 192])).
% 0.20/0.49 tff(198,plain,
% 0.20/0.49 (((apply(R!40, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43)) <=> apply(S!39, tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))) | (~member(tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | (~apply(F!43, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43)))) | apply(F!43, tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(199,plain,
% 0.20/0.49 (apply(F!43, tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[198, 114])).
% 0.20/0.49 tff(200,plain,
% 0.20/0.49 (((apply(R!40, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43)) <=> apply(S!39, tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))) | (~member(tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | (~apply(F!43, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43)))) | member(tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), A!42)),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(201,plain,
% 0.20/0.49 (member(tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), A!42)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[200, 114])).
% 0.20/0.49 tff(202,plain,
% 0.20/0.49 (((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!43, X1, Y)) | (~member(X1, A!42)) | (~member(Y, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X2, Y)))) | ((~member(tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | (~apply(F!43, tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))) | (~member(tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))) | (tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43) = tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43)))) <=> ((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!43, X1, Y)) | (~member(X1, A!42)) | (~member(Y, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X2, Y)))) | (~member(tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | (~apply(F!43, tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))) | (~member(tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))) | (tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43) = tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(203,plain,
% 0.20/0.49 (((tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43) = tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43)) | (~apply(F!43, tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))) | (~member(tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43)))) <=> ((~member(tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | (~apply(F!43, tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))) | (~member(tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))) | (tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43) = tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(204,plain,
% 0.20/0.49 (((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!43, X1, Y)) | (~member(X1, A!42)) | (~member(Y, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X2, Y)))) | ((tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43) = tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43)) | (~apply(F!43, tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))) | (~member(tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))))) <=> ((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!43, X1, Y)) | (~member(X1, A!42)) | (~member(Y, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X2, Y)))) | ((~member(tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | (~apply(F!43, tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))) | (~member(tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))) | (tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43) = tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43))))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[203])).
% 0.20/0.50 tff(205,plain,
% 0.20/0.50 (((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!43, X1, Y)) | (~member(X1, A!42)) | (~member(Y, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X2, Y)))) | ((tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43) = tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43)) | (~apply(F!43, tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))) | (~member(tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))))) <=> ((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!43, X1, Y)) | (~member(X1, A!42)) | (~member(Y, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X2, Y)))) | (~member(tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | (~apply(F!43, tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))) | (~member(tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))) | (tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43) = tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43)))),
% 0.20/0.50 inference(transitivity,[status(thm)],[204, 202])).
% 0.20/0.50 tff(206,plain,
% 0.20/0.50 ((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!43, X1, Y)) | (~member(X1, A!42)) | (~member(Y, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X2, Y)))) | ((tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43) = tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43)) | (~apply(F!43, tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))) | (~member(tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(207,plain,
% 0.20/0.50 ((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!43, X1, Y)) | (~member(X1, A!42)) | (~member(Y, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X2, Y)))) | (~member(tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | (~apply(F!43, tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))) | (~member(tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))) | (tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43) = tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[206, 205])).
% 0.20/0.50 tff(208,plain,
% 0.20/0.50 (tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43) = tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[207, 201, 116, 199, 197, 167, 165])).
% 0.20/0.50 tff(209,assumption,(tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43) = tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43)), introduced(assumption)).
% 0.20/0.50 tff(210,plain,
% 0.20/0.50 (tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43) = tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43)),
% 0.20/0.50 inference(symmetry,[status(thm)],[209])).
% 0.20/0.50 tff(211,plain,
% 0.20/0.50 (apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43)) <=> apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[210])).
% 0.20/0.50 tff(212,plain,
% 0.20/0.50 (apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43)) <=> apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43))),
% 0.20/0.50 inference(symmetry,[status(thm)],[211])).
% 0.20/0.50 tff(213,plain,
% 0.20/0.50 ((~apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43))) <=> (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43)))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[212])).
% 0.20/0.50 tff(214,assumption,(~apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43))), introduced(assumption)).
% 0.20/0.50 tff(215,plain,
% 0.20/0.50 (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[214, 213])).
% 0.20/0.50 tff(216,assumption,(member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)), introduced(assumption)).
% 0.20/0.50 tff(217,plain,
% 0.20/0.50 (~((~member(tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[162, 216, 159])).
% 0.20/0.50 tff(218,plain,
% 0.20/0.50 (member(tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43), A!42)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[166, 217])).
% 0.20/0.50 tff(219,plain,
% 0.20/0.50 (^[F: $i, A: $i, B: $i, X: $i, Y: $i] : refl(((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A))) <=> ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(220,plain,
% 0.20/0.50 (![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A))) <=> ![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[219])).
% 0.20/0.50 tff(221,plain,
% 0.20/0.50 (^[F: $i, A: $i, B: $i, X: $i, Y: $i] : trans(monotonicity(trans(monotonicity(rewrite((member(X, A) & member(Y, B)) <=> (~((~member(Y, B)) | (~member(X, A))))), ((~(member(X, A) & member(Y, B))) <=> (~(~((~member(Y, B)) | (~member(X, A))))))), rewrite((~(~((~member(Y, B)) | (~member(X, A))))) <=> ((~member(Y, B)) | (~member(X, A)))), ((~(member(X, A) & member(Y, B))) <=> ((~member(Y, B)) | (~member(X, A))))), (((~(member(X, A) & member(Y, B))) | (apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X))) <=> (((~member(Y, B)) | (~member(X, A))) | (apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X))))), rewrite((((~member(Y, B)) | (~member(X, A))) | (apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X))) <=> ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))), (((~(member(X, A) & member(Y, B))) | (apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X))) <=> ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(222,plain,
% 0.20/0.50 (![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((~(member(X, A) & member(Y, B))) | (apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X))) <=> ![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[221])).
% 0.20/0.50 tff(223,plain,
% 0.20/0.50 (![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((~(member(X, A) & member(Y, B))) | (apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X))) <=> ![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((~(member(X, A) & member(Y, B))) | (apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(224,plain,
% 0.20/0.50 (^[F: $i, A: $i, B: $i, X: $i, Y: $i] : rewrite(((member(X, A) & member(Y, B)) => (apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X))) <=> ((~(member(X, A) & member(Y, B))) | (apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(225,plain,
% 0.20/0.50 (![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((member(X, A) & member(Y, B)) => (apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X))) <=> ![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((~(member(X, A) & member(Y, B))) | (apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[224])).
% 0.20/0.50 tff(226,axiom,(![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((member(X, A) & member(Y, B)) => (apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+1.ax','inverse_function')).
% 0.20/0.50 tff(227,plain,
% 0.20/0.50 (![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((~(member(X, A) & member(Y, B))) | (apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[226, 225])).
% 0.20/0.50 tff(228,plain,
% 0.20/0.50 (![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((~(member(X, A) & member(Y, B))) | (apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[227, 223])).
% 0.20/0.50 tff(229,plain,(
% 0.20/0.50 ![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((~(member(X, A) & member(Y, B))) | (apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)))),
% 0.20/0.50 inference(skolemize,[status(sab)],[228])).
% 0.20/0.50 tff(230,plain,
% 0.20/0.50 (![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[229, 222])).
% 0.20/0.50 tff(231,plain,
% 0.20/0.50 (![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[230, 220])).
% 0.20/0.50 tff(232,plain,
% 0.20/0.50 (((~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))) | ((~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43), A!42)) | (apply(F!43, tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43)) <=> apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43))))) <=> ((~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))) | (~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43), A!42)) | (apply(F!43, tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43)) <=> apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(233,plain,
% 0.20/0.50 (((apply(F!43, tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43)) <=> apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43))) | (~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43), A!42))) <=> ((~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43), A!42)) | (apply(F!43, tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43)) <=> apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(234,plain,
% 0.20/0.50 (((~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))) | ((apply(F!43, tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43)) <=> apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43))) | (~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43), A!42)))) <=> ((~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))) | ((~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43), A!42)) | (apply(F!43, tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43)) <=> apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43)))))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[233])).
% 0.20/0.50 tff(235,plain,
% 0.20/0.50 (((~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))) | ((apply(F!43, tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43)) <=> apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43))) | (~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43), A!42)))) <=> ((~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))) | (~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43), A!42)) | (apply(F!43, tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43)) <=> apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43))))),
% 0.20/0.50 inference(transitivity,[status(thm)],[234, 232])).
% 0.20/0.50 tff(236,plain,
% 0.20/0.50 ((~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))) | ((apply(F!43, tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43)) <=> apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43))) | (~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43), A!42)))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(237,plain,
% 0.20/0.50 ((~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))) | (~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43), A!42)) | (apply(F!43, tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43)) <=> apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[236, 235])).
% 0.20/0.50 tff(238,plain,
% 0.20/0.50 (apply(F!43, tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43)) <=> apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[237, 231, 216, 218])).
% 0.20/0.50 tff(239,plain,
% 0.20/0.50 (apply(F!43, tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[164, 217])).
% 0.20/0.50 tff(240,plain,
% 0.20/0.50 ((~(apply(F!43, tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43)) <=> apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43)))) | (~apply(F!43, tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))) | apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43))),
% 0.20/0.50 inference(tautology,[status(thm)],[])).
% 0.20/0.50 tff(241,plain,
% 0.20/0.50 ((~(apply(F!43, tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43)) <=> apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43)))) | apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[240, 239])).
% 0.20/0.50 tff(242,plain,
% 0.20/0.50 (apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[241, 238])).
% 0.20/0.50 tff(243,plain,
% 0.20/0.50 ($false),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[242, 215])).
% 0.20/0.50 tff(244,plain,(apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43)) | (~(tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43) = tptp_fun_E_19(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), A!42, F!43))) | (~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.50 tff(245,plain,
% 0.20/0.50 (apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[244, 208, 116])).
% 0.20/0.51 tff(246,plain,
% 0.20/0.51 (((apply(R!40, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43)) <=> apply(S!39, tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))) | (~member(tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | (~apply(F!43, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43)))) | member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(247,plain,
% 0.20/0.51 (member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[246, 114])).
% 0.20/0.51 tff(248,plain,
% 0.20/0.51 (((~![Y: $i] : ((~member(Y, B!41)) | (~((~member(tptp_fun_E_19(Y, A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_E_19(Y, A!42, F!43), Y)))))) | ((~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~((~member(tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43))))))) <=> ((~![Y: $i] : ((~member(Y, B!41)) | (~((~member(tptp_fun_E_19(Y, A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_E_19(Y, A!42, F!43), Y)))))) | (~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~((~member(tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43))))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(249,plain,
% 0.20/0.51 ((~![Y: $i] : ((~member(Y, B!41)) | (~((~member(tptp_fun_E_19(Y, A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_E_19(Y, A!42, F!43), Y)))))) | ((~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~((~member(tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43))))))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(250,plain,
% 0.20/0.51 ((~![Y: $i] : ((~member(Y, B!41)) | (~((~member(tptp_fun_E_19(Y, A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_E_19(Y, A!42, F!43), Y)))))) | (~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~((~member(tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43)))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[249, 248])).
% 0.20/0.51 tff(251,plain,
% 0.20/0.51 (~((~member(tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43))))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[250, 247, 159])).
% 0.20/0.51 tff(252,plain,
% 0.20/0.51 (((~member(tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43)))) | apply(F!43, tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43))),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(253,plain,
% 0.20/0.51 (apply(F!43, tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[252, 251])).
% 0.20/0.51 tff(254,plain,
% 0.20/0.51 (((~member(tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43)))) | member(tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43), A!42)),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(255,plain,
% 0.20/0.51 (member(tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43), A!42)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[254, 251])).
% 0.20/0.51 tff(256,plain,
% 0.20/0.51 (((apply(R!40, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43)) <=> apply(S!39, tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))) | (~member(tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | (~apply(F!43, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43)))) | apply(F!43, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43))),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(257,plain,
% 0.20/0.51 (apply(F!43, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[256, 114])).
% 0.20/0.51 tff(258,plain,
% 0.20/0.51 (((apply(R!40, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43)) <=> apply(S!39, tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))) | (~member(tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | (~apply(F!43, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43)))) | member(tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), A!42)),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(259,plain,
% 0.20/0.51 (member(tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), A!42)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[258, 114])).
% 0.20/0.51 tff(260,plain,
% 0.20/0.51 (((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!43, X1, Y)) | (~member(X1, A!42)) | (~member(Y, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X2, Y)))) | ((~member(tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~apply(F!43, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43))) | (~member(tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43))) | (tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43) = tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43)))) <=> ((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!43, X1, Y)) | (~member(X1, A!42)) | (~member(Y, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X2, Y)))) | (~member(tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~apply(F!43, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43))) | (~member(tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43))) | (tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43) = tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(261,plain,
% 0.20/0.51 (((tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43) = tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43)) | (~apply(F!43, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43))) | (~member(tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43)))) <=> ((~member(tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~apply(F!43, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43))) | (~member(tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43))) | (tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43) = tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(262,plain,
% 0.20/0.51 (((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!43, X1, Y)) | (~member(X1, A!42)) | (~member(Y, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X2, Y)))) | ((tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43) = tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43)) | (~apply(F!43, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43))) | (~member(tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43))))) <=> ((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!43, X1, Y)) | (~member(X1, A!42)) | (~member(Y, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X2, Y)))) | ((~member(tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~apply(F!43, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43))) | (~member(tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43))) | (tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43) = tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43))))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[261])).
% 0.20/0.51 tff(263,plain,
% 0.20/0.51 (((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!43, X1, Y)) | (~member(X1, A!42)) | (~member(Y, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X2, Y)))) | ((tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43) = tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43)) | (~apply(F!43, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43))) | (~member(tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43))))) <=> ((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!43, X1, Y)) | (~member(X1, A!42)) | (~member(Y, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X2, Y)))) | (~member(tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~apply(F!43, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43))) | (~member(tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43))) | (tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43) = tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43)))),
% 0.20/0.52 inference(transitivity,[status(thm)],[262, 260])).
% 0.20/0.52 tff(264,plain,
% 0.20/0.52 ((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!43, X1, Y)) | (~member(X1, A!42)) | (~member(Y, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X2, Y)))) | ((tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43) = tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43)) | (~apply(F!43, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43))) | (~member(tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43))))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(265,plain,
% 0.20/0.52 ((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!43, X1, Y)) | (~member(X1, A!42)) | (~member(Y, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X2, Y)))) | (~member(tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~apply(F!43, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43))) | (~member(tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43))) | (tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43) = tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[264, 263])).
% 0.20/0.52 tff(266,plain,
% 0.20/0.52 (tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43) = tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[265, 259, 247, 257, 197, 255, 253])).
% 0.20/0.52 tff(267,assumption,(tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43) = tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43)), introduced(assumption)).
% 0.20/0.52 tff(268,plain,
% 0.20/0.52 (tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43) = tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43)),
% 0.20/0.52 inference(symmetry,[status(thm)],[267])).
% 0.20/0.52 tff(269,plain,
% 0.20/0.52 (apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43)) <=> apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[268])).
% 0.20/0.52 tff(270,plain,
% 0.20/0.52 (apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43)) <=> apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43))),
% 0.20/0.52 inference(symmetry,[status(thm)],[269])).
% 0.20/0.52 tff(271,plain,
% 0.20/0.52 ((~apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43))) <=> (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43)))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[270])).
% 0.20/0.52 tff(272,assumption,(~apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43))), introduced(assumption)).
% 0.20/0.52 tff(273,plain,
% 0.20/0.52 (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[272, 271])).
% 0.20/0.52 tff(274,assumption,(member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)), introduced(assumption)).
% 0.20/0.52 tff(275,plain,
% 0.20/0.52 (~((~member(tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43))))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[250, 274, 159])).
% 0.20/0.52 tff(276,plain,
% 0.20/0.52 (member(tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43), A!42)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[254, 275])).
% 0.20/0.52 tff(277,plain,
% 0.20/0.52 (((~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))) | ((~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43), A!42)) | (apply(F!43, tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43)) <=> apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43))))) <=> ((~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))) | (~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43), A!42)) | (apply(F!43, tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43)) <=> apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(278,plain,
% 0.20/0.52 (((apply(F!43, tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43)) <=> apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43))) | (~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43), A!42))) <=> ((~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43), A!42)) | (apply(F!43, tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43)) <=> apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(279,plain,
% 0.20/0.52 (((~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))) | ((apply(F!43, tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43)) <=> apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43))) | (~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43), A!42)))) <=> ((~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))) | ((~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43), A!42)) | (apply(F!43, tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43)) <=> apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43)))))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[278])).
% 0.20/0.52 tff(280,plain,
% 0.20/0.52 (((~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))) | ((apply(F!43, tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43)) <=> apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43))) | (~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43), A!42)))) <=> ((~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))) | (~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43), A!42)) | (apply(F!43, tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43)) <=> apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43))))),
% 0.20/0.52 inference(transitivity,[status(thm)],[279, 277])).
% 0.20/0.52 tff(281,plain,
% 0.20/0.52 ((~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))) | ((apply(F!43, tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43)) <=> apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43))) | (~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43), A!42)))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(282,plain,
% 0.20/0.52 ((~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))) | (~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43), A!42)) | (apply(F!43, tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43)) <=> apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43)))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[281, 280])).
% 0.20/0.52 tff(283,plain,
% 0.20/0.52 (apply(F!43, tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43)) <=> apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[282, 231, 274, 276])).
% 0.20/0.52 tff(284,plain,
% 0.20/0.52 (apply(F!43, tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[252, 275])).
% 0.20/0.52 tff(285,plain,
% 0.20/0.52 ((~(apply(F!43, tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43)) <=> apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43)))) | (~apply(F!43, tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43))) | apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43))),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(286,plain,
% 0.20/0.52 ((~(apply(F!43, tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43)) <=> apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43)))) | apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[285, 284])).
% 0.20/0.52 tff(287,plain,
% 0.20/0.52 (apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[286, 283])).
% 0.20/0.52 tff(288,plain,
% 0.20/0.52 ($false),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[287, 273])).
% 0.20/0.52 tff(289,plain,(apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43)) | (~(tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43) = tptp_fun_E_19(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), A!42, F!43))) | (~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.52 tff(290,plain,
% 0.20/0.52 (apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[289, 266, 247])).
% 0.20/0.52 tff(291,plain,
% 0.20/0.52 (((apply(R!40, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43)) <=> apply(S!39, tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))) | (~member(tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | (~apply(F!43, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43)))) | (~(apply(R!40, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43)) <=> apply(S!39, tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))))),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(292,plain,
% 0.20/0.52 (~(apply(R!40, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43)) <=> apply(S!39, tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43)))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[291, 114])).
% 0.20/0.52 tff(293,plain,
% 0.20/0.52 (~((~((~increasing(F!43, A!42, R!40, B!41, S!39)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!41)) | apply(S!39, Y1, Y2) | (~member(X1, A!42)) | (~member(Y1, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X1, Y1)) | (~apply(F!43, X2, Y2)) | (~apply(R!40, X1, X2))))) | (~(increasing(F!43, A!42, R!40, B!41, S!39) | (~(apply(S!39, tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43)) | (~member(tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43), B!41)) | (~apply(R!40, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43))))))))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[32, 16])).
% 0.20/0.52 tff(294,plain,
% 0.20/0.52 (((~((~increasing(F!43, A!42, R!40, B!41, S!39)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!41)) | apply(S!39, Y1, Y2) | (~member(X1, A!42)) | (~member(Y1, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X1, Y1)) | (~apply(F!43, X2, Y2)) | (~apply(R!40, X1, X2))))) | (~(increasing(F!43, A!42, R!40, B!41, S!39) | (~(apply(S!39, tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43)) | (~member(tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43), B!41)) | (~apply(R!40, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43)))))))) | ((~increasing(F!43, A!42, R!40, B!41, S!39)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!41)) | apply(S!39, Y1, Y2) | (~member(X1, A!42)) | (~member(Y1, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X1, Y1)) | (~apply(F!43, X2, Y2)) | (~apply(R!40, X1, X2))))),
% 0.20/0.53 inference(tautology,[status(thm)],[])).
% 0.20/0.53 tff(295,plain,
% 0.20/0.53 ((~increasing(F!43, A!42, R!40, B!41, S!39)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!41)) | apply(S!39, Y1, Y2) | (~member(X1, A!42)) | (~member(Y1, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X1, Y1)) | (~apply(F!43, X2, Y2)) | (~apply(R!40, X1, X2)))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[294, 293])).
% 0.20/0.53 tff(296,plain,
% 0.20/0.53 (((~increasing(F!43, A!42, R!40, B!41, S!39)) | (~increasing(inverse_function(F!43, A!42, B!41), B!41, S!39, A!42, R!40))) | increasing(F!43, A!42, R!40, B!41, S!39)),
% 0.20/0.53 inference(tautology,[status(thm)],[])).
% 0.20/0.53 tff(297,plain,
% 0.20/0.53 (increasing(F!43, A!42, R!40, B!41, S!39)),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[296, 56])).
% 0.20/0.53 tff(298,plain,
% 0.20/0.53 ((~((~increasing(F!43, A!42, R!40, B!41, S!39)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!41)) | apply(S!39, Y1, Y2) | (~member(X1, A!42)) | (~member(Y1, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X1, Y1)) | (~apply(F!43, X2, Y2)) | (~apply(R!40, X1, X2))))) | (~increasing(F!43, A!42, R!40, B!41, S!39)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!41)) | apply(S!39, Y1, Y2) | (~member(X1, A!42)) | (~member(Y1, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X1, Y1)) | (~apply(F!43, X2, Y2)) | (~apply(R!40, X1, X2)))),
% 0.20/0.53 inference(tautology,[status(thm)],[])).
% 0.20/0.53 tff(299,plain,
% 0.20/0.53 ((~((~increasing(F!43, A!42, R!40, B!41, S!39)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!41)) | apply(S!39, Y1, Y2) | (~member(X1, A!42)) | (~member(Y1, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X1, Y1)) | (~apply(F!43, X2, Y2)) | (~apply(R!40, X1, X2))))) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!41)) | apply(S!39, Y1, Y2) | (~member(X1, A!42)) | (~member(Y1, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X1, Y1)) | (~apply(F!43, X2, Y2)) | (~apply(R!40, X1, X2)))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[298, 297])).
% 0.20/0.53 tff(300,plain,
% 0.20/0.53 (![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!41)) | apply(S!39, Y1, Y2) | (~member(X1, A!42)) | (~member(Y1, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X1, Y1)) | (~apply(F!43, X2, Y2)) | (~apply(R!40, X1, X2)))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[299, 295])).
% 0.20/0.53 tff(301,assumption,(~apply(S!39, tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))), introduced(assumption)).
% 0.20/0.53 tff(302,assumption,(~(apply(R!40, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43)) <=> apply(S!39, tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43)))), introduced(assumption)).
% 0.20/0.53 tff(303,plain,
% 0.20/0.53 ((apply(R!40, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43)) <=> apply(S!39, tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))) | apply(R!40, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43)) | apply(S!39, tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))),
% 0.20/0.53 inference(tautology,[status(thm)],[])).
% 0.20/0.53 tff(304,plain,
% 0.20/0.53 (apply(R!40, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[303, 301, 302])).
% 0.20/0.53 tff(305,assumption,(![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!41)) | apply(S!39, Y1, Y2) | (~member(X1, A!42)) | (~member(Y1, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X1, Y1)) | (~apply(F!43, X2, Y2)) | (~apply(R!40, X1, X2)))), introduced(assumption)).
% 0.20/0.53 tff(306,assumption,(apply(F!43, tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))), introduced(assumption)).
% 0.20/0.53 tff(307,assumption,(apply(F!43, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43))), introduced(assumption)).
% 0.20/0.53 tff(308,assumption,(member(tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), A!42)), introduced(assumption)).
% 0.20/0.53 tff(309,assumption,(member(tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), A!42)), introduced(assumption)).
% 0.20/0.53 tff(310,plain,
% 0.20/0.53 (((~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!41)) | apply(S!39, Y1, Y2) | (~member(X1, A!42)) | (~member(Y1, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X1, Y1)) | (~apply(F!43, X2, Y2)) | (~apply(R!40, X1, X2)))) | (apply(S!39, tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43)) | (~member(tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | (~apply(F!43, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))) | (~apply(R!40, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43))))) <=> ((~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!41)) | apply(S!39, Y1, Y2) | (~member(X1, A!42)) | (~member(Y1, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X1, Y1)) | (~apply(F!43, X2, Y2)) | (~apply(R!40, X1, X2)))) | apply(S!39, tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43)) | (~member(tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | (~apply(F!43, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))) | (~apply(R!40, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43))))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(311,plain,
% 0.20/0.53 (((~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | apply(S!39, tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43)) | (~member(tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))) | (~apply(R!40, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43)))) <=> (apply(S!39, tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43)) | (~member(tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | (~apply(F!43, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))) | (~apply(R!40, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43))))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(312,plain,
% 0.20/0.53 (((~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!41)) | apply(S!39, Y1, Y2) | (~member(X1, A!42)) | (~member(Y1, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X1, Y1)) | (~apply(F!43, X2, Y2)) | (~apply(R!40, X1, X2)))) | ((~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | apply(S!39, tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43)) | (~member(tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))) | (~apply(R!40, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43))))) <=> ((~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!41)) | apply(S!39, Y1, Y2) | (~member(X1, A!42)) | (~member(Y1, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X1, Y1)) | (~apply(F!43, X2, Y2)) | (~apply(R!40, X1, X2)))) | (apply(S!39, tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43)) | (~member(tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | (~apply(F!43, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))) | (~apply(R!40, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43)))))),
% 0.20/0.53 inference(monotonicity,[status(thm)],[311])).
% 0.20/0.53 tff(313,plain,
% 0.20/0.53 (((~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!41)) | apply(S!39, Y1, Y2) | (~member(X1, A!42)) | (~member(Y1, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X1, Y1)) | (~apply(F!43, X2, Y2)) | (~apply(R!40, X1, X2)))) | ((~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | apply(S!39, tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43)) | (~member(tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))) | (~apply(R!40, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43))))) <=> ((~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!41)) | apply(S!39, Y1, Y2) | (~member(X1, A!42)) | (~member(Y1, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X1, Y1)) | (~apply(F!43, X2, Y2)) | (~apply(R!40, X1, X2)))) | apply(S!39, tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43)) | (~member(tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | (~apply(F!43, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))) | (~apply(R!40, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43))))),
% 0.20/0.53 inference(transitivity,[status(thm)],[312, 310])).
% 0.20/0.53 tff(314,plain,
% 0.20/0.53 ((~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!41)) | apply(S!39, Y1, Y2) | (~member(X1, A!42)) | (~member(Y1, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X1, Y1)) | (~apply(F!43, X2, Y2)) | (~apply(R!40, X1, X2)))) | ((~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | apply(S!39, tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43)) | (~member(tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))) | (~apply(R!40, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43))))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(315,plain,
% 0.20/0.53 ((~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!41)) | apply(S!39, Y1, Y2) | (~member(X1, A!42)) | (~member(Y1, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X1, Y1)) | (~apply(F!43, X2, Y2)) | (~apply(R!40, X1, X2)))) | apply(S!39, tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43)) | (~member(tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | (~apply(F!43, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))) | (~apply(R!40, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43)))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[314, 313])).
% 0.20/0.53 tff(316,plain,
% 0.20/0.53 (apply(S!39, tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43)) | (~apply(R!40, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43)))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[315, 309, 274, 308, 216, 307, 306, 305])).
% 0.20/0.53 tff(317,plain,
% 0.20/0.53 ($false),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[316, 304, 301])).
% 0.20/0.53 tff(318,plain,(apply(S!39, tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43)) | (~member(tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | (~apply(F!43, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))) | (~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!41)) | apply(S!39, Y1, Y2) | (~member(X1, A!42)) | (~member(Y1, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X1, Y1)) | (~apply(F!43, X2, Y2)) | (~apply(R!40, X1, X2)))) | (apply(R!40, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43)) <=> apply(S!39, tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.53 tff(319,plain,
% 0.20/0.53 (apply(S!39, tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[318, 259, 247, 201, 116, 257, 199, 300, 292])).
% 0.20/0.53 tff(320,plain,
% 0.20/0.53 ((apply(R!40, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43)) <=> apply(S!39, tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))) | (~apply(R!40, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43))) | (~apply(S!39, tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43)))),
% 0.20/0.53 inference(tautology,[status(thm)],[])).
% 0.20/0.53 tff(321,plain,
% 0.20/0.53 (~apply(R!40, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[320, 319, 292])).
% 0.20/0.53 tff(322,plain,
% 0.20/0.54 (((~((~increasing(inverse_function(F!43, A!42, B!41), B!41, S!39, A!42, R!40)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, A!42)) | (~member(Y1, A!42)) | (~member(X2, B!41)) | apply(R!40, Y1, Y2) | (~member(X1, B!41)) | (~apply(S!39, X1, X2)) | (~apply(inverse_function(F!43, A!42, B!41), X1, Y1)) | (~apply(inverse_function(F!43, A!42, B!41), X2, Y2))))) | (~(increasing(inverse_function(F!43, A!42, B!41), B!41, S!39, A!42, R!40) | (~(apply(R!40, tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))) | (~member(tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (~member(tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~member(tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (~member(tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~apply(S!39, tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))))))))) | ((~increasing(inverse_function(F!43, A!42, B!41), B!41, S!39, A!42, R!40)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, A!42)) | (~member(Y1, A!42)) | (~member(X2, B!41)) | apply(R!40, Y1, Y2) | (~member(X1, B!41)) | (~apply(S!39, X1, X2)) | (~apply(inverse_function(F!43, A!42, B!41), X1, Y1)) | (~apply(inverse_function(F!43, A!42, B!41), X2, Y2))))),
% 0.20/0.54 inference(tautology,[status(thm)],[])).
% 0.20/0.54 tff(323,plain,
% 0.20/0.54 ((~increasing(inverse_function(F!43, A!42, B!41), B!41, S!39, A!42, R!40)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, A!42)) | (~member(Y1, A!42)) | (~member(X2, B!41)) | apply(R!40, Y1, Y2) | (~member(X1, B!41)) | (~apply(S!39, X1, X2)) | (~apply(inverse_function(F!43, A!42, B!41), X1, Y1)) | (~apply(inverse_function(F!43, A!42, B!41), X2, Y2)))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[322, 23])).
% 0.20/0.54 tff(324,plain,
% 0.20/0.54 (((~increasing(F!43, A!42, R!40, B!41, S!39)) | (~increasing(inverse_function(F!43, A!42, B!41), B!41, S!39, A!42, R!40))) | increasing(inverse_function(F!43, A!42, B!41), B!41, S!39, A!42, R!40)),
% 0.20/0.54 inference(tautology,[status(thm)],[])).
% 0.20/0.54 tff(325,plain,
% 0.20/0.54 (increasing(inverse_function(F!43, A!42, B!41), B!41, S!39, A!42, R!40)),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[324, 56])).
% 0.20/0.54 tff(326,plain,
% 0.20/0.54 ((~((~increasing(inverse_function(F!43, A!42, B!41), B!41, S!39, A!42, R!40)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, A!42)) | (~member(Y1, A!42)) | (~member(X2, B!41)) | apply(R!40, Y1, Y2) | (~member(X1, B!41)) | (~apply(S!39, X1, X2)) | (~apply(inverse_function(F!43, A!42, B!41), X1, Y1)) | (~apply(inverse_function(F!43, A!42, B!41), X2, Y2))))) | (~increasing(inverse_function(F!43, A!42, B!41), B!41, S!39, A!42, R!40)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, A!42)) | (~member(Y1, A!42)) | (~member(X2, B!41)) | apply(R!40, Y1, Y2) | (~member(X1, B!41)) | (~apply(S!39, X1, X2)) | (~apply(inverse_function(F!43, A!42, B!41), X1, Y1)) | (~apply(inverse_function(F!43, A!42, B!41), X2, Y2)))),
% 0.20/0.54 inference(tautology,[status(thm)],[])).
% 0.20/0.54 tff(327,plain,
% 0.20/0.54 ((~((~increasing(inverse_function(F!43, A!42, B!41), B!41, S!39, A!42, R!40)) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, A!42)) | (~member(Y1, A!42)) | (~member(X2, B!41)) | apply(R!40, Y1, Y2) | (~member(X1, B!41)) | (~apply(S!39, X1, X2)) | (~apply(inverse_function(F!43, A!42, B!41), X1, Y1)) | (~apply(inverse_function(F!43, A!42, B!41), X2, Y2))))) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, A!42)) | (~member(Y1, A!42)) | (~member(X2, B!41)) | apply(R!40, Y1, Y2) | (~member(X1, B!41)) | (~apply(S!39, X1, X2)) | (~apply(inverse_function(F!43, A!42, B!41), X1, Y1)) | (~apply(inverse_function(F!43, A!42, B!41), X2, Y2)))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[326, 325])).
% 0.20/0.54 tff(328,plain,
% 0.20/0.54 (![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, A!42)) | (~member(Y1, A!42)) | (~member(X2, B!41)) | apply(R!40, Y1, Y2) | (~member(X1, B!41)) | (~apply(S!39, X1, X2)) | (~apply(inverse_function(F!43, A!42, B!41), X1, Y1)) | (~apply(inverse_function(F!43, A!42, B!41), X2, Y2)))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[327, 323])).
% 0.20/0.54 tff(329,plain,
% 0.20/0.54 (((~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, A!42)) | (~member(Y1, A!42)) | (~member(X2, B!41)) | apply(R!40, Y1, Y2) | (~member(X1, B!41)) | (~apply(S!39, X1, X2)) | (~apply(inverse_function(F!43, A!42, B!41), X1, Y1)) | (~apply(inverse_function(F!43, A!42, B!41), X2, Y2)))) | (apply(R!40, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43)) | (~member(tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | (~apply(S!39, tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))) | (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43))) | (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43))))) <=> ((~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, A!42)) | (~member(Y1, A!42)) | (~member(X2, B!41)) | apply(R!40, Y1, Y2) | (~member(X1, B!41)) | (~apply(S!39, X1, X2)) | (~apply(inverse_function(F!43, A!42, B!41), X1, Y1)) | (~apply(inverse_function(F!43, A!42, B!41), X2, Y2)))) | apply(R!40, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43)) | (~member(tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | (~apply(S!39, tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))) | (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43))) | (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43))))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(330,plain,
% 0.20/0.54 (((~member(tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | apply(R!40, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43)) | (~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~apply(S!39, tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))) | (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43))) | (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43)))) <=> (apply(R!40, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43)) | (~member(tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | (~apply(S!39, tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))) | (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43))) | (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43))))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(331,plain,
% 0.20/0.54 (((~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, A!42)) | (~member(Y1, A!42)) | (~member(X2, B!41)) | apply(R!40, Y1, Y2) | (~member(X1, B!41)) | (~apply(S!39, X1, X2)) | (~apply(inverse_function(F!43, A!42, B!41), X1, Y1)) | (~apply(inverse_function(F!43, A!42, B!41), X2, Y2)))) | ((~member(tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | apply(R!40, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43)) | (~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~apply(S!39, tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))) | (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43))) | (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43))))) <=> ((~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, A!42)) | (~member(Y1, A!42)) | (~member(X2, B!41)) | apply(R!40, Y1, Y2) | (~member(X1, B!41)) | (~apply(S!39, X1, X2)) | (~apply(inverse_function(F!43, A!42, B!41), X1, Y1)) | (~apply(inverse_function(F!43, A!42, B!41), X2, Y2)))) | (apply(R!40, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43)) | (~member(tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | (~apply(S!39, tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))) | (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43))) | (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43)))))),
% 0.20/0.54 inference(monotonicity,[status(thm)],[330])).
% 0.20/0.54 tff(332,plain,
% 0.20/0.54 (((~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, A!42)) | (~member(Y1, A!42)) | (~member(X2, B!41)) | apply(R!40, Y1, Y2) | (~member(X1, B!41)) | (~apply(S!39, X1, X2)) | (~apply(inverse_function(F!43, A!42, B!41), X1, Y1)) | (~apply(inverse_function(F!43, A!42, B!41), X2, Y2)))) | ((~member(tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | apply(R!40, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43)) | (~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~apply(S!39, tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))) | (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43))) | (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43))))) <=> ((~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, A!42)) | (~member(Y1, A!42)) | (~member(X2, B!41)) | apply(R!40, Y1, Y2) | (~member(X1, B!41)) | (~apply(S!39, X1, X2)) | (~apply(inverse_function(F!43, A!42, B!41), X1, Y1)) | (~apply(inverse_function(F!43, A!42, B!41), X2, Y2)))) | apply(R!40, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43)) | (~member(tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | (~apply(S!39, tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))) | (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43))) | (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43))))),
% 0.20/0.54 inference(transitivity,[status(thm)],[331, 329])).
% 0.20/0.54 tff(333,plain,
% 0.20/0.54 ((~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, A!42)) | (~member(Y1, A!42)) | (~member(X2, B!41)) | apply(R!40, Y1, Y2) | (~member(X1, B!41)) | (~apply(S!39, X1, X2)) | (~apply(inverse_function(F!43, A!42, B!41), X1, Y1)) | (~apply(inverse_function(F!43, A!42, B!41), X2, Y2)))) | ((~member(tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | apply(R!40, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43)) | (~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~apply(S!39, tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))) | (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43))) | (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43))))),
% 0.20/0.54 inference(quant_inst,[status(thm)],[])).
% 0.20/0.54 tff(334,plain,
% 0.20/0.54 ((~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, A!42)) | (~member(Y1, A!42)) | (~member(X2, B!41)) | apply(R!40, Y1, Y2) | (~member(X1, B!41)) | (~apply(S!39, X1, X2)) | (~apply(inverse_function(F!43, A!42, B!41), X1, Y1)) | (~apply(inverse_function(F!43, A!42, B!41), X2, Y2)))) | apply(R!40, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43)) | (~member(tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | (~apply(S!39, tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))) | (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43))) | (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43)))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[333, 332])).
% 0.20/0.54 tff(335,plain,
% 0.20/0.54 (apply(R!40, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43)) | (~apply(S!39, tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))) | (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43))) | (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43)))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[334, 259, 247, 201, 116, 328])).
% 0.20/0.54 tff(336,plain,
% 0.20/0.54 ($false),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[335, 321, 319, 290, 245])).
% 0.20/0.54 tff(337,plain,((~increasing(F!43, A!42, R!40, B!41, S!39)) | (~increasing(inverse_function(F!43, A!42, B!41), B!41, S!39, A!42, R!40))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.54 tff(338,plain,
% 0.20/0.54 (isomorphism(F!43, A!42, R!40, B!41, S!39) | (~((~increasing(F!43, A!42, R!40, B!41, S!39)) | (~increasing(inverse_function(F!43, A!42, B!41), B!41, S!39, A!42, R!40)))) | (~(isomorphism(F!43, A!42, R!40, B!41, S!39) <=> ((~increasing(F!43, A!42, R!40, B!41, S!39)) | (~increasing(inverse_function(F!43, A!42, B!41), B!41, S!39, A!42, R!40)))))),
% 0.20/0.54 inference(tautology,[status(thm)],[])).
% 0.20/0.54 tff(339,plain,
% 0.20/0.54 (isomorphism(F!43, A!42, R!40, B!41, S!39) | (~((~increasing(F!43, A!42, R!40, B!41, S!39)) | (~increasing(inverse_function(F!43, A!42, B!41), B!41, S!39, A!42, R!40))))),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[338, 73])).
% 0.20/0.55 tff(340,plain,
% 0.20/0.55 (isomorphism(F!43, A!42, R!40, B!41, S!39)),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[339, 337])).
% 0.20/0.55 tff(341,plain,
% 0.20/0.55 (((~(isomorphism(F!43, A!42, R!40, B!41, S!39) | (~maps(F!43, A!42, B!41)) | (~one_to_one(F!43, A!42, B!41)) | (~((apply(R!40, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43)) <=> apply(S!39, tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))) | (~member(tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43), B!41)) | (~apply(F!43, tptp_fun_X1_38(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_37(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X2_36(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_35(S!39, B!41, R!40, A!42, F!43))))))) | (~((~isomorphism(F!43, A!42, R!40, B!41, S!39)) | (~((~maps(F!43, A!42, B!41)) | (~one_to_one(F!43, A!42, B!41)) | (~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!41)) | (apply(R!40, X1, X2) <=> apply(S!39, Y1, Y2)) | (~member(X1, A!42)) | (~member(Y1, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X1, Y1)) | (~apply(F!43, X2, Y2))))))))) | ((~isomorphism(F!43, A!42, R!40, B!41, S!39)) | (~((~maps(F!43, A!42, B!41)) | (~one_to_one(F!43, A!42, B!41)) | (~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!41)) | (apply(R!40, X1, X2) <=> apply(S!39, Y1, Y2)) | (~member(X1, A!42)) | (~member(Y1, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X1, Y1)) | (~apply(F!43, X2, Y2)))))))),
% 0.20/0.55 inference(tautology,[status(thm)],[])).
% 0.20/0.55 tff(342,plain,
% 0.20/0.55 ((~isomorphism(F!43, A!42, R!40, B!41, S!39)) | (~((~maps(F!43, A!42, B!41)) | (~one_to_one(F!43, A!42, B!41)) | (~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!41)) | (apply(R!40, X1, X2) <=> apply(S!39, Y1, Y2)) | (~member(X1, A!42)) | (~member(Y1, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X1, Y1)) | (~apply(F!43, X2, Y2))))))),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[341, 105])).
% 0.20/0.55 tff(343,plain,
% 0.20/0.55 ((~((~isomorphism(F!43, A!42, R!40, B!41, S!39)) | (~((~maps(F!43, A!42, B!41)) | (~one_to_one(F!43, A!42, B!41)) | (~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!41)) | (apply(R!40, X1, X2) <=> apply(S!39, Y1, Y2)) | (~member(X1, A!42)) | (~member(Y1, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X1, Y1)) | (~apply(F!43, X2, Y2)))))))) | (~isomorphism(F!43, A!42, R!40, B!41, S!39)) | (~((~maps(F!43, A!42, B!41)) | (~one_to_one(F!43, A!42, B!41)) | (~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!41)) | (apply(R!40, X1, X2) <=> apply(S!39, Y1, Y2)) | (~member(X1, A!42)) | (~member(Y1, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X1, Y1)) | (~apply(F!43, X2, Y2))))))),
% 0.20/0.55 inference(tautology,[status(thm)],[])).
% 0.20/0.55 tff(344,plain,
% 0.20/0.55 ((~isomorphism(F!43, A!42, R!40, B!41, S!39)) | (~((~maps(F!43, A!42, B!41)) | (~one_to_one(F!43, A!42, B!41)) | (~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!41)) | (apply(R!40, X1, X2) <=> apply(S!39, Y1, Y2)) | (~member(X1, A!42)) | (~member(Y1, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X1, Y1)) | (~apply(F!43, X2, Y2))))))),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[343, 342])).
% 0.20/0.55 tff(345,plain,
% 0.20/0.55 (~((~maps(F!43, A!42, B!41)) | (~one_to_one(F!43, A!42, B!41)) | (~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!41)) | (apply(R!40, X1, X2) <=> apply(S!39, Y1, Y2)) | (~member(X1, A!42)) | (~member(Y1, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X1, Y1)) | (~apply(F!43, X2, Y2)))))),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[344, 340])).
% 0.20/0.55 tff(346,plain,
% 0.20/0.55 (((~maps(F!43, A!42, B!41)) | (~one_to_one(F!43, A!42, B!41)) | (~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!41)) | (apply(R!40, X1, X2) <=> apply(S!39, Y1, Y2)) | (~member(X1, A!42)) | (~member(Y1, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X1, Y1)) | (~apply(F!43, X2, Y2))))) | ![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!41)) | (apply(R!40, X1, X2) <=> apply(S!39, Y1, Y2)) | (~member(X1, A!42)) | (~member(Y1, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X1, Y1)) | (~apply(F!43, X2, Y2)))),
% 0.20/0.55 inference(tautology,[status(thm)],[])).
% 0.20/0.55 tff(347,plain,
% 0.20/0.55 (![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!41)) | (apply(R!40, X1, X2) <=> apply(S!39, Y1, Y2)) | (~member(X1, A!42)) | (~member(Y1, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X1, Y1)) | (~apply(F!43, X2, Y2)))),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[346, 345])).
% 0.20/0.55 tff(348,plain,
% 0.20/0.55 (((~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!41)) | (apply(R!40, X1, X2) <=> apply(S!39, Y1, Y2)) | (~member(X1, A!42)) | (~member(Y1, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X1, Y1)) | (~apply(F!43, X2, Y2)))) | ((~member(tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43), B!41)) | (~apply(F!43, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43))) | (apply(R!40, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43)) <=> apply(S!39, tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43))))) <=> ((~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!41)) | (apply(R!40, X1, X2) <=> apply(S!39, Y1, Y2)) | (~member(X1, A!42)) | (~member(Y1, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X1, Y1)) | (~apply(F!43, X2, Y2)))) | (~member(tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43), B!41)) | (~apply(F!43, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43))) | (apply(R!40, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43)) <=> apply(S!39, tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43))))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(349,plain,
% 0.20/0.55 (((~member(tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43), B!41)) | (apply(R!40, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43)) <=> apply(S!39, tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43))) | (~member(tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43)))) <=> ((~member(tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43), B!41)) | (~apply(F!43, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43))) | (apply(R!40, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43)) <=> apply(S!39, tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43))))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(350,plain,
% 0.20/0.55 (((~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!41)) | (apply(R!40, X1, X2) <=> apply(S!39, Y1, Y2)) | (~member(X1, A!42)) | (~member(Y1, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X1, Y1)) | (~apply(F!43, X2, Y2)))) | ((~member(tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43), B!41)) | (apply(R!40, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43)) <=> apply(S!39, tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43))) | (~member(tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43))))) <=> ((~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!41)) | (apply(R!40, X1, X2) <=> apply(S!39, Y1, Y2)) | (~member(X1, A!42)) | (~member(Y1, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X1, Y1)) | (~apply(F!43, X2, Y2)))) | ((~member(tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43), B!41)) | (~apply(F!43, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43))) | (apply(R!40, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43)) <=> apply(S!39, tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43)))))),
% 0.20/0.55 inference(monotonicity,[status(thm)],[349])).
% 0.20/0.55 tff(351,plain,
% 0.20/0.55 (((~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!41)) | (apply(R!40, X1, X2) <=> apply(S!39, Y1, Y2)) | (~member(X1, A!42)) | (~member(Y1, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X1, Y1)) | (~apply(F!43, X2, Y2)))) | ((~member(tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43), B!41)) | (apply(R!40, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43)) <=> apply(S!39, tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43))) | (~member(tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43))))) <=> ((~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!41)) | (apply(R!40, X1, X2) <=> apply(S!39, Y1, Y2)) | (~member(X1, A!42)) | (~member(Y1, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X1, Y1)) | (~apply(F!43, X2, Y2)))) | (~member(tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43), B!41)) | (~apply(F!43, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43))) | (apply(R!40, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43)) <=> apply(S!39, tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43))))),
% 0.20/0.55 inference(transitivity,[status(thm)],[350, 348])).
% 0.20/0.55 tff(352,plain,
% 0.20/0.55 ((~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!41)) | (apply(R!40, X1, X2) <=> apply(S!39, Y1, Y2)) | (~member(X1, A!42)) | (~member(Y1, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X1, Y1)) | (~apply(F!43, X2, Y2)))) | ((~member(tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43), B!41)) | (apply(R!40, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43)) <=> apply(S!39, tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43))) | (~member(tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), A!42)) | (~apply(F!43, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43))))),
% 0.20/0.55 inference(quant_inst,[status(thm)],[])).
% 0.20/0.55 tff(353,plain,
% 0.20/0.55 ((~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!41)) | (apply(R!40, X1, X2) <=> apply(S!39, Y1, Y2)) | (~member(X1, A!42)) | (~member(Y1, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X1, Y1)) | (~apply(F!43, X2, Y2)))) | (~member(tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43), B!41)) | (~apply(F!43, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43))) | (apply(R!40, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43)) <=> apply(S!39, tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43)))),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[352, 351])).
% 0.20/0.55 tff(354,plain,
% 0.20/0.55 ($false),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[353, 347, 55, 53, 51, 49, 47, 45, 43])).
% 0.20/0.55 tff(355,plain,(apply(S!39, tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43)) | (~member(tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43), B!41)) | (~apply(R!40, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.55 tff(356,plain,
% 0.20/0.55 ((~(increasing(F!43, A!42, R!40, B!41, S!39) | (~(apply(S!39, tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43)) | (~member(tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43), B!41)) | (~apply(R!40, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43))))))) | increasing(F!43, A!42, R!40, B!41, S!39) | (~(apply(S!39, tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43)) | (~member(tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43), B!41)) | (~apply(R!40, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43)))))),
% 0.20/0.55 inference(tautology,[status(thm)],[])).
% 0.20/0.55 tff(357,plain,
% 0.20/0.55 ((~(increasing(F!43, A!42, R!40, B!41, S!39) | (~(apply(S!39, tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43)) | (~member(tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43), B!41)) | (~member(tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), A!42)) | (~member(tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43), B!41)) | (~apply(R!40, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X1_30(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y1_29(S!39, B!41, R!40, A!42, F!43))) | (~apply(F!43, tptp_fun_X2_28(S!39, B!41, R!40, A!42, F!43), tptp_fun_Y2_27(S!39, B!41, R!40, A!42, F!43))))))) | increasing(F!43, A!42, R!40, B!41, S!39)),
% 0.20/0.56 inference(unit_resolution,[status(thm)],[356, 355])).
% 0.20/0.56 tff(358,plain,
% 0.20/0.56 (increasing(F!43, A!42, R!40, B!41, S!39)),
% 0.20/0.56 inference(unit_resolution,[status(thm)],[357, 36])).
% 0.20/0.56 tff(359,plain,
% 0.20/0.56 ((~((~increasing(F!43, A!42, R!40, B!41, S!39)) | (~increasing(inverse_function(F!43, A!42, B!41), B!41, S!39, A!42, R!40)))) | (~increasing(F!43, A!42, R!40, B!41, S!39)) | (~increasing(inverse_function(F!43, A!42, B!41), B!41, S!39, A!42, R!40))),
% 0.20/0.56 inference(tautology,[status(thm)],[])).
% 0.20/0.56 tff(360,plain,
% 0.20/0.56 ((~increasing(F!43, A!42, R!40, B!41, S!39)) | (~increasing(inverse_function(F!43, A!42, B!41), B!41, S!39, A!42, R!40))),
% 0.20/0.56 inference(unit_resolution,[status(thm)],[359, 337])).
% 0.20/0.56 tff(361,plain,
% 0.20/0.56 (~increasing(inverse_function(F!43, A!42, B!41), B!41, S!39, A!42, R!40)),
% 0.20/0.56 inference(unit_resolution,[status(thm)],[360, 358])).
% 0.20/0.56 tff(362,plain,
% 0.20/0.56 ((~(increasing(inverse_function(F!43, A!42, B!41), B!41, S!39, A!42, R!40) | (~(apply(R!40, tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))) | (~member(tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (~member(tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~member(tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (~member(tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~apply(S!39, tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))))))) | increasing(inverse_function(F!43, A!42, B!41), B!41, S!39, A!42, R!40) | (~(apply(R!40, tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))) | (~member(tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (~member(tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~member(tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (~member(tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~apply(S!39, tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))))))),
% 0.20/0.56 inference(tautology,[status(thm)],[])).
% 0.20/0.56 tff(363,plain,
% 0.20/0.56 ((~(increasing(inverse_function(F!43, A!42, B!41), B!41, S!39, A!42, R!40) | (~(apply(R!40, tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))) | (~member(tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (~member(tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~member(tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (~member(tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~apply(S!39, tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))))))) | (~(apply(R!40, tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))) | (~member(tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (~member(tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~member(tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (~member(tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~apply(S!39, tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))))))),
% 0.20/0.56 inference(unit_resolution,[status(thm)],[362, 361])).
% 0.20/0.56 tff(364,plain,
% 0.20/0.56 (~(apply(R!40, tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))) | (~member(tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (~member(tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~member(tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (~member(tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~apply(S!39, tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))))),
% 0.20/0.56 inference(unit_resolution,[status(thm)],[363, 25])).
% 0.20/0.56 tff(365,plain,
% 0.20/0.56 ((apply(R!40, tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))) | (~member(tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (~member(tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~member(tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (~member(tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~apply(S!39, tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))))) | member(tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)),
% 0.20/0.56 inference(tautology,[status(thm)],[])).
% 0.20/0.56 tff(366,plain,
% 0.20/0.56 (member(tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)),
% 0.20/0.56 inference(unit_resolution,[status(thm)],[365, 364])).
% 0.20/0.56 tff(367,plain,
% 0.20/0.56 ((apply(R!40, tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))) | (~member(tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (~member(tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~member(tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (~member(tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~apply(S!39, tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))))) | member(tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)),
% 0.20/0.56 inference(tautology,[status(thm)],[])).
% 0.20/0.56 tff(368,plain,
% 0.20/0.56 (member(tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)),
% 0.20/0.56 inference(unit_resolution,[status(thm)],[367, 364])).
% 0.20/0.56 tff(369,plain,
% 0.20/0.56 (((~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))) | ((~member(tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (~member(tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (apply(F!43, tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))) <=> apply(inverse_function(F!43, A!42, B!41), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))))) <=> ((~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))) | (~member(tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (~member(tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (apply(F!43, tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))) <=> apply(inverse_function(F!43, A!42, B!41), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))))),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(370,plain,
% 0.20/0.56 (((apply(F!43, tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))) <=> apply(inverse_function(F!43, A!42, B!41), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~member(tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (~member(tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42))) <=> ((~member(tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (~member(tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (apply(F!43, tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))) <=> apply(inverse_function(F!43, A!42, B!41), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))))),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(371,plain,
% 0.20/0.56 (((~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))) | ((apply(F!43, tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))) <=> apply(inverse_function(F!43, A!42, B!41), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~member(tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (~member(tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)))) <=> ((~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))) | ((~member(tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (~member(tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (apply(F!43, tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))) <=> apply(inverse_function(F!43, A!42, B!41), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))))))),
% 0.20/0.56 inference(monotonicity,[status(thm)],[370])).
% 0.20/0.56 tff(372,plain,
% 0.20/0.56 (((~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))) | ((apply(F!43, tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))) <=> apply(inverse_function(F!43, A!42, B!41), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~member(tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (~member(tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)))) <=> ((~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))) | (~member(tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (~member(tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (apply(F!43, tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))) <=> apply(inverse_function(F!43, A!42, B!41), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))))),
% 0.20/0.56 inference(transitivity,[status(thm)],[371, 369])).
% 0.20/0.56 tff(373,plain,
% 0.20/0.56 ((~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))) | ((apply(F!43, tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))) <=> apply(inverse_function(F!43, A!42, B!41), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~member(tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (~member(tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)))),
% 0.20/0.56 inference(quant_inst,[status(thm)],[])).
% 0.20/0.56 tff(374,plain,
% 0.20/0.56 ((~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))) | (~member(tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (~member(tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (apply(F!43, tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))) <=> apply(inverse_function(F!43, A!42, B!41), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))))),
% 0.20/0.56 inference(modus_ponens,[status(thm)],[373, 372])).
% 0.20/0.56 tff(375,plain,
% 0.20/0.56 (apply(F!43, tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))) <=> apply(inverse_function(F!43, A!42, B!41), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))),
% 0.20/0.56 inference(unit_resolution,[status(thm)],[374, 231, 368, 366])).
% 0.20/0.56 tff(376,plain,
% 0.20/0.56 ((apply(R!40, tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))) | (~member(tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (~member(tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~member(tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (~member(tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~apply(S!39, tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))))) | apply(inverse_function(F!43, A!42, B!41), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))),
% 0.20/0.56 inference(tautology,[status(thm)],[])).
% 0.20/0.56 tff(377,plain,
% 0.20/0.56 (apply(inverse_function(F!43, A!42, B!41), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))),
% 0.20/0.56 inference(unit_resolution,[status(thm)],[376, 364])).
% 0.20/0.56 tff(378,plain,
% 0.20/0.56 ((~(apply(F!43, tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))) <=> apply(inverse_function(F!43, A!42, B!41), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))))) | apply(F!43, tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))) | (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))))),
% 0.20/0.56 inference(tautology,[status(thm)],[])).
% 0.20/0.56 tff(379,plain,
% 0.20/0.56 ((~(apply(F!43, tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))) <=> apply(inverse_function(F!43, A!42, B!41), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))))) | apply(F!43, tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))),
% 0.20/0.57 inference(unit_resolution,[status(thm)],[378, 377])).
% 0.20/0.57 tff(380,plain,
% 0.20/0.57 (apply(F!43, tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))),
% 0.20/0.57 inference(unit_resolution,[status(thm)],[379, 375])).
% 0.20/0.57 tff(381,plain,
% 0.20/0.57 ((apply(R!40, tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))) | (~member(tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (~member(tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~member(tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (~member(tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~apply(S!39, tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))))) | member(tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)),
% 0.20/0.57 inference(tautology,[status(thm)],[])).
% 0.20/0.57 tff(382,plain,
% 0.20/0.57 (member(tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)),
% 0.20/0.57 inference(unit_resolution,[status(thm)],[381, 364])).
% 0.20/0.57 tff(383,plain,
% 0.20/0.57 ((apply(R!40, tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))) | (~member(tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (~member(tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~member(tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (~member(tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~apply(S!39, tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))))) | member(tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)),
% 0.20/0.57 inference(tautology,[status(thm)],[])).
% 0.20/0.57 tff(384,plain,
% 0.20/0.57 (member(tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)),
% 0.20/0.57 inference(unit_resolution,[status(thm)],[383, 364])).
% 0.20/0.57 tff(385,plain,
% 0.20/0.57 (((~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))) | ((~member(tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (~member(tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (apply(F!43, tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))) <=> apply(inverse_function(F!43, A!42, B!41), tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))))) <=> ((~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))) | (~member(tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (~member(tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (apply(F!43, tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))) <=> apply(inverse_function(F!43, A!42, B!41), tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))))),
% 0.20/0.57 inference(rewrite,[status(thm)],[])).
% 0.20/0.57 tff(386,plain,
% 0.20/0.57 (((apply(F!43, tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))) <=> apply(inverse_function(F!43, A!42, B!41), tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~member(tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (~member(tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42))) <=> ((~member(tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (~member(tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (apply(F!43, tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))) <=> apply(inverse_function(F!43, A!42, B!41), tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))))),
% 0.20/0.57 inference(rewrite,[status(thm)],[])).
% 0.20/0.57 tff(387,plain,
% 0.20/0.57 (((~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))) | ((apply(F!43, tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))) <=> apply(inverse_function(F!43, A!42, B!41), tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~member(tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (~member(tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)))) <=> ((~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))) | ((~member(tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (~member(tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (apply(F!43, tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))) <=> apply(inverse_function(F!43, A!42, B!41), tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))))))),
% 0.20/0.57 inference(monotonicity,[status(thm)],[386])).
% 0.20/0.57 tff(388,plain,
% 0.20/0.57 (((~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))) | ((apply(F!43, tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))) <=> apply(inverse_function(F!43, A!42, B!41), tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~member(tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (~member(tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)))) <=> ((~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))) | (~member(tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (~member(tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (apply(F!43, tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))) <=> apply(inverse_function(F!43, A!42, B!41), tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))))),
% 0.20/0.57 inference(transitivity,[status(thm)],[387, 385])).
% 0.20/0.57 tff(389,plain,
% 0.20/0.57 ((~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))) | ((apply(F!43, tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))) <=> apply(inverse_function(F!43, A!42, B!41), tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~member(tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (~member(tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)))),
% 0.20/0.57 inference(quant_inst,[status(thm)],[])).
% 0.20/0.57 tff(390,plain,
% 0.20/0.57 ((~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))) | (~member(tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (~member(tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (apply(F!43, tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))) <=> apply(inverse_function(F!43, A!42, B!41), tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))))),
% 0.20/0.57 inference(modus_ponens,[status(thm)],[389, 388])).
% 0.20/0.57 tff(391,plain,
% 0.20/0.57 (apply(F!43, tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))) <=> apply(inverse_function(F!43, A!42, B!41), tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))),
% 0.20/0.57 inference(unit_resolution,[status(thm)],[390, 231, 384, 382])).
% 0.20/0.57 tff(392,plain,
% 0.20/0.57 ((apply(R!40, tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))) | (~member(tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (~member(tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~member(tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (~member(tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~apply(S!39, tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))))) | apply(inverse_function(F!43, A!42, B!41), tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))),
% 0.20/0.57 inference(tautology,[status(thm)],[])).
% 0.20/0.57 tff(393,plain,
% 0.20/0.57 (apply(inverse_function(F!43, A!42, B!41), tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))),
% 0.20/0.57 inference(unit_resolution,[status(thm)],[392, 364])).
% 0.20/0.57 tff(394,plain,
% 0.20/0.57 ((~(apply(F!43, tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))) <=> apply(inverse_function(F!43, A!42, B!41), tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))))) | apply(F!43, tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))) | (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))))),
% 0.20/0.57 inference(tautology,[status(thm)],[])).
% 0.20/0.57 tff(395,plain,
% 0.20/0.57 ((~(apply(F!43, tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))) <=> apply(inverse_function(F!43, A!42, B!41), tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))))) | apply(F!43, tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))),
% 0.20/0.57 inference(unit_resolution,[status(thm)],[394, 393])).
% 0.20/0.57 tff(396,plain,
% 0.20/0.57 (apply(F!43, tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))),
% 0.20/0.57 inference(unit_resolution,[status(thm)],[395, 391])).
% 0.20/0.57 tff(397,plain,
% 0.20/0.57 ((apply(R!40, tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))) | (~member(tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (~member(tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~member(tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (~member(tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~apply(S!39, tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))))) | apply(S!39, tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))),
% 0.20/0.57 inference(tautology,[status(thm)],[])).
% 0.20/0.57 tff(398,plain,
% 0.20/0.57 (apply(S!39, tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))),
% 0.20/0.57 inference(unit_resolution,[status(thm)],[397, 364])).
% 0.20/0.57 tff(399,plain,
% 0.20/0.57 ((apply(R!40, tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))) | (~member(tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (~member(tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~member(tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (~member(tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~apply(S!39, tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(inverse_function(F!43, A!42, B!41), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))))) | (~apply(R!40, tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))))),
% 0.20/0.58 inference(tautology,[status(thm)],[])).
% 0.20/0.58 tff(400,plain,
% 0.20/0.58 (~apply(R!40, tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))),
% 0.20/0.58 inference(unit_resolution,[status(thm)],[399, 364])).
% 0.20/0.58 tff(401,plain,
% 0.20/0.58 ((~(apply(R!40, tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))) <=> apply(S!39, tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))))) | apply(R!40, tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))) | (~apply(S!39, tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))))),
% 0.20/0.58 inference(tautology,[status(thm)],[])).
% 0.20/0.58 tff(402,plain,
% 0.20/0.58 (~(apply(R!40, tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))) <=> apply(S!39, tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))))),
% 0.20/0.58 inference(unit_resolution,[status(thm)],[401, 400, 398])).
% 0.20/0.58 tff(403,plain,
% 0.20/0.58 (((~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!41)) | (apply(R!40, X1, X2) <=> apply(S!39, Y1, Y2)) | (~member(X1, A!42)) | (~member(Y1, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X1, Y1)) | (~apply(F!43, X2, Y2)))) | ((~member(tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (~member(tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~member(tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (~member(tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~apply(F!43, tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(F!43, tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (apply(R!40, tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))) <=> apply(S!39, tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))))) <=> ((~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!41)) | (apply(R!40, X1, X2) <=> apply(S!39, Y1, Y2)) | (~member(X1, A!42)) | (~member(Y1, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X1, Y1)) | (~apply(F!43, X2, Y2)))) | (~member(tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (~member(tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~member(tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (~member(tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~apply(F!43, tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(F!43, tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (apply(R!40, tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))) <=> apply(S!39, tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))))),
% 0.20/0.58 inference(rewrite,[status(thm)],[])).
% 0.20/0.58 tff(404,plain,
% 0.20/0.58 (((~member(tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (apply(R!40, tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))) <=> apply(S!39, tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~member(tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~member(tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (~member(tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~apply(F!43, tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(F!43, tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))))) <=> ((~member(tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (~member(tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~member(tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (~member(tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~apply(F!43, tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(F!43, tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (apply(R!40, tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))) <=> apply(S!39, tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))))),
% 0.20/0.58 inference(rewrite,[status(thm)],[])).
% 0.20/0.58 tff(405,plain,
% 0.20/0.58 (((~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!41)) | (apply(R!40, X1, X2) <=> apply(S!39, Y1, Y2)) | (~member(X1, A!42)) | (~member(Y1, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X1, Y1)) | (~apply(F!43, X2, Y2)))) | ((~member(tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (apply(R!40, tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))) <=> apply(S!39, tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~member(tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~member(tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (~member(tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~apply(F!43, tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(F!43, tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))))) <=> ((~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!41)) | (apply(R!40, X1, X2) <=> apply(S!39, Y1, Y2)) | (~member(X1, A!42)) | (~member(Y1, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X1, Y1)) | (~apply(F!43, X2, Y2)))) | ((~member(tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (~member(tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~member(tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (~member(tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~apply(F!43, tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(F!43, tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (apply(R!40, tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))) <=> apply(S!39, tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))))))),
% 0.20/0.58 inference(monotonicity,[status(thm)],[404])).
% 0.20/0.58 tff(406,plain,
% 0.20/0.58 (((~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!41)) | (apply(R!40, X1, X2) <=> apply(S!39, Y1, Y2)) | (~member(X1, A!42)) | (~member(Y1, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X1, Y1)) | (~apply(F!43, X2, Y2)))) | ((~member(tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (apply(R!40, tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))) <=> apply(S!39, tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~member(tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~member(tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (~member(tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~apply(F!43, tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(F!43, tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))))) <=> ((~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!41)) | (apply(R!40, X1, X2) <=> apply(S!39, Y1, Y2)) | (~member(X1, A!42)) | (~member(Y1, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X1, Y1)) | (~apply(F!43, X2, Y2)))) | (~member(tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (~member(tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~member(tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (~member(tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~apply(F!43, tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(F!43, tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (apply(R!40, tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))) <=> apply(S!39, tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))))),
% 0.20/0.59 inference(transitivity,[status(thm)],[405, 403])).
% 0.20/0.59 tff(407,plain,
% 0.20/0.59 ((~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!41)) | (apply(R!40, X1, X2) <=> apply(S!39, Y1, Y2)) | (~member(X1, A!42)) | (~member(Y1, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X1, Y1)) | (~apply(F!43, X2, Y2)))) | ((~member(tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (apply(R!40, tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))) <=> apply(S!39, tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~member(tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~member(tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (~member(tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~apply(F!43, tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(F!43, tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))))),
% 0.20/0.59 inference(quant_inst,[status(thm)],[])).
% 0.20/0.59 tff(408,plain,
% 0.20/0.59 ((~![X1: $i, Y1: $i, X2: $i, Y2: $i] : ((~member(Y2, B!41)) | (apply(R!40, X1, X2) <=> apply(S!39, Y1, Y2)) | (~member(X1, A!42)) | (~member(Y1, B!41)) | (~member(X2, A!42)) | (~apply(F!43, X1, Y1)) | (~apply(F!43, X2, Y2)))) | (~member(tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (~member(tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~member(tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), B!41)) | (~member(tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), A!42)) | (~apply(F!43, tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(F!43, tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (apply(R!40, tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))) <=> apply(S!39, tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))))),
% 0.20/0.59 inference(modus_ponens,[status(thm)],[407, 406])).
% 0.20/0.59 tff(409,plain,
% 0.20/0.59 ((~apply(F!43, tptp_fun_Y2_27(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X2_28(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)))) | (~apply(F!43, tptp_fun_Y1_29(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41)), tptp_fun_X1_30(R!40, A!42, S!39, B!41, inverse_function(F!43, A!42, B!41))))),
% 0.20/0.59 inference(unit_resolution,[status(thm)],[408, 347, 384, 382, 368, 366, 402])).
% 0.20/0.59 tff(410,plain,
% 0.20/0.59 ($false),
% 0.20/0.59 inference(unit_resolution,[status(thm)],[409, 396, 380])).
% 0.20/0.59 % SZS output end Proof
%------------------------------------------------------------------------------