%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : SET715+4 : TPTP v8.1.0. Bugfixed v2.2.1.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n003.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 05:07:43 EDT 2022

% Result   : Theorem 0.22s 0.42s
% Output   : Proof 0.22s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SET715+4 : TPTP v8.1.0. Bugfixed v2.2.1.
% 0.07/0.13  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.35  % Computer : n003.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Sat Sep  3 07:28:40 EDT 2022
% 0.14/0.35  % CPUTime  : 
% 0.14/0.35  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.35  Usage: tptp [options] [-file:]file
% 0.14/0.35    -h, -?       prints this message.
% 0.14/0.35    -smt2        print SMT-LIB2 benchmark.
% 0.14/0.35    -m, -model   generate model.
% 0.14/0.35    -p, -proof   generate proof.
% 0.14/0.35    -c, -core    generate unsat core of named formulas.
% 0.14/0.35    -st, -statistics display statistics.
% 0.14/0.35    -t:timeout   set timeout (in second).
% 0.14/0.35    -smt2status  display status in smt2 format instead of SZS.
% 0.14/0.35    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.35    -<param>:<value> configuration parameter and value.
% 0.14/0.35    -o:<output-file> file to place output in.
% 0.22/0.42  % SZS status Theorem
% 0.22/0.42  % SZS output start Proof
% 0.22/0.42  tff(apply_type, type, (
% 0.22/0.42     apply: ( $i * $i * $i ) > $o)).
% 0.22/0.42  tff(tptp_fun_E_19_type, type, (
% 0.22/0.42     tptp_fun_E_19: ( $i * $i * $i ) > $i)).
% 0.22/0.42  tff(tptp_fun_F_41_type, type, (
% 0.22/0.42     tptp_fun_F_41: $i)).
% 0.22/0.42  tff(tptp_fun_A_40_type, type, (
% 0.22/0.42     tptp_fun_A_40: $i)).
% 0.22/0.42  tff(tptp_fun_X_15_type, type, (
% 0.22/0.42     tptp_fun_X_15: ( $i * $i ) > $i)).
% 0.22/0.42  tff(compose_function_type, type, (
% 0.22/0.42     compose_function: ( $i * $i * $i * $i * $i ) > $i)).
% 0.22/0.42  tff(tptp_fun_B_39_type, type, (
% 0.22/0.42     tptp_fun_B_39: $i)).
% 0.22/0.42  tff(inverse_function_type, type, (
% 0.22/0.42     inverse_function: ( $i * $i * $i ) > $i)).
% 0.22/0.42  tff(member_type, type, (
% 0.22/0.42     member: ( $i * $i ) > $o)).
% 0.22/0.42  tff(surjective_type, type, (
% 0.22/0.42     surjective: ( $i * $i * $i ) > $o)).
% 0.22/0.42  tff(tptp_fun_Y_20_type, type, (
% 0.22/0.42     tptp_fun_Y_20: ( $i * $i * $i ) > $i)).
% 0.22/0.42  tff(injective_type, type, (
% 0.22/0.42     injective: ( $i * $i * $i ) > $o)).
% 0.22/0.42  tff(one_to_one_type, type, (
% 0.22/0.42     one_to_one: ( $i * $i * $i ) > $o)).
% 0.22/0.42  tff(maps_type, type, (
% 0.22/0.42     maps: ( $i * $i * $i ) > $o)).
% 0.22/0.42  tff(identity_type, type, (
% 0.22/0.42     identity: ( $i * $i ) > $o)).
% 0.22/0.42  tff(tptp_fun_Y_8_type, type, (
% 0.22/0.42     tptp_fun_Y_8: ( $i * $i * $i * $i * $i ) > $i)).
% 0.22/0.42  tff(1,plain,
% 0.22/0.42      (^[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))))))))))))),
% 0.22/0.42      inference(bind,[status(th)],[])).
% 0.22/0.42  tff(2,plain,
% 0.22/0.42      (![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)))))))))))),
% 0.22/0.42      inference(quant_intro,[status(thm)],[1])).
% 0.22/0.42  tff(3,plain,
% 0.22/0.42      (^[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))))))))))))),
% 0.22/0.42      inference(bind,[status(th)],[])).
% 0.22/0.42  tff(4,plain,
% 0.22/0.42      (![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)))))))))))),
% 0.22/0.42      inference(quant_intro,[status(thm)],[3])).
% 0.22/0.42  tff(5,plain,
% 0.22/0.42      (![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)))))))))))),
% 0.22/0.42      inference(transitivity,[status(thm)],[4, 2])).
% 0.22/0.42  tff(6,plain,
% 0.22/0.42      (^[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)))))))))))))),
% 0.22/0.42      inference(bind,[status(th)],[])).
% 0.22/0.42  tff(7,plain,
% 0.22/0.42      (![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)))))))))))),
% 0.22/0.42      inference(quant_intro,[status(thm)],[6])).
% 0.22/0.42  tff(8,plain,
% 0.22/0.42      (^[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))))))))),
% 0.22/0.42      inference(bind,[status(th)],[])).
% 0.22/0.42  tff(9,plain,
% 0.22/0.42      (![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)))))))),
% 0.22/0.42      inference(quant_intro,[status(thm)],[8])).
% 0.22/0.42  tff(10,plain,
% 0.22/0.42      (![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))))),
% 0.22/0.42      inference(rewrite,[status(thm)],[])).
% 0.22/0.42  tff(11,plain,
% 0.22/0.42      (^[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)))))),
% 0.22/0.42      inference(bind,[status(th)],[])).
% 0.22/0.42  tff(12,plain,
% 0.22/0.42      (![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))))),
% 0.22/0.42      inference(quant_intro,[status(thm)],[11])).
% 0.22/0.42  tff(13,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/sandbox/benchmark/Axioms/SET006+1.ax','surjective')).
% 0.22/0.42  tff(14,plain,
% 0.22/0.42      (![F: $i, A: $i, B: $i] : (surjective(F, A, B) <=> ![Y: $i] : ((~member(Y, B)) | ?[E: $i] : (member(E, A) & apply(F, E, Y))))),
% 0.22/0.43      inference(modus_ponens,[status(thm)],[13, 12])).
% 0.22/0.43  tff(15,plain,
% 0.22/0.43      (![F: $i, A: $i, B: $i] : (surjective(F, A, B) <=> ![Y: $i] : ((~member(Y, B)) | ?[E: $i] : (member(E, A) & apply(F, E, Y))))),
% 0.22/0.43      inference(modus_ponens,[status(thm)],[14, 10])).
% 0.22/0.43  tff(16,plain,(
% 0.22/0.43      ![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)))))))),
% 0.22/0.43      inference(skolemize,[status(sab)],[15])).
% 0.22/0.43  tff(17,plain,
% 0.22/0.43      (![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)))))))),
% 0.22/0.43      inference(modus_ponens,[status(thm)],[16, 9])).
% 0.22/0.43  tff(18,plain,
% 0.22/0.43      (![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)))))))))))),
% 0.22/0.43      inference(modus_ponens,[status(thm)],[17, 7])).
% 0.22/0.43  tff(19,plain,
% 0.22/0.43      (![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)))))))))))),
% 0.22/0.43      inference(modus_ponens,[status(thm)],[18, 5])).
% 0.22/0.43  tff(20,plain,
% 0.22/0.43      ((~![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!41, A!40, B!39)) | ![Y: $i] : ((~member(Y, B!39)) | (~((~member(tptp_fun_E_19(Y, A!40, F!41), A!40)) | (~apply(F!41, tptp_fun_E_19(Y, A!40, F!41), Y))))))) | (~(surjective(F!41, A!40, B!39) | (~((~member(tptp_fun_Y_20(B!39, A!40, F!41), B!39)) | (~![E: $i] : ((~member(E, A!40)) | (~apply(F!41, E, tptp_fun_Y_20(B!39, A!40, F!41)))))))))))),
% 0.22/0.43      inference(quant_inst,[status(thm)],[])).
% 0.22/0.43  tff(21,plain,
% 0.22/0.43      (~((~((~surjective(F!41, A!40, B!39)) | ![Y: $i] : ((~member(Y, B!39)) | (~((~member(tptp_fun_E_19(Y, A!40, F!41), A!40)) | (~apply(F!41, tptp_fun_E_19(Y, A!40, F!41), Y))))))) | (~(surjective(F!41, A!40, B!39) | (~((~member(tptp_fun_Y_20(B!39, A!40, F!41), B!39)) | (~![E: $i] : ((~member(E, A!40)) | (~apply(F!41, E, tptp_fun_Y_20(B!39, A!40, F!41))))))))))),
% 0.22/0.43      inference(unit_resolution,[status(thm)],[20, 19])).
% 0.22/0.43  tff(22,plain,
% 0.22/0.43      (((~((~surjective(F!41, A!40, B!39)) | ![Y: $i] : ((~member(Y, B!39)) | (~((~member(tptp_fun_E_19(Y, A!40, F!41), A!40)) | (~apply(F!41, tptp_fun_E_19(Y, A!40, F!41), Y))))))) | (~(surjective(F!41, A!40, B!39) | (~((~member(tptp_fun_Y_20(B!39, A!40, F!41), B!39)) | (~![E: $i] : ((~member(E, A!40)) | (~apply(F!41, E, tptp_fun_Y_20(B!39, A!40, F!41)))))))))) | ((~surjective(F!41, A!40, B!39)) | ![Y: $i] : ((~member(Y, B!39)) | (~((~member(tptp_fun_E_19(Y, A!40, F!41), A!40)) | (~apply(F!41, tptp_fun_E_19(Y, A!40, F!41), Y))))))),
% 0.22/0.43      inference(tautology,[status(thm)],[])).
% 0.22/0.43  tff(23,plain,
% 0.22/0.43      ((~surjective(F!41, A!40, B!39)) | ![Y: $i] : ((~member(Y, B!39)) | (~((~member(tptp_fun_E_19(Y, A!40, F!41), A!40)) | (~apply(F!41, tptp_fun_E_19(Y, A!40, F!41), Y)))))),
% 0.22/0.43      inference(unit_resolution,[status(thm)],[22, 21])).
% 0.22/0.43  tff(24,plain,
% 0.22/0.43      (^[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))))))),
% 0.22/0.43      inference(bind,[status(th)],[])).
% 0.22/0.43  tff(25,plain,
% 0.22/0.43      (![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)))))),
% 0.22/0.43      inference(quant_intro,[status(thm)],[24])).
% 0.22/0.43  tff(26,plain,
% 0.22/0.43      (^[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))))))),
% 0.22/0.43      inference(bind,[status(th)],[])).
% 0.22/0.43  tff(27,plain,
% 0.22/0.43      (![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)))))),
% 0.22/0.43      inference(quant_intro,[status(thm)],[26])).
% 0.22/0.43  tff(28,plain,
% 0.22/0.43      (![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)))),
% 0.22/0.43      inference(rewrite,[status(thm)],[])).
% 0.22/0.43  tff(29,axiom,(![F: $i, A: $i, B: $i] : (one_to_one(F, A, B) <=> (injective(F, A, B) & surjective(F, A, B)))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+1.ax','one_to_one')).
% 0.22/0.43  tff(30,plain,
% 0.22/0.43      (![F: $i, A: $i, B: $i] : (one_to_one(F, A, B) <=> (injective(F, A, B) & surjective(F, A, B)))),
% 0.22/0.43      inference(modus_ponens,[status(thm)],[29, 28])).
% 0.22/0.43  tff(31,plain,(
% 0.22/0.43      ![F: $i, A: $i, B: $i] : (one_to_one(F, A, B) <=> (injective(F, A, B) & surjective(F, A, B)))),
% 0.22/0.43      inference(skolemize,[status(sab)],[30])).
% 0.22/0.43  tff(32,plain,
% 0.22/0.43      (![F: $i, A: $i, B: $i] : (one_to_one(F, A, B) <=> (~((~injective(F, A, B)) | (~surjective(F, A, B)))))),
% 0.22/0.43      inference(modus_ponens,[status(thm)],[31, 27])).
% 0.22/0.43  tff(33,plain,
% 0.22/0.43      (![F: $i, A: $i, B: $i] : (one_to_one(F, A, B) <=> (~((~injective(F, A, B)) | (~surjective(F, A, B)))))),
% 0.22/0.43      inference(modus_ponens,[status(thm)],[32, 25])).
% 0.22/0.43  tff(34,plain,
% 0.22/0.43      ((~![F: $i, A: $i, B: $i] : (one_to_one(F, A, B) <=> (~((~injective(F, A, B)) | (~surjective(F, A, B)))))) | (one_to_one(F!41, A!40, B!39) <=> (~((~injective(F!41, A!40, B!39)) | (~surjective(F!41, A!40, B!39)))))),
% 0.22/0.43      inference(quant_inst,[status(thm)],[])).
% 0.22/0.43  tff(35,plain,
% 0.22/0.43      (one_to_one(F!41, A!40, B!39) <=> (~((~injective(F!41, A!40, B!39)) | (~surjective(F!41, A!40, B!39))))),
% 0.22/0.43      inference(unit_resolution,[status(thm)],[34, 33])).
% 0.22/0.43  tff(36,plain,
% 0.22/0.43      ((~![F: $i, A: $i, B: $i] : ((~(maps(F, A, B) & one_to_one(F, A, B))) | identity(compose_function(F, inverse_function(F, A, B), B, A, B), B))) <=> (~![F: $i, A: $i, B: $i] : ((~(maps(F, A, B) & one_to_one(F, A, B))) | identity(compose_function(F, inverse_function(F, A, B), B, A, B), B)))),
% 0.22/0.43      inference(rewrite,[status(thm)],[])).
% 0.22/0.43  tff(37,plain,
% 0.22/0.43      ((~![F: $i, A: $i, B: $i] : ((maps(F, A, B) & one_to_one(F, A, B)) => identity(compose_function(F, inverse_function(F, A, B), B, A, B), B))) <=> (~![F: $i, A: $i, B: $i] : ((~(maps(F, A, B) & one_to_one(F, A, B))) | identity(compose_function(F, inverse_function(F, A, B), B, A, B), B)))),
% 0.22/0.43      inference(rewrite,[status(thm)],[])).
% 0.22/0.43  tff(38,axiom,(~![F: $i, A: $i, B: $i] : ((maps(F, A, B) & one_to_one(F, A, B)) => identity(compose_function(F, inverse_function(F, A, B), B, A, B), B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','thII06')).
% 0.22/0.43  tff(39,plain,
% 0.22/0.43      (~![F: $i, A: $i, B: $i] : ((~(maps(F, A, B) & one_to_one(F, A, B))) | identity(compose_function(F, inverse_function(F, A, B), B, A, B), B))),
% 0.22/0.43      inference(modus_ponens,[status(thm)],[38, 37])).
% 0.22/0.43  tff(40,plain,
% 0.22/0.43      (~![F: $i, A: $i, B: $i] : ((~(maps(F, A, B) & one_to_one(F, A, B))) | identity(compose_function(F, inverse_function(F, A, B), B, A, B), B))),
% 0.22/0.43      inference(modus_ponens,[status(thm)],[39, 36])).
% 0.22/0.43  tff(41,plain,
% 0.22/0.43      (~![F: $i, A: $i, B: $i] : ((~(maps(F, A, B) & one_to_one(F, A, B))) | identity(compose_function(F, inverse_function(F, A, B), B, A, B), B))),
% 0.22/0.43      inference(modus_ponens,[status(thm)],[40, 36])).
% 0.22/0.43  tff(42,plain,
% 0.22/0.43      (~![F: $i, A: $i, B: $i] : ((~(maps(F, A, B) & one_to_one(F, A, B))) | identity(compose_function(F, inverse_function(F, A, B), B, A, B), B))),
% 0.22/0.43      inference(modus_ponens,[status(thm)],[41, 36])).
% 0.22/0.43  tff(43,plain,
% 0.22/0.43      (~![F: $i, A: $i, B: $i] : ((~(maps(F, A, B) & one_to_one(F, A, B))) | identity(compose_function(F, inverse_function(F, A, B), B, A, B), B))),
% 0.22/0.43      inference(modus_ponens,[status(thm)],[42, 36])).
% 0.22/0.43  tff(44,plain,
% 0.22/0.43      (~![F: $i, A: $i, B: $i] : ((~(maps(F, A, B) & one_to_one(F, A, B))) | identity(compose_function(F, inverse_function(F, A, B), B, A, B), B))),
% 0.22/0.43      inference(modus_ponens,[status(thm)],[43, 36])).
% 0.22/0.43  tff(45,plain,
% 0.22/0.43      (~![F: $i, A: $i, B: $i] : ((~(maps(F, A, B) & one_to_one(F, A, B))) | identity(compose_function(F, inverse_function(F, A, B), B, A, B), B))),
% 0.22/0.43      inference(modus_ponens,[status(thm)],[44, 36])).
% 0.22/0.43  tff(46,plain,(
% 0.22/0.43      ~((~(maps(F!41, A!40, B!39) & one_to_one(F!41, A!40, B!39))) | identity(compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39), B!39))),
% 0.22/0.43      inference(skolemize,[status(sab)],[45])).
% 0.22/0.43  tff(47,plain,
% 0.22/0.43      (maps(F!41, A!40, B!39) & one_to_one(F!41, A!40, B!39)),
% 0.22/0.43      inference(or_elim,[status(thm)],[46])).
% 0.22/0.43  tff(48,plain,
% 0.22/0.43      (one_to_one(F!41, A!40, B!39)),
% 0.22/0.43      inference(and_elim,[status(thm)],[47])).
% 0.22/0.43  tff(49,plain,
% 0.22/0.43      ((~(one_to_one(F!41, A!40, B!39) <=> (~((~injective(F!41, A!40, B!39)) | (~surjective(F!41, A!40, B!39)))))) | (~one_to_one(F!41, A!40, B!39)) | (~((~injective(F!41, A!40, B!39)) | (~surjective(F!41, A!40, B!39))))),
% 0.22/0.43      inference(tautology,[status(thm)],[])).
% 0.22/0.43  tff(50,plain,
% 0.22/0.43      ((~(one_to_one(F!41, A!40, B!39) <=> (~((~injective(F!41, A!40, B!39)) | (~surjective(F!41, A!40, B!39)))))) | (~((~injective(F!41, A!40, B!39)) | (~surjective(F!41, A!40, B!39))))),
% 0.22/0.43      inference(unit_resolution,[status(thm)],[49, 48])).
% 0.22/0.43  tff(51,plain,
% 0.22/0.43      (~((~injective(F!41, A!40, B!39)) | (~surjective(F!41, A!40, B!39)))),
% 0.22/0.43      inference(unit_resolution,[status(thm)],[50, 35])).
% 0.22/0.43  tff(52,plain,
% 0.22/0.43      (((~injective(F!41, A!40, B!39)) | (~surjective(F!41, A!40, B!39))) | surjective(F!41, A!40, B!39)),
% 0.22/0.43      inference(tautology,[status(thm)],[])).
% 0.22/0.43  tff(53,plain,
% 0.22/0.43      (surjective(F!41, A!40, B!39)),
% 0.22/0.43      inference(unit_resolution,[status(thm)],[52, 51])).
% 0.22/0.43  tff(54,plain,
% 0.22/0.43      ((~((~surjective(F!41, A!40, B!39)) | ![Y: $i] : ((~member(Y, B!39)) | (~((~member(tptp_fun_E_19(Y, A!40, F!41), A!40)) | (~apply(F!41, tptp_fun_E_19(Y, A!40, F!41), Y))))))) | (~surjective(F!41, A!40, B!39)) | ![Y: $i] : ((~member(Y, B!39)) | (~((~member(tptp_fun_E_19(Y, A!40, F!41), A!40)) | (~apply(F!41, tptp_fun_E_19(Y, A!40, F!41), Y)))))),
% 0.22/0.43      inference(tautology,[status(thm)],[])).
% 0.22/0.43  tff(55,plain,
% 0.22/0.43      ((~((~surjective(F!41, A!40, B!39)) | ![Y: $i] : ((~member(Y, B!39)) | (~((~member(tptp_fun_E_19(Y, A!40, F!41), A!40)) | (~apply(F!41, tptp_fun_E_19(Y, A!40, F!41), Y))))))) | ![Y: $i] : ((~member(Y, B!39)) | (~((~member(tptp_fun_E_19(Y, A!40, F!41), A!40)) | (~apply(F!41, tptp_fun_E_19(Y, A!40, F!41), Y)))))),
% 0.22/0.43      inference(unit_resolution,[status(thm)],[54, 53])).
% 0.22/0.43  tff(56,plain,
% 0.22/0.43      (![Y: $i] : ((~member(Y, B!39)) | (~((~member(tptp_fun_E_19(Y, A!40, F!41), A!40)) | (~apply(F!41, tptp_fun_E_19(Y, A!40, F!41), Y)))))),
% 0.22/0.43      inference(unit_resolution,[status(thm)],[55, 23])).
% 0.22/0.43  tff(57,plain,
% 0.22/0.43      (^[F: $i, A: $i] : refl((~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F)))))))) <=> (~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F)))))))))),
% 0.22/0.43      inference(bind,[status(th)],[])).
% 0.22/0.43  tff(58,plain,
% 0.22/0.43      (![F: $i, A: $i] : (~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F)))))))) <=> ![F: $i, A: $i] : (~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F))))))))),
% 0.22/0.43      inference(quant_intro,[status(thm)],[57])).
% 0.22/0.43  tff(59,plain,
% 0.22/0.43      (^[F: $i, A: $i] : rewrite((~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F)))))))) <=> (~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F)))))))))),
% 0.22/0.43      inference(bind,[status(th)],[])).
% 0.22/0.43  tff(60,plain,
% 0.22/0.43      (![F: $i, A: $i] : (~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F)))))))) <=> ![F: $i, A: $i] : (~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F))))))))),
% 0.22/0.43      inference(quant_intro,[status(thm)],[59])).
% 0.22/0.43  tff(61,plain,
% 0.22/0.43      (![F: $i, A: $i] : (~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F)))))))) <=> ![F: $i, A: $i] : (~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F))))))))),
% 0.22/0.43      inference(transitivity,[status(thm)],[60, 58])).
% 0.22/0.43  tff(62,plain,
% 0.22/0.43      (^[F: $i, A: $i] : trans(monotonicity(rewrite(((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X))) <=> ((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))), rewrite((identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F))))) <=> (identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F)))))), ((((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X))) & (identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F)))))) <=> (((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X))) & (identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F)))))))), rewrite((((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X))) & (identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F)))))) <=> (~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F))))))))), ((((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X))) & (identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F)))))) <=> (~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F))))))))))),
% 0.22/0.43      inference(bind,[status(th)],[])).
% 0.22/0.43  tff(63,plain,
% 0.22/0.43      (![F: $i, A: $i] : (((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X))) & (identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F)))))) <=> ![F: $i, A: $i] : (~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F))))))))),
% 0.22/0.43      inference(quant_intro,[status(thm)],[62])).
% 0.22/0.43  tff(64,plain,
% 0.22/0.43      (![F: $i, A: $i] : (identity(F, A) <=> ![X: $i] : ((~member(X, A)) | apply(F, X, X))) <=> ![F: $i, A: $i] : (identity(F, A) <=> ![X: $i] : ((~member(X, A)) | apply(F, X, X)))),
% 0.22/0.43      inference(rewrite,[status(thm)],[])).
% 0.22/0.43  tff(65,plain,
% 0.22/0.43      (^[F: $i, A: $i] : rewrite((identity(F, A) <=> ![X: $i] : (member(X, A) => apply(F, X, X))) <=> (identity(F, A) <=> ![X: $i] : ((~member(X, A)) | apply(F, X, X))))),
% 0.22/0.43      inference(bind,[status(th)],[])).
% 0.22/0.43  tff(66,plain,
% 0.22/0.43      (![F: $i, A: $i] : (identity(F, A) <=> ![X: $i] : (member(X, A) => apply(F, X, X))) <=> ![F: $i, A: $i] : (identity(F, A) <=> ![X: $i] : ((~member(X, A)) | apply(F, X, X)))),
% 0.22/0.44      inference(quant_intro,[status(thm)],[65])).
% 0.22/0.44  tff(67,axiom,(![F: $i, A: $i] : (identity(F, A) <=> ![X: $i] : (member(X, A) => apply(F, X, X)))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+1.ax','identity')).
% 0.22/0.44  tff(68,plain,
% 0.22/0.44      (![F: $i, A: $i] : (identity(F, A) <=> ![X: $i] : ((~member(X, A)) | apply(F, X, X)))),
% 0.22/0.44      inference(modus_ponens,[status(thm)],[67, 66])).
% 0.22/0.44  tff(69,plain,
% 0.22/0.44      (![F: $i, A: $i] : (identity(F, A) <=> ![X: $i] : ((~member(X, A)) | apply(F, X, X)))),
% 0.22/0.44      inference(modus_ponens,[status(thm)],[68, 64])).
% 0.22/0.44  tff(70,plain,(
% 0.22/0.44      ![F: $i, A: $i] : (((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X))) & (identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F))))))),
% 0.22/0.44      inference(skolemize,[status(sab)],[69])).
% 0.22/0.44  tff(71,plain,
% 0.22/0.44      (![F: $i, A: $i] : (~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F))))))))),
% 0.22/0.44      inference(modus_ponens,[status(thm)],[70, 63])).
% 0.22/0.44  tff(72,plain,
% 0.22/0.44      (![F: $i, A: $i] : (~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F))))))))),
% 0.22/0.44      inference(modus_ponens,[status(thm)],[71, 61])).
% 0.22/0.44  tff(73,plain,
% 0.22/0.44      ((~![F: $i, A: $i] : (~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F))))))))) | (~((~((~identity(compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39), B!39)) | ![X: $i] : ((~member(X, B!39)) | apply(compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39), X, X)))) | (~(identity(compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39), B!39) | (~((~member(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), B!39)) | apply(compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)))))))))),
% 0.22/0.44      inference(quant_inst,[status(thm)],[])).
% 0.22/0.44  tff(74,plain,
% 0.22/0.44      (~((~((~identity(compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39), B!39)) | ![X: $i] : ((~member(X, B!39)) | apply(compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39), X, X)))) | (~(identity(compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39), B!39) | (~((~member(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), B!39)) | apply(compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39))))))))),
% 0.22/0.44      inference(unit_resolution,[status(thm)],[73, 72])).
% 0.22/0.44  tff(75,plain,
% 0.22/0.44      (((~((~identity(compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39), B!39)) | ![X: $i] : ((~member(X, B!39)) | apply(compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39), X, X)))) | (~(identity(compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39), B!39) | (~((~member(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), B!39)) | apply(compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)))))))) | (identity(compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39), B!39) | (~((~member(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), B!39)) | apply(compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39))))))),
% 0.22/0.44      inference(tautology,[status(thm)],[])).
% 0.22/0.44  tff(76,plain,
% 0.22/0.44      (identity(compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39), B!39) | (~((~member(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), B!39)) | apply(compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)))))),
% 0.22/0.44      inference(unit_resolution,[status(thm)],[75, 74])).
% 0.22/0.44  tff(77,plain,
% 0.22/0.44      (~identity(compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39), B!39)),
% 0.22/0.44      inference(or_elim,[status(thm)],[46])).
% 0.22/0.44  tff(78,plain,
% 0.22/0.44      ((~(identity(compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39), B!39) | (~((~member(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), B!39)) | apply(compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39))))))) | identity(compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39), B!39) | (~((~member(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), B!39)) | apply(compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)))))),
% 0.22/0.44      inference(tautology,[status(thm)],[])).
% 0.22/0.44  tff(79,plain,
% 0.22/0.44      ((~(identity(compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39), B!39) | (~((~member(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), B!39)) | apply(compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39))))))) | (~((~member(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), B!39)) | apply(compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)))))),
% 0.22/0.44      inference(unit_resolution,[status(thm)],[78, 77])).
% 0.22/0.44  tff(80,plain,
% 0.22/0.44      (~((~member(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), B!39)) | apply(compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39))))),
% 0.22/0.44      inference(unit_resolution,[status(thm)],[79, 76])).
% 0.22/0.44  tff(81,plain,
% 0.22/0.44      (((~member(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), B!39)) | apply(compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)))) | member(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), B!39)),
% 0.22/0.45      inference(tautology,[status(thm)],[])).
% 0.22/0.45  tff(82,plain,
% 0.22/0.45      (member(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), B!39)),
% 0.22/0.45      inference(unit_resolution,[status(thm)],[81, 80])).
% 0.22/0.45  tff(83,plain,
% 0.22/0.45      (((~![Y: $i] : ((~member(Y, B!39)) | (~((~member(tptp_fun_E_19(Y, A!40, F!41), A!40)) | (~apply(F!41, tptp_fun_E_19(Y, A!40, F!41), Y)))))) | ((~member(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), B!39)) | (~((~member(tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41), A!40)) | (~apply(F!41, tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)))))))) <=> ((~![Y: $i] : ((~member(Y, B!39)) | (~((~member(tptp_fun_E_19(Y, A!40, F!41), A!40)) | (~apply(F!41, tptp_fun_E_19(Y, A!40, F!41), Y)))))) | (~member(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), B!39)) | (~((~member(tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41), A!40)) | (~apply(F!41, tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)))))))),
% 0.22/0.45      inference(rewrite,[status(thm)],[])).
% 0.22/0.45  tff(84,plain,
% 0.22/0.45      ((~![Y: $i] : ((~member(Y, B!39)) | (~((~member(tptp_fun_E_19(Y, A!40, F!41), A!40)) | (~apply(F!41, tptp_fun_E_19(Y, A!40, F!41), Y)))))) | ((~member(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), B!39)) | (~((~member(tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41), A!40)) | (~apply(F!41, tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)))))))),
% 0.22/0.45      inference(quant_inst,[status(thm)],[])).
% 0.22/0.45  tff(85,plain,
% 0.22/0.45      ((~![Y: $i] : ((~member(Y, B!39)) | (~((~member(tptp_fun_E_19(Y, A!40, F!41), A!40)) | (~apply(F!41, tptp_fun_E_19(Y, A!40, F!41), Y)))))) | (~member(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), B!39)) | (~((~member(tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41), A!40)) | (~apply(F!41, tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39))))))),
% 0.22/0.45      inference(modus_ponens,[status(thm)],[84, 83])).
% 0.22/0.45  tff(86,plain,
% 0.22/0.45      (~((~member(tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41), A!40)) | (~apply(F!41, tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)))))),
% 0.22/0.45      inference(unit_resolution,[status(thm)],[85, 82, 56])).
% 0.22/0.45  tff(87,plain,
% 0.22/0.45      (((~member(tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41), A!40)) | (~apply(F!41, tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39))))) | apply(F!41, tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)))),
% 0.22/0.45      inference(tautology,[status(thm)],[])).
% 0.22/0.45  tff(88,plain,
% 0.22/0.45      (apply(F!41, tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)))),
% 0.22/0.45      inference(unit_resolution,[status(thm)],[87, 86])).
% 0.22/0.45  tff(89,plain,
% 0.22/0.45      (((~member(tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41), A!40)) | (~apply(F!41, tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39))))) | member(tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41), A!40)),
% 0.22/0.45      inference(tautology,[status(thm)],[])).
% 0.22/0.45  tff(90,plain,
% 0.22/0.45      (member(tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41), A!40)),
% 0.22/0.45      inference(unit_resolution,[status(thm)],[89, 86])).
% 0.22/0.45  tff(91,plain,
% 0.22/0.45      (^[G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : refl(((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z)))))))) <=> ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z)))))))))),
% 0.22/0.45      inference(bind,[status(th)],[])).
% 0.22/0.45  tff(92,plain,
% 0.22/0.45      (![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z)))))))) <=> ![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))),
% 0.22/0.45      inference(quant_intro,[status(thm)],[91])).
% 0.22/0.45  tff(93,plain,
% 0.22/0.45      (^[G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : rewrite(((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z)))))))) <=> ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z)))))))))),
% 0.22/0.45      inference(bind,[status(th)],[])).
% 0.22/0.45  tff(94,plain,
% 0.22/0.45      (![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z)))))))) <=> ![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))),
% 0.22/0.45      inference(quant_intro,[status(thm)],[93])).
% 0.22/0.45  tff(95,plain,
% 0.22/0.45      (![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z)))))))) <=> ![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))),
% 0.22/0.45      inference(transitivity,[status(thm)],[94, 92])).
% 0.22/0.45  tff(96,plain,
% 0.22/0.45      (^[G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : trans(monotonicity(trans(monotonicity(rewrite((member(X, A) & member(Z, C)) <=> (~((~member(Z, C)) | (~member(X, A))))), ((~(member(X, A) & member(Z, C))) <=> (~(~((~member(Z, C)) | (~member(X, A))))))), rewrite((~(~((~member(Z, C)) | (~member(X, A))))) <=> ((~member(Z, C)) | (~member(X, A)))), ((~(member(X, A) & member(Z, C))) <=> ((~member(Z, C)) | (~member(X, A))))), trans(monotonicity(rewrite(((~apply(compose_function(G, F, A, B, C), X, Z)) | (member(tptp_fun_Y_8(Z, X, B, F, G), B) & apply(F, X, tptp_fun_Y_8(Z, X, B, F, G)) & apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z))) <=> ((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))), rewrite((apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y) & apply(G, Y, Z)))) <=> (apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))), ((((~apply(compose_function(G, F, A, B, C), X, Z)) | (member(tptp_fun_Y_8(Z, X, B, F, G), B) & apply(F, X, tptp_fun_Y_8(Z, X, B, F, G)) & apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z))) & (apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y) & apply(G, Y, Z))))) <=> (((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z))))) & (apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))), rewrite((((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z))))) & (apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))) <=> (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z)))))))), ((((~apply(compose_function(G, F, A, B, C), X, Z)) | (member(tptp_fun_Y_8(Z, X, B, F, G), B) & apply(F, X, tptp_fun_Y_8(Z, X, B, F, G)) & apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z))) & (apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y) & apply(G, Y, Z))))) <=> (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))), (((~(member(X, A) & member(Z, C))) | (((~apply(compose_function(G, F, A, B, C), X, Z)) | (member(tptp_fun_Y_8(Z, X, B, F, G), B) & apply(F, X, tptp_fun_Y_8(Z, X, B, F, G)) & apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z))) & (apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y) & apply(G, Y, Z)))))) <=> (((~member(Z, C)) | (~member(X, A))) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z)))))))))), rewrite((((~member(Z, C)) | (~member(X, A))) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z)))))))) <=> ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))), (((~(member(X, A) & member(Z, C))) | (((~apply(compose_function(G, F, A, B, C), X, Z)) | (member(tptp_fun_Y_8(Z, X, B, F, G), B) & apply(F, X, tptp_fun_Y_8(Z, X, B, F, G)) & apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z))) & (apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y) & apply(G, Y, Z)))))) <=> ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))))),
% 0.22/0.45      inference(bind,[status(th)],[])).
% 0.22/0.45  tff(97,plain,
% 0.22/0.45      (![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~(member(X, A) & member(Z, C))) | (((~apply(compose_function(G, F, A, B, C), X, Z)) | (member(tptp_fun_Y_8(Z, X, B, F, G), B) & apply(F, X, tptp_fun_Y_8(Z, X, B, F, G)) & apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z))) & (apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y) & apply(G, Y, Z)))))) <=> ![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))),
% 0.22/0.45      inference(quant_intro,[status(thm)],[96])).
% 0.22/0.45  tff(98,plain,
% 0.22/0.45      (![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~(member(X, A) & member(Z, C))) | (apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : (member(Y, B) & apply(F, X, Y) & apply(G, Y, Z)))) <=> ![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~(member(X, A) & member(Z, C))) | (apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : (member(Y, B) & apply(F, X, Y) & apply(G, Y, Z))))),
% 0.22/0.45      inference(rewrite,[status(thm)],[])).
% 0.22/0.46  tff(99,plain,
% 0.22/0.46      (^[G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : trans(monotonicity(rewrite((apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : ((member(Y, B) & apply(F, X, Y)) & apply(G, Y, Z))) <=> (apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : (member(Y, B) & apply(F, X, Y) & apply(G, Y, Z)))), (((member(X, A) & member(Z, C)) => (apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : ((member(Y, B) & apply(F, X, Y)) & apply(G, Y, Z)))) <=> ((member(X, A) & member(Z, C)) => (apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : (member(Y, B) & apply(F, X, Y) & apply(G, Y, Z)))))), rewrite(((member(X, A) & member(Z, C)) => (apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : (member(Y, B) & apply(F, X, Y) & apply(G, Y, Z)))) <=> ((~(member(X, A) & member(Z, C))) | (apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : (member(Y, B) & apply(F, X, Y) & apply(G, Y, Z))))), (((member(X, A) & member(Z, C)) => (apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : ((member(Y, B) & apply(F, X, Y)) & apply(G, Y, Z)))) <=> ((~(member(X, A) & member(Z, C))) | (apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : (member(Y, B) & apply(F, X, Y) & apply(G, Y, Z))))))),
% 0.22/0.46      inference(bind,[status(th)],[])).
% 0.22/0.46  tff(100,plain,
% 0.22/0.46      (![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((member(X, A) & member(Z, C)) => (apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : ((member(Y, B) & apply(F, X, Y)) & apply(G, Y, Z)))) <=> ![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~(member(X, A) & member(Z, C))) | (apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : (member(Y, B) & apply(F, X, Y) & apply(G, Y, Z))))),
% 0.22/0.46      inference(quant_intro,[status(thm)],[99])).
% 0.22/0.46  tff(101,axiom,(![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((member(X, A) & member(Z, C)) => (apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : ((member(Y, B) & apply(F, X, Y)) & apply(G, Y, Z))))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+1.ax','compose_function')).
% 0.22/0.46  tff(102,plain,
% 0.22/0.46      (![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~(member(X, A) & member(Z, C))) | (apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : (member(Y, B) & apply(F, X, Y) & apply(G, Y, Z))))),
% 0.22/0.46      inference(modus_ponens,[status(thm)],[101, 100])).
% 0.22/0.46  tff(103,plain,
% 0.22/0.46      (![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~(member(X, A) & member(Z, C))) | (apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : (member(Y, B) & apply(F, X, Y) & apply(G, Y, Z))))),
% 0.22/0.46      inference(modus_ponens,[status(thm)],[102, 98])).
% 0.22/0.46  tff(104,plain,(
% 0.22/0.46      ![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~(member(X, A) & member(Z, C))) | (((~apply(compose_function(G, F, A, B, C), X, Z)) | (member(tptp_fun_Y_8(Z, X, B, F, G), B) & apply(F, X, tptp_fun_Y_8(Z, X, B, F, G)) & apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z))) & (apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y) & apply(G, Y, Z))))))),
% 0.22/0.46      inference(skolemize,[status(sab)],[103])).
% 0.22/0.46  tff(105,plain,
% 0.22/0.46      (![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))),
% 0.22/0.46      inference(modus_ponens,[status(thm)],[104, 97])).
% 0.22/0.46  tff(106,plain,
% 0.22/0.46      (![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))),
% 0.22/0.46      inference(modus_ponens,[status(thm)],[105, 95])).
% 0.22/0.46  tff(107,plain,
% 0.22/0.46      (((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), B!39)) | (~((~((~apply(compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, inverse_function(F!41, A!40, B!39), F!41), A!40)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_Y_8(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, inverse_function(F!41, A!40, B!39), F!41))) | (~apply(F!41, tptp_fun_Y_8(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, inverse_function(F!41, A!40, B!39), F!41), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)))))))) | (~(apply(compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39))) | ![Y: $i] : ((~member(Y, A!40)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), Y)) | (~apply(F!41, Y, tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39))))))))))) <=> ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | (~member(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), B!39)) | (~((~((~apply(compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, inverse_function(F!41, A!40, B!39), F!41), A!40)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_Y_8(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, inverse_function(F!41, A!40, B!39), F!41))) | (~apply(F!41, tptp_fun_Y_8(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, inverse_function(F!41, A!40, B!39), F!41), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)))))))) | (~(apply(compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39))) | ![Y: $i] : ((~member(Y, A!40)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), Y)) | (~apply(F!41, Y, tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39))))))))))),
% 0.22/0.46      inference(rewrite,[status(thm)],[])).
% 0.22/0.46  tff(108,plain,
% 0.22/0.46      (((~member(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), B!39)) | (~member(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), B!39)) | (~((~((~apply(compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, inverse_function(F!41, A!40, B!39), F!41), A!40)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_Y_8(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, inverse_function(F!41, A!40, B!39), F!41))) | (~apply(F!41, tptp_fun_Y_8(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, inverse_function(F!41, A!40, B!39), F!41), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)))))))) | (~(apply(compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39))) | ![Y: $i] : ((~member(Y, A!40)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), Y)) | (~apply(F!41, Y, tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)))))))))) <=> ((~member(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), B!39)) | (~((~((~apply(compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, inverse_function(F!41, A!40, B!39), F!41), A!40)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_Y_8(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, inverse_function(F!41, A!40, B!39), F!41))) | (~apply(F!41, tptp_fun_Y_8(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, inverse_function(F!41, A!40, B!39), F!41), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)))))))) | (~(apply(compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39))) | ![Y: $i] : ((~member(Y, A!40)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), Y)) | (~apply(F!41, Y, tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39))))))))))),
% 0.22/0.47      inference(rewrite,[status(thm)],[])).
% 0.22/0.47  tff(109,plain,
% 0.22/0.47      ((~((~((~apply(compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, inverse_function(F!41, A!40, B!39), F!41), A!40)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_Y_8(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, inverse_function(F!41, A!40, B!39), F!41))) | (~apply(F!41, tptp_fun_Y_8(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, inverse_function(F!41, A!40, B!39), F!41), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)))))))) | (~(apply(compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39))) | ![Y: $i] : ((~member(Y, A!40)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), Y)) | (~apply(F!41, Y, tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39))))))))) <=> (~((~((~apply(compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, inverse_function(F!41, A!40, B!39), F!41), A!40)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_Y_8(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, inverse_function(F!41, A!40, B!39), F!41))) | (~apply(F!41, tptp_fun_Y_8(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, inverse_function(F!41, A!40, B!39), F!41), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)))))))) | (~(apply(compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39))) | ![Y: $i] : ((~member(Y, A!40)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), Y)) | (~apply(F!41, Y, tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)))))))))),
% 0.22/0.47      inference(rewrite,[status(thm)],[])).
% 0.22/0.47  tff(110,plain,
% 0.22/0.47      (((~member(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), B!39)) | (~member(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), B!39)) | (~((~((~apply(compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, inverse_function(F!41, A!40, B!39), F!41), A!40)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_Y_8(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, inverse_function(F!41, A!40, B!39), F!41))) | (~apply(F!41, tptp_fun_Y_8(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, inverse_function(F!41, A!40, B!39), F!41), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)))))))) | (~(apply(compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39))) | ![Y: $i] : ((~member(Y, A!40)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), Y)) | (~apply(F!41, Y, tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)))))))))) <=> ((~member(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), B!39)) | (~member(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), B!39)) | (~((~((~apply(compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, inverse_function(F!41, A!40, B!39), F!41), A!40)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_Y_8(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, inverse_function(F!41, A!40, B!39), F!41))) | (~apply(F!41, tptp_fun_Y_8(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, inverse_function(F!41, A!40, B!39), F!41), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)))))))) | (~(apply(compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39))) | ![Y: $i] : ((~member(Y, A!40)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), Y)) | (~apply(F!41, Y, tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39))))))))))),
% 0.22/0.47      inference(monotonicity,[status(thm)],[109])).
% 0.22/0.47  tff(111,plain,
% 0.22/0.47      (((~member(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), B!39)) | (~member(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), B!39)) | (~((~((~apply(compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, inverse_function(F!41, A!40, B!39), F!41), A!40)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_Y_8(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, inverse_function(F!41, A!40, B!39), F!41))) | (~apply(F!41, tptp_fun_Y_8(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, inverse_function(F!41, A!40, B!39), F!41), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)))))))) | (~(apply(compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39))) | ![Y: $i] : ((~member(Y, A!40)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), Y)) | (~apply(F!41, Y, tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)))))))))) <=> ((~member(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), B!39)) | (~((~((~apply(compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, inverse_function(F!41, A!40, B!39), F!41), A!40)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_Y_8(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, inverse_function(F!41, A!40, B!39), F!41))) | (~apply(F!41, tptp_fun_Y_8(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, inverse_function(F!41, A!40, B!39), F!41), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)))))))) | (~(apply(compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39))) | ![Y: $i] : ((~member(Y, A!40)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), Y)) | (~apply(F!41, Y, tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39))))))))))),
% 0.22/0.47      inference(transitivity,[status(thm)],[110, 108])).
% 0.22/0.47  tff(112,plain,
% 0.22/0.47      (((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), B!39)) | (~member(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), B!39)) | (~((~((~apply(compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, inverse_function(F!41, A!40, B!39), F!41), A!40)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_Y_8(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, inverse_function(F!41, A!40, B!39), F!41))) | (~apply(F!41, tptp_fun_Y_8(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, inverse_function(F!41, A!40, B!39), F!41), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)))))))) | (~(apply(compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39))) | ![Y: $i] : ((~member(Y, A!40)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), Y)) | (~apply(F!41, Y, tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39))))))))))) <=> ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), B!39)) | (~((~((~apply(compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, inverse_function(F!41, A!40, B!39), F!41), A!40)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_Y_8(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, inverse_function(F!41, A!40, B!39), F!41))) | (~apply(F!41, tptp_fun_Y_8(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, inverse_function(F!41, A!40, B!39), F!41), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)))))))) | (~(apply(compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39))) | ![Y: $i] : ((~member(Y, A!40)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), Y)) | (~apply(F!41, Y, tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)))))))))))),
% 0.22/0.48      inference(monotonicity,[status(thm)],[111])).
% 0.22/0.48  tff(113,plain,
% 0.22/0.48      (((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), B!39)) | (~member(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), B!39)) | (~((~((~apply(compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, inverse_function(F!41, A!40, B!39), F!41), A!40)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_Y_8(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, inverse_function(F!41, A!40, B!39), F!41))) | (~apply(F!41, tptp_fun_Y_8(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, inverse_function(F!41, A!40, B!39), F!41), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)))))))) | (~(apply(compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39))) | ![Y: $i] : ((~member(Y, A!40)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), Y)) | (~apply(F!41, Y, tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39))))))))))) <=> ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | (~member(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), B!39)) | (~((~((~apply(compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, inverse_function(F!41, A!40, B!39), F!41), A!40)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_Y_8(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, inverse_function(F!41, A!40, B!39), F!41))) | (~apply(F!41, tptp_fun_Y_8(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, inverse_function(F!41, A!40, B!39), F!41), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)))))))) | (~(apply(compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39))) | ![Y: $i] : ((~member(Y, A!40)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), Y)) | (~apply(F!41, Y, tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39))))))))))),
% 0.22/0.48      inference(transitivity,[status(thm)],[112, 107])).
% 0.22/0.48  tff(114,plain,
% 0.22/0.48      ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), B!39)) | (~member(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), B!39)) | (~((~((~apply(compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, inverse_function(F!41, A!40, B!39), F!41), A!40)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_Y_8(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, inverse_function(F!41, A!40, B!39), F!41))) | (~apply(F!41, tptp_fun_Y_8(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, inverse_function(F!41, A!40, B!39), F!41), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)))))))) | (~(apply(compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39))) | ![Y: $i] : ((~member(Y, A!40)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), Y)) | (~apply(F!41, Y, tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39))))))))))),
% 0.22/0.48      inference(quant_inst,[status(thm)],[])).
% 0.22/0.48  tff(115,plain,
% 0.22/0.48      ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | (~member(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), B!39)) | (~((~((~apply(compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, inverse_function(F!41, A!40, B!39), F!41), A!40)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_Y_8(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, inverse_function(F!41, A!40, B!39), F!41))) | (~apply(F!41, tptp_fun_Y_8(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, inverse_function(F!41, A!40, B!39), F!41), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)))))))) | (~(apply(compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39))) | ![Y: $i] : ((~member(Y, A!40)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), Y)) | (~apply(F!41, Y, tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)))))))))),
% 0.22/0.49      inference(modus_ponens,[status(thm)],[114, 113])).
% 0.22/0.49  tff(116,plain,
% 0.22/0.49      (~((~((~apply(compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, inverse_function(F!41, A!40, B!39), F!41), A!40)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_Y_8(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, inverse_function(F!41, A!40, B!39), F!41))) | (~apply(F!41, tptp_fun_Y_8(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, inverse_function(F!41, A!40, B!39), F!41), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)))))))) | (~(apply(compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39))) | ![Y: $i] : ((~member(Y, A!40)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), Y)) | (~apply(F!41, Y, tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39))))))))),
% 0.22/0.49      inference(unit_resolution,[status(thm)],[115, 106, 82])).
% 0.22/0.49  tff(117,plain,
% 0.22/0.49      (((~((~apply(compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, inverse_function(F!41, A!40, B!39), F!41), A!40)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_Y_8(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, inverse_function(F!41, A!40, B!39), F!41))) | (~apply(F!41, tptp_fun_Y_8(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, inverse_function(F!41, A!40, B!39), F!41), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)))))))) | (~(apply(compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39))) | ![Y: $i] : ((~member(Y, A!40)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), Y)) | (~apply(F!41, Y, tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)))))))) | (apply(compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39))) | ![Y: $i] : ((~member(Y, A!40)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), Y)) | (~apply(F!41, Y, tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39))))))),
% 0.22/0.49      inference(tautology,[status(thm)],[])).
% 0.22/0.49  tff(118,plain,
% 0.22/0.49      (apply(compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39))) | ![Y: $i] : ((~member(Y, A!40)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), Y)) | (~apply(F!41, Y, tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)))))),
% 0.22/0.49      inference(unit_resolution,[status(thm)],[117, 116])).
% 0.22/0.49  tff(119,plain,
% 0.22/0.49      (((~member(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), B!39)) | apply(compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)))) | (~apply(compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39))))),
% 0.22/0.49      inference(tautology,[status(thm)],[])).
% 0.22/0.49  tff(120,plain,
% 0.22/0.49      (~apply(compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)))),
% 0.22/0.49      inference(unit_resolution,[status(thm)],[119, 80])).
% 0.22/0.49  tff(121,plain,
% 0.22/0.49      ((~(apply(compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39))) | ![Y: $i] : ((~member(Y, A!40)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), Y)) | (~apply(F!41, Y, tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39))))))) | apply(compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39))) | ![Y: $i] : ((~member(Y, A!40)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), Y)) | (~apply(F!41, Y, tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)))))),
% 0.22/0.49      inference(tautology,[status(thm)],[])).
% 0.22/0.49  tff(122,plain,
% 0.22/0.49      ((~(apply(compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39))) | ![Y: $i] : ((~member(Y, A!40)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), Y)) | (~apply(F!41, Y, tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39))))))) | ![Y: $i] : ((~member(Y, A!40)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), Y)) | (~apply(F!41, Y, tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)))))),
% 0.22/0.49      inference(unit_resolution,[status(thm)],[121, 120])).
% 0.22/0.49  tff(123,plain,
% 0.22/0.49      (![Y: $i] : ((~member(Y, A!40)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), Y)) | (~apply(F!41, Y, tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)))))),
% 0.22/0.49      inference(unit_resolution,[status(thm)],[122, 118])).
% 0.22/0.49  tff(124,plain,
% 0.22/0.49      (((~![Y: $i] : ((~member(Y, A!40)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), Y)) | (~apply(F!41, Y, tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)))))) | ((~member(tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41), A!40)) | (~apply(F!41, tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)))) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41))))) <=> ((~![Y: $i] : ((~member(Y, A!40)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), Y)) | (~apply(F!41, Y, tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)))))) | (~member(tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41), A!40)) | (~apply(F!41, tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)))) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41))))),
% 0.22/0.49      inference(rewrite,[status(thm)],[])).
% 0.22/0.49  tff(125,plain,
% 0.22/0.49      (((~member(tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41), A!40)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41))) | (~apply(F!41, tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39))))) <=> ((~member(tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41), A!40)) | (~apply(F!41, tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)))) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41))))),
% 0.22/0.50      inference(rewrite,[status(thm)],[])).
% 0.22/0.50  tff(126,plain,
% 0.22/0.50      (((~![Y: $i] : ((~member(Y, A!40)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), Y)) | (~apply(F!41, Y, tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)))))) | ((~member(tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41), A!40)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41))) | (~apply(F!41, tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)))))) <=> ((~![Y: $i] : ((~member(Y, A!40)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), Y)) | (~apply(F!41, Y, tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)))))) | ((~member(tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41), A!40)) | (~apply(F!41, tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)))) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41)))))),
% 0.22/0.50      inference(monotonicity,[status(thm)],[125])).
% 0.22/0.50  tff(127,plain,
% 0.22/0.50      (((~![Y: $i] : ((~member(Y, A!40)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), Y)) | (~apply(F!41, Y, tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)))))) | ((~member(tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41), A!40)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41))) | (~apply(F!41, tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)))))) <=> ((~![Y: $i] : ((~member(Y, A!40)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), Y)) | (~apply(F!41, Y, tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)))))) | (~member(tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41), A!40)) | (~apply(F!41, tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)))) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41))))),
% 0.22/0.50      inference(transitivity,[status(thm)],[126, 124])).
% 0.22/0.50  tff(128,plain,
% 0.22/0.50      ((~![Y: $i] : ((~member(Y, A!40)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), Y)) | (~apply(F!41, Y, tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)))))) | ((~member(tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41), A!40)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41))) | (~apply(F!41, tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)))))),
% 0.22/0.50      inference(quant_inst,[status(thm)],[])).
% 0.22/0.50  tff(129,plain,
% 0.22/0.50      ((~![Y: $i] : ((~member(Y, A!40)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), Y)) | (~apply(F!41, Y, tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)))))) | (~member(tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41), A!40)) | (~apply(F!41, tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)))) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41)))),
% 0.22/0.50      inference(modus_ponens,[status(thm)],[128, 127])).
% 0.22/0.50  tff(130,plain,
% 0.22/0.50      (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41))),
% 0.22/0.50      inference(unit_resolution,[status(thm)],[129, 123, 90, 88])).
% 0.22/0.50  tff(131,plain,
% 0.22/0.50      ((~(apply(F!41, tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39))) <=> apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41)))) | (~apply(F!41, tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)))) | apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41))),
% 0.22/0.50      inference(tautology,[status(thm)],[])).
% 0.22/0.50  tff(132,plain,
% 0.22/0.50      (~(apply(F!41, tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39))) <=> apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41)))),
% 0.22/0.50      inference(unit_resolution,[status(thm)],[131, 88, 130])).
% 0.22/0.50  tff(133,plain,
% 0.22/0.50      (^[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))))),
% 0.22/0.50      inference(bind,[status(th)],[])).
% 0.22/0.50  tff(134,plain,
% 0.22/0.50      (![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)))),
% 0.22/0.50      inference(quant_intro,[status(thm)],[133])).
% 0.22/0.50  tff(135,plain,
% 0.22/0.50      (^[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)))))),
% 0.22/0.50      inference(bind,[status(th)],[])).
% 0.22/0.50  tff(136,plain,
% 0.22/0.50      (![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)))),
% 0.22/0.50      inference(quant_intro,[status(thm)],[135])).
% 0.22/0.50  tff(137,plain,
% 0.22/0.50      (![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)))),
% 0.22/0.50      inference(rewrite,[status(thm)],[])).
% 0.22/0.50  tff(138,plain,
% 0.22/0.50      (^[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))))),
% 0.22/0.50      inference(bind,[status(th)],[])).
% 0.22/0.50  tff(139,plain,
% 0.22/0.50      (![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)))),
% 0.22/0.50      inference(quant_intro,[status(thm)],[138])).
% 0.22/0.50  tff(140,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/sandbox/benchmark/Axioms/SET006+1.ax','inverse_function')).
% 0.22/0.50  tff(141,plain,
% 0.22/0.50      (![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)))),
% 0.22/0.50      inference(modus_ponens,[status(thm)],[140, 139])).
% 0.22/0.50  tff(142,plain,
% 0.22/0.50      (![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)))),
% 0.22/0.50      inference(modus_ponens,[status(thm)],[141, 137])).
% 0.22/0.50  tff(143,plain,(
% 0.22/0.50      ![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)))),
% 0.22/0.50      inference(skolemize,[status(sab)],[142])).
% 0.22/0.50  tff(144,plain,
% 0.22/0.50      (![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)))),
% 0.22/0.50      inference(modus_ponens,[status(thm)],[143, 136])).
% 0.22/0.50  tff(145,plain,
% 0.22/0.50      (![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)))),
% 0.22/0.50      inference(modus_ponens,[status(thm)],[144, 134])).
% 0.22/0.50  tff(146,plain,
% 0.22/0.50      (((~![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_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), B!39)) | (~member(tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41), A!40)) | (apply(F!41, tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39))) <=> apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!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_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), B!39)) | (~member(tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41), A!40)) | (apply(F!41, tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39))) <=> apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41))))),
% 0.22/0.50      inference(rewrite,[status(thm)],[])).
% 0.22/0.50  tff(147,plain,
% 0.22/0.50      (((apply(F!41, tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39))) <=> apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41))) | (~member(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), B!39)) | (~member(tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41), A!40))) <=> ((~member(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), B!39)) | (~member(tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41), A!40)) | (apply(F!41, tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39))) <=> apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41))))),
% 0.22/0.51      inference(rewrite,[status(thm)],[])).
% 0.22/0.51  tff(148,plain,
% 0.22/0.51      (((~![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!41, tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39))) <=> apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41))) | (~member(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), B!39)) | (~member(tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41), A!40)))) <=> ((~![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_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), B!39)) | (~member(tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41), A!40)) | (apply(F!41, tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39))) <=> apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41)))))),
% 0.22/0.51      inference(monotonicity,[status(thm)],[147])).
% 0.22/0.51  tff(149,plain,
% 0.22/0.51      (((~![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!41, tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39))) <=> apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41))) | (~member(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), B!39)) | (~member(tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41), A!40)))) <=> ((~![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_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), B!39)) | (~member(tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41), A!40)) | (apply(F!41, tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39))) <=> apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41))))),
% 0.22/0.51      inference(transitivity,[status(thm)],[148, 146])).
% 0.22/0.51  tff(150,plain,
% 0.22/0.51      ((~![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!41, tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39))) <=> apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41))) | (~member(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), B!39)) | (~member(tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41), A!40)))),
% 0.22/0.51      inference(quant_inst,[status(thm)],[])).
% 0.22/0.51  tff(151,plain,
% 0.22/0.51      ((~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))) | (~member(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), B!39)) | (~member(tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41), A!40)) | (apply(F!41, tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39))) <=> apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41)))),
% 0.22/0.51      inference(modus_ponens,[status(thm)],[150, 149])).
% 0.22/0.51  tff(152,plain,
% 0.22/0.51      ($false),
% 0.22/0.51      inference(unit_resolution,[status(thm)],[151, 145, 82, 90, 132])).
% 0.22/0.51  % SZS output end Proof
%------------------------------------------------------------------------------