TSTP Solution File: SET718+4 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET718+4 : TPTP v8.1.0. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n017.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 05:07:44 EDT 2022
% Result : Theorem 0.18s 0.41s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SET718+4 : TPTP v8.1.0. Bugfixed v2.2.1.
% 0.11/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n017.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sat Sep 3 06:53:38 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.33 Usage: tptp [options] [-file:]file
% 0.12/0.33 -h, -? prints this message.
% 0.12/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.33 -m, -model generate model.
% 0.12/0.33 -p, -proof generate proof.
% 0.12/0.33 -c, -core generate unsat core of named formulas.
% 0.12/0.33 -st, -statistics display statistics.
% 0.12/0.33 -t:timeout set timeout (in second).
% 0.12/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.33 -<param>:<value> configuration parameter and value.
% 0.12/0.33 -o:<output-file> file to place output in.
% 0.18/0.41 % SZS status Theorem
% 0.18/0.41 % SZS output start Proof
% 0.18/0.41 tff(apply_type, type, (
% 0.18/0.41 apply: ( $i * $i * $i ) > $o)).
% 0.18/0.41 tff(tptp_fun_Y_20_type, type, (
% 0.18/0.41 tptp_fun_Y_20: ( $i * $i * $i ) > $i)).
% 0.18/0.41 tff(compose_function_type, type, (
% 0.18/0.41 compose_function: ( $i * $i * $i * $i * $i ) > $i)).
% 0.18/0.41 tff(tptp_fun_C_39_type, type, (
% 0.18/0.41 tptp_fun_C_39: $i)).
% 0.18/0.41 tff(tptp_fun_B_40_type, type, (
% 0.18/0.41 tptp_fun_B_40: $i)).
% 0.18/0.41 tff(tptp_fun_A_41_type, type, (
% 0.18/0.41 tptp_fun_A_41: $i)).
% 0.18/0.41 tff(tptp_fun_F_43_type, type, (
% 0.18/0.41 tptp_fun_F_43: $i)).
% 0.18/0.41 tff(tptp_fun_G_42_type, type, (
% 0.18/0.41 tptp_fun_G_42: $i)).
% 0.18/0.41 tff(tptp_fun_E_19_type, type, (
% 0.18/0.41 tptp_fun_E_19: ( $i * $i * $i ) > $i)).
% 0.18/0.41 tff(member_type, type, (
% 0.18/0.41 member: ( $i * $i ) > $o)).
% 0.18/0.41 tff(tptp_fun_Y_8_type, type, (
% 0.18/0.41 tptp_fun_Y_8: ( $i * $i * $i * $i * $i ) > $i)).
% 0.18/0.41 tff(surjective_type, type, (
% 0.18/0.41 surjective: ( $i * $i * $i ) > $o)).
% 0.18/0.41 tff(injective_type, type, (
% 0.18/0.41 injective: ( $i * $i * $i ) > $o)).
% 0.18/0.41 tff(tptp_fun_Y_16_type, type, (
% 0.18/0.41 tptp_fun_Y_16: ( $i * $i * $i ) > $i)).
% 0.18/0.41 tff(tptp_fun_X2_17_type, type, (
% 0.18/0.41 tptp_fun_X2_17: ( $i * $i * $i ) > $i)).
% 0.18/0.41 tff(tptp_fun_X1_18_type, type, (
% 0.18/0.41 tptp_fun_X1_18: ( $i * $i * $i ) > $i)).
% 0.18/0.41 tff(one_to_one_type, type, (
% 0.18/0.41 one_to_one: ( $i * $i * $i ) > $o)).
% 0.18/0.41 tff(maps_type, type, (
% 0.18/0.41 maps: ( $i * $i * $i ) > $o)).
% 0.18/0.41 tff(1,plain,
% 0.18/0.41 (^[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))))))))))))),
% 0.18/0.41 inference(bind,[status(th)],[])).
% 0.18/0.41 tff(2,plain,
% 0.18/0.41 (![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)))))))))))),
% 0.18/0.41 inference(quant_intro,[status(thm)],[1])).
% 0.18/0.41 tff(3,plain,
% 0.18/0.41 (^[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))))))))))))),
% 0.18/0.41 inference(bind,[status(th)],[])).
% 0.18/0.41 tff(4,plain,
% 0.18/0.41 (![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)))))))))))),
% 0.18/0.41 inference(quant_intro,[status(thm)],[3])).
% 0.18/0.41 tff(5,plain,
% 0.18/0.41 (![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)))))))))))),
% 0.18/0.41 inference(transitivity,[status(thm)],[4, 2])).
% 0.18/0.41 tff(6,plain,
% 0.18/0.41 (^[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)))))))))))))),
% 0.18/0.41 inference(bind,[status(th)],[])).
% 0.18/0.41 tff(7,plain,
% 0.18/0.41 (![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)))))))))))),
% 0.18/0.41 inference(quant_intro,[status(thm)],[6])).
% 0.18/0.41 tff(8,plain,
% 0.18/0.41 (^[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))))))))),
% 0.18/0.41 inference(bind,[status(th)],[])).
% 0.18/0.41 tff(9,plain,
% 0.18/0.41 (![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)))))))),
% 0.18/0.41 inference(quant_intro,[status(thm)],[8])).
% 0.18/0.41 tff(10,plain,
% 0.18/0.41 (![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))))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(11,plain,
% 0.18/0.41 (^[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)))))),
% 0.18/0.41 inference(bind,[status(th)],[])).
% 0.18/0.41 tff(12,plain,
% 0.18/0.41 (![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))))),
% 0.18/0.41 inference(quant_intro,[status(thm)],[11])).
% 0.18/0.41 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')).
% 0.18/0.42 tff(14,plain,
% 0.18/0.42 (![F: $i, A: $i, B: $i] : (surjective(F, A, B) <=> ![Y: $i] : ((~member(Y, B)) | ?[E: $i] : (member(E, A) & apply(F, E, Y))))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.18/0.42 tff(15,plain,
% 0.18/0.42 (![F: $i, A: $i, B: $i] : (surjective(F, A, B) <=> ![Y: $i] : ((~member(Y, B)) | ?[E: $i] : (member(E, A) & apply(F, E, Y))))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[14, 10])).
% 0.18/0.42 tff(16,plain,(
% 0.18/0.42 ![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)))))))),
% 0.18/0.42 inference(skolemize,[status(sab)],[15])).
% 0.18/0.42 tff(17,plain,
% 0.18/0.42 (![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)))))))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[16, 9])).
% 0.18/0.42 tff(18,plain,
% 0.18/0.42 (![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)))))))))))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[17, 7])).
% 0.18/0.42 tff(19,plain,
% 0.18/0.42 (![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)))))))))))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[18, 5])).
% 0.18/0.42 tff(20,plain,
% 0.18/0.42 ((~![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)))))))))))) | (~((~((~surjective(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)) | ![Y: $i] : ((~member(Y, C!39)) | (~((~member(tptp_fun_E_19(Y, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_E_19(Y, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y))))))) | (~(surjective(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39) | (~((~member(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~![E: $i] : ((~member(E, A!41)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), E, tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))))))))),
% 0.18/0.42 inference(quant_inst,[status(thm)],[])).
% 0.18/0.42 tff(21,plain,
% 0.18/0.42 (~((~((~surjective(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)) | ![Y: $i] : ((~member(Y, C!39)) | (~((~member(tptp_fun_E_19(Y, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_E_19(Y, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y))))))) | (~(surjective(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39) | (~((~member(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~![E: $i] : ((~member(E, A!41)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), E, tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))))))),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[20, 19])).
% 0.18/0.42 tff(22,plain,
% 0.18/0.42 (((~((~surjective(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)) | ![Y: $i] : ((~member(Y, C!39)) | (~((~member(tptp_fun_E_19(Y, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_E_19(Y, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y))))))) | (~(surjective(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39) | (~((~member(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~![E: $i] : ((~member(E, A!41)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), E, tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))))))) | (surjective(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39) | (~((~member(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~![E: $i] : ((~member(E, A!41)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), E, tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))))),
% 0.18/0.42 inference(tautology,[status(thm)],[])).
% 0.18/0.42 tff(23,plain,
% 0.18/0.42 (surjective(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39) | (~((~member(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~![E: $i] : ((~member(E, A!41)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), E, tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))))),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[22, 21])).
% 0.18/0.42 tff(24,assumption,((~((~injective(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X1, A!41)) | (~member(Y, C!39)) | (~member(X2, A!41)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), X1, Y)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), X2, Y))))) | (~(injective(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39) | (~((tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)) = tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~member(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39))))))), introduced(assumption)).
% 0.18/0.42 tff(25,plain,
% 0.18/0.42 (^[F: $i, A: $i, B: $i] : refl((~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B)))))))) <=> (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B)))))))))),
% 0.18/0.42 inference(bind,[status(th)],[])).
% 0.18/0.42 tff(26,plain,
% 0.18/0.42 (![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B)))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))),
% 0.18/0.42 inference(quant_intro,[status(thm)],[25])).
% 0.18/0.42 tff(27,plain,
% 0.18/0.42 (^[F: $i, A: $i, B: $i] : rewrite((~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B)))))))) <=> (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B)))))))))),
% 0.18/0.42 inference(bind,[status(th)],[])).
% 0.18/0.42 tff(28,plain,
% 0.18/0.42 (![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B)))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))),
% 0.18/0.42 inference(quant_intro,[status(thm)],[27])).
% 0.18/0.42 tff(29,plain,
% 0.18/0.42 (![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B)))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))),
% 0.18/0.42 inference(transitivity,[status(thm)],[28, 26])).
% 0.18/0.42 tff(30,plain,
% 0.18/0.42 (^[F: $i, A: $i, B: $i] : trans(monotonicity(rewrite(((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~(apply(F, X1, Y) & apply(F, X2, Y))) | (~(member(X1, A) & member(X2, A) & member(Y, B))))) <=> ((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))), trans(monotonicity(rewrite((~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~(apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F)) & apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F)))) | (~(member(tptp_fun_X1_18(B, A, F), A) & member(tptp_fun_X2_17(B, A, F), A) & member(tptp_fun_Y_16(B, A, F), B))))) <=> (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))), ((injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~(apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F)) & apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F)))) | (~(member(tptp_fun_X1_18(B, A, F), A) & member(tptp_fun_X2_17(B, A, F), A) & member(tptp_fun_Y_16(B, A, F), B)))))) <=> (injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))), rewrite((injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))) <=> (injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B)))))), ((injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~(apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F)) & apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F)))) | (~(member(tptp_fun_X1_18(B, A, F), A) & member(tptp_fun_X2_17(B, A, F), A) & member(tptp_fun_Y_16(B, A, F), B)))))) <=> (injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))), ((((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~(apply(F, X1, Y) & apply(F, X2, Y))) | (~(member(X1, A) & member(X2, A) & member(Y, B))))) & (injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~(apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F)) & apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F)))) | (~(member(tptp_fun_X1_18(B, A, F), A) & member(tptp_fun_X2_17(B, A, F), A) & member(tptp_fun_Y_16(B, A, F), B))))))) <=> (((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y)))) & (injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B)))))))), rewrite((((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y)))) & (injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B)))))) <=> (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))), ((((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~(apply(F, X1, Y) & apply(F, X2, Y))) | (~(member(X1, A) & member(X2, A) & member(Y, B))))) & (injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~(apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F)) & apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F)))) | (~(member(tptp_fun_X1_18(B, A, F), A) & member(tptp_fun_X2_17(B, A, F), A) & member(tptp_fun_Y_16(B, A, F), B))))))) <=> (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))))),
% 0.18/0.42 inference(bind,[status(th)],[])).
% 0.18/0.42 tff(31,plain,
% 0.18/0.42 (![F: $i, A: $i, B: $i] : (((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~(apply(F, X1, Y) & apply(F, X2, Y))) | (~(member(X1, A) & member(X2, A) & member(Y, B))))) & (injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~(apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F)) & apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F)))) | (~(member(tptp_fun_X1_18(B, A, F), A) & member(tptp_fun_X2_17(B, A, F), A) & member(tptp_fun_Y_16(B, A, F), B))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))),
% 0.18/0.42 inference(quant_intro,[status(thm)],[30])).
% 0.18/0.42 tff(32,plain,
% 0.18/0.42 (![F: $i, A: $i, B: $i] : (injective(F, A, B) <=> ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~(apply(F, X1, Y) & apply(F, X2, Y))) | (~(member(X1, A) & member(X2, A) & member(Y, B))))) <=> ![F: $i, A: $i, B: $i] : (injective(F, A, B) <=> ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~(apply(F, X1, Y) & apply(F, X2, Y))) | (~(member(X1, A) & member(X2, A) & member(Y, B)))))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(33,plain,
% 0.18/0.42 (^[F: $i, A: $i, B: $i] : rewrite((injective(F, A, B) <=> ![X1: $i, X2: $i, Y: $i] : (((member(X1, A) & member(X2, A)) & member(Y, B)) => ((apply(F, X1, Y) & apply(F, X2, Y)) => (X1 = X2)))) <=> (injective(F, A, B) <=> ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~(apply(F, X1, Y) & apply(F, X2, Y))) | (~(member(X1, A) & member(X2, A) & member(Y, B))))))),
% 0.18/0.42 inference(bind,[status(th)],[])).
% 0.18/0.42 tff(34,plain,
% 0.18/0.42 (![F: $i, A: $i, B: $i] : (injective(F, A, B) <=> ![X1: $i, X2: $i, Y: $i] : (((member(X1, A) & member(X2, A)) & member(Y, B)) => ((apply(F, X1, Y) & apply(F, X2, Y)) => (X1 = X2)))) <=> ![F: $i, A: $i, B: $i] : (injective(F, A, B) <=> ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~(apply(F, X1, Y) & apply(F, X2, Y))) | (~(member(X1, A) & member(X2, A) & member(Y, B)))))),
% 0.18/0.43 inference(quant_intro,[status(thm)],[33])).
% 0.18/0.43 tff(35,axiom,(![F: $i, A: $i, B: $i] : (injective(F, A, B) <=> ![X1: $i, X2: $i, Y: $i] : (((member(X1, A) & member(X2, A)) & member(Y, B)) => ((apply(F, X1, Y) & apply(F, X2, Y)) => (X1 = X2))))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+1.ax','injective')).
% 0.18/0.43 tff(36,plain,
% 0.18/0.43 (![F: $i, A: $i, B: $i] : (injective(F, A, B) <=> ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~(apply(F, X1, Y) & apply(F, X2, Y))) | (~(member(X1, A) & member(X2, A) & member(Y, B)))))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.18/0.43 tff(37,plain,
% 0.18/0.43 (![F: $i, A: $i, B: $i] : (injective(F, A, B) <=> ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~(apply(F, X1, Y) & apply(F, X2, Y))) | (~(member(X1, A) & member(X2, A) & member(Y, B)))))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[36, 32])).
% 0.18/0.43 tff(38,plain,(
% 0.18/0.43 ![F: $i, A: $i, B: $i] : (((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~(apply(F, X1, Y) & apply(F, X2, Y))) | (~(member(X1, A) & member(X2, A) & member(Y, B))))) & (injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~(apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F)) & apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F)))) | (~(member(tptp_fun_X1_18(B, A, F), A) & member(tptp_fun_X2_17(B, A, F), A) & member(tptp_fun_Y_16(B, A, F), B)))))))),
% 0.18/0.43 inference(skolemize,[status(sab)],[37])).
% 0.18/0.43 tff(39,plain,
% 0.18/0.43 (![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[38, 31])).
% 0.18/0.43 tff(40,plain,
% 0.18/0.43 (![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[39, 29])).
% 0.18/0.43 tff(41,plain,
% 0.18/0.43 (((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X1, A!41)) | (~member(Y, C!39)) | (~member(X2, A!41)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), X1, Y)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), X2, Y))))) | (~(injective(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39) | (~((tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)) = tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~member(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39))))))))) <=> ((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X1, A!41)) | (~member(Y, C!39)) | (~member(X2, A!41)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), X1, Y)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), X2, Y))))) | (~(injective(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39) | (~((tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)) = tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~member(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)))))))))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(42,plain,
% 0.18/0.43 ((~((~((~injective(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), X1, Y)) | (~member(X2, A!41)) | (~member(X1, A!41)) | (~member(Y, C!39)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), X2, Y))))) | (~(injective(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39) | (~((tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)) = tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~member(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)))))))) <=> (~((~((~injective(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X1, A!41)) | (~member(Y, C!39)) | (~member(X2, A!41)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), X1, Y)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), X2, Y))))) | (~(injective(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39) | (~((tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)) = tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~member(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39))))))))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(43,plain,
% 0.18/0.43 (((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), X1, Y)) | (~member(X2, A!41)) | (~member(X1, A!41)) | (~member(Y, C!39)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), X2, Y))))) | (~(injective(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39) | (~((tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)) = tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~member(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39))))))))) <=> ((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X1, A!41)) | (~member(Y, C!39)) | (~member(X2, A!41)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), X1, Y)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), X2, Y))))) | (~(injective(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39) | (~((tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)) = tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~member(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)))))))))),
% 0.18/0.44 inference(monotonicity,[status(thm)],[42])).
% 0.18/0.44 tff(44,plain,
% 0.18/0.44 (((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), X1, Y)) | (~member(X2, A!41)) | (~member(X1, A!41)) | (~member(Y, C!39)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), X2, Y))))) | (~(injective(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39) | (~((tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)) = tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~member(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39))))))))) <=> ((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X1, A!41)) | (~member(Y, C!39)) | (~member(X2, A!41)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), X1, Y)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), X2, Y))))) | (~(injective(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39) | (~((tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)) = tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~member(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)))))))))),
% 0.18/0.44 inference(transitivity,[status(thm)],[43, 41])).
% 0.18/0.44 tff(45,plain,
% 0.18/0.44 ((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), X1, Y)) | (~member(X2, A!41)) | (~member(X1, A!41)) | (~member(Y, C!39)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), X2, Y))))) | (~(injective(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39) | (~((tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)) = tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~member(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39))))))))),
% 0.18/0.44 inference(quant_inst,[status(thm)],[])).
% 0.18/0.44 tff(46,plain,
% 0.18/0.44 ((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X1, A!41)) | (~member(Y, C!39)) | (~member(X2, A!41)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), X1, Y)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), X2, Y))))) | (~(injective(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39) | (~((tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)) = tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~member(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39))))))))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.18/0.44 tff(47,plain,
% 0.18/0.44 ($false),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[46, 40, 24])).
% 0.18/0.44 tff(48,plain,(~((~((~injective(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X1, A!41)) | (~member(Y, C!39)) | (~member(X2, A!41)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), X1, Y)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), X2, Y))))) | (~(injective(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39) | (~((tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)) = tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~member(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)))))))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.44 tff(49,plain,
% 0.18/0.44 (((~((~injective(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X1, A!41)) | (~member(Y, C!39)) | (~member(X2, A!41)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), X1, Y)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), X2, Y))))) | (~(injective(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39) | (~((tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)) = tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~member(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39))))))) | (injective(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39) | (~((tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)) = tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~member(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)))))),
% 0.18/0.44 inference(tautology,[status(thm)],[])).
% 0.18/0.44 tff(50,plain,
% 0.18/0.44 (injective(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39) | (~((tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)) = tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~member(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39))))),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[49, 48])).
% 0.18/0.45 tff(51,assumption,(~((tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)) = tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~member(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)))), introduced(assumption)).
% 0.18/0.45 tff(52,plain,
% 0.18/0.45 (((tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)) = tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~member(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39))) | member(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)),
% 0.18/0.45 inference(tautology,[status(thm)],[])).
% 0.18/0.45 tff(53,plain,
% 0.18/0.45 (member(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[52, 51])).
% 0.18/0.45 tff(54,plain,
% 0.18/0.45 (((tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)) = tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~member(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39))) | member(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)),
% 0.18/0.45 inference(tautology,[status(thm)],[])).
% 0.18/0.45 tff(55,plain,
% 0.18/0.45 (member(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[54, 51])).
% 0.18/0.45 tff(56,plain,
% 0.18/0.45 (^[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)))))))))),
% 0.18/0.45 inference(bind,[status(th)],[])).
% 0.18/0.45 tff(57,plain,
% 0.18/0.45 (![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z)))))))) <=> ![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))),
% 0.18/0.45 inference(quant_intro,[status(thm)],[56])).
% 0.18/0.45 tff(58,plain,
% 0.18/0.45 (^[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)))))))))),
% 0.18/0.45 inference(bind,[status(th)],[])).
% 0.18/0.45 tff(59,plain,
% 0.18/0.45 (![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z)))))))) <=> ![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))),
% 0.18/0.45 inference(quant_intro,[status(thm)],[58])).
% 0.18/0.45 tff(60,plain,
% 0.18/0.45 (![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z)))))))) <=> ![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))),
% 0.18/0.45 inference(transitivity,[status(thm)],[59, 57])).
% 0.18/0.45 tff(61,plain,
% 0.18/0.45 (^[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))))))))))),
% 0.18/0.45 inference(bind,[status(th)],[])).
% 0.18/0.45 tff(62,plain,
% 0.18/0.45 (![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~(member(X, A) & member(Z, C))) | (((~apply(compose_function(G, F, A, B, C), X, Z)) | (member(tptp_fun_Y_8(Z, X, B, F, G), B) & apply(F, X, tptp_fun_Y_8(Z, X, B, F, G)) & apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z))) & (apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y) & apply(G, Y, Z)))))) <=> ![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))),
% 0.18/0.45 inference(quant_intro,[status(thm)],[61])).
% 0.18/0.45 tff(63,plain,
% 0.18/0.45 (![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~(member(X, A) & member(Z, C))) | (apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : (member(Y, B) & apply(F, X, Y) & apply(G, Y, Z)))) <=> ![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~(member(X, A) & member(Z, C))) | (apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : (member(Y, B) & apply(F, X, Y) & apply(G, Y, Z))))),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(64,plain,
% 0.18/0.45 (^[G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : trans(monotonicity(rewrite((apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : ((member(Y, B) & apply(F, X, Y)) & apply(G, Y, Z))) <=> (apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : (member(Y, B) & apply(F, X, Y) & apply(G, Y, Z)))), (((member(X, A) & member(Z, C)) => (apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : ((member(Y, B) & apply(F, X, Y)) & apply(G, Y, Z)))) <=> ((member(X, A) & member(Z, C)) => (apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : (member(Y, B) & apply(F, X, Y) & apply(G, Y, Z)))))), rewrite(((member(X, A) & member(Z, C)) => (apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : (member(Y, B) & apply(F, X, Y) & apply(G, Y, Z)))) <=> ((~(member(X, A) & member(Z, C))) | (apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : (member(Y, B) & apply(F, X, Y) & apply(G, Y, Z))))), (((member(X, A) & member(Z, C)) => (apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : ((member(Y, B) & apply(F, X, Y)) & apply(G, Y, Z)))) <=> ((~(member(X, A) & member(Z, C))) | (apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : (member(Y, B) & apply(F, X, Y) & apply(G, Y, Z))))))),
% 0.18/0.45 inference(bind,[status(th)],[])).
% 0.18/0.45 tff(65,plain,
% 0.18/0.45 (![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((member(X, A) & member(Z, C)) => (apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : ((member(Y, B) & apply(F, X, Y)) & apply(G, Y, Z)))) <=> ![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~(member(X, A) & member(Z, C))) | (apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : (member(Y, B) & apply(F, X, Y) & apply(G, Y, Z))))),
% 0.18/0.45 inference(quant_intro,[status(thm)],[64])).
% 0.18/0.45 tff(66,axiom,(![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((member(X, A) & member(Z, C)) => (apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : ((member(Y, B) & apply(F, X, Y)) & apply(G, Y, Z))))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+1.ax','compose_function')).
% 0.18/0.45 tff(67,plain,
% 0.18/0.45 (![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~(member(X, A) & member(Z, C))) | (apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : (member(Y, B) & apply(F, X, Y) & apply(G, Y, Z))))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.18/0.45 tff(68,plain,
% 0.18/0.45 (![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~(member(X, A) & member(Z, C))) | (apply(compose_function(G, F, A, B, C), X, Z) <=> ?[Y: $i] : (member(Y, B) & apply(F, X, Y) & apply(G, Y, Z))))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[67, 63])).
% 0.18/0.45 tff(69,plain,(
% 0.18/0.45 ![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~(member(X, A) & member(Z, C))) | (((~apply(compose_function(G, F, A, B, C), X, Z)) | (member(tptp_fun_Y_8(Z, X, B, F, G), B) & apply(F, X, tptp_fun_Y_8(Z, X, B, F, G)) & apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z))) & (apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : (~(member(Y, B) & apply(F, X, Y) & apply(G, Y, Z))))))),
% 0.18/0.45 inference(skolemize,[status(sab)],[68])).
% 0.18/0.45 tff(70,plain,
% 0.18/0.45 (![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[69, 62])).
% 0.18/0.45 tff(71,plain,
% 0.18/0.45 (![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[70, 60])).
% 0.18/0.45 tff(72,plain,
% 0.18/0.45 (((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~((~((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))) | (~(apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))))))) <=> ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | (~member(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~((~((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))) | (~(apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))))))),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(73,plain,
% 0.18/0.45 (((~member(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~((~((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))) | (~(apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))))) <=> ((~member(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~((~((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))) | (~(apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))))))),
% 0.18/0.46 inference(rewrite,[status(thm)],[])).
% 0.18/0.46 tff(74,plain,
% 0.18/0.46 ((~((~((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))) | (~(apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))))) <=> (~((~((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))) | (~(apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))))),
% 0.18/0.46 inference(rewrite,[status(thm)],[])).
% 0.18/0.46 tff(75,plain,
% 0.18/0.46 (((~member(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~((~((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))) | (~(apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))))) <=> ((~member(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~((~((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))) | (~(apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))))))),
% 0.18/0.46 inference(monotonicity,[status(thm)],[74])).
% 0.18/0.46 tff(76,plain,
% 0.18/0.46 (((~member(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~((~((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))) | (~(apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))))) <=> ((~member(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~((~((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))) | (~(apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))))))),
% 0.18/0.46 inference(transitivity,[status(thm)],[75, 73])).
% 0.18/0.46 tff(77,plain,
% 0.18/0.46 (((~![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_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~((~((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))) | (~(apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))))))) <=> ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~((~((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))) | (~(apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))))))),
% 0.18/0.46 inference(monotonicity,[status(thm)],[76])).
% 0.18/0.46 tff(78,plain,
% 0.18/0.46 (((~![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_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~((~((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))) | (~(apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))))))) <=> ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | (~member(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~((~((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))) | (~(apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))))))),
% 0.18/0.46 inference(transitivity,[status(thm)],[77, 72])).
% 0.18/0.46 tff(79,plain,
% 0.18/0.46 ((~![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_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~((~((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))) | (~(apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))))))),
% 0.18/0.47 inference(quant_inst,[status(thm)],[])).
% 0.18/0.47 tff(80,plain,
% 0.18/0.47 ((~![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_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~((~((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))) | (~(apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.18/0.47 tff(81,plain,
% 0.18/0.47 (~((~((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))) | (~(apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))))),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[80, 71, 55, 53])).
% 0.18/0.47 tff(82,plain,
% 0.18/0.47 (((~((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))) | (~(apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))) | ((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))),
% 0.18/0.47 inference(tautology,[status(thm)],[])).
% 0.18/0.47 tff(83,plain,
% 0.18/0.47 ((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[82, 81])).
% 0.18/0.47 tff(84,plain,
% 0.18/0.47 (((tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)) = tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~member(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39))) | apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))),
% 0.18/0.47 inference(tautology,[status(thm)],[])).
% 0.18/0.47 tff(85,plain,
% 0.18/0.47 (apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[84, 51])).
% 0.18/0.47 tff(86,plain,
% 0.18/0.47 ((~((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))),
% 0.18/0.47 inference(tautology,[status(thm)],[])).
% 0.18/0.47 tff(87,plain,
% 0.18/0.47 ((~((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[86, 85])).
% 0.18/0.47 tff(88,plain,
% 0.18/0.47 (~((~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[87, 83])).
% 0.18/0.47 tff(89,plain,
% 0.18/0.47 (((~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))) | apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))),
% 0.18/0.47 inference(tautology,[status(thm)],[])).
% 0.18/0.47 tff(90,plain,
% 0.18/0.47 (apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[89, 88])).
% 0.18/0.47 tff(91,plain,
% 0.18/0.47 (((~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))) | member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)),
% 0.18/0.47 inference(tautology,[status(thm)],[])).
% 0.18/0.47 tff(92,plain,
% 0.18/0.47 (member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[91, 88])).
% 0.18/0.47 tff(93,plain,
% 0.18/0.47 ((~![F: $i, A: $i, B: $i] : (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))))))) | (~((~((~surjective(G!42, B!40, C!39)) | ![Y: $i] : ((~member(Y, C!39)) | (~((~member(tptp_fun_E_19(Y, B!40, G!42), B!40)) | (~apply(G!42, tptp_fun_E_19(Y, B!40, G!42), Y))))))) | (~(surjective(G!42, B!40, C!39) | (~((~member(tptp_fun_Y_20(C!39, B!40, G!42), C!39)) | (~![E: $i] : ((~member(E, B!40)) | (~apply(G!42, E, tptp_fun_Y_20(C!39, B!40, G!42)))))))))))),
% 0.18/0.48 inference(quant_inst,[status(thm)],[])).
% 0.18/0.48 tff(94,plain,
% 0.18/0.48 (~((~((~surjective(G!42, B!40, C!39)) | ![Y: $i] : ((~member(Y, C!39)) | (~((~member(tptp_fun_E_19(Y, B!40, G!42), B!40)) | (~apply(G!42, tptp_fun_E_19(Y, B!40, G!42), Y))))))) | (~(surjective(G!42, B!40, C!39) | (~((~member(tptp_fun_Y_20(C!39, B!40, G!42), C!39)) | (~![E: $i] : ((~member(E, B!40)) | (~apply(G!42, E, tptp_fun_Y_20(C!39, B!40, G!42))))))))))),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[93, 19])).
% 0.18/0.48 tff(95,plain,
% 0.18/0.48 (((~((~surjective(G!42, B!40, C!39)) | ![Y: $i] : ((~member(Y, C!39)) | (~((~member(tptp_fun_E_19(Y, B!40, G!42), B!40)) | (~apply(G!42, tptp_fun_E_19(Y, B!40, G!42), Y))))))) | (~(surjective(G!42, B!40, C!39) | (~((~member(tptp_fun_Y_20(C!39, B!40, G!42), C!39)) | (~![E: $i] : ((~member(E, B!40)) | (~apply(G!42, E, tptp_fun_Y_20(C!39, B!40, G!42)))))))))) | ((~surjective(G!42, B!40, C!39)) | ![Y: $i] : ((~member(Y, C!39)) | (~((~member(tptp_fun_E_19(Y, B!40, G!42), B!40)) | (~apply(G!42, tptp_fun_E_19(Y, B!40, G!42), Y))))))),
% 0.18/0.48 inference(tautology,[status(thm)],[])).
% 0.18/0.48 tff(96,plain,
% 0.18/0.48 ((~surjective(G!42, B!40, C!39)) | ![Y: $i] : ((~member(Y, C!39)) | (~((~member(tptp_fun_E_19(Y, B!40, G!42), B!40)) | (~apply(G!42, tptp_fun_E_19(Y, B!40, G!42), Y)))))),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[95, 94])).
% 0.18/0.48 tff(97,plain,
% 0.18/0.48 (^[F: $i, A: $i, B: $i] : refl((one_to_one(F, A, B) <=> (~((~injective(F, A, B)) | (~surjective(F, A, B))))) <=> (one_to_one(F, A, B) <=> (~((~injective(F, A, B)) | (~surjective(F, A, B))))))),
% 0.18/0.48 inference(bind,[status(th)],[])).
% 0.18/0.48 tff(98,plain,
% 0.18/0.48 (![F: $i, A: $i, B: $i] : (one_to_one(F, A, B) <=> (~((~injective(F, A, B)) | (~surjective(F, A, B))))) <=> ![F: $i, A: $i, B: $i] : (one_to_one(F, A, B) <=> (~((~injective(F, A, B)) | (~surjective(F, A, B)))))),
% 0.18/0.48 inference(quant_intro,[status(thm)],[97])).
% 0.18/0.48 tff(99,plain,
% 0.18/0.48 (^[F: $i, A: $i, B: $i] : rewrite((one_to_one(F, A, B) <=> (injective(F, A, B) & surjective(F, A, B))) <=> (one_to_one(F, A, B) <=> (~((~injective(F, A, B)) | (~surjective(F, A, B))))))),
% 0.18/0.48 inference(bind,[status(th)],[])).
% 0.18/0.48 tff(100,plain,
% 0.18/0.48 (![F: $i, A: $i, B: $i] : (one_to_one(F, A, B) <=> (injective(F, A, B) & surjective(F, A, B))) <=> ![F: $i, A: $i, B: $i] : (one_to_one(F, A, B) <=> (~((~injective(F, A, B)) | (~surjective(F, A, B)))))),
% 0.18/0.48 inference(quant_intro,[status(thm)],[99])).
% 0.18/0.48 tff(101,plain,
% 0.18/0.48 (![F: $i, A: $i, B: $i] : (one_to_one(F, A, B) <=> (injective(F, A, B) & surjective(F, A, B))) <=> ![F: $i, A: $i, B: $i] : (one_to_one(F, A, B) <=> (injective(F, A, B) & surjective(F, A, B)))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(102,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')).
% 0.18/0.48 tff(103,plain,
% 0.18/0.48 (![F: $i, A: $i, B: $i] : (one_to_one(F, A, B) <=> (injective(F, A, B) & surjective(F, A, B)))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[102, 101])).
% 0.18/0.48 tff(104,plain,(
% 0.18/0.48 ![F: $i, A: $i, B: $i] : (one_to_one(F, A, B) <=> (injective(F, A, B) & surjective(F, A, B)))),
% 0.18/0.48 inference(skolemize,[status(sab)],[103])).
% 0.18/0.48 tff(105,plain,
% 0.18/0.48 (![F: $i, A: $i, B: $i] : (one_to_one(F, A, B) <=> (~((~injective(F, A, B)) | (~surjective(F, A, B)))))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[104, 100])).
% 0.18/0.48 tff(106,plain,
% 0.18/0.48 (![F: $i, A: $i, B: $i] : (one_to_one(F, A, B) <=> (~((~injective(F, A, B)) | (~surjective(F, A, B)))))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[105, 98])).
% 0.18/0.48 tff(107,plain,
% 0.18/0.48 ((~![F: $i, A: $i, B: $i] : (one_to_one(F, A, B) <=> (~((~injective(F, A, B)) | (~surjective(F, A, B)))))) | (one_to_one(G!42, B!40, C!39) <=> (~((~injective(G!42, B!40, C!39)) | (~surjective(G!42, B!40, C!39)))))),
% 0.18/0.48 inference(quant_inst,[status(thm)],[])).
% 0.18/0.48 tff(108,plain,
% 0.18/0.48 (one_to_one(G!42, B!40, C!39) <=> (~((~injective(G!42, B!40, C!39)) | (~surjective(G!42, B!40, C!39))))),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[107, 106])).
% 0.18/0.48 tff(109,plain,
% 0.18/0.48 ((~![F: $i, G: $i, A: $i, B: $i, C: $i] : ((~(maps(F, A, B) & maps(G, B, C) & one_to_one(F, A, B) & one_to_one(G, B, C))) | one_to_one(compose_function(G, F, A, B, C), A, C))) <=> (~![F: $i, G: $i, A: $i, B: $i, C: $i] : ((~(maps(F, A, B) & maps(G, B, C) & one_to_one(F, A, B) & one_to_one(G, B, C))) | one_to_one(compose_function(G, F, A, B, C), A, C)))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(110,plain,
% 0.18/0.48 ((~![F: $i, G: $i, A: $i, B: $i, C: $i] : ((((maps(F, A, B) & maps(G, B, C)) & one_to_one(F, A, B)) & one_to_one(G, B, C)) => one_to_one(compose_function(G, F, A, B, C), A, C))) <=> (~![F: $i, G: $i, A: $i, B: $i, C: $i] : ((~(maps(F, A, B) & maps(G, B, C) & one_to_one(F, A, B) & one_to_one(G, B, C))) | one_to_one(compose_function(G, F, A, B, C), A, C)))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(111,axiom,(~![F: $i, G: $i, A: $i, B: $i, C: $i] : ((((maps(F, A, B) & maps(G, B, C)) & one_to_one(F, A, B)) & one_to_one(G, B, C)) => one_to_one(compose_function(G, F, A, B, C), A, C))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','thII09')).
% 0.18/0.48 tff(112,plain,
% 0.18/0.48 (~![F: $i, G: $i, A: $i, B: $i, C: $i] : ((~(maps(F, A, B) & maps(G, B, C) & one_to_one(F, A, B) & one_to_one(G, B, C))) | one_to_one(compose_function(G, F, A, B, C), A, C))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[111, 110])).
% 0.18/0.48 tff(113,plain,
% 0.18/0.48 (~![F: $i, G: $i, A: $i, B: $i, C: $i] : ((~(maps(F, A, B) & maps(G, B, C) & one_to_one(F, A, B) & one_to_one(G, B, C))) | one_to_one(compose_function(G, F, A, B, C), A, C))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[112, 109])).
% 0.18/0.48 tff(114,plain,
% 0.18/0.48 (~![F: $i, G: $i, A: $i, B: $i, C: $i] : ((~(maps(F, A, B) & maps(G, B, C) & one_to_one(F, A, B) & one_to_one(G, B, C))) | one_to_one(compose_function(G, F, A, B, C), A, C))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[113, 109])).
% 0.18/0.48 tff(115,plain,
% 0.18/0.48 (~![F: $i, G: $i, A: $i, B: $i, C: $i] : ((~(maps(F, A, B) & maps(G, B, C) & one_to_one(F, A, B) & one_to_one(G, B, C))) | one_to_one(compose_function(G, F, A, B, C), A, C))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[114, 109])).
% 0.18/0.48 tff(116,plain,
% 0.18/0.48 (~![F: $i, G: $i, A: $i, B: $i, C: $i] : ((~(maps(F, A, B) & maps(G, B, C) & one_to_one(F, A, B) & one_to_one(G, B, C))) | one_to_one(compose_function(G, F, A, B, C), A, C))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[115, 109])).
% 0.18/0.48 tff(117,plain,
% 0.18/0.48 (~![F: $i, G: $i, A: $i, B: $i, C: $i] : ((~(maps(F, A, B) & maps(G, B, C) & one_to_one(F, A, B) & one_to_one(G, B, C))) | one_to_one(compose_function(G, F, A, B, C), A, C))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[116, 109])).
% 0.18/0.48 tff(118,plain,
% 0.18/0.48 (~![F: $i, G: $i, A: $i, B: $i, C: $i] : ((~(maps(F, A, B) & maps(G, B, C) & one_to_one(F, A, B) & one_to_one(G, B, C))) | one_to_one(compose_function(G, F, A, B, C), A, C))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[117, 109])).
% 0.18/0.48 tff(119,plain,(
% 0.18/0.48 ~((~(maps(F!43, A!41, B!40) & maps(G!42, B!40, C!39) & one_to_one(F!43, A!41, B!40) & one_to_one(G!42, B!40, C!39))) | one_to_one(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39))),
% 0.18/0.48 inference(skolemize,[status(sab)],[118])).
% 0.18/0.48 tff(120,plain,
% 0.18/0.48 (maps(F!43, A!41, B!40) & maps(G!42, B!40, C!39) & one_to_one(F!43, A!41, B!40) & one_to_one(G!42, B!40, C!39)),
% 0.18/0.48 inference(or_elim,[status(thm)],[119])).
% 0.18/0.48 tff(121,plain,
% 0.18/0.48 (one_to_one(G!42, B!40, C!39)),
% 0.18/0.48 inference(and_elim,[status(thm)],[120])).
% 0.18/0.48 tff(122,plain,
% 0.18/0.48 ((~(one_to_one(G!42, B!40, C!39) <=> (~((~injective(G!42, B!40, C!39)) | (~surjective(G!42, B!40, C!39)))))) | (~one_to_one(G!42, B!40, C!39)) | (~((~injective(G!42, B!40, C!39)) | (~surjective(G!42, B!40, C!39))))),
% 0.18/0.48 inference(tautology,[status(thm)],[])).
% 0.18/0.48 tff(123,plain,
% 0.18/0.48 ((~(one_to_one(G!42, B!40, C!39) <=> (~((~injective(G!42, B!40, C!39)) | (~surjective(G!42, B!40, C!39)))))) | (~((~injective(G!42, B!40, C!39)) | (~surjective(G!42, B!40, C!39))))),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[122, 121])).
% 0.18/0.48 tff(124,plain,
% 0.18/0.48 (~((~injective(G!42, B!40, C!39)) | (~surjective(G!42, B!40, C!39)))),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[123, 108])).
% 0.18/0.48 tff(125,plain,
% 0.18/0.48 (((~injective(G!42, B!40, C!39)) | (~surjective(G!42, B!40, C!39))) | surjective(G!42, B!40, C!39)),
% 0.18/0.48 inference(tautology,[status(thm)],[])).
% 0.18/0.48 tff(126,plain,
% 0.18/0.48 (surjective(G!42, B!40, C!39)),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[125, 124])).
% 0.18/0.48 tff(127,plain,
% 0.18/0.48 ((~((~surjective(G!42, B!40, C!39)) | ![Y: $i] : ((~member(Y, C!39)) | (~((~member(tptp_fun_E_19(Y, B!40, G!42), B!40)) | (~apply(G!42, tptp_fun_E_19(Y, B!40, G!42), Y))))))) | (~surjective(G!42, B!40, C!39)) | ![Y: $i] : ((~member(Y, C!39)) | (~((~member(tptp_fun_E_19(Y, B!40, G!42), B!40)) | (~apply(G!42, tptp_fun_E_19(Y, B!40, G!42), Y)))))),
% 0.18/0.48 inference(tautology,[status(thm)],[])).
% 0.18/0.48 tff(128,plain,
% 0.18/0.48 ((~((~surjective(G!42, B!40, C!39)) | ![Y: $i] : ((~member(Y, C!39)) | (~((~member(tptp_fun_E_19(Y, B!40, G!42), B!40)) | (~apply(G!42, tptp_fun_E_19(Y, B!40, G!42), Y))))))) | ![Y: $i] : ((~member(Y, C!39)) | (~((~member(tptp_fun_E_19(Y, B!40, G!42), B!40)) | (~apply(G!42, tptp_fun_E_19(Y, B!40, G!42), Y)))))),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[127, 126])).
% 0.18/0.48 tff(129,plain,
% 0.18/0.48 (![Y: $i] : ((~member(Y, C!39)) | (~((~member(tptp_fun_E_19(Y, B!40, G!42), B!40)) | (~apply(G!42, tptp_fun_E_19(Y, B!40, G!42), Y)))))),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[128, 96])).
% 0.18/0.48 tff(130,plain,
% 0.18/0.48 (((~![Y: $i] : ((~member(Y, C!39)) | (~((~member(tptp_fun_E_19(Y, B!40, G!42), B!40)) | (~apply(G!42, tptp_fun_E_19(Y, B!40, G!42), Y)))))) | ((~member(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~((~member(tptp_fun_E_19(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), B!40)) | (~apply(G!42, tptp_fun_E_19(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))) <=> ((~![Y: $i] : ((~member(Y, C!39)) | (~((~member(tptp_fun_E_19(Y, B!40, G!42), B!40)) | (~apply(G!42, tptp_fun_E_19(Y, B!40, G!42), Y)))))) | (~member(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~((~member(tptp_fun_E_19(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), B!40)) | (~apply(G!42, tptp_fun_E_19(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(131,plain,
% 0.18/0.48 ((~![Y: $i] : ((~member(Y, C!39)) | (~((~member(tptp_fun_E_19(Y, B!40, G!42), B!40)) | (~apply(G!42, tptp_fun_E_19(Y, B!40, G!42), Y)))))) | ((~member(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~((~member(tptp_fun_E_19(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), B!40)) | (~apply(G!42, tptp_fun_E_19(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))),
% 0.18/0.48 inference(quant_inst,[status(thm)],[])).
% 0.18/0.48 tff(132,plain,
% 0.18/0.48 ((~![Y: $i] : ((~member(Y, C!39)) | (~((~member(tptp_fun_E_19(Y, B!40, G!42), B!40)) | (~apply(G!42, tptp_fun_E_19(Y, B!40, G!42), Y)))))) | (~member(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~((~member(tptp_fun_E_19(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), B!40)) | (~apply(G!42, tptp_fun_E_19(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[131, 130])).
% 0.18/0.48 tff(133,plain,
% 0.18/0.48 (~((~member(tptp_fun_E_19(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), B!40)) | (~apply(G!42, tptp_fun_E_19(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[132, 129, 53])).
% 0.18/0.48 tff(134,plain,
% 0.18/0.48 (((~member(tptp_fun_E_19(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), B!40)) | (~apply(G!42, tptp_fun_E_19(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))) | apply(G!42, tptp_fun_E_19(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))),
% 0.18/0.48 inference(tautology,[status(thm)],[])).
% 0.18/0.48 tff(135,plain,
% 0.18/0.48 (apply(G!42, tptp_fun_E_19(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[134, 133])).
% 0.18/0.48 tff(136,plain,
% 0.18/0.48 (((~member(tptp_fun_E_19(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), B!40)) | (~apply(G!42, tptp_fun_E_19(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))) | member(tptp_fun_E_19(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), B!40)),
% 0.18/0.48 inference(tautology,[status(thm)],[])).
% 0.18/0.48 tff(137,plain,
% 0.18/0.48 (member(tptp_fun_E_19(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), B!40)),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[136, 133])).
% 0.18/0.48 tff(138,plain,
% 0.18/0.48 (((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(G!42, B!40, C!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, B!40)) | (~apply(G!42, X1, Y)) | (~member(X1, B!40)) | (~member(Y, C!39)) | (~apply(G!42, X2, Y))))) | (~(injective(G!42, B!40, C!39) | (~((tptp_fun_X1_18(C!39, B!40, G!42) = tptp_fun_X2_17(C!39, B!40, G!42)) | (~apply(G!42, tptp_fun_X1_18(C!39, B!40, G!42), tptp_fun_Y_16(C!39, B!40, G!42))) | (~apply(G!42, tptp_fun_X2_17(C!39, B!40, G!42), tptp_fun_Y_16(C!39, B!40, G!42))) | (~member(tptp_fun_X1_18(C!39, B!40, G!42), B!40)) | (~member(tptp_fun_X2_17(C!39, B!40, G!42), B!40)) | (~member(tptp_fun_Y_16(C!39, B!40, G!42), C!39))))))))) <=> ((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(G!42, B!40, C!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, B!40)) | (~apply(G!42, X1, Y)) | (~member(X1, B!40)) | (~member(Y, C!39)) | (~apply(G!42, X2, Y))))) | (~(injective(G!42, B!40, C!39) | (~((tptp_fun_X1_18(C!39, B!40, G!42) = tptp_fun_X2_17(C!39, B!40, G!42)) | (~apply(G!42, tptp_fun_X1_18(C!39, B!40, G!42), tptp_fun_Y_16(C!39, B!40, G!42))) | (~apply(G!42, tptp_fun_X2_17(C!39, B!40, G!42), tptp_fun_Y_16(C!39, B!40, G!42))) | (~member(tptp_fun_X1_18(C!39, B!40, G!42), B!40)) | (~member(tptp_fun_X2_17(C!39, B!40, G!42), B!40)) | (~member(tptp_fun_Y_16(C!39, B!40, G!42), C!39)))))))))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(139,plain,
% 0.18/0.48 ((~((~((~injective(G!42, B!40, C!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(G!42, X1, Y)) | (~member(X2, B!40)) | (~member(X1, B!40)) | (~member(Y, C!39)) | (~apply(G!42, X2, Y))))) | (~(injective(G!42, B!40, C!39) | (~((tptp_fun_X1_18(C!39, B!40, G!42) = tptp_fun_X2_17(C!39, B!40, G!42)) | (~apply(G!42, tptp_fun_X1_18(C!39, B!40, G!42), tptp_fun_Y_16(C!39, B!40, G!42))) | (~apply(G!42, tptp_fun_X2_17(C!39, B!40, G!42), tptp_fun_Y_16(C!39, B!40, G!42))) | (~member(tptp_fun_X1_18(C!39, B!40, G!42), B!40)) | (~member(tptp_fun_X2_17(C!39, B!40, G!42), B!40)) | (~member(tptp_fun_Y_16(C!39, B!40, G!42), C!39)))))))) <=> (~((~((~injective(G!42, B!40, C!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, B!40)) | (~apply(G!42, X1, Y)) | (~member(X1, B!40)) | (~member(Y, C!39)) | (~apply(G!42, X2, Y))))) | (~(injective(G!42, B!40, C!39) | (~((tptp_fun_X1_18(C!39, B!40, G!42) = tptp_fun_X2_17(C!39, B!40, G!42)) | (~apply(G!42, tptp_fun_X1_18(C!39, B!40, G!42), tptp_fun_Y_16(C!39, B!40, G!42))) | (~apply(G!42, tptp_fun_X2_17(C!39, B!40, G!42), tptp_fun_Y_16(C!39, B!40, G!42))) | (~member(tptp_fun_X1_18(C!39, B!40, G!42), B!40)) | (~member(tptp_fun_X2_17(C!39, B!40, G!42), B!40)) | (~member(tptp_fun_Y_16(C!39, B!40, G!42), C!39))))))))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(140,plain,
% 0.18/0.48 (((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(G!42, B!40, C!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(G!42, X1, Y)) | (~member(X2, B!40)) | (~member(X1, B!40)) | (~member(Y, C!39)) | (~apply(G!42, X2, Y))))) | (~(injective(G!42, B!40, C!39) | (~((tptp_fun_X1_18(C!39, B!40, G!42) = tptp_fun_X2_17(C!39, B!40, G!42)) | (~apply(G!42, tptp_fun_X1_18(C!39, B!40, G!42), tptp_fun_Y_16(C!39, B!40, G!42))) | (~apply(G!42, tptp_fun_X2_17(C!39, B!40, G!42), tptp_fun_Y_16(C!39, B!40, G!42))) | (~member(tptp_fun_X1_18(C!39, B!40, G!42), B!40)) | (~member(tptp_fun_X2_17(C!39, B!40, G!42), B!40)) | (~member(tptp_fun_Y_16(C!39, B!40, G!42), C!39))))))))) <=> ((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(G!42, B!40, C!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, B!40)) | (~apply(G!42, X1, Y)) | (~member(X1, B!40)) | (~member(Y, C!39)) | (~apply(G!42, X2, Y))))) | (~(injective(G!42, B!40, C!39) | (~((tptp_fun_X1_18(C!39, B!40, G!42) = tptp_fun_X2_17(C!39, B!40, G!42)) | (~apply(G!42, tptp_fun_X1_18(C!39, B!40, G!42), tptp_fun_Y_16(C!39, B!40, G!42))) | (~apply(G!42, tptp_fun_X2_17(C!39, B!40, G!42), tptp_fun_Y_16(C!39, B!40, G!42))) | (~member(tptp_fun_X1_18(C!39, B!40, G!42), B!40)) | (~member(tptp_fun_X2_17(C!39, B!40, G!42), B!40)) | (~member(tptp_fun_Y_16(C!39, B!40, G!42), C!39)))))))))),
% 0.18/0.48 inference(monotonicity,[status(thm)],[139])).
% 0.18/0.48 tff(141,plain,
% 0.18/0.48 (((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(G!42, B!40, C!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(G!42, X1, Y)) | (~member(X2, B!40)) | (~member(X1, B!40)) | (~member(Y, C!39)) | (~apply(G!42, X2, Y))))) | (~(injective(G!42, B!40, C!39) | (~((tptp_fun_X1_18(C!39, B!40, G!42) = tptp_fun_X2_17(C!39, B!40, G!42)) | (~apply(G!42, tptp_fun_X1_18(C!39, B!40, G!42), tptp_fun_Y_16(C!39, B!40, G!42))) | (~apply(G!42, tptp_fun_X2_17(C!39, B!40, G!42), tptp_fun_Y_16(C!39, B!40, G!42))) | (~member(tptp_fun_X1_18(C!39, B!40, G!42), B!40)) | (~member(tptp_fun_X2_17(C!39, B!40, G!42), B!40)) | (~member(tptp_fun_Y_16(C!39, B!40, G!42), C!39))))))))) <=> ((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(G!42, B!40, C!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, B!40)) | (~apply(G!42, X1, Y)) | (~member(X1, B!40)) | (~member(Y, C!39)) | (~apply(G!42, X2, Y))))) | (~(injective(G!42, B!40, C!39) | (~((tptp_fun_X1_18(C!39, B!40, G!42) = tptp_fun_X2_17(C!39, B!40, G!42)) | (~apply(G!42, tptp_fun_X1_18(C!39, B!40, G!42), tptp_fun_Y_16(C!39, B!40, G!42))) | (~apply(G!42, tptp_fun_X2_17(C!39, B!40, G!42), tptp_fun_Y_16(C!39, B!40, G!42))) | (~member(tptp_fun_X1_18(C!39, B!40, G!42), B!40)) | (~member(tptp_fun_X2_17(C!39, B!40, G!42), B!40)) | (~member(tptp_fun_Y_16(C!39, B!40, G!42), C!39)))))))))),
% 0.18/0.48 inference(transitivity,[status(thm)],[140, 138])).
% 0.18/0.48 tff(142,plain,
% 0.18/0.48 ((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(G!42, B!40, C!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(G!42, X1, Y)) | (~member(X2, B!40)) | (~member(X1, B!40)) | (~member(Y, C!39)) | (~apply(G!42, X2, Y))))) | (~(injective(G!42, B!40, C!39) | (~((tptp_fun_X1_18(C!39, B!40, G!42) = tptp_fun_X2_17(C!39, B!40, G!42)) | (~apply(G!42, tptp_fun_X1_18(C!39, B!40, G!42), tptp_fun_Y_16(C!39, B!40, G!42))) | (~apply(G!42, tptp_fun_X2_17(C!39, B!40, G!42), tptp_fun_Y_16(C!39, B!40, G!42))) | (~member(tptp_fun_X1_18(C!39, B!40, G!42), B!40)) | (~member(tptp_fun_X2_17(C!39, B!40, G!42), B!40)) | (~member(tptp_fun_Y_16(C!39, B!40, G!42), C!39))))))))),
% 0.18/0.48 inference(quant_inst,[status(thm)],[])).
% 0.18/0.48 tff(143,plain,
% 0.18/0.48 ((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(G!42, B!40, C!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, B!40)) | (~apply(G!42, X1, Y)) | (~member(X1, B!40)) | (~member(Y, C!39)) | (~apply(G!42, X2, Y))))) | (~(injective(G!42, B!40, C!39) | (~((tptp_fun_X1_18(C!39, B!40, G!42) = tptp_fun_X2_17(C!39, B!40, G!42)) | (~apply(G!42, tptp_fun_X1_18(C!39, B!40, G!42), tptp_fun_Y_16(C!39, B!40, G!42))) | (~apply(G!42, tptp_fun_X2_17(C!39, B!40, G!42), tptp_fun_Y_16(C!39, B!40, G!42))) | (~member(tptp_fun_X1_18(C!39, B!40, G!42), B!40)) | (~member(tptp_fun_X2_17(C!39, B!40, G!42), B!40)) | (~member(tptp_fun_Y_16(C!39, B!40, G!42), C!39))))))))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[142, 141])).
% 0.18/0.48 tff(144,plain,
% 0.18/0.48 (~((~((~injective(G!42, B!40, C!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, B!40)) | (~apply(G!42, X1, Y)) | (~member(X1, B!40)) | (~member(Y, C!39)) | (~apply(G!42, X2, Y))))) | (~(injective(G!42, B!40, C!39) | (~((tptp_fun_X1_18(C!39, B!40, G!42) = tptp_fun_X2_17(C!39, B!40, G!42)) | (~apply(G!42, tptp_fun_X1_18(C!39, B!40, G!42), tptp_fun_Y_16(C!39, B!40, G!42))) | (~apply(G!42, tptp_fun_X2_17(C!39, B!40, G!42), tptp_fun_Y_16(C!39, B!40, G!42))) | (~member(tptp_fun_X1_18(C!39, B!40, G!42), B!40)) | (~member(tptp_fun_X2_17(C!39, B!40, G!42), B!40)) | (~member(tptp_fun_Y_16(C!39, B!40, G!42), C!39)))))))),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[143, 40])).
% 0.18/0.49 tff(145,plain,
% 0.18/0.49 (((~((~injective(G!42, B!40, C!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, B!40)) | (~apply(G!42, X1, Y)) | (~member(X1, B!40)) | (~member(Y, C!39)) | (~apply(G!42, X2, Y))))) | (~(injective(G!42, B!40, C!39) | (~((tptp_fun_X1_18(C!39, B!40, G!42) = tptp_fun_X2_17(C!39, B!40, G!42)) | (~apply(G!42, tptp_fun_X1_18(C!39, B!40, G!42), tptp_fun_Y_16(C!39, B!40, G!42))) | (~apply(G!42, tptp_fun_X2_17(C!39, B!40, G!42), tptp_fun_Y_16(C!39, B!40, G!42))) | (~member(tptp_fun_X1_18(C!39, B!40, G!42), B!40)) | (~member(tptp_fun_X2_17(C!39, B!40, G!42), B!40)) | (~member(tptp_fun_Y_16(C!39, B!40, G!42), C!39))))))) | ((~injective(G!42, B!40, C!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, B!40)) | (~apply(G!42, X1, Y)) | (~member(X1, B!40)) | (~member(Y, C!39)) | (~apply(G!42, X2, Y))))),
% 0.18/0.49 inference(tautology,[status(thm)],[])).
% 0.18/0.49 tff(146,plain,
% 0.18/0.49 ((~injective(G!42, B!40, C!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, B!40)) | (~apply(G!42, X1, Y)) | (~member(X1, B!40)) | (~member(Y, C!39)) | (~apply(G!42, X2, Y)))),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[145, 144])).
% 0.18/0.49 tff(147,plain,
% 0.18/0.49 (((~injective(G!42, B!40, C!39)) | (~surjective(G!42, B!40, C!39))) | injective(G!42, B!40, C!39)),
% 0.18/0.49 inference(tautology,[status(thm)],[])).
% 0.18/0.49 tff(148,plain,
% 0.18/0.49 (injective(G!42, B!40, C!39)),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[147, 124])).
% 0.18/0.49 tff(149,plain,
% 0.18/0.49 ((~((~injective(G!42, B!40, C!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, B!40)) | (~apply(G!42, X1, Y)) | (~member(X1, B!40)) | (~member(Y, C!39)) | (~apply(G!42, X2, Y))))) | (~injective(G!42, B!40, C!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, B!40)) | (~apply(G!42, X1, Y)) | (~member(X1, B!40)) | (~member(Y, C!39)) | (~apply(G!42, X2, Y)))),
% 0.18/0.49 inference(tautology,[status(thm)],[])).
% 0.18/0.49 tff(150,plain,
% 0.18/0.49 ((~((~injective(G!42, B!40, C!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, B!40)) | (~apply(G!42, X1, Y)) | (~member(X1, B!40)) | (~member(Y, C!39)) | (~apply(G!42, X2, Y))))) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, B!40)) | (~apply(G!42, X1, Y)) | (~member(X1, B!40)) | (~member(Y, C!39)) | (~apply(G!42, X2, Y)))),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[149, 148])).
% 0.18/0.49 tff(151,plain,
% 0.18/0.49 (![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, B!40)) | (~apply(G!42, X1, Y)) | (~member(X1, B!40)) | (~member(Y, C!39)) | (~apply(G!42, X2, Y)))),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[150, 146])).
% 0.18/0.49 tff(152,plain,
% 0.18/0.49 (((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, B!40)) | (~apply(G!42, X1, Y)) | (~member(X1, B!40)) | (~member(Y, C!39)) | (~apply(G!42, X2, Y)))) | ((~member(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_E_19(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), B!40)) | (~apply(G!42, tptp_fun_E_19(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42) = tptp_fun_E_19(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42)))) <=> ((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, B!40)) | (~apply(G!42, X1, Y)) | (~member(X1, B!40)) | (~member(Y, C!39)) | (~apply(G!42, X2, Y)))) | (~member(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_E_19(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), B!40)) | (~apply(G!42, tptp_fun_E_19(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42) = tptp_fun_E_19(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42)))),
% 0.18/0.49 inference(rewrite,[status(thm)],[])).
% 0.18/0.49 tff(153,plain,
% 0.18/0.49 (((tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42) = tptp_fun_E_19(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42)) | (~member(tptp_fun_E_19(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), B!40)) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~member(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~apply(G!42, tptp_fun_E_19(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))) <=> ((~member(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_E_19(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), B!40)) | (~apply(G!42, tptp_fun_E_19(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42) = tptp_fun_E_19(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42)))),
% 0.18/0.49 inference(rewrite,[status(thm)],[])).
% 0.18/0.49 tff(154,plain,
% 0.18/0.49 (((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, B!40)) | (~apply(G!42, X1, Y)) | (~member(X1, B!40)) | (~member(Y, C!39)) | (~apply(G!42, X2, Y)))) | ((tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42) = tptp_fun_E_19(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42)) | (~member(tptp_fun_E_19(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), B!40)) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~member(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~apply(G!42, tptp_fun_E_19(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))) <=> ((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, B!40)) | (~apply(G!42, X1, Y)) | (~member(X1, B!40)) | (~member(Y, C!39)) | (~apply(G!42, X2, Y)))) | ((~member(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_E_19(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), B!40)) | (~apply(G!42, tptp_fun_E_19(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42) = tptp_fun_E_19(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42))))),
% 0.18/0.49 inference(monotonicity,[status(thm)],[153])).
% 0.18/0.49 tff(155,plain,
% 0.18/0.49 (((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, B!40)) | (~apply(G!42, X1, Y)) | (~member(X1, B!40)) | (~member(Y, C!39)) | (~apply(G!42, X2, Y)))) | ((tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42) = tptp_fun_E_19(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42)) | (~member(tptp_fun_E_19(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), B!40)) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~member(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~apply(G!42, tptp_fun_E_19(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))) <=> ((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, B!40)) | (~apply(G!42, X1, Y)) | (~member(X1, B!40)) | (~member(Y, C!39)) | (~apply(G!42, X2, Y)))) | (~member(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_E_19(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), B!40)) | (~apply(G!42, tptp_fun_E_19(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42) = tptp_fun_E_19(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42)))),
% 0.18/0.49 inference(transitivity,[status(thm)],[154, 152])).
% 0.18/0.49 tff(156,plain,
% 0.18/0.49 ((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, B!40)) | (~apply(G!42, X1, Y)) | (~member(X1, B!40)) | (~member(Y, C!39)) | (~apply(G!42, X2, Y)))) | ((tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42) = tptp_fun_E_19(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42)) | (~member(tptp_fun_E_19(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), B!40)) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~member(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~apply(G!42, tptp_fun_E_19(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))),
% 0.18/0.49 inference(quant_inst,[status(thm)],[])).
% 0.18/0.49 tff(157,plain,
% 0.18/0.49 ((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, B!40)) | (~apply(G!42, X1, Y)) | (~member(X1, B!40)) | (~member(Y, C!39)) | (~apply(G!42, X2, Y)))) | (~member(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_E_19(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), B!40)) | (~apply(G!42, tptp_fun_E_19(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42) = tptp_fun_E_19(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42))),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[156, 155])).
% 0.18/0.49 tff(158,plain,
% 0.18/0.49 (tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42) = tptp_fun_E_19(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42)),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[157, 151, 53, 137, 135, 92, 90])).
% 0.18/0.49 tff(159,plain,
% 0.18/0.49 (tptp_fun_E_19(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42) = tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42)),
% 0.18/0.49 inference(symmetry,[status(thm)],[158])).
% 0.18/0.49 tff(160,plain,
% 0.18/0.49 (apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_E_19(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42)) <=> apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))),
% 0.18/0.49 inference(monotonicity,[status(thm)],[159])).
% 0.18/0.49 tff(161,plain,
% 0.18/0.49 (apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42)) <=> apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_E_19(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42))),
% 0.18/0.49 inference(symmetry,[status(thm)],[160])).
% 0.18/0.49 tff(162,plain,
% 0.18/0.49 (((~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))) | apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))),
% 0.18/0.49 inference(tautology,[status(thm)],[])).
% 0.18/0.49 tff(163,plain,
% 0.18/0.49 (apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[162, 88])).
% 0.18/0.49 tff(164,plain,
% 0.18/0.49 (apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_E_19(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[163, 161])).
% 0.18/0.50 tff(165,plain,
% 0.18/0.50 (((tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)) = tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~member(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39))) | member(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)),
% 0.18/0.50 inference(tautology,[status(thm)],[])).
% 0.18/0.50 tff(166,plain,
% 0.18/0.50 (member(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[165, 51])).
% 0.18/0.50 tff(167,plain,
% 0.18/0.50 (((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~((~((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))) | (~(apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))))))) <=> ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | (~member(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~((~((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))) | (~(apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))))))),
% 0.18/0.50 inference(rewrite,[status(thm)],[])).
% 0.18/0.50 tff(168,plain,
% 0.18/0.50 (((~member(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~((~((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))) | (~(apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))))) <=> ((~member(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~((~((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))) | (~(apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))))))),
% 0.18/0.50 inference(rewrite,[status(thm)],[])).
% 0.18/0.50 tff(169,plain,
% 0.18/0.50 ((~((~((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))) | (~(apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))))) <=> (~((~((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))) | (~(apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))))),
% 0.18/0.50 inference(rewrite,[status(thm)],[])).
% 0.18/0.50 tff(170,plain,
% 0.18/0.50 (((~member(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~((~((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))) | (~(apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))))) <=> ((~member(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~((~((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))) | (~(apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))))))),
% 0.18/0.51 inference(monotonicity,[status(thm)],[169])).
% 0.18/0.51 tff(171,plain,
% 0.18/0.51 (((~member(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~((~((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))) | (~(apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))))) <=> ((~member(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~((~((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))) | (~(apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))))))),
% 0.18/0.51 inference(transitivity,[status(thm)],[170, 168])).
% 0.18/0.51 tff(172,plain,
% 0.18/0.51 (((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~((~((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))) | (~(apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))))))) <=> ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~((~((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))) | (~(apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))))))),
% 0.18/0.51 inference(monotonicity,[status(thm)],[171])).
% 0.18/0.51 tff(173,plain,
% 0.18/0.51 (((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~((~((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))) | (~(apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))))))) <=> ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | (~member(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~((~((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))) | (~(apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))))))),
% 0.18/0.51 inference(transitivity,[status(thm)],[172, 167])).
% 0.18/0.51 tff(174,plain,
% 0.18/0.51 ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~((~((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))) | (~(apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))))))),
% 0.18/0.51 inference(quant_inst,[status(thm)],[])).
% 0.18/0.51 tff(175,plain,
% 0.18/0.51 ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | (~member(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~((~((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))) | (~(apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))))),
% 0.18/0.51 inference(modus_ponens,[status(thm)],[174, 173])).
% 0.18/0.51 tff(176,plain,
% 0.18/0.51 (~((~((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))) | (~(apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))))),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[175, 71, 166, 53])).
% 0.18/0.51 tff(177,plain,
% 0.18/0.51 (((~((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))) | (~(apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), Y)) | (~apply(G!42, Y, tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))) | ((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))),
% 0.18/0.52 inference(tautology,[status(thm)],[])).
% 0.18/0.52 tff(178,plain,
% 0.18/0.52 ((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))),
% 0.18/0.52 inference(unit_resolution,[status(thm)],[177, 176])).
% 0.18/0.52 tff(179,plain,
% 0.18/0.52 (((tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)) = tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~member(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39))) | apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))),
% 0.18/0.52 inference(tautology,[status(thm)],[])).
% 0.18/0.52 tff(180,plain,
% 0.18/0.52 (apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))),
% 0.18/0.52 inference(unit_resolution,[status(thm)],[179, 51])).
% 0.18/0.52 tff(181,plain,
% 0.18/0.52 ((~((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))),
% 0.18/0.52 inference(tautology,[status(thm)],[])).
% 0.18/0.52 tff(182,plain,
% 0.18/0.52 ((~((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))),
% 0.18/0.52 inference(unit_resolution,[status(thm)],[181, 180])).
% 0.18/0.52 tff(183,plain,
% 0.18/0.52 (~((~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))),
% 0.18/0.52 inference(unit_resolution,[status(thm)],[182, 178])).
% 0.18/0.52 tff(184,plain,
% 0.18/0.52 (((~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))) | apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))),
% 0.18/0.52 inference(tautology,[status(thm)],[])).
% 0.18/0.52 tff(185,plain,
% 0.18/0.52 (apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))),
% 0.18/0.52 inference(unit_resolution,[status(thm)],[184, 183])).
% 0.18/0.52 tff(186,plain,
% 0.18/0.52 (((~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))) | member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)),
% 0.18/0.52 inference(tautology,[status(thm)],[])).
% 0.18/0.52 tff(187,plain,
% 0.18/0.52 (member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)),
% 0.18/0.52 inference(unit_resolution,[status(thm)],[186, 183])).
% 0.18/0.52 tff(188,plain,
% 0.18/0.52 (((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, B!40)) | (~apply(G!42, X1, Y)) | (~member(X1, B!40)) | (~member(Y, C!39)) | (~apply(G!42, X2, Y)))) | ((~member(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_E_19(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), B!40)) | (~apply(G!42, tptp_fun_E_19(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42) = tptp_fun_E_19(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42)))) <=> ((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, B!40)) | (~apply(G!42, X1, Y)) | (~member(X1, B!40)) | (~member(Y, C!39)) | (~apply(G!42, X2, Y)))) | (~member(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_E_19(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), B!40)) | (~apply(G!42, tptp_fun_E_19(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42) = tptp_fun_E_19(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42)))),
% 0.18/0.52 inference(rewrite,[status(thm)],[])).
% 0.18/0.52 tff(189,plain,
% 0.18/0.52 (((tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42) = tptp_fun_E_19(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42)) | (~member(tptp_fun_E_19(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), B!40)) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~member(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~apply(G!42, tptp_fun_E_19(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))) <=> ((~member(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_E_19(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), B!40)) | (~apply(G!42, tptp_fun_E_19(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42) = tptp_fun_E_19(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42)))),
% 0.18/0.53 inference(rewrite,[status(thm)],[])).
% 0.18/0.53 tff(190,plain,
% 0.18/0.53 (((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, B!40)) | (~apply(G!42, X1, Y)) | (~member(X1, B!40)) | (~member(Y, C!39)) | (~apply(G!42, X2, Y)))) | ((tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42) = tptp_fun_E_19(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42)) | (~member(tptp_fun_E_19(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), B!40)) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~member(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~apply(G!42, tptp_fun_E_19(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))) <=> ((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, B!40)) | (~apply(G!42, X1, Y)) | (~member(X1, B!40)) | (~member(Y, C!39)) | (~apply(G!42, X2, Y)))) | ((~member(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_E_19(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), B!40)) | (~apply(G!42, tptp_fun_E_19(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42) = tptp_fun_E_19(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42))))),
% 0.18/0.53 inference(monotonicity,[status(thm)],[189])).
% 0.18/0.53 tff(191,plain,
% 0.18/0.53 (((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, B!40)) | (~apply(G!42, X1, Y)) | (~member(X1, B!40)) | (~member(Y, C!39)) | (~apply(G!42, X2, Y)))) | ((tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42) = tptp_fun_E_19(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42)) | (~member(tptp_fun_E_19(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), B!40)) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~member(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~apply(G!42, tptp_fun_E_19(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))) <=> ((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, B!40)) | (~apply(G!42, X1, Y)) | (~member(X1, B!40)) | (~member(Y, C!39)) | (~apply(G!42, X2, Y)))) | (~member(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_E_19(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), B!40)) | (~apply(G!42, tptp_fun_E_19(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42) = tptp_fun_E_19(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42)))),
% 0.18/0.53 inference(transitivity,[status(thm)],[190, 188])).
% 0.18/0.53 tff(192,plain,
% 0.18/0.53 ((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, B!40)) | (~apply(G!42, X1, Y)) | (~member(X1, B!40)) | (~member(Y, C!39)) | (~apply(G!42, X2, Y)))) | ((tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42) = tptp_fun_E_19(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42)) | (~member(tptp_fun_E_19(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), B!40)) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~member(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~apply(G!42, tptp_fun_E_19(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))),
% 0.18/0.53 inference(quant_inst,[status(thm)],[])).
% 0.18/0.53 tff(193,plain,
% 0.18/0.53 ((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, B!40)) | (~apply(G!42, X1, Y)) | (~member(X1, B!40)) | (~member(Y, C!39)) | (~apply(G!42, X2, Y)))) | (~member(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_E_19(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), B!40)) | (~apply(G!42, tptp_fun_E_19(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42) = tptp_fun_E_19(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42))),
% 0.18/0.53 inference(modus_ponens,[status(thm)],[192, 191])).
% 0.18/0.53 tff(194,plain,
% 0.18/0.53 (tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42) = tptp_fun_E_19(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42)),
% 0.18/0.53 inference(unit_resolution,[status(thm)],[193, 151, 53, 137, 135, 187, 185])).
% 0.18/0.53 tff(195,plain,
% 0.18/0.53 (tptp_fun_E_19(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42) = tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42)),
% 0.18/0.53 inference(symmetry,[status(thm)],[194])).
% 0.18/0.53 tff(196,plain,
% 0.18/0.53 (apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_E_19(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42)) <=> apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))),
% 0.18/0.53 inference(monotonicity,[status(thm)],[195])).
% 0.18/0.53 tff(197,plain,
% 0.18/0.53 (apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42)) <=> apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_E_19(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42))),
% 0.18/0.53 inference(symmetry,[status(thm)],[196])).
% 0.18/0.53 tff(198,plain,
% 0.18/0.53 (((~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))) | apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))),
% 0.18/0.53 inference(tautology,[status(thm)],[])).
% 0.18/0.53 tff(199,plain,
% 0.18/0.53 (apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))),
% 0.18/0.53 inference(unit_resolution,[status(thm)],[198, 183])).
% 0.18/0.53 tff(200,plain,
% 0.18/0.53 (apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_E_19(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42))),
% 0.18/0.53 inference(modus_ponens,[status(thm)],[199, 197])).
% 0.18/0.53 tff(201,plain,
% 0.18/0.53 (((tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)) = tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~member(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39))) | (~(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)) = tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))),
% 0.18/0.53 inference(tautology,[status(thm)],[])).
% 0.18/0.53 tff(202,plain,
% 0.18/0.53 (~(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)) = tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))),
% 0.18/0.53 inference(unit_resolution,[status(thm)],[201, 51])).
% 0.18/0.53 tff(203,plain,
% 0.18/0.53 (((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(F!43, A!41, B!40)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!43, X1, Y)) | (~member(X1, A!41)) | (~member(Y, B!40)) | (~member(X2, A!41)) | (~apply(F!43, X2, Y))))) | (~(injective(F!43, A!41, B!40) | (~((tptp_fun_X1_18(B!40, A!41, F!43) = tptp_fun_X2_17(B!40, A!41, F!43)) | (~apply(F!43, tptp_fun_X1_18(B!40, A!41, F!43), tptp_fun_Y_16(B!40, A!41, F!43))) | (~apply(F!43, tptp_fun_X2_17(B!40, A!41, F!43), tptp_fun_Y_16(B!40, A!41, F!43))) | (~member(tptp_fun_X1_18(B!40, A!41, F!43), A!41)) | (~member(tptp_fun_X2_17(B!40, A!41, F!43), A!41)) | (~member(tptp_fun_Y_16(B!40, A!41, F!43), B!40))))))))) <=> ((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(F!43, A!41, B!40)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!43, X1, Y)) | (~member(X1, A!41)) | (~member(Y, B!40)) | (~member(X2, A!41)) | (~apply(F!43, X2, Y))))) | (~(injective(F!43, A!41, B!40) | (~((tptp_fun_X1_18(B!40, A!41, F!43) = tptp_fun_X2_17(B!40, A!41, F!43)) | (~apply(F!43, tptp_fun_X1_18(B!40, A!41, F!43), tptp_fun_Y_16(B!40, A!41, F!43))) | (~apply(F!43, tptp_fun_X2_17(B!40, A!41, F!43), tptp_fun_Y_16(B!40, A!41, F!43))) | (~member(tptp_fun_X1_18(B!40, A!41, F!43), A!41)) | (~member(tptp_fun_X2_17(B!40, A!41, F!43), A!41)) | (~member(tptp_fun_Y_16(B!40, A!41, F!43), B!40)))))))))),
% 0.18/0.53 inference(rewrite,[status(thm)],[])).
% 0.18/0.53 tff(204,plain,
% 0.18/0.53 ((~((~((~injective(F!43, A!41, B!40)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!43, X1, Y)) | (~member(X2, A!41)) | (~member(X1, A!41)) | (~member(Y, B!40)) | (~apply(F!43, X2, Y))))) | (~(injective(F!43, A!41, B!40) | (~((tptp_fun_X1_18(B!40, A!41, F!43) = tptp_fun_X2_17(B!40, A!41, F!43)) | (~apply(F!43, tptp_fun_X1_18(B!40, A!41, F!43), tptp_fun_Y_16(B!40, A!41, F!43))) | (~apply(F!43, tptp_fun_X2_17(B!40, A!41, F!43), tptp_fun_Y_16(B!40, A!41, F!43))) | (~member(tptp_fun_X1_18(B!40, A!41, F!43), A!41)) | (~member(tptp_fun_X2_17(B!40, A!41, F!43), A!41)) | (~member(tptp_fun_Y_16(B!40, A!41, F!43), B!40)))))))) <=> (~((~((~injective(F!43, A!41, B!40)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!43, X1, Y)) | (~member(X1, A!41)) | (~member(Y, B!40)) | (~member(X2, A!41)) | (~apply(F!43, X2, Y))))) | (~(injective(F!43, A!41, B!40) | (~((tptp_fun_X1_18(B!40, A!41, F!43) = tptp_fun_X2_17(B!40, A!41, F!43)) | (~apply(F!43, tptp_fun_X1_18(B!40, A!41, F!43), tptp_fun_Y_16(B!40, A!41, F!43))) | (~apply(F!43, tptp_fun_X2_17(B!40, A!41, F!43), tptp_fun_Y_16(B!40, A!41, F!43))) | (~member(tptp_fun_X1_18(B!40, A!41, F!43), A!41)) | (~member(tptp_fun_X2_17(B!40, A!41, F!43), A!41)) | (~member(tptp_fun_Y_16(B!40, A!41, F!43), B!40))))))))),
% 0.18/0.53 inference(rewrite,[status(thm)],[])).
% 0.18/0.53 tff(205,plain,
% 0.18/0.53 (((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(F!43, A!41, B!40)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!43, X1, Y)) | (~member(X2, A!41)) | (~member(X1, A!41)) | (~member(Y, B!40)) | (~apply(F!43, X2, Y))))) | (~(injective(F!43, A!41, B!40) | (~((tptp_fun_X1_18(B!40, A!41, F!43) = tptp_fun_X2_17(B!40, A!41, F!43)) | (~apply(F!43, tptp_fun_X1_18(B!40, A!41, F!43), tptp_fun_Y_16(B!40, A!41, F!43))) | (~apply(F!43, tptp_fun_X2_17(B!40, A!41, F!43), tptp_fun_Y_16(B!40, A!41, F!43))) | (~member(tptp_fun_X1_18(B!40, A!41, F!43), A!41)) | (~member(tptp_fun_X2_17(B!40, A!41, F!43), A!41)) | (~member(tptp_fun_Y_16(B!40, A!41, F!43), B!40))))))))) <=> ((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(F!43, A!41, B!40)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!43, X1, Y)) | (~member(X1, A!41)) | (~member(Y, B!40)) | (~member(X2, A!41)) | (~apply(F!43, X2, Y))))) | (~(injective(F!43, A!41, B!40) | (~((tptp_fun_X1_18(B!40, A!41, F!43) = tptp_fun_X2_17(B!40, A!41, F!43)) | (~apply(F!43, tptp_fun_X1_18(B!40, A!41, F!43), tptp_fun_Y_16(B!40, A!41, F!43))) | (~apply(F!43, tptp_fun_X2_17(B!40, A!41, F!43), tptp_fun_Y_16(B!40, A!41, F!43))) | (~member(tptp_fun_X1_18(B!40, A!41, F!43), A!41)) | (~member(tptp_fun_X2_17(B!40, A!41, F!43), A!41)) | (~member(tptp_fun_Y_16(B!40, A!41, F!43), B!40)))))))))),
% 0.18/0.53 inference(monotonicity,[status(thm)],[204])).
% 0.18/0.53 tff(206,plain,
% 0.18/0.53 (((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(F!43, A!41, B!40)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!43, X1, Y)) | (~member(X2, A!41)) | (~member(X1, A!41)) | (~member(Y, B!40)) | (~apply(F!43, X2, Y))))) | (~(injective(F!43, A!41, B!40) | (~((tptp_fun_X1_18(B!40, A!41, F!43) = tptp_fun_X2_17(B!40, A!41, F!43)) | (~apply(F!43, tptp_fun_X1_18(B!40, A!41, F!43), tptp_fun_Y_16(B!40, A!41, F!43))) | (~apply(F!43, tptp_fun_X2_17(B!40, A!41, F!43), tptp_fun_Y_16(B!40, A!41, F!43))) | (~member(tptp_fun_X1_18(B!40, A!41, F!43), A!41)) | (~member(tptp_fun_X2_17(B!40, A!41, F!43), A!41)) | (~member(tptp_fun_Y_16(B!40, A!41, F!43), B!40))))))))) <=> ((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(F!43, A!41, B!40)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!43, X1, Y)) | (~member(X1, A!41)) | (~member(Y, B!40)) | (~member(X2, A!41)) | (~apply(F!43, X2, Y))))) | (~(injective(F!43, A!41, B!40) | (~((tptp_fun_X1_18(B!40, A!41, F!43) = tptp_fun_X2_17(B!40, A!41, F!43)) | (~apply(F!43, tptp_fun_X1_18(B!40, A!41, F!43), tptp_fun_Y_16(B!40, A!41, F!43))) | (~apply(F!43, tptp_fun_X2_17(B!40, A!41, F!43), tptp_fun_Y_16(B!40, A!41, F!43))) | (~member(tptp_fun_X1_18(B!40, A!41, F!43), A!41)) | (~member(tptp_fun_X2_17(B!40, A!41, F!43), A!41)) | (~member(tptp_fun_Y_16(B!40, A!41, F!43), B!40)))))))))),
% 0.18/0.54 inference(transitivity,[status(thm)],[205, 203])).
% 0.18/0.54 tff(207,plain,
% 0.18/0.54 ((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(F!43, A!41, B!40)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!43, X1, Y)) | (~member(X2, A!41)) | (~member(X1, A!41)) | (~member(Y, B!40)) | (~apply(F!43, X2, Y))))) | (~(injective(F!43, A!41, B!40) | (~((tptp_fun_X1_18(B!40, A!41, F!43) = tptp_fun_X2_17(B!40, A!41, F!43)) | (~apply(F!43, tptp_fun_X1_18(B!40, A!41, F!43), tptp_fun_Y_16(B!40, A!41, F!43))) | (~apply(F!43, tptp_fun_X2_17(B!40, A!41, F!43), tptp_fun_Y_16(B!40, A!41, F!43))) | (~member(tptp_fun_X1_18(B!40, A!41, F!43), A!41)) | (~member(tptp_fun_X2_17(B!40, A!41, F!43), A!41)) | (~member(tptp_fun_Y_16(B!40, A!41, F!43), B!40))))))))),
% 0.18/0.54 inference(quant_inst,[status(thm)],[])).
% 0.18/0.54 tff(208,plain,
% 0.18/0.54 ((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(F!43, A!41, B!40)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!43, X1, Y)) | (~member(X1, A!41)) | (~member(Y, B!40)) | (~member(X2, A!41)) | (~apply(F!43, X2, Y))))) | (~(injective(F!43, A!41, B!40) | (~((tptp_fun_X1_18(B!40, A!41, F!43) = tptp_fun_X2_17(B!40, A!41, F!43)) | (~apply(F!43, tptp_fun_X1_18(B!40, A!41, F!43), tptp_fun_Y_16(B!40, A!41, F!43))) | (~apply(F!43, tptp_fun_X2_17(B!40, A!41, F!43), tptp_fun_Y_16(B!40, A!41, F!43))) | (~member(tptp_fun_X1_18(B!40, A!41, F!43), A!41)) | (~member(tptp_fun_X2_17(B!40, A!41, F!43), A!41)) | (~member(tptp_fun_Y_16(B!40, A!41, F!43), B!40))))))))),
% 0.18/0.54 inference(modus_ponens,[status(thm)],[207, 206])).
% 0.18/0.54 tff(209,plain,
% 0.18/0.54 (~((~((~injective(F!43, A!41, B!40)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!43, X1, Y)) | (~member(X1, A!41)) | (~member(Y, B!40)) | (~member(X2, A!41)) | (~apply(F!43, X2, Y))))) | (~(injective(F!43, A!41, B!40) | (~((tptp_fun_X1_18(B!40, A!41, F!43) = tptp_fun_X2_17(B!40, A!41, F!43)) | (~apply(F!43, tptp_fun_X1_18(B!40, A!41, F!43), tptp_fun_Y_16(B!40, A!41, F!43))) | (~apply(F!43, tptp_fun_X2_17(B!40, A!41, F!43), tptp_fun_Y_16(B!40, A!41, F!43))) | (~member(tptp_fun_X1_18(B!40, A!41, F!43), A!41)) | (~member(tptp_fun_X2_17(B!40, A!41, F!43), A!41)) | (~member(tptp_fun_Y_16(B!40, A!41, F!43), B!40)))))))),
% 0.18/0.54 inference(unit_resolution,[status(thm)],[208, 40])).
% 0.18/0.54 tff(210,plain,
% 0.18/0.54 (((~((~injective(F!43, A!41, B!40)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!43, X1, Y)) | (~member(X1, A!41)) | (~member(Y, B!40)) | (~member(X2, A!41)) | (~apply(F!43, X2, Y))))) | (~(injective(F!43, A!41, B!40) | (~((tptp_fun_X1_18(B!40, A!41, F!43) = tptp_fun_X2_17(B!40, A!41, F!43)) | (~apply(F!43, tptp_fun_X1_18(B!40, A!41, F!43), tptp_fun_Y_16(B!40, A!41, F!43))) | (~apply(F!43, tptp_fun_X2_17(B!40, A!41, F!43), tptp_fun_Y_16(B!40, A!41, F!43))) | (~member(tptp_fun_X1_18(B!40, A!41, F!43), A!41)) | (~member(tptp_fun_X2_17(B!40, A!41, F!43), A!41)) | (~member(tptp_fun_Y_16(B!40, A!41, F!43), B!40))))))) | ((~injective(F!43, A!41, B!40)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!43, X1, Y)) | (~member(X1, A!41)) | (~member(Y, B!40)) | (~member(X2, A!41)) | (~apply(F!43, X2, Y))))),
% 0.18/0.54 inference(tautology,[status(thm)],[])).
% 0.18/0.54 tff(211,plain,
% 0.18/0.54 ((~injective(F!43, A!41, B!40)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!43, X1, Y)) | (~member(X1, A!41)) | (~member(Y, B!40)) | (~member(X2, A!41)) | (~apply(F!43, X2, Y)))),
% 0.18/0.54 inference(unit_resolution,[status(thm)],[210, 209])).
% 0.18/0.54 tff(212,plain,
% 0.18/0.54 ((~![F: $i, A: $i, B: $i] : (one_to_one(F, A, B) <=> (~((~injective(F, A, B)) | (~surjective(F, A, B)))))) | (one_to_one(F!43, A!41, B!40) <=> (~((~injective(F!43, A!41, B!40)) | (~surjective(F!43, A!41, B!40)))))),
% 0.18/0.54 inference(quant_inst,[status(thm)],[])).
% 0.18/0.54 tff(213,plain,
% 0.18/0.54 (one_to_one(F!43, A!41, B!40) <=> (~((~injective(F!43, A!41, B!40)) | (~surjective(F!43, A!41, B!40))))),
% 0.18/0.54 inference(unit_resolution,[status(thm)],[212, 106])).
% 0.18/0.54 tff(214,plain,
% 0.18/0.54 (one_to_one(F!43, A!41, B!40)),
% 0.18/0.54 inference(and_elim,[status(thm)],[120])).
% 0.18/0.54 tff(215,plain,
% 0.18/0.54 ((~(one_to_one(F!43, A!41, B!40) <=> (~((~injective(F!43, A!41, B!40)) | (~surjective(F!43, A!41, B!40)))))) | (~one_to_one(F!43, A!41, B!40)) | (~((~injective(F!43, A!41, B!40)) | (~surjective(F!43, A!41, B!40))))),
% 0.18/0.54 inference(tautology,[status(thm)],[])).
% 0.18/0.54 tff(216,plain,
% 0.18/0.54 ((~(one_to_one(F!43, A!41, B!40) <=> (~((~injective(F!43, A!41, B!40)) | (~surjective(F!43, A!41, B!40)))))) | (~((~injective(F!43, A!41, B!40)) | (~surjective(F!43, A!41, B!40))))),
% 0.18/0.54 inference(unit_resolution,[status(thm)],[215, 214])).
% 0.18/0.54 tff(217,plain,
% 0.18/0.54 (~((~injective(F!43, A!41, B!40)) | (~surjective(F!43, A!41, B!40)))),
% 0.18/0.54 inference(unit_resolution,[status(thm)],[216, 213])).
% 0.18/0.54 tff(218,plain,
% 0.18/0.54 (((~injective(F!43, A!41, B!40)) | (~surjective(F!43, A!41, B!40))) | injective(F!43, A!41, B!40)),
% 0.18/0.54 inference(tautology,[status(thm)],[])).
% 0.18/0.54 tff(219,plain,
% 0.18/0.54 (injective(F!43, A!41, B!40)),
% 0.18/0.54 inference(unit_resolution,[status(thm)],[218, 217])).
% 0.18/0.54 tff(220,plain,
% 0.18/0.54 ((~((~injective(F!43, A!41, B!40)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!43, X1, Y)) | (~member(X1, A!41)) | (~member(Y, B!40)) | (~member(X2, A!41)) | (~apply(F!43, X2, Y))))) | (~injective(F!43, A!41, B!40)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!43, X1, Y)) | (~member(X1, A!41)) | (~member(Y, B!40)) | (~member(X2, A!41)) | (~apply(F!43, X2, Y)))),
% 0.18/0.54 inference(tautology,[status(thm)],[])).
% 0.18/0.54 tff(221,plain,
% 0.18/0.54 ((~((~injective(F!43, A!41, B!40)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!43, X1, Y)) | (~member(X1, A!41)) | (~member(Y, B!40)) | (~member(X2, A!41)) | (~apply(F!43, X2, Y))))) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!43, X1, Y)) | (~member(X1, A!41)) | (~member(Y, B!40)) | (~member(X2, A!41)) | (~apply(F!43, X2, Y)))),
% 0.18/0.54 inference(unit_resolution,[status(thm)],[220, 219])).
% 0.18/0.54 tff(222,plain,
% 0.18/0.54 (![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!43, X1, Y)) | (~member(X1, A!41)) | (~member(Y, B!40)) | (~member(X2, A!41)) | (~apply(F!43, X2, Y)))),
% 0.18/0.54 inference(unit_resolution,[status(thm)],[221, 211])).
% 0.18/0.54 tff(223,plain,
% 0.18/0.54 (((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!43, X1, Y)) | (~member(X1, A!41)) | (~member(Y, B!40)) | (~member(X2, A!41)) | (~apply(F!43, X2, Y)))) | ((tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)) = tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | (~member(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_E_19(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), B!40)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_E_19(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42))) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_E_19(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42))))) <=> ((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!43, X1, Y)) | (~member(X1, A!41)) | (~member(Y, B!40)) | (~member(X2, A!41)) | (~apply(F!43, X2, Y)))) | (tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)) = tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | (~member(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_E_19(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), B!40)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_E_19(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42))) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_E_19(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42))))),
% 0.18/0.54 inference(rewrite,[status(thm)],[])).
% 0.18/0.54 tff(224,plain,
% 0.18/0.54 (((tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)) = tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_E_19(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42))) | (~member(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_E_19(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), B!40)) | (~member(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_E_19(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42)))) <=> ((tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)) = tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | (~member(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_E_19(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), B!40)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_E_19(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42))) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_E_19(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42))))),
% 0.18/0.54 inference(rewrite,[status(thm)],[])).
% 0.18/0.54 tff(225,plain,
% 0.18/0.54 (((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!43, X1, Y)) | (~member(X1, A!41)) | (~member(Y, B!40)) | (~member(X2, A!41)) | (~apply(F!43, X2, Y)))) | ((tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)) = tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_E_19(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42))) | (~member(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_E_19(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), B!40)) | (~member(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_E_19(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42))))) <=> ((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!43, X1, Y)) | (~member(X1, A!41)) | (~member(Y, B!40)) | (~member(X2, A!41)) | (~apply(F!43, X2, Y)))) | ((tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)) = tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | (~member(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_E_19(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), B!40)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_E_19(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42))) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_E_19(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42)))))),
% 0.18/0.54 inference(monotonicity,[status(thm)],[224])).
% 0.18/0.54 tff(226,plain,
% 0.18/0.54 (((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!43, X1, Y)) | (~member(X1, A!41)) | (~member(Y, B!40)) | (~member(X2, A!41)) | (~apply(F!43, X2, Y)))) | ((tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)) = tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_E_19(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42))) | (~member(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_E_19(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), B!40)) | (~member(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_E_19(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42))))) <=> ((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!43, X1, Y)) | (~member(X1, A!41)) | (~member(Y, B!40)) | (~member(X2, A!41)) | (~apply(F!43, X2, Y)))) | (tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)) = tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | (~member(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_E_19(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), B!40)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_E_19(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42))) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_E_19(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42))))),
% 0.18/0.54 inference(transitivity,[status(thm)],[225, 223])).
% 0.18/0.54 tff(227,plain,
% 0.18/0.54 ((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!43, X1, Y)) | (~member(X1, A!41)) | (~member(Y, B!40)) | (~member(X2, A!41)) | (~apply(F!43, X2, Y)))) | ((tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)) = tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_E_19(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42))) | (~member(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_E_19(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), B!40)) | (~member(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_E_19(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42))))),
% 0.18/0.54 inference(quant_inst,[status(thm)],[])).
% 0.18/0.54 tff(228,plain,
% 0.18/0.54 ((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!43, X1, Y)) | (~member(X1, A!41)) | (~member(Y, B!40)) | (~member(X2, A!41)) | (~apply(F!43, X2, Y)))) | (tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)) = tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | (~member(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_E_19(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), B!40)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_E_19(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42))) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_E_19(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42)))),
% 0.18/0.54 inference(modus_ponens,[status(thm)],[227, 226])).
% 0.18/0.54 tff(229,plain,
% 0.18/0.54 ((~apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_E_19(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42))) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_E_19(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42)))),
% 0.18/0.54 inference(unit_resolution,[status(thm)],[228, 222, 202, 166, 55, 137])).
% 0.18/0.54 tff(230,plain,
% 0.18/0.54 ($false),
% 0.18/0.54 inference(unit_resolution,[status(thm)],[229, 200, 164])).
% 0.18/0.54 tff(231,plain,((tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)) = tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~member(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.54 tff(232,plain,
% 0.18/0.54 ((~(injective(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39) | (~((tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)) = tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~member(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)))))) | injective(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39) | (~((tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)) = tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~member(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39))))),
% 0.18/0.55 inference(tautology,[status(thm)],[])).
% 0.18/0.55 tff(233,plain,
% 0.18/0.55 ((~(injective(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39) | (~((tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)) = tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~member(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)))))) | injective(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)),
% 0.18/0.55 inference(unit_resolution,[status(thm)],[232, 231])).
% 0.18/0.55 tff(234,plain,
% 0.18/0.55 (injective(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)),
% 0.18/0.55 inference(unit_resolution,[status(thm)],[233, 50])).
% 0.18/0.55 tff(235,plain,
% 0.18/0.55 ((~![F: $i, A: $i, B: $i] : (one_to_one(F, A, B) <=> (~((~injective(F, A, B)) | (~surjective(F, A, B)))))) | (one_to_one(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39) <=> (~((~injective(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)) | (~surjective(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)))))),
% 0.18/0.55 inference(quant_inst,[status(thm)],[])).
% 0.18/0.55 tff(236,plain,
% 0.18/0.55 (one_to_one(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39) <=> (~((~injective(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)) | (~surjective(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39))))),
% 0.18/0.55 inference(unit_resolution,[status(thm)],[235, 106])).
% 0.18/0.55 tff(237,plain,
% 0.18/0.55 (~one_to_one(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)),
% 0.18/0.55 inference(or_elim,[status(thm)],[119])).
% 0.18/0.55 tff(238,plain,
% 0.18/0.55 ((~(one_to_one(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39) <=> (~((~injective(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)) | (~surjective(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)))))) | one_to_one(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39) | ((~injective(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)) | (~surjective(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)))),
% 0.18/0.55 inference(tautology,[status(thm)],[])).
% 0.18/0.55 tff(239,plain,
% 0.18/0.55 ((~(one_to_one(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39) <=> (~((~injective(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)) | (~surjective(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)))))) | ((~injective(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)) | (~surjective(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)))),
% 0.18/0.55 inference(unit_resolution,[status(thm)],[238, 237])).
% 0.18/0.55 tff(240,plain,
% 0.18/0.55 ((~injective(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)) | (~surjective(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39))),
% 0.18/0.55 inference(unit_resolution,[status(thm)],[239, 236])).
% 0.18/0.55 tff(241,plain,
% 0.18/0.55 ((~((~injective(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)) | (~surjective(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)))) | (~injective(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)) | (~surjective(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39))),
% 0.18/0.55 inference(tautology,[status(thm)],[])).
% 0.18/0.55 tff(242,plain,
% 0.18/0.55 ((~injective(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)) | (~surjective(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39))),
% 0.18/0.55 inference(unit_resolution,[status(thm)],[241, 240])).
% 0.18/0.55 tff(243,plain,
% 0.18/0.55 (~surjective(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)),
% 0.18/0.55 inference(unit_resolution,[status(thm)],[242, 234])).
% 0.18/0.55 tff(244,plain,
% 0.18/0.55 ((~(surjective(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39) | (~((~member(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~![E: $i] : ((~member(E, A!41)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), E, tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))))) | surjective(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39) | (~((~member(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~![E: $i] : ((~member(E, A!41)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), E, tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))))),
% 0.18/0.55 inference(tautology,[status(thm)],[])).
% 0.18/0.55 tff(245,plain,
% 0.18/0.55 ((~(surjective(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39) | (~((~member(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~![E: $i] : ((~member(E, A!41)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), E, tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))))) | (~((~member(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~![E: $i] : ((~member(E, A!41)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), E, tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))))),
% 0.18/0.55 inference(unit_resolution,[status(thm)],[244, 243])).
% 0.18/0.55 tff(246,plain,
% 0.18/0.55 (~((~member(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~![E: $i] : ((~member(E, A!41)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), E, tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))),
% 0.18/0.55 inference(unit_resolution,[status(thm)],[245, 23])).
% 0.18/0.55 tff(247,plain,
% 0.18/0.55 (((~member(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~![E: $i] : ((~member(E, A!41)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), E, tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))) | member(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)),
% 0.18/0.55 inference(tautology,[status(thm)],[])).
% 0.18/0.55 tff(248,plain,
% 0.18/0.55 (member(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)),
% 0.18/0.55 inference(unit_resolution,[status(thm)],[247, 246])).
% 0.18/0.55 tff(249,plain,
% 0.18/0.55 (((~![Y: $i] : ((~member(Y, C!39)) | (~((~member(tptp_fun_E_19(Y, B!40, G!42), B!40)) | (~apply(G!42, tptp_fun_E_19(Y, B!40, G!42), Y)))))) | ((~member(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~((~member(tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), B!40)) | (~apply(G!42, tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))) <=> ((~![Y: $i] : ((~member(Y, C!39)) | (~((~member(tptp_fun_E_19(Y, B!40, G!42), B!40)) | (~apply(G!42, tptp_fun_E_19(Y, B!40, G!42), Y)))))) | (~member(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~((~member(tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), B!40)) | (~apply(G!42, tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))),
% 0.18/0.55 inference(rewrite,[status(thm)],[])).
% 0.18/0.55 tff(250,plain,
% 0.18/0.55 ((~![Y: $i] : ((~member(Y, C!39)) | (~((~member(tptp_fun_E_19(Y, B!40, G!42), B!40)) | (~apply(G!42, tptp_fun_E_19(Y, B!40, G!42), Y)))))) | ((~member(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~((~member(tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), B!40)) | (~apply(G!42, tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))),
% 0.18/0.55 inference(quant_inst,[status(thm)],[])).
% 0.18/0.55 tff(251,plain,
% 0.18/0.55 ((~![Y: $i] : ((~member(Y, C!39)) | (~((~member(tptp_fun_E_19(Y, B!40, G!42), B!40)) | (~apply(G!42, tptp_fun_E_19(Y, B!40, G!42), Y)))))) | (~member(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~((~member(tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), B!40)) | (~apply(G!42, tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))),
% 0.18/0.55 inference(modus_ponens,[status(thm)],[250, 249])).
% 0.18/0.55 tff(252,plain,
% 0.18/0.55 (~((~member(tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), B!40)) | (~apply(G!42, tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))),
% 0.18/0.55 inference(unit_resolution,[status(thm)],[251, 129, 248])).
% 0.18/0.55 tff(253,plain,
% 0.18/0.55 (((~member(tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), B!40)) | (~apply(G!42, tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))) | member(tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), B!40)),
% 0.18/0.55 inference(tautology,[status(thm)],[])).
% 0.18/0.55 tff(254,plain,
% 0.18/0.55 (member(tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), B!40)),
% 0.18/0.55 inference(unit_resolution,[status(thm)],[253, 252])).
% 0.18/0.55 tff(255,plain,
% 0.18/0.55 ((~![F: $i, A: $i, B: $i] : (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))))))) | (~((~((~surjective(F!43, A!41, B!40)) | ![Y: $i] : ((~member(Y, B!40)) | (~((~member(tptp_fun_E_19(Y, A!41, F!43), A!41)) | (~apply(F!43, tptp_fun_E_19(Y, A!41, F!43), Y))))))) | (~(surjective(F!43, A!41, B!40) | (~((~member(tptp_fun_Y_20(B!40, A!41, F!43), B!40)) | (~![E: $i] : ((~member(E, A!41)) | (~apply(F!43, E, tptp_fun_Y_20(B!40, A!41, F!43)))))))))))),
% 0.18/0.55 inference(quant_inst,[status(thm)],[])).
% 0.18/0.55 tff(256,plain,
% 0.18/0.55 (~((~((~surjective(F!43, A!41, B!40)) | ![Y: $i] : ((~member(Y, B!40)) | (~((~member(tptp_fun_E_19(Y, A!41, F!43), A!41)) | (~apply(F!43, tptp_fun_E_19(Y, A!41, F!43), Y))))))) | (~(surjective(F!43, A!41, B!40) | (~((~member(tptp_fun_Y_20(B!40, A!41, F!43), B!40)) | (~![E: $i] : ((~member(E, A!41)) | (~apply(F!43, E, tptp_fun_Y_20(B!40, A!41, F!43))))))))))),
% 0.18/0.55 inference(unit_resolution,[status(thm)],[255, 19])).
% 0.18/0.55 tff(257,plain,
% 0.18/0.55 (((~((~surjective(F!43, A!41, B!40)) | ![Y: $i] : ((~member(Y, B!40)) | (~((~member(tptp_fun_E_19(Y, A!41, F!43), A!41)) | (~apply(F!43, tptp_fun_E_19(Y, A!41, F!43), Y))))))) | (~(surjective(F!43, A!41, B!40) | (~((~member(tptp_fun_Y_20(B!40, A!41, F!43), B!40)) | (~![E: $i] : ((~member(E, A!41)) | (~apply(F!43, E, tptp_fun_Y_20(B!40, A!41, F!43)))))))))) | ((~surjective(F!43, A!41, B!40)) | ![Y: $i] : ((~member(Y, B!40)) | (~((~member(tptp_fun_E_19(Y, A!41, F!43), A!41)) | (~apply(F!43, tptp_fun_E_19(Y, A!41, F!43), Y))))))),
% 0.18/0.55 inference(tautology,[status(thm)],[])).
% 0.18/0.55 tff(258,plain,
% 0.18/0.55 ((~surjective(F!43, A!41, B!40)) | ![Y: $i] : ((~member(Y, B!40)) | (~((~member(tptp_fun_E_19(Y, A!41, F!43), A!41)) | (~apply(F!43, tptp_fun_E_19(Y, A!41, F!43), Y)))))),
% 0.18/0.55 inference(unit_resolution,[status(thm)],[257, 256])).
% 0.18/0.55 tff(259,plain,
% 0.18/0.55 (((~injective(F!43, A!41, B!40)) | (~surjective(F!43, A!41, B!40))) | surjective(F!43, A!41, B!40)),
% 0.18/0.55 inference(tautology,[status(thm)],[])).
% 0.18/0.55 tff(260,plain,
% 0.18/0.55 (surjective(F!43, A!41, B!40)),
% 0.18/0.55 inference(unit_resolution,[status(thm)],[259, 217])).
% 0.18/0.55 tff(261,plain,
% 0.18/0.55 ((~((~surjective(F!43, A!41, B!40)) | ![Y: $i] : ((~member(Y, B!40)) | (~((~member(tptp_fun_E_19(Y, A!41, F!43), A!41)) | (~apply(F!43, tptp_fun_E_19(Y, A!41, F!43), Y))))))) | (~surjective(F!43, A!41, B!40)) | ![Y: $i] : ((~member(Y, B!40)) | (~((~member(tptp_fun_E_19(Y, A!41, F!43), A!41)) | (~apply(F!43, tptp_fun_E_19(Y, A!41, F!43), Y)))))),
% 0.18/0.55 inference(tautology,[status(thm)],[])).
% 0.18/0.55 tff(262,plain,
% 0.18/0.55 ((~((~surjective(F!43, A!41, B!40)) | ![Y: $i] : ((~member(Y, B!40)) | (~((~member(tptp_fun_E_19(Y, A!41, F!43), A!41)) | (~apply(F!43, tptp_fun_E_19(Y, A!41, F!43), Y))))))) | ![Y: $i] : ((~member(Y, B!40)) | (~((~member(tptp_fun_E_19(Y, A!41, F!43), A!41)) | (~apply(F!43, tptp_fun_E_19(Y, A!41, F!43), Y)))))),
% 0.18/0.55 inference(unit_resolution,[status(thm)],[261, 260])).
% 0.18/0.55 tff(263,plain,
% 0.18/0.55 (![Y: $i] : ((~member(Y, B!40)) | (~((~member(tptp_fun_E_19(Y, A!41, F!43), A!41)) | (~apply(F!43, tptp_fun_E_19(Y, A!41, F!43), Y)))))),
% 0.18/0.55 inference(unit_resolution,[status(thm)],[262, 258])).
% 0.18/0.55 tff(264,plain,
% 0.18/0.55 (((~![Y: $i] : ((~member(Y, B!40)) | (~((~member(tptp_fun_E_19(Y, A!41, F!43), A!41)) | (~apply(F!43, tptp_fun_E_19(Y, A!41, F!43), Y)))))) | ((~member(tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), B!40)) | (~((~member(tptp_fun_E_19(tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), A!41, F!43), A!41)) | (~apply(F!43, tptp_fun_E_19(tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), A!41, F!43), tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42))))))) <=> ((~![Y: $i] : ((~member(Y, B!40)) | (~((~member(tptp_fun_E_19(Y, A!41, F!43), A!41)) | (~apply(F!43, tptp_fun_E_19(Y, A!41, F!43), Y)))))) | (~member(tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), B!40)) | (~((~member(tptp_fun_E_19(tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), A!41, F!43), A!41)) | (~apply(F!43, tptp_fun_E_19(tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), A!41, F!43), tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42))))))),
% 0.18/0.55 inference(rewrite,[status(thm)],[])).
% 0.18/0.55 tff(265,plain,
% 0.18/0.55 ((~![Y: $i] : ((~member(Y, B!40)) | (~((~member(tptp_fun_E_19(Y, A!41, F!43), A!41)) | (~apply(F!43, tptp_fun_E_19(Y, A!41, F!43), Y)))))) | ((~member(tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), B!40)) | (~((~member(tptp_fun_E_19(tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), A!41, F!43), A!41)) | (~apply(F!43, tptp_fun_E_19(tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), A!41, F!43), tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42))))))),
% 0.18/0.55 inference(quant_inst,[status(thm)],[])).
% 0.18/0.55 tff(266,plain,
% 0.18/0.55 ((~![Y: $i] : ((~member(Y, B!40)) | (~((~member(tptp_fun_E_19(Y, A!41, F!43), A!41)) | (~apply(F!43, tptp_fun_E_19(Y, A!41, F!43), Y)))))) | (~member(tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), B!40)) | (~((~member(tptp_fun_E_19(tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), A!41, F!43), A!41)) | (~apply(F!43, tptp_fun_E_19(tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), A!41, F!43), tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42)))))),
% 0.18/0.55 inference(modus_ponens,[status(thm)],[265, 264])).
% 0.18/0.55 tff(267,plain,
% 0.18/0.55 (~((~member(tptp_fun_E_19(tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), A!41, F!43), A!41)) | (~apply(F!43, tptp_fun_E_19(tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), A!41, F!43), tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42))))),
% 0.18/0.55 inference(unit_resolution,[status(thm)],[266, 263, 254])).
% 0.18/0.55 tff(268,plain,
% 0.18/0.55 (((~member(tptp_fun_E_19(tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), A!41, F!43), A!41)) | (~apply(F!43, tptp_fun_E_19(tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), A!41, F!43), tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42)))) | member(tptp_fun_E_19(tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), A!41, F!43), A!41)),
% 0.18/0.55 inference(tautology,[status(thm)],[])).
% 0.18/0.55 tff(269,plain,
% 0.18/0.55 (member(tptp_fun_E_19(tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), A!41, F!43), A!41)),
% 0.18/0.55 inference(unit_resolution,[status(thm)],[268, 267])).
% 0.18/0.55 tff(270,plain,
% 0.18/0.55 (((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_E_19(tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), A!41, F!43), A!41)) | (~((~((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_E_19(tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), A!41, F!43), tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_E_19(tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), A!41, F!43), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_E_19(tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), A!41, F!43), tptp_fun_Y_8(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_E_19(tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), A!41, F!43), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_E_19(tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), A!41, F!43), B!40, F!43, G!42), tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))) | (~(apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_E_19(tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), A!41, F!43), tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_E_19(tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), A!41, F!43), Y)) | (~apply(G!42, Y, tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))))))) <=> ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | (~member(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_E_19(tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), A!41, F!43), A!41)) | (~((~((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_E_19(tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), A!41, F!43), tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_E_19(tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), A!41, F!43), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_E_19(tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), A!41, F!43), tptp_fun_Y_8(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_E_19(tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), A!41, F!43), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_E_19(tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), A!41, F!43), B!40, F!43, G!42), tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))) | (~(apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_E_19(tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), A!41, F!43), tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_E_19(tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), A!41, F!43), Y)) | (~apply(G!42, Y, tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))))))),
% 0.18/0.56 inference(rewrite,[status(thm)],[])).
% 0.18/0.56 tff(271,plain,
% 0.18/0.56 ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_E_19(tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), A!41, F!43), A!41)) | (~((~((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_E_19(tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), A!41, F!43), tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_E_19(tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), A!41, F!43), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_E_19(tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), A!41, F!43), tptp_fun_Y_8(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_E_19(tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), A!41, F!43), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_E_19(tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), A!41, F!43), B!40, F!43, G!42), tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))) | (~(apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_E_19(tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), A!41, F!43), tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_E_19(tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), A!41, F!43), Y)) | (~apply(G!42, Y, tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))))))),
% 0.18/0.56 inference(quant_inst,[status(thm)],[])).
% 0.18/0.56 tff(272,plain,
% 0.18/0.56 ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | (~member(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_E_19(tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), A!41, F!43), A!41)) | (~((~((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_E_19(tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), A!41, F!43), tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_E_19(tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), A!41, F!43), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_E_19(tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), A!41, F!43), tptp_fun_Y_8(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_E_19(tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), A!41, F!43), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_E_19(tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), A!41, F!43), B!40, F!43, G!42), tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))) | (~(apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_E_19(tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), A!41, F!43), tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_E_19(tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), A!41, F!43), Y)) | (~apply(G!42, Y, tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))))),
% 0.18/0.56 inference(modus_ponens,[status(thm)],[271, 270])).
% 0.18/0.56 tff(273,plain,
% 0.18/0.56 (~((~((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_E_19(tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), A!41, F!43), tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_E_19(tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), A!41, F!43), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_E_19(tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), A!41, F!43), tptp_fun_Y_8(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_E_19(tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), A!41, F!43), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_E_19(tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), A!41, F!43), B!40, F!43, G!42), tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))) | (~(apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_E_19(tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), A!41, F!43), tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_E_19(tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), A!41, F!43), Y)) | (~apply(G!42, Y, tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))))),
% 0.18/0.56 inference(unit_resolution,[status(thm)],[272, 71, 248, 269])).
% 0.18/0.56 tff(274,plain,
% 0.18/0.56 (((~((~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_E_19(tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), A!41, F!43), tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_E_19(tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), A!41, F!43), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_E_19(tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), A!41, F!43), tptp_fun_Y_8(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_E_19(tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), A!41, F!43), B!40, F!43, G!42))) | (~apply(G!42, tptp_fun_Y_8(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_E_19(tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), A!41, F!43), B!40, F!43, G!42), tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))) | (~(apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_E_19(tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), A!41, F!43), tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_E_19(tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), A!41, F!43), Y)) | (~apply(G!42, Y, tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))) | (apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_E_19(tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), A!41, F!43), tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_E_19(tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), A!41, F!43), Y)) | (~apply(G!42, Y, tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))),
% 0.18/0.56 inference(tautology,[status(thm)],[])).
% 0.18/0.56 tff(275,plain,
% 0.18/0.56 (apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_E_19(tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), A!41, F!43), tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_E_19(tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), A!41, F!43), Y)) | (~apply(G!42, Y, tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))),
% 0.18/0.56 inference(unit_resolution,[status(thm)],[274, 273])).
% 0.18/0.56 tff(276,plain,
% 0.18/0.56 (((~member(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~![E: $i] : ((~member(E, A!41)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), E, tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))) | ![E: $i] : ((~member(E, A!41)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), E, tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))),
% 0.18/0.56 inference(tautology,[status(thm)],[])).
% 0.18/0.56 tff(277,plain,
% 0.18/0.56 (![E: $i] : ((~member(E, A!41)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), E, tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))),
% 0.18/0.56 inference(unit_resolution,[status(thm)],[276, 246])).
% 0.18/0.56 tff(278,plain,
% 0.18/0.56 (((~![E: $i] : ((~member(E, A!41)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), E, tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))) | ((~member(tptp_fun_E_19(tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), A!41, F!43), A!41)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_E_19(tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), A!41, F!43), tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))) <=> ((~![E: $i] : ((~member(E, A!41)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), E, tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))) | (~member(tptp_fun_E_19(tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), A!41, F!43), A!41)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_E_19(tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), A!41, F!43), tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))),
% 0.18/0.56 inference(rewrite,[status(thm)],[])).
% 0.18/0.56 tff(279,plain,
% 0.18/0.56 ((~![E: $i] : ((~member(E, A!41)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), E, tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))) | ((~member(tptp_fun_E_19(tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), A!41, F!43), A!41)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_E_19(tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), A!41, F!43), tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))),
% 0.18/0.56 inference(quant_inst,[status(thm)],[])).
% 0.18/0.56 tff(280,plain,
% 0.18/0.56 ((~![E: $i] : ((~member(E, A!41)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), E, tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))) | (~member(tptp_fun_E_19(tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), A!41, F!43), A!41)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_E_19(tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), A!41, F!43), tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))),
% 0.18/0.57 inference(modus_ponens,[status(thm)],[279, 278])).
% 0.18/0.57 tff(281,plain,
% 0.18/0.57 (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_E_19(tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), A!41, F!43), tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))),
% 0.18/0.57 inference(unit_resolution,[status(thm)],[280, 277, 269])).
% 0.18/0.57 tff(282,plain,
% 0.18/0.57 ((~(apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_E_19(tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), A!41, F!43), tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_E_19(tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), A!41, F!43), Y)) | (~apply(G!42, Y, tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))) | apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_E_19(tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), A!41, F!43), tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_E_19(tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), A!41, F!43), Y)) | (~apply(G!42, Y, tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))),
% 0.18/0.57 inference(tautology,[status(thm)],[])).
% 0.18/0.57 tff(283,plain,
% 0.18/0.57 ((~(apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_E_19(tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), A!41, F!43), tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_E_19(tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), A!41, F!43), Y)) | (~apply(G!42, Y, tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))))) | ![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_E_19(tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), A!41, F!43), Y)) | (~apply(G!42, Y, tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))),
% 0.18/0.57 inference(unit_resolution,[status(thm)],[282, 281])).
% 0.18/0.57 tff(284,plain,
% 0.18/0.57 (![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_E_19(tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), A!41, F!43), Y)) | (~apply(G!42, Y, tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))),
% 0.18/0.57 inference(unit_resolution,[status(thm)],[283, 275])).
% 0.18/0.57 tff(285,plain,
% 0.18/0.57 (((~member(tptp_fun_E_19(tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), A!41, F!43), A!41)) | (~apply(F!43, tptp_fun_E_19(tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), A!41, F!43), tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42)))) | apply(F!43, tptp_fun_E_19(tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), A!41, F!43), tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42))),
% 0.18/0.57 inference(tautology,[status(thm)],[])).
% 0.18/0.57 tff(286,plain,
% 0.18/0.57 (apply(F!43, tptp_fun_E_19(tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), A!41, F!43), tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42))),
% 0.18/0.57 inference(unit_resolution,[status(thm)],[285, 267])).
% 0.18/0.57 tff(287,plain,
% 0.18/0.57 (((~member(tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), B!40)) | (~apply(G!42, tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))) | apply(G!42, tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))),
% 0.18/0.57 inference(tautology,[status(thm)],[])).
% 0.18/0.57 tff(288,plain,
% 0.18/0.57 (apply(G!42, tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))),
% 0.18/0.57 inference(unit_resolution,[status(thm)],[287, 252])).
% 0.18/0.57 tff(289,plain,
% 0.18/0.57 (((~![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_E_19(tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), A!41, F!43), Y)) | (~apply(G!42, Y, tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))) | ((~member(tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), B!40)) | (~apply(G!42, tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~apply(F!43, tptp_fun_E_19(tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), A!41, F!43), tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42))))) <=> ((~![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_E_19(tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), A!41, F!43), Y)) | (~apply(G!42, Y, tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))) | (~member(tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), B!40)) | (~apply(G!42, tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~apply(F!43, tptp_fun_E_19(tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), A!41, F!43), tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42))))),
% 0.18/0.57 inference(rewrite,[status(thm)],[])).
% 0.18/0.57 tff(290,plain,
% 0.18/0.57 (((~member(tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), B!40)) | (~apply(F!43, tptp_fun_E_19(tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), A!41, F!43), tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42))) | (~apply(G!42, tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))))) <=> ((~member(tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), B!40)) | (~apply(G!42, tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~apply(F!43, tptp_fun_E_19(tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), A!41, F!43), tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42))))),
% 0.18/0.57 inference(rewrite,[status(thm)],[])).
% 0.18/0.57 tff(291,plain,
% 0.18/0.57 (((~![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_E_19(tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), A!41, F!43), Y)) | (~apply(G!42, Y, tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))) | ((~member(tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), B!40)) | (~apply(F!43, tptp_fun_E_19(tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), A!41, F!43), tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42))) | (~apply(G!42, tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))) <=> ((~![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_E_19(tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), A!41, F!43), Y)) | (~apply(G!42, Y, tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))) | ((~member(tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), B!40)) | (~apply(G!42, tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~apply(F!43, tptp_fun_E_19(tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), A!41, F!43), tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42)))))),
% 0.18/0.57 inference(monotonicity,[status(thm)],[290])).
% 0.18/0.57 tff(292,plain,
% 0.18/0.57 (((~![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_E_19(tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), A!41, F!43), Y)) | (~apply(G!42, Y, tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))) | ((~member(tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), B!40)) | (~apply(F!43, tptp_fun_E_19(tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), A!41, F!43), tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42))) | (~apply(G!42, tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))) <=> ((~![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_E_19(tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), A!41, F!43), Y)) | (~apply(G!42, Y, tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))) | (~member(tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), B!40)) | (~apply(G!42, tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~apply(F!43, tptp_fun_E_19(tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), A!41, F!43), tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42))))),
% 0.18/0.57 inference(transitivity,[status(thm)],[291, 289])).
% 0.18/0.57 tff(293,plain,
% 0.18/0.57 ((~![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_E_19(tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), A!41, F!43), Y)) | (~apply(G!42, Y, tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))) | ((~member(tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), B!40)) | (~apply(F!43, tptp_fun_E_19(tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), A!41, F!43), tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42))) | (~apply(G!42, tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))),
% 0.18/0.57 inference(quant_inst,[status(thm)],[])).
% 0.18/0.57 tff(294,plain,
% 0.18/0.57 ((~![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_E_19(tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), A!41, F!43), Y)) | (~apply(G!42, Y, tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))) | (~member(tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), B!40)) | (~apply(G!42, tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~apply(F!43, tptp_fun_E_19(tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), A!41, F!43), tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42)))),
% 0.18/0.57 inference(modus_ponens,[status(thm)],[293, 292])).
% 0.18/0.57 tff(295,plain,
% 0.18/0.57 ($false),
% 0.18/0.57 inference(unit_resolution,[status(thm)],[294, 254, 288, 286, 284])).
% 0.18/0.57 % SZS output end Proof
%------------------------------------------------------------------------------