TSTP Solution File: SET717+4 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET717+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 0.13s 0.41s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET717+4 : TPTP v8.1.0. Bugfixed v2.2.1.
% 0.11/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n017.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Sat Sep 3 06:53:23 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.13/0.41 % SZS status Theorem
% 0.13/0.41 % SZS output start Proof
% 0.13/0.41 tff(apply_type, type, (
% 0.13/0.41 apply: ( $i * $i * $i ) > $o)).
% 0.13/0.41 tff(tptp_fun_Y_20_type, type, (
% 0.13/0.41 tptp_fun_Y_20: ( $i * $i * $i ) > $i)).
% 0.13/0.41 tff(compose_function_type, type, (
% 0.13/0.41 compose_function: ( $i * $i * $i * $i * $i ) > $i)).
% 0.13/0.41 tff(tptp_fun_C_39_type, type, (
% 0.13/0.41 tptp_fun_C_39: $i)).
% 0.13/0.41 tff(tptp_fun_B_40_type, type, (
% 0.13/0.41 tptp_fun_B_40: $i)).
% 0.13/0.41 tff(tptp_fun_A_41_type, type, (
% 0.13/0.41 tptp_fun_A_41: $i)).
% 0.13/0.41 tff(tptp_fun_F_43_type, type, (
% 0.13/0.41 tptp_fun_F_43: $i)).
% 0.13/0.41 tff(tptp_fun_G_42_type, type, (
% 0.13/0.41 tptp_fun_G_42: $i)).
% 0.13/0.41 tff(tptp_fun_E_19_type, type, (
% 0.13/0.41 tptp_fun_E_19: ( $i * $i * $i ) > $i)).
% 0.13/0.41 tff(member_type, type, (
% 0.13/0.41 member: ( $i * $i ) > $o)).
% 0.13/0.41 tff(tptp_fun_Y_8_type, type, (
% 0.13/0.41 tptp_fun_Y_8: ( $i * $i * $i * $i * $i ) > $i)).
% 0.13/0.41 tff(surjective_type, type, (
% 0.13/0.41 surjective: ( $i * $i * $i ) > $o)).
% 0.13/0.41 tff(maps_type, type, (
% 0.13/0.41 maps: ( $i * $i * $i ) > $o)).
% 0.13/0.41 tff(1,plain,
% 0.13/0.41 (^[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))))))))))))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(2,plain,
% 0.13/0.41 (![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)))))))))))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[1])).
% 0.13/0.41 tff(3,plain,
% 0.13/0.41 (^[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))))))))))))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(4,plain,
% 0.13/0.41 (![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)))))))))))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[3])).
% 0.13/0.41 tff(5,plain,
% 0.13/0.41 (![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)))))))))))),
% 0.19/0.41 inference(transitivity,[status(thm)],[4, 2])).
% 0.19/0.41 tff(6,plain,
% 0.19/0.41 (^[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)))))))))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(7,plain,
% 0.19/0.41 (![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)))))))))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[6])).
% 0.19/0.41 tff(8,plain,
% 0.19/0.41 (^[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))))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(9,plain,
% 0.19/0.41 (![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)))))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[8])).
% 0.19/0.41 tff(10,plain,
% 0.19/0.41 (![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))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(11,plain,
% 0.19/0.41 (^[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)))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(12,plain,
% 0.19/0.41 (![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))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[11])).
% 0.19/0.41 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')).
% 0.19/0.41 tff(14,plain,
% 0.19/0.41 (![F: $i, A: $i, B: $i] : (surjective(F, A, B) <=> ![Y: $i] : ((~member(Y, B)) | ?[E: $i] : (member(E, A) & apply(F, E, Y))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.19/0.41 tff(15,plain,
% 0.19/0.41 (![F: $i, A: $i, B: $i] : (surjective(F, A, B) <=> ![Y: $i] : ((~member(Y, B)) | ?[E: $i] : (member(E, A) & apply(F, E, Y))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[14, 10])).
% 0.19/0.41 tff(16,plain,(
% 0.19/0.41 ![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)))))))),
% 0.19/0.41 inference(skolemize,[status(sab)],[15])).
% 0.19/0.41 tff(17,plain,
% 0.19/0.41 (![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)))))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[16, 9])).
% 0.19/0.41 tff(18,plain,
% 0.19/0.41 (![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)))))))))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[17, 7])).
% 0.19/0.41 tff(19,plain,
% 0.19/0.41 (![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)))))))))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[18, 5])).
% 0.19/0.41 tff(20,plain,
% 0.19/0.41 ((~![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)))))))))))) | (~((~((~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))))))))))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(21,plain,
% 0.19/0.41 (~((~((~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)))))))))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[20, 19])).
% 0.19/0.41 tff(22,plain,
% 0.19/0.41 (((~((~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)))))))))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(23,plain,
% 0.19/0.42 (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))))))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[22, 21])).
% 0.19/0.42 tff(24,plain,
% 0.19/0.42 ((~![F: $i, G: $i, A: $i, B: $i, C: $i] : ((~(maps(F, A, B) & maps(G, B, C) & surjective(F, A, B) & surjective(G, B, C))) | surjective(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) & surjective(F, A, B) & surjective(G, B, C))) | surjective(compose_function(G, F, A, B, C), A, C)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(25,plain,
% 0.19/0.42 ((~![F: $i, G: $i, A: $i, B: $i, C: $i] : ((((maps(F, A, B) & maps(G, B, C)) & surjective(F, A, B)) & surjective(G, B, C)) => surjective(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) & surjective(F, A, B) & surjective(G, B, C))) | surjective(compose_function(G, F, A, B, C), A, C)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(26,axiom,(~![F: $i, G: $i, A: $i, B: $i, C: $i] : ((((maps(F, A, B) & maps(G, B, C)) & surjective(F, A, B)) & surjective(G, B, C)) => surjective(compose_function(G, F, A, B, C), A, C))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','thII08')).
% 0.19/0.42 tff(27,plain,
% 0.19/0.42 (~![F: $i, G: $i, A: $i, B: $i, C: $i] : ((~(maps(F, A, B) & maps(G, B, C) & surjective(F, A, B) & surjective(G, B, C))) | surjective(compose_function(G, F, A, B, C), A, C))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.19/0.42 tff(28,plain,
% 0.19/0.42 (~![F: $i, G: $i, A: $i, B: $i, C: $i] : ((~(maps(F, A, B) & maps(G, B, C) & surjective(F, A, B) & surjective(G, B, C))) | surjective(compose_function(G, F, A, B, C), A, C))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[27, 24])).
% 0.19/0.42 tff(29,plain,
% 0.19/0.42 (~![F: $i, G: $i, A: $i, B: $i, C: $i] : ((~(maps(F, A, B) & maps(G, B, C) & surjective(F, A, B) & surjective(G, B, C))) | surjective(compose_function(G, F, A, B, C), A, C))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[28, 24])).
% 0.19/0.42 tff(30,plain,
% 0.19/0.42 (~![F: $i, G: $i, A: $i, B: $i, C: $i] : ((~(maps(F, A, B) & maps(G, B, C) & surjective(F, A, B) & surjective(G, B, C))) | surjective(compose_function(G, F, A, B, C), A, C))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[29, 24])).
% 0.19/0.42 tff(31,plain,
% 0.19/0.42 (~![F: $i, G: $i, A: $i, B: $i, C: $i] : ((~(maps(F, A, B) & maps(G, B, C) & surjective(F, A, B) & surjective(G, B, C))) | surjective(compose_function(G, F, A, B, C), A, C))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[30, 24])).
% 0.19/0.42 tff(32,plain,
% 0.19/0.42 (~![F: $i, G: $i, A: $i, B: $i, C: $i] : ((~(maps(F, A, B) & maps(G, B, C) & surjective(F, A, B) & surjective(G, B, C))) | surjective(compose_function(G, F, A, B, C), A, C))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[31, 24])).
% 0.19/0.42 tff(33,plain,
% 0.19/0.42 (~![F: $i, G: $i, A: $i, B: $i, C: $i] : ((~(maps(F, A, B) & maps(G, B, C) & surjective(F, A, B) & surjective(G, B, C))) | surjective(compose_function(G, F, A, B, C), A, C))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[32, 24])).
% 0.19/0.42 tff(34,plain,(
% 0.19/0.42 ~((~(maps(F!43, A!41, B!40) & maps(G!42, B!40, C!39) & surjective(F!43, A!41, B!40) & surjective(G!42, B!40, C!39))) | surjective(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39))),
% 0.19/0.42 inference(skolemize,[status(sab)],[33])).
% 0.19/0.42 tff(35,plain,
% 0.19/0.42 (~surjective(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)),
% 0.19/0.42 inference(or_elim,[status(thm)],[34])).
% 0.19/0.42 tff(36,plain,
% 0.19/0.42 ((~(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)))))))))) | 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))))))))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(37,plain,
% 0.19/0.42 ((~(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)))))))))) | (~((~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))))))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[36, 35])).
% 0.19/0.42 tff(38,plain,
% 0.19/0.42 (~((~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)))))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[37, 23])).
% 0.19/0.42 tff(39,plain,
% 0.19/0.42 (((~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)),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(40,plain,
% 0.19/0.42 (member(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[39, 38])).
% 0.19/0.42 tff(41,plain,
% 0.19/0.42 ((~![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(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)))))))))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(42,plain,
% 0.19/0.42 (~((~((~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))))))) | (~(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))))))))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[41, 19])).
% 0.19/0.42 tff(43,plain,
% 0.19/0.42 (((~((~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))))))) | (~(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))))))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(44,plain,
% 0.19/0.43 ((~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)))))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[43, 42])).
% 0.19/0.43 tff(45,plain,
% 0.19/0.43 (maps(F!43, A!41, B!40) & maps(G!42, B!40, C!39) & surjective(F!43, A!41, B!40) & surjective(G!42, B!40, C!39)),
% 0.19/0.43 inference(or_elim,[status(thm)],[34])).
% 0.19/0.43 tff(46,plain,
% 0.19/0.43 (surjective(G!42, B!40, C!39)),
% 0.19/0.43 inference(and_elim,[status(thm)],[45])).
% 0.19/0.43 tff(47,plain,
% 0.19/0.43 ((~((~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)))))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(48,plain,
% 0.19/0.43 ((~((~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)))))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[47, 46])).
% 0.19/0.43 tff(49,plain,
% 0.19/0.43 (![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)))))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[48, 44])).
% 0.19/0.43 tff(50,plain,
% 0.19/0.43 (((~![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)))))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(51,plain,
% 0.19/0.43 ((~![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)))))))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(52,plain,
% 0.19/0.43 ((~![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))))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.19/0.43 tff(53,plain,
% 0.19/0.43 (~((~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)))))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[52, 49, 40])).
% 0.19/0.43 tff(54,plain,
% 0.19/0.43 (((~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)),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(55,plain,
% 0.19/0.43 (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)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[54, 53])).
% 0.19/0.43 tff(56,plain,
% 0.19/0.43 ((~![F: $i, A: $i, B: $i] : (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))))))) | (~((~((~surjective(F!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)))))))))))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(57,plain,
% 0.19/0.43 (~((~((~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))))))) | (~(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))))))))))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[56, 19])).
% 0.19/0.43 tff(58,plain,
% 0.19/0.43 (((~((~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))))))) | (~(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))))))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(59,plain,
% 0.19/0.43 ((~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)))))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[58, 57])).
% 0.19/0.43 tff(60,plain,
% 0.19/0.43 (surjective(F!43, A!41, B!40)),
% 0.19/0.43 inference(and_elim,[status(thm)],[45])).
% 0.19/0.43 tff(61,plain,
% 0.19/0.43 ((~((~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))))))) | (~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)))))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(62,plain,
% 0.19/0.43 ((~((~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))))))) | ![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)))))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[61, 60])).
% 0.19/0.43 tff(63,plain,
% 0.19/0.43 (![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)))))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[62, 59])).
% 0.19/0.44 tff(64,plain,
% 0.19/0.44 (((~![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))))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(65,plain,
% 0.19/0.44 ((~![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))))))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(66,plain,
% 0.19/0.44 ((~![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)))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.19/0.44 tff(67,plain,
% 0.19/0.44 (~((~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))))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[66, 63, 55])).
% 0.19/0.44 tff(68,plain,
% 0.19/0.44 (((~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)),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(69,plain,
% 0.19/0.44 (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)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[68, 67])).
% 0.19/0.44 tff(70,plain,
% 0.19/0.44 (^[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)))))))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(71,plain,
% 0.19/0.44 (![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))))))))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[70])).
% 0.19/0.44 tff(72,plain,
% 0.19/0.44 (^[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)))))))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(73,plain,
% 0.19/0.44 (![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))))))))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[72])).
% 0.19/0.44 tff(74,plain,
% 0.19/0.44 (![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))))))))),
% 0.19/0.44 inference(transitivity,[status(thm)],[73, 71])).
% 0.19/0.44 tff(75,plain,
% 0.19/0.44 (^[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))))))))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(76,plain,
% 0.19/0.44 (![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))))))))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[75])).
% 0.19/0.44 tff(77,plain,
% 0.19/0.44 (![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))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(78,plain,
% 0.19/0.44 (^[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))))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(79,plain,
% 0.19/0.44 (![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))))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[78])).
% 0.19/0.44 tff(80,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')).
% 0.19/0.44 tff(81,plain,
% 0.19/0.44 (![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))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.19/0.44 tff(82,plain,
% 0.19/0.44 (![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))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[81, 77])).
% 0.19/0.44 tff(83,plain,(
% 0.19/0.44 ![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))))))),
% 0.19/0.44 inference(skolemize,[status(sab)],[82])).
% 0.19/0.44 tff(84,plain,
% 0.19/0.44 (![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))))))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[83, 76])).
% 0.19/0.44 tff(85,plain,
% 0.19/0.44 (![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))))))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[84, 74])).
% 0.19/0.44 tff(86,plain,
% 0.19/0.44 (((~![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))))))))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(87,plain,
% 0.19/0.45 ((~![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_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))))))))))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(88,plain,
% 0.19/0.45 ((~![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_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)))))))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.19/0.46 tff(89,plain,
% 0.19/0.46 (~((~((~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))))))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[88, 85, 40, 69])).
% 0.19/0.46 tff(90,plain,
% 0.19/0.46 (((~((~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))))))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(91,plain,
% 0.19/0.46 (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)))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[90, 89])).
% 0.19/0.46 tff(92,plain,
% 0.19/0.46 (((~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)))))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(93,plain,
% 0.19/0.46 (![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)))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[92, 38])).
% 0.19/0.46 tff(94,plain,
% 0.19/0.46 (((~![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)))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(95,plain,
% 0.19/0.46 ((~![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)))))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(96,plain,
% 0.19/0.46 ((~![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))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.19/0.46 tff(97,plain,
% 0.19/0.46 (~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)))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[96, 93, 69])).
% 0.19/0.46 tff(98,plain,
% 0.19/0.46 ((~(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)))))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(99,plain,
% 0.19/0.46 ((~(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)))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[98, 97])).
% 0.19/0.46 tff(100,plain,
% 0.19/0.46 (![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)))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[99, 91])).
% 0.19/0.46 tff(101,plain,
% 0.19/0.46 (((~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))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(102,plain,
% 0.19/0.46 (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))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[101, 67])).
% 0.19/0.47 tff(103,plain,
% 0.19/0.47 (((~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)))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(104,plain,
% 0.19/0.47 (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)))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[103, 53])).
% 0.19/0.47 tff(105,plain,
% 0.19/0.47 (((~![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))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(106,plain,
% 0.19/0.47 (((~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))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(107,plain,
% 0.19/0.47 (((~![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)))))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[106])).
% 0.19/0.47 tff(108,plain,
% 0.19/0.47 (((~![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))))),
% 0.19/0.47 inference(transitivity,[status(thm)],[107, 105])).
% 0.19/0.47 tff(109,plain,
% 0.19/0.47 ((~![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)))))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(110,plain,
% 0.19/0.47 ((~![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_E_19(tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), A!41, F!43), Y)) | (~apply(G!42, Y, tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))) | (~member(tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), B!40)) | (~apply(G!42, tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~apply(F!43, tptp_fun_E_19(tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), A!41, F!43), tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[109, 108])).
% 0.19/0.47 tff(111,plain,
% 0.19/0.47 ($false),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[110, 55, 104, 102, 100])).
% 0.19/0.47 % SZS output end Proof
%------------------------------------------------------------------------------