%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET718+4 : TPTP v9.0.0. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:26:12 AM UTC 2025
% Result : Theorem 0.20s 0.40s
% Output : Proof 0.47s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET718+4 : TPTP v9.0.0. Bugfixed v2.2.1.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n003.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 05:38:54 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.20/0.40 % SZS status Theorem
% 0.20/0.40 % SZS output start Proof
% 0.20/0.40 tff(apply_type, type, (
% 0.20/0.40 apply: ( $i * $i * $i ) > $o)).
% 0.20/0.40 tff(tptp_fun_Y_20_type, type, (
% 0.20/0.40 tptp_fun_Y_20: ( $i * $i * $i ) > $i)).
% 0.20/0.40 tff(compose_function_type, type, (
% 0.20/0.40 compose_function: ( $i * $i * $i * $i * $i ) > $i)).
% 0.20/0.40 tff(tptp_fun_C_39_type, type, (
% 0.20/0.40 tptp_fun_C_39: $i)).
% 0.20/0.40 tff(tptp_fun_B_40_type, type, (
% 0.20/0.40 tptp_fun_B_40: $i)).
% 0.20/0.40 tff(tptp_fun_A_41_type, type, (
% 0.20/0.40 tptp_fun_A_41: $i)).
% 0.20/0.40 tff(tptp_fun_F_43_type, type, (
% 0.20/0.40 tptp_fun_F_43: $i)).
% 0.20/0.40 tff(tptp_fun_G_42_type, type, (
% 0.20/0.40 tptp_fun_G_42: $i)).
% 0.20/0.40 tff(tptp_fun_E_19_type, type, (
% 0.20/0.40 tptp_fun_E_19: ( $i * $i * $i ) > $i)).
% 0.20/0.40 tff(member_type, type, (
% 0.20/0.40 member: ( $i * $i ) > $o)).
% 0.20/0.40 tff(tptp_fun_Y_8_type, type, (
% 0.20/0.40 tptp_fun_Y_8: ( $i * $i * $i * $i * $i ) > $i)).
% 0.20/0.40 tff(surjective_type, type, (
% 0.20/0.40 surjective: ( $i * $i * $i ) > $o)).
% 0.20/0.40 tff(injective_type, type, (
% 0.20/0.40 injective: ( $i * $i * $i ) > $o)).
% 0.20/0.40 tff(tptp_fun_X2_17_type, type, (
% 0.20/0.40 tptp_fun_X2_17: ( $i * $i * $i ) > $i)).
% 0.20/0.40 tff(tptp_fun_X1_18_type, type, (
% 0.20/0.40 tptp_fun_X1_18: ( $i * $i * $i ) > $i)).
% 0.20/0.40 tff(tptp_fun_Y_16_type, type, (
% 0.20/0.40 tptp_fun_Y_16: ( $i * $i * $i ) > $i)).
% 0.20/0.40 tff(one_to_one_type, type, (
% 0.20/0.40 one_to_one: ( $i * $i * $i ) > $o)).
% 0.20/0.40 tff(maps_type, type, (
% 0.20/0.40 maps: ( $i * $i * $i ) > $o)).
% 0.20/0.40 tff(1,plain,
% 0.20/0.40 (^[F: $i, A: $i, B: $i] : refl((~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))))))) <=> (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(2,plain,
% 0.20/0.40 (![F: $i, A: $i, B: $i] : (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.40 tff(3,plain,
% 0.20/0.40 (^[F: $i, A: $i, B: $i] : rewrite((~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))))))) <=> (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(4,plain,
% 0.20/0.40 (![F: $i, A: $i, B: $i] : (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[3])).
% 0.20/0.40 tff(5,plain,
% 0.20/0.40 (![F: $i, A: $i, B: $i] : (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))))))),
% 0.20/0.40 inference(transitivity,[status(thm)],[4, 2])).
% 0.20/0.40 tff(6,plain,
% 0.20/0.40 (^[F: $i, A: $i, B: $i] : trans(monotonicity(rewrite(((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (member(tptp_fun_E_19(Y, A, F), A) & apply(F, tptp_fun_E_19(Y, A, F), Y)))) <=> ((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))), trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[E: $i] : trans(monotonicity(rewrite((member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F))) <=> (~((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))), ((~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F)))) <=> (~(~((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))), rewrite((~(~((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))) <=> ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))), ((~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F)))) <=> ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))), (![E: $i] : (~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F)))) <=> ![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))), ((member(tptp_fun_Y_20(B, A, F), B) & ![E: $i] : (~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F))))) <=> (member(tptp_fun_Y_20(B, A, F), B) & ![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))), rewrite((member(tptp_fun_Y_20(B, A, F), B) & ![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))) <=> (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))), ((member(tptp_fun_Y_20(B, A, F), B) & ![E: $i] : (~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F))))) <=> (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))))), ((surjective(F, A, B) | (member(tptp_fun_Y_20(B, A, F), B) & ![E: $i] : (~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F)))))) <=> (surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))))), rewrite((surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))) <=> (surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))))), ((surjective(F, A, B) | (member(tptp_fun_Y_20(B, A, F), B) & ![E: $i] : (~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F)))))) <=> (surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))))), ((((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (member(tptp_fun_E_19(Y, A, F), A) & apply(F, tptp_fun_E_19(Y, A, F), Y)))) & (surjective(F, A, B) | (member(tptp_fun_Y_20(B, A, F), B) & ![E: $i] : (~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F))))))) <=> (((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y)))))) & (surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))))))), rewrite((((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y)))))) & (surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))))) <=> (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))))))), ((((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (member(tptp_fun_E_19(Y, A, F), A) & apply(F, tptp_fun_E_19(Y, A, F), Y)))) & (surjective(F, A, B) | (member(tptp_fun_Y_20(B, A, F), B) & ![E: $i] : (~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F))))))) <=> (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))))))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(7,plain,
% 0.20/0.41 (![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)))))))))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[6])).
% 0.20/0.41 tff(8,plain,
% 0.20/0.41 (![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))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(9,plain,
% 0.20/0.41 (^[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)))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(10,plain,
% 0.20/0.41 (![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))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[9])).
% 0.20/0.41 tff(11,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')).
% 0.20/0.41 tff(12,plain,
% 0.20/0.41 (![F: $i, A: $i, B: $i] : (surjective(F, A, B) <=> ![Y: $i] : ((~member(Y, B)) | ?[E: $i] : (member(E, A) & apply(F, E, Y))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.20/0.41 tff(13,plain,
% 0.20/0.41 (![F: $i, A: $i, B: $i] : (surjective(F, A, B) <=> ![Y: $i] : ((~member(Y, B)) | ?[E: $i] : (member(E, A) & apply(F, E, Y))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[12, 8])).
% 0.20/0.41 tff(14,plain,(
% 0.20/0.41 ![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)))))))),
% 0.20/0.41 inference(skolemize,[status(sab)],[13])).
% 0.20/0.41 tff(15,plain,
% 0.20/0.41 (![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)))))))))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[14, 7])).
% 0.20/0.41 tff(16,plain,
% 0.20/0.41 (![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)))))))))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[15, 5])).
% 0.20/0.41 tff(17,plain,
% 0.20/0.41 ((~![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))))))))))))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(18,plain,
% 0.20/0.41 (~((~((~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)))))))))))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.20/0.41 tff(19,plain,
% 0.20/0.41 (((~((~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)))))))))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(20,plain,
% 0.20/0.41 (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))))))))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[19, 18])).
% 0.20/0.41 tff(21,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) | (~((~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)) | (~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_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)))) | (~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)))) | (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)))))))), introduced(assumption)).
% 0.20/0.41 tff(22,plain,
% 0.20/0.41 (^[F: $i, A: $i, B: $i] : refl((~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B)))))))) <=> (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B)))))))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(23,plain,
% 0.20/0.41 (![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B)))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[22])).
% 0.20/0.41 tff(24,plain,
% 0.20/0.41 (^[F: $i, A: $i, B: $i] : rewrite((~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B)))))))) <=> (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B)))))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(25,plain,
% 0.20/0.42 (![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))))))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[24])).
% 0.20/0.42 tff(26,plain,
% 0.20/0.42 (![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))))))))),
% 0.20/0.42 inference(transitivity,[status(thm)],[25, 23])).
% 0.20/0.42 tff(27,plain,
% 0.20/0.42 (^[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))))))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(28,plain,
% 0.20/0.42 (![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))))))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[27])).
% 0.20/0.42 tff(29,plain,
% 0.20/0.42 (![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)))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(30,plain,
% 0.20/0.42 (^[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))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(31,plain,
% 0.20/0.42 (![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)))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[30])).
% 0.20/0.42 tff(32,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')).
% 0.20/0.42 tff(33,plain,
% 0.20/0.42 (![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)))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.20/0.42 tff(34,plain,
% 0.20/0.42 (![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)))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[33, 29])).
% 0.20/0.42 tff(35,plain,(
% 0.20/0.42 ![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)))))))),
% 0.20/0.42 inference(skolemize,[status(sab)],[34])).
% 0.20/0.42 tff(36,plain,
% 0.20/0.42 (![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))))))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[35, 28])).
% 0.20/0.42 tff(37,plain,
% 0.20/0.42 (![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))))))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[36, 26])).
% 0.20/0.42 tff(38,plain,
% 0.20/0.42 (((~![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))))))))) | (~((~((~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) | (~((~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)) | (~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_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)))) | (~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)))) | (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)))))))))) <=> ((~![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) | (~((~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)) | (~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_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)))) | (~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)))) | (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))))))))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(39,plain,
% 0.20/0.43 ((~((~((~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) | (~((~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)) | (~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_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)))) | (~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)))) | (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)))))))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(40,plain,
% 0.20/0.43 (((~![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) | (~((~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)) | (~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_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)))) | (~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)))) | (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))))))))))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[39])).
% 0.20/0.43 tff(41,plain,
% 0.20/0.43 (((~![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) | (~((~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)) | (~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_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)))) | (~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)))) | (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))))))))))),
% 0.20/0.44 inference(transitivity,[status(thm)],[40, 38])).
% 0.20/0.44 tff(42,plain,
% 0.20/0.44 ((~![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))))))))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(43,plain,
% 0.20/0.44 ((~![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: $i] : ((X1 = X2) | (~member(X1, A!41)) | (~member(Y, C!39)) | (~member(X2, A!41)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), X1, Y)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), X2, Y))))) | (~(injective(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39) | (~((~member(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)) | (~member(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~apply(compose_function(G!42, F!43, A!41, B!40, C!39), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)) = tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.20/0.44 tff(44,plain,
% 0.20/0.44 ($false),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[43, 37, 21])).
% 0.20/0.44 tff(45,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) | (~((~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)) | (~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_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)))) | (~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)))) | (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))))))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.44 tff(46,plain,
% 0.20/0.44 (((~((~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) | (~((~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)) | (~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_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)))) | (~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)))) | (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)))))))) | (injective(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, 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)) | (~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_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)))) | (~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)))) | (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))))))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(47,plain,
% 0.20/0.45 (injective(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, 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)) | (~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_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)))) | (~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)))) | (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)))))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[46, 45])).
% 0.20/0.45 tff(48,assumption,(~((~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)) | (~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_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)))) | (~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)))) | (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))))), introduced(assumption)).
% 0.20/0.45 tff(49,plain,
% 0.20/0.45 (((~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)) | (~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_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)))) | (~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)))) | (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_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(50,plain,
% 0.20/0.45 (member(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[49, 48])).
% 0.20/0.45 tff(51,plain,
% 0.20/0.45 ((~![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)))))))))))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(52,plain,
% 0.20/0.45 (~((~((~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))))))))))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[51, 16])).
% 0.20/0.45 tff(53,plain,
% 0.20/0.45 (((~((~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))))))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(54,plain,
% 0.20/0.45 ((~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)))))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[53, 52])).
% 0.20/0.45 tff(55,plain,
% 0.20/0.45 (^[F: $i, A: $i, B: $i] : refl((~(((~injective(F, A, B)) | (~surjective(F, A, B))) <=> one_to_one(F, A, B))) <=> (~(((~injective(F, A, B)) | (~surjective(F, A, B))) <=> one_to_one(F, A, B))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(56,plain,
% 0.20/0.45 (![F: $i, A: $i, B: $i] : (~(((~injective(F, A, B)) | (~surjective(F, A, B))) <=> one_to_one(F, A, B))) <=> ![F: $i, A: $i, B: $i] : (~(((~injective(F, A, B)) | (~surjective(F, A, B))) <=> one_to_one(F, A, B)))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[55])).
% 0.20/0.45 tff(57,plain,
% 0.20/0.45 (^[F: $i, A: $i, B: $i] : trans(trans(monotonicity(rewrite((injective(F, A, B) & surjective(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))) <=> (one_to_one(F, A, B) <=> (~((~injective(F, A, B)) | (~surjective(F, A, B))))))), rewrite((one_to_one(F, A, B) <=> (~((~injective(F, A, B)) | (~surjective(F, A, B))))) <=> (~(((~injective(F, A, B)) | (~surjective(F, A, B))) <=> one_to_one(F, A, B)))), ((one_to_one(F, A, B) <=> (injective(F, A, B) & surjective(F, A, B))) <=> (~(((~injective(F, A, B)) | (~surjective(F, A, B))) <=> one_to_one(F, A, B))))), rewrite((~(((~injective(F, A, B)) | (~surjective(F, A, B))) <=> one_to_one(F, A, B))) <=> (~(((~injective(F, A, B)) | (~surjective(F, A, B))) <=> one_to_one(F, A, B)))), ((one_to_one(F, A, B) <=> (injective(F, A, B) & surjective(F, A, B))) <=> (~(((~injective(F, A, B)) | (~surjective(F, A, B))) <=> one_to_one(F, A, B)))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(58,plain,
% 0.20/0.45 (![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] : (~(((~injective(F, A, B)) | (~surjective(F, A, B))) <=> one_to_one(F, A, B)))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[57])).
% 0.20/0.45 tff(59,plain,
% 0.20/0.45 (![F: $i, A: $i, B: $i] : (one_to_one(F, A, B) <=> (injective(F, A, B) & surjective(F, A, B))) <=> ![F: $i, A: $i, B: $i] : (one_to_one(F, A, B) <=> (injective(F, A, B) & surjective(F, A, B)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(60,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')).
% 0.20/0.45 tff(61,plain,
% 0.20/0.45 (![F: $i, A: $i, B: $i] : (one_to_one(F, A, B) <=> (injective(F, A, B) & surjective(F, A, B)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.20/0.45 tff(62,plain,(
% 0.20/0.45 ![F: $i, A: $i, B: $i] : (one_to_one(F, A, B) <=> (injective(F, A, B) & surjective(F, A, B)))),
% 0.20/0.45 inference(skolemize,[status(sab)],[61])).
% 0.20/0.45 tff(63,plain,
% 0.20/0.45 (![F: $i, A: $i, B: $i] : (~(((~injective(F, A, B)) | (~surjective(F, A, B))) <=> one_to_one(F, A, B)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[62, 58])).
% 0.20/0.45 tff(64,plain,
% 0.20/0.45 (![F: $i, A: $i, B: $i] : (~(((~injective(F, A, B)) | (~surjective(F, A, B))) <=> one_to_one(F, A, B)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[63, 56])).
% 0.20/0.45 tff(65,plain,
% 0.20/0.45 ((~![F: $i, A: $i, B: $i] : (~(((~injective(F, A, B)) | (~surjective(F, A, B))) <=> one_to_one(F, A, B)))) | (~(((~injective(G!42, B!40, C!39)) | (~surjective(G!42, B!40, C!39))) <=> one_to_one(G!42, B!40, C!39)))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(66,plain,
% 0.20/0.45 (~(((~injective(G!42, B!40, C!39)) | (~surjective(G!42, B!40, C!39))) <=> one_to_one(G!42, B!40, C!39))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[65, 64])).
% 0.20/0.45 tff(67,plain,
% 0.20/0.45 ((~![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)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(68,plain,
% 0.20/0.45 ((~![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)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(69,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')).
% 0.20/0.45 tff(70,plain,
% 0.20/0.45 (~![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))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.20/0.45 tff(71,plain,
% 0.20/0.45 (~![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))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[70, 67])).
% 0.20/0.45 tff(72,plain,
% 0.20/0.45 (~![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))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[71, 67])).
% 0.20/0.45 tff(73,plain,
% 0.20/0.45 (~![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))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[72, 67])).
% 0.20/0.45 tff(74,plain,(
% 0.20/0.45 ~((~(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))),
% 0.20/0.45 inference(skolemize,[status(sab)],[73])).
% 0.20/0.46 tff(75,plain,
% 0.20/0.46 (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)),
% 0.20/0.46 inference(or_elim,[status(thm)],[74])).
% 0.20/0.46 tff(76,plain,
% 0.20/0.46 (one_to_one(G!42, B!40, C!39)),
% 0.20/0.46 inference(and_elim,[status(thm)],[75])).
% 0.20/0.46 tff(77,plain,
% 0.20/0.46 ((((~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)))) | (~one_to_one(G!42, B!40, C!39))),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(78,plain,
% 0.20/0.46 ((((~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))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[77, 76])).
% 0.20/0.46 tff(79,plain,
% 0.20/0.46 (~((~injective(G!42, B!40, C!39)) | (~surjective(G!42, B!40, C!39)))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[78, 66])).
% 0.20/0.46 tff(80,plain,
% 0.20/0.46 (((~injective(G!42, B!40, C!39)) | (~surjective(G!42, B!40, C!39))) | surjective(G!42, B!40, C!39)),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(81,plain,
% 0.20/0.46 (surjective(G!42, B!40, C!39)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[80, 79])).
% 0.20/0.46 tff(82,plain,
% 0.20/0.46 ((~((~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)))))),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(83,plain,
% 0.20/0.46 ((~((~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)))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[82, 81])).
% 0.20/0.46 tff(84,plain,
% 0.20/0.46 (![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)))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[83, 54])).
% 0.20/0.46 tff(85,plain,
% 0.20/0.46 (((~![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)))))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(86,plain,
% 0.20/0.46 ((~![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)))))))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(87,plain,
% 0.20/0.46 ((~![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))))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.20/0.46 tff(88,plain,
% 0.20/0.46 (~((~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)))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[87, 84, 50])).
% 0.20/0.46 tff(89,plain,
% 0.20/0.46 (((~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)))),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(90,plain,
% 0.20/0.46 (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)))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[89, 88])).
% 0.20/0.46 tff(91,plain,
% 0.20/0.46 (((~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)),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(92,plain,
% 0.20/0.46 (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)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[91, 88])).
% 0.20/0.46 tff(93,plain,
% 0.20/0.46 (((~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)) | (~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_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)))) | (~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)))) | (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_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(94,plain,
% 0.20/0.46 (member(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[93, 48])).
% 0.20/0.46 tff(95,plain,
% 0.20/0.46 (^[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)))))))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(96,plain,
% 0.20/0.46 (![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)))))))) <=> ![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))))))))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[95])).
% 0.20/0.46 tff(97,plain,
% 0.20/0.46 (^[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)))))))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(98,plain,
% 0.20/0.46 (![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)))))))) <=> ![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))))))))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[97])).
% 0.20/0.46 tff(99,plain,
% 0.20/0.46 (![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)))))))) <=> ![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))))))))),
% 0.20/0.46 inference(transitivity,[status(thm)],[98, 96])).
% 0.20/0.46 tff(100,plain,
% 0.20/0.46 (^[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))))))))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(101,plain,
% 0.20/0.47 (![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))))))))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[100])).
% 0.20/0.47 tff(102,plain,
% 0.20/0.47 (![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))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(103,plain,
% 0.20/0.47 (^[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))))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(104,plain,
% 0.20/0.47 (![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))))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[103])).
% 0.20/0.47 tff(105,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')).
% 0.20/0.47 tff(106,plain,
% 0.20/0.47 (![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))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[105, 104])).
% 0.20/0.47 tff(107,plain,
% 0.20/0.47 (![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))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[106, 102])).
% 0.20/0.47 tff(108,plain,(
% 0.20/0.47 ![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))))))),
% 0.20/0.47 inference(skolemize,[status(sab)],[107])).
% 0.20/0.47 tff(109,plain,
% 0.20/0.47 (![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))))))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[108, 101])).
% 0.20/0.47 tff(110,plain,
% 0.20/0.47 (![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))))))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[109, 99])).
% 0.20/0.47 tff(111,plain,
% 0.20/0.47 (((~![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_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))) | ![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)))))))))))) <=> ((~![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))) | ![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)))))))))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(112,plain,
% 0.20/0.47 (((~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))) | ![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))))))))))) <=> ((~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))) | ![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)))))))))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(113,plain,
% 0.20/0.48 ((~((~((~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))) | ![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))))))))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(114,plain,
% 0.20/0.48 (((~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))) | ![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)))))))))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[113])).
% 0.20/0.48 tff(115,plain,
% 0.20/0.48 (((~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))) | ![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)))))))))))),
% 0.20/0.49 inference(transitivity,[status(thm)],[114, 112])).
% 0.20/0.49 tff(116,plain,
% 0.20/0.49 (((~![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_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))) | ![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))))))))))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[115])).
% 0.20/0.49 tff(117,plain,
% 0.20/0.49 (((~![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_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))) | ![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)))))))))))),
% 0.20/0.49 inference(transitivity,[status(thm)],[116, 111])).
% 0.20/0.49 tff(118,plain,
% 0.20/0.49 ((~![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))))))))))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(119,plain,
% 0.20/0.49 ((~![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))) | ![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))))))))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[118, 117])).
% 0.20/0.49 tff(120,plain,
% 0.20/0.49 (~((~(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)))))))))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[119, 110, 50, 94])).
% 0.20/0.50 tff(121,plain,
% 0.20/0.50 (((~(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)))) | (~((~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)))))))),
% 0.20/0.50 inference(tautology,[status(thm)],[])).
% 0.20/0.50 tff(122,plain,
% 0.20/0.50 ((~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))))))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[121, 120])).
% 0.20/0.50 tff(123,plain,
% 0.20/0.50 (((~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_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~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_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)))) | (~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)))) | (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_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)))),
% 0.20/0.50 inference(tautology,[status(thm)],[])).
% 0.20/0.50 tff(124,plain,
% 0.20/0.50 (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)))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[123, 48])).
% 0.20/0.50 tff(125,plain,
% 0.20/0.50 ((~((~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))))))),
% 0.20/0.50 inference(tautology,[status(thm)],[])).
% 0.20/0.50 tff(126,plain,
% 0.20/0.50 ((~((~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))))))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[125, 124])).
% 0.20/0.50 tff(127,plain,
% 0.20/0.50 (~((~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)))))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[126, 122])).
% 0.20/0.50 tff(128,plain,
% 0.20/0.50 (((~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)))),
% 0.20/0.50 inference(tautology,[status(thm)],[])).
% 0.20/0.50 tff(129,plain,
% 0.20/0.50 (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)))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[128, 127])).
% 0.20/0.50 tff(130,plain,
% 0.20/0.50 (((~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)),
% 0.20/0.50 inference(tautology,[status(thm)],[])).
% 0.20/0.50 tff(131,plain,
% 0.20/0.50 (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)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[130, 127])).
% 0.20/0.51 tff(132,plain,
% 0.20/0.51 (((~![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)) | (~member(Y, C!39)) | (~apply(G!42, X1, Y)) | (~member(X1, B!40)) | (~apply(G!42, X2, Y))))) | (~(injective(G!42, B!40, C!39) | (~((~member(tptp_fun_Y_16(C!39, B!40, G!42), C!39)) | (~member(tptp_fun_X2_17(C!39, B!40, G!42), B!40)) | (~member(tptp_fun_X1_18(C!39, B!40, G!42), B!40)) | (~apply(G!42, tptp_fun_X2_17(C!39, B!40, G!42), tptp_fun_Y_16(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))) | (tptp_fun_X1_18(C!39, B!40, G!42) = tptp_fun_X2_17(C!39, B!40, G!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))))))))) | (~((~((~injective(G!42, B!40, C!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, B!40)) | (~member(Y, C!39)) | (~apply(G!42, X1, Y)) | (~member(X1, B!40)) | (~apply(G!42, X2, Y))))) | (~(injective(G!42, B!40, C!39) | (~((~member(tptp_fun_Y_16(C!39, B!40, G!42), C!39)) | (~member(tptp_fun_X2_17(C!39, B!40, G!42), B!40)) | (~member(tptp_fun_X1_18(C!39, B!40, G!42), B!40)) | (~apply(G!42, tptp_fun_X2_17(C!39, B!40, G!42), tptp_fun_Y_16(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))) | (tptp_fun_X1_18(C!39, B!40, G!42) = tptp_fun_X2_17(C!39, B!40, G!42)))))))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(133,plain,
% 0.20/0.51 ((~((~((~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)) | (~member(Y, C!39)) | (~apply(G!42, X1, Y)) | (~member(X1, B!40)) | (~apply(G!42, X2, Y))))) | (~(injective(G!42, B!40, C!39) | (~((~member(tptp_fun_Y_16(C!39, B!40, G!42), C!39)) | (~member(tptp_fun_X2_17(C!39, B!40, G!42), B!40)) | (~member(tptp_fun_X1_18(C!39, B!40, G!42), B!40)) | (~apply(G!42, tptp_fun_X2_17(C!39, B!40, G!42), tptp_fun_Y_16(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))) | (tptp_fun_X1_18(C!39, B!40, G!42) = tptp_fun_X2_17(C!39, B!40, G!42))))))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(134,plain,
% 0.20/0.51 (((~![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)) | (~member(Y, C!39)) | (~apply(G!42, X1, Y)) | (~member(X1, B!40)) | (~apply(G!42, X2, Y))))) | (~(injective(G!42, B!40, C!39) | (~((~member(tptp_fun_Y_16(C!39, B!40, G!42), C!39)) | (~member(tptp_fun_X2_17(C!39, B!40, G!42), B!40)) | (~member(tptp_fun_X1_18(C!39, B!40, G!42), B!40)) | (~apply(G!42, tptp_fun_X2_17(C!39, B!40, G!42), tptp_fun_Y_16(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))) | (tptp_fun_X1_18(C!39, B!40, G!42) = tptp_fun_X2_17(C!39, B!40, G!42)))))))))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[133])).
% 0.20/0.51 tff(135,plain,
% 0.20/0.51 (((~![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)) | (~member(Y, C!39)) | (~apply(G!42, X1, Y)) | (~member(X1, B!40)) | (~apply(G!42, X2, Y))))) | (~(injective(G!42, B!40, C!39) | (~((~member(tptp_fun_Y_16(C!39, B!40, G!42), C!39)) | (~member(tptp_fun_X2_17(C!39, B!40, G!42), B!40)) | (~member(tptp_fun_X1_18(C!39, B!40, G!42), B!40)) | (~apply(G!42, tptp_fun_X2_17(C!39, B!40, G!42), tptp_fun_Y_16(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))) | (tptp_fun_X1_18(C!39, B!40, G!42) = tptp_fun_X2_17(C!39, B!40, G!42)))))))))),
% 0.20/0.51 inference(transitivity,[status(thm)],[134, 132])).
% 0.20/0.51 tff(136,plain,
% 0.20/0.51 ((~![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))))))))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(137,plain,
% 0.20/0.51 ((~![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)) | (~member(Y, C!39)) | (~apply(G!42, X1, Y)) | (~member(X1, B!40)) | (~apply(G!42, X2, Y))))) | (~(injective(G!42, B!40, C!39) | (~((~member(tptp_fun_Y_16(C!39, B!40, G!42), C!39)) | (~member(tptp_fun_X2_17(C!39, B!40, G!42), B!40)) | (~member(tptp_fun_X1_18(C!39, B!40, G!42), B!40)) | (~apply(G!42, tptp_fun_X2_17(C!39, B!40, G!42), tptp_fun_Y_16(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))) | (tptp_fun_X1_18(C!39, B!40, G!42) = tptp_fun_X2_17(C!39, B!40, G!42))))))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[136, 135])).
% 0.20/0.51 tff(138,plain,
% 0.20/0.51 (~((~((~injective(G!42, B!40, C!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, B!40)) | (~member(Y, C!39)) | (~apply(G!42, X1, Y)) | (~member(X1, B!40)) | (~apply(G!42, X2, Y))))) | (~(injective(G!42, B!40, C!39) | (~((~member(tptp_fun_Y_16(C!39, B!40, G!42), C!39)) | (~member(tptp_fun_X2_17(C!39, B!40, G!42), B!40)) | (~member(tptp_fun_X1_18(C!39, B!40, G!42), B!40)) | (~apply(G!42, tptp_fun_X2_17(C!39, B!40, G!42), tptp_fun_Y_16(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))) | (tptp_fun_X1_18(C!39, B!40, G!42) = tptp_fun_X2_17(C!39, B!40, G!42)))))))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[137, 37])).
% 0.20/0.51 tff(139,plain,
% 0.20/0.51 (((~((~injective(G!42, B!40, C!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, B!40)) | (~member(Y, C!39)) | (~apply(G!42, X1, Y)) | (~member(X1, B!40)) | (~apply(G!42, X2, Y))))) | (~(injective(G!42, B!40, C!39) | (~((~member(tptp_fun_Y_16(C!39, B!40, G!42), C!39)) | (~member(tptp_fun_X2_17(C!39, B!40, G!42), B!40)) | (~member(tptp_fun_X1_18(C!39, B!40, G!42), B!40)) | (~apply(G!42, tptp_fun_X2_17(C!39, B!40, G!42), tptp_fun_Y_16(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))) | (tptp_fun_X1_18(C!39, B!40, G!42) = tptp_fun_X2_17(C!39, B!40, G!42))))))) | ((~injective(G!42, B!40, C!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, B!40)) | (~member(Y, C!39)) | (~apply(G!42, X1, Y)) | (~member(X1, B!40)) | (~apply(G!42, X2, Y))))),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(140,plain,
% 0.20/0.51 ((~injective(G!42, B!40, C!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, B!40)) | (~member(Y, C!39)) | (~apply(G!42, X1, Y)) | (~member(X1, B!40)) | (~apply(G!42, X2, Y)))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[139, 138])).
% 0.20/0.51 tff(141,plain,
% 0.20/0.51 (((~injective(G!42, B!40, C!39)) | (~surjective(G!42, B!40, C!39))) | injective(G!42, B!40, C!39)),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(142,plain,
% 0.20/0.51 (injective(G!42, B!40, C!39)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[141, 79])).
% 0.20/0.51 tff(143,plain,
% 0.20/0.51 ((~((~injective(G!42, B!40, C!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, B!40)) | (~member(Y, C!39)) | (~apply(G!42, X1, Y)) | (~member(X1, B!40)) | (~apply(G!42, X2, Y))))) | (~injective(G!42, B!40, C!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, B!40)) | (~member(Y, C!39)) | (~apply(G!42, X1, Y)) | (~member(X1, B!40)) | (~apply(G!42, X2, Y)))),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(144,plain,
% 0.20/0.51 ((~((~injective(G!42, B!40, C!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, B!40)) | (~member(Y, C!39)) | (~apply(G!42, X1, Y)) | (~member(X1, B!40)) | (~apply(G!42, X2, Y))))) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, B!40)) | (~member(Y, C!39)) | (~apply(G!42, X1, Y)) | (~member(X1, B!40)) | (~apply(G!42, X2, Y)))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[143, 142])).
% 0.20/0.51 tff(145,plain,
% 0.20/0.51 (![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, B!40)) | (~member(Y, C!39)) | (~apply(G!42, X1, Y)) | (~member(X1, B!40)) | (~apply(G!42, X2, Y)))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[144, 140])).
% 0.20/0.51 tff(146,plain,
% 0.20/0.51 (((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, B!40)) | (~member(Y, C!39)) | (~apply(G!42, X1, Y)) | (~member(X1, B!40)) | (~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)) | (~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_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)))) | (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)) | (~member(Y, C!39)) | (~apply(G!42, X1, Y)) | (~member(X1, B!40)) | (~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)) | (~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_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)))) | (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)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(147,plain,
% 0.20/0.51 (((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)) | (~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_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(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)) | (~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_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)))) | (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)))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(148,plain,
% 0.20/0.52 (((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, B!40)) | (~member(Y, C!39)) | (~apply(G!42, X1, Y)) | (~member(X1, B!40)) | (~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)) | (~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_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(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)) | (~member(Y, C!39)) | (~apply(G!42, X1, Y)) | (~member(X1, B!40)) | (~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)) | (~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_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)))) | (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))))),
% 0.35/0.52 inference(monotonicity,[status(thm)],[147])).
% 0.35/0.52 tff(149,plain,
% 0.35/0.52 (((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, B!40)) | (~member(Y, C!39)) | (~apply(G!42, X1, Y)) | (~member(X1, B!40)) | (~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)) | (~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_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(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)) | (~member(Y, C!39)) | (~apply(G!42, X1, Y)) | (~member(X1, B!40)) | (~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)) | (~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_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)))) | (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)))),
% 0.35/0.52 inference(transitivity,[status(thm)],[148, 146])).
% 0.35/0.52 tff(150,plain,
% 0.35/0.52 ((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, B!40)) | (~member(Y, C!39)) | (~apply(G!42, X1, Y)) | (~member(X1, B!40)) | (~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)) | (~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_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(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)))))),
% 0.35/0.52 inference(quant_inst,[status(thm)],[])).
% 0.35/0.52 tff(151,plain,
% 0.35/0.52 ((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, B!40)) | (~member(Y, C!39)) | (~apply(G!42, X1, Y)) | (~member(X1, B!40)) | (~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)) | (~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_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)))) | (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))),
% 0.35/0.52 inference(modus_ponens,[status(thm)],[150, 149])).
% 0.35/0.52 tff(152,plain,
% 0.35/0.52 (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_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)),
% 0.35/0.52 inference(unit_resolution,[status(thm)],[151, 145, 50, 131, 129, 92, 90])).
% 0.35/0.52 tff(153,plain,
% 0.35/0.52 (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)),
% 0.35/0.52 inference(symmetry,[status(thm)],[152])).
% 0.35/0.52 tff(154,plain,
% 0.35/0.52 (((~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)) | (~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_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)))) | (~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)))) | (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)),
% 0.35/0.52 inference(tautology,[status(thm)],[])).
% 0.35/0.52 tff(155,plain,
% 0.35/0.52 (member(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)),
% 0.35/0.52 inference(unit_resolution,[status(thm)],[154, 48])).
% 0.35/0.52 tff(156,plain,
% 0.35/0.52 (((~![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))) | ![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)))))))))))) <=> ((~![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))) | ![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)))))))))))),
% 0.35/0.53 inference(rewrite,[status(thm)],[])).
% 0.35/0.53 tff(157,plain,
% 0.35/0.53 (((~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))) | ![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))))))))))) <=> ((~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))) | ![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)))))))))))),
% 0.35/0.53 inference(rewrite,[status(thm)],[])).
% 0.35/0.53 tff(158,plain,
% 0.35/0.53 ((~((~((~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))) | ![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))))))))))),
% 0.35/0.53 inference(rewrite,[status(thm)],[])).
% 0.35/0.53 tff(159,plain,
% 0.35/0.53 (((~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))) | ![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)))))))))))),
% 0.35/0.53 inference(monotonicity,[status(thm)],[158])).
% 0.35/0.53 tff(160,plain,
% 0.35/0.53 (((~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))) | ![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)))))))))))),
% 0.37/0.54 inference(transitivity,[status(thm)],[159, 157])).
% 0.37/0.54 tff(161,plain,
% 0.37/0.54 (((~![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_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))) | ![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))))))))))))),
% 0.37/0.54 inference(monotonicity,[status(thm)],[160])).
% 0.37/0.54 tff(162,plain,
% 0.37/0.54 (((~![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_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))) | ![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)))))))))))),
% 0.37/0.54 inference(transitivity,[status(thm)],[161, 156])).
% 0.37/0.54 tff(163,plain,
% 0.37/0.54 ((~![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))))))))))),
% 0.37/0.54 inference(quant_inst,[status(thm)],[])).
% 0.37/0.54 tff(164,plain,
% 0.37/0.54 ((~![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))) | ![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))))))))))),
% 0.37/0.54 inference(modus_ponens,[status(thm)],[163, 162])).
% 0.37/0.54 tff(165,plain,
% 0.37/0.54 (~((~(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)))))))))),
% 0.37/0.54 inference(unit_resolution,[status(thm)],[164, 110, 50, 155])).
% 0.37/0.54 tff(166,plain,
% 0.37/0.54 (((~(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)))) | (~((~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)))))))),
% 0.37/0.55 inference(tautology,[status(thm)],[])).
% 0.37/0.55 tff(167,plain,
% 0.37/0.55 ((~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))))))),
% 0.37/0.55 inference(unit_resolution,[status(thm)],[166, 165])).
% 0.37/0.55 tff(168,plain,
% 0.37/0.55 (((~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)) | (~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_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)))) | (~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)))) | (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)))),
% 0.37/0.55 inference(tautology,[status(thm)],[])).
% 0.37/0.55 tff(169,plain,
% 0.37/0.55 (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)))),
% 0.37/0.55 inference(unit_resolution,[status(thm)],[168, 48])).
% 0.37/0.55 tff(170,plain,
% 0.37/0.55 ((~((~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))))))),
% 0.37/0.55 inference(tautology,[status(thm)],[])).
% 0.37/0.55 tff(171,plain,
% 0.37/0.55 ((~((~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))))))),
% 0.37/0.55 inference(unit_resolution,[status(thm)],[170, 169])).
% 0.37/0.55 tff(172,plain,
% 0.37/0.55 (~((~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)))))),
% 0.37/0.55 inference(unit_resolution,[status(thm)],[171, 167])).
% 0.37/0.55 tff(173,plain,
% 0.37/0.55 (((~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)))),
% 0.37/0.55 inference(tautology,[status(thm)],[])).
% 0.37/0.55 tff(174,plain,
% 0.37/0.55 (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)))),
% 0.37/0.55 inference(unit_resolution,[status(thm)],[173, 172])).
% 0.37/0.55 tff(175,plain,
% 0.37/0.55 (((~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)),
% 0.37/0.55 inference(tautology,[status(thm)],[])).
% 0.37/0.55 tff(176,plain,
% 0.37/0.55 (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)),
% 0.37/0.55 inference(unit_resolution,[status(thm)],[175, 172])).
% 0.37/0.55 tff(177,plain,
% 0.37/0.55 (((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, B!40)) | (~member(Y, C!39)) | (~apply(G!42, X1, Y)) | (~member(X1, B!40)) | (~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)) | (~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_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)))) | (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)) | (~member(Y, C!39)) | (~apply(G!42, X1, Y)) | (~member(X1, B!40)) | (~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)) | (~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_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)))) | (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)))),
% 0.37/0.56 inference(rewrite,[status(thm)],[])).
% 0.37/0.56 tff(178,plain,
% 0.37/0.56 (((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)) | (~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_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(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)) | (~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_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)))) | (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)))),
% 0.37/0.56 inference(rewrite,[status(thm)],[])).
% 0.37/0.56 tff(179,plain,
% 0.37/0.56 (((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, B!40)) | (~member(Y, C!39)) | (~apply(G!42, X1, Y)) | (~member(X1, B!40)) | (~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)) | (~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_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(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)) | (~member(Y, C!39)) | (~apply(G!42, X1, Y)) | (~member(X1, B!40)) | (~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)) | (~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_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)))) | (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))))),
% 0.37/0.56 inference(monotonicity,[status(thm)],[178])).
% 0.37/0.56 tff(180,plain,
% 0.37/0.56 (((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, B!40)) | (~member(Y, C!39)) | (~apply(G!42, X1, Y)) | (~member(X1, B!40)) | (~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)) | (~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_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(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)) | (~member(Y, C!39)) | (~apply(G!42, X1, Y)) | (~member(X1, B!40)) | (~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)) | (~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_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)))) | (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)))),
% 0.37/0.56 inference(transitivity,[status(thm)],[179, 177])).
% 0.37/0.56 tff(181,plain,
% 0.37/0.56 ((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, B!40)) | (~member(Y, C!39)) | (~apply(G!42, X1, Y)) | (~member(X1, B!40)) | (~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)) | (~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_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(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)))))),
% 0.37/0.56 inference(quant_inst,[status(thm)],[])).
% 0.37/0.56 tff(182,plain,
% 0.37/0.56 ((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(X2, B!40)) | (~member(Y, C!39)) | (~apply(G!42, X1, Y)) | (~member(X1, B!40)) | (~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)) | (~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_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)))) | (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))),
% 0.37/0.57 inference(modus_ponens,[status(thm)],[181, 180])).
% 0.37/0.57 tff(183,plain,
% 0.37/0.57 (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)),
% 0.37/0.57 inference(unit_resolution,[status(thm)],[182, 145, 50, 176, 174, 92, 90])).
% 0.37/0.57 tff(184,plain,
% 0.37/0.57 (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_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)),
% 0.37/0.57 inference(transitivity,[status(thm)],[183, 153])).
% 0.37/0.57 tff(185,plain,
% 0.37/0.57 (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_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_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))),
% 0.37/0.57 inference(monotonicity,[status(thm)],[184])).
% 0.37/0.57 tff(186,plain,
% 0.37/0.57 (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_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))),
% 0.37/0.57 inference(symmetry,[status(thm)],[185])).
% 0.37/0.57 tff(187,plain,
% 0.37/0.57 (((~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))),
% 0.37/0.57 inference(tautology,[status(thm)],[])).
% 0.37/0.57 tff(188,plain,
% 0.37/0.57 (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))),
% 0.37/0.57 inference(unit_resolution,[status(thm)],[187, 127])).
% 0.37/0.57 tff(189,plain,
% 0.37/0.57 (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_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))),
% 0.37/0.57 inference(modus_ponens,[status(thm)],[188, 186])).
% 0.37/0.57 tff(190,plain,
% 0.37/0.57 (((~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))),
% 0.37/0.57 inference(tautology,[status(thm)],[])).
% 0.37/0.57 tff(191,plain,
% 0.37/0.57 (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))),
% 0.37/0.57 inference(unit_resolution,[status(thm)],[190, 172])).
% 0.37/0.57 tff(192,plain,
% 0.37/0.57 (((~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)) | (~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_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)))) | (~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)))) | (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)))) | (~(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))))),
% 0.37/0.57 inference(tautology,[status(thm)],[])).
% 0.37/0.57 tff(193,plain,
% 0.37/0.57 (~(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)))),
% 0.37/0.57 inference(unit_resolution,[status(thm)],[192, 48])).
% 0.37/0.57 tff(194,plain,
% 0.37/0.57 (((~![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) | (~member(Y, B!40)) | (~apply(F!43, X1, Y)) | (~member(X1, A!41)) | (~member(X2, A!41)) | (~apply(F!43, X2, Y))))) | (~(injective(F!43, A!41, B!40) | (~((~member(tptp_fun_Y_16(B!40, A!41, F!43), B!40)) | (~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)) | (~apply(F!43, tptp_fun_X2_17(B!40, A!41, F!43), tptp_fun_Y_16(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))) | (tptp_fun_X1_18(B!40, A!41, F!43) = tptp_fun_X2_17(B!40, A!41, F!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(F!43, A!41, B!40)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!40)) | (~apply(F!43, X1, Y)) | (~member(X1, A!41)) | (~member(X2, A!41)) | (~apply(F!43, X2, Y))))) | (~(injective(F!43, A!41, B!40) | (~((~member(tptp_fun_Y_16(B!40, A!41, F!43), B!40)) | (~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)) | (~apply(F!43, tptp_fun_X2_17(B!40, A!41, F!43), tptp_fun_Y_16(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))) | (tptp_fun_X1_18(B!40, A!41, F!43) = tptp_fun_X2_17(B!40, A!41, F!43)))))))))),
% 0.37/0.57 inference(rewrite,[status(thm)],[])).
% 0.37/0.57 tff(195,plain,
% 0.37/0.57 ((~((~((~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) | (~member(Y, B!40)) | (~apply(F!43, X1, Y)) | (~member(X1, A!41)) | (~member(X2, A!41)) | (~apply(F!43, X2, Y))))) | (~(injective(F!43, A!41, B!40) | (~((~member(tptp_fun_Y_16(B!40, A!41, F!43), B!40)) | (~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)) | (~apply(F!43, tptp_fun_X2_17(B!40, A!41, F!43), tptp_fun_Y_16(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))) | (tptp_fun_X1_18(B!40, A!41, F!43) = tptp_fun_X2_17(B!40, A!41, F!43))))))))),
% 0.37/0.57 inference(rewrite,[status(thm)],[])).
% 0.37/0.57 tff(196,plain,
% 0.37/0.57 (((~![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) | (~member(Y, B!40)) | (~apply(F!43, X1, Y)) | (~member(X1, A!41)) | (~member(X2, A!41)) | (~apply(F!43, X2, Y))))) | (~(injective(F!43, A!41, B!40) | (~((~member(tptp_fun_Y_16(B!40, A!41, F!43), B!40)) | (~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)) | (~apply(F!43, tptp_fun_X2_17(B!40, A!41, F!43), tptp_fun_Y_16(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))) | (tptp_fun_X1_18(B!40, A!41, F!43) = tptp_fun_X2_17(B!40, A!41, F!43)))))))))),
% 0.37/0.57 inference(monotonicity,[status(thm)],[195])).
% 0.37/0.57 tff(197,plain,
% 0.37/0.57 (((~![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) | (~member(Y, B!40)) | (~apply(F!43, X1, Y)) | (~member(X1, A!41)) | (~member(X2, A!41)) | (~apply(F!43, X2, Y))))) | (~(injective(F!43, A!41, B!40) | (~((~member(tptp_fun_Y_16(B!40, A!41, F!43), B!40)) | (~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)) | (~apply(F!43, tptp_fun_X2_17(B!40, A!41, F!43), tptp_fun_Y_16(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))) | (tptp_fun_X1_18(B!40, A!41, F!43) = tptp_fun_X2_17(B!40, A!41, F!43)))))))))),
% 0.37/0.57 inference(transitivity,[status(thm)],[196, 194])).
% 0.37/0.57 tff(198,plain,
% 0.37/0.57 ((~![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))))))))),
% 0.37/0.57 inference(quant_inst,[status(thm)],[])).
% 0.37/0.57 tff(199,plain,
% 0.37/0.57 ((~![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) | (~member(Y, B!40)) | (~apply(F!43, X1, Y)) | (~member(X1, A!41)) | (~member(X2, A!41)) | (~apply(F!43, X2, Y))))) | (~(injective(F!43, A!41, B!40) | (~((~member(tptp_fun_Y_16(B!40, A!41, F!43), B!40)) | (~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)) | (~apply(F!43, tptp_fun_X2_17(B!40, A!41, F!43), tptp_fun_Y_16(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))) | (tptp_fun_X1_18(B!40, A!41, F!43) = tptp_fun_X2_17(B!40, A!41, F!43))))))))),
% 0.37/0.57 inference(modus_ponens,[status(thm)],[198, 197])).
% 0.37/0.57 tff(200,plain,
% 0.37/0.57 (~((~((~injective(F!43, A!41, B!40)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!40)) | (~apply(F!43, X1, Y)) | (~member(X1, A!41)) | (~member(X2, A!41)) | (~apply(F!43, X2, Y))))) | (~(injective(F!43, A!41, B!40) | (~((~member(tptp_fun_Y_16(B!40, A!41, F!43), B!40)) | (~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)) | (~apply(F!43, tptp_fun_X2_17(B!40, A!41, F!43), tptp_fun_Y_16(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))) | (tptp_fun_X1_18(B!40, A!41, F!43) = tptp_fun_X2_17(B!40, A!41, F!43)))))))),
% 0.37/0.57 inference(unit_resolution,[status(thm)],[199, 37])).
% 0.37/0.57 tff(201,plain,
% 0.37/0.57 (((~((~injective(F!43, A!41, B!40)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!40)) | (~apply(F!43, X1, Y)) | (~member(X1, A!41)) | (~member(X2, A!41)) | (~apply(F!43, X2, Y))))) | (~(injective(F!43, A!41, B!40) | (~((~member(tptp_fun_Y_16(B!40, A!41, F!43), B!40)) | (~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)) | (~apply(F!43, tptp_fun_X2_17(B!40, A!41, F!43), tptp_fun_Y_16(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))) | (tptp_fun_X1_18(B!40, A!41, F!43) = tptp_fun_X2_17(B!40, A!41, F!43))))))) | ((~injective(F!43, A!41, B!40)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!40)) | (~apply(F!43, X1, Y)) | (~member(X1, A!41)) | (~member(X2, A!41)) | (~apply(F!43, X2, Y))))),
% 0.37/0.57 inference(tautology,[status(thm)],[])).
% 0.37/0.57 tff(202,plain,
% 0.37/0.57 ((~injective(F!43, A!41, B!40)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!40)) | (~apply(F!43, X1, Y)) | (~member(X1, A!41)) | (~member(X2, A!41)) | (~apply(F!43, X2, Y)))),
% 0.37/0.57 inference(unit_resolution,[status(thm)],[201, 200])).
% 0.37/0.57 tff(203,plain,
% 0.37/0.57 ((~![F: $i, A: $i, B: $i] : (~(((~injective(F, A, B)) | (~surjective(F, A, B))) <=> one_to_one(F, A, B)))) | (~(((~injective(F!43, A!41, B!40)) | (~surjective(F!43, A!41, B!40))) <=> one_to_one(F!43, A!41, B!40)))),
% 0.37/0.57 inference(quant_inst,[status(thm)],[])).
% 0.37/0.57 tff(204,plain,
% 0.37/0.57 (~(((~injective(F!43, A!41, B!40)) | (~surjective(F!43, A!41, B!40))) <=> one_to_one(F!43, A!41, B!40))),
% 0.37/0.57 inference(unit_resolution,[status(thm)],[203, 64])).
% 0.37/0.57 tff(205,plain,
% 0.37/0.57 (one_to_one(F!43, A!41, B!40)),
% 0.37/0.57 inference(and_elim,[status(thm)],[75])).
% 0.37/0.57 tff(206,plain,
% 0.37/0.57 ((((~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)))) | (~one_to_one(F!43, A!41, B!40))),
% 0.37/0.57 inference(tautology,[status(thm)],[])).
% 0.37/0.58 tff(207,plain,
% 0.37/0.58 ((((~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))))),
% 0.37/0.58 inference(unit_resolution,[status(thm)],[206, 205])).
% 0.37/0.58 tff(208,plain,
% 0.37/0.58 (~((~injective(F!43, A!41, B!40)) | (~surjective(F!43, A!41, B!40)))),
% 0.37/0.58 inference(unit_resolution,[status(thm)],[207, 204])).
% 0.37/0.58 tff(209,plain,
% 0.37/0.58 (((~injective(F!43, A!41, B!40)) | (~surjective(F!43, A!41, B!40))) | injective(F!43, A!41, B!40)),
% 0.37/0.58 inference(tautology,[status(thm)],[])).
% 0.37/0.58 tff(210,plain,
% 0.37/0.58 (injective(F!43, A!41, B!40)),
% 0.37/0.58 inference(unit_resolution,[status(thm)],[209, 208])).
% 0.37/0.58 tff(211,plain,
% 0.37/0.58 ((~((~injective(F!43, A!41, B!40)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!40)) | (~apply(F!43, X1, Y)) | (~member(X1, A!41)) | (~member(X2, A!41)) | (~apply(F!43, X2, Y))))) | (~injective(F!43, A!41, B!40)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!40)) | (~apply(F!43, X1, Y)) | (~member(X1, A!41)) | (~member(X2, A!41)) | (~apply(F!43, X2, Y)))),
% 0.37/0.58 inference(tautology,[status(thm)],[])).
% 0.37/0.58 tff(212,plain,
% 0.37/0.58 ((~((~injective(F!43, A!41, B!40)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!40)) | (~apply(F!43, X1, Y)) | (~member(X1, A!41)) | (~member(X2, A!41)) | (~apply(F!43, X2, Y))))) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!40)) | (~apply(F!43, X1, Y)) | (~member(X1, A!41)) | (~member(X2, A!41)) | (~apply(F!43, X2, Y)))),
% 0.37/0.58 inference(unit_resolution,[status(thm)],[211, 210])).
% 0.37/0.58 tff(213,plain,
% 0.37/0.58 (![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!40)) | (~apply(F!43, X1, Y)) | (~member(X1, A!41)) | (~member(X2, A!41)) | (~apply(F!43, X2, Y)))),
% 0.37/0.58 inference(unit_resolution,[status(thm)],[212, 202])).
% 0.37/0.58 tff(214,plain,
% 0.37/0.58 (((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!40)) | (~apply(F!43, X1, Y)) | (~member(X1, A!41)) | (~member(X2, A!41)) | (~apply(F!43, X2, Y)))) | ((~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_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (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_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))) | (~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_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_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))))) <=> ((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!40)) | (~apply(F!43, X1, Y)) | (~member(X1, A!41)) | (~member(X2, A!41)) | (~apply(F!43, X2, Y)))) | (~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_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (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_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))) | (~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_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_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))))),
% 0.37/0.58 inference(rewrite,[status(thm)],[])).
% 0.37/0.58 tff(215,plain,
% 0.37/0.58 (((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_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))) | (~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)) | (~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_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42)))) <=> ((~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_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (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_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))) | (~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_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_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))))),
% 0.37/0.58 inference(rewrite,[status(thm)],[])).
% 0.37/0.58 tff(216,plain,
% 0.37/0.58 (((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!40)) | (~apply(F!43, X1, Y)) | (~member(X1, A!41)) | (~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_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))) | (~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)) | (~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_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))))) <=> ((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!40)) | (~apply(F!43, X1, Y)) | (~member(X1, A!41)) | (~member(X2, A!41)) | (~apply(F!43, X2, Y)))) | ((~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_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (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_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))) | (~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_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_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42)))))),
% 0.37/0.58 inference(monotonicity,[status(thm)],[215])).
% 0.37/0.58 tff(217,plain,
% 0.37/0.58 (((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!40)) | (~apply(F!43, X1, Y)) | (~member(X1, A!41)) | (~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_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))) | (~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)) | (~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_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))))) <=> ((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!40)) | (~apply(F!43, X1, Y)) | (~member(X1, A!41)) | (~member(X2, A!41)) | (~apply(F!43, X2, Y)))) | (~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_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (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_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))) | (~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_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_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))))),
% 0.37/0.58 inference(transitivity,[status(thm)],[216, 214])).
% 0.37/0.58 tff(218,plain,
% 0.37/0.58 ((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!40)) | (~apply(F!43, X1, Y)) | (~member(X1, A!41)) | (~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_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))) | (~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)) | (~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_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))))),
% 0.37/0.59 inference(quant_inst,[status(thm)],[])).
% 0.37/0.59 tff(219,plain,
% 0.37/0.59 ((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!40)) | (~apply(F!43, X1, Y)) | (~member(X1, A!41)) | (~member(X2, A!41)) | (~apply(F!43, X2, Y)))) | (~member(tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (~member(tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), A!41)) | (tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)) = tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39))) | (~apply(F!43, tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))) | (~member(tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42), B!40)) | (~apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42)))),
% 0.37/0.59 inference(modus_ponens,[status(thm)],[218, 217])).
% 0.37/0.59 tff(220,plain,
% 0.37/0.59 (~apply(F!43, tptp_fun_X2_17(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_Y_8(tptp_fun_Y_16(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), tptp_fun_X1_18(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, F!43, G!42))),
% 0.37/0.59 inference(unit_resolution,[status(thm)],[219, 213, 94, 155, 193, 176, 191])).
% 0.37/0.59 tff(221,plain,
% 0.37/0.59 ($false),
% 0.37/0.59 inference(unit_resolution,[status(thm)],[220, 189])).
% 0.37/0.59 tff(222,plain,((~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)) | (~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_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)))) | (~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)))) | (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)))), inference(lemma,lemma(discharge,[]))).
% 0.37/0.59 tff(223,plain,
% 0.37/0.59 ((~(injective(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, 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)) | (~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_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)))) | (~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)))) | (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))))))) | injective(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, 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)) | (~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_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)))) | (~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)))) | (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)))))),
% 0.37/0.59 inference(tautology,[status(thm)],[])).
% 0.37/0.59 tff(224,plain,
% 0.37/0.59 ((~(injective(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, 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)) | (~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_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)))) | (~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)))) | (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))))))) | injective(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)),
% 0.37/0.59 inference(unit_resolution,[status(thm)],[223, 222])).
% 0.37/0.59 tff(225,plain,
% 0.37/0.59 (injective(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)),
% 0.37/0.59 inference(unit_resolution,[status(thm)],[224, 47])).
% 0.37/0.59 tff(226,plain,
% 0.37/0.59 ((~![F: $i, A: $i, B: $i] : (~(((~injective(F, A, B)) | (~surjective(F, A, B))) <=> one_to_one(F, A, B)))) | (~(((~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)))),
% 0.37/0.59 inference(quant_inst,[status(thm)],[])).
% 0.37/0.59 tff(227,plain,
% 0.37/0.59 (~(((~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))),
% 0.37/0.59 inference(unit_resolution,[status(thm)],[226, 64])).
% 0.37/0.59 tff(228,plain,
% 0.37/0.59 (~one_to_one(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)),
% 0.37/0.59 inference(or_elim,[status(thm)],[74])).
% 0.37/0.59 tff(229,plain,
% 0.37/0.59 ((((~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))) | one_to_one(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)),
% 0.37/0.59 inference(tautology,[status(thm)],[])).
% 0.37/0.59 tff(230,plain,
% 0.37/0.59 ((((~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)))),
% 0.37/0.59 inference(unit_resolution,[status(thm)],[229, 228])).
% 0.37/0.59 tff(231,plain,
% 0.37/0.59 ((~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))),
% 0.37/0.59 inference(unit_resolution,[status(thm)],[230, 227])).
% 0.37/0.59 tff(232,plain,
% 0.37/0.59 ((~((~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))),
% 0.37/0.59 inference(tautology,[status(thm)],[])).
% 0.37/0.59 tff(233,plain,
% 0.37/0.59 ((~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))),
% 0.37/0.59 inference(unit_resolution,[status(thm)],[232, 231])).
% 0.37/0.59 tff(234,plain,
% 0.37/0.59 (~surjective(compose_function(G!42, F!43, A!41, B!40, C!39), A!41, C!39)),
% 0.37/0.59 inference(unit_resolution,[status(thm)],[233, 225])).
% 0.37/0.59 tff(235,plain,
% 0.37/0.59 ((~(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))))))))),
% 0.37/0.59 inference(tautology,[status(thm)],[])).
% 0.37/0.59 tff(236,plain,
% 0.37/0.59 ((~(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))))))))),
% 0.37/0.59 inference(unit_resolution,[status(thm)],[235, 234])).
% 0.37/0.59 tff(237,plain,
% 0.37/0.59 (~((~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)))))))),
% 0.37/0.59 inference(unit_resolution,[status(thm)],[236, 20])).
% 0.37/0.59 tff(238,plain,
% 0.37/0.59 (((~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)),
% 0.37/0.59 inference(tautology,[status(thm)],[])).
% 0.37/0.59 tff(239,plain,
% 0.37/0.59 (member(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), C!39)),
% 0.37/0.59 inference(unit_resolution,[status(thm)],[238, 237])).
% 0.37/0.59 tff(240,plain,
% 0.37/0.59 (((~![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)))))))),
% 0.37/0.59 inference(rewrite,[status(thm)],[])).
% 0.37/0.59 tff(241,plain,
% 0.37/0.59 ((~![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)))))))),
% 0.37/0.59 inference(quant_inst,[status(thm)],[])).
% 0.37/0.59 tff(242,plain,
% 0.37/0.59 ((~![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))))))),
% 0.37/0.59 inference(modus_ponens,[status(thm)],[241, 240])).
% 0.37/0.59 tff(243,plain,
% 0.37/0.59 (~((~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)))))),
% 0.37/0.59 inference(unit_resolution,[status(thm)],[242, 84, 239])).
% 0.37/0.59 tff(244,plain,
% 0.37/0.59 (((~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)),
% 0.37/0.59 inference(tautology,[status(thm)],[])).
% 0.37/0.59 tff(245,plain,
% 0.37/0.59 (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)),
% 0.37/0.59 inference(unit_resolution,[status(thm)],[244, 243])).
% 0.37/0.59 tff(246,plain,
% 0.37/0.59 ((~![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)))))))))))),
% 0.37/0.59 inference(quant_inst,[status(thm)],[])).
% 0.37/0.59 tff(247,plain,
% 0.37/0.59 (~((~((~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))))))))))),
% 0.37/0.60 inference(unit_resolution,[status(thm)],[246, 16])).
% 0.37/0.60 tff(248,plain,
% 0.37/0.60 (((~((~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))))))),
% 0.37/0.60 inference(tautology,[status(thm)],[])).
% 0.37/0.60 tff(249,plain,
% 0.37/0.60 ((~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)))))),
% 0.37/0.60 inference(unit_resolution,[status(thm)],[248, 247])).
% 0.37/0.60 tff(250,plain,
% 0.37/0.60 (((~injective(F!43, A!41, B!40)) | (~surjective(F!43, A!41, B!40))) | surjective(F!43, A!41, B!40)),
% 0.37/0.60 inference(tautology,[status(thm)],[])).
% 0.37/0.60 tff(251,plain,
% 0.37/0.60 (surjective(F!43, A!41, B!40)),
% 0.37/0.60 inference(unit_resolution,[status(thm)],[250, 208])).
% 0.37/0.60 tff(252,plain,
% 0.37/0.60 ((~((~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)))))),
% 0.37/0.60 inference(tautology,[status(thm)],[])).
% 0.37/0.60 tff(253,plain,
% 0.37/0.60 ((~((~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)))))),
% 0.37/0.60 inference(unit_resolution,[status(thm)],[252, 251])).
% 0.37/0.60 tff(254,plain,
% 0.37/0.60 (![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)))))),
% 0.37/0.60 inference(unit_resolution,[status(thm)],[253, 249])).
% 0.37/0.60 tff(255,plain,
% 0.37/0.60 (((~![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))))))),
% 0.37/0.60 inference(rewrite,[status(thm)],[])).
% 0.37/0.60 tff(256,plain,
% 0.37/0.60 ((~![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))))))),
% 0.37/0.60 inference(quant_inst,[status(thm)],[])).
% 0.37/0.60 tff(257,plain,
% 0.37/0.60 ((~![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)))))),
% 0.37/0.60 inference(modus_ponens,[status(thm)],[256, 255])).
% 0.37/0.60 tff(258,plain,
% 0.37/0.60 (~((~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))))),
% 0.37/0.60 inference(unit_resolution,[status(thm)],[257, 254, 245])).
% 0.37/0.60 tff(259,plain,
% 0.37/0.60 (((~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)),
% 0.37/0.60 inference(tautology,[status(thm)],[])).
% 0.37/0.60 tff(260,plain,
% 0.37/0.60 (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)),
% 0.37/0.60 inference(unit_resolution,[status(thm)],[259, 258])).
% 0.37/0.60 tff(261,plain,
% 0.37/0.60 (((~![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))) | ![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)))) | (~((~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)))))))))))) <=> ((~![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))) | ![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)))) | (~((~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)))))))))))),
% 0.37/0.60 inference(rewrite,[status(thm)],[])).
% 0.37/0.60 tff(262,plain,
% 0.37/0.60 (((~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)))))))))) <=> ((~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))) | ![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)))) | (~((~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)))))))))))),
% 0.37/0.61 inference(rewrite,[status(thm)],[])).
% 0.37/0.61 tff(263,plain,
% 0.37/0.61 (((~![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))) | ![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)))) | (~((~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))))))))))))),
% 0.37/0.61 inference(monotonicity,[status(thm)],[262])).
% 0.37/0.61 tff(264,plain,
% 0.37/0.61 (((~![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))) | ![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)))) | (~((~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)))))))))))),
% 0.37/0.61 inference(transitivity,[status(thm)],[263, 261])).
% 0.37/0.61 tff(265,plain,
% 0.37/0.61 ((~![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))))))))))),
% 0.37/0.61 inference(quant_inst,[status(thm)],[])).
% 0.37/0.61 tff(266,plain,
% 0.37/0.61 ((~![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))) | ![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)))) | (~((~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))))))))))),
% 0.37/0.62 inference(modus_ponens,[status(thm)],[265, 264])).
% 0.37/0.62 tff(267,plain,
% 0.37/0.62 (~((~(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)))) | (~((~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)))))))))),
% 0.37/0.62 inference(unit_resolution,[status(thm)],[266, 110, 239, 260])).
% 0.37/0.62 tff(268,plain,
% 0.37/0.62 (((~(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)))) | (~((~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))))))),
% 0.37/0.62 inference(tautology,[status(thm)],[])).
% 0.37/0.62 tff(269,plain,
% 0.37/0.62 (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)))))),
% 0.37/0.62 inference(unit_resolution,[status(thm)],[268, 267])).
% 0.37/0.62 tff(270,plain,
% 0.37/0.62 (((~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)))))),
% 0.37/0.62 inference(tautology,[status(thm)],[])).
% 0.37/0.62 tff(271,plain,
% 0.37/0.62 (![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)))))),
% 0.37/0.62 inference(unit_resolution,[status(thm)],[270, 237])).
% 0.37/0.62 tff(272,plain,
% 0.37/0.62 (((~![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)))))),
% 0.37/0.62 inference(rewrite,[status(thm)],[])).
% 0.37/0.62 tff(273,plain,
% 0.37/0.62 ((~![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)))))),
% 0.37/0.62 inference(quant_inst,[status(thm)],[])).
% 0.37/0.62 tff(274,plain,
% 0.37/0.62 ((~![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))))),
% 0.37/0.62 inference(modus_ponens,[status(thm)],[273, 272])).
% 0.37/0.62 tff(275,plain,
% 0.37/0.62 (~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)))),
% 0.37/0.62 inference(unit_resolution,[status(thm)],[274, 271, 260])).
% 0.37/0.62 tff(276,plain,
% 0.37/0.62 ((~(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)))))),
% 0.37/0.62 inference(tautology,[status(thm)],[])).
% 0.37/0.62 tff(277,plain,
% 0.37/0.62 ((~(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)))))),
% 0.37/0.62 inference(unit_resolution,[status(thm)],[276, 275])).
% 0.37/0.62 tff(278,plain,
% 0.37/0.62 (![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)))))),
% 0.37/0.62 inference(unit_resolution,[status(thm)],[277, 269])).
% 0.37/0.62 tff(279,plain,
% 0.37/0.62 (((~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))),
% 0.37/0.62 inference(tautology,[status(thm)],[])).
% 0.37/0.62 tff(280,plain,
% 0.37/0.62 (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))),
% 0.37/0.62 inference(unit_resolution,[status(thm)],[279, 258])).
% 0.37/0.62 tff(281,plain,
% 0.37/0.62 (((~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)))),
% 0.37/0.63 inference(tautology,[status(thm)],[])).
% 0.37/0.63 tff(282,plain,
% 0.37/0.63 (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)))),
% 0.37/0.63 inference(unit_resolution,[status(thm)],[281, 243])).
% 0.37/0.63 tff(283,plain,
% 0.37/0.63 (((~![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))))),
% 0.37/0.63 inference(rewrite,[status(thm)],[])).
% 0.37/0.63 tff(284,plain,
% 0.37/0.63 (((~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))))),
% 0.37/0.63 inference(rewrite,[status(thm)],[])).
% 0.37/0.63 tff(285,plain,
% 0.37/0.63 (((~![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)))))),
% 0.37/0.63 inference(monotonicity,[status(thm)],[284])).
% 0.37/0.63 tff(286,plain,
% 0.37/0.63 (((~![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))))),
% 0.47/0.63 inference(transitivity,[status(thm)],[285, 283])).
% 0.47/0.63 tff(287,plain,
% 0.47/0.63 ((~![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)))))),
% 0.47/0.63 inference(quant_inst,[status(thm)],[])).
% 0.47/0.63 tff(288,plain,
% 0.47/0.63 ((~![Y: $i] : ((~member(Y, B!40)) | (~apply(F!43, tptp_fun_E_19(tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), A!41, F!43), Y)) | (~apply(G!42, Y, tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))))) | (~member(tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), B!40)) | (~apply(G!42, tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)))) | (~apply(F!43, tptp_fun_E_19(tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42), A!41, F!43), tptp_fun_E_19(tptp_fun_Y_20(C!39, A!41, compose_function(G!42, F!43, A!41, B!40, C!39)), B!40, G!42)))),
% 0.47/0.63 inference(modus_ponens,[status(thm)],[287, 286])).
% 0.47/0.63 tff(289,plain,
% 0.47/0.63 ($false),
% 0.47/0.63 inference(unit_resolution,[status(thm)],[288, 245, 282, 280, 278])).
% 0.47/0.63 % SZS output end Proof
% 0.47/0.63 % E exiting
%------------------------------------------------------------------------------