%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET715+4 : TPTP v9.0.0. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n008.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 0.12s 0.40s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SET715+4 : TPTP v9.0.0. Bugfixed v2.2.1.
% 0.12/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n008.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 05:38:48 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.12/0.40 % SZS status Theorem
% 0.12/0.40 % SZS output start Proof
% 0.12/0.40 tff(apply_type, type, (
% 0.12/0.40 apply: ( $i * $i * $i ) > $o)).
% 0.12/0.40 tff(tptp_fun_E_19_type, type, (
% 0.12/0.40 tptp_fun_E_19: ( $i * $i * $i ) > $i)).
% 0.12/0.40 tff(tptp_fun_F_41_type, type, (
% 0.12/0.40 tptp_fun_F_41: $i)).
% 0.12/0.40 tff(tptp_fun_A_40_type, type, (
% 0.12/0.40 tptp_fun_A_40: $i)).
% 0.12/0.40 tff(tptp_fun_X_15_type, type, (
% 0.12/0.40 tptp_fun_X_15: ( $i * $i ) > $i)).
% 0.12/0.40 tff(compose_function_type, type, (
% 0.12/0.40 compose_function: ( $i * $i * $i * $i * $i ) > $i)).
% 0.12/0.40 tff(tptp_fun_B_39_type, type, (
% 0.12/0.40 tptp_fun_B_39: $i)).
% 0.12/0.40 tff(inverse_function_type, type, (
% 0.12/0.40 inverse_function: ( $i * $i * $i ) > $i)).
% 0.12/0.40 tff(member_type, type, (
% 0.12/0.40 member: ( $i * $i ) > $o)).
% 0.12/0.40 tff(surjective_type, type, (
% 0.12/0.40 surjective: ( $i * $i * $i ) > $o)).
% 0.12/0.40 tff(tptp_fun_Y_20_type, type, (
% 0.12/0.40 tptp_fun_Y_20: ( $i * $i * $i ) > $i)).
% 0.12/0.40 tff(injective_type, type, (
% 0.12/0.40 injective: ( $i * $i * $i ) > $o)).
% 0.12/0.40 tff(one_to_one_type, type, (
% 0.12/0.40 one_to_one: ( $i * $i * $i ) > $o)).
% 0.12/0.40 tff(maps_type, type, (
% 0.12/0.40 maps: ( $i * $i * $i ) > $o)).
% 0.12/0.40 tff(identity_type, type, (
% 0.12/0.40 identity: ( $i * $i ) > $o)).
% 0.12/0.40 tff(tptp_fun_Y_8_type, type, (
% 0.12/0.40 tptp_fun_Y_8: ( $i * $i * $i * $i * $i ) > $i)).
% 0.12/0.40 tff(1,plain,
% 0.12/0.40 (^[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))))))))))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(2,plain,
% 0.12/0.40 (![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)))))))))))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[1])).
% 0.12/0.40 tff(3,plain,
% 0.12/0.40 (^[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))))))))))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(4,plain,
% 0.12/0.40 (![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)))))))))))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[3])).
% 0.12/0.40 tff(5,plain,
% 0.12/0.40 (![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)))))))))))),
% 0.12/0.40 inference(transitivity,[status(thm)],[4, 2])).
% 0.12/0.40 tff(6,plain,
% 0.12/0.40 (^[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)))))))))))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(7,plain,
% 0.12/0.40 (![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)))))))))))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[6])).
% 0.12/0.40 tff(8,plain,
% 0.12/0.40 (![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))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(9,plain,
% 0.12/0.40 (^[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)))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(10,plain,
% 0.12/0.40 (![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))))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[9])).
% 0.12/0.40 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/sandbox2/benchmark/Axioms/SET006+1.ax','surjective')).
% 0.12/0.40 tff(12,plain,
% 0.12/0.40 (![F: $i, A: $i, B: $i] : (surjective(F, A, B) <=> ![Y: $i] : ((~member(Y, B)) | ?[E: $i] : (member(E, A) & apply(F, E, Y))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.12/0.40 tff(13,plain,
% 0.12/0.40 (![F: $i, A: $i, B: $i] : (surjective(F, A, B) <=> ![Y: $i] : ((~member(Y, B)) | ?[E: $i] : (member(E, A) & apply(F, E, Y))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[12, 8])).
% 0.12/0.40 tff(14,plain,(
% 0.12/0.40 ![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)))))))),
% 0.12/0.40 inference(skolemize,[status(sab)],[13])).
% 0.12/0.40 tff(15,plain,
% 0.12/0.40 (![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)))))))))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[14, 7])).
% 0.12/0.40 tff(16,plain,
% 0.12/0.40 (![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)))))))))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[15, 5])).
% 0.12/0.40 tff(17,plain,
% 0.12/0.40 ((~![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)))))))))))) | (~((~((~surjective(F!41, A!40, B!39)) | ![Y: $i] : ((~member(Y, B!39)) | (~((~member(tptp_fun_E_19(Y, A!40, F!41), A!40)) | (~apply(F!41, tptp_fun_E_19(Y, A!40, F!41), Y))))))) | (~(surjective(F!41, A!40, B!39) | (~((~member(tptp_fun_Y_20(B!39, A!40, F!41), B!39)) | (~![E: $i] : ((~member(E, A!40)) | (~apply(F!41, E, tptp_fun_Y_20(B!39, A!40, F!41)))))))))))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(18,plain,
% 0.12/0.40 (~((~((~surjective(F!41, A!40, B!39)) | ![Y: $i] : ((~member(Y, B!39)) | (~((~member(tptp_fun_E_19(Y, A!40, F!41), A!40)) | (~apply(F!41, tptp_fun_E_19(Y, A!40, F!41), Y))))))) | (~(surjective(F!41, A!40, B!39) | (~((~member(tptp_fun_Y_20(B!39, A!40, F!41), B!39)) | (~![E: $i] : ((~member(E, A!40)) | (~apply(F!41, E, tptp_fun_Y_20(B!39, A!40, F!41))))))))))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.12/0.40 tff(19,plain,
% 0.12/0.40 (((~((~surjective(F!41, A!40, B!39)) | ![Y: $i] : ((~member(Y, B!39)) | (~((~member(tptp_fun_E_19(Y, A!40, F!41), A!40)) | (~apply(F!41, tptp_fun_E_19(Y, A!40, F!41), Y))))))) | (~(surjective(F!41, A!40, B!39) | (~((~member(tptp_fun_Y_20(B!39, A!40, F!41), B!39)) | (~![E: $i] : ((~member(E, A!40)) | (~apply(F!41, E, tptp_fun_Y_20(B!39, A!40, F!41)))))))))) | ((~surjective(F!41, A!40, B!39)) | ![Y: $i] : ((~member(Y, B!39)) | (~((~member(tptp_fun_E_19(Y, A!40, F!41), A!40)) | (~apply(F!41, tptp_fun_E_19(Y, A!40, F!41), Y))))))),
% 0.12/0.40 inference(tautology,[status(thm)],[])).
% 0.12/0.40 tff(20,plain,
% 0.12/0.40 ((~surjective(F!41, A!40, B!39)) | ![Y: $i] : ((~member(Y, B!39)) | (~((~member(tptp_fun_E_19(Y, A!40, F!41), A!40)) | (~apply(F!41, tptp_fun_E_19(Y, A!40, F!41), Y)))))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[19, 18])).
% 0.12/0.40 tff(21,plain,
% 0.12/0.40 (^[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))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(22,plain,
% 0.12/0.40 (![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)))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[21])).
% 0.12/0.40 tff(23,plain,
% 0.12/0.40 (^[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)))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(24,plain,
% 0.12/0.40 (![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)))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[23])).
% 0.12/0.40 tff(25,plain,
% 0.12/0.40 (![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)))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(26,axiom,(![F: $i, A: $i, B: $i] : (one_to_one(F, A, B) <=> (injective(F, A, B) & surjective(F, A, B)))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+1.ax','one_to_one')).
% 0.12/0.41 tff(27,plain,
% 0.12/0.41 (![F: $i, A: $i, B: $i] : (one_to_one(F, A, B) <=> (injective(F, A, B) & surjective(F, A, B)))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.12/0.41 tff(28,plain,(
% 0.12/0.41 ![F: $i, A: $i, B: $i] : (one_to_one(F, A, B) <=> (injective(F, A, B) & surjective(F, A, B)))),
% 0.12/0.41 inference(skolemize,[status(sab)],[27])).
% 0.12/0.41 tff(29,plain,
% 0.12/0.41 (![F: $i, A: $i, B: $i] : (~(((~injective(F, A, B)) | (~surjective(F, A, B))) <=> one_to_one(F, A, B)))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[28, 24])).
% 0.12/0.41 tff(30,plain,
% 0.12/0.41 (![F: $i, A: $i, B: $i] : (~(((~injective(F, A, B)) | (~surjective(F, A, B))) <=> one_to_one(F, A, B)))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[29, 22])).
% 0.12/0.41 tff(31,plain,
% 0.12/0.41 ((~![F: $i, A: $i, B: $i] : (~(((~injective(F, A, B)) | (~surjective(F, A, B))) <=> one_to_one(F, A, B)))) | (~(((~injective(F!41, A!40, B!39)) | (~surjective(F!41, A!40, B!39))) <=> one_to_one(F!41, A!40, B!39)))),
% 0.12/0.41 inference(quant_inst,[status(thm)],[])).
% 0.12/0.41 tff(32,plain,
% 0.12/0.41 (~(((~injective(F!41, A!40, B!39)) | (~surjective(F!41, A!40, B!39))) <=> one_to_one(F!41, A!40, B!39))),
% 0.12/0.41 inference(unit_resolution,[status(thm)],[31, 30])).
% 0.12/0.41 tff(33,plain,
% 0.12/0.41 ((~![F: $i, A: $i, B: $i] : ((~(maps(F, A, B) & one_to_one(F, A, B))) | identity(compose_function(F, inverse_function(F, A, B), B, A, B), B))) <=> (~![F: $i, A: $i, B: $i] : ((~(maps(F, A, B) & one_to_one(F, A, B))) | identity(compose_function(F, inverse_function(F, A, B), B, A, B), B)))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(34,plain,
% 0.12/0.41 ((~![F: $i, A: $i, B: $i] : ((maps(F, A, B) & one_to_one(F, A, B)) => identity(compose_function(F, inverse_function(F, A, B), B, A, B), B))) <=> (~![F: $i, A: $i, B: $i] : ((~(maps(F, A, B) & one_to_one(F, A, B))) | identity(compose_function(F, inverse_function(F, A, B), B, A, B), B)))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(35,axiom,(~![F: $i, A: $i, B: $i] : ((maps(F, A, B) & one_to_one(F, A, B)) => identity(compose_function(F, inverse_function(F, A, B), B, A, B), B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thII06')).
% 0.12/0.41 tff(36,plain,
% 0.12/0.41 (~![F: $i, A: $i, B: $i] : ((~(maps(F, A, B) & one_to_one(F, A, B))) | identity(compose_function(F, inverse_function(F, A, B), B, A, B), B))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.12/0.41 tff(37,plain,
% 0.12/0.41 (~![F: $i, A: $i, B: $i] : ((~(maps(F, A, B) & one_to_one(F, A, B))) | identity(compose_function(F, inverse_function(F, A, B), B, A, B), B))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[36, 33])).
% 0.12/0.41 tff(38,plain,
% 0.12/0.41 (~![F: $i, A: $i, B: $i] : ((~(maps(F, A, B) & one_to_one(F, A, B))) | identity(compose_function(F, inverse_function(F, A, B), B, A, B), B))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[37, 33])).
% 0.12/0.41 tff(39,plain,
% 0.12/0.41 (~![F: $i, A: $i, B: $i] : ((~(maps(F, A, B) & one_to_one(F, A, B))) | identity(compose_function(F, inverse_function(F, A, B), B, A, B), B))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[38, 33])).
% 0.12/0.41 tff(40,plain,(
% 0.12/0.41 ~((~(maps(F!41, A!40, B!39) & one_to_one(F!41, A!40, B!39))) | identity(compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39), B!39))),
% 0.12/0.41 inference(skolemize,[status(sab)],[39])).
% 0.12/0.41 tff(41,plain,
% 0.12/0.41 (maps(F!41, A!40, B!39) & one_to_one(F!41, A!40, B!39)),
% 0.12/0.41 inference(or_elim,[status(thm)],[40])).
% 0.12/0.41 tff(42,plain,
% 0.12/0.41 (one_to_one(F!41, A!40, B!39)),
% 0.12/0.41 inference(and_elim,[status(thm)],[41])).
% 0.12/0.41 tff(43,plain,
% 0.12/0.41 ((((~injective(F!41, A!40, B!39)) | (~surjective(F!41, A!40, B!39))) <=> one_to_one(F!41, A!40, B!39)) | (~((~injective(F!41, A!40, B!39)) | (~surjective(F!41, A!40, B!39)))) | (~one_to_one(F!41, A!40, B!39))),
% 0.12/0.41 inference(tautology,[status(thm)],[])).
% 0.12/0.41 tff(44,plain,
% 0.12/0.41 ((((~injective(F!41, A!40, B!39)) | (~surjective(F!41, A!40, B!39))) <=> one_to_one(F!41, A!40, B!39)) | (~((~injective(F!41, A!40, B!39)) | (~surjective(F!41, A!40, B!39))))),
% 0.12/0.41 inference(unit_resolution,[status(thm)],[43, 42])).
% 0.12/0.41 tff(45,plain,
% 0.12/0.41 (~((~injective(F!41, A!40, B!39)) | (~surjective(F!41, A!40, B!39)))),
% 0.12/0.41 inference(unit_resolution,[status(thm)],[44, 32])).
% 0.12/0.41 tff(46,plain,
% 0.12/0.41 (((~injective(F!41, A!40, B!39)) | (~surjective(F!41, A!40, B!39))) | surjective(F!41, A!40, B!39)),
% 0.12/0.41 inference(tautology,[status(thm)],[])).
% 0.12/0.41 tff(47,plain,
% 0.12/0.41 (surjective(F!41, A!40, B!39)),
% 0.12/0.41 inference(unit_resolution,[status(thm)],[46, 45])).
% 0.12/0.41 tff(48,plain,
% 0.12/0.41 ((~((~surjective(F!41, A!40, B!39)) | ![Y: $i] : ((~member(Y, B!39)) | (~((~member(tptp_fun_E_19(Y, A!40, F!41), A!40)) | (~apply(F!41, tptp_fun_E_19(Y, A!40, F!41), Y))))))) | (~surjective(F!41, A!40, B!39)) | ![Y: $i] : ((~member(Y, B!39)) | (~((~member(tptp_fun_E_19(Y, A!40, F!41), A!40)) | (~apply(F!41, tptp_fun_E_19(Y, A!40, F!41), Y)))))),
% 0.12/0.41 inference(tautology,[status(thm)],[])).
% 0.12/0.41 tff(49,plain,
% 0.12/0.41 ((~((~surjective(F!41, A!40, B!39)) | ![Y: $i] : ((~member(Y, B!39)) | (~((~member(tptp_fun_E_19(Y, A!40, F!41), A!40)) | (~apply(F!41, tptp_fun_E_19(Y, A!40, F!41), Y))))))) | ![Y: $i] : ((~member(Y, B!39)) | (~((~member(tptp_fun_E_19(Y, A!40, F!41), A!40)) | (~apply(F!41, tptp_fun_E_19(Y, A!40, F!41), Y)))))),
% 0.12/0.41 inference(unit_resolution,[status(thm)],[48, 47])).
% 0.12/0.41 tff(50,plain,
% 0.12/0.41 (![Y: $i] : ((~member(Y, B!39)) | (~((~member(tptp_fun_E_19(Y, A!40, F!41), A!40)) | (~apply(F!41, tptp_fun_E_19(Y, A!40, F!41), Y)))))),
% 0.12/0.41 inference(unit_resolution,[status(thm)],[49, 20])).
% 0.12/0.41 tff(51,plain,
% 0.12/0.41 (^[F: $i, A: $i] : refl((~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F)))))))) <=> (~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F)))))))))),
% 0.12/0.41 inference(bind,[status(th)],[])).
% 0.12/0.41 tff(52,plain,
% 0.12/0.41 (![F: $i, A: $i] : (~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F)))))))) <=> ![F: $i, A: $i] : (~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F))))))))),
% 0.12/0.41 inference(quant_intro,[status(thm)],[51])).
% 0.12/0.41 tff(53,plain,
% 0.12/0.41 (^[F: $i, A: $i] : rewrite((~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F)))))))) <=> (~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F)))))))))),
% 0.12/0.41 inference(bind,[status(th)],[])).
% 0.12/0.41 tff(54,plain,
% 0.12/0.41 (![F: $i, A: $i] : (~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F)))))))) <=> ![F: $i, A: $i] : (~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F))))))))),
% 0.12/0.41 inference(quant_intro,[status(thm)],[53])).
% 0.12/0.41 tff(55,plain,
% 0.12/0.41 (![F: $i, A: $i] : (~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F)))))))) <=> ![F: $i, A: $i] : (~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F))))))))),
% 0.12/0.41 inference(transitivity,[status(thm)],[54, 52])).
% 0.12/0.41 tff(56,plain,
% 0.12/0.41 (^[F: $i, A: $i] : trans(monotonicity(rewrite(((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X))) <=> ((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))), rewrite((identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F))))) <=> (identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F)))))), ((((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X))) & (identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F)))))) <=> (((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X))) & (identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F)))))))), rewrite((((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X))) & (identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F)))))) <=> (~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F))))))))), ((((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X))) & (identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F)))))) <=> (~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F))))))))))),
% 0.12/0.41 inference(bind,[status(th)],[])).
% 0.12/0.41 tff(57,plain,
% 0.12/0.41 (![F: $i, A: $i] : (((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X))) & (identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F)))))) <=> ![F: $i, A: $i] : (~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F))))))))),
% 0.12/0.41 inference(quant_intro,[status(thm)],[56])).
% 0.12/0.41 tff(58,plain,
% 0.12/0.41 (![F: $i, A: $i] : (identity(F, A) <=> ![X: $i] : ((~member(X, A)) | apply(F, X, X))) <=> ![F: $i, A: $i] : (identity(F, A) <=> ![X: $i] : ((~member(X, A)) | apply(F, X, X)))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(59,plain,
% 0.12/0.41 (^[F: $i, A: $i] : rewrite((identity(F, A) <=> ![X: $i] : (member(X, A) => apply(F, X, X))) <=> (identity(F, A) <=> ![X: $i] : ((~member(X, A)) | apply(F, X, X))))),
% 0.12/0.41 inference(bind,[status(th)],[])).
% 0.12/0.41 tff(60,plain,
% 0.12/0.41 (![F: $i, A: $i] : (identity(F, A) <=> ![X: $i] : (member(X, A) => apply(F, X, X))) <=> ![F: $i, A: $i] : (identity(F, A) <=> ![X: $i] : ((~member(X, A)) | apply(F, X, X)))),
% 0.12/0.41 inference(quant_intro,[status(thm)],[59])).
% 0.12/0.41 tff(61,axiom,(![F: $i, A: $i] : (identity(F, A) <=> ![X: $i] : (member(X, A) => apply(F, X, X)))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+1.ax','identity')).
% 0.12/0.41 tff(62,plain,
% 0.12/0.41 (![F: $i, A: $i] : (identity(F, A) <=> ![X: $i] : ((~member(X, A)) | apply(F, X, X)))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.12/0.41 tff(63,plain,
% 0.12/0.41 (![F: $i, A: $i] : (identity(F, A) <=> ![X: $i] : ((~member(X, A)) | apply(F, X, X)))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[62, 58])).
% 0.12/0.41 tff(64,plain,(
% 0.12/0.41 ![F: $i, A: $i] : (((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X))) & (identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F))))))),
% 0.12/0.41 inference(skolemize,[status(sab)],[63])).
% 0.12/0.41 tff(65,plain,
% 0.12/0.41 (![F: $i, A: $i] : (~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F))))))))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[64, 57])).
% 0.12/0.41 tff(66,plain,
% 0.12/0.41 (![F: $i, A: $i] : (~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F))))))))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[65, 55])).
% 0.12/0.41 tff(67,plain,
% 0.12/0.41 ((~![F: $i, A: $i] : (~((~((~identity(F, A)) | ![X: $i] : ((~member(X, A)) | apply(F, X, X)))) | (~(identity(F, A) | (~((~member(tptp_fun_X_15(A, F), A)) | apply(F, tptp_fun_X_15(A, F), tptp_fun_X_15(A, F))))))))) | (~((~((~identity(compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39), B!39)) | ![X: $i] : ((~member(X, B!39)) | apply(compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39), X, X)))) | (~(identity(compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39), B!39) | (~((~member(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), B!39)) | apply(compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)))))))))),
% 0.12/0.41 inference(quant_inst,[status(thm)],[])).
% 0.12/0.41 tff(68,plain,
% 0.12/0.41 (~((~((~identity(compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39), B!39)) | ![X: $i] : ((~member(X, B!39)) | apply(compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39), X, X)))) | (~(identity(compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39), B!39) | (~((~member(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), B!39)) | apply(compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39))))))))),
% 0.12/0.41 inference(unit_resolution,[status(thm)],[67, 66])).
% 0.12/0.41 tff(69,plain,
% 0.12/0.41 (((~((~identity(compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39), B!39)) | ![X: $i] : ((~member(X, B!39)) | apply(compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39), X, X)))) | (~(identity(compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39), B!39) | (~((~member(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), B!39)) | apply(compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)))))))) | (identity(compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39), B!39) | (~((~member(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), B!39)) | apply(compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39))))))),
% 0.12/0.41 inference(tautology,[status(thm)],[])).
% 0.12/0.41 tff(70,plain,
% 0.12/0.41 (identity(compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39), B!39) | (~((~member(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), B!39)) | apply(compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)))))),
% 0.12/0.41 inference(unit_resolution,[status(thm)],[69, 68])).
% 0.12/0.41 tff(71,plain,
% 0.12/0.41 (~identity(compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39), B!39)),
% 0.12/0.41 inference(or_elim,[status(thm)],[40])).
% 0.12/0.41 tff(72,plain,
% 0.12/0.41 ((~(identity(compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39), B!39) | (~((~member(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), B!39)) | apply(compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39))))))) | identity(compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39), B!39) | (~((~member(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), B!39)) | apply(compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)))))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(73,plain,
% 0.20/0.42 ((~(identity(compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39), B!39) | (~((~member(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), B!39)) | apply(compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39))))))) | (~((~member(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), B!39)) | apply(compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)))))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[72, 71])).
% 0.20/0.42 tff(74,plain,
% 0.20/0.42 (~((~member(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), B!39)) | apply(compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39))))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[73, 70])).
% 0.20/0.42 tff(75,plain,
% 0.20/0.42 (((~member(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), B!39)) | apply(compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)))) | member(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), B!39)),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(76,plain,
% 0.20/0.42 (member(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), B!39)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[75, 74])).
% 0.20/0.42 tff(77,plain,
% 0.20/0.42 (((~![Y: $i] : ((~member(Y, B!39)) | (~((~member(tptp_fun_E_19(Y, A!40, F!41), A!40)) | (~apply(F!41, tptp_fun_E_19(Y, A!40, F!41), Y)))))) | ((~member(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), B!39)) | (~((~member(tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41), A!40)) | (~apply(F!41, tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)))))))) <=> ((~![Y: $i] : ((~member(Y, B!39)) | (~((~member(tptp_fun_E_19(Y, A!40, F!41), A!40)) | (~apply(F!41, tptp_fun_E_19(Y, A!40, F!41), Y)))))) | (~member(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), B!39)) | (~((~member(tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41), A!40)) | (~apply(F!41, tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)))))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(78,plain,
% 0.20/0.42 ((~![Y: $i] : ((~member(Y, B!39)) | (~((~member(tptp_fun_E_19(Y, A!40, F!41), A!40)) | (~apply(F!41, tptp_fun_E_19(Y, A!40, F!41), Y)))))) | ((~member(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), B!39)) | (~((~member(tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41), A!40)) | (~apply(F!41, tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)))))))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(79,plain,
% 0.20/0.42 ((~![Y: $i] : ((~member(Y, B!39)) | (~((~member(tptp_fun_E_19(Y, A!40, F!41), A!40)) | (~apply(F!41, tptp_fun_E_19(Y, A!40, F!41), Y)))))) | (~member(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), B!39)) | (~((~member(tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41), A!40)) | (~apply(F!41, tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39))))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.20/0.42 tff(80,plain,
% 0.20/0.42 (~((~member(tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41), A!40)) | (~apply(F!41, tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)))))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[79, 76, 50])).
% 0.20/0.42 tff(81,plain,
% 0.20/0.42 (((~member(tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41), A!40)) | (~apply(F!41, tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39))))) | apply(F!41, tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(82,plain,
% 0.20/0.42 (apply(F!41, tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[81, 80])).
% 0.20/0.42 tff(83,plain,
% 0.20/0.42 (((~member(tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41), A!40)) | (~apply(F!41, tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39))))) | member(tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41), A!40)),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(84,plain,
% 0.20/0.42 (member(tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41), A!40)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[83, 80])).
% 0.20/0.42 tff(85,plain,
% 0.20/0.42 (^[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)))))))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(86,plain,
% 0.20/0.43 (![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))))))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[85])).
% 0.20/0.43 tff(87,plain,
% 0.20/0.43 (^[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)))))))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(88,plain,
% 0.20/0.43 (![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))))))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[87])).
% 0.20/0.43 tff(89,plain,
% 0.20/0.43 (![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))))))))),
% 0.20/0.43 inference(transitivity,[status(thm)],[88, 86])).
% 0.20/0.43 tff(90,plain,
% 0.20/0.43 (^[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))))))))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(91,plain,
% 0.20/0.43 (![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))))))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[90])).
% 0.20/0.43 tff(92,plain,
% 0.20/0.43 (![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))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(93,plain,
% 0.20/0.43 (^[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))))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(94,plain,
% 0.20/0.43 (![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))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[93])).
% 0.20/0.43 tff(95,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/sandbox2/benchmark/Axioms/SET006+1.ax','compose_function')).
% 0.20/0.43 tff(96,plain,
% 0.20/0.43 (![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))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.20/0.43 tff(97,plain,
% 0.20/0.43 (![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))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[96, 92])).
% 0.20/0.43 tff(98,plain,(
% 0.20/0.43 ![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))))))),
% 0.20/0.43 inference(skolemize,[status(sab)],[97])).
% 0.20/0.43 tff(99,plain,
% 0.20/0.43 (![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))))))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[98, 91])).
% 0.20/0.43 tff(100,plain,
% 0.20/0.43 (![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))))))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[99, 89])).
% 0.20/0.43 tff(101,plain,
% 0.20/0.43 (((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), B!39)) | (~((~(apply(compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39))) | ![Y: $i] : ((~member(Y, A!40)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), Y)) | (~apply(F!41, Y, tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39))))))) | (~((~apply(compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)))) | (~((~apply(F!41, tptp_fun_Y_8(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, inverse_function(F!41, A!40, B!39), F!41), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)))) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_Y_8(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, inverse_function(F!41, A!40, B!39), F!41))) | (~member(tptp_fun_Y_8(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, inverse_function(F!41, A!40, B!39), F!41), A!40)))))))))) <=> ((~![G: $i, F: $i, A: $i, B: $i, C: $i, X: $i, Z: $i] : ((~member(Z, C)) | (~member(X, A)) | (~((~((~apply(compose_function(G, F, A, B, C), X, Z)) | (~((~member(tptp_fun_Y_8(Z, X, B, F, G), B)) | (~apply(F, X, tptp_fun_Y_8(Z, X, B, F, G))) | (~apply(G, tptp_fun_Y_8(Z, X, B, F, G), Z)))))) | (~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | (~member(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), B!39)) | (~((~(apply(compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39))) | ![Y: $i] : ((~member(Y, A!40)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), Y)) | (~apply(F!41, Y, tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39))))))) | (~((~apply(compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)))) | (~((~apply(F!41, tptp_fun_Y_8(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, inverse_function(F!41, A!40, B!39), F!41), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)))) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_Y_8(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, inverse_function(F!41, A!40, B!39), F!41))) | (~member(tptp_fun_Y_8(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, inverse_function(F!41, A!40, B!39), F!41), A!40)))))))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(102,plain,
% 0.20/0.44 (((~member(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), B!39)) | (~member(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), B!39)) | (~((~(apply(compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39))) | ![Y: $i] : ((~member(Y, A!40)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), Y)) | (~apply(F!41, Y, tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39))))))) | (~((~apply(compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)))) | (~((~apply(F!41, tptp_fun_Y_8(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, inverse_function(F!41, A!40, B!39), F!41), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)))) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_Y_8(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, inverse_function(F!41, A!40, B!39), F!41))) | (~member(tptp_fun_Y_8(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, inverse_function(F!41, A!40, B!39), F!41), A!40))))))))) <=> ((~member(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), B!39)) | (~((~(apply(compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39))) | ![Y: $i] : ((~member(Y, A!40)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), Y)) | (~apply(F!41, Y, tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39))))))) | (~((~apply(compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)))) | (~((~apply(F!41, tptp_fun_Y_8(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, inverse_function(F!41, A!40, B!39), F!41), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)))) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_Y_8(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, inverse_function(F!41, A!40, B!39), F!41))) | (~member(tptp_fun_Y_8(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, inverse_function(F!41, A!40, B!39), F!41), A!40)))))))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(103,plain,
% 0.20/0.44 ((~((~((~apply(compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, inverse_function(F!41, A!40, B!39), F!41), A!40)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_Y_8(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, inverse_function(F!41, A!40, B!39), F!41))) | (~apply(F!41, tptp_fun_Y_8(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, inverse_function(F!41, A!40, B!39), F!41), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)))))))) | (~(apply(compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39))) | ![Y: $i] : ((~member(Y, A!40)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), Y)) | (~apply(F!41, Y, tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39))))))))) <=> (~((~(apply(compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39))) | ![Y: $i] : ((~member(Y, A!40)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), Y)) | (~apply(F!41, Y, tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39))))))) | (~((~apply(compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)))) | (~((~apply(F!41, tptp_fun_Y_8(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, inverse_function(F!41, A!40, B!39), F!41), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)))) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_Y_8(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, inverse_function(F!41, A!40, B!39), F!41))) | (~member(tptp_fun_Y_8(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, inverse_function(F!41, A!40, B!39), F!41), A!40))))))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(104,plain,
% 0.20/0.45 (((~member(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), B!39)) | (~member(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), B!39)) | (~((~((~apply(compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, inverse_function(F!41, A!40, B!39), F!41), A!40)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_Y_8(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, inverse_function(F!41, A!40, B!39), F!41))) | (~apply(F!41, tptp_fun_Y_8(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, inverse_function(F!41, A!40, B!39), F!41), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)))))))) | (~(apply(compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39))) | ![Y: $i] : ((~member(Y, A!40)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), Y)) | (~apply(F!41, Y, tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)))))))))) <=> ((~member(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), B!39)) | (~member(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), B!39)) | (~((~(apply(compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39))) | ![Y: $i] : ((~member(Y, A!40)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), Y)) | (~apply(F!41, Y, tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39))))))) | (~((~apply(compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)))) | (~((~apply(F!41, tptp_fun_Y_8(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, inverse_function(F!41, A!40, B!39), F!41), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)))) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_Y_8(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, inverse_function(F!41, A!40, B!39), F!41))) | (~member(tptp_fun_Y_8(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, inverse_function(F!41, A!40, B!39), F!41), A!40)))))))))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[103])).
% 0.20/0.45 tff(105,plain,
% 0.20/0.45 (((~member(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), B!39)) | (~member(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), B!39)) | (~((~((~apply(compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)))) | (~((~member(tptp_fun_Y_8(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, inverse_function(F!41, A!40, B!39), F!41), A!40)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_Y_8(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, inverse_function(F!41, A!40, B!39), F!41))) | (~apply(F!41, tptp_fun_Y_8(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, inverse_function(F!41, A!40, B!39), F!41), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)))))))) | (~(apply(compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39))) | ![Y: $i] : ((~member(Y, A!40)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), Y)) | (~apply(F!41, Y, tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)))))))))) <=> ((~member(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), B!39)) | (~((~(apply(compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39))) | ![Y: $i] : ((~member(Y, A!40)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), Y)) | (~apply(F!41, Y, tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39))))))) | (~((~apply(compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)))) | (~((~apply(F!41, tptp_fun_Y_8(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, inverse_function(F!41, A!40, B!39), F!41), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)))) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_Y_8(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, inverse_function(F!41, A!40, B!39), F!41))) | (~member(tptp_fun_Y_8(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, inverse_function(F!41, A!40, B!39), F!41), A!40)))))))))),
% 0.20/0.46 inference(transitivity,[status(thm)],[104, 102])).
% 0.20/0.46 tff(106,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))))))))) | ((~member(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), B!39)) | (~member(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), B!39)) | (~((~((~apply(compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)))) | 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(~(apply(compose_function(G, F, A, B, C), X, Z) | ![Y: $i] : ((~member(Y, B)) | (~apply(F, X, Y)) | (~apply(G, Y, Z))))))))) | ((~member(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), B!39)) | (~((~(apply(compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39))) | ![Y: $i] : ((~member(Y, A!40)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), Y)) | (~apply(F!41, Y, tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39))))))) | (~((~apply(compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, 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% 0.20/0.46 inference(monotonicity,[status(thm)],[105])).
% 0.20/0.46 tff(107,plain,
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% 0.20/0.47 inference(transitivity,[status(thm)],[106, 101])).
% 0.20/0.47 tff(108,plain,
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% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 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))))))))) | (~member(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), B!39)) | (~((~(apply(compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39))) | ![Y: $i] : ((~member(Y, A!40)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), Y)) | (~apply(F!41, Y, tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39))))))) | (~((~apply(compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)))) | (~((~apply(F!41, tptp_fun_Y_8(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, inverse_function(F!41, A!40, B!39), F!41), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)))) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_Y_8(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, inverse_function(F!41, A!40, B!39), F!41))) | (~member(tptp_fun_Y_8(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, inverse_function(F!41, A!40, B!39), F!41), A!40))))))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[108, 107])).
% 0.20/0.47 tff(110,plain,
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% 0.20/0.47 inference(unit_resolution,[status(thm)],[109, 100, 76])).
% 0.20/0.47 tff(111,plain,
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% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(112,plain,
% 0.20/0.47 (apply(compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39))) | ![Y: $i] : ((~member(Y, A!40)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), Y)) | (~apply(F!41, Y, tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[111, 110])).
% 0.20/0.48 tff(113,plain,
% 0.20/0.48 (((~member(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), B!39)) | apply(compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)))) | (~apply(compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39))))),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(114,plain,
% 0.20/0.48 (~apply(compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[113, 74])).
% 0.20/0.48 tff(115,plain,
% 0.20/0.48 ((~(apply(compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39))) | ![Y: $i] : ((~member(Y, A!40)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), Y)) | (~apply(F!41, Y, tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39))))))) | apply(compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39))) | ![Y: $i] : ((~member(Y, A!40)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), Y)) | (~apply(F!41, Y, tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)))))),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(116,plain,
% 0.20/0.48 ((~(apply(compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39))) | ![Y: $i] : ((~member(Y, A!40)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), Y)) | (~apply(F!41, Y, tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39))))))) | ![Y: $i] : ((~member(Y, A!40)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), Y)) | (~apply(F!41, Y, tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[115, 114])).
% 0.20/0.48 tff(117,plain,
% 0.20/0.48 (![Y: $i] : ((~member(Y, A!40)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), Y)) | (~apply(F!41, Y, tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[116, 112])).
% 0.20/0.48 tff(118,plain,
% 0.20/0.48 (((~![Y: $i] : ((~member(Y, A!40)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), Y)) | (~apply(F!41, Y, tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)))))) | ((~member(tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41), A!40)) | (~apply(F!41, tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)))) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41))))) <=> ((~![Y: $i] : ((~member(Y, A!40)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), Y)) | (~apply(F!41, Y, tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)))))) | (~member(tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41), A!40)) | (~apply(F!41, tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)))) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(119,plain,
% 0.20/0.48 (((~member(tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41), A!40)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41))) | (~apply(F!41, tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39))))) <=> ((~member(tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41), A!40)) | (~apply(F!41, tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)))) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(120,plain,
% 0.20/0.48 (((~![Y: $i] : ((~member(Y, A!40)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), Y)) | (~apply(F!41, Y, tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)))))) | ((~member(tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41), A!40)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41))) | (~apply(F!41, tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)))))) <=> ((~![Y: $i] : ((~member(Y, A!40)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), Y)) | (~apply(F!41, Y, tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)))))) | ((~member(tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41), A!40)) | (~apply(F!41, tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)))) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41)))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[119])).
% 0.20/0.48 tff(121,plain,
% 0.20/0.48 (((~![Y: $i] : ((~member(Y, A!40)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), Y)) | (~apply(F!41, Y, tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)))))) | ((~member(tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41), A!40)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41))) | (~apply(F!41, tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)))))) <=> ((~![Y: $i] : ((~member(Y, A!40)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), Y)) | (~apply(F!41, Y, tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)))))) | (~member(tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41), A!40)) | (~apply(F!41, tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)))) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41))))),
% 0.20/0.48 inference(transitivity,[status(thm)],[120, 118])).
% 0.20/0.48 tff(122,plain,
% 0.20/0.48 ((~![Y: $i] : ((~member(Y, A!40)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), Y)) | (~apply(F!41, Y, tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)))))) | ((~member(tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41), A!40)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41))) | (~apply(F!41, tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)))))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(123,plain,
% 0.20/0.48 ((~![Y: $i] : ((~member(Y, A!40)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), Y)) | (~apply(F!41, Y, tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)))))) | (~member(tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41), A!40)) | (~apply(F!41, tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)))) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[122, 121])).
% 0.20/0.48 tff(124,plain,
% 0.20/0.48 (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[123, 117, 84, 82])).
% 0.20/0.48 tff(125,plain,
% 0.20/0.48 ((~(apply(F!41, tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39))) <=> apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41)))) | (~apply(F!41, tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)))) | apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41))),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(126,plain,
% 0.20/0.48 (~(apply(F!41, tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39))) <=> apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41)))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[125, 82, 124])).
% 0.20/0.48 tff(127,plain,
% 0.20/0.48 (^[F: $i, A: $i, B: $i, X: $i, Y: $i] : refl(((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A))) <=> ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(128,plain,
% 0.20/0.48 (![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A))) <=> ![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[127])).
% 0.20/0.48 tff(129,plain,
% 0.20/0.48 (^[F: $i, A: $i, B: $i, X: $i, Y: $i] : trans(monotonicity(trans(monotonicity(rewrite((member(X, A) & member(Y, B)) <=> (~((~member(Y, B)) | (~member(X, A))))), ((~(member(X, A) & member(Y, B))) <=> (~(~((~member(Y, B)) | (~member(X, A))))))), rewrite((~(~((~member(Y, B)) | (~member(X, A))))) <=> ((~member(Y, B)) | (~member(X, A)))), ((~(member(X, A) & member(Y, B))) <=> ((~member(Y, B)) | (~member(X, A))))), (((~(member(X, A) & member(Y, B))) | (apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X))) <=> (((~member(Y, B)) | (~member(X, A))) | (apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X))))), rewrite((((~member(Y, B)) | (~member(X, A))) | (apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X))) <=> ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))), (((~(member(X, A) & member(Y, B))) | (apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X))) <=> ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(130,plain,
% 0.20/0.48 (![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((~(member(X, A) & member(Y, B))) | (apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X))) <=> ![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[129])).
% 0.20/0.48 tff(131,plain,
% 0.20/0.48 (![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((~(member(X, A) & member(Y, B))) | (apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X))) <=> ![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((~(member(X, A) & member(Y, B))) | (apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(132,plain,
% 0.20/0.48 (^[F: $i, A: $i, B: $i, X: $i, Y: $i] : rewrite(((member(X, A) & member(Y, B)) => (apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X))) <=> ((~(member(X, A) & member(Y, B))) | (apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(133,plain,
% 0.20/0.48 (![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((member(X, A) & member(Y, B)) => (apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X))) <=> ![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((~(member(X, A) & member(Y, B))) | (apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[132])).
% 0.20/0.48 tff(134,axiom,(![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((member(X, A) & member(Y, B)) => (apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)))), file('/export/starexec/sandbox2/benchmark/Axioms/SET006+1.ax','inverse_function')).
% 0.20/0.48 tff(135,plain,
% 0.20/0.48 (![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((~(member(X, A) & member(Y, B))) | (apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[134, 133])).
% 0.20/0.48 tff(136,plain,
% 0.20/0.48 (![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((~(member(X, A) & member(Y, B))) | (apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[135, 131])).
% 0.20/0.48 tff(137,plain,(
% 0.20/0.48 ![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((~(member(X, A) & member(Y, B))) | (apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)))),
% 0.20/0.48 inference(skolemize,[status(sab)],[136])).
% 0.20/0.48 tff(138,plain,
% 0.20/0.48 (![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[137, 130])).
% 0.20/0.48 tff(139,plain,
% 0.20/0.48 (![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[138, 128])).
% 0.20/0.48 tff(140,plain,
% 0.20/0.48 (((~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))) | ((~member(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), B!39)) | (~member(tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41), A!40)) | (apply(F!41, tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39))) <=> apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41))))) <=> ((~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))) | (~member(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), B!39)) | (~member(tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41), A!40)) | (apply(F!41, tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39))) <=> apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(141,plain,
% 0.20/0.49 (((apply(F!41, tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39))) <=> apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41))) | (~member(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), B!39)) | (~member(tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41), A!40))) <=> ((~member(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), B!39)) | (~member(tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41), A!40)) | (apply(F!41, tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39))) <=> apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(142,plain,
% 0.20/0.49 (((~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))) | ((apply(F!41, tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39))) <=> apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41))) | (~member(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), B!39)) | (~member(tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41), A!40)))) <=> ((~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))) | ((~member(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), B!39)) | (~member(tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41), A!40)) | (apply(F!41, tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39))) <=> apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41)))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[141])).
% 0.20/0.49 tff(143,plain,
% 0.20/0.49 (((~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))) | ((apply(F!41, tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39))) <=> apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41))) | (~member(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), B!39)) | (~member(tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41), A!40)))) <=> ((~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))) | (~member(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), B!39)) | (~member(tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41), A!40)) | (apply(F!41, tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39))) <=> apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41))))),
% 0.20/0.49 inference(transitivity,[status(thm)],[142, 140])).
% 0.20/0.49 tff(144,plain,
% 0.20/0.49 ((~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))) | ((apply(F!41, tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39))) <=> apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41))) | (~member(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), B!39)) | (~member(tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41), A!40)))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(145,plain,
% 0.20/0.49 ((~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))) | (~member(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), B!39)) | (~member(tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41), A!40)) | (apply(F!41, tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39))) <=> apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), tptp_fun_E_19(tptp_fun_X_15(B!39, compose_function(F!41, inverse_function(F!41, A!40, B!39), B!39, A!40, B!39)), A!40, F!41)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[144, 143])).
% 0.20/0.49 tff(146,plain,
% 0.20/0.49 ($false),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[145, 139, 76, 84, 126])).
% 0.20/0.49 % SZS output end Proof
% 0.20/0.49 % E exiting
%------------------------------------------------------------------------------