%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET712+4 : TPTP v9.0.0. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:26:12 AM UTC 2025
% Result : Theorem 0.20s 0.39s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET712+4 : TPTP v9.0.0. Bugfixed v2.2.1.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n010.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 05:40:26 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.20/0.39 % SZS status Theorem
% 0.20/0.39 % SZS output start Proof
% 0.20/0.39 tff(apply_type, type, (
% 0.20/0.39 apply: ( $i * $i * $i ) > $o)).
% 0.20/0.39 tff(tptp_fun_X_7_type, type, (
% 0.20/0.39 tptp_fun_X_7: ( $i * $i * $i ) > $i)).
% 0.20/0.39 tff(inverse_function_type, type, (
% 0.20/0.39 inverse_function: ( $i * $i * $i ) > $i)).
% 0.20/0.39 tff(tptp_fun_B_39_type, type, (
% 0.20/0.39 tptp_fun_B_39: $i)).
% 0.20/0.39 tff(tptp_fun_A_40_type, type, (
% 0.20/0.39 tptp_fun_A_40: $i)).
% 0.20/0.39 tff(tptp_fun_F_41_type, type, (
% 0.20/0.39 tptp_fun_F_41: $i)).
% 0.20/0.39 tff(tptp_fun_Y2_5_type, type, (
% 0.20/0.39 tptp_fun_Y2_5: ( $i * $i * $i ) > $i)).
% 0.20/0.39 tff(member_type, type, (
% 0.20/0.39 member: ( $i * $i ) > $o)).
% 0.20/0.39 tff(tptp_fun_Y1_6_type, type, (
% 0.20/0.39 tptp_fun_Y1_6: ( $i * $i * $i ) > $i)).
% 0.20/0.39 tff(tptp_fun_X_4_type, type, (
% 0.20/0.39 tptp_fun_X_4: ( $i * $i * $i ) > $i)).
% 0.20/0.39 tff(tptp_fun_E_19_type, type, (
% 0.20/0.39 tptp_fun_E_19: ( $i * $i * $i ) > $i)).
% 0.20/0.39 tff(surjective_type, type, (
% 0.20/0.39 surjective: ( $i * $i * $i ) > $o)).
% 0.20/0.39 tff(tptp_fun_Y_20_type, type, (
% 0.20/0.39 tptp_fun_Y_20: ( $i * $i * $i ) > $i)).
% 0.20/0.39 tff(injective_type, type, (
% 0.20/0.39 injective: ( $i * $i * $i ) > $o)).
% 0.20/0.39 tff(one_to_one_type, type, (
% 0.20/0.39 one_to_one: ( $i * $i * $i ) > $o)).
% 0.20/0.39 tff(maps_type, type, (
% 0.20/0.39 maps: ( $i * $i * $i ) > $o)).
% 0.20/0.39 tff(tptp_fun_Y_3_type, type, (
% 0.20/0.39 tptp_fun_Y_3: ( $i * $i * $i ) > $i)).
% 0.20/0.39 tff(tptp_fun_X2_17_type, type, (
% 0.20/0.39 tptp_fun_X2_17: ( $i * $i * $i ) > $i)).
% 0.20/0.39 tff(tptp_fun_X1_18_type, type, (
% 0.20/0.39 tptp_fun_X1_18: ( $i * $i * $i ) > $i)).
% 0.20/0.39 tff(tptp_fun_Y_16_type, type, (
% 0.20/0.39 tptp_fun_Y_16: ( $i * $i * $i ) > $i)).
% 0.20/0.39 tff(1,plain,
% 0.20/0.39 (^[F: $i, A: $i, B: $i] : refl((~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))))))) <=> (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))))))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(2,plain,
% 0.20/0.39 (![F: $i, A: $i, B: $i] : (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))))))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.39 tff(3,plain,
% 0.20/0.39 (^[F: $i, A: $i, B: $i] : rewrite((~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))))))) <=> (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))))))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(4,plain,
% 0.20/0.39 (![F: $i, A: $i, B: $i] : (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))))))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[3])).
% 0.20/0.39 tff(5,plain,
% 0.20/0.39 (![F: $i, A: $i, B: $i] : (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))))))),
% 0.20/0.39 inference(transitivity,[status(thm)],[4, 2])).
% 0.20/0.39 tff(6,plain,
% 0.20/0.39 (^[F: $i, A: $i, B: $i] : trans(monotonicity(rewrite(((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (member(tptp_fun_E_19(Y, A, F), A) & apply(F, tptp_fun_E_19(Y, A, F), Y)))) <=> ((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))), trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[E: $i] : trans(monotonicity(rewrite((member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F))) <=> (~((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))), ((~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F)))) <=> (~(~((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))), rewrite((~(~((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))) <=> ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))), ((~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F)))) <=> ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))), (![E: $i] : (~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F)))) <=> ![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))), ((member(tptp_fun_Y_20(B, A, F), B) & ![E: $i] : (~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F))))) <=> (member(tptp_fun_Y_20(B, A, F), B) & ![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))), rewrite((member(tptp_fun_Y_20(B, A, F), B) & ![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))) <=> (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))), ((member(tptp_fun_Y_20(B, A, F), B) & ![E: $i] : (~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F))))) <=> (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))))), ((surjective(F, A, B) | (member(tptp_fun_Y_20(B, A, F), B) & ![E: $i] : (~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F)))))) <=> (surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))))), rewrite((surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))) <=> (surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))))), ((surjective(F, A, B) | (member(tptp_fun_Y_20(B, A, F), B) & ![E: $i] : (~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F)))))) <=> (surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))))), ((((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (member(tptp_fun_E_19(Y, A, F), A) & apply(F, tptp_fun_E_19(Y, A, F), Y)))) & (surjective(F, A, B) | (member(tptp_fun_Y_20(B, A, F), B) & ![E: $i] : (~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F))))))) <=> (((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y)))))) & (surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))))))), rewrite((((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y)))))) & (surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F))))))))) <=> (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))))))), ((((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (member(tptp_fun_E_19(Y, A, F), A) & apply(F, tptp_fun_E_19(Y, A, F), Y)))) & (surjective(F, A, B) | (member(tptp_fun_Y_20(B, A, F), B) & ![E: $i] : (~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F))))))) <=> (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))))))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(7,plain,
% 0.20/0.39 (![F: $i, A: $i, B: $i] : (((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (member(tptp_fun_E_19(Y, A, F), A) & apply(F, tptp_fun_E_19(Y, A, F), Y)))) & (surjective(F, A, B) | (member(tptp_fun_Y_20(B, A, F), B) & ![E: $i] : (~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))))))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[6])).
% 0.20/0.39 tff(8,plain,
% 0.20/0.39 (![F: $i, A: $i, B: $i] : (surjective(F, A, B) <=> ![Y: $i] : ((~member(Y, B)) | ?[E: $i] : (member(E, A) & apply(F, E, Y)))) <=> ![F: $i, A: $i, B: $i] : (surjective(F, A, B) <=> ![Y: $i] : ((~member(Y, B)) | ?[E: $i] : (member(E, A) & apply(F, E, Y))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(9,plain,
% 0.20/0.39 (^[F: $i, A: $i, B: $i] : rewrite((surjective(F, A, B) <=> ![Y: $i] : (member(Y, B) => ?[E: $i] : (member(E, A) & apply(F, E, Y)))) <=> (surjective(F, A, B) <=> ![Y: $i] : ((~member(Y, B)) | ?[E: $i] : (member(E, A) & apply(F, E, Y)))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(10,plain,
% 0.20/0.39 (![F: $i, A: $i, B: $i] : (surjective(F, A, B) <=> ![Y: $i] : (member(Y, B) => ?[E: $i] : (member(E, A) & apply(F, E, Y)))) <=> ![F: $i, A: $i, B: $i] : (surjective(F, A, B) <=> ![Y: $i] : ((~member(Y, B)) | ?[E: $i] : (member(E, A) & apply(F, E, Y))))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[9])).
% 0.20/0.39 tff(11,axiom,(![F: $i, A: $i, B: $i] : (surjective(F, A, B) <=> ![Y: $i] : (member(Y, B) => ?[E: $i] : (member(E, A) & apply(F, E, Y))))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+1.ax','surjective')).
% 0.20/0.39 tff(12,plain,
% 0.20/0.39 (![F: $i, A: $i, B: $i] : (surjective(F, A, B) <=> ![Y: $i] : ((~member(Y, B)) | ?[E: $i] : (member(E, A) & apply(F, E, Y))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.20/0.39 tff(13,plain,
% 0.20/0.39 (![F: $i, A: $i, B: $i] : (surjective(F, A, B) <=> ![Y: $i] : ((~member(Y, B)) | ?[E: $i] : (member(E, A) & apply(F, E, Y))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[12, 8])).
% 0.20/0.39 tff(14,plain,(
% 0.20/0.39 ![F: $i, A: $i, B: $i] : (((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (member(tptp_fun_E_19(Y, A, F), A) & apply(F, tptp_fun_E_19(Y, A, F), Y)))) & (surjective(F, A, B) | (member(tptp_fun_Y_20(B, A, F), B) & ![E: $i] : (~(member(E, A) & apply(F, E, tptp_fun_Y_20(B, A, F)))))))),
% 0.20/0.39 inference(skolemize,[status(sab)],[13])).
% 0.20/0.39 tff(15,plain,
% 0.20/0.39 (![F: $i, A: $i, B: $i] : (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[14, 7])).
% 0.20/0.39 tff(16,plain,
% 0.20/0.39 (![F: $i, A: $i, B: $i] : (~((~((~surjective(F, A, B)) | ![Y: $i] : ((~member(Y, B)) | (~((~member(tptp_fun_E_19(Y, A, F), A)) | (~apply(F, tptp_fun_E_19(Y, A, F), Y))))))) | (~(surjective(F, A, B) | (~((~member(tptp_fun_Y_20(B, A, F), B)) | (~![E: $i] : ((~member(E, A)) | (~apply(F, E, tptp_fun_Y_20(B, A, F)))))))))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[15, 5])).
% 0.20/0.39 tff(17,plain,
% 0.20/0.39 ((~![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)))))))))))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(18,plain,
% 0.20/0.39 (~((~((~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))))))))))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.20/0.39 tff(19,plain,
% 0.20/0.39 (((~((~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))))))),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(20,plain,
% 0.20/0.39 ((~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)))))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[19, 18])).
% 0.20/0.39 tff(21,plain,
% 0.20/0.39 (^[F: $i, A: $i, B: $i] : refl((~(((~injective(F, A, B)) | (~surjective(F, A, B))) <=> one_to_one(F, A, B))) <=> (~(((~injective(F, A, B)) | (~surjective(F, A, B))) <=> one_to_one(F, A, B))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(22,plain,
% 0.20/0.39 (![F: $i, A: $i, B: $i] : (~(((~injective(F, A, B)) | (~surjective(F, A, B))) <=> one_to_one(F, A, B))) <=> ![F: $i, A: $i, B: $i] : (~(((~injective(F, A, B)) | (~surjective(F, A, B))) <=> one_to_one(F, A, B)))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[21])).
% 0.20/0.39 tff(23,plain,
% 0.20/0.39 (^[F: $i, A: $i, B: $i] : trans(trans(monotonicity(rewrite((injective(F, A, B) & surjective(F, A, B)) <=> (~((~injective(F, A, B)) | (~surjective(F, A, B))))), ((one_to_one(F, A, B) <=> (injective(F, A, B) & surjective(F, A, B))) <=> (one_to_one(F, A, B) <=> (~((~injective(F, A, B)) | (~surjective(F, A, B))))))), rewrite((one_to_one(F, A, B) <=> (~((~injective(F, A, B)) | (~surjective(F, A, B))))) <=> (~(((~injective(F, A, B)) | (~surjective(F, A, B))) <=> one_to_one(F, A, B)))), ((one_to_one(F, A, B) <=> (injective(F, A, B) & surjective(F, A, B))) <=> (~(((~injective(F, A, B)) | (~surjective(F, A, B))) <=> one_to_one(F, A, B))))), rewrite((~(((~injective(F, A, B)) | (~surjective(F, A, B))) <=> one_to_one(F, A, B))) <=> (~(((~injective(F, A, B)) | (~surjective(F, A, B))) <=> one_to_one(F, A, B)))), ((one_to_one(F, A, B) <=> (injective(F, A, B) & surjective(F, A, B))) <=> (~(((~injective(F, A, B)) | (~surjective(F, A, B))) <=> one_to_one(F, A, B)))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(24,plain,
% 0.20/0.39 (![F: $i, A: $i, B: $i] : (one_to_one(F, A, B) <=> (injective(F, A, B) & surjective(F, A, B))) <=> ![F: $i, A: $i, B: $i] : (~(((~injective(F, A, B)) | (~surjective(F, A, B))) <=> one_to_one(F, A, B)))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[23])).
% 0.20/0.40 tff(25,plain,
% 0.20/0.40 (![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)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 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/sandbox/benchmark/Axioms/SET006+1.ax','one_to_one')).
% 0.20/0.40 tff(27,plain,
% 0.20/0.40 (![F: $i, A: $i, B: $i] : (one_to_one(F, A, B) <=> (injective(F, A, B) & surjective(F, A, B)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.20/0.40 tff(28,plain,(
% 0.20/0.40 ![F: $i, A: $i, B: $i] : (one_to_one(F, A, B) <=> (injective(F, A, B) & surjective(F, A, B)))),
% 0.20/0.40 inference(skolemize,[status(sab)],[27])).
% 0.20/0.40 tff(29,plain,
% 0.20/0.40 (![F: $i, A: $i, B: $i] : (~(((~injective(F, A, B)) | (~surjective(F, A, B))) <=> one_to_one(F, A, B)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[28, 24])).
% 0.20/0.40 tff(30,plain,
% 0.20/0.40 (![F: $i, A: $i, B: $i] : (~(((~injective(F, A, B)) | (~surjective(F, A, B))) <=> one_to_one(F, A, B)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[29, 22])).
% 0.20/0.40 tff(31,plain,
% 0.20/0.40 ((~![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)))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(32,plain,
% 0.20/0.40 (~(((~injective(F!41, A!40, B!39)) | (~surjective(F!41, A!40, B!39))) <=> one_to_one(F!41, A!40, B!39))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[31, 30])).
% 0.20/0.40 tff(33,plain,
% 0.20/0.40 ((~![F: $i, A: $i, B: $i] : ((~(maps(F, A, B) & one_to_one(F, A, B))) | maps(inverse_function(F, A, B), B, A))) <=> (~![F: $i, A: $i, B: $i] : ((~(maps(F, A, B) & one_to_one(F, A, B))) | maps(inverse_function(F, A, B), B, A)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(34,plain,
% 0.20/0.40 ((~![F: $i, A: $i, B: $i] : ((maps(F, A, B) & one_to_one(F, A, B)) => maps(inverse_function(F, A, B), B, A))) <=> (~![F: $i, A: $i, B: $i] : ((~(maps(F, A, B) & one_to_one(F, A, B))) | maps(inverse_function(F, A, B), B, A)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(35,axiom,(~![F: $i, A: $i, B: $i] : ((maps(F, A, B) & one_to_one(F, A, B)) => maps(inverse_function(F, A, B), B, A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','thII03')).
% 0.20/0.40 tff(36,plain,
% 0.20/0.40 (~![F: $i, A: $i, B: $i] : ((~(maps(F, A, B) & one_to_one(F, A, B))) | maps(inverse_function(F, A, B), B, A))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.20/0.40 tff(37,plain,
% 0.20/0.40 (~![F: $i, A: $i, B: $i] : ((~(maps(F, A, B) & one_to_one(F, A, B))) | maps(inverse_function(F, A, B), B, A))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[36, 33])).
% 0.20/0.40 tff(38,plain,
% 0.20/0.40 (~![F: $i, A: $i, B: $i] : ((~(maps(F, A, B) & one_to_one(F, A, B))) | maps(inverse_function(F, A, B), B, A))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[37, 33])).
% 0.20/0.40 tff(39,plain,
% 0.20/0.40 (~![F: $i, A: $i, B: $i] : ((~(maps(F, A, B) & one_to_one(F, A, B))) | maps(inverse_function(F, A, B), B, A))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[38, 33])).
% 0.20/0.40 tff(40,plain,(
% 0.20/0.40 ~((~(maps(F!41, A!40, B!39) & one_to_one(F!41, A!40, B!39))) | maps(inverse_function(F!41, A!40, B!39), B!39, A!40))),
% 0.20/0.40 inference(skolemize,[status(sab)],[39])).
% 0.20/0.40 tff(41,plain,
% 0.20/0.40 (maps(F!41, A!40, B!39) & one_to_one(F!41, A!40, B!39)),
% 0.20/0.40 inference(or_elim,[status(thm)],[40])).
% 0.20/0.40 tff(42,plain,
% 0.20/0.40 (one_to_one(F!41, A!40, B!39)),
% 0.20/0.40 inference(and_elim,[status(thm)],[41])).
% 0.20/0.40 tff(43,plain,
% 0.20/0.40 ((((~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))),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(44,plain,
% 0.20/0.40 ((((~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))))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[43, 42])).
% 0.20/0.40 tff(45,plain,
% 0.20/0.40 (~((~injective(F!41, A!40, B!39)) | (~surjective(F!41, A!40, B!39)))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[44, 32])).
% 0.20/0.40 tff(46,plain,
% 0.20/0.40 (((~injective(F!41, A!40, B!39)) | (~surjective(F!41, A!40, B!39))) | surjective(F!41, A!40, B!39)),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(47,plain,
% 0.20/0.40 (surjective(F!41, A!40, B!39)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[46, 45])).
% 0.20/0.40 tff(48,plain,
% 0.20/0.40 ((~((~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)) | ![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)))))),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(49,plain,
% 0.20/0.40 ((~((~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))))))) | ![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)))))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[48, 47])).
% 0.20/0.40 tff(50,plain,
% 0.20/0.40 (![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)))))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[49, 20])).
% 0.20/0.40 tff(51,assumption,(~((~member(tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (~![Y: $i] : ((~member(Y, A!40)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), Y)))))), introduced(assumption)).
% 0.20/0.40 tff(52,plain,
% 0.20/0.40 (((~member(tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (~![Y: $i] : ((~member(Y, A!40)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), Y))))) | member(tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(53,plain,
% 0.20/0.40 (member(tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[52, 51])).
% 0.20/0.40 tff(54,plain,
% 0.20/0.40 (((~![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_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (~((~member(tptp_fun_E_19(tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40, F!41), A!40)) | (~apply(F!41, tptp_fun_E_19(tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40, F!41), tptp_fun_X_4(A!40, B!39, inverse_function(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)))))) | (~member(tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (~((~member(tptp_fun_E_19(tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40, F!41), A!40)) | (~apply(F!41, tptp_fun_E_19(tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40, F!41), tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39)))))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(55,plain,
% 0.20/0.40 ((~![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_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (~((~member(tptp_fun_E_19(tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40, F!41), A!40)) | (~apply(F!41, tptp_fun_E_19(tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40, F!41), tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39)))))))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(56,plain,
% 0.20/0.40 ((~![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_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (~((~member(tptp_fun_E_19(tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40, F!41), A!40)) | (~apply(F!41, tptp_fun_E_19(tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40, F!41), tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39))))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.20/0.40 tff(57,plain,
% 0.20/0.40 (~((~member(tptp_fun_E_19(tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40, F!41), A!40)) | (~apply(F!41, tptp_fun_E_19(tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40, F!41), tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39)))))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[56, 53, 50])).
% 0.20/0.40 tff(58,plain,
% 0.20/0.40 (((~member(tptp_fun_E_19(tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40, F!41), A!40)) | (~apply(F!41, tptp_fun_E_19(tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40, F!41), tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39))))) | member(tptp_fun_E_19(tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40, F!41), A!40)),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(59,plain,
% 0.20/0.40 (member(tptp_fun_E_19(tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40, F!41), A!40)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[58, 57])).
% 0.20/0.40 tff(60,plain,
% 0.20/0.40 (((~member(tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (~![Y: $i] : ((~member(Y, A!40)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), Y))))) | ![Y: $i] : ((~member(Y, A!40)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), Y)))),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(61,plain,
% 0.20/0.40 (![Y: $i] : ((~member(Y, A!40)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), Y)))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[60, 51])).
% 0.20/0.40 tff(62,plain,
% 0.20/0.40 (((~![Y: $i] : ((~member(Y, A!40)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), Y)))) | ((~member(tptp_fun_E_19(tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40, F!41), A!40)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_E_19(tptp_fun_X_4(A!40, B!39, inverse_function(F!41, 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_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), Y)))) | (~member(tptp_fun_E_19(tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40, F!41), A!40)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_E_19(tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40, F!41))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(63,plain,
% 0.20/0.40 ((~![Y: $i] : ((~member(Y, A!40)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), Y)))) | ((~member(tptp_fun_E_19(tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40, F!41), A!40)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_E_19(tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40, F!41))))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(64,plain,
% 0.20/0.40 ((~![Y: $i] : ((~member(Y, A!40)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), Y)))) | (~member(tptp_fun_E_19(tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40, F!41), A!40)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_E_19(tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40, F!41)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.20/0.40 tff(65,plain,
% 0.20/0.40 (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_E_19(tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40, F!41))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[64, 61, 59])).
% 0.20/0.41 tff(66,plain,
% 0.20/0.41 (((~member(tptp_fun_E_19(tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40, F!41), A!40)) | (~apply(F!41, tptp_fun_E_19(tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40, F!41), tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39))))) | apply(F!41, tptp_fun_E_19(tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40, F!41), tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39)))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(67,plain,
% 0.20/0.41 (apply(F!41, tptp_fun_E_19(tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40, F!41), tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39)))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[66, 57])).
% 0.20/0.41 tff(68,plain,
% 0.20/0.41 ((~(apply(F!41, tptp_fun_E_19(tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40, F!41), tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39))) <=> apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_E_19(tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40, F!41)))) | (~apply(F!41, tptp_fun_E_19(tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40, F!41), tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39)))) | apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_E_19(tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40, F!41))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(69,plain,
% 0.20/0.41 (~(apply(F!41, tptp_fun_E_19(tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40, F!41), tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39))) <=> apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_E_19(tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40, F!41)))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[68, 67, 65])).
% 0.20/0.41 tff(70,plain,
% 0.20/0.41 (^[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))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(71,plain,
% 0.20/0.41 (![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))) <=> ![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)))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[70])).
% 0.20/0.41 tff(72,plain,
% 0.20/0.41 (^[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)))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(73,plain,
% 0.20/0.41 (![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)))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[72])).
% 0.20/0.41 tff(74,plain,
% 0.20/0.41 (![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)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(75,plain,
% 0.20/0.41 (^[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))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(76,plain,
% 0.20/0.41 (![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)))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[75])).
% 0.20/0.41 tff(77,axiom,(![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((member(X, A) & member(Y, B)) => (apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+1.ax','inverse_function')).
% 0.20/0.41 tff(78,plain,
% 0.20/0.41 (![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)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.20/0.41 tff(79,plain,
% 0.20/0.41 (![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)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[78, 74])).
% 0.20/0.41 tff(80,plain,(
% 0.20/0.41 ![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)))),
% 0.20/0.41 inference(skolemize,[status(sab)],[79])).
% 0.20/0.41 tff(81,plain,
% 0.20/0.41 (![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)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[80, 73])).
% 0.20/0.41 tff(82,plain,
% 0.20/0.41 (![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)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[81, 71])).
% 0.20/0.41 tff(83,plain,
% 0.20/0.41 (((~![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_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (~member(tptp_fun_E_19(tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40, F!41), A!40)) | (apply(F!41, tptp_fun_E_19(tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40, F!41), tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39))) <=> apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_E_19(tptp_fun_X_4(A!40, B!39, inverse_function(F!41, 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_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (~member(tptp_fun_E_19(tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40, F!41), A!40)) | (apply(F!41, tptp_fun_E_19(tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40, F!41), tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39))) <=> apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_E_19(tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40, F!41))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(84,plain,
% 0.20/0.41 (((apply(F!41, tptp_fun_E_19(tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40, F!41), tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39))) <=> apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_E_19(tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40, F!41))) | (~member(tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (~member(tptp_fun_E_19(tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40, F!41), A!40))) <=> ((~member(tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (~member(tptp_fun_E_19(tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40, F!41), A!40)) | (apply(F!41, tptp_fun_E_19(tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40, F!41), tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39))) <=> apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_E_19(tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40, F!41))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(85,plain,
% 0.20/0.42 (((~![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_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40, F!41), tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39))) <=> apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_E_19(tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40, F!41))) | (~member(tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (~member(tptp_fun_E_19(tptp_fun_X_4(A!40, B!39, inverse_function(F!41, 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_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (~member(tptp_fun_E_19(tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40, F!41), A!40)) | (apply(F!41, tptp_fun_E_19(tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40, F!41), tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39))) <=> apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_E_19(tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40, F!41)))))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[84])).
% 0.20/0.42 tff(86,plain,
% 0.20/0.42 (((~![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_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40, F!41), tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39))) <=> apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_E_19(tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40, F!41))) | (~member(tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (~member(tptp_fun_E_19(tptp_fun_X_4(A!40, B!39, inverse_function(F!41, 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_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (~member(tptp_fun_E_19(tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40, F!41), A!40)) | (apply(F!41, tptp_fun_E_19(tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40, F!41), tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39))) <=> apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_E_19(tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40, F!41))))),
% 0.20/0.42 inference(transitivity,[status(thm)],[85, 83])).
% 0.20/0.42 tff(87,plain,
% 0.20/0.42 ((~![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_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40, F!41), tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39))) <=> apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_E_19(tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40, F!41))) | (~member(tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (~member(tptp_fun_E_19(tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40, F!41), A!40)))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(88,plain,
% 0.20/0.42 ((~![F: $i, A: $i, B: $i, X: $i, Y: $i] : ((apply(F, X, Y) <=> apply(inverse_function(F, A, B), Y, X)) | (~member(Y, B)) | (~member(X, A)))) | (~member(tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (~member(tptp_fun_E_19(tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40, F!41), A!40)) | (apply(F!41, tptp_fun_E_19(tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40, F!41), tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39))) <=> apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_E_19(tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40, F!41)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.20/0.42 tff(89,plain,
% 0.20/0.42 ($false),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[88, 82, 53, 59, 69])).
% 0.20/0.42 tff(90,plain,((~member(tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (~![Y: $i] : ((~member(Y, A!40)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), Y))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.42 tff(91,plain,
% 0.20/0.42 (^[F: $i, A: $i, B: $i] : rewrite((~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))) <=> (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(92,plain,
% 0.20/0.42 (![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[91])).
% 0.20/0.42 tff(93,plain,
% 0.20/0.42 (^[F: $i, A: $i, B: $i] : refl((~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))) <=> (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(94,plain,
% 0.20/0.42 (![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[93])).
% 0.20/0.42 tff(95,plain,
% 0.20/0.42 (^[F: $i, A: $i, B: $i] : rewrite((~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))) <=> (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(96,plain,
% 0.20/0.42 (![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[95])).
% 0.20/0.42 tff(97,plain,
% 0.20/0.42 (![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))))))),
% 0.20/0.42 inference(transitivity,[status(thm)],[96, 94])).
% 0.20/0.42 tff(98,plain,
% 0.20/0.42 (^[F: $i, A: $i, B: $i] : trans(monotonicity(rewrite(((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) <=> ((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))), trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[Y: $i] : trans(monotonicity(rewrite((member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)) <=> (~((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))), ((~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y))) <=> (~(~((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))), rewrite((~(~((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))) <=> ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))), ((~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y))) <=> ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))), (![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y))) <=> ![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))), ((member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) <=> (member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))), rewrite((member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))) <=> (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))), ((member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) <=> (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))))), rewrite((~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B))))) <=> (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))), ((maps(F, A, B) | (member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B)))))) <=> (maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))))), rewrite((maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))) <=> (maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))), ((maps(F, A, B) | (member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B)))))) <=> (maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))))), ((((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) & (maps(F, A, B) | (member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B))))))) <=> (((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B))))))) & (maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))))), rewrite((((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B))))))) & (maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))))) <=> (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))))))), ((((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) & (maps(F, A, B) | (member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B))))))) <=> (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))))))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(99,plain,
% 0.20/0.43 (![F: $i, A: $i, B: $i] : (((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) & (maps(F, A, B) | (member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[98])).
% 0.20/0.43 tff(100,plain,
% 0.20/0.43 (^[F: $i, A: $i, B: $i] : rewrite((((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) & (maps(F, A, B) | ((member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B)))))))) <=> (((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) & (maps(F, A, B) | (member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B))))))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(101,plain,
% 0.20/0.43 (![F: $i, A: $i, B: $i] : (((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) & (maps(F, A, B) | ((member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B)))))))) <=> ![F: $i, A: $i, B: $i] : (((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) & (maps(F, A, B) | (member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B)))))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[100])).
% 0.20/0.43 tff(102,plain,
% 0.20/0.43 (![F: $i, A: $i, B: $i] : (maps(F, A, B) <=> (![X: $i] : ((~member(X, A)) | ?[Y: $i] : (member(Y, B) & apply(F, X, Y))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) <=> ![F: $i, A: $i, B: $i] : (maps(F, A, B) <=> (![X: $i] : ((~member(X, A)) | ?[Y: $i] : (member(Y, B) & apply(F, X, Y))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B))))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(103,plain,
% 0.20/0.43 (^[F: $i, A: $i, B: $i] : rewrite((maps(F, A, B) <=> (![X: $i] : (member(X, A) => ?[Y: $i] : (member(Y, B) & apply(F, X, Y))) & ![X: $i, Y1: $i, Y2: $i] : (((member(X, A) & member(Y1, B)) & member(Y2, B)) => ((apply(F, X, Y1) & apply(F, X, Y2)) => (Y1 = Y2))))) <=> (maps(F, A, B) <=> (![X: $i] : ((~member(X, A)) | ?[Y: $i] : (member(Y, B) & apply(F, X, Y))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(104,plain,
% 0.20/0.43 (![F: $i, A: $i, B: $i] : (maps(F, A, B) <=> (![X: $i] : (member(X, A) => ?[Y: $i] : (member(Y, B) & apply(F, X, Y))) & ![X: $i, Y1: $i, Y2: $i] : (((member(X, A) & member(Y1, B)) & member(Y2, B)) => ((apply(F, X, Y1) & apply(F, X, Y2)) => (Y1 = Y2))))) <=> ![F: $i, A: $i, B: $i] : (maps(F, A, B) <=> (![X: $i] : ((~member(X, A)) | ?[Y: $i] : (member(Y, B) & apply(F, X, Y))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B))))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[103])).
% 0.20/0.43 tff(105,axiom,(![F: $i, A: $i, B: $i] : (maps(F, A, B) <=> (![X: $i] : (member(X, A) => ?[Y: $i] : (member(Y, B) & apply(F, X, Y))) & ![X: $i, Y1: $i, Y2: $i] : (((member(X, A) & member(Y1, B)) & member(Y2, B)) => ((apply(F, X, Y1) & apply(F, X, Y2)) => (Y1 = Y2)))))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+1.ax','maps')).
% 0.20/0.43 tff(106,plain,
% 0.20/0.43 (![F: $i, A: $i, B: $i] : (maps(F, A, B) <=> (![X: $i] : ((~member(X, A)) | ?[Y: $i] : (member(Y, B) & apply(F, X, Y))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B))))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[105, 104])).
% 0.20/0.43 tff(107,plain,
% 0.20/0.43 (![F: $i, A: $i, B: $i] : (maps(F, A, B) <=> (![X: $i] : ((~member(X, A)) | ?[Y: $i] : (member(Y, B) & apply(F, X, Y))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B))))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[106, 102])).
% 0.20/0.43 tff(108,plain,(
% 0.20/0.43 ![F: $i, A: $i, B: $i] : (((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) & (maps(F, A, B) | ((member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B))))))))),
% 0.20/0.43 inference(skolemize,[status(sab)],[107])).
% 0.20/0.43 tff(109,plain,
% 0.20/0.43 (![F: $i, A: $i, B: $i] : (((~maps(F, A, B)) | (![X: $i] : ((~member(X, A)) | (member(tptp_fun_Y_3(X, B, F), B) & apply(F, X, tptp_fun_Y_3(X, B, F)))) & ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~(apply(F, X, Y1) & apply(F, X, Y2))) | (~(member(X, A) & member(Y1, B) & member(Y2, B)))))) & (maps(F, A, B) | (member(tptp_fun_X_4(B, A, F), A) & ![Y: $i] : (~(member(Y, B) & apply(F, tptp_fun_X_4(B, A, F), Y)))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~(apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F)) & apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F)))) | (~(member(tptp_fun_X_7(B, A, F), A) & member(tptp_fun_Y1_6(B, A, F), B) & member(tptp_fun_Y2_5(B, A, F), B)))))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[108, 101])).
% 0.20/0.43 tff(110,plain,
% 0.20/0.43 (![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[109, 99])).
% 0.20/0.43 tff(111,plain,
% 0.20/0.43 (![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y)))))) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B))))))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[110, 97])).
% 0.20/0.43 tff(112,plain,
% 0.20/0.43 (![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[111, 92])).
% 0.20/0.43 tff(113,plain,
% 0.20/0.43 (((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(inverse_function(F!41, A!40, B!39), B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, inverse_function(F!41, A!40, B!39)), A!40)) | (~apply(inverse_function(F!41, A!40, B!39), X, tptp_fun_Y_3(X, A!40, inverse_function(F!41, A!40, B!39)))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(inverse_function(F!41, A!40, B!39), X, Y1)) | (~apply(inverse_function(F!41, A!40, B!39), X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))))))) | (~(maps(inverse_function(F!41, A!40, B!39), B!39, A!40) | (~((~member(tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (~![Y: $i] : ((~member(Y, A!40)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), Y)))))) | (~((~member(tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (~member(tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (~member(tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39)))) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)))) | (tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)) = tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39)))))))))) <=> ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(inverse_function(F!41, A!40, B!39), B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, inverse_function(F!41, A!40, B!39)), A!40)) | (~apply(inverse_function(F!41, A!40, B!39), X, tptp_fun_Y_3(X, A!40, inverse_function(F!41, A!40, B!39)))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(inverse_function(F!41, A!40, B!39), X, Y1)) | (~apply(inverse_function(F!41, A!40, B!39), X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))))))) | (~(maps(inverse_function(F!41, A!40, B!39), B!39, A!40) | (~((~member(tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (~![Y: $i] : ((~member(Y, A!40)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), Y)))))) | (~((~member(tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (~member(tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (~member(tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39)))) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)))) | (tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)) = tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39))))))))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(114,plain,
% 0.20/0.44 ((~((~((~maps(inverse_function(F!41, A!40, B!39), B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, inverse_function(F!41, A!40, B!39)), A!40)) | (~apply(inverse_function(F!41, A!40, B!39), X, tptp_fun_Y_3(X, A!40, inverse_function(F!41, A!40, B!39)))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(inverse_function(F!41, A!40, B!39), X, Y1)) | (~apply(inverse_function(F!41, A!40, B!39), X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)) | (~member(Y2, A!40)))))))) | (~(maps(inverse_function(F!41, A!40, B!39), B!39, A!40) | (~((tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)) = tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39))) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)))) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39)))) | (~member(tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (~member(tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (~member(tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)))) | (~((~member(tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (~![Y: $i] : ((~member(Y, A!40)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), Y)))))))))) <=> (~((~((~maps(inverse_function(F!41, A!40, B!39), B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, inverse_function(F!41, A!40, B!39)), A!40)) | (~apply(inverse_function(F!41, A!40, B!39), X, tptp_fun_Y_3(X, A!40, inverse_function(F!41, A!40, B!39)))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(inverse_function(F!41, A!40, B!39), X, Y1)) | (~apply(inverse_function(F!41, A!40, B!39), X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))))))) | (~(maps(inverse_function(F!41, A!40, B!39), B!39, A!40) | (~((~member(tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (~![Y: $i] : ((~member(Y, A!40)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), Y)))))) | (~((~member(tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (~member(tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (~member(tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39)))) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)))) | (tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)) = tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39)))))))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(115,plain,
% 0.20/0.44 (((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(inverse_function(F!41, A!40, B!39), B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, inverse_function(F!41, A!40, B!39)), A!40)) | (~apply(inverse_function(F!41, A!40, B!39), X, tptp_fun_Y_3(X, A!40, inverse_function(F!41, A!40, B!39)))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(inverse_function(F!41, A!40, B!39), X, Y1)) | (~apply(inverse_function(F!41, A!40, B!39), X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)) | (~member(Y2, A!40)))))))) | (~(maps(inverse_function(F!41, A!40, B!39), B!39, A!40) | (~((tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)) = tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39))) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)))) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39)))) | (~member(tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (~member(tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (~member(tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)))) | (~((~member(tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (~![Y: $i] : ((~member(Y, A!40)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), Y))))))))))) <=> ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(inverse_function(F!41, A!40, B!39), B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, inverse_function(F!41, A!40, B!39)), A!40)) | (~apply(inverse_function(F!41, A!40, B!39), X, tptp_fun_Y_3(X, A!40, inverse_function(F!41, A!40, B!39)))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(inverse_function(F!41, A!40, B!39), X, Y1)) | (~apply(inverse_function(F!41, A!40, B!39), X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))))))) | (~(maps(inverse_function(F!41, A!40, B!39), B!39, A!40) | (~((~member(tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (~![Y: $i] : ((~member(Y, A!40)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), Y)))))) | (~((~member(tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (~member(tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (~member(tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39)))) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)))) | (tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)) = tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39))))))))))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[114])).
% 0.20/0.45 tff(116,plain,
% 0.20/0.45 (((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(inverse_function(F!41, A!40, B!39), B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, inverse_function(F!41, A!40, B!39)), A!40)) | (~apply(inverse_function(F!41, A!40, B!39), X, tptp_fun_Y_3(X, A!40, inverse_function(F!41, A!40, B!39)))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(inverse_function(F!41, A!40, B!39), X, Y1)) | (~apply(inverse_function(F!41, A!40, B!39), X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)) | (~member(Y2, A!40)))))))) | (~(maps(inverse_function(F!41, A!40, B!39), B!39, A!40) | (~((tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)) = tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39))) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)))) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39)))) | (~member(tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (~member(tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (~member(tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)))) | (~((~member(tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (~![Y: $i] : ((~member(Y, A!40)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), Y))))))))))) <=> ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(inverse_function(F!41, A!40, B!39), B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, inverse_function(F!41, A!40, B!39)), A!40)) | (~apply(inverse_function(F!41, A!40, B!39), X, tptp_fun_Y_3(X, A!40, inverse_function(F!41, A!40, B!39)))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(inverse_function(F!41, A!40, B!39), X, Y1)) | (~apply(inverse_function(F!41, A!40, B!39), X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))))))) | (~(maps(inverse_function(F!41, A!40, B!39), B!39, A!40) | (~((~member(tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (~![Y: $i] : ((~member(Y, A!40)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), Y)))))) | (~((~member(tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (~member(tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (~member(tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39)))) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)))) | (tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)) = tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39))))))))))),
% 0.20/0.45 inference(transitivity,[status(thm)],[115, 113])).
% 0.20/0.45 tff(117,plain,
% 0.20/0.45 ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(inverse_function(F!41, A!40, B!39), B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, inverse_function(F!41, A!40, B!39)), A!40)) | (~apply(inverse_function(F!41, A!40, B!39), X, tptp_fun_Y_3(X, A!40, inverse_function(F!41, A!40, B!39)))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(inverse_function(F!41, A!40, B!39), X, Y1)) | (~apply(inverse_function(F!41, A!40, B!39), X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)) | (~member(Y2, A!40)))))))) | (~(maps(inverse_function(F!41, A!40, B!39), B!39, A!40) | (~((tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)) = tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39))) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)))) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39)))) | (~member(tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (~member(tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (~member(tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)))) | (~((~member(tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (~![Y: $i] : ((~member(Y, A!40)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), Y))))))))))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(118,plain,
% 0.20/0.45 ((~![F: $i, A: $i, B: $i] : (~((~((~maps(F, A, B)) | (~((~![X: $i] : ((~member(X, A)) | (~((~member(tptp_fun_Y_3(X, B, F), B)) | (~apply(F, X, tptp_fun_Y_3(X, B, F))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~apply(F, X, Y1)) | (~apply(F, X, Y2)) | (~member(X, A)) | (~member(Y1, B)) | (~member(Y2, B)))))))) | (~(maps(F, A, B) | (~((tptp_fun_Y1_6(B, A, F) = tptp_fun_Y2_5(B, A, F)) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y1_6(B, A, F))) | (~apply(F, tptp_fun_X_7(B, A, F), tptp_fun_Y2_5(B, A, F))) | (~member(tptp_fun_X_7(B, A, F), A)) | (~member(tptp_fun_Y1_6(B, A, F), B)) | (~member(tptp_fun_Y2_5(B, A, F), B)))) | (~((~member(tptp_fun_X_4(B, A, F), A)) | (~![Y: $i] : ((~member(Y, B)) | (~apply(F, tptp_fun_X_4(B, A, F), Y))))))))))) | (~((~((~maps(inverse_function(F!41, A!40, B!39), B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, inverse_function(F!41, A!40, B!39)), A!40)) | (~apply(inverse_function(F!41, A!40, B!39), X, tptp_fun_Y_3(X, A!40, inverse_function(F!41, A!40, B!39)))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(inverse_function(F!41, A!40, B!39), X, Y1)) | (~apply(inverse_function(F!41, A!40, B!39), X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))))))) | (~(maps(inverse_function(F!41, A!40, B!39), B!39, A!40) | (~((~member(tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (~![Y: $i] : ((~member(Y, A!40)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), Y)))))) | (~((~member(tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (~member(tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (~member(tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39)))) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)))) | (tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)) = tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39)))))))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[117, 116])).
% 0.20/0.45 tff(119,plain,
% 0.20/0.45 (~((~((~maps(inverse_function(F!41, A!40, B!39), B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, inverse_function(F!41, A!40, B!39)), A!40)) | (~apply(inverse_function(F!41, A!40, B!39), X, tptp_fun_Y_3(X, A!40, inverse_function(F!41, A!40, B!39)))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(inverse_function(F!41, A!40, B!39), X, Y1)) | (~apply(inverse_function(F!41, A!40, B!39), X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))))))) | (~(maps(inverse_function(F!41, A!40, B!39), B!39, A!40) | (~((~member(tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (~![Y: $i] : ((~member(Y, A!40)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), Y)))))) | (~((~member(tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (~member(tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (~member(tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39)))) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)))) | (tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)) = tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39))))))))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[118, 112])).
% 0.20/0.45 tff(120,plain,
% 0.20/0.45 (((~((~maps(inverse_function(F!41, A!40, B!39), B!39, A!40)) | (~((~![X: $i] : ((~member(X, B!39)) | (~((~member(tptp_fun_Y_3(X, A!40, inverse_function(F!41, A!40, B!39)), A!40)) | (~apply(inverse_function(F!41, A!40, B!39), X, tptp_fun_Y_3(X, A!40, inverse_function(F!41, A!40, B!39)))))))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~member(Y2, A!40)) | (~apply(inverse_function(F!41, A!40, B!39), X, Y1)) | (~apply(inverse_function(F!41, A!40, B!39), X, Y2)) | (~member(X, B!39)) | (~member(Y1, A!40)))))))) | (~(maps(inverse_function(F!41, A!40, B!39), B!39, A!40) | (~((~member(tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (~![Y: $i] : ((~member(Y, A!40)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), Y)))))) | (~((~member(tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (~member(tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (~member(tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39)))) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)))) | (tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)) = tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39)))))))) | (maps(inverse_function(F!41, A!40, B!39), B!39, A!40) | (~((~member(tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (~![Y: $i] : ((~member(Y, A!40)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), Y)))))) | (~((~member(tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (~member(tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (~member(tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39)))) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)))) | (tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)) = tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39))))))),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(121,plain,
% 0.20/0.46 (maps(inverse_function(F!41, A!40, B!39), B!39, A!40) | (~((~member(tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (~![Y: $i] : ((~member(Y, A!40)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), Y)))))) | (~((~member(tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (~member(tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (~member(tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39)))) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)))) | (tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)) = tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39)))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[120, 119])).
% 0.20/0.46 tff(122,plain,
% 0.20/0.46 (~maps(inverse_function(F!41, A!40, B!39), B!39, A!40)),
% 0.20/0.46 inference(or_elim,[status(thm)],[40])).
% 0.20/0.46 tff(123,plain,
% 0.20/0.46 ((~(maps(inverse_function(F!41, A!40, B!39), B!39, A!40) | (~((~member(tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (~![Y: $i] : ((~member(Y, A!40)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), Y)))))) | (~((~member(tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (~member(tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (~member(tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39)))) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)))) | (tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)) = tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39))))))) | maps(inverse_function(F!41, A!40, B!39), B!39, A!40) | (~((~member(tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (~![Y: $i] : ((~member(Y, A!40)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), Y)))))) | (~((~member(tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (~member(tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (~member(tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39)))) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)))) | (tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)) = tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39)))))),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(124,plain,
% 0.20/0.46 ((~(maps(inverse_function(F!41, A!40, B!39), B!39, A!40) | (~((~member(tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (~![Y: $i] : ((~member(Y, A!40)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), Y)))))) | (~((~member(tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (~member(tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (~member(tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39)))) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)))) | (tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)) = tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39))))))) | (~((~member(tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (~![Y: $i] : ((~member(Y, A!40)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), Y)))))) | (~((~member(tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (~member(tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (~member(tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39)))) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)))) | (tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)) = tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39)))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[123, 122])).
% 0.20/0.46 tff(125,plain,
% 0.20/0.46 ((~((~member(tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (~![Y: $i] : ((~member(Y, A!40)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_4(A!40, B!39, inverse_function(F!41, A!40, B!39)), Y)))))) | (~((~member(tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (~member(tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (~member(tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39)))) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)))) | (tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)) = tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39)))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[124, 121])).
% 0.20/0.46 tff(126,plain,
% 0.20/0.46 (~((~member(tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (~member(tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (~member(tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39)))) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)))) | (tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)) = tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[125, 90])).
% 0.20/0.46 tff(127,plain,
% 0.20/0.46 (((~member(tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (~member(tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (~member(tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39)))) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)))) | (tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)) = tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39)))) | member(tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(128,plain,
% 0.20/0.46 (member(tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[127, 126])).
% 0.20/0.46 tff(129,plain,
% 0.20/0.46 (((~member(tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (~member(tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (~member(tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39)))) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)))) | (tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)) = tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39)))) | member(tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(130,plain,
% 0.20/0.46 (member(tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[129, 126])).
% 0.20/0.46 tff(131,plain,
% 0.20/0.46 (((~![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_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (~member(tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (apply(F!41, tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39))) <=> apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39)))))) <=> ((~![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_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (~member(tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (apply(F!41, tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39))) <=> apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39)))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(132,plain,
% 0.20/0.46 (((apply(F!41, tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39))) <=> apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39)))) | (~member(tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (~member(tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40))) <=> ((~member(tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (~member(tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (apply(F!41, tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39))) <=> apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39)))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(133,plain,
% 0.20/0.46 (((~![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_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39))) <=> apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39)))) | (~member(tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (~member(tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39)), 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_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (~member(tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (apply(F!41, tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39))) <=> apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39))))))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[132])).
% 0.20/0.46 tff(134,plain,
% 0.20/0.46 (((~![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_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39))) <=> apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39)))) | (~member(tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (~member(tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39)), 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_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (~member(tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (apply(F!41, tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39))) <=> apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39)))))),
% 0.20/0.46 inference(transitivity,[status(thm)],[133, 131])).
% 0.20/0.46 tff(135,plain,
% 0.20/0.46 ((~![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_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39))) <=> apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39)))) | (~member(tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (~member(tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(136,plain,
% 0.20/0.47 ((~![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_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (~member(tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (apply(F!41, tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39))) <=> apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[135, 134])).
% 0.20/0.47 tff(137,plain,
% 0.20/0.47 (apply(F!41, tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39))) <=> apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39)))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[136, 82, 130, 128])).
% 0.20/0.47 tff(138,plain,
% 0.20/0.47 (((~member(tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (~member(tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (~member(tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39)))) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)))) | (tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)) = tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39)))) | apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39)))),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(139,plain,
% 0.20/0.47 (apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39)))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[138, 126])).
% 0.20/0.47 tff(140,plain,
% 0.20/0.47 ((~(apply(F!41, tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39))) <=> apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39))))) | apply(F!41, tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39))) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39))))),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(141,plain,
% 0.20/0.47 ((~(apply(F!41, tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39))) <=> apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39))))) | apply(F!41, tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[140, 139])).
% 0.20/0.47 tff(142,plain,
% 0.20/0.47 (apply(F!41, tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[141, 137])).
% 0.20/0.47 tff(143,plain,
% 0.20/0.47 (((~member(tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (~member(tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (~member(tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39)))) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)))) | (tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)) = tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39)))) | member(tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(144,plain,
% 0.20/0.47 (member(tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[143, 126])).
% 0.20/0.47 tff(145,plain,
% 0.20/0.47 (((~![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_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (~member(tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (apply(F!41, tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39))) <=> apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)))))) <=> ((~![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_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (~member(tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (apply(F!41, tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39))) <=> apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(146,plain,
% 0.20/0.47 (((apply(F!41, tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39))) <=> apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)))) | (~member(tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (~member(tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40))) <=> ((~member(tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (~member(tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (apply(F!41, tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39))) <=> apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(147,plain,
% 0.20/0.47 (((~![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_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39))) <=> apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)))) | (~member(tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (~member(tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)), 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_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (~member(tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (apply(F!41, tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39))) <=> apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39))))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[146])).
% 0.20/0.47 tff(148,plain,
% 0.20/0.47 (((~![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_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39))) <=> apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)))) | (~member(tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (~member(tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)), 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_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (~member(tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (apply(F!41, tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39))) <=> apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)))))),
% 0.20/0.47 inference(transitivity,[status(thm)],[147, 145])).
% 0.20/0.47 tff(149,plain,
% 0.20/0.47 ((~![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_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39))) <=> apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)))) | (~member(tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (~member(tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(150,plain,
% 0.20/0.47 ((~![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_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (~member(tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (apply(F!41, tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39))) <=> apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[149, 148])).
% 0.20/0.47 tff(151,plain,
% 0.20/0.47 (apply(F!41, tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39))) <=> apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[150, 82, 144, 128])).
% 0.20/0.47 tff(152,plain,
% 0.20/0.47 (((~member(tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (~member(tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (~member(tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39)))) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)))) | (tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)) = tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39)))) | apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)))),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(153,plain,
% 0.20/0.47 (apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[152, 126])).
% 0.20/0.47 tff(154,plain,
% 0.20/0.47 ((~(apply(F!41, tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39))) <=> apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39))))) | apply(F!41, tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39))) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39))))),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(155,plain,
% 0.20/0.47 ((~(apply(F!41, tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39))) <=> apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39))))) | apply(F!41, tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[154, 153])).
% 0.20/0.47 tff(156,plain,
% 0.20/0.47 (apply(F!41, tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[155, 151])).
% 0.20/0.47 tff(157,plain,
% 0.20/0.47 (^[F: $i, A: $i, B: $i] : refl((~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B)))))))) <=> (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B)))))))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(158,plain,
% 0.20/0.47 (![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B)))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[157])).
% 0.20/0.47 tff(159,plain,
% 0.20/0.47 (^[F: $i, A: $i, B: $i] : rewrite((~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B)))))))) <=> (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B)))))))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(160,plain,
% 0.20/0.47 (![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B)))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[159])).
% 0.20/0.47 tff(161,plain,
% 0.20/0.47 (![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B)))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))),
% 0.20/0.47 inference(transitivity,[status(thm)],[160, 158])).
% 0.20/0.47 tff(162,plain,
% 0.20/0.47 (^[F: $i, A: $i, B: $i] : trans(monotonicity(rewrite(((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~(apply(F, X1, Y) & apply(F, X2, Y))) | (~(member(X1, A) & member(X2, A) & member(Y, B))))) <=> ((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))), trans(monotonicity(rewrite((~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~(apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F)) & apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F)))) | (~(member(tptp_fun_X1_18(B, A, F), A) & member(tptp_fun_X2_17(B, A, F), A) & member(tptp_fun_Y_16(B, A, F), B))))) <=> (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))), ((injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~(apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F)) & apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F)))) | (~(member(tptp_fun_X1_18(B, A, F), A) & member(tptp_fun_X2_17(B, A, F), A) & member(tptp_fun_Y_16(B, A, F), B)))))) <=> (injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))), rewrite((injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))) <=> (injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B)))))), ((injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~(apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F)) & apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F)))) | (~(member(tptp_fun_X1_18(B, A, F), A) & member(tptp_fun_X2_17(B, A, F), A) & member(tptp_fun_Y_16(B, A, F), B)))))) <=> (injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))), ((((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~(apply(F, X1, Y) & apply(F, X2, Y))) | (~(member(X1, A) & member(X2, A) & member(Y, B))))) & (injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~(apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F)) & apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F)))) | (~(member(tptp_fun_X1_18(B, A, F), A) & member(tptp_fun_X2_17(B, A, F), A) & member(tptp_fun_Y_16(B, A, F), B))))))) <=> (((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y)))) & (injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B)))))))), rewrite((((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y)))) & (injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B)))))) <=> (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))), ((((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~(apply(F, X1, Y) & apply(F, X2, Y))) | (~(member(X1, A) & member(X2, A) & member(Y, B))))) & (injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~(apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F)) & apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F)))) | (~(member(tptp_fun_X1_18(B, A, F), A) & member(tptp_fun_X2_17(B, A, F), A) & member(tptp_fun_Y_16(B, A, F), B))))))) <=> (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(163,plain,
% 0.20/0.48 (![F: $i, A: $i, B: $i] : (((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~(apply(F, X1, Y) & apply(F, X2, Y))) | (~(member(X1, A) & member(X2, A) & member(Y, B))))) & (injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~(apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F)) & apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F)))) | (~(member(tptp_fun_X1_18(B, A, F), A) & member(tptp_fun_X2_17(B, A, F), A) & member(tptp_fun_Y_16(B, A, F), B))))))) <=> ![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[162])).
% 0.20/0.48 tff(164,plain,
% 0.20/0.48 (![F: $i, A: $i, B: $i] : (injective(F, A, B) <=> ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~(apply(F, X1, Y) & apply(F, X2, Y))) | (~(member(X1, A) & member(X2, A) & member(Y, B))))) <=> ![F: $i, A: $i, B: $i] : (injective(F, A, B) <=> ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~(apply(F, X1, Y) & apply(F, X2, Y))) | (~(member(X1, A) & member(X2, A) & member(Y, B)))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(165,plain,
% 0.20/0.48 (^[F: $i, A: $i, B: $i] : rewrite((injective(F, A, B) <=> ![X1: $i, X2: $i, Y: $i] : (((member(X1, A) & member(X2, A)) & member(Y, B)) => ((apply(F, X1, Y) & apply(F, X2, Y)) => (X1 = X2)))) <=> (injective(F, A, B) <=> ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~(apply(F, X1, Y) & apply(F, X2, Y))) | (~(member(X1, A) & member(X2, A) & member(Y, B))))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(166,plain,
% 0.20/0.48 (![F: $i, A: $i, B: $i] : (injective(F, A, B) <=> ![X1: $i, X2: $i, Y: $i] : (((member(X1, A) & member(X2, A)) & member(Y, B)) => ((apply(F, X1, Y) & apply(F, X2, Y)) => (X1 = X2)))) <=> ![F: $i, A: $i, B: $i] : (injective(F, A, B) <=> ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~(apply(F, X1, Y) & apply(F, X2, Y))) | (~(member(X1, A) & member(X2, A) & member(Y, B)))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[165])).
% 0.20/0.48 tff(167,axiom,(![F: $i, A: $i, B: $i] : (injective(F, A, B) <=> ![X1: $i, X2: $i, Y: $i] : (((member(X1, A) & member(X2, A)) & member(Y, B)) => ((apply(F, X1, Y) & apply(F, X2, Y)) => (X1 = X2))))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+1.ax','injective')).
% 0.20/0.48 tff(168,plain,
% 0.20/0.48 (![F: $i, A: $i, B: $i] : (injective(F, A, B) <=> ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~(apply(F, X1, Y) & apply(F, X2, Y))) | (~(member(X1, A) & member(X2, A) & member(Y, B)))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[167, 166])).
% 0.20/0.48 tff(169,plain,
% 0.20/0.48 (![F: $i, A: $i, B: $i] : (injective(F, A, B) <=> ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~(apply(F, X1, Y) & apply(F, X2, Y))) | (~(member(X1, A) & member(X2, A) & member(Y, B)))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[168, 164])).
% 0.20/0.48 tff(170,plain,(
% 0.20/0.48 ![F: $i, A: $i, B: $i] : (((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~(apply(F, X1, Y) & apply(F, X2, Y))) | (~(member(X1, A) & member(X2, A) & member(Y, B))))) & (injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~(apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F)) & apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F)))) | (~(member(tptp_fun_X1_18(B, A, F), A) & member(tptp_fun_X2_17(B, A, F), A) & member(tptp_fun_Y_16(B, A, F), B)))))))),
% 0.20/0.48 inference(skolemize,[status(sab)],[169])).
% 0.20/0.48 tff(171,plain,
% 0.20/0.48 (![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[170, 163])).
% 0.20/0.48 tff(172,plain,
% 0.20/0.48 (![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[171, 161])).
% 0.20/0.48 tff(173,plain,
% 0.20/0.48 (((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(F!41, A!40, B!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!39)) | (~apply(F!41, X1, Y)) | (~member(X1, A!40)) | (~member(X2, A!40)) | (~apply(F!41, X2, Y))))) | (~(injective(F!41, A!40, B!39) | (~((~member(tptp_fun_Y_16(B!39, A!40, F!41), B!39)) | (~member(tptp_fun_X1_18(B!39, A!40, F!41), A!40)) | (~member(tptp_fun_X2_17(B!39, A!40, F!41), A!40)) | (~apply(F!41, tptp_fun_X2_17(B!39, A!40, F!41), tptp_fun_Y_16(B!39, A!40, F!41))) | (~apply(F!41, tptp_fun_X1_18(B!39, A!40, F!41), tptp_fun_Y_16(B!39, A!40, F!41))) | (tptp_fun_X1_18(B!39, A!40, F!41) = tptp_fun_X2_17(B!39, A!40, F!41))))))))) <=> ((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(F!41, A!40, B!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!39)) | (~apply(F!41, X1, Y)) | (~member(X1, A!40)) | (~member(X2, A!40)) | (~apply(F!41, X2, Y))))) | (~(injective(F!41, A!40, B!39) | (~((~member(tptp_fun_Y_16(B!39, A!40, F!41), B!39)) | (~member(tptp_fun_X1_18(B!39, A!40, F!41), A!40)) | (~member(tptp_fun_X2_17(B!39, A!40, F!41), A!40)) | (~apply(F!41, tptp_fun_X2_17(B!39, A!40, F!41), tptp_fun_Y_16(B!39, A!40, F!41))) | (~apply(F!41, tptp_fun_X1_18(B!39, A!40, F!41), tptp_fun_Y_16(B!39, A!40, F!41))) | (tptp_fun_X1_18(B!39, A!40, F!41) = tptp_fun_X2_17(B!39, A!40, F!41)))))))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(174,plain,
% 0.20/0.48 ((~((~((~injective(F!41, A!40, B!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!41, X1, Y)) | (~member(X2, A!40)) | (~member(X1, A!40)) | (~member(Y, B!39)) | (~apply(F!41, X2, Y))))) | (~(injective(F!41, A!40, B!39) | (~((tptp_fun_X1_18(B!39, A!40, F!41) = tptp_fun_X2_17(B!39, A!40, F!41)) | (~apply(F!41, tptp_fun_X1_18(B!39, A!40, F!41), tptp_fun_Y_16(B!39, A!40, F!41))) | (~apply(F!41, tptp_fun_X2_17(B!39, A!40, F!41), tptp_fun_Y_16(B!39, A!40, F!41))) | (~member(tptp_fun_X1_18(B!39, A!40, F!41), A!40)) | (~member(tptp_fun_X2_17(B!39, A!40, F!41), A!40)) | (~member(tptp_fun_Y_16(B!39, A!40, F!41), B!39)))))))) <=> (~((~((~injective(F!41, A!40, B!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!39)) | (~apply(F!41, X1, Y)) | (~member(X1, A!40)) | (~member(X2, A!40)) | (~apply(F!41, X2, Y))))) | (~(injective(F!41, A!40, B!39) | (~((~member(tptp_fun_Y_16(B!39, A!40, F!41), B!39)) | (~member(tptp_fun_X1_18(B!39, A!40, F!41), A!40)) | (~member(tptp_fun_X2_17(B!39, A!40, F!41), A!40)) | (~apply(F!41, tptp_fun_X2_17(B!39, A!40, F!41), tptp_fun_Y_16(B!39, A!40, F!41))) | (~apply(F!41, tptp_fun_X1_18(B!39, A!40, F!41), tptp_fun_Y_16(B!39, A!40, F!41))) | (tptp_fun_X1_18(B!39, A!40, F!41) = tptp_fun_X2_17(B!39, A!40, F!41))))))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(175,plain,
% 0.20/0.48 (((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(F!41, A!40, B!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!41, X1, Y)) | (~member(X2, A!40)) | (~member(X1, A!40)) | (~member(Y, B!39)) | (~apply(F!41, X2, Y))))) | (~(injective(F!41, A!40, B!39) | (~((tptp_fun_X1_18(B!39, A!40, F!41) = tptp_fun_X2_17(B!39, A!40, F!41)) | (~apply(F!41, tptp_fun_X1_18(B!39, A!40, F!41), tptp_fun_Y_16(B!39, A!40, F!41))) | (~apply(F!41, tptp_fun_X2_17(B!39, A!40, F!41), tptp_fun_Y_16(B!39, A!40, F!41))) | (~member(tptp_fun_X1_18(B!39, A!40, F!41), A!40)) | (~member(tptp_fun_X2_17(B!39, A!40, F!41), A!40)) | (~member(tptp_fun_Y_16(B!39, A!40, F!41), B!39))))))))) <=> ((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(F!41, A!40, B!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!39)) | (~apply(F!41, X1, Y)) | (~member(X1, A!40)) | (~member(X2, A!40)) | (~apply(F!41, X2, Y))))) | (~(injective(F!41, A!40, B!39) | (~((~member(tptp_fun_Y_16(B!39, A!40, F!41), B!39)) | (~member(tptp_fun_X1_18(B!39, A!40, F!41), A!40)) | (~member(tptp_fun_X2_17(B!39, A!40, F!41), A!40)) | (~apply(F!41, tptp_fun_X2_17(B!39, A!40, F!41), tptp_fun_Y_16(B!39, A!40, F!41))) | (~apply(F!41, tptp_fun_X1_18(B!39, A!40, F!41), tptp_fun_Y_16(B!39, A!40, F!41))) | (tptp_fun_X1_18(B!39, A!40, F!41) = tptp_fun_X2_17(B!39, A!40, F!41)))))))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[174])).
% 0.20/0.48 tff(176,plain,
% 0.20/0.48 (((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(F!41, A!40, B!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!41, X1, Y)) | (~member(X2, A!40)) | (~member(X1, A!40)) | (~member(Y, B!39)) | (~apply(F!41, X2, Y))))) | (~(injective(F!41, A!40, B!39) | (~((tptp_fun_X1_18(B!39, A!40, F!41) = tptp_fun_X2_17(B!39, A!40, F!41)) | (~apply(F!41, tptp_fun_X1_18(B!39, A!40, F!41), tptp_fun_Y_16(B!39, A!40, F!41))) | (~apply(F!41, tptp_fun_X2_17(B!39, A!40, F!41), tptp_fun_Y_16(B!39, A!40, F!41))) | (~member(tptp_fun_X1_18(B!39, A!40, F!41), A!40)) | (~member(tptp_fun_X2_17(B!39, A!40, F!41), A!40)) | (~member(tptp_fun_Y_16(B!39, A!40, F!41), B!39))))))))) <=> ((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(F!41, A!40, B!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!39)) | (~apply(F!41, X1, Y)) | (~member(X1, A!40)) | (~member(X2, A!40)) | (~apply(F!41, X2, Y))))) | (~(injective(F!41, A!40, B!39) | (~((~member(tptp_fun_Y_16(B!39, A!40, F!41), B!39)) | (~member(tptp_fun_X1_18(B!39, A!40, F!41), A!40)) | (~member(tptp_fun_X2_17(B!39, A!40, F!41), A!40)) | (~apply(F!41, tptp_fun_X2_17(B!39, A!40, F!41), tptp_fun_Y_16(B!39, A!40, F!41))) | (~apply(F!41, tptp_fun_X1_18(B!39, A!40, F!41), tptp_fun_Y_16(B!39, A!40, F!41))) | (tptp_fun_X1_18(B!39, A!40, F!41) = tptp_fun_X2_17(B!39, A!40, F!41)))))))))),
% 0.20/0.48 inference(transitivity,[status(thm)],[175, 173])).
% 0.20/0.48 tff(177,plain,
% 0.20/0.48 ((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(F!41, A!40, B!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F!41, X1, Y)) | (~member(X2, A!40)) | (~member(X1, A!40)) | (~member(Y, B!39)) | (~apply(F!41, X2, Y))))) | (~(injective(F!41, A!40, B!39) | (~((tptp_fun_X1_18(B!39, A!40, F!41) = tptp_fun_X2_17(B!39, A!40, F!41)) | (~apply(F!41, tptp_fun_X1_18(B!39, A!40, F!41), tptp_fun_Y_16(B!39, A!40, F!41))) | (~apply(F!41, tptp_fun_X2_17(B!39, A!40, F!41), tptp_fun_Y_16(B!39, A!40, F!41))) | (~member(tptp_fun_X1_18(B!39, A!40, F!41), A!40)) | (~member(tptp_fun_X2_17(B!39, A!40, F!41), A!40)) | (~member(tptp_fun_Y_16(B!39, A!40, F!41), B!39))))))))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(178,plain,
% 0.20/0.48 ((~![F: $i, A: $i, B: $i] : (~((~((~injective(F, A, B)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~apply(F, X1, Y)) | (~member(X2, A)) | (~member(X1, A)) | (~member(Y, B)) | (~apply(F, X2, Y))))) | (~(injective(F, A, B) | (~((tptp_fun_X1_18(B, A, F) = tptp_fun_X2_17(B, A, F)) | (~apply(F, tptp_fun_X1_18(B, A, F), tptp_fun_Y_16(B, A, F))) | (~apply(F, tptp_fun_X2_17(B, A, F), tptp_fun_Y_16(B, A, F))) | (~member(tptp_fun_X1_18(B, A, F), A)) | (~member(tptp_fun_X2_17(B, A, F), A)) | (~member(tptp_fun_Y_16(B, A, F), B))))))))) | (~((~((~injective(F!41, A!40, B!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!39)) | (~apply(F!41, X1, Y)) | (~member(X1, A!40)) | (~member(X2, A!40)) | (~apply(F!41, X2, Y))))) | (~(injective(F!41, A!40, B!39) | (~((~member(tptp_fun_Y_16(B!39, A!40, F!41), B!39)) | (~member(tptp_fun_X1_18(B!39, A!40, F!41), A!40)) | (~member(tptp_fun_X2_17(B!39, A!40, F!41), A!40)) | (~apply(F!41, tptp_fun_X2_17(B!39, A!40, F!41), tptp_fun_Y_16(B!39, A!40, F!41))) | (~apply(F!41, tptp_fun_X1_18(B!39, A!40, F!41), tptp_fun_Y_16(B!39, A!40, F!41))) | (tptp_fun_X1_18(B!39, A!40, F!41) = tptp_fun_X2_17(B!39, A!40, F!41))))))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[177, 176])).
% 0.20/0.48 tff(179,plain,
% 0.20/0.48 (~((~((~injective(F!41, A!40, B!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!39)) | (~apply(F!41, X1, Y)) | (~member(X1, A!40)) | (~member(X2, A!40)) | (~apply(F!41, X2, Y))))) | (~(injective(F!41, A!40, B!39) | (~((~member(tptp_fun_Y_16(B!39, A!40, F!41), B!39)) | (~member(tptp_fun_X1_18(B!39, A!40, F!41), A!40)) | (~member(tptp_fun_X2_17(B!39, A!40, F!41), A!40)) | (~apply(F!41, tptp_fun_X2_17(B!39, A!40, F!41), tptp_fun_Y_16(B!39, A!40, F!41))) | (~apply(F!41, tptp_fun_X1_18(B!39, A!40, F!41), tptp_fun_Y_16(B!39, A!40, F!41))) | (tptp_fun_X1_18(B!39, A!40, F!41) = tptp_fun_X2_17(B!39, A!40, F!41)))))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[178, 172])).
% 0.20/0.48 tff(180,plain,
% 0.20/0.48 (((~((~injective(F!41, A!40, B!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!39)) | (~apply(F!41, X1, Y)) | (~member(X1, A!40)) | (~member(X2, A!40)) | (~apply(F!41, X2, Y))))) | (~(injective(F!41, A!40, B!39) | (~((~member(tptp_fun_Y_16(B!39, A!40, F!41), B!39)) | (~member(tptp_fun_X1_18(B!39, A!40, F!41), A!40)) | (~member(tptp_fun_X2_17(B!39, A!40, F!41), A!40)) | (~apply(F!41, tptp_fun_X2_17(B!39, A!40, F!41), tptp_fun_Y_16(B!39, A!40, F!41))) | (~apply(F!41, tptp_fun_X1_18(B!39, A!40, F!41), tptp_fun_Y_16(B!39, A!40, F!41))) | (tptp_fun_X1_18(B!39, A!40, F!41) = tptp_fun_X2_17(B!39, A!40, F!41))))))) | ((~injective(F!41, A!40, B!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!39)) | (~apply(F!41, X1, Y)) | (~member(X1, A!40)) | (~member(X2, A!40)) | (~apply(F!41, X2, Y))))),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(181,plain,
% 0.20/0.48 ((~injective(F!41, A!40, B!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!39)) | (~apply(F!41, X1, Y)) | (~member(X1, A!40)) | (~member(X2, A!40)) | (~apply(F!41, X2, Y)))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[180, 179])).
% 0.20/0.48 tff(182,plain,
% 0.20/0.48 (((~injective(F!41, A!40, B!39)) | (~surjective(F!41, A!40, B!39))) | injective(F!41, A!40, B!39)),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(183,plain,
% 0.20/0.48 (injective(F!41, A!40, B!39)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[182, 45])).
% 0.20/0.48 tff(184,plain,
% 0.20/0.48 ((~((~injective(F!41, A!40, B!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!39)) | (~apply(F!41, X1, Y)) | (~member(X1, A!40)) | (~member(X2, A!40)) | (~apply(F!41, X2, Y))))) | (~injective(F!41, A!40, B!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!39)) | (~apply(F!41, X1, Y)) | (~member(X1, A!40)) | (~member(X2, A!40)) | (~apply(F!41, X2, Y)))),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(185,plain,
% 0.20/0.48 ((~((~injective(F!41, A!40, B!39)) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!39)) | (~apply(F!41, X1, Y)) | (~member(X1, A!40)) | (~member(X2, A!40)) | (~apply(F!41, X2, Y))))) | ![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!39)) | (~apply(F!41, X1, Y)) | (~member(X1, A!40)) | (~member(X2, A!40)) | (~apply(F!41, X2, Y)))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[184, 183])).
% 0.20/0.49 tff(186,plain,
% 0.20/0.49 (![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!39)) | (~apply(F!41, X1, Y)) | (~member(X1, A!40)) | (~member(X2, A!40)) | (~apply(F!41, X2, Y)))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[185, 181])).
% 0.20/0.49 tff(187,plain,
% 0.20/0.49 (((~member(tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (~member(tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (~member(tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39)))) | (~apply(inverse_function(F!41, A!40, B!39), tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)))) | (tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)) = tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39)))) | (~(tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)) = tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39))))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(188,plain,
% 0.20/0.49 (~(tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)) = tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39)))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[187, 126])).
% 0.20/0.49 tff(189,plain,
% 0.20/0.49 (((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!39)) | (~apply(F!41, X1, Y)) | (~member(X1, A!40)) | (~member(X2, A!40)) | (~apply(F!41, X2, Y)))) | ((~member(tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (~member(tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (~member(tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)) = tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39))) | (~apply(F!41, tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)))) | (~apply(F!41, tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)))))) <=> ((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!39)) | (~apply(F!41, X1, Y)) | (~member(X1, A!40)) | (~member(X2, A!40)) | (~apply(F!41, X2, Y)))) | (~member(tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (~member(tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (~member(tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)) = tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39))) | (~apply(F!41, tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)))) | (~apply(F!41, tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(190,plain,
% 0.20/0.49 (((tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)) = tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39))) | (~member(tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (~apply(F!41, tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)))) | (~member(tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (~member(tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (~apply(F!41, tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39))))) <=> ((~member(tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (~member(tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (~member(tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)) = tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39))) | (~apply(F!41, tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)))) | (~apply(F!41, tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(191,plain,
% 0.20/0.49 (((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!39)) | (~apply(F!41, X1, Y)) | (~member(X1, A!40)) | (~member(X2, A!40)) | (~apply(F!41, X2, Y)))) | ((tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)) = tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39))) | (~member(tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (~apply(F!41, tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)))) | (~member(tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (~member(tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (~apply(F!41, tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)))))) <=> ((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!39)) | (~apply(F!41, X1, Y)) | (~member(X1, A!40)) | (~member(X2, A!40)) | (~apply(F!41, X2, Y)))) | ((~member(tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (~member(tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (~member(tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)) = tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39))) | (~apply(F!41, tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)))) | (~apply(F!41, tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39))))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[190])).
% 0.20/0.49 tff(192,plain,
% 0.20/0.49 (((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!39)) | (~apply(F!41, X1, Y)) | (~member(X1, A!40)) | (~member(X2, A!40)) | (~apply(F!41, X2, Y)))) | ((tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)) = tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39))) | (~member(tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (~apply(F!41, tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)))) | (~member(tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (~member(tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (~apply(F!41, tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)))))) <=> ((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!39)) | (~apply(F!41, X1, Y)) | (~member(X1, A!40)) | (~member(X2, A!40)) | (~apply(F!41, X2, Y)))) | (~member(tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (~member(tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (~member(tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)) = tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39))) | (~apply(F!41, tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)))) | (~apply(F!41, tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)))))),
% 0.20/0.49 inference(transitivity,[status(thm)],[191, 189])).
% 0.20/0.49 tff(193,plain,
% 0.20/0.49 ((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!39)) | (~apply(F!41, X1, Y)) | (~member(X1, A!40)) | (~member(X2, A!40)) | (~apply(F!41, X2, Y)))) | ((tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)) = tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39))) | (~member(tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (~apply(F!41, tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)))) | (~member(tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (~member(tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (~apply(F!41, tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)))))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(194,plain,
% 0.20/0.49 ((~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~member(Y, B!39)) | (~apply(F!41, X1, Y)) | (~member(X1, A!40)) | (~member(X2, A!40)) | (~apply(F!41, X2, Y)))) | (~member(tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (~member(tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)), A!40)) | (~member(tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)), B!39)) | (tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)) = tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39))) | (~apply(F!41, tptp_fun_Y1_6(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39)))) | (~apply(F!41, tptp_fun_Y2_5(A!40, B!39, inverse_function(F!41, A!40, B!39)), tptp_fun_X_7(A!40, B!39, inverse_function(F!41, A!40, B!39))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[193, 192])).
% 0.20/0.49 tff(195,plain,
% 0.20/0.49 ($false),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[194, 130, 144, 128, 188, 186, 156, 142])).
% 0.20/0.49 % SZS output end Proof
% 0.20/0.49 % E exiting
%------------------------------------------------------------------------------