%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : SET988+1 : TPTP v8.1.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n028.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 : 600s % DateTime : Tue Jul 19 06:40:03 EDT 2022 % Result : Theorem 0.37s 0.59s % Output : Proof 0.37s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.11 % Problem : SET988+1 : TPTP v8.1.0. Released v3.2.0. % 0.06/0.12 % Command : run_zenon %s %d % 0.12/0.32 % Computer : n028.cluster.edu % 0.12/0.32 % Model : x86_64 x86_64 % 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.32 % Memory : 8042.1875MB % 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.32 % CPULimit : 300 % 0.12/0.32 % WCLimit : 600 % 0.12/0.32 % DateTime : Sun Jul 10 15:13:57 EDT 2022 % 0.12/0.33 % CPUTime : % 0.37/0.59 Zenon warning: unused variable (B : zenon_U) in reflexivity_r1_tarski % 0.37/0.59 (* PROOF-FOUND *) % 0.37/0.59 % SZS status Theorem % 0.37/0.59 (* BEGIN-PROOF *) % 0.37/0.59 % SZS output start Proof % 0.37/0.59 Theorem t2_funct_1 : (forall A : zenon_U, (((forall B : zenon_U, (~((in B A)/\(forall C : zenon_U, (forall D : zenon_U, (~((ordered_pair C D) = B)))))))/\(forall B : zenon_U, (forall C : zenon_U, (forall D : zenon_U, (((in (ordered_pair B C) A)/\(in (ordered_pair B D) A))->(C = D))))))->((relation A)/\(function A)))). % 0.37/0.59 Proof. % 0.37/0.59 apply NNPP. intro zenon_G. % 0.37/0.59 apply (zenon_notallex_s (fun A : zenon_U => (((forall B : zenon_U, (~((in B A)/\(forall C : zenon_U, (forall D : zenon_U, (~((ordered_pair C D) = B)))))))/\(forall B : zenon_U, (forall C : zenon_U, (forall D : zenon_U, (((in (ordered_pair B C) A)/\(in (ordered_pair B D) A))->(C = D))))))->((relation A)/\(function A)))) zenon_G); [ zenon_intro zenon_H21; idtac ]. % 0.37/0.59 elim zenon_H21. zenon_intro zenon_TA_bi. zenon_intro zenon_H23. % 0.37/0.59 apply (zenon_notimply_s _ _ zenon_H23). zenon_intro zenon_H25. zenon_intro zenon_H24. % 0.37/0.59 apply (zenon_and_s _ _ zenon_H25). zenon_intro zenon_H27. zenon_intro zenon_H26. % 0.37/0.59 apply (zenon_notand_s _ _ zenon_H24); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 0.37/0.59 generalize (d1_relat_1 zenon_TA_bi). zenon_intro zenon_H2a. % 0.37/0.59 apply (zenon_equiv_s _ _ zenon_H2a); [ zenon_intro zenon_H29; zenon_intro zenon_H2d | zenon_intro zenon_H2c; zenon_intro zenon_H2b ]. % 0.37/0.59 apply (zenon_notallex_s (fun B : zenon_U => (~((in B zenon_TA_bi)/\(forall C : zenon_U, (forall D : zenon_U, (~(B = (ordered_pair C D)))))))) zenon_H2d); [ zenon_intro zenon_H2e; idtac ]. % 0.37/0.59 elim zenon_H2e. zenon_intro zenon_TB_bv. zenon_intro zenon_H30. % 0.37/0.59 apply zenon_H30. zenon_intro zenon_H31. % 0.37/0.59 apply (zenon_and_s _ _ zenon_H31). zenon_intro zenon_H33. zenon_intro zenon_H32. % 0.37/0.59 generalize (zenon_H27 zenon_TB_bv). zenon_intro zenon_H34. % 0.37/0.59 apply (zenon_notand_s _ _ zenon_H34); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ]. % 0.37/0.59 exact (zenon_H36 zenon_H33). % 0.37/0.59 apply (zenon_notallex_s (fun C : zenon_U => (forall D : zenon_U, (~((ordered_pair C D) = zenon_TB_bv)))) zenon_H35); [ zenon_intro zenon_H37; idtac ]. % 0.37/0.59 elim zenon_H37. zenon_intro zenon_TC_ce. zenon_intro zenon_H39. % 0.37/0.59 apply (zenon_notallex_s (fun D : zenon_U => (~((ordered_pair zenon_TC_ce D) = zenon_TB_bv))) zenon_H39); [ zenon_intro zenon_H3a; idtac ]. % 0.37/0.59 elim zenon_H3a. zenon_intro zenon_TD_ch. zenon_intro zenon_H3c. % 0.37/0.59 apply zenon_H3c. zenon_intro zenon_H3d. % 0.37/0.59 generalize (d5_tarski zenon_TC_ce). zenon_intro zenon_H3e. % 0.37/0.59 generalize (zenon_H3e zenon_TD_ch). zenon_intro zenon_H3f. % 0.37/0.59 apply (zenon_congruence_lr_s _ (fun zenon_Vh : _ => (zenon_Vh = zenon_TB_bv)) _ _ zenon_H3d zenon_H3f). zenon_intro zenon_H40. % 0.37/0.59 generalize (zenon_H32 zenon_TC_ce). zenon_intro zenon_H41. % 0.37/0.59 generalize (zenon_H41 zenon_TD_ch). zenon_intro zenon_H42. % 0.37/0.59 generalize (d5_tarski zenon_TC_ce). zenon_intro zenon_H3e. % 0.37/0.59 generalize (zenon_H3e zenon_TD_ch). zenon_intro zenon_H3f. % 0.37/0.59 apply (zenon_congruence_lr_s _ (fun zenon_Vj : _ => (~(zenon_TB_bv = zenon_Vj))) _ _ zenon_H42 zenon_H3f). zenon_intro zenon_H43. % 0.37/0.59 apply zenon_H43. apply sym_equal. exact zenon_H40. % 0.37/0.59 exact (zenon_H29 zenon_H2c). % 0.37/0.59 generalize (d1_funct_1 zenon_TA_bi). zenon_intro zenon_H44. % 0.37/0.59 apply (zenon_equiv_s _ _ zenon_H44); [ zenon_intro zenon_H28; zenon_intro zenon_H46 | zenon_intro zenon_H45; zenon_intro zenon_H26 ]. % 0.37/0.59 exact (zenon_H46 zenon_H26). % 0.37/0.59 exact (zenon_H28 zenon_H45). % 0.37/0.59 Qed. % 0.37/0.59 % SZS output end Proof % 0.37/0.59 (* END-PROOF *) % 0.37/0.59 nodes searched: 4423 % 0.37/0.59 max branch formulas: 1063 % 0.37/0.59 proof nodes created: 336 % 0.37/0.59 formulas created: 11603 % 0.37/0.59 %------------------------------------------------------------------------------