%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : SET912+1 : TPTP v8.1.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n004.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 06:39:34 EDT 2022 % Result : Theorem 11.91s 12.11s % Output : Proof 11.91s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.12 % Problem : SET912+1 : TPTP v8.1.0. Released v3.2.0. % 0.08/0.13 % Command : run_zenon %s %d % 0.13/0.34 % Computer : n004.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 600 % 0.13/0.34 % DateTime : Sun Jul 10 04:58:22 EDT 2022 % 0.13/0.34 % CPUTime : % 11.91/12.11 Zenon warning: unused variable (B : zenon_U) in idempotence_k3_xboole_0 % 11.91/12.11 Zenon warning: unused variable (B : zenon_U) in reflexivity_r1_tarski % 11.91/12.11 (* PROOF-FOUND *) % 11.91/12.11 % SZS status Theorem % 11.91/12.11 (* BEGIN-PROOF *) % 11.91/12.11 % SZS output start Proof % 11.91/12.11 Theorem t53_zfmisc_1 : (forall A : zenon_U, (forall B : zenon_U, (forall C : zenon_U, (((in A B)/\(in C B))->((set_intersection2 (unordered_pair A C) B) = (unordered_pair A C)))))). % 11.91/12.11 Proof. % 11.91/12.11 apply NNPP. intro zenon_G. % 11.91/12.11 apply (zenon_notallex_s (fun A : zenon_U => (forall B : zenon_U, (forall C : zenon_U, (((in A B)/\(in C B))->((set_intersection2 (unordered_pair A C) B) = (unordered_pair A C)))))) zenon_G); [ zenon_intro zenon_Ha; idtac ]. % 11.91/12.11 elim zenon_Ha. zenon_intro zenon_TA_l. zenon_intro zenon_Hc. % 11.91/12.11 apply (zenon_notallex_s (fun B : zenon_U => (forall C : zenon_U, (((in zenon_TA_l B)/\(in C B))->((set_intersection2 (unordered_pair zenon_TA_l C) B) = (unordered_pair zenon_TA_l C))))) zenon_Hc); [ zenon_intro zenon_Hd; idtac ]. % 11.91/12.11 elim zenon_Hd. zenon_intro zenon_TB_o. zenon_intro zenon_Hf. % 11.91/12.11 apply (zenon_notallex_s (fun C : zenon_U => (((in zenon_TA_l zenon_TB_o)/\(in C zenon_TB_o))->((set_intersection2 (unordered_pair zenon_TA_l C) zenon_TB_o) = (unordered_pair zenon_TA_l C)))) zenon_Hf); [ zenon_intro zenon_H10; idtac ]. % 11.91/12.11 elim zenon_H10. zenon_intro zenon_TC_r. zenon_intro zenon_H12. % 11.91/12.11 apply (zenon_notimply_s _ _ zenon_H12). zenon_intro zenon_H14. zenon_intro zenon_H13. % 11.91/12.11 apply (zenon_and_s _ _ zenon_H14). zenon_intro zenon_H16. zenon_intro zenon_H15. % 11.91/12.11 generalize (t38_zfmisc_1 zenon_TA_l). zenon_intro zenon_H17. % 11.91/12.11 generalize (t28_xboole_1 (unordered_pair zenon_TA_l zenon_TC_r)). zenon_intro zenon_H18. % 11.91/12.11 generalize (zenon_H17 zenon_TC_r). zenon_intro zenon_H19. % 11.91/12.11 generalize (zenon_H19 zenon_TB_o). zenon_intro zenon_H1a. % 11.91/12.11 apply (zenon_equiv_s _ _ zenon_H1a); [ zenon_intro zenon_H1d; zenon_intro zenon_H1c | zenon_intro zenon_H1b; zenon_intro zenon_H14 ]. % 11.91/12.11 apply (zenon_notand_s _ _ zenon_H1c); [ zenon_intro zenon_H1f | zenon_intro zenon_H1e ]. % 11.91/12.11 exact (zenon_H1f zenon_H16). % 11.91/12.11 exact (zenon_H1e zenon_H15). % 11.91/12.11 generalize (zenon_H18 zenon_TB_o). zenon_intro zenon_H20. % 11.91/12.11 apply (zenon_imply_s _ _ zenon_H20); [ zenon_intro zenon_H1d | zenon_intro zenon_H21 ]. % 11.91/12.11 exact (zenon_H1d zenon_H1b). % 11.91/12.11 exact (zenon_H13 zenon_H21). % 11.91/12.11 Qed. % 11.91/12.11 % SZS output end Proof % 11.91/12.11 (* END-PROOF *) % 11.91/12.11 nodes searched: 235642 % 11.91/12.11 max branch formulas: 5106 % 11.91/12.11 proof nodes created: 9721 % 11.91/12.11 formulas created: 335201 % 11.91/12.11 %------------------------------------------------------------------------------