%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : SET907+1 : TPTP v8.1.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n022.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 06:39:32 EDT 2022 % Result : Theorem 0.20s 0.52s % Output : Proof 0.20s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.10/0.12 % Problem : SET907+1 : TPTP v8.1.0. Released v3.2.0. % 0.10/0.12 % Command : run_zenon %s %d % 0.12/0.33 % Computer : n022.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 600 % 0.12/0.33 % DateTime : Sat Jul 9 21:50:10 EDT 2022 % 0.12/0.33 % CPUTime : % 0.20/0.52 Zenon warning: unused variable (B : zenon_U) in idempotence_k2_xboole_0 % 0.20/0.52 Zenon warning: unused variable (B : zenon_U) in reflexivity_r1_tarski % 0.20/0.52 (* PROOF-FOUND *) % 0.20/0.52 % SZS status Theorem % 0.20/0.52 (* BEGIN-PROOF *) % 0.20/0.52 % SZS output start Proof % 0.20/0.52 Theorem t48_zfmisc_1 : (forall A : zenon_U, (forall B : zenon_U, (forall C : zenon_U, (((in A B)/\(in C B))->((set_union2 (unordered_pair A C) B) = B))))). % 0.20/0.52 Proof. % 0.20/0.52 apply NNPP. intro zenon_G. % 0.20/0.52 apply (zenon_notallex_s (fun A : zenon_U => (forall B : zenon_U, (forall C : zenon_U, (((in A B)/\(in C B))->((set_union2 (unordered_pair A C) B) = B))))) zenon_G); [ zenon_intro zenon_Hc; idtac ]. % 0.20/0.52 elim zenon_Hc. zenon_intro zenon_TA_n. zenon_intro zenon_He. % 0.20/0.52 apply (zenon_notallex_s (fun B : zenon_U => (forall C : zenon_U, (((in zenon_TA_n B)/\(in C B))->((set_union2 (unordered_pair zenon_TA_n C) B) = B)))) zenon_He); [ zenon_intro zenon_Hf; idtac ]. % 0.20/0.52 elim zenon_Hf. zenon_intro zenon_TB_q. zenon_intro zenon_H11. % 0.20/0.52 apply (zenon_notallex_s (fun C : zenon_U => (((in zenon_TA_n zenon_TB_q)/\(in C zenon_TB_q))->((set_union2 (unordered_pair zenon_TA_n C) zenon_TB_q) = zenon_TB_q))) zenon_H11); [ zenon_intro zenon_H12; idtac ]. % 0.20/0.52 elim zenon_H12. zenon_intro zenon_TC_t. zenon_intro zenon_H14. % 0.20/0.52 apply (zenon_notimply_s _ _ zenon_H14). zenon_intro zenon_H16. zenon_intro zenon_H15. % 0.20/0.52 apply (zenon_and_s _ _ zenon_H16). zenon_intro zenon_H18. zenon_intro zenon_H17. % 0.20/0.52 generalize (t12_xboole_1 (unordered_pair zenon_TA_n zenon_TC_t)). zenon_intro zenon_H19. % 0.20/0.52 generalize (zenon_H19 zenon_TB_q). zenon_intro zenon_H1a. % 0.20/0.52 apply (zenon_imply_s _ _ zenon_H1a); [ zenon_intro zenon_H1c | zenon_intro zenon_H1b ]. % 0.20/0.52 generalize (t38_zfmisc_1 zenon_TA_n). zenon_intro zenon_H1d. % 0.20/0.52 generalize (zenon_H1d zenon_TC_t). zenon_intro zenon_H1e. % 0.20/0.52 generalize (zenon_H1e zenon_TB_q). zenon_intro zenon_H1f. % 0.20/0.52 apply (zenon_equiv_s _ _ zenon_H1f); [ zenon_intro zenon_H1c; zenon_intro zenon_H21 | zenon_intro zenon_H20; zenon_intro zenon_H16 ]. % 0.20/0.52 apply (zenon_notand_s _ _ zenon_H21); [ zenon_intro zenon_H23 | zenon_intro zenon_H22 ]. % 0.20/0.52 exact (zenon_H23 zenon_H18). % 0.20/0.52 exact (zenon_H22 zenon_H17). % 0.20/0.52 exact (zenon_H1c zenon_H20). % 0.20/0.52 exact (zenon_H15 zenon_H1b). % 0.20/0.52 Qed. % 0.20/0.52 % SZS output end Proof % 0.20/0.52 (* END-PROOF *) % 0.20/0.52 nodes searched: 557 % 0.20/0.52 max branch formulas: 219 % 0.20/0.52 proof nodes created: 84 % 0.20/0.52 formulas created: 2264 % 0.20/0.52 %------------------------------------------------------------------------------