%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : SET881+1 : TPTP v8.1.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n003.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 06:39:23 EDT 2022 % Result : Theorem 1.95s 2.11s % Output : Proof 1.95s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.12 % Problem : SET881+1 : TPTP v8.1.0. Released v3.2.0. % 0.04/0.12 % Command : run_zenon %s %d % 0.12/0.33 % Computer : n003.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 : Sun Jul 10 11:53:44 EDT 2022 % 0.12/0.33 % CPUTime : % 1.95/2.11 (* PROOF-FOUND *) % 1.95/2.11 % SZS status Theorem % 1.95/2.11 (* BEGIN-PROOF *) % 1.95/2.11 % SZS output start Proof % 1.95/2.11 Theorem t22_zfmisc_1 : (forall A : zenon_U, (forall B : zenon_U, ((set_difference (singleton A) (unordered_pair A B)) = (empty_set)))). % 1.95/2.11 Proof. % 1.95/2.11 assert (zenon_L1_ : forall (zenon_TB_j : zenon_U) (zenon_TA_k : zenon_U), (~((zenon_TA_k = zenon_TA_k)\/(zenon_TA_k = zenon_TB_j))) -> False). % 1.95/2.11 do 2 intro. intros zenon_H8. % 1.95/2.11 apply (zenon_notor_s _ _ zenon_H8). zenon_intro zenon_Hc. zenon_intro zenon_Hb. % 1.95/2.11 apply zenon_Hc. apply refl_equal. % 1.95/2.11 (* end of lemma zenon_L1_ *) % 1.95/2.11 apply NNPP. intro zenon_G. % 1.95/2.11 apply (zenon_notallex_s (fun A : zenon_U => (forall B : zenon_U, ((set_difference (singleton A) (unordered_pair A B)) = (empty_set)))) zenon_G); [ zenon_intro zenon_Hd; idtac ]. % 1.95/2.11 elim zenon_Hd. zenon_intro zenon_TA_k. zenon_intro zenon_He. % 1.95/2.11 apply (zenon_notallex_s (fun B : zenon_U => ((set_difference (singleton zenon_TA_k) (unordered_pair zenon_TA_k B)) = (empty_set))) zenon_He); [ zenon_intro zenon_Hf; idtac ]. % 1.95/2.11 elim zenon_Hf. zenon_intro zenon_TB_j. zenon_intro zenon_H10. % 1.95/2.11 generalize (d2_tarski zenon_TA_k). zenon_intro zenon_H11. % 1.95/2.11 generalize (zenon_H11 zenon_TB_j). zenon_intro zenon_H12. % 1.95/2.11 generalize (zenon_H12 (unordered_pair zenon_TA_k zenon_TB_j)). zenon_intro zenon_H13. % 1.95/2.11 apply (zenon_equiv_s _ _ zenon_H13); [ zenon_intro zenon_H17; zenon_intro zenon_H16 | zenon_intro zenon_H15; zenon_intro zenon_H14 ]. % 1.95/2.11 apply zenon_H17. apply refl_equal. % 1.95/2.11 generalize (zenon_H14 zenon_TA_k). zenon_intro zenon_H18. % 1.95/2.11 apply (zenon_equiv_s _ _ zenon_H18); [ zenon_intro zenon_H1b; zenon_intro zenon_H8 | zenon_intro zenon_H1a; zenon_intro zenon_H19 ]. % 1.95/2.11 apply (zenon_L1_ zenon_TB_j zenon_TA_k); trivial. % 1.95/2.11 generalize (l36_zfmisc_1 zenon_TA_k). zenon_intro zenon_H1c. % 1.95/2.11 generalize (zenon_H1c (unordered_pair zenon_TA_k zenon_TB_j)). zenon_intro zenon_H1d. % 1.95/2.11 apply (zenon_equiv_s _ _ zenon_H1d); [ zenon_intro zenon_H10; zenon_intro zenon_H1b | zenon_intro zenon_H1e; zenon_intro zenon_H1a ]. % 1.95/2.11 exact (zenon_H1b zenon_H1a). % 1.95/2.11 exact (zenon_H10 zenon_H1e). % 1.95/2.11 Qed. % 1.95/2.11 % SZS output end Proof % 1.95/2.11 (* END-PROOF *) % 1.95/2.11 nodes searched: 12180 % 1.95/2.11 max branch formulas: 1412 % 1.95/2.11 proof nodes created: 595 % 1.95/2.11 formulas created: 76636 % 1.95/2.11 %------------------------------------------------------------------------------