%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : SET886+1 : TPTP v8.1.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n021.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 06:39:25 EDT 2022 % Result : Theorem 1.22s 1.45s % Output : Proof 1.22s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SET886+1 : TPTP v8.1.0. Released v3.2.0. % 0.11/0.13 % Command : run_zenon %s %d % 0.13/0.34 % Computer : n021.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 : Mon Jul 11 08:38:38 EDT 2022 % 0.13/0.34 % CPUTime : % 1.22/1.45 Zenon warning: unused variable (B : zenon_U) in reflexivity_r1_tarski % 1.22/1.45 (* PROOF-FOUND *) % 1.22/1.45 % SZS status Theorem % 1.22/1.45 (* BEGIN-PROOF *) % 1.22/1.45 % SZS output start Proof % 1.22/1.45 Theorem t27_zfmisc_1 : (forall A : zenon_U, (forall B : zenon_U, (forall C : zenon_U, ((subset (unordered_pair A B) (singleton C))->((unordered_pair A B) = (singleton C)))))). % 1.22/1.45 Proof. % 1.22/1.45 assert (zenon_L1_ : forall (zenon_TC_m : zenon_U) (zenon_TB_n : zenon_U) (zenon_TA_o : zenon_U), (~((unordered_pair zenon_TA_o zenon_TB_n) = (singleton zenon_TC_m))) -> ((unordered_pair zenon_TC_m zenon_TC_m) = (singleton zenon_TC_m)) -> (zenon_TA_o = zenon_TC_m) -> (subset (unordered_pair zenon_TA_o zenon_TB_n) (singleton zenon_TC_m)) -> ((unordered_pair zenon_TB_n zenon_TA_o) = (unordered_pair zenon_TA_o zenon_TB_n)) -> False). % 1.22/1.45 do 3 intro. intros zenon_H7 zenon_H8 zenon_H9 zenon_Ha zenon_Hb. % 1.22/1.45 cut (((unordered_pair zenon_TC_m zenon_TC_m) = (singleton zenon_TC_m)) = ((unordered_pair zenon_TA_o zenon_TB_n) = (singleton zenon_TC_m))). % 1.22/1.45 intro zenon_D_pnotp. % 1.22/1.45 apply zenon_H7. % 1.22/1.45 rewrite <- zenon_D_pnotp. % 1.22/1.45 exact zenon_H8. % 1.22/1.45 cut (((singleton zenon_TC_m) = (singleton zenon_TC_m))); [idtac | apply NNPP; zenon_intro zenon_Hf]. % 1.22/1.45 cut (((unordered_pair zenon_TC_m zenon_TC_m) = (unordered_pair zenon_TA_o zenon_TB_n))); [idtac | apply NNPP; zenon_intro zenon_H10]. % 1.22/1.45 congruence. % 1.22/1.45 elim (classic ((unordered_pair zenon_TA_o zenon_TB_n) = (unordered_pair zenon_TA_o zenon_TB_n))); [ zenon_intro zenon_H11 | zenon_intro zenon_H12 ]. % 1.22/1.45 cut (((unordered_pair zenon_TA_o zenon_TB_n) = (unordered_pair zenon_TA_o zenon_TB_n)) = ((unordered_pair zenon_TC_m zenon_TC_m) = (unordered_pair zenon_TA_o zenon_TB_n))). % 1.22/1.45 intro zenon_D_pnotp. % 1.22/1.45 apply zenon_H10. % 1.22/1.45 rewrite <- zenon_D_pnotp. % 1.22/1.45 exact zenon_H11. % 1.22/1.45 cut (((unordered_pair zenon_TA_o zenon_TB_n) = (unordered_pair zenon_TA_o zenon_TB_n))); [idtac | apply NNPP; zenon_intro zenon_H12]. % 1.22/1.45 cut (((unordered_pair zenon_TA_o zenon_TB_n) = (unordered_pair zenon_TC_m zenon_TC_m))); [idtac | apply NNPP; zenon_intro zenon_H13]. % 1.22/1.45 congruence. % 1.22/1.45 cut ((zenon_TB_n = zenon_TC_m)); [idtac | apply NNPP; zenon_intro zenon_H14]. % 1.22/1.45 cut ((zenon_TA_o = zenon_TC_m)); [idtac | apply NNPP; zenon_intro zenon_H15]. % 1.22/1.45 congruence. % 1.22/1.45 exact (zenon_H15 zenon_H9). % 1.22/1.45 generalize (t26_zfmisc_1 zenon_TB_n). zenon_intro zenon_H16. % 1.22/1.45 generalize (zenon_H16 zenon_TA_o). zenon_intro zenon_H17. % 1.22/1.45 generalize (zenon_H17 zenon_TC_m). zenon_intro zenon_H18. % 1.22/1.45 apply (zenon_imply_s _ _ zenon_H18); [ zenon_intro zenon_H1a | zenon_intro zenon_H19 ]. % 1.22/1.45 cut ((subset (unordered_pair zenon_TA_o zenon_TB_n) (singleton zenon_TC_m)) = (subset (unordered_pair zenon_TB_n zenon_TA_o) (singleton zenon_TC_m))). % 1.22/1.45 intro zenon_D_pnotp. % 1.22/1.45 apply zenon_H1a. % 1.22/1.45 rewrite <- zenon_D_pnotp. % 1.22/1.45 exact zenon_Ha. % 1.22/1.45 cut (((singleton zenon_TC_m) = (singleton zenon_TC_m))); [idtac | apply NNPP; zenon_intro zenon_Hf]. % 1.22/1.45 cut (((unordered_pair zenon_TA_o zenon_TB_n) = (unordered_pair zenon_TB_n zenon_TA_o))); [idtac | apply NNPP; zenon_intro zenon_H1b]. % 1.22/1.45 congruence. % 1.22/1.45 apply zenon_H1b. apply sym_equal. exact zenon_Hb. % 1.22/1.45 apply zenon_Hf. apply refl_equal. % 1.22/1.45 exact (zenon_H14 zenon_H19). % 1.22/1.45 apply zenon_H12. apply refl_equal. % 1.22/1.45 apply zenon_H12. apply refl_equal. % 1.22/1.45 apply zenon_Hf. apply refl_equal. % 1.22/1.45 (* end of lemma zenon_L1_ *) % 1.22/1.45 apply NNPP. intro zenon_G. % 1.22/1.45 apply (zenon_notallex_s (fun A : zenon_U => (forall B : zenon_U, (forall C : zenon_U, ((subset (unordered_pair A B) (singleton C))->((unordered_pair A B) = (singleton C)))))) zenon_G); [ zenon_intro zenon_H1c; idtac ]. % 1.22/1.45 elim zenon_H1c. zenon_intro zenon_TA_o. zenon_intro zenon_H1d. % 1.22/1.45 apply (zenon_notallex_s (fun B : zenon_U => (forall C : zenon_U, ((subset (unordered_pair zenon_TA_o B) (singleton C))->((unordered_pair zenon_TA_o B) = (singleton C))))) zenon_H1d); [ zenon_intro zenon_H1e; idtac ]. % 1.22/1.45 elim zenon_H1e. zenon_intro zenon_TB_n. zenon_intro zenon_H1f. % 1.22/1.45 apply (zenon_notallex_s (fun C : zenon_U => ((subset (unordered_pair zenon_TA_o zenon_TB_n) (singleton C))->((unordered_pair zenon_TA_o zenon_TB_n) = (singleton C)))) zenon_H1f); [ zenon_intro zenon_H20; idtac ]. % 1.22/1.45 elim zenon_H20. zenon_intro zenon_TC_m. zenon_intro zenon_H21. % 1.22/1.45 apply (zenon_notimply_s _ _ zenon_H21). zenon_intro zenon_Ha. zenon_intro zenon_H7. % 1.22/1.45 generalize (commutativity_k2_tarski zenon_TB_n). zenon_intro zenon_H22. % 1.22/1.45 generalize (t69_enumset1 zenon_TC_m). zenon_intro zenon_H8. % 1.22/1.45 generalize (zenon_H22 zenon_TA_o). zenon_intro zenon_Hb. % 1.22/1.45 generalize (t26_zfmisc_1 zenon_TA_o). zenon_intro zenon_H23. % 1.22/1.45 generalize (zenon_H23 zenon_TB_n). zenon_intro zenon_H24. % 1.22/1.45 generalize (zenon_H24 zenon_TC_m). zenon_intro zenon_H25. % 1.22/1.45 apply (zenon_imply_s _ _ zenon_H25); [ zenon_intro zenon_H26 | zenon_intro zenon_H9 ]. % 1.22/1.45 exact (zenon_H26 zenon_Ha). % 1.22/1.45 apply (zenon_L1_ zenon_TC_m zenon_TB_n zenon_TA_o); trivial. % 1.22/1.45 Qed. % 1.22/1.45 % SZS output end Proof % 1.22/1.45 (* END-PROOF *) % 1.22/1.45 nodes searched: 10573 % 1.22/1.45 max branch formulas: 1974 % 1.22/1.45 proof nodes created: 307 % 1.22/1.45 formulas created: 49601 % 1.22/1.45 %------------------------------------------------------------------------------