%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : SEU159+1 : TPTP v8.1.0. Released v3.3.0. % 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 15:59:50 EDT 2022 % Result : Theorem 73.28s 73.48s % Output : Proof 73.28s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : SEU159+1 : TPTP v8.1.0. Released v3.3.0. % 0.06/0.12 % Command : run_zenon %s %d % 0.12/0.33 % Computer : n028.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 Jun 18 23:00:29 EDT 2022 % 0.12/0.33 % CPUTime : % 73.28/73.48 Zenon warning: unused variable (B : zenon_U) in reflexivity_r1_tarski % 73.28/73.48 (* PROOF-FOUND *) % 73.28/73.48 % SZS status Theorem % 73.28/73.48 (* BEGIN-PROOF *) % 73.28/73.48 % SZS output start Proof % 73.28/73.48 Theorem t38_zfmisc_1 : (forall A : zenon_U, (forall B : zenon_U, (forall C : zenon_U, ((subset (unordered_pair A B) C)<->((in A C)/\(in B C)))))). % 73.28/73.48 Proof. % 73.28/73.48 assert (zenon_L1_ : forall (zenon_TC_l : zenon_U) (zenon_TB_m : zenon_U) (zenon_TA_n : zenon_U) (zenon_TC_o : zenon_U), ((zenon_TC_o = zenon_TA_n)\/(zenon_TC_o = zenon_TB_m)) -> (~(zenon_TB_m = zenon_TC_o)) -> (in zenon_TA_n zenon_TC_l) -> (~(in zenon_TC_o zenon_TC_l)) -> False). % 73.28/73.48 do 4 intro. intros zenon_H7 zenon_H8 zenon_H9 zenon_Ha. % 73.28/73.48 apply (zenon_or_s _ _ zenon_H7); [ zenon_intro zenon_H10 | zenon_intro zenon_Hf ]. % 73.28/73.48 cut ((in zenon_TA_n zenon_TC_l) = (in zenon_TC_o zenon_TC_l)). % 73.28/73.48 intro zenon_D_pnotp. % 73.28/73.48 apply zenon_Ha. % 73.28/73.48 rewrite <- zenon_D_pnotp. % 73.28/73.48 exact zenon_H9. % 73.28/73.48 cut ((zenon_TC_l = zenon_TC_l)); [idtac | apply NNPP; zenon_intro zenon_H11]. % 73.28/73.48 cut ((zenon_TA_n = zenon_TC_o)); [idtac | apply NNPP; zenon_intro zenon_H12]. % 73.28/73.48 congruence. % 73.28/73.48 apply zenon_H12. apply sym_equal. exact zenon_H10. % 73.28/73.48 apply zenon_H11. apply refl_equal. % 73.28/73.48 apply zenon_H8. apply sym_equal. exact zenon_Hf. % 73.28/73.48 (* end of lemma zenon_L1_ *) % 73.28/73.48 assert (zenon_L2_ : forall (zenon_TB_m : zenon_U) (zenon_TA_n : zenon_U), (~((zenon_TA_n = zenon_TA_n)\/(zenon_TA_n = zenon_TB_m))) -> False). % 73.28/73.48 do 2 intro. intros zenon_H13. % 73.28/73.48 apply (zenon_notor_s _ _ zenon_H13). zenon_intro zenon_H15. zenon_intro zenon_H14. % 73.28/73.48 apply zenon_H15. apply refl_equal. % 73.28/73.48 (* end of lemma zenon_L2_ *) % 73.28/73.48 assert (zenon_L3_ : forall (zenon_TA_n : zenon_U) (zenon_TB_m : zenon_U), (~((zenon_TB_m = zenon_TA_n)\/(zenon_TB_m = zenon_TB_m))) -> False). % 73.28/73.48 do 2 intro. intros zenon_H16. % 73.28/73.48 apply (zenon_notor_s _ _ zenon_H16). zenon_intro zenon_H18. zenon_intro zenon_H17. % 73.28/73.48 apply zenon_H17. apply refl_equal. % 73.28/73.48 (* end of lemma zenon_L3_ *) % 73.28/73.48 apply NNPP. intro zenon_G. % 73.28/73.48 apply (zenon_notallex_s (fun A : zenon_U => (forall B : zenon_U, (forall C : zenon_U, ((subset (unordered_pair A B) C)<->((in A C)/\(in B C)))))) zenon_G); [ zenon_intro zenon_H19; idtac ]. % 73.28/73.48 elim zenon_H19. zenon_intro zenon_TA_n. zenon_intro zenon_H1a. % 73.28/73.48 apply (zenon_notallex_s (fun B : zenon_U => (forall C : zenon_U, ((subset (unordered_pair zenon_TA_n B) C)<->((in zenon_TA_n C)/\(in B C))))) zenon_H1a); [ zenon_intro zenon_H1b; idtac ]. % 73.28/73.48 elim zenon_H1b. zenon_intro zenon_TB_m. zenon_intro zenon_H1c. % 73.28/73.48 apply (zenon_notallex_s (fun C : zenon_U => ((subset (unordered_pair zenon_TA_n zenon_TB_m) C)<->((in zenon_TA_n C)/\(in zenon_TB_m C)))) zenon_H1c); [ zenon_intro zenon_H1d; idtac ]. % 73.28/73.48 elim zenon_H1d. zenon_intro zenon_TC_l. zenon_intro zenon_H1e. % 73.28/73.48 apply (zenon_notequiv_s _ _ zenon_H1e); [ zenon_intro zenon_H22; zenon_intro zenon_H21 | zenon_intro zenon_H20; zenon_intro zenon_H1f ]. % 73.28/73.48 generalize (d3_tarski (unordered_pair zenon_TA_n zenon_TB_m)). zenon_intro zenon_H23. % 73.28/73.48 generalize (zenon_H23 zenon_TC_l). zenon_intro zenon_H24. % 73.28/73.48 apply (zenon_equiv_s _ _ zenon_H24); [ zenon_intro zenon_H22; zenon_intro zenon_H26 | zenon_intro zenon_H20; zenon_intro zenon_H25 ]. % 73.28/73.48 apply (zenon_notallex_s (fun C : zenon_U => ((in C (unordered_pair zenon_TA_n zenon_TB_m))->(in C zenon_TC_l))) zenon_H26); [ zenon_intro zenon_H27; idtac ]. % 73.28/73.48 elim zenon_H27. zenon_intro zenon_TC_o. zenon_intro zenon_H28. % 73.28/73.48 apply (zenon_notimply_s _ _ zenon_H28). zenon_intro zenon_H29. zenon_intro zenon_Ha. % 73.28/73.48 apply (zenon_and_s _ _ zenon_H21). zenon_intro zenon_H9. zenon_intro zenon_H2a. % 73.28/73.48 generalize (d2_tarski zenon_TA_n). zenon_intro zenon_H2b. % 73.28/73.48 cut ((in zenon_TB_m zenon_TC_l) = (in zenon_TC_o zenon_TC_l)). % 73.28/73.48 intro zenon_D_pnotp. % 73.28/73.48 apply zenon_Ha. % 73.28/73.48 rewrite <- zenon_D_pnotp. % 73.28/73.48 exact zenon_H2a. % 73.28/73.48 cut ((zenon_TC_l = zenon_TC_l)); [idtac | apply NNPP; zenon_intro zenon_H11]. % 73.28/73.48 cut ((zenon_TB_m = zenon_TC_o)); [idtac | apply NNPP; zenon_intro zenon_H8]. % 73.28/73.48 congruence. % 73.28/73.48 generalize (zenon_H2b zenon_TB_m). zenon_intro zenon_H2c. % 73.28/73.48 generalize (zenon_H2c (unordered_pair zenon_TA_n zenon_TB_m)). zenon_intro zenon_H2d. % 73.28/73.48 apply (zenon_equiv_s _ _ zenon_H2d); [ zenon_intro zenon_H31; zenon_intro zenon_H30 | zenon_intro zenon_H2f; zenon_intro zenon_H2e ]. % 73.28/73.48 apply zenon_H31. apply refl_equal. % 73.28/73.49 generalize (zenon_H2e zenon_TC_o). zenon_intro zenon_H32. % 73.28/73.49 apply (zenon_equiv_s _ _ zenon_H32); [ zenon_intro zenon_H34; zenon_intro zenon_H33 | zenon_intro zenon_H29; zenon_intro zenon_H7 ]. % 73.28/73.49 exact (zenon_H34 zenon_H29). % 73.28/73.49 apply (zenon_L1_ zenon_TC_l zenon_TB_m zenon_TA_n zenon_TC_o); trivial. % 73.28/73.49 apply zenon_H11. apply refl_equal. % 73.28/73.49 exact (zenon_H22 zenon_H20). % 73.28/73.49 generalize (d3_tarski (unordered_pair zenon_TA_n zenon_TB_m)). zenon_intro zenon_H23. % 73.28/73.49 generalize (zenon_H23 zenon_TC_l). zenon_intro zenon_H24. % 73.28/73.49 apply (zenon_equiv_s _ _ zenon_H24); [ zenon_intro zenon_H22; zenon_intro zenon_H26 | zenon_intro zenon_H20; zenon_intro zenon_H25 ]. % 73.28/73.49 exact (zenon_H22 zenon_H20). % 73.28/73.49 apply (zenon_notand_s _ _ zenon_H1f); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ]. % 73.28/73.49 generalize (zenon_H25 zenon_TA_n). zenon_intro zenon_H37. % 73.28/73.49 apply (zenon_imply_s _ _ zenon_H37); [ zenon_intro zenon_H38 | zenon_intro zenon_H9 ]. % 73.28/73.49 generalize (d2_tarski zenon_TA_n). zenon_intro zenon_H2b. % 73.28/73.49 generalize (zenon_H2b zenon_TB_m). zenon_intro zenon_H2c. % 73.28/73.49 generalize (zenon_H2c (unordered_pair zenon_TA_n zenon_TB_m)). zenon_intro zenon_H2d. % 73.28/73.49 apply (zenon_equiv_s _ _ zenon_H2d); [ zenon_intro zenon_H31; zenon_intro zenon_H30 | zenon_intro zenon_H2f; zenon_intro zenon_H2e ]. % 73.28/73.49 apply zenon_H31. apply refl_equal. % 73.28/73.49 generalize (zenon_H2e zenon_TA_n). zenon_intro zenon_H39. % 73.28/73.49 apply (zenon_equiv_s _ _ zenon_H39); [ zenon_intro zenon_H38; zenon_intro zenon_H13 | zenon_intro zenon_H3b; zenon_intro zenon_H3a ]. % 73.28/73.49 apply (zenon_L2_ zenon_TB_m zenon_TA_n); trivial. % 73.28/73.49 exact (zenon_H38 zenon_H3b). % 73.28/73.49 exact (zenon_H36 zenon_H9). % 73.28/73.49 generalize (zenon_H25 zenon_TB_m). zenon_intro zenon_H3c. % 73.28/73.49 apply (zenon_imply_s _ _ zenon_H3c); [ zenon_intro zenon_H3d | zenon_intro zenon_H2a ]. % 73.28/73.49 generalize (d2_tarski zenon_TA_n). zenon_intro zenon_H2b. % 73.28/73.49 generalize (zenon_H2b zenon_TB_m). zenon_intro zenon_H2c. % 73.28/73.49 generalize (zenon_H2c (unordered_pair zenon_TA_n zenon_TB_m)). zenon_intro zenon_H2d. % 73.28/73.49 apply (zenon_equiv_s _ _ zenon_H2d); [ zenon_intro zenon_H31; zenon_intro zenon_H30 | zenon_intro zenon_H2f; zenon_intro zenon_H2e ]. % 73.28/73.49 apply zenon_H31. apply refl_equal. % 73.28/73.49 generalize (zenon_H2e zenon_TB_m). zenon_intro zenon_H3e. % 73.28/73.49 apply (zenon_equiv_s _ _ zenon_H3e); [ zenon_intro zenon_H3d; zenon_intro zenon_H16 | zenon_intro zenon_H40; zenon_intro zenon_H3f ]. % 73.28/73.49 apply (zenon_L3_ zenon_TA_n zenon_TB_m); trivial. % 73.28/73.49 exact (zenon_H3d zenon_H40). % 73.28/73.49 exact (zenon_H35 zenon_H2a). % 73.28/73.49 Qed. % 73.28/73.49 % SZS output end Proof % 73.28/73.49 (* END-PROOF *) % 73.28/73.49 nodes searched: 514194 % 73.28/73.49 max branch formulas: 7016 % 73.28/73.49 proof nodes created: 20871 % 73.28/73.49 formulas created: 2632270 % 73.28/73.49 %------------------------------------------------------------------------------