%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : SET631+3 : TPTP v8.1.0. Released v2.2.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n011.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 06:37:35 EDT 2022 % Result : Theorem 3.99s 4.22s % Output : Proof 3.99s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.01/0.08 % Problem : SET631+3 : TPTP v8.1.0. Released v2.2.0. % 0.01/0.09 % Command : run_zenon %s %d % 0.08/0.28 % Computer : n011.cluster.edu % 0.08/0.28 % Model : x86_64 x86_64 % 0.08/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.08/0.28 % Memory : 8042.1875MB % 0.08/0.28 % OS : Linux 3.10.0-693.el7.x86_64 % 0.08/0.28 % CPULimit : 300 % 0.08/0.28 % WCLimit : 600 % 0.08/0.28 % DateTime : Sat Jul 9 23:52:11 EDT 2022 % 0.08/0.28 % CPUTime : % 3.99/4.22 (* PROOF-FOUND *) % 3.99/4.22 % SZS status Theorem % 3.99/4.22 (* BEGIN-PROOF *) % 3.99/4.22 % SZS output start Proof % 3.99/4.22 Theorem prove_th113 : (forall B : zenon_U, (forall C : zenon_U, (forall D : zenon_U, ((intersect B (difference C D))->(intersect B C))))). % 3.99/4.22 Proof. % 3.99/4.22 assert (zenon_L1_ : forall (zenon_TD_h : zenon_U) (zenon_TC_i : zenon_U) (zenon_TB_j : zenon_U), (~(exists D : zenon_U, ((member D zenon_TB_j)/\(member D zenon_TC_i)))) -> (member zenon_TD_h zenon_TB_j) -> (member zenon_TD_h zenon_TC_i) -> False). % 3.99/4.22 do 3 intro. intros zenon_H4 zenon_H5 zenon_H6. % 3.99/4.22 apply zenon_H4. exists zenon_TD_h. apply NNPP. zenon_intro zenon_Ha. % 3.99/4.22 apply (zenon_notand_s _ _ zenon_Ha); [ zenon_intro zenon_Hc | zenon_intro zenon_Hb ]. % 3.99/4.22 exact (zenon_Hc zenon_H5). % 3.99/4.22 exact (zenon_Hb zenon_H6). % 3.99/4.22 (* end of lemma zenon_L1_ *) % 3.99/4.22 apply NNPP. intro zenon_G. % 3.99/4.22 apply (zenon_notallex_s (fun B : zenon_U => (forall C : zenon_U, (forall D : zenon_U, ((intersect B (difference C D))->(intersect B C))))) zenon_G); [ zenon_intro zenon_Hd; idtac ]. % 3.99/4.22 elim zenon_Hd. zenon_intro zenon_TB_j. zenon_intro zenon_He. % 3.99/4.22 apply (zenon_notallex_s (fun C : zenon_U => (forall D : zenon_U, ((intersect zenon_TB_j (difference C D))->(intersect zenon_TB_j C)))) zenon_He); [ zenon_intro zenon_Hf; idtac ]. % 3.99/4.22 elim zenon_Hf. zenon_intro zenon_TC_i. zenon_intro zenon_H10. % 3.99/4.22 apply (zenon_notallex_s (fun D : zenon_U => ((intersect zenon_TB_j (difference zenon_TC_i D))->(intersect zenon_TB_j zenon_TC_i))) zenon_H10); [ zenon_intro zenon_H11; idtac ]. % 3.99/4.22 elim zenon_H11. zenon_intro zenon_TD_s. zenon_intro zenon_H13. % 3.99/4.22 apply (zenon_notimply_s _ _ zenon_H13). zenon_intro zenon_H15. zenon_intro zenon_H14. % 3.99/4.22 generalize (intersect_defn zenon_TB_j). zenon_intro zenon_H16. % 3.99/4.22 generalize (zenon_H16 (difference zenon_TC_i zenon_TD_s)). zenon_intro zenon_H17. % 3.99/4.22 apply (zenon_equiv_s _ _ zenon_H17); [ zenon_intro zenon_H1a; zenon_intro zenon_H19 | zenon_intro zenon_H15; zenon_intro zenon_H18 ]. % 3.99/4.22 exact (zenon_H1a zenon_H15). % 3.99/4.22 elim zenon_H18. zenon_intro zenon_TD_h. zenon_intro zenon_H1b. % 3.99/4.22 apply (zenon_and_s _ _ zenon_H1b). zenon_intro zenon_H5. zenon_intro zenon_H1c. % 3.99/4.22 generalize (intersect_defn zenon_TB_j). zenon_intro zenon_H16. % 3.99/4.22 generalize (zenon_H16 zenon_TC_i). zenon_intro zenon_H1d. % 3.99/4.22 apply (zenon_equiv_s _ _ zenon_H1d); [ zenon_intro zenon_H14; zenon_intro zenon_H4 | zenon_intro zenon_H1f; zenon_intro zenon_H1e ]. % 3.99/4.22 generalize (difference_defn zenon_TC_i). zenon_intro zenon_H20. % 3.99/4.22 generalize (zenon_H20 zenon_TC_i). zenon_intro zenon_H21. % 3.99/4.22 generalize (zenon_H20 zenon_TD_s). zenon_intro zenon_H22. % 3.99/4.22 generalize (zenon_H21 zenon_TD_h). zenon_intro zenon_H23. % 3.99/4.22 apply (zenon_equiv_s _ _ zenon_H23); [ zenon_intro zenon_H27; zenon_intro zenon_H26 | zenon_intro zenon_H25; zenon_intro zenon_H24 ]. % 3.99/4.22 apply (zenon_notand_s _ _ zenon_H26); [ zenon_intro zenon_Hb | zenon_intro zenon_H28 ]. % 3.99/4.22 generalize (zenon_H22 zenon_TD_h). zenon_intro zenon_H29. % 3.99/4.22 apply (zenon_equiv_s _ _ zenon_H29); [ zenon_intro zenon_H2c; zenon_intro zenon_H2b | zenon_intro zenon_H1c; zenon_intro zenon_H2a ]. % 3.99/4.22 exact (zenon_H2c zenon_H1c). % 3.99/4.22 apply (zenon_and_s _ _ zenon_H2a). zenon_intro zenon_H6. zenon_intro zenon_H2d. % 3.99/4.22 exact (zenon_Hb zenon_H6). % 3.99/4.22 apply zenon_H28. zenon_intro zenon_H6. % 3.99/4.22 apply (zenon_L1_ zenon_TD_h zenon_TC_i zenon_TB_j); trivial. % 3.99/4.22 apply (zenon_and_s _ _ zenon_H24). zenon_intro zenon_H6. zenon_intro zenon_Hb. % 3.99/4.22 exact (zenon_Hb zenon_H6). % 3.99/4.22 exact (zenon_H14 zenon_H1f). % 3.99/4.22 Qed. % 3.99/4.22 % SZS output end Proof % 3.99/4.22 (* END-PROOF *) % 3.99/4.22 nodes searched: 240547 % 3.99/4.22 max branch formulas: 40541 % 3.99/4.22 proof nodes created: 4198 % 3.99/4.22 formulas created: 527260 % 3.99/4.22 %------------------------------------------------------------------------------