%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : SEU122+2 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n024.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 15:59:29 EDT 2022 % Result : Theorem 0.60s 0.77s % Output : Proof 0.60s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.11 % Problem : SEU122+2 : TPTP v8.1.0. Released v3.3.0. % 0.07/0.12 % Command : run_zenon %s %d % 0.12/0.33 % Computer : n024.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 : Mon Jun 20 11:56:47 EDT 2022 % 0.12/0.33 % CPUTime : % 0.60/0.77 Zenon warning: unused variable (B : zenon_U) in idempotence_k3_xboole_0 % 0.60/0.77 Zenon warning: unused variable (B : zenon_U) in reflexivity_r1_tarski % 0.60/0.77 (* PROOF-FOUND *) % 0.60/0.77 % SZS status Theorem % 0.60/0.77 (* BEGIN-PROOF *) % 0.60/0.77 % SZS output start Proof % 0.60/0.77 Theorem t2_xboole_1 : (forall A : zenon_U, (subset (empty_set) A)). % 0.60/0.77 Proof. % 0.60/0.77 assert (zenon_L1_ : (~((empty_set) = (empty_set))) -> False). % 0.60/0.77 do 0 intro. intros zenon_H14. % 0.60/0.77 apply zenon_H14. apply refl_equal. % 0.60/0.77 (* end of lemma zenon_L1_ *) % 0.60/0.77 apply NNPP. intro zenon_G. % 0.60/0.77 apply (zenon_notallex_s (fun A : zenon_U => (subset (empty_set) A)) zenon_G); [ zenon_intro zenon_H15; idtac ]. % 0.60/0.77 elim zenon_H15. zenon_intro zenon_TA_w. zenon_intro zenon_H17. % 0.60/0.77 generalize (d3_tarski (empty_set)). zenon_intro zenon_H18. % 0.60/0.77 generalize (zenon_H18 zenon_TA_w). zenon_intro zenon_H19. % 0.60/0.77 apply (zenon_equiv_s _ _ zenon_H19); [ zenon_intro zenon_H17; zenon_intro zenon_H1c | zenon_intro zenon_H1b; zenon_intro zenon_H1a ]. % 0.60/0.77 apply (zenon_notallex_s (fun C : zenon_U => ((in C (empty_set))->(in C zenon_TA_w))) zenon_H1c); [ zenon_intro zenon_H1d; idtac ]. % 0.60/0.77 elim zenon_H1d. zenon_intro zenon_TC_be. zenon_intro zenon_H1f. % 0.60/0.77 apply (zenon_notimply_s _ _ zenon_H1f). zenon_intro zenon_H21. zenon_intro zenon_H20. % 0.60/0.77 generalize (d1_xboole_0 (empty_set)). zenon_intro zenon_H22. % 0.60/0.77 apply (zenon_equiv_s _ _ zenon_H22); [ zenon_intro zenon_H14; zenon_intro zenon_H25 | zenon_intro zenon_H24; zenon_intro zenon_H23 ]. % 0.60/0.77 apply zenon_H14. apply refl_equal. % 0.60/0.77 generalize (zenon_H23 zenon_TC_be). zenon_intro zenon_H26. % 0.60/0.77 exact (zenon_H26 zenon_H21). % 0.60/0.77 exact (zenon_H17 zenon_H1b). % 0.60/0.77 Qed. % 0.60/0.77 % SZS output end Proof % 0.60/0.77 (* END-PROOF *) % 0.60/0.77 nodes searched: 10980 % 0.60/0.77 max branch formulas: 1127 % 0.60/0.77 proof nodes created: 735 % 0.60/0.77 formulas created: 25949 % 0.60/0.77 %------------------------------------------------------------------------------