%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : SEU126+1 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n015.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 15:59:31 EDT 2022 % Result : Theorem 1.02s 1.18s % Output : Proof 1.02s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.11 % Problem : SEU126+1 : TPTP v8.1.0. Released v3.3.0. % 0.03/0.12 % Command : run_zenon %s %d % 0.12/0.32 % Computer : n015.cluster.edu % 0.12/0.32 % Model : x86_64 x86_64 % 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.32 % Memory : 8042.1875MB % 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.32 % CPULimit : 300 % 0.12/0.32 % WCLimit : 600 % 0.12/0.32 % DateTime : Sun Jun 19 23:09:15 EDT 2022 % 0.12/0.32 % CPUTime : % 1.02/1.18 Zenon warning: unused variable (B : zenon_U) in idempotence_k2_xboole_0 % 1.02/1.18 Zenon warning: unused variable (B : zenon_U) in reflexivity_r1_tarski % 1.02/1.18 (* PROOF-FOUND *) % 1.02/1.18 % SZS status Theorem % 1.02/1.18 (* BEGIN-PROOF *) % 1.02/1.18 % SZS output start Proof % 1.02/1.18 Theorem t12_xboole_1 : (forall A : zenon_U, (forall B : zenon_U, ((subset A B)->((set_union2 A B) = B)))). % 1.02/1.18 Proof. % 1.02/1.18 assert (zenon_L1_ : forall (zenon_TB_u : zenon_U) (zenon_TA_v : zenon_U) (zenon_TD_w : zenon_U), (~((in zenon_TD_w zenon_TA_v)\/(in zenon_TD_w zenon_TB_u))) -> (in zenon_TD_w zenon_TB_u) -> False). % 1.02/1.18 do 3 intro. intros zenon_H12 zenon_H13. % 1.02/1.18 apply (zenon_notor_s _ _ zenon_H12). zenon_intro zenon_H18. zenon_intro zenon_H17. % 1.02/1.18 exact (zenon_H17 zenon_H13). % 1.02/1.18 (* end of lemma zenon_L1_ *) % 1.02/1.18 apply NNPP. intro zenon_G. % 1.02/1.18 apply (zenon_notallex_s (fun A : zenon_U => (forall B : zenon_U, ((subset A B)->((set_union2 A B) = B)))) zenon_G); [ zenon_intro zenon_H19; idtac ]. % 1.02/1.18 elim zenon_H19. zenon_intro zenon_TA_v. zenon_intro zenon_H1a. % 1.02/1.18 apply (zenon_notallex_s (fun B : zenon_U => ((subset zenon_TA_v B)->((set_union2 zenon_TA_v B) = B))) zenon_H1a); [ zenon_intro zenon_H1b; idtac ]. % 1.02/1.18 elim zenon_H1b. zenon_intro zenon_TB_u. zenon_intro zenon_H1c. % 1.02/1.18 apply (zenon_notimply_s _ _ zenon_H1c). zenon_intro zenon_H1e. zenon_intro zenon_H1d. % 1.02/1.18 generalize (d3_tarski zenon_TA_v). zenon_intro zenon_H1f. % 1.02/1.18 generalize (zenon_H1f zenon_TB_u). zenon_intro zenon_H20. % 1.02/1.18 apply (zenon_equiv_s _ _ zenon_H20); [ zenon_intro zenon_H23; zenon_intro zenon_H22 | zenon_intro zenon_H1e; zenon_intro zenon_H21 ]. % 1.02/1.18 exact (zenon_H23 zenon_H1e). % 1.02/1.18 generalize (d2_xboole_0 zenon_TA_v). zenon_intro zenon_H24. % 1.02/1.18 generalize (zenon_H24 zenon_TB_u). zenon_intro zenon_H25. % 1.02/1.18 generalize (zenon_H25 zenon_TB_u). zenon_intro zenon_H26. % 1.02/1.18 apply (zenon_equiv_s _ _ zenon_H26); [ zenon_intro zenon_H2a; zenon_intro zenon_H29 | zenon_intro zenon_H28; zenon_intro zenon_H27 ]. % 1.02/1.18 apply (zenon_notallex_s (fun D : zenon_U => ((in D zenon_TB_u)<->((in D zenon_TA_v)\/(in D zenon_TB_u)))) zenon_H29); [ zenon_intro zenon_H2b; idtac ]. % 1.02/1.18 elim zenon_H2b. zenon_intro zenon_TD_w. zenon_intro zenon_H2c. % 1.02/1.18 apply (zenon_notequiv_s _ _ zenon_H2c); [ zenon_intro zenon_H17; zenon_intro zenon_H2d | zenon_intro zenon_H13; zenon_intro zenon_H12 ]. % 1.02/1.18 apply (zenon_or_s _ _ zenon_H2d); [ zenon_intro zenon_H2e | zenon_intro zenon_H13 ]. % 1.02/1.18 generalize (zenon_H21 zenon_TD_w). zenon_intro zenon_H2f. % 1.02/1.18 apply (zenon_imply_s _ _ zenon_H2f); [ zenon_intro zenon_H18 | zenon_intro zenon_H13 ]. % 1.02/1.18 exact (zenon_H18 zenon_H2e). % 1.02/1.18 exact (zenon_H17 zenon_H13). % 1.02/1.18 exact (zenon_H17 zenon_H13). % 1.02/1.18 apply (zenon_L1_ zenon_TB_u zenon_TA_v zenon_TD_w); trivial. % 1.02/1.18 apply zenon_H1d. apply sym_equal. exact zenon_H28. % 1.02/1.18 Qed. % 1.02/1.18 % SZS output end Proof % 1.02/1.18 (* END-PROOF *) % 1.02/1.18 nodes searched: 19156 % 1.02/1.18 max branch formulas: 1233 % 1.02/1.18 proof nodes created: 1647 % 1.02/1.18 formulas created: 40455 % 1.02/1.18 %------------------------------------------------------------------------------