%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : SEU267+1 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n016.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 16:00:44 EDT 2022 % Result : Theorem 0.41s 0.59s % Output : Proof 0.41s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.13 % Problem : SEU267+1 : TPTP v8.1.0. Released v3.3.0. % 0.07/0.13 % Command : run_zenon %s %d % 0.13/0.35 % Computer : n016.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 600 % 0.13/0.35 % DateTime : Sun Jun 19 10:24:38 EDT 2022 % 0.13/0.35 % CPUTime : % 0.41/0.59 (* PROOF-FOUND *) % 0.41/0.59 % SZS status Theorem % 0.41/0.59 (* BEGIN-PROOF *) % 0.41/0.59 % SZS output start Proof % 0.41/0.59 Theorem t7_mcart_1 : (forall A : zenon_U, (forall B : zenon_U, (((pair_first (ordered_pair A B)) = A)/\((pair_second (ordered_pair A B)) = B)))). % 0.41/0.59 Proof. % 0.41/0.59 assert (zenon_L1_ : forall (zenon_TB_q : zenon_U) (zenon_TA_r : zenon_U), (~(exists B : zenon_U, (exists C : zenon_U, ((ordered_pair zenon_TA_r zenon_TB_q) = (ordered_pair B C))))) -> False). % 0.41/0.59 do 2 intro. intros zenon_Hf. % 0.41/0.59 apply zenon_Hf. exists zenon_TA_r. apply NNPP. zenon_intro zenon_H12. % 0.41/0.59 apply zenon_H12. exists zenon_TB_q. apply NNPP. zenon_intro zenon_H13. % 0.41/0.59 apply zenon_H13. apply refl_equal. % 0.41/0.59 (* end of lemma zenon_L1_ *) % 0.41/0.59 apply NNPP. intro zenon_G. % 0.41/0.59 apply (zenon_notallex_s (fun A : zenon_U => (forall B : zenon_U, (((pair_first (ordered_pair A B)) = A)/\((pair_second (ordered_pair A B)) = B)))) zenon_G); [ zenon_intro zenon_H14; idtac ]. % 0.41/0.59 elim zenon_H14. zenon_intro zenon_TA_r. zenon_intro zenon_H15. % 0.41/0.59 apply (zenon_notallex_s (fun B : zenon_U => (((pair_first (ordered_pair zenon_TA_r B)) = zenon_TA_r)/\((pair_second (ordered_pair zenon_TA_r B)) = B))) zenon_H15); [ zenon_intro zenon_H16; idtac ]. % 0.41/0.59 elim zenon_H16. zenon_intro zenon_TB_q. zenon_intro zenon_H17. % 0.41/0.59 apply (zenon_notand_s _ _ zenon_H17); [ zenon_intro zenon_H19 | zenon_intro zenon_H18 ]. % 0.41/0.59 generalize (d1_mcart_1 (ordered_pair zenon_TA_r zenon_TB_q)). zenon_intro zenon_H1a. % 0.41/0.59 apply (zenon_imply_s _ _ zenon_H1a); [ zenon_intro zenon_Hf | zenon_intro zenon_H1b ]. % 0.41/0.59 apply (zenon_L1_ zenon_TB_q zenon_TA_r); trivial. % 0.41/0.59 generalize (zenon_H1b (pair_first (ordered_pair zenon_TA_r zenon_TB_q))). zenon_intro zenon_H1c. % 0.41/0.59 apply (zenon_equiv_s _ _ zenon_H1c); [ zenon_intro zenon_H20; zenon_intro zenon_H1f | zenon_intro zenon_H1e; zenon_intro zenon_H1d ]. % 0.41/0.59 apply zenon_H20. apply refl_equal. % 0.41/0.59 generalize (zenon_H1d zenon_TA_r). zenon_intro zenon_H21. % 0.41/0.59 generalize (zenon_H21 zenon_TB_q). zenon_intro zenon_H22. % 0.41/0.59 apply (zenon_imply_s _ _ zenon_H22); [ zenon_intro zenon_H13 | zenon_intro zenon_H23 ]. % 0.41/0.59 apply zenon_H13. apply refl_equal. % 0.41/0.59 exact (zenon_H19 zenon_H23). % 0.41/0.59 generalize (d2_mcart_1 (ordered_pair zenon_TA_r zenon_TB_q)). zenon_intro zenon_H24. % 0.41/0.59 apply (zenon_imply_s _ _ zenon_H24); [ zenon_intro zenon_Hf | zenon_intro zenon_H25 ]. % 0.41/0.59 apply (zenon_L1_ zenon_TB_q zenon_TA_r); trivial. % 0.41/0.59 generalize (zenon_H25 (pair_second (ordered_pair zenon_TA_r zenon_TB_q))). zenon_intro zenon_H26. % 0.41/0.59 apply (zenon_equiv_s _ _ zenon_H26); [ zenon_intro zenon_H2a; zenon_intro zenon_H29 | zenon_intro zenon_H28; zenon_intro zenon_H27 ]. % 0.41/0.59 apply zenon_H2a. apply refl_equal. % 0.41/0.59 generalize (zenon_H27 zenon_TA_r). zenon_intro zenon_H2b. % 0.41/0.59 generalize (zenon_H2b zenon_TB_q). zenon_intro zenon_H2c. % 0.41/0.59 apply (zenon_imply_s _ _ zenon_H2c); [ zenon_intro zenon_H13 | zenon_intro zenon_H2d ]. % 0.41/0.59 apply zenon_H13. apply refl_equal. % 0.41/0.59 exact (zenon_H18 zenon_H2d). % 0.41/0.59 Qed. % 0.41/0.59 % SZS output end Proof % 0.41/0.59 (* END-PROOF *) % 0.41/0.59 nodes searched: 2353 % 0.41/0.59 max branch formulas: 304 % 0.41/0.59 proof nodes created: 235 % 0.41/0.59 formulas created: 6658 % 0.41/0.59 %------------------------------------------------------------------------------