%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : KLE004+1 : TPTP v8.1.0. Released v4.0.0. % 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 : Sun Jul 17 02:37:10 EDT 2022 % Result : Theorem 257.37s 257.58s % Output : Proof 257.37s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.11 % Problem : KLE004+1 : TPTP v8.1.0. Released v4.0.0. % 0.03/0.12 % 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 : Thu Jun 16 09:43:33 EDT 2022 % 0.12/0.33 % CPUTime : % 257.37/257.58 (* PROOF-FOUND *) % 257.37/257.58 % SZS status Theorem % 257.37/257.58 (* BEGIN-PROOF *) % 257.37/257.58 % SZS output start Proof % 257.37/257.58 Theorem goals : ((c (zero)) = (one)). % 257.37/257.58 Proof. % 257.37/257.58 assert (zenon_L1_ : (~((one) = (one))) -> False). % 257.37/257.58 do 0 intro. intros zenon_H11. % 257.37/257.58 apply zenon_H11. apply refl_equal. % 257.37/257.58 (* end of lemma zenon_L1_ *) % 257.37/257.58 assert (zenon_L2_ : (((c (zero)) = (c (zero)))<->(complement (zero) (c (zero)))) -> (~((c (zero)) = (one))) -> False). % 257.37/257.58 do 0 intro. intros zenon_H12 zenon_G. % 257.37/257.58 apply (zenon_equiv_s _ _ zenon_H12); [ zenon_intro zenon_H16; zenon_intro zenon_H15 | zenon_intro zenon_H14; zenon_intro zenon_H13 ]. % 257.37/257.58 apply zenon_H16. apply refl_equal. % 257.37/257.58 generalize (test_2 (c (zero))). zenon_intro zenon_H17. % 257.37/257.58 generalize (zenon_H17 (zero)). zenon_intro zenon_H18. % 257.37/257.58 apply (zenon_equiv_s _ _ zenon_H18); [ zenon_intro zenon_H15; zenon_intro zenon_H1a | zenon_intro zenon_H13; zenon_intro zenon_H19 ]. % 257.37/257.58 exact (zenon_H15 zenon_H13). % 257.37/257.58 apply (zenon_and_s _ _ zenon_H19). zenon_intro zenon_H1c. zenon_intro zenon_H1b. % 257.37/257.58 apply (zenon_and_s _ _ zenon_H1b). zenon_intro zenon_H1e. zenon_intro zenon_H1d. % 257.37/257.58 generalize (additive_identity (c (zero))). zenon_intro zenon_H1f. % 257.37/257.58 cut (((addition (c (zero)) (zero)) = (one)) = ((c (zero)) = (one))). % 257.37/257.58 intro zenon_D_pnotp. % 257.37/257.58 apply zenon_G. % 257.37/257.58 rewrite <- zenon_D_pnotp. % 257.37/257.58 exact zenon_H1d. % 257.37/257.58 cut (((one) = (one))); [idtac | apply NNPP; zenon_intro zenon_H11]. % 257.37/257.58 cut (((addition (c (zero)) (zero)) = (c (zero)))); [idtac | apply NNPP; zenon_intro zenon_H20]. % 257.37/257.58 congruence. % 257.37/257.58 exact (zenon_H20 zenon_H1f). % 257.37/257.58 apply zenon_H11. apply refl_equal. % 257.37/257.58 (* end of lemma zenon_L2_ *) % 257.37/257.58 apply NNPP. intro zenon_G. % 257.37/257.58 generalize (additive_identity (one)). zenon_intro zenon_H21. % 257.37/257.58 generalize (test_3 (zero)). zenon_intro zenon_H22. % 257.37/257.58 generalize (zenon_H22 (c (zero))). zenon_intro zenon_H23. % 257.37/257.58 apply (zenon_imply_s _ _ zenon_H23); [ zenon_intro zenon_H24 | zenon_intro zenon_H12 ]. % 257.37/257.58 generalize (test_1 (zero)). zenon_intro zenon_H25. % 257.37/257.58 apply (zenon_equiv_s _ _ zenon_H25); [ zenon_intro zenon_H24; zenon_intro zenon_H28 | zenon_intro zenon_H27; zenon_intro zenon_H26 ]. % 257.37/257.58 generalize (additive_commutativity (zero)). zenon_intro zenon_H29. % 257.37/257.58 generalize (multiplicative_left_identity (zero)). zenon_intro zenon_H2a. % 257.37/257.58 apply zenon_H28. exists (one). apply NNPP. zenon_intro zenon_H2b. % 257.37/257.58 generalize (test_2 (zero)). zenon_intro zenon_H2c. % 257.37/257.58 generalize (zenon_H2c (one)). zenon_intro zenon_H2d. % 257.37/257.58 apply (zenon_equiv_s _ _ zenon_H2d); [ zenon_intro zenon_H2b; zenon_intro zenon_H30 | zenon_intro zenon_H2f; zenon_intro zenon_H2e ]. % 257.37/257.58 apply (zenon_notand_s _ _ zenon_H30); [ zenon_intro zenon_H32 | zenon_intro zenon_H31 ]. % 257.37/257.58 generalize (multiplicative_right_identity (zero)). zenon_intro zenon_H33. % 257.37/257.58 exact (zenon_H32 zenon_H33). % 257.37/257.58 apply (zenon_notand_s _ _ zenon_H31); [ zenon_intro zenon_H35 | zenon_intro zenon_H34 ]. % 257.37/257.58 exact (zenon_H35 zenon_H2a). % 257.37/257.58 generalize (zenon_H29 (one)). zenon_intro zenon_H36. % 257.37/257.58 cut (((addition (one) (zero)) = (one)) = ((addition (zero) (one)) = (one))). % 257.37/257.58 intro zenon_D_pnotp. % 257.37/257.58 apply zenon_H34. % 257.37/257.58 rewrite <- zenon_D_pnotp. % 257.37/257.58 exact zenon_H21. % 257.37/257.58 cut (((one) = (one))); [idtac | apply NNPP; zenon_intro zenon_H11]. % 257.37/257.58 cut (((addition (one) (zero)) = (addition (zero) (one)))); [idtac | apply NNPP; zenon_intro zenon_H37]. % 257.37/257.58 congruence. % 257.37/257.58 elim (classic ((addition (zero) (one)) = (addition (zero) (one)))); [ zenon_intro zenon_H38 | zenon_intro zenon_H39 ]. % 257.37/257.58 cut (((addition (zero) (one)) = (addition (zero) (one))) = ((addition (one) (zero)) = (addition (zero) (one)))). % 257.37/257.58 intro zenon_D_pnotp. % 257.37/257.58 apply zenon_H37. % 257.37/257.58 rewrite <- zenon_D_pnotp. % 257.37/257.58 exact zenon_H38. % 257.37/257.58 cut (((addition (zero) (one)) = (addition (zero) (one)))); [idtac | apply NNPP; zenon_intro zenon_H39]. % 257.37/257.58 cut (((addition (zero) (one)) = (addition (one) (zero)))); [idtac | apply NNPP; zenon_intro zenon_H3a]. % 257.37/257.58 congruence. % 257.37/257.58 exact (zenon_H3a zenon_H36). % 257.37/257.58 apply zenon_H39. apply refl_equal. % 257.37/257.58 apply zenon_H39. apply refl_equal. % 257.37/257.58 apply zenon_H11. apply refl_equal. % 257.37/257.58 exact (zenon_H2b zenon_H2f). % 257.37/257.58 exact (zenon_H24 zenon_H27). % 257.37/257.58 apply (zenon_L2_); trivial. % 257.37/257.58 Qed. % 257.37/257.58 % SZS output end Proof % 257.37/257.58 (* END-PROOF *) % 257.37/257.58 nodes searched: 145805 % 257.37/257.58 max branch formulas: 12403 % 257.37/257.58 proof nodes created: 3119 % 257.37/257.58 formulas created: 4603049 % 257.37/257.58 %------------------------------------------------------------------------------