%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : KLE076+1 : TPTP v8.1.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n008.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 02:37:32 EDT 2022 % Result : Theorem 0.36s 0.55s % Output : Proof 0.38s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.11 % Problem : KLE076+1 : TPTP v8.1.0. Released v4.0.0. % 0.06/0.12 % Command : run_zenon %s %d % 0.12/0.33 % Computer : n008.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 10:53:07 EDT 2022 % 0.12/0.33 % CPUTime : % 0.36/0.55 (* PROOF-FOUND *) % 0.36/0.55 % SZS status Theorem % 0.36/0.55 (* BEGIN-PROOF *) % 0.36/0.55 % SZS output start Proof % 0.36/0.55 Theorem goals : (forall X0 : zenon_U, ((domain (multiplication X0 (domain (zero)))) = (zero))). % 0.36/0.55 Proof. % 0.36/0.55 assert (zenon_L1_ : (~((zero) = (zero))) -> False). % 0.36/0.55 do 0 intro. intros zenon_H12. % 0.36/0.55 apply zenon_H12. apply refl_equal. % 0.36/0.55 (* end of lemma zenon_L1_ *) % 0.36/0.55 apply NNPP. intro zenon_G. % 0.36/0.55 apply (zenon_notallex_s (fun X0 : zenon_U => ((domain (multiplication X0 (domain (zero)))) = (zero))) zenon_G); [ zenon_intro zenon_H13; idtac ]. % 0.36/0.55 elim zenon_H13. zenon_intro zenon_TX0_u. zenon_intro zenon_H15. % 0.36/0.55 generalize (right_annihilation zenon_E). zenon_intro zenon_H16. % 0.36/0.55 cut (((domain (zero)) = (zero)) = ((domain (multiplication zenon_TX0_u (domain (zero)))) = (zero))). % 0.36/0.55 intro zenon_D_pnotp. % 0.36/0.55 apply zenon_H15. % 0.36/0.55 rewrite <- zenon_D_pnotp. % 0.36/0.55 exact domain4. % 0.36/0.55 cut (((zero) = (zero))); [idtac | apply NNPP; zenon_intro zenon_H12]. % 0.36/0.55 cut (((domain (zero)) = (domain (multiplication zenon_TX0_u (domain (zero)))))); [idtac | apply NNPP; zenon_intro zenon_H17]. % 0.36/0.55 congruence. % 0.36/0.55 elim (classic ((domain (multiplication zenon_TX0_u (domain (zero)))) = (domain (multiplication zenon_TX0_u (domain (zero)))))); [ zenon_intro zenon_H18 | zenon_intro zenon_H19 ]. % 0.36/0.55 cut (((domain (multiplication zenon_TX0_u (domain (zero)))) = (domain (multiplication zenon_TX0_u (domain (zero))))) = ((domain (zero)) = (domain (multiplication zenon_TX0_u (domain (zero)))))). % 0.36/0.55 intro zenon_D_pnotp. % 0.36/0.55 apply zenon_H17. % 0.36/0.55 rewrite <- zenon_D_pnotp. % 0.36/0.55 exact zenon_H18. % 0.36/0.55 cut (((domain (multiplication zenon_TX0_u (domain (zero)))) = (domain (multiplication zenon_TX0_u (domain (zero)))))); [idtac | apply NNPP; zenon_intro zenon_H19]. % 0.36/0.55 cut (((domain (multiplication zenon_TX0_u (domain (zero)))) = (domain (zero)))); [idtac | apply NNPP; zenon_intro zenon_H1a]. % 0.36/0.55 congruence. % 0.36/0.55 cut (((multiplication zenon_TX0_u (domain (zero))) = (zero))); [idtac | apply NNPP; zenon_intro zenon_H1b]. % 0.36/0.55 congruence. % 0.36/0.55 cut (((multiplication zenon_E (zero)) = (zero)) = ((multiplication zenon_TX0_u (domain (zero))) = (zero))). % 0.36/0.55 intro zenon_D_pnotp. % 0.36/0.55 apply zenon_H1b. % 0.36/0.55 rewrite <- zenon_D_pnotp. % 0.36/0.55 exact zenon_H16. % 0.36/0.55 cut (((zero) = (zero))); [idtac | apply NNPP; zenon_intro zenon_H12]. % 0.36/0.55 cut (((multiplication zenon_E (zero)) = (multiplication zenon_TX0_u (domain (zero))))); [idtac | apply NNPP; zenon_intro zenon_H1c]. % 0.36/0.55 congruence. % 0.36/0.55 elim (classic ((multiplication zenon_TX0_u (domain (zero))) = (multiplication zenon_TX0_u (domain (zero))))); [ zenon_intro zenon_H1d | zenon_intro zenon_H1e ]. % 0.36/0.55 cut (((multiplication zenon_TX0_u (domain (zero))) = (multiplication zenon_TX0_u (domain (zero)))) = ((multiplication zenon_E (zero)) = (multiplication zenon_TX0_u (domain (zero))))). % 0.36/0.55 intro zenon_D_pnotp. % 0.36/0.55 apply zenon_H1c. % 0.36/0.55 rewrite <- zenon_D_pnotp. % 0.36/0.55 exact zenon_H1d. % 0.36/0.55 cut (((multiplication zenon_TX0_u (domain (zero))) = (multiplication zenon_TX0_u (domain (zero))))); [idtac | apply NNPP; zenon_intro zenon_H1e]. % 0.36/0.55 cut (((multiplication zenon_TX0_u (domain (zero))) = (multiplication zenon_E (zero)))); [idtac | apply NNPP; zenon_intro zenon_H1f]. % 0.36/0.55 congruence. % 0.36/0.55 generalize (right_annihilation zenon_TX0_u). zenon_intro zenon_H20. % 0.36/0.55 cut (((multiplication zenon_TX0_u (zero)) = (zero)) = ((multiplication zenon_TX0_u (domain (zero))) = (multiplication zenon_E (zero)))). % 0.36/0.55 intro zenon_D_pnotp. % 0.36/0.55 apply zenon_H1f. % 0.36/0.55 rewrite <- zenon_D_pnotp. % 0.36/0.55 exact zenon_H20. % 0.36/0.55 cut (((zero) = (multiplication zenon_E (zero)))); [idtac | apply NNPP; zenon_intro zenon_H21]. % 0.36/0.55 cut (((multiplication zenon_TX0_u (zero)) = (multiplication zenon_TX0_u (domain (zero))))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 0.36/0.55 congruence. % 0.36/0.55 elim (classic ((multiplication zenon_TX0_u (domain (zero))) = (multiplication zenon_TX0_u (domain (zero))))); [ zenon_intro zenon_H1d | zenon_intro zenon_H1e ]. % 0.36/0.55 cut (((multiplication zenon_TX0_u (domain (zero))) = (multiplication zenon_TX0_u (domain (zero)))) = ((multiplication zenon_TX0_u (zero)) = (multiplication zenon_TX0_u (domain (zero))))). % 0.36/0.55 intro zenon_D_pnotp. % 0.36/0.55 apply zenon_H22. % 0.36/0.55 rewrite <- zenon_D_pnotp. % 0.36/0.55 exact zenon_H1d. % 0.36/0.55 cut (((multiplication zenon_TX0_u (domain (zero))) = (multiplication zenon_TX0_u (domain (zero))))); [idtac | apply NNPP; zenon_intro zenon_H1e]. % 0.38/0.55 cut (((multiplication zenon_TX0_u (domain (zero))) = (multiplication zenon_TX0_u (zero)))); [idtac | apply NNPP; zenon_intro zenon_H23]. % 0.38/0.55 congruence. % 0.38/0.55 cut (((domain (zero)) = (zero))); [idtac | apply NNPP; zenon_intro zenon_H24]. % 0.38/0.55 cut ((zenon_TX0_u = zenon_TX0_u)); [idtac | apply NNPP; zenon_intro zenon_H25]. % 0.38/0.55 congruence. % 0.38/0.55 apply zenon_H25. apply refl_equal. % 0.38/0.55 exact (zenon_H24 domain4). % 0.38/0.55 apply zenon_H1e. apply refl_equal. % 0.38/0.55 apply zenon_H1e. apply refl_equal. % 0.38/0.55 apply zenon_H21. apply sym_equal. exact zenon_H16. % 0.38/0.55 apply zenon_H1e. apply refl_equal. % 0.38/0.55 apply zenon_H1e. apply refl_equal. % 0.38/0.55 apply zenon_H12. apply refl_equal. % 0.38/0.55 apply zenon_H19. apply refl_equal. % 0.38/0.55 apply zenon_H19. apply refl_equal. % 0.38/0.55 apply zenon_H12. apply refl_equal. % 0.38/0.55 Qed. % 0.38/0.55 % SZS output end Proof % 0.38/0.55 (* END-PROOF *) % 0.38/0.55 nodes searched: 375 % 0.38/0.55 max branch formulas: 216 % 0.38/0.55 proof nodes created: 24 % 0.38/0.55 formulas created: 4720 % 0.38/0.55 %------------------------------------------------------------------------------