%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : SEU189+2 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n028.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 16:00:06 EDT 2022 % Result : Theorem 13.22s 13.41s % Output : Proof 13.22s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SEU189+2 : TPTP v8.1.0. Released v3.3.0. % 0.07/0.13 % Command : run_zenon %s %d % 0.12/0.34 % Computer : n028.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 600 % 0.12/0.34 % DateTime : Sun Jun 19 12:26:45 EDT 2022 % 0.12/0.34 % CPUTime : % 13.22/13.41 Zenon warning: unused variable (B : zenon_U) in idempotence_k2_xboole_0 % 13.22/13.41 Zenon warning: unused variable (B : zenon_U) in idempotence_k3_xboole_0 % 13.22/13.41 Zenon warning: unused variable (B : zenon_U) in irreflexivity_r2_xboole_0 % 13.22/13.41 Zenon warning: unused variable (B : zenon_U) in reflexivity_r1_tarski % 13.22/13.41 (* PROOF-FOUND *) % 13.22/13.41 % SZS status Theorem % 13.22/13.41 (* BEGIN-PROOF *) % 13.22/13.41 % SZS output start Proof % 13.22/13.41 Theorem t65_relat_1 : (forall A : zenon_U, ((relation A)->(((relation_dom A) = (empty_set))<->((relation_rng A) = (empty_set))))). % 13.22/13.41 Proof. % 13.22/13.41 assert (zenon_L1_ : forall (zenon_TA_fx : zenon_U), (forall B : zenon_U, (~((in B zenon_TA_fx)/\(forall C : zenon_U, (forall D : zenon_U, (~(B = (ordered_pair C D)))))))) -> (~(relation zenon_TA_fx)) -> False). % 13.22/13.41 do 1 intro. intros zenon_H97 zenon_H98. % 13.22/13.41 generalize (d1_relat_1 zenon_TA_fx). zenon_intro zenon_H9a. % 13.22/13.41 apply (zenon_equiv_s _ _ zenon_H9a); [ zenon_intro zenon_H98; zenon_intro zenon_H9c | zenon_intro zenon_H9b; zenon_intro zenon_H97 ]. % 13.22/13.41 exact (zenon_H9c zenon_H97). % 13.22/13.41 exact (zenon_H98 zenon_H9b). % 13.22/13.41 (* end of lemma zenon_L1_ *) % 13.22/13.41 assert (zenon_L2_ : (~((empty_set) = (empty_set))) -> False). % 13.22/13.41 do 0 intro. intros zenon_H9d. % 13.22/13.41 apply zenon_H9d. apply refl_equal. % 13.22/13.41 (* end of lemma zenon_L2_ *) % 13.22/13.41 apply NNPP. intro zenon_G. % 13.22/13.41 apply (zenon_and_s _ _ t60_relat_1). zenon_intro zenon_H9f. zenon_intro zenon_H9e. % 13.22/13.41 apply (zenon_notallex_s (fun A : zenon_U => ((relation A)->(((relation_dom A) = (empty_set))<->((relation_rng A) = (empty_set))))) zenon_G); [ zenon_intro zenon_Ha0; idtac ]. % 13.22/13.41 elim zenon_Ha0. zenon_intro zenon_TA_fx. zenon_intro zenon_Ha1. % 13.22/13.41 apply (zenon_notimply_s _ _ zenon_Ha1). zenon_intro zenon_H9b. zenon_intro zenon_Ha2. % 13.22/13.41 generalize (d1_relat_1 zenon_TA_fx). zenon_intro zenon_H9a. % 13.22/13.41 apply (zenon_equiv_s _ _ zenon_H9a); [ zenon_intro zenon_H98; zenon_intro zenon_H9c | zenon_intro zenon_H9b; zenon_intro zenon_H97 ]. % 13.22/13.41 exact (zenon_H98 zenon_H9b). % 13.22/13.41 apply (zenon_notequiv_s _ _ zenon_Ha2); [ zenon_intro zenon_Ha6; zenon_intro zenon_Ha5 | zenon_intro zenon_Ha4; zenon_intro zenon_Ha3 ]. % 13.22/13.41 cut (((relation_dom (empty_set)) = (empty_set)) = ((relation_dom zenon_TA_fx) = (empty_set))). % 13.22/13.41 intro zenon_D_pnotp. % 13.22/13.41 apply zenon_Ha6. % 13.22/13.41 rewrite <- zenon_D_pnotp. % 13.22/13.41 exact zenon_H9f. % 13.22/13.41 cut (((empty_set) = (empty_set))); [idtac | apply NNPP; zenon_intro zenon_H9d]. % 13.22/13.41 cut (((relation_dom (empty_set)) = (relation_dom zenon_TA_fx))); [idtac | apply NNPP; zenon_intro zenon_Ha7]. % 13.22/13.41 congruence. % 13.22/13.41 elim (classic ((relation_dom zenon_TA_fx) = (relation_dom zenon_TA_fx))); [ zenon_intro zenon_Ha8 | zenon_intro zenon_Ha9 ]. % 13.22/13.41 cut (((relation_dom zenon_TA_fx) = (relation_dom zenon_TA_fx)) = ((relation_dom (empty_set)) = (relation_dom zenon_TA_fx))). % 13.22/13.41 intro zenon_D_pnotp. % 13.22/13.41 apply zenon_Ha7. % 13.22/13.41 rewrite <- zenon_D_pnotp. % 13.22/13.41 exact zenon_Ha8. % 13.22/13.41 cut (((relation_dom zenon_TA_fx) = (relation_dom zenon_TA_fx))); [idtac | apply NNPP; zenon_intro zenon_Ha9]. % 13.22/13.41 cut (((relation_dom zenon_TA_fx) = (relation_dom (empty_set)))); [idtac | apply NNPP; zenon_intro zenon_Haa]. % 13.22/13.41 congruence. % 13.22/13.41 cut ((zenon_TA_fx = (empty_set))); [idtac | apply NNPP; zenon_intro zenon_Hab]. % 13.22/13.41 congruence. % 13.22/13.41 generalize (t64_relat_1 zenon_TA_fx). zenon_intro zenon_Hac. % 13.22/13.42 apply (zenon_imply_s _ _ zenon_Hac); [ zenon_intro zenon_H98 | zenon_intro zenon_Had ]. % 13.22/13.42 apply (zenon_L1_ zenon_TA_fx); trivial. % 13.22/13.42 apply (zenon_imply_s _ _ zenon_Had); [ zenon_intro zenon_Haf | zenon_intro zenon_Hae ]. % 13.22/13.42 apply (zenon_notor_s _ _ zenon_Haf). zenon_intro zenon_Ha6. zenon_intro zenon_Ha3. % 13.22/13.42 exact (zenon_Ha3 zenon_Ha5). % 13.22/13.42 exact (zenon_Hab zenon_Hae). % 13.22/13.42 apply zenon_Ha9. apply refl_equal. % 13.22/13.42 apply zenon_Ha9. apply refl_equal. % 13.22/13.42 apply zenon_H9d. apply refl_equal. % 13.22/13.42 cut (((relation_rng (empty_set)) = (empty_set)) = ((relation_rng zenon_TA_fx) = (empty_set))). % 13.22/13.42 intro zenon_D_pnotp. % 13.22/13.42 apply zenon_Ha3. % 13.22/13.42 rewrite <- zenon_D_pnotp. % 13.22/13.42 exact zenon_H9e. % 13.22/13.42 cut (((empty_set) = (empty_set))); [idtac | apply NNPP; zenon_intro zenon_H9d]. % 13.22/13.42 cut (((relation_rng (empty_set)) = (relation_rng zenon_TA_fx))); [idtac | apply NNPP; zenon_intro zenon_Hb0]. % 13.22/13.42 congruence. % 13.22/13.42 elim (classic ((relation_rng zenon_TA_fx) = (relation_rng zenon_TA_fx))); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hb2 ]. % 13.22/13.42 cut (((relation_rng zenon_TA_fx) = (relation_rng zenon_TA_fx)) = ((relation_rng (empty_set)) = (relation_rng zenon_TA_fx))). % 13.22/13.43 intro zenon_D_pnotp. % 13.22/13.43 apply zenon_Hb0. % 13.22/13.43 rewrite <- zenon_D_pnotp. % 13.22/13.43 exact zenon_Hb1. % 13.22/13.43 cut (((relation_rng zenon_TA_fx) = (relation_rng zenon_TA_fx))); [idtac | apply NNPP; zenon_intro zenon_Hb2]. % 13.22/13.43 cut (((relation_rng zenon_TA_fx) = (relation_rng (empty_set)))); [idtac | apply NNPP; zenon_intro zenon_Hb3]. % 13.22/13.43 congruence. % 13.22/13.43 cut ((zenon_TA_fx = (empty_set))); [idtac | apply NNPP; zenon_intro zenon_Hab]. % 13.22/13.43 congruence. % 13.22/13.43 generalize (t64_relat_1 zenon_TA_fx). zenon_intro zenon_Hac. % 13.22/13.43 apply (zenon_imply_s _ _ zenon_Hac); [ zenon_intro zenon_H98 | zenon_intro zenon_Had ]. % 13.22/13.43 apply (zenon_L1_ zenon_TA_fx); trivial. % 13.22/13.43 apply (zenon_imply_s _ _ zenon_Had); [ zenon_intro zenon_Haf | zenon_intro zenon_Hae ]. % 13.22/13.43 apply (zenon_notor_s _ _ zenon_Haf). zenon_intro zenon_Ha6. zenon_intro zenon_Ha3. % 13.22/13.43 exact (zenon_Ha6 zenon_Ha4). % 13.22/13.43 exact (zenon_Hab zenon_Hae). % 13.22/13.43 apply zenon_Hb2. apply refl_equal. % 13.22/13.43 apply zenon_Hb2. apply refl_equal. % 13.22/13.43 apply zenon_H9d. apply refl_equal. % 13.22/13.43 Qed. % 13.22/13.43 % SZS output end Proof % 13.22/13.43 (* END-PROOF *) % 13.22/13.43 nodes searched: 929942 % 13.22/13.43 max branch formulas: 35082 % 13.22/13.43 proof nodes created: 7269 % 13.22/13.43 formulas created: 945730 % 13.22/13.43 %------------------------------------------------------------------------------