%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : SEU044+1 : TPTP v8.1.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n017.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 15:59:08 EDT 2022 % Result : Theorem 17.24s 17.42s % Output : Proof 17.24s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : SEU044+1 : TPTP v8.1.0. Released v3.2.0. % 0.06/0.12 % Command : run_zenon %s %d % 0.13/0.33 % Computer : n017.cluster.edu % 0.13/0.33 % Model : x86_64 x86_64 % 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.33 % Memory : 8042.1875MB % 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.33 % CPULimit : 300 % 0.13/0.33 % WCLimit : 600 % 0.13/0.33 % DateTime : Sat Jun 18 19:53:27 EDT 2022 % 0.13/0.33 % CPUTime : % 17.24/17.42 Zenon warning: unused variable (B : zenon_U) in reflexivity_r1_tarski % 17.24/17.42 (* PROOF-FOUND *) % 17.24/17.42 % SZS status Theorem % 17.24/17.42 (* BEGIN-PROOF *) % 17.24/17.42 % SZS output start Proof % 17.24/17.42 Theorem t86_funct_1 : (forall A : zenon_U, (forall B : zenon_U, (forall C : zenon_U, (((relation C)/\(function C))->((in B (relation_dom (relation_rng_restriction A C)))<->((in B (relation_dom C))/\(in (apply C B) A))))))). % 17.24/17.42 Proof. % 17.24/17.42 assert (zenon_L1_ : forall (zenon_TC_bk : zenon_U) (zenon_TA_bl : zenon_U), (~(relation (relation_rng_restriction zenon_TA_bl zenon_TC_bk))) -> (relation zenon_TC_bk) -> False). % 17.24/17.42 do 2 intro. intros zenon_H22 zenon_H23. % 17.24/17.42 generalize (dt_k8_relat_1 zenon_TA_bl). zenon_intro zenon_H26. % 17.24/17.42 generalize (zenon_H26 zenon_TC_bk). zenon_intro zenon_H27. % 17.24/17.42 apply (zenon_imply_s _ _ zenon_H27); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 17.24/17.42 exact (zenon_H29 zenon_H23). % 17.24/17.42 exact (zenon_H22 zenon_H28). % 17.24/17.42 (* end of lemma zenon_L1_ *) % 17.24/17.42 assert (zenon_L2_ : forall (zenon_TC_bk : zenon_U) (zenon_TA_bl : zenon_U), (~(function (relation_rng_restriction zenon_TA_bl zenon_TC_bk))) -> (function zenon_TC_bk) -> (relation zenon_TC_bk) -> False). % 17.24/17.42 do 2 intro. intros zenon_H2a zenon_H2b zenon_H23. % 17.24/17.42 generalize (fc5_funct_1 zenon_TA_bl). zenon_intro zenon_H2c. % 17.24/17.42 generalize (zenon_H2c zenon_TC_bk). zenon_intro zenon_H2d. % 17.24/17.42 apply (zenon_imply_s _ _ zenon_H2d); [ zenon_intro zenon_H2f | zenon_intro zenon_H2e ]. % 17.24/17.42 apply (zenon_notand_s _ _ zenon_H2f); [ zenon_intro zenon_H29 | zenon_intro zenon_H30 ]. % 17.24/17.42 exact (zenon_H29 zenon_H23). % 17.24/17.42 exact (zenon_H30 zenon_H2b). % 17.24/17.42 apply (zenon_and_s _ _ zenon_H2e). zenon_intro zenon_H28. zenon_intro zenon_H31. % 17.24/17.42 exact (zenon_H2a zenon_H31). % 17.24/17.42 (* end of lemma zenon_L2_ *) % 17.24/17.42 apply NNPP. intro zenon_G. % 17.24/17.42 apply (zenon_notallex_s (fun A : zenon_U => (forall B : zenon_U, (forall C : zenon_U, (((relation C)/\(function C))->((in B (relation_dom (relation_rng_restriction A C)))<->((in B (relation_dom C))/\(in (apply C B) A))))))) zenon_G); [ zenon_intro zenon_H32; idtac ]. % 17.24/17.42 elim zenon_H32. zenon_intro zenon_TA_bl. zenon_intro zenon_H33. % 17.24/17.42 apply (zenon_notallex_s (fun B : zenon_U => (forall C : zenon_U, (((relation C)/\(function C))->((in B (relation_dom (relation_rng_restriction zenon_TA_bl C)))<->((in B (relation_dom C))/\(in (apply C B) zenon_TA_bl)))))) zenon_H33); [ zenon_intro zenon_H34; idtac ]. % 17.24/17.42 elim zenon_H34. zenon_intro zenon_TB_cb. zenon_intro zenon_H36. % 17.24/17.42 apply (zenon_notallex_s (fun C : zenon_U => (((relation C)/\(function C))->((in zenon_TB_cb (relation_dom (relation_rng_restriction zenon_TA_bl C)))<->((in zenon_TB_cb (relation_dom C))/\(in (apply C zenon_TB_cb) zenon_TA_bl))))) zenon_H36); [ zenon_intro zenon_H37; idtac ]. % 17.24/17.42 elim zenon_H37. zenon_intro zenon_TC_bk. zenon_intro zenon_H38. % 17.24/17.42 apply (zenon_notimply_s _ _ zenon_H38). zenon_intro zenon_H3a. zenon_intro zenon_H39. % 17.24/17.42 apply (zenon_and_s _ _ zenon_H3a). zenon_intro zenon_H23. zenon_intro zenon_H2b. % 17.24/17.42 generalize (t85_funct_1 zenon_TA_bl). zenon_intro zenon_H3b. % 17.24/17.42 generalize (zenon_H3b (relation_rng_restriction zenon_TA_bl zenon_TC_bk)). zenon_intro zenon_H3c. % 17.24/17.42 apply (zenon_imply_s _ _ zenon_H3c); [ zenon_intro zenon_H3e | zenon_intro zenon_H3d ]. % 17.24/17.42 apply (zenon_notand_s _ _ zenon_H3e); [ zenon_intro zenon_H22 | zenon_intro zenon_H2a ]. % 17.24/17.42 apply (zenon_L1_ zenon_TC_bk zenon_TA_bl); trivial. % 17.24/17.42 apply (zenon_L2_ zenon_TC_bk zenon_TA_bl); trivial. % 17.24/17.42 generalize (zenon_H3d zenon_TC_bk). zenon_intro zenon_H3f. % 17.24/17.42 apply (zenon_imply_s _ _ zenon_H3f); [ zenon_intro zenon_H2f | zenon_intro zenon_H40 ]. % 17.24/17.42 apply (zenon_notand_s _ _ zenon_H2f); [ zenon_intro zenon_H29 | zenon_intro zenon_H30 ]. % 17.24/17.42 exact (zenon_H29 zenon_H23). % 17.24/17.42 exact (zenon_H30 zenon_H2b). % 17.24/17.42 apply (zenon_equiv_s _ _ zenon_H40); [ zenon_intro zenon_H44; zenon_intro zenon_H43 | zenon_intro zenon_H42; zenon_intro zenon_H41 ]. % 17.24/17.42 apply zenon_H44. apply refl_equal. % 17.24/17.42 apply (zenon_and_s _ _ zenon_H41). zenon_intro zenon_H46. zenon_intro zenon_H45. % 17.24/17.42 generalize (zenon_H46 zenon_TB_cb). zenon_intro zenon_H47. % 17.24/17.42 exact (zenon_H39 zenon_H47). % 17.24/17.42 Qed. % 17.24/17.42 % SZS output end Proof % 17.24/17.42 (* END-PROOF *) % 17.24/17.42 nodes searched: 208111 % 17.24/17.42 max branch formulas: 13321 % 17.24/17.42 proof nodes created: 10346 % 17.24/17.42 formulas created: 942668 % 17.24/17.42 %------------------------------------------------------------------------------