%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : ITP010+2 : TPTP v8.1.0. Bugfixed v7.5.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n019.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 01:27:11 EDT 2022 % Result : Theorem 0.18s 0.50s % Output : Proof 0.18s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.12 % Problem : ITP010+2 : TPTP v8.1.0. Bugfixed v7.5.0. % 0.04/0.13 % Command : run_zenon %s %d % 0.13/0.33 % Computer : n019.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 : Fri Jun 3 03:12:40 EDT 2022 % 0.13/0.33 % CPUTime : % 0.18/0.50 (* PROOF-FOUND *) % 0.18/0.50 % SZS status Theorem % 0.18/0.50 (* BEGIN-PROOF *) % 0.18/0.50 % SZS output start Proof % 0.18/0.50 Theorem conj_thm_2Ecardinal_2ECARD__NOT__LE : (forall A_27a : zenon_U, ((ne A_27a)->(forall A_27b : zenon_U, ((ne A_27b)->(forall V0s : zenon_U, ((mem V0s (arr A_27a (bool)))->(forall V1t : zenon_U, ((mem V1t (arr A_27b (bool)))->((~(p (ap (ap (c_2Ecardinal_2Ecardleq A_27a A_27b) V0s) V1t)))<->(~(p (ap (ap (c_2Ecardinal_2Ecardleq A_27a A_27b) V0s) V1t)))))))))))). % 0.18/0.50 Proof. % 0.18/0.50 apply NNPP. intro zenon_G. % 0.18/0.50 apply (zenon_notallex_s (fun A_27a : zenon_U => ((ne A_27a)->(forall A_27b : zenon_U, ((ne A_27b)->(forall V0s : zenon_U, ((mem V0s (arr A_27a (bool)))->(forall V1t : zenon_U, ((mem V1t (arr A_27b (bool)))->((~(p (ap (ap (c_2Ecardinal_2Ecardleq A_27a A_27b) V0s) V1t)))<->(~(p (ap (ap (c_2Ecardinal_2Ecardleq A_27a A_27b) V0s) V1t)))))))))))) zenon_G); [ zenon_intro zenon_H29; idtac ]. % 0.18/0.50 elim zenon_H29. zenon_intro zenon_TA_27a_bq. zenon_intro zenon_H2b. % 0.18/0.50 apply (zenon_notimply_s _ _ zenon_H2b). zenon_intro zenon_H2d. zenon_intro zenon_H2c. % 0.18/0.50 apply (zenon_notallex_s (fun A_27b : zenon_U => ((ne A_27b)->(forall V0s : zenon_U, ((mem V0s (arr zenon_TA_27a_bq (bool)))->(forall V1t : zenon_U, ((mem V1t (arr A_27b (bool)))->((~(p (ap (ap (c_2Ecardinal_2Ecardleq zenon_TA_27a_bq A_27b) V0s) V1t)))<->(~(p (ap (ap (c_2Ecardinal_2Ecardleq zenon_TA_27a_bq A_27b) V0s) V1t)))))))))) zenon_H2c); [ zenon_intro zenon_H2e; idtac ]. % 0.18/0.50 elim zenon_H2e. zenon_intro zenon_TA_27b_bv. zenon_intro zenon_H30. % 0.18/0.50 apply (zenon_notimply_s _ _ zenon_H30). zenon_intro zenon_H32. zenon_intro zenon_H31. % 0.18/0.50 apply (zenon_notallex_s (fun V0s : zenon_U => ((mem V0s (arr zenon_TA_27a_bq (bool)))->(forall V1t : zenon_U, ((mem V1t (arr zenon_TA_27b_bv (bool)))->((~(p (ap (ap (c_2Ecardinal_2Ecardleq zenon_TA_27a_bq zenon_TA_27b_bv) V0s) V1t)))<->(~(p (ap (ap (c_2Ecardinal_2Ecardleq zenon_TA_27a_bq zenon_TA_27b_bv) V0s) V1t)))))))) zenon_H31); [ zenon_intro zenon_H33; idtac ]. % 0.18/0.50 elim zenon_H33. zenon_intro zenon_TV0s_ca. zenon_intro zenon_H35. % 0.18/0.50 apply (zenon_notimply_s _ _ zenon_H35). zenon_intro zenon_H37. zenon_intro zenon_H36. % 0.18/0.50 apply (zenon_notallex_s (fun V1t : zenon_U => ((mem V1t (arr zenon_TA_27b_bv (bool)))->((~(p (ap (ap (c_2Ecardinal_2Ecardleq zenon_TA_27a_bq zenon_TA_27b_bv) zenon_TV0s_ca) V1t)))<->(~(p (ap (ap (c_2Ecardinal_2Ecardleq zenon_TA_27a_bq zenon_TA_27b_bv) zenon_TV0s_ca) V1t)))))) zenon_H36); [ zenon_intro zenon_H38; idtac ]. % 0.18/0.50 elim zenon_H38. zenon_intro zenon_TV1t_cf. zenon_intro zenon_H3a. % 0.18/0.50 apply (zenon_notimply_s _ _ zenon_H3a). zenon_intro zenon_H3c. zenon_intro zenon_H3b. % 0.18/0.50 apply (zenon_notequiv_s _ _ zenon_H3b); [ zenon_intro zenon_H3d; zenon_intro zenon_H3e | zenon_intro zenon_H3e; zenon_intro zenon_H3d ]. % 0.18/0.50 exact (zenon_H3d zenon_H3e). % 0.18/0.50 exact (zenon_H3d zenon_H3e). % 0.18/0.50 Qed. % 0.18/0.50 % SZS output end Proof % 0.18/0.50 (* END-PROOF *) % 0.18/0.50 nodes searched: 17 % 0.18/0.50 max branch formulas: 61 % 0.18/0.50 proof nodes created: 12 % 0.18/0.50 formulas created: 828 % 0.18/0.50 %------------------------------------------------------------------------------