%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : ITP010+5 : TPTP v8.1.0. Bugfixed v7.5.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n020.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 1.91s 2.10s % Output : Proof 1.91s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : ITP010+5 : TPTP v8.1.0. Bugfixed v7.5.0. % 0.03/0.13 % Command : run_zenon %s %d % 0.12/0.34 % Computer : n020.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 : Thu Jun 2 23:23:39 EDT 2022 % 0.12/0.34 % CPUTime : % 1.91/2.10 (* PROOF-FOUND *) % 1.91/2.10 % SZS status Theorem % 1.91/2.10 (* BEGIN-PROOF *) % 1.91/2.10 % SZS output start Proof % 1.91/2.10 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)))))))))))). % 1.91/2.10 Proof. % 1.91/2.10 apply NNPP. intro zenon_G. % 1.91/2.10 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_H2139; idtac ]. % 1.91/2.10 elim zenon_H2139. zenon_intro zenon_TA_27a_mpe. zenon_intro zenon_H213b. % 1.91/2.10 apply (zenon_notimply_s _ _ zenon_H213b). zenon_intro zenon_H213d. zenon_intro zenon_H213c. % 1.91/2.10 apply (zenon_notallex_s (fun A_27b : zenon_U => ((ne A_27b)->(forall V0s : zenon_U, ((mem V0s (arr zenon_TA_27a_mpe (bool)))->(forall V1t : zenon_U, ((mem V1t (arr A_27b (bool)))->((~(p (ap (ap (c_2Ecardinal_2Ecardleq zenon_TA_27a_mpe A_27b) V0s) V1t)))<->(~(p (ap (ap (c_2Ecardinal_2Ecardleq zenon_TA_27a_mpe A_27b) V0s) V1t)))))))))) zenon_H213c); [ zenon_intro zenon_H213e; idtac ]. % 1.91/2.10 elim zenon_H213e. zenon_intro zenon_TA_27b_mpj. zenon_intro zenon_H2140. % 1.91/2.10 apply (zenon_notimply_s _ _ zenon_H2140). zenon_intro zenon_H2142. zenon_intro zenon_H2141. % 1.91/2.10 apply (zenon_notallex_s (fun V0s : zenon_U => ((mem V0s (arr zenon_TA_27a_mpe (bool)))->(forall V1t : zenon_U, ((mem V1t (arr zenon_TA_27b_mpj (bool)))->((~(p (ap (ap (c_2Ecardinal_2Ecardleq zenon_TA_27a_mpe zenon_TA_27b_mpj) V0s) V1t)))<->(~(p (ap (ap (c_2Ecardinal_2Ecardleq zenon_TA_27a_mpe zenon_TA_27b_mpj) V0s) V1t)))))))) zenon_H2141); [ zenon_intro zenon_H2143; idtac ]. % 1.91/2.10 elim zenon_H2143. zenon_intro zenon_TV0s_mpo. zenon_intro zenon_H2145. % 1.91/2.10 apply (zenon_notimply_s _ _ zenon_H2145). zenon_intro zenon_H2147. zenon_intro zenon_H2146. % 1.91/2.10 apply (zenon_notallex_s (fun V1t : zenon_U => ((mem V1t (arr zenon_TA_27b_mpj (bool)))->((~(p (ap (ap (c_2Ecardinal_2Ecardleq zenon_TA_27a_mpe zenon_TA_27b_mpj) zenon_TV0s_mpo) V1t)))<->(~(p (ap (ap (c_2Ecardinal_2Ecardleq zenon_TA_27a_mpe zenon_TA_27b_mpj) zenon_TV0s_mpo) V1t)))))) zenon_H2146); [ zenon_intro zenon_H2148; idtac ]. % 1.91/2.10 elim zenon_H2148. zenon_intro zenon_TV1t_mpt. zenon_intro zenon_H214a. % 1.91/2.10 apply (zenon_notimply_s _ _ zenon_H214a). zenon_intro zenon_H214c. zenon_intro zenon_H214b. % 1.91/2.10 apply (zenon_notequiv_s _ _ zenon_H214b); [ zenon_intro zenon_H214d; zenon_intro zenon_H214e | zenon_intro zenon_H214e; zenon_intro zenon_H214d ]. % 1.91/2.10 exact (zenon_H214d zenon_H214e). % 1.91/2.10 exact (zenon_H214d zenon_H214e). % 1.91/2.10 Qed. % 1.91/2.10 % SZS output end Proof % 1.91/2.10 (* END-PROOF *) % 1.91/2.10 nodes searched: 145 % 1.91/2.10 max branch formulas: 8768 % 1.91/2.10 proof nodes created: 12 % 1.91/2.10 formulas created: 408056 % 1.91/2.10 %------------------------------------------------------------------------------