%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : ITP010+1 : TPTP v8.1.0. Bugfixed v7.5.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n022.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 01:27:10 EDT 2022 % Result : Theorem 0.19s 0.50s % Output : Proof 0.19s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.10/0.12 % Problem : ITP010+1 : TPTP v8.1.0. Bugfixed v7.5.0. % 0.10/0.13 % Command : run_zenon %s %d % 0.13/0.34 % Computer : n022.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 600 % 0.13/0.34 % DateTime : Fri Jun 3 23:15:51 EDT 2022 % 0.13/0.34 % CPUTime : % 0.19/0.50 Zenon warning: unused variable (A_27a : zenon_U) in thm_2Ebool_2EFORALL__SIMP % 0.19/0.50 Zenon warning: unused variable (V1x_2E0 : zenon_U) in thm_2Ebool_2EFORALL__SIMP % 0.19/0.50 (* PROOF-FOUND *) % 0.19/0.50 % SZS status Theorem % 0.19/0.50 (* BEGIN-PROOF *) % 0.19/0.50 % SZS output start Proof % 0.19/0.50 Theorem thm_2Ecardinal_2ECARD__NOT__LE : (forall A_27a : zenon_U, (forall A_27b : zenon_U, (forall V0s_2E0 : zenon_U, (forall V1t_2E0 : zenon_U, ((~(p (s (tyop_2Emin_2Ebool) (c_2Ecardinal_2Ecardleq_2E2 (s (tyop_2Emin_2Efun A_27a (tyop_2Emin_2Ebool)) V0s_2E0) (s (tyop_2Emin_2Efun A_27b (tyop_2Emin_2Ebool)) V1t_2E0)))))<->(~(p (s (tyop_2Emin_2Ebool) (c_2Ecardinal_2Ecardleq_2E2 (s (tyop_2Emin_2Efun A_27a (tyop_2Emin_2Ebool)) V0s_2E0) (s (tyop_2Emin_2Efun A_27b (tyop_2Emin_2Ebool)) V1t_2E0)))))))))). % 0.19/0.50 Proof. % 0.19/0.50 apply NNPP. intro zenon_G. % 0.19/0.50 apply (zenon_notallex_s (fun A_27a : zenon_U => (forall A_27b : zenon_U, (forall V0s_2E0 : zenon_U, (forall V1t_2E0 : zenon_U, ((~(p (s (tyop_2Emin_2Ebool) (c_2Ecardinal_2Ecardleq_2E2 (s (tyop_2Emin_2Efun A_27a (tyop_2Emin_2Ebool)) V0s_2E0) (s (tyop_2Emin_2Efun A_27b (tyop_2Emin_2Ebool)) V1t_2E0)))))<->(~(p (s (tyop_2Emin_2Ebool) (c_2Ecardinal_2Ecardleq_2E2 (s (tyop_2Emin_2Efun A_27a (tyop_2Emin_2Ebool)) V0s_2E0) (s (tyop_2Emin_2Efun A_27b (tyop_2Emin_2Ebool)) V1t_2E0)))))))))) zenon_G); [ zenon_intro zenon_H27; idtac ]. % 0.19/0.50 elim zenon_H27. zenon_intro zenon_TA_27a_bo. zenon_intro zenon_H29. % 0.19/0.50 apply (zenon_notallex_s (fun A_27b : zenon_U => (forall V0s_2E0 : zenon_U, (forall V1t_2E0 : zenon_U, ((~(p (s (tyop_2Emin_2Ebool) (c_2Ecardinal_2Ecardleq_2E2 (s (tyop_2Emin_2Efun zenon_TA_27a_bo (tyop_2Emin_2Ebool)) V0s_2E0) (s (tyop_2Emin_2Efun A_27b (tyop_2Emin_2Ebool)) V1t_2E0)))))<->(~(p (s (tyop_2Emin_2Ebool) (c_2Ecardinal_2Ecardleq_2E2 (s (tyop_2Emin_2Efun zenon_TA_27a_bo (tyop_2Emin_2Ebool)) V0s_2E0) (s (tyop_2Emin_2Efun A_27b (tyop_2Emin_2Ebool)) V1t_2E0))))))))) zenon_H29); [ zenon_intro zenon_H2a; idtac ]. % 0.19/0.50 elim zenon_H2a. zenon_intro zenon_TA_27b_br. zenon_intro zenon_H2c. % 0.19/0.50 apply (zenon_notallex_s (fun V0s_2E0 : zenon_U => (forall V1t_2E0 : zenon_U, ((~(p (s (tyop_2Emin_2Ebool) (c_2Ecardinal_2Ecardleq_2E2 (s (tyop_2Emin_2Efun zenon_TA_27a_bo (tyop_2Emin_2Ebool)) V0s_2E0) (s (tyop_2Emin_2Efun zenon_TA_27b_br (tyop_2Emin_2Ebool)) V1t_2E0)))))<->(~(p (s (tyop_2Emin_2Ebool) (c_2Ecardinal_2Ecardleq_2E2 (s (tyop_2Emin_2Efun zenon_TA_27a_bo (tyop_2Emin_2Ebool)) V0s_2E0) (s (tyop_2Emin_2Efun zenon_TA_27b_br (tyop_2Emin_2Ebool)) V1t_2E0)))))))) zenon_H2c); [ zenon_intro zenon_H2d; idtac ]. % 0.19/0.50 elim zenon_H2d. zenon_intro zenon_TV0s_2E0_bu. zenon_intro zenon_H2f. % 0.19/0.50 apply (zenon_notallex_s (fun V1t_2E0 : zenon_U => ((~(p (s (tyop_2Emin_2Ebool) (c_2Ecardinal_2Ecardleq_2E2 (s (tyop_2Emin_2Efun zenon_TA_27a_bo (tyop_2Emin_2Ebool)) zenon_TV0s_2E0_bu) (s (tyop_2Emin_2Efun zenon_TA_27b_br (tyop_2Emin_2Ebool)) V1t_2E0)))))<->(~(p (s (tyop_2Emin_2Ebool) (c_2Ecardinal_2Ecardleq_2E2 (s (tyop_2Emin_2Efun zenon_TA_27a_bo (tyop_2Emin_2Ebool)) zenon_TV0s_2E0_bu) (s (tyop_2Emin_2Efun zenon_TA_27b_br (tyop_2Emin_2Ebool)) V1t_2E0))))))) zenon_H2f); [ zenon_intro zenon_H30; idtac ]. % 0.19/0.50 elim zenon_H30. zenon_intro zenon_TV1t_2E0_bx. zenon_intro zenon_H32. % 0.19/0.50 apply (zenon_notequiv_s _ _ zenon_H32); [ zenon_intro zenon_H33; zenon_intro zenon_H34 | zenon_intro zenon_H34; zenon_intro zenon_H33 ]. % 0.19/0.50 exact (zenon_H33 zenon_H34). % 0.19/0.50 exact (zenon_H33 zenon_H34). % 0.19/0.50 Qed. % 0.19/0.50 % SZS output end Proof % 0.19/0.50 (* END-PROOF *) % 0.19/0.50 nodes searched: 13 % 0.19/0.50 max branch formulas: 52 % 0.19/0.50 proof nodes created: 8 % 0.19/0.50 formulas created: 1064 % 0.19/0.50 %------------------------------------------------------------------------------