%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : SWV376+1 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n025.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 : Wed Jul 20 23:04:08 EDT 2022 % Result : Theorem 0.20s 0.55s % Output : Proof 0.20s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.13 % Problem : SWV376+1 : TPTP v8.1.0. Released v3.3.0. % 0.08/0.13 % Command : run_zenon %s %d % 0.14/0.35 % Computer : n025.cluster.edu % 0.14/0.35 % Model : x86_64 x86_64 % 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.35 % Memory : 8042.1875MB % 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.35 % CPULimit : 300 % 0.14/0.35 % WCLimit : 600 % 0.14/0.35 % DateTime : Wed Jun 15 20:51:11 EDT 2022 % 0.14/0.35 % CPUTime : % 0.20/0.55 Zenon warning: unused variable (X : zenon_U) in ax47 % 0.20/0.55 Zenon warning: unused variable (X : zenon_U) in ax48 % 0.20/0.55 Zenon warning: unused variable (X : zenon_U) in ax49 % 0.20/0.55 Zenon warning: unused variable (X : zenon_U) in ax51 % 0.20/0.55 (* PROOF-FOUND *) % 0.20/0.55 % SZS status Theorem % 0.20/0.55 (* BEGIN-PROOF *) % 0.20/0.55 % SZS output start Proof % 0.20/0.55 Theorem l12_co : (forall X1 : zenon_U, (forall X2 : zenon_U, (forall X3 : zenon_U, ((~(ok (triple X1 X2 X3)))->(forall X4 : zenon_U, (forall X5 : zenon_U, (forall X6 : zenon_U, ((succ_cpq (triple X1 X2 X3) (triple X4 X5 X6))->(~(ok (triple X4 X5 X6))))))))))). % 0.20/0.55 Proof. % 0.20/0.55 apply NNPP. intro zenon_G. % 0.20/0.55 apply (zenon_imply_s _ _ l12_induction); [ zenon_intro zenon_H2d | zenon_intro zenon_H2c ]. % 0.20/0.55 apply (zenon_notallex_s (fun U : zenon_U => (forall V : zenon_U, (forall W : zenon_U, (forall X : zenon_U, (forall Y : zenon_U, (forall Z : zenon_U, ((succ_cpq (triple U V W) (triple X Y Z))->((~(ok (triple X Y Z)))->(~(ok (im_succ_cpq (triple X Y Z)))))))))))) zenon_H2d); [ zenon_intro zenon_H2e; idtac ]. % 0.20/0.55 elim zenon_H2e. zenon_intro zenon_TU_bv. zenon_intro zenon_H30. % 0.20/0.55 apply (zenon_notallex_s (fun V : zenon_U => (forall W : zenon_U, (forall X : zenon_U, (forall Y : zenon_U, (forall Z : zenon_U, ((succ_cpq (triple zenon_TU_bv V W) (triple X Y Z))->((~(ok (triple X Y Z)))->(~(ok (im_succ_cpq (triple X Y Z))))))))))) zenon_H30); [ zenon_intro zenon_H31; idtac ]. % 0.20/0.55 elim zenon_H31. zenon_intro zenon_TV_by. zenon_intro zenon_H33. % 0.20/0.55 apply (zenon_notallex_s (fun W : zenon_U => (forall X : zenon_U, (forall Y : zenon_U, (forall Z : zenon_U, ((succ_cpq (triple zenon_TU_bv zenon_TV_by W) (triple X Y Z))->((~(ok (triple X Y Z)))->(~(ok (im_succ_cpq (triple X Y Z)))))))))) zenon_H33); [ zenon_intro zenon_H34; idtac ]. % 0.20/0.55 elim zenon_H34. zenon_intro zenon_TW_cb. zenon_intro zenon_H36. % 0.20/0.55 apply (zenon_notallex_s (fun X : zenon_U => (forall Y : zenon_U, (forall Z : zenon_U, ((succ_cpq (triple zenon_TU_bv zenon_TV_by zenon_TW_cb) (triple X Y Z))->((~(ok (triple X Y Z)))->(~(ok (im_succ_cpq (triple X Y Z))))))))) zenon_H36); [ zenon_intro zenon_H37; idtac ]. % 0.20/0.55 elim zenon_H37. zenon_intro zenon_TX_ce. zenon_intro zenon_H39. % 0.20/0.55 apply (zenon_notallex_s (fun Y : zenon_U => (forall Z : zenon_U, ((succ_cpq (triple zenon_TU_bv zenon_TV_by zenon_TW_cb) (triple zenon_TX_ce Y Z))->((~(ok (triple zenon_TX_ce Y Z)))->(~(ok (im_succ_cpq (triple zenon_TX_ce Y Z)))))))) zenon_H39); [ zenon_intro zenon_H3a; idtac ]. % 0.20/0.55 elim zenon_H3a. zenon_intro zenon_TY_ch. zenon_intro zenon_H3c. % 0.20/0.55 apply (zenon_notallex_s (fun Z : zenon_U => ((succ_cpq (triple zenon_TU_bv zenon_TV_by zenon_TW_cb) (triple zenon_TX_ce zenon_TY_ch Z))->((~(ok (triple zenon_TX_ce zenon_TY_ch Z)))->(~(ok (im_succ_cpq (triple zenon_TX_ce zenon_TY_ch Z))))))) zenon_H3c); [ zenon_intro zenon_H3d; idtac ]. % 0.20/0.55 elim zenon_H3d. zenon_intro zenon_TZ_ck. zenon_intro zenon_H3f. % 0.20/0.55 apply (zenon_notimply_s _ _ zenon_H3f). zenon_intro zenon_H41. zenon_intro zenon_H40. % 0.20/0.55 apply (zenon_notimply_s _ _ zenon_H40). zenon_intro zenon_H43. zenon_intro zenon_H42. % 0.20/0.55 apply zenon_H42. zenon_intro zenon_H44. % 0.20/0.55 generalize (l12_l13 zenon_TX_ce). zenon_intro zenon_H45. % 0.20/0.55 generalize (zenon_H45 zenon_TY_ch). zenon_intro zenon_H46. % 0.20/0.55 generalize (zenon_H46 zenon_TZ_ck). zenon_intro zenon_H47. % 0.20/0.55 apply (zenon_imply_s _ _ zenon_H47); [ zenon_intro zenon_H49 | zenon_intro zenon_H48 ]. % 0.20/0.55 exact (zenon_H49 zenon_H43). % 0.20/0.55 exact (zenon_H48 zenon_H44). % 0.20/0.55 exact (zenon_G zenon_H2c). % 0.20/0.55 Qed. % 0.20/0.55 % SZS output end Proof % 0.20/0.55 (* END-PROOF *) % 0.20/0.55 nodes searched: 413 % 0.20/0.55 max branch formulas: 364 % 0.20/0.55 proof nodes created: 26 % 0.20/0.55 formulas created: 4366 % 0.20/0.55 %------------------------------------------------------------------------------