%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : COM125+1 : TPTP v8.1.0. Released v6.4.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n010.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 : Fri Jul 15 01:53:20 EDT 2022 % Result : Theorem 0.18s 0.56s % Output : Proof 0.18s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.10/0.12 % Problem : COM125+1 : TPTP v8.1.0. Released v6.4.0. % 0.10/0.12 % Command : run_zenon %s %d % 0.12/0.33 % Computer : n010.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 600 % 0.12/0.33 % DateTime : Thu Jun 16 18:08:38 EDT 2022 % 0.12/0.33 % CPUTime : % 0.18/0.56 (* PROOF-FOUND *) % 0.18/0.56 % SZS status Theorem % 0.18/0.56 (* BEGIN-PROOF *) % 0.18/0.56 % SZS output start Proof % 0.18/0.56 Theorem T-Weak-FreeVar-abs : (forall Vx : zenon_U, (forall VS : zenon_U, (forall VC : zenon_U, (forall Vy : zenon_U, (forall VS1 : zenon_U, (forall VT : zenon_U, (((~(visFreeVar Vx (vabs Vy VS1 (veabs))))/\(vtcheck VC (vabs Vy VS1 (veabs)) VT))->(vtcheck (vbind Vx VS VC) (vabs Vy VS1 (veabs)) VT)))))))). % 0.18/0.56 Proof. % 0.18/0.56 apply NNPP. intro zenon_G. % 0.18/0.56 apply (zenon_notallex_s (fun Vx : zenon_U => (forall VS : zenon_U, (forall VC : zenon_U, (forall Vy : zenon_U, (forall VS1 : zenon_U, (forall VT : zenon_U, (((~(visFreeVar Vx (vabs Vy VS1 (veabs))))/\(vtcheck VC (vabs Vy VS1 (veabs)) VT))->(vtcheck (vbind Vx VS VC) (vabs Vy VS1 (veabs)) VT)))))))) zenon_G); [ zenon_intro zenon_H3c; idtac ]. % 0.18/0.56 elim zenon_H3c. zenon_intro zenon_TVx_cj. zenon_intro zenon_H3e. % 0.18/0.56 apply (zenon_notallex_s (fun VS : zenon_U => (forall VC : zenon_U, (forall Vy : zenon_U, (forall VS1 : zenon_U, (forall VT : zenon_U, (((~(visFreeVar zenon_TVx_cj (vabs Vy VS1 (veabs))))/\(vtcheck VC (vabs Vy VS1 (veabs)) VT))->(vtcheck (vbind zenon_TVx_cj VS VC) (vabs Vy VS1 (veabs)) VT))))))) zenon_H3e); [ zenon_intro zenon_H3f; idtac ]. % 0.18/0.56 elim zenon_H3f. zenon_intro zenon_TVS_cm. zenon_intro zenon_H41. % 0.18/0.56 apply (zenon_notallex_s (fun VC : zenon_U => (forall Vy : zenon_U, (forall VS1 : zenon_U, (forall VT : zenon_U, (((~(visFreeVar zenon_TVx_cj (vabs Vy VS1 (veabs))))/\(vtcheck VC (vabs Vy VS1 (veabs)) VT))->(vtcheck (vbind zenon_TVx_cj zenon_TVS_cm VC) (vabs Vy VS1 (veabs)) VT)))))) zenon_H41); [ zenon_intro zenon_H42; idtac ]. % 0.18/0.56 elim zenon_H42. zenon_intro zenon_TVC_cp. zenon_intro zenon_H44. % 0.18/0.56 apply (zenon_notallex_s (fun Vy : zenon_U => (forall VS1 : zenon_U, (forall VT : zenon_U, (((~(visFreeVar zenon_TVx_cj (vabs Vy VS1 (veabs))))/\(vtcheck zenon_TVC_cp (vabs Vy VS1 (veabs)) VT))->(vtcheck (vbind zenon_TVx_cj zenon_TVS_cm zenon_TVC_cp) (vabs Vy VS1 (veabs)) VT))))) zenon_H44); [ zenon_intro zenon_H45; idtac ]. % 0.18/0.56 elim zenon_H45. zenon_intro zenon_TVy_cs. zenon_intro zenon_H47. % 0.18/0.56 apply (zenon_notallex_s (fun VS1 : zenon_U => (forall VT : zenon_U, (((~(visFreeVar zenon_TVx_cj (vabs zenon_TVy_cs VS1 (veabs))))/\(vtcheck zenon_TVC_cp (vabs zenon_TVy_cs VS1 (veabs)) VT))->(vtcheck (vbind zenon_TVx_cj zenon_TVS_cm zenon_TVC_cp) (vabs zenon_TVy_cs VS1 (veabs)) VT)))) zenon_H47); [ zenon_intro zenon_H48; idtac ]. % 0.18/0.56 elim zenon_H48. zenon_intro zenon_TVS1_cv. zenon_intro zenon_H4a. % 0.18/0.56 apply (zenon_notallex_s (fun VT : zenon_U => (((~(visFreeVar zenon_TVx_cj (vabs zenon_TVy_cs zenon_TVS1_cv (veabs))))/\(vtcheck zenon_TVC_cp (vabs zenon_TVy_cs zenon_TVS1_cv (veabs)) VT))->(vtcheck (vbind zenon_TVx_cj zenon_TVS_cm zenon_TVC_cp) (vabs zenon_TVy_cs zenon_TVS1_cv (veabs)) VT))) zenon_H4a); [ zenon_intro zenon_H4b; idtac ]. % 0.18/0.56 elim zenon_H4b. zenon_intro zenon_TVT_cy. zenon_intro zenon_H4d. % 0.18/0.56 apply (zenon_notimply_s _ _ zenon_H4d). zenon_intro zenon_H4f. zenon_intro zenon_H4e. % 0.18/0.56 apply (zenon_and_s _ _ zenon_H4f). zenon_intro zenon_H51. zenon_intro zenon_H50. % 0.18/0.56 generalize (T-Weak-FreeVar-abs-2 zenon_TVx_cj). zenon_intro zenon_H52. % 0.18/0.56 generalize (T-Weak-FreeVar-abs-1 zenon_TVx_cj). zenon_intro zenon_H53. % 0.18/0.56 generalize (zenon_H52 zenon_TVS_cm). zenon_intro zenon_H54. % 0.18/0.56 generalize (zenon_H54 zenon_TVC_cp). zenon_intro zenon_H55. % 0.18/0.56 generalize (zenon_H53 zenon_TVS_cm). zenon_intro zenon_H56. % 0.18/0.56 generalize (zenon_H55 zenon_TVy_cs). zenon_intro zenon_H57. % 0.18/0.56 generalize (zenon_H56 zenon_TVC_cp). zenon_intro zenon_H58. % 0.18/0.56 generalize (zenon_H57 zenon_TVS1_cv). zenon_intro zenon_H59. % 0.18/0.56 generalize (zenon_H58 zenon_TVy_cs). zenon_intro zenon_H5a. % 0.18/0.56 generalize (zenon_H59 zenon_TVT_cy). zenon_intro zenon_H5b. % 0.18/0.56 apply (zenon_imply_s _ _ zenon_H5b); [ zenon_intro zenon_H5d | zenon_intro zenon_H5c ]. % 0.18/0.56 apply (zenon_notand_s _ _ zenon_H5d); [ zenon_intro zenon_H5f | zenon_intro zenon_H5e ]. % 0.18/0.56 generalize (zenon_H5a zenon_TVS1_cv). zenon_intro zenon_H60. % 0.18/0.56 generalize (zenon_H60 zenon_TVT_cy). zenon_intro zenon_H61. % 0.18/0.56 apply (zenon_imply_s _ _ zenon_H61); [ zenon_intro zenon_H62 | zenon_intro zenon_H5c ]. % 0.18/0.56 apply (zenon_notand_s _ _ zenon_H62); [ zenon_intro zenon_H63 | zenon_intro zenon_H5e ]. % 0.18/0.56 exact (zenon_H63 zenon_H5f). % 0.18/0.56 apply (zenon_notand_s _ _ zenon_H5e); [ zenon_intro zenon_H65 | zenon_intro zenon_H64 ]. % 0.18/0.56 exact (zenon_H65 zenon_H51). % 0.18/0.56 exact (zenon_H64 zenon_H50). % 0.18/0.56 exact (zenon_H4e zenon_H5c). % 0.18/0.56 apply (zenon_notand_s _ _ zenon_H5e); [ zenon_intro zenon_H65 | zenon_intro zenon_H64 ]. % 0.18/0.56 exact (zenon_H65 zenon_H51). % 0.18/0.56 exact (zenon_H64 zenon_H50). % 0.18/0.56 exact (zenon_H4e zenon_H5c). % 0.18/0.56 Qed. % 0.18/0.56 % SZS output end Proof % 0.18/0.56 (* END-PROOF *) % 0.18/0.56 nodes searched: 1497 % 0.18/0.56 max branch formulas: 1093 % 0.18/0.56 proof nodes created: 135 % 0.18/0.56 formulas created: 15535 % 0.18/0.56 %------------------------------------------------------------------------------