%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : COM133+1 : TPTP v8.1.0. Released v6.4.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n016.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 01:53:22 EDT 2022 % Result : Theorem 2.35s 2.57s % Output : Proof 2.35s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : COM133+1 : TPTP v8.1.0. Released v6.4.0. % 0.13/0.12 % Command : run_zenon %s %d % 0.13/0.34 % Computer : n016.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 : Thu Jun 16 19:32:04 EDT 2022 % 0.13/0.34 % CPUTime : % 2.35/2.57 (* PROOF-FOUND *) % 2.35/2.57 % SZS status Theorem % 2.35/2.57 (* BEGIN-PROOF *) % 2.35/2.57 % SZS output start Proof % 2.35/2.57 Theorem T-subst-abs : (forall VT : zenon_U, (forall VC : zenon_U, (forall Vx : zenon_U, (forall Ve : zenon_U, (forall Vy : zenon_U, (forall VS : zenon_U, (forall VT2 : zenon_U, (((vtcheck VC Ve VT)/\(vtcheck (vbind Vx VT VC) (vabs Vy VS (veabs)) VT2))->(vtcheck VC (vsubst Vx Ve (vabs Vy VS (veabs))) VT2))))))))). % 2.35/2.57 Proof. % 2.35/2.57 assert (zenon_L1_ : forall (zenon_TVT2_cp : zenon_U) (zenon_TVS_cq : zenon_U) (zenon_TVe_cr : zenon_U) (zenon_TVC_cs : zenon_U) (zenon_TVy_ct : zenon_U) (zenon_TVx_cu : zenon_U) (zenon_TVT_cv : zenon_U), (forall VC : zenon_U, (forall Vx : zenon_U, (forall Ve : zenon_U, (forall Vy : zenon_U, (forall VS : zenon_U, (forall Ve1 : zenon_U, (forall VT2 : zenon_U, (((Vx = Vy)/\((vtcheck VC Ve zenon_TVT_cv)/\(vtcheck (vbind Vx zenon_TVT_cv VC) (vabs Vy VS Ve1) VT2)))->(vtcheck VC (vsubst Vx Ve (vabs Vy VS Ve1)) VT2))))))))) -> (zenon_TVx_cu = zenon_TVy_ct) -> (vtcheck zenon_TVC_cs zenon_TVe_cr zenon_TVT_cv) -> (vtcheck (vbind zenon_TVx_cu zenon_TVT_cv zenon_TVC_cs) (vabs zenon_TVy_ct zenon_TVS_cq (veabs)) zenon_TVT2_cp) -> (~(vtcheck zenon_TVC_cs (vsubst zenon_TVx_cu zenon_TVe_cr (vabs zenon_TVy_ct zenon_TVS_cq (veabs))) zenon_TVT2_cp)) -> False). % 2.35/2.57 do 7 intro. intros zenon_H3e zenon_H3f zenon_H40 zenon_H41 zenon_H42. % 2.35/2.57 generalize (zenon_H3e zenon_TVC_cs). zenon_intro zenon_H4a. % 2.35/2.57 generalize (zenon_H4a zenon_TVx_cu). zenon_intro zenon_H4b. % 2.35/2.57 generalize (zenon_H4b zenon_TVe_cr). zenon_intro zenon_H4c. % 2.35/2.57 generalize (zenon_H4c zenon_TVy_ct). zenon_intro zenon_H4d. % 2.35/2.57 generalize (zenon_H4d zenon_TVS_cq). zenon_intro zenon_H4e. % 2.35/2.57 generalize (zenon_H4e (veabs)). zenon_intro zenon_H4f. % 2.35/2.57 generalize (zenon_H4f zenon_TVT2_cp). zenon_intro zenon_H50. % 2.35/2.57 apply (zenon_imply_s _ _ zenon_H50); [ zenon_intro zenon_H52 | zenon_intro zenon_H51 ]. % 2.35/2.57 apply (zenon_notand_s _ _ zenon_H52); [ zenon_intro zenon_H54 | zenon_intro zenon_H53 ]. % 2.35/2.57 exact (zenon_H54 zenon_H3f). % 2.35/2.57 apply (zenon_notand_s _ _ zenon_H53); [ zenon_intro zenon_H56 | zenon_intro zenon_H55 ]. % 2.35/2.57 exact (zenon_H56 zenon_H40). % 2.35/2.57 exact (zenon_H55 zenon_H41). % 2.35/2.57 exact (zenon_H42 zenon_H51). % 2.35/2.57 (* end of lemma zenon_L1_ *) % 2.35/2.57 assert (zenon_L2_ : forall (zenon_TVT_cv : zenon_U) (zenon_TVT2_cp : zenon_U) (zenon_TVS_cq : zenon_U) (zenon_TVy_ct : zenon_U) (zenon_TVe_cr : zenon_U) (zenon_TVx_cu : zenon_U) (zenon_TVC_cs : zenon_U), (~(vtcheck zenon_TVC_cs (vsubst zenon_TVx_cu zenon_TVe_cr (vabs zenon_TVy_ct zenon_TVS_cq (veabs))) zenon_TVT2_cp)) -> (vtcheck (vbind zenon_TVx_cu zenon_TVT_cv zenon_TVC_cs) (vabs zenon_TVy_ct zenon_TVS_cq (veabs)) zenon_TVT2_cp) -> (vtcheck zenon_TVC_cs zenon_TVe_cr zenon_TVT_cv) -> (zenon_TVx_cu = zenon_TVy_ct) -> False). % 2.35/2.57 do 7 intro. intros zenon_H42 zenon_H41 zenon_H40 zenon_H3f. % 2.35/2.57 generalize (T-subst-abs-1 zenon_TVT_cv). zenon_intro zenon_H3e. % 2.35/2.57 apply (zenon_L1_ zenon_TVT2_cp zenon_TVS_cq zenon_TVe_cr zenon_TVC_cs zenon_TVy_ct zenon_TVx_cu zenon_TVT_cv); trivial. % 2.35/2.57 (* end of lemma zenon_L2_ *) % 2.35/2.57 assert (zenon_L3_ : forall (zenon_TVT2_cp : zenon_U) (zenon_TVS_cq : zenon_U) (zenon_TVe_cr : zenon_U) (zenon_TVy_ct : zenon_U) (zenon_TVT_cv : zenon_U) (zenon_TVC_cs : zenon_U) (zenon_TVx_cu : zenon_U), (forall Ve : zenon_U, (forall Vy : zenon_U, (forall VS : zenon_U, (forall VT2 : zenon_U, (((~(zenon_TVx_cu = Vy))/\((~(visFreeVar Vy Ve))/\((vtcheck zenon_TVC_cs Ve zenon_TVT_cv)/\(vtcheck (vbind zenon_TVx_cu zenon_TVT_cv zenon_TVC_cs) (vabs Vy VS (veabs)) VT2))))->(vtcheck zenon_TVC_cs (vsubst zenon_TVx_cu Ve (vabs Vy VS (veabs))) VT2)))))) -> (~(visFreeVar zenon_TVy_ct zenon_TVe_cr)) -> (vtcheck zenon_TVC_cs zenon_TVe_cr zenon_TVT_cv) -> (vtcheck (vbind zenon_TVx_cu zenon_TVT_cv zenon_TVC_cs) (vabs zenon_TVy_ct zenon_TVS_cq (veabs)) zenon_TVT2_cp) -> (~(vtcheck zenon_TVC_cs (vsubst zenon_TVx_cu zenon_TVe_cr (vabs zenon_TVy_ct zenon_TVS_cq (veabs))) zenon_TVT2_cp)) -> False). % 2.35/2.57 do 7 intro. intros zenon_H57 zenon_H58 zenon_H40 zenon_H41 zenon_H42. % 2.35/2.57 generalize (zenon_H57 zenon_TVe_cr). zenon_intro zenon_H59. % 2.35/2.57 generalize (zenon_H59 zenon_TVy_ct). zenon_intro zenon_H5a. % 2.35/2.57 generalize (zenon_H5a zenon_TVS_cq). zenon_intro zenon_H5b. % 2.35/2.57 generalize (zenon_H5b zenon_TVT2_cp). zenon_intro zenon_H5c. % 2.35/2.57 apply (zenon_imply_s _ _ zenon_H5c); [ zenon_intro zenon_H5d | zenon_intro zenon_H51 ]. % 2.35/2.57 apply (zenon_notand_s _ _ zenon_H5d); [ zenon_intro zenon_H5f | zenon_intro zenon_H5e ]. % 2.35/2.57 apply zenon_H5f. zenon_intro zenon_H3f. % 2.35/2.57 apply (zenon_L2_ zenon_TVT_cv zenon_TVT2_cp zenon_TVS_cq zenon_TVy_ct zenon_TVe_cr zenon_TVx_cu zenon_TVC_cs); trivial. % 2.35/2.57 apply (zenon_notand_s _ _ zenon_H5e); [ zenon_intro zenon_H60 | zenon_intro zenon_H53 ]. % 2.35/2.57 exact (zenon_H60 zenon_H58). % 2.35/2.57 apply (zenon_notand_s _ _ zenon_H53); [ zenon_intro zenon_H56 | zenon_intro zenon_H55 ]. % 2.35/2.57 exact (zenon_H56 zenon_H40). % 2.35/2.57 exact (zenon_H55 zenon_H41). % 2.35/2.57 exact (zenon_H42 zenon_H51). % 2.35/2.57 (* end of lemma zenon_L3_ *) % 2.35/2.57 apply NNPP. intro zenon_G. % 2.35/2.57 apply (zenon_notallex_s (fun VT : zenon_U => (forall VC : zenon_U, (forall Vx : zenon_U, (forall Ve : zenon_U, (forall Vy : zenon_U, (forall VS : zenon_U, (forall VT2 : zenon_U, (((vtcheck VC Ve VT)/\(vtcheck (vbind Vx VT VC) (vabs Vy VS (veabs)) VT2))->(vtcheck VC (vsubst Vx Ve (vabs Vy VS (veabs))) VT2))))))))) zenon_G); [ zenon_intro zenon_H61; idtac ]. % 2.35/2.57 elim zenon_H61. zenon_intro zenon_TVT_cv. zenon_intro zenon_H62. % 2.35/2.57 apply (zenon_notallex_s (fun VC : zenon_U => (forall Vx : zenon_U, (forall Ve : zenon_U, (forall Vy : zenon_U, (forall VS : zenon_U, (forall VT2 : zenon_U, (((vtcheck VC Ve zenon_TVT_cv)/\(vtcheck (vbind Vx zenon_TVT_cv VC) (vabs Vy VS (veabs)) VT2))->(vtcheck VC (vsubst Vx Ve (vabs Vy VS (veabs))) VT2)))))))) zenon_H62); [ zenon_intro zenon_H63; idtac ]. % 2.35/2.57 elim zenon_H63. zenon_intro zenon_TVC_cs. zenon_intro zenon_H64. % 2.35/2.57 apply (zenon_notallex_s (fun Vx : zenon_U => (forall Ve : zenon_U, (forall Vy : zenon_U, (forall VS : zenon_U, (forall VT2 : zenon_U, (((vtcheck zenon_TVC_cs Ve zenon_TVT_cv)/\(vtcheck (vbind Vx zenon_TVT_cv zenon_TVC_cs) (vabs Vy VS (veabs)) VT2))->(vtcheck zenon_TVC_cs (vsubst Vx Ve (vabs Vy VS (veabs))) VT2))))))) zenon_H64); [ zenon_intro zenon_H65; idtac ]. % 2.35/2.57 elim zenon_H65. zenon_intro zenon_TVx_cu. zenon_intro zenon_H66. % 2.35/2.57 apply (zenon_notallex_s (fun Ve : zenon_U => (forall Vy : zenon_U, (forall VS : zenon_U, (forall VT2 : zenon_U, (((vtcheck zenon_TVC_cs Ve zenon_TVT_cv)/\(vtcheck (vbind zenon_TVx_cu zenon_TVT_cv zenon_TVC_cs) (vabs Vy VS (veabs)) VT2))->(vtcheck zenon_TVC_cs (vsubst zenon_TVx_cu Ve (vabs Vy VS (veabs))) VT2)))))) zenon_H66); [ zenon_intro zenon_H67; idtac ]. % 2.35/2.57 elim zenon_H67. zenon_intro zenon_TVe_cr. zenon_intro zenon_H68. % 2.35/2.57 apply (zenon_notallex_s (fun Vy : zenon_U => (forall VS : zenon_U, (forall VT2 : zenon_U, (((vtcheck zenon_TVC_cs zenon_TVe_cr zenon_TVT_cv)/\(vtcheck (vbind zenon_TVx_cu zenon_TVT_cv zenon_TVC_cs) (vabs Vy VS (veabs)) VT2))->(vtcheck zenon_TVC_cs (vsubst zenon_TVx_cu zenon_TVe_cr (vabs Vy VS (veabs))) VT2))))) zenon_H68); [ zenon_intro zenon_H69; idtac ]. % 2.35/2.57 elim zenon_H69. zenon_intro zenon_TVy_ct. zenon_intro zenon_H6a. % 2.35/2.57 apply (zenon_notallex_s (fun VS : zenon_U => (forall VT2 : zenon_U, (((vtcheck zenon_TVC_cs zenon_TVe_cr zenon_TVT_cv)/\(vtcheck (vbind zenon_TVx_cu zenon_TVT_cv zenon_TVC_cs) (vabs zenon_TVy_ct VS (veabs)) VT2))->(vtcheck zenon_TVC_cs (vsubst zenon_TVx_cu zenon_TVe_cr (vabs zenon_TVy_ct VS (veabs))) VT2)))) zenon_H6a); [ zenon_intro zenon_H6b; idtac ]. % 2.35/2.57 elim zenon_H6b. zenon_intro zenon_TVS_cq. zenon_intro zenon_H6c. % 2.35/2.57 apply (zenon_notallex_s (fun VT2 : zenon_U => (((vtcheck zenon_TVC_cs zenon_TVe_cr zenon_TVT_cv)/\(vtcheck (vbind zenon_TVx_cu zenon_TVT_cv zenon_TVC_cs) (vabs zenon_TVy_ct zenon_TVS_cq (veabs)) VT2))->(vtcheck zenon_TVC_cs (vsubst zenon_TVx_cu zenon_TVe_cr (vabs zenon_TVy_ct zenon_TVS_cq (veabs))) VT2))) zenon_H6c); [ zenon_intro zenon_H6d; idtac ]. % 2.35/2.57 elim zenon_H6d. zenon_intro zenon_TVT2_cp. zenon_intro zenon_H6e. % 2.35/2.57 apply (zenon_notimply_s _ _ zenon_H6e). zenon_intro zenon_H6f. zenon_intro zenon_H42. % 2.35/2.57 apply (zenon_and_s _ _ zenon_H6f). zenon_intro zenon_H40. zenon_intro zenon_H41. % 2.35/2.57 generalize (T-subst-abs-3 zenon_TVT_cv). zenon_intro zenon_H70. % 2.35/2.57 generalize (T-subst-abs-2 zenon_TVT_cv). zenon_intro zenon_H71. % 2.35/2.57 generalize (zenon_H70 zenon_TVC_cs). zenon_intro zenon_H72. % 2.35/2.57 generalize (zenon_H72 zenon_TVx_cu). zenon_intro zenon_H73. % 2.35/2.57 generalize (zenon_H71 zenon_TVC_cs). zenon_intro zenon_H74. % 2.35/2.57 generalize (zenon_H73 zenon_TVe_cr). zenon_intro zenon_H75. % 2.35/2.57 generalize (zenon_H75 zenon_TVy_ct). zenon_intro zenon_H76. % 2.35/2.57 generalize (zenon_H74 zenon_TVx_cu). zenon_intro zenon_H57. % 2.35/2.57 generalize (zenon_H76 zenon_TVS_cq). zenon_intro zenon_H77. % 2.35/2.57 generalize (zenon_H77 zenon_TVT2_cp). zenon_intro zenon_H78. % 2.35/2.57 apply (zenon_imply_s _ _ zenon_H78); [ zenon_intro zenon_H79 | zenon_intro zenon_H51 ]. % 2.35/2.57 apply (zenon_notand_s _ _ zenon_H79); [ zenon_intro zenon_H5f | zenon_intro zenon_H7a ]. % 2.35/2.57 apply zenon_H5f. zenon_intro zenon_H3f. % 2.35/2.57 apply (zenon_L2_ zenon_TVT_cv zenon_TVT2_cp zenon_TVS_cq zenon_TVy_ct zenon_TVe_cr zenon_TVx_cu zenon_TVC_cs); trivial. % 2.35/2.57 apply (zenon_notand_s _ _ zenon_H7a); [ zenon_intro zenon_H58 | zenon_intro zenon_H53 ]. % 2.35/2.57 apply (zenon_L3_ zenon_TVT2_cp zenon_TVS_cq zenon_TVe_cr zenon_TVy_ct zenon_TVT_cv zenon_TVC_cs zenon_TVx_cu); trivial. % 2.35/2.57 apply (zenon_notand_s _ _ zenon_H53); [ zenon_intro zenon_H56 | zenon_intro zenon_H55 ]. % 2.35/2.57 exact (zenon_H56 zenon_H40). % 2.35/2.57 exact (zenon_H55 zenon_H41). % 2.35/2.57 exact (zenon_H42 zenon_H51). % 2.35/2.57 Qed. % 2.35/2.57 % SZS output end Proof % 2.35/2.57 (* END-PROOF *) % 2.35/2.57 nodes searched: 48757 % 2.35/2.57 max branch formulas: 4219 % 2.35/2.57 proof nodes created: 2830 % 2.35/2.57 formulas created: 203691 % 2.35/2.57 %------------------------------------------------------------------------------