TSTP Solution File: COM133+1 by Zenon---0.7.1
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%------------------------------------------------------------------------------
% 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
%------------------------------------------------------------------------------