TSTP Solution File: SWV381+1 by Zenon---0.7.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : SWV381+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_zenon %s %d
% Computer : n018.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 23:04:09 EDT 2022
% Result : Theorem 0.93s 1.08s
% Output : Proof 0.93s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWV381+1 : TPTP v8.1.0. Released v3.3.0.
% 0.11/0.13 % Command : run_zenon %s %d
% 0.12/0.34 % Computer : n018.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Tue Jun 14 18:57:59 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.93/1.08 Zenon warning: unused variable (X : zenon_U) in ax47
% 0.93/1.08 Zenon warning: unused variable (X : zenon_U) in ax48
% 0.93/1.08 Zenon warning: unused variable (X : zenon_U) in ax49
% 0.93/1.08 Zenon warning: unused variable (X : zenon_U) in ax51
% 0.93/1.08 (* PROOF-FOUND *)
% 0.93/1.08 % SZS status Theorem
% 0.93/1.08 (* BEGIN-PROOF *)
% 0.93/1.08 % SZS output start Proof
% 0.93/1.08 Theorem l17_co : (forall U : zenon_U, (forall V : zenon_U, (forall W : zenon_U, ((phi (findmin_cpq_eff (triple U V W)))->(issmallestelement_pq (i (triple U V W)) (findmin_cpq_res (triple U V W))))))).
% 0.93/1.08 Proof.
% 0.93/1.08 assert (zenon_L1_ : forall (zenon_TW_cp : zenon_U) (zenon_TW_cq : zenon_U) (zenon_TV_cr : zenon_U) (zenon_TU_cs : zenon_U), (~(contains_cpq (triple zenon_TU_cs zenon_TV_cr zenon_TW_cq) zenon_TW_cp)) -> (contains_pq (i (triple zenon_TU_cs zenon_TV_cr zenon_TW_cq)) zenon_TW_cp) -> False).
% 0.93/1.08 do 4 intro. intros zenon_H41 zenon_H42.
% 0.93/1.08 generalize (l17_li56 zenon_TU_cs). zenon_intro zenon_H47.
% 0.93/1.08 generalize (zenon_H47 zenon_TV_cr). zenon_intro zenon_H48.
% 0.93/1.08 generalize (zenon_H48 zenon_TW_cq). zenon_intro zenon_H49.
% 0.93/1.08 generalize (zenon_H49 zenon_TW_cp). zenon_intro zenon_H4a.
% 0.93/1.08 apply (zenon_equiv_s _ _ zenon_H4a); [ zenon_intro zenon_H41; zenon_intro zenon_H4c | zenon_intro zenon_H4b; zenon_intro zenon_H42 ].
% 0.93/1.08 exact (zenon_H4c zenon_H42).
% 0.93/1.08 exact (zenon_H41 zenon_H4b).
% 0.93/1.08 (* end of lemma zenon_L1_ *)
% 0.93/1.08 assert (zenon_L2_ : forall (zenon_TW_cp : zenon_U) (zenon_TW_cq : zenon_U) (zenon_TV_cr : zenon_U) (zenon_TU_cs : zenon_U), (~(~(less_than (findmin_cpq_res (triple zenon_TU_cs zenon_TV_cr zenon_TW_cq)) zenon_TW_cp))) -> (~(less_than (findmin_cpq_res (triple zenon_TU_cs zenon_TV_cr zenon_TW_cq)) zenon_TW_cp)) -> False).
% 0.93/1.08 do 4 intro. intros zenon_H4d zenon_H4e.
% 0.93/1.08 exact (zenon_H4d zenon_H4e).
% 0.93/1.08 (* end of lemma zenon_L2_ *)
% 0.93/1.08 assert (zenon_L3_ : forall (zenon_TW_cq : zenon_U) (zenon_TV_cr : zenon_U) (zenon_TU_cs : zenon_U), (exists V : zenon_U, ((succ_cpq (findmin_cpq_eff (triple zenon_TU_cs zenon_TV_cr zenon_TW_cq)) V)/\((ok V)/\(check_cpq V)))) -> (~(phi (findmin_cpq_eff (triple zenon_TU_cs zenon_TV_cr zenon_TW_cq)))) -> False).
% 0.93/1.08 do 3 intro. intros zenon_H4f zenon_H50.
% 0.93/1.08 generalize (ax62 (findmin_cpq_eff (triple zenon_TU_cs zenon_TV_cr zenon_TW_cq))). zenon_intro zenon_H51.
% 0.93/1.08 apply (zenon_equiv_s _ _ zenon_H51); [ zenon_intro zenon_H50; zenon_intro zenon_H53 | zenon_intro zenon_H52; zenon_intro zenon_H4f ].
% 0.93/1.08 exact (zenon_H53 zenon_H4f).
% 0.93/1.08 exact (zenon_H50 zenon_H52).
% 0.93/1.08 (* end of lemma zenon_L3_ *)
% 0.93/1.08 apply NNPP. intro zenon_G.
% 0.93/1.08 apply (zenon_notallex_s (fun U : zenon_U => (forall V : zenon_U, (forall W : zenon_U, ((phi (findmin_cpq_eff (triple U V W)))->(issmallestelement_pq (i (triple U V W)) (findmin_cpq_res (triple U V W))))))) zenon_G); [ zenon_intro zenon_H54; idtac ].
% 0.93/1.08 elim zenon_H54. zenon_intro zenon_TU_cs. zenon_intro zenon_H55.
% 0.93/1.08 apply (zenon_notallex_s (fun V : zenon_U => (forall W : zenon_U, ((phi (findmin_cpq_eff (triple zenon_TU_cs V W)))->(issmallestelement_pq (i (triple zenon_TU_cs V W)) (findmin_cpq_res (triple zenon_TU_cs V W)))))) zenon_H55); [ zenon_intro zenon_H56; idtac ].
% 0.93/1.08 elim zenon_H56. zenon_intro zenon_TV_cr. zenon_intro zenon_H57.
% 0.93/1.08 apply (zenon_notallex_s (fun W : zenon_U => ((phi (findmin_cpq_eff (triple zenon_TU_cs zenon_TV_cr W)))->(issmallestelement_pq (i (triple zenon_TU_cs zenon_TV_cr W)) (findmin_cpq_res (triple zenon_TU_cs zenon_TV_cr W))))) zenon_H57); [ zenon_intro zenon_H58; idtac ].
% 0.93/1.08 elim zenon_H58. zenon_intro zenon_TW_cq. zenon_intro zenon_H59.
% 0.93/1.08 apply (zenon_notimply_s _ _ zenon_H59). zenon_intro zenon_H52. zenon_intro zenon_H5a.
% 0.93/1.08 generalize (ax62 (findmin_cpq_eff (triple zenon_TU_cs zenon_TV_cr zenon_TW_cq))). zenon_intro zenon_H51.
% 0.93/1.08 apply (zenon_equiv_s _ _ zenon_H51); [ zenon_intro zenon_H50; zenon_intro zenon_H53 | zenon_intro zenon_H52; zenon_intro zenon_H4f ].
% 0.93/1.08 exact (zenon_H50 zenon_H52).
% 0.93/1.08 generalize (ax10 (i (triple zenon_TU_cs zenon_TV_cr zenon_TW_cq))). zenon_intro zenon_H5b.
% 0.93/1.08 generalize (zenon_H5b (findmin_cpq_res (triple zenon_TU_cs zenon_TV_cr zenon_TW_cq))). zenon_intro zenon_H5c.
% 0.93/1.08 apply (zenon_equiv_s _ _ zenon_H5c); [ zenon_intro zenon_H5a; zenon_intro zenon_H5f | zenon_intro zenon_H5e; zenon_intro zenon_H5d ].
% 0.93/1.08 apply (zenon_notallex_s (fun W : zenon_U => ((contains_pq (i (triple zenon_TU_cs zenon_TV_cr zenon_TW_cq)) W)->(less_than (findmin_cpq_res (triple zenon_TU_cs zenon_TV_cr zenon_TW_cq)) W))) zenon_H5f); [ zenon_intro zenon_H60; idtac ].
% 0.93/1.08 elim zenon_H60. zenon_intro zenon_TW_cp. zenon_intro zenon_H61.
% 0.93/1.08 apply (zenon_notimply_s _ _ zenon_H61). zenon_intro zenon_H42. zenon_intro zenon_H4e.
% 0.93/1.08 generalize (l17_l18 zenon_TU_cs). zenon_intro zenon_H62.
% 0.93/1.08 generalize (zenon_H62 zenon_TV_cr). zenon_intro zenon_H63.
% 0.93/1.08 generalize (zenon_H63 zenon_TW_cq). zenon_intro zenon_H64.
% 0.93/1.08 apply (zenon_imply_s _ _ zenon_H64); [ zenon_intro zenon_H65 | zenon_intro zenon_H50 ].
% 0.93/1.08 apply zenon_H65. exists zenon_TW_cp. apply NNPP. zenon_intro zenon_H66.
% 0.93/1.08 apply (zenon_notand_s _ _ zenon_H66); [ zenon_intro zenon_H41 | zenon_intro zenon_H67 ].
% 0.93/1.08 apply (zenon_L1_ zenon_TW_cp zenon_TW_cq zenon_TV_cr zenon_TU_cs); trivial.
% 0.93/1.08 generalize (stricly_smaller_definition zenon_TW_cp). zenon_intro zenon_H68.
% 0.93/1.08 generalize (zenon_H68 (findmin_cpq_res (triple zenon_TU_cs zenon_TV_cr zenon_TW_cq))). zenon_intro zenon_H69.
% 0.93/1.08 apply (zenon_equiv_s _ _ zenon_H69); [ zenon_intro zenon_H67; zenon_intro zenon_H6c | zenon_intro zenon_H6b; zenon_intro zenon_H6a ].
% 0.93/1.08 apply (zenon_notand_s _ _ zenon_H6c); [ zenon_intro zenon_H6d | zenon_intro zenon_H4d ].
% 0.93/1.08 generalize (totality (findmin_cpq_res (triple zenon_TU_cs zenon_TV_cr zenon_TW_cq))). zenon_intro zenon_H6e.
% 0.93/1.08 generalize (zenon_H6e zenon_TW_cp). zenon_intro zenon_H6f.
% 0.93/1.08 apply (zenon_or_s _ _ zenon_H6f); [ zenon_intro zenon_H71 | zenon_intro zenon_H70 ].
% 0.93/1.08 exact (zenon_H4e zenon_H71).
% 0.93/1.08 exact (zenon_H6d zenon_H70).
% 0.93/1.08 exact (zenon_H4d zenon_H4e).
% 0.93/1.08 exact (zenon_H67 zenon_H6b).
% 0.93/1.08 apply (zenon_L3_ zenon_TW_cq zenon_TV_cr zenon_TU_cs); trivial.
% 0.93/1.08 exact (zenon_H5a zenon_H5e).
% 0.93/1.08 Qed.
% 0.93/1.08 % SZS output end Proof
% 0.93/1.08 (* END-PROOF *)
% 0.93/1.08 nodes searched: 28476
% 0.93/1.08 max branch formulas: 1992
% 0.93/1.08 proof nodes created: 1061
% 0.93/1.08 formulas created: 43813
% 0.93/1.08
%------------------------------------------------------------------------------