%------------------------------------------------------------------------------
% File     : Lash---1.13
% Problem  : ITP142^1 : TPTP v8.1.2. Released v7.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : lash -P picomus -M modes -p tstp -t %d %s

% Computer : n021.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  : 300s
% DateTime : Thu Aug 31 04:02:28 EDT 2023

% Result   : Theorem 0.19s 0.49s
% Output   : Proof 0.19s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_state,type,
    state: $tType ).

thf(ty_produc1204172211_state,type,
    produc1204172211_state: list_com > state > produc2041926651_state ).

thf(ty_s,type,
    s: state ).

thf(ty_cs,type,
    cs: list_com ).

thf(ty_member1069318160_state,type,
    member1069318160_state: produc410756839_state > set_Pr1165141447_state > $o ).

thf(ty_c2,type,
    c2: com ).

thf(ty_exec,type,
    exec: state > com > state > $o ).

thf(ty_pHoare806997636termis,type,
    pHoare806997636termis: list_com > state > $o ).

thf(ty_produc1909270103_state,type,
    produc1909270103_state: produc2041926651_state > produc2041926651_state > produc410756839_state ).

thf(ty_transi1302705790_state,type,
    transi1302705790_state: set_Pr1165141447_state > set_Pr1165141447_state ).

thf(ty_c,type,
    c: com ).

thf(ty_nil_com,type,
    nil_com: list_com ).

thf(ty_s2,type,
    s2: state ).

thf(ty_termi,type,
    termi: com > state > $o ).

thf(ty_cons_com,type,
    cons_com: com > list_com > list_com ).

thf(ty_pHoare259243666_exec1,type,
    pHoare259243666_exec1: set_Pr1165141447_state ).

thf(sP1,plain,
    ( sP1
  <=> ( ( termi @ c @ s )
     => ~ ( ( termi @ c2 @ s2 )
         => ~ ! [X1: state] :
                ( ( exec @ s2 @ c2 @ X1 )
               => ( pHoare806997636termis @ cs @ X1 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ( termi @ c @ s ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ! [X1: state,X2: state] :
        ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ c @ nil_com ) @ X1 ) @ ( produc1204172211_state @ ( cons_com @ c2 @ cs ) @ X2 ) ) @ ( transi1302705790_state @ pHoare259243666_exec1 ) )
       => ( ( termi @ c @ X1 )
         => ~ ( ( termi @ c2 @ X2 )
             => ~ ! [X3: state] :
                    ( ( exec @ X2 @ c2 @ X3 )
                   => ( pHoare806997636termis @ cs @ X3 ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ( termi @ c2 @ s2 ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ c @ nil_com ) @ s ) @ ( produc1204172211_state @ ( cons_com @ c2 @ cs ) @ s2 ) ) @ ( transi1302705790_state @ pHoare259243666_exec1 ) )
     => sP1 ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
    ( sP6
  <=> ! [X1: state] :
        ( ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ c @ nil_com ) @ s ) @ ( produc1204172211_state @ ( cons_com @ c2 @ cs ) @ X1 ) ) @ ( transi1302705790_state @ pHoare259243666_exec1 ) )
       => ( sP2
         => ~ ( ( termi @ c2 @ X1 )
             => ~ ! [X2: state] :
                    ( ( exec @ X1 @ c2 @ X2 )
                   => ( pHoare806997636termis @ cs @ X2 ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
    ( sP7
  <=> ( member1069318160_state @ ( produc1909270103_state @ ( produc1204172211_state @ ( cons_com @ c @ nil_com ) @ s ) @ ( produc1204172211_state @ ( cons_com @ c2 @ cs ) @ s2 ) ) @ ( transi1302705790_state @ pHoare259243666_exec1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(sP8,plain,
    ( sP8
  <=> ( sP4
     => ~ ! [X1: state] :
            ( ( exec @ s2 @ c2 @ X1 )
           => ( pHoare806997636termis @ cs @ X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP8])]) ).

thf(conj_3,conjecture,
    sP4 ).

thf(h0,negated_conjecture,
    ~ sP4,
    inference(assume_negation,[status(cth)],[conj_3]) ).

thf(1,plain,
    ( ~ sP1
    | ~ sP2
    | ~ sP8 ),
    inference(prop_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP5
    | ~ sP7
    | sP1 ),
    inference(prop_rule,[status(thm)],]) ).

thf(3,plain,
    ( sP8
    | sP4 ),
    inference(prop_rule,[status(thm)],]) ).

thf(4,plain,
    ( ~ sP6
    | sP5 ),
    inference(all_rule,[status(thm)],]) ).

thf(5,plain,
    ( ~ sP3
    | sP6 ),
    inference(all_rule,[status(thm)],]) ).

thf(conj_2,axiom,
    sP3 ).

thf(conj_1,axiom,
    sP2 ).

thf(conj_0,axiom,
    sP7 ).

thf(6,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h0])],[1,2,3,4,5,h0,conj_2,conj_1,conj_0]) ).

thf(0,theorem,
    sP4,
    inference(contra,[status(thm),contra(discharge,[h0])],[6,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : ITP142^1 : TPTP v8.1.2. Released v7.5.0.
% 0.00/0.13  % Command  : lash -P picomus -M modes -p tstp -t %d %s
% 0.16/0.34  % Computer : n021.cluster.edu
% 0.16/0.34  % Model    : x86_64 x86_64
% 0.16/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34  % Memory   : 8042.1875MB
% 0.16/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34  % CPULimit : 300
% 0.16/0.34  % WCLimit  : 300
% 0.16/0.34  % DateTime : Sun Aug 27 15:06:43 EDT 2023
% 0.16/0.34  % CPUTime  : 
% 0.19/0.49  % SZS status Theorem
% 0.19/0.49  % Mode: cade22sinegrackle2x6978
% 0.19/0.49  % Steps: 1167
% 0.19/0.49  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------