%------------------------------------------------------------------------------
% File     : Lash---1.13
% Problem  : ITP166^1 : 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 : n028.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 04:02:41 EDT 2023

% Result   : Theorem 0.20s 0.44s
% Output   : Proof 0.20s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_int,type,
    int: $tType ).

thf(ty_list_char,type,
    list_char: $tType ).

thf(ty_produc1193801173ar_int,type,
    produc1193801173ar_int: com > ( list_char > int ) > produc1260470173ar_int ).

thf(ty_p,type,
    p: ( list_char > int ) > ( list_char > int ) > $o ).

thf(ty_c,type,
    c: com ).

thf(ty_relati23543761ar_int,type,
    relati23543761ar_int: ( ( list_char > int ) > ( list_char > int ) > $o ) > bexp > com > nat > ( list_char > int ) > ( list_char > int ) > $o ).

thf(ty_bval,type,
    bval: bexp > ( list_char > int ) > $o ).

thf(ty_suc,type,
    suc: nat > nat ).

thf(ty_ka,type,
    ka: nat ).

thf(ty_s_a,type,
    s_a: list_char > int ).

thf(ty_big_big_step,type,
    big_big_step: produc1260470173ar_int > ( list_char > int ) > $o ).

thf(ty_b,type,
    b: bexp ).

thf(ty_c2,type,
    c2: com ).

thf(ty_ta,type,
    ta: list_char > int ).

thf(ty_sa,type,
    sa: list_char > int ).

thf(ty_t_a,type,
    t_a: list_char > int ).

thf(sP1,plain,
    ( sP1
  <=> ( big_big_step @ ( produc1193801173ar_int @ c @ sa ) @ ta ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ( ~ ( ( relati23543761ar_int @ p @ b @ c @ ( suc @ ka ) @ sa @ s_a )
         => ~ ( bval @ b @ sa ) )
     => ~ sP1 ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ( ( relati23543761ar_int @ p @ b @ c @ ( suc @ ka ) @ sa @ s_a )
     => ~ ( bval @ b @ sa ) ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ! [X1: list_char > int,X2: list_char > int] :
        ( ~ ( ~ ( ( relati23543761ar_int @ p @ b @ c @ ( suc @ ka ) @ X1 @ X2 )
               => ~ ( bval @ b @ X1 ) )
           => ~ ( big_big_step @ ( produc1193801173ar_int @ c @ X1 ) @ ta ) )
       => ~ ( big_big_step @ ( produc1193801173ar_int @ c2 @ X2 ) @ t_a ) ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> ( ~ sP2
     => ~ ( big_big_step @ ( produc1193801173ar_int @ c2 @ s_a ) @ t_a ) ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
    ( sP6
  <=> ( big_big_step @ ( produc1193801173ar_int @ c2 @ s_a ) @ t_a ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
    ( sP7
  <=> ( bval @ b @ sa ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(sP8,plain,
    ( sP8
  <=> ! [X1: list_char > int] :
        ( ~ ( ~ ( ( relati23543761ar_int @ p @ b @ c @ ( suc @ ka ) @ sa @ X1 )
               => ~ sP7 )
           => ~ sP1 )
       => ~ ( big_big_step @ ( produc1193801173ar_int @ c2 @ X1 ) @ t_a ) ) ),
    introduced(definition,[new_symbols(definition,[sP8])]) ).

thf(sP9,plain,
    ( sP9
  <=> ( relati23543761ar_int @ p @ b @ c @ ( suc @ ka ) @ sa @ s_a ) ),
    introduced(definition,[new_symbols(definition,[sP9])]) ).

thf(conj_0,conjecture,
    ~ sP4 ).

thf(h0,negated_conjecture,
    sP4,
    inference(assume_negation,[status(cth)],[conj_0]) ).

thf(1,plain,
    ( ~ sP3
    | ~ sP9
    | ~ sP7 ),
    inference(prop_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP2
    | sP3
    | ~ sP1 ),
    inference(prop_rule,[status(thm)],]) ).

thf(3,plain,
    ( ~ sP5
    | sP2
    | ~ sP6 ),
    inference(prop_rule,[status(thm)],]) ).

thf(4,plain,
    ( ~ sP8
    | sP5 ),
    inference(all_rule,[status(thm)],]) ).

thf(5,plain,
    ( ~ sP4
    | sP8 ),
    inference(all_rule,[status(thm)],]) ).

thf(fact_4_Suc_Oprems_I7_J,axiom,
    sP9 ).

thf(fact_3_Suc_Oprems_I4_J,axiom,
    sP6 ).

thf(fact_2_Suc_Oprems_I3_J,axiom,
    sP1 ).

thf(fact_0_Suc_Oprems_I6_J,axiom,
    sP7 ).

thf(6,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h0])],[1,2,3,4,5,h0,fact_4_Suc_Oprems_I7_J,fact_3_Suc_Oprems_I4_J,fact_2_Suc_Oprems_I3_J,fact_0_Suc_Oprems_I6_J]) ).

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

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : ITP166^1 : TPTP v8.1.2. Released v7.5.0.
% 0.00/0.14  % Command  : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.35  % Computer : n028.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Sun Aug 27 16:53:38 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.20/0.44  % SZS status Theorem
% 0.20/0.44  % Mode: cade22sinegrackle2x6978
% 0.20/0.44  % Steps: 343
% 0.20/0.44  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------