%------------------------------------------------------------------------------
% File     : Lash---1.13
% Problem  : ITP065^1 : 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 04:01:51 EDT 2023

% Result   : Theorem 0.19s 0.40s
% Output   : Proof 0.19s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_b,type,
    b: $tType ).

thf(ty_tree_b,type,
    tree_b: $tType ).

thf(ty_t_b,type,
    t_b: b > tree_b > tree_b > tree_b ).

thf(ty_e_b,type,
    e_b: tree_b ).

thf(ty_heapIm229596387mpty_b,type,
    heapIm229596387mpty_b: tree_b > $o ).

thf(sP1,plain,
    ( sP1
  <=> ! [X1: tree_b] :
        ( ( X1 != e_b )
       => ~ ! [X2: b,X3: tree_b,X4: tree_b] :
              ( X1
             != ( t_b @ X2 @ X3 @ X4 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ( ( heapIm229596387mpty_b @ e_b )
      = ~ $false ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ( heapIm229596387mpty_b
      = ( ^ [X1: tree_b] : ( X1 = e_b ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ! [X1: tree_b] :
        ( ( heapIm229596387mpty_b @ X1 )
        = ( X1 = e_b ) ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> ( heapIm229596387mpty_b @ e_b ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
    ( sP6
  <=> $false ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(conj_0,conjecture,
    sP5 ).

thf(h0,negated_conjecture,
    ~ sP5,
    inference(assume_negation,[status(cth)],[conj_0]) ).

thf(1,plain,
    ( ~ sP2
    | sP5
    | sP6 ),
    inference(prop_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP4
    | sP2 ),
    inference(all_rule,[status(thm)],]) ).

thf(3,plain,
    ( ~ sP1
    | ~ sP6 ),
    inference(all_rule,[status(thm)],]) ).

thf(4,plain,
    ( ~ sP3
    | sP4 ),
    inference(prop_rule,[status(thm)],]) ).

thf(fact_6_Tree_Oexhaust,axiom,
    sP1 ).

thf(fact_0_hs__is__empty__def,axiom,
    sP3 ).

thf(5,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h0])],[1,2,3,4,h0,fact_6_Tree_Oexhaust,fact_0_hs__is__empty__def]) ).

thf(0,theorem,
    sP5,
    inference(contra,[status(thm),contra(discharge,[h0])],[5,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : ITP065^1 : TPTP v8.1.2. Released v7.5.0.
% 0.00/0.12  % Command  : lash -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33  % Computer : n021.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Sun Aug 27 14:58:43 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 0.19/0.40  % SZS status Theorem
% 0.19/0.40  % Mode: cade22grackle2xfee4
% 0.19/0.40  % Steps: 21
% 0.19/0.40  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------