%------------------------------------------------------------------------------
% File     : Satallax---3.5
% Problem  : ITP065^1 : TPTP v8.1.0. Released v7.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s

% Computer : n026.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 : Sun Jul 17 00:28:58 EDT 2022

% Result   : Theorem 1.94s 2.19s
% Output   : Proof 1.94s
% 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_heapIm229596387mpty_b,type,
    heapIm229596387mpty_b: tree_b > $o ).

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

thf(ty_e_b,type,
    e_b: tree_b ).

thf(sP1,plain,
    ( sP1
  <=> ( heapIm229596387mpty_b
      = ( ^ [X1: tree_b] : ( X1 = e_b ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ! [X1: b,X2: tree_b,X3: tree_b] :
        ( e_b
       != ( t_b @ X1 @ X2 @ X3 ) ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ( ( heapIm229596387mpty_b @ e_b )
      = ( e_b = e_b ) ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ( sP3
     => ( heapIm229596387mpty_b @ e_b ) ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> ( ( e_b = e_b )
     => ! [X1: $o] :
          ( ( X1
            = ( e_b = e_b ) )
         => X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
    ( sP6
  <=> ! [X1: $o] :
        ( ( X1
          = ( e_b = e_b ) )
       => X1 ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
    ( sP7
  <=> ! [X1: tree_b] :
        ( ( heapIm229596387mpty_b @ X1 )
        = ( X1 = e_b ) ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(sP8,plain,
    ( sP8
  <=> ! [X1: $o > $o] :
        ( ( X1 @ ( e_b = e_b ) )
       => ! [X2: $o] :
            ( ( X2
              = ( e_b = e_b ) )
           => ( X1 @ X2 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP8])]) ).

thf(sP9,plain,
    ( sP9
  <=> ( ( e_b != e_b )
     => ~ sP2 ) ),
    introduced(definition,[new_symbols(definition,[sP9])]) ).

thf(sP10,plain,
    ( sP10
  <=> ! [X1: $o,X2: $o > $o] :
        ( ( X2 @ X1 )
       => ! [X3: $o] :
            ( ( X3 = X1 )
           => ( X2 @ X3 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP10])]) ).

thf(sP11,plain,
    ( sP11
  <=> ( heapIm229596387mpty_b @ e_b ) ),
    introduced(definition,[new_symbols(definition,[sP11])]) ).

thf(sP12,plain,
    ( sP12
  <=> ! [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,[sP12])]) ).

thf(sP13,plain,
    ( sP13
  <=> ( e_b = e_b ) ),
    introduced(definition,[new_symbols(definition,[sP13])]) ).

thf(conj_0,conjecture,
    sP11 ).

thf(h0,negated_conjecture,
    ~ sP11,
    inference(assume_negation,[status(cth)],[conj_0]) ).

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

thf(2,plain,
    ( ~ sP4
    | ~ sP3
    | sP11 ),
    inference(prop_rule,[status(thm)],]) ).

thf(3,plain,
    ( ~ sP6
    | sP4 ),
    inference(all_rule,[status(thm)],]) ).

thf(4,plain,
    ( ~ sP5
    | ~ sP13
    | sP6 ),
    inference(prop_rule,[status(thm)],]) ).

thf(5,plain,
    ( ~ sP8
    | sP5 ),
    inference(all_rule,[status(thm)],]) ).

thf(6,plain,
    ( ~ sP10
    | sP8 ),
    inference(all_rule,[status(thm)],]) ).

thf(7,plain,
    sP10,
    inference(eq_ind_sym,[status(thm)],]) ).

thf(8,plain,
    ( ~ sP1
    | sP7 ),
    inference(prop_rule,[status(thm)],]) ).

thf(9,plain,
    ( ~ sP12
    | sP9 ),
    inference(all_rule,[status(thm)],]) ).

thf(10,plain,
    ( ~ sP9
    | sP13
    | ~ sP2 ),
    inference(prop_rule,[status(thm)],]) ).

thf(fact_8_Tree_Odistinct_I1_J,axiom,
    sP2 ).

thf(fact_6_Tree_Oexhaust,axiom,
    sP12 ).

thf(fact_0_hs__is__empty__def,axiom,
    sP1 ).

thf(11,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h0])],[1,2,3,4,5,6,7,8,9,10,fact_8_Tree_Odistinct_I1_J,fact_6_Tree_Oexhaust,fact_0_hs__is__empty__def,h0]) ).

thf(0,theorem,
    sP11,
    inference(contra,[status(thm),contra(discharge,[h0])],[11,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10  % Problem  : ITP065^1 : TPTP v8.1.0. Released v7.5.0.
% 0.00/0.10  % Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.10/0.31  % Computer : n026.cluster.edu
% 0.10/0.31  % Model    : x86_64 x86_64
% 0.10/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31  % Memory   : 8042.1875MB
% 0.10/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31  % CPULimit : 300
% 0.10/0.31  % WCLimit  : 600
% 0.10/0.31  % DateTime : Fri Jun  3 15:07:13 EDT 2022
% 0.10/0.32  % CPUTime  : 
% 1.94/2.19  % SZS status Theorem
% 1.94/2.19  % Mode: mode506
% 1.94/2.19  % Inferences: 8215
% 1.94/2.19  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------