%------------------------------------------------------------------------------
% File     : Satallax---3.5
% Problem  : PUZ137^1 : TPTP v8.1.0. Released v5.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s

% Computer : n022.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 : Mon Jul 18 18:26:06 EDT 2022

% Result   : Theorem 0.11s 0.35s
% Output   : Proof 0.11s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :   29
% Syntax   : Number of formulae    :   35 (   8 unt;   4 typ;   1 def)
%            Number of atoms       :   73 (   4 equ;   0 cnn)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :   83 (  22   ~;  16   |;   0   &;  24   @)
%                                         (  11 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    3 (   3   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   19 (  16 usr;  17 con; 0-2 aty)
%                                         (   3  !!;   0  ??;   0 @@+;   0 @@-)
%            Number of variables   :    6 (   1   ^   5   !;   0   ?;   6   :)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_peter,type,
    peter: $i ).

thf(ty_eigen__1,type,
    eigen__1: $o ).

thf(ty_eigen__0,type,
    eigen__0: $o ).

thf(ty_says,type,
    says: $i > $o > $o ).

thf(h0,assumption,
    ! [X1: $o > $o,X2: $o] :
      ( ( X1 @ X2 )
     => ( X1 @ ( eps__0 @ X1 ) ) ),
    introduced(assumption,[]) ).

thf(eigendef_eigen__1,definition,
    ( eigen__1
    = ( eps__0
      @ ^ [X1: $o] :
          ~ ( ( says @ peter @ X1 )
           => ~ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__1])]) ).

thf(sP1,plain,
    ( sP1
  <=> ( says @ peter
      @ ! [X1: $o] :
          ( ( says @ peter @ X1 )
         => ~ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ( says @ peter @ eigen__1 ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ( sP1
     => ~ ! [X1: $o] :
            ( ( says @ peter @ X1 )
           => ~ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ! [X1: $o] :
        ( ( says @ peter @ X1 )
       => ~ X1 ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> ( eigen__1 = eigen__0 ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
    ( sP6
  <=> eigen__1 ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
    ( sP7
  <=> ( peter = peter ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(sP8,plain,
    ( sP8
  <=> ( says @ peter @ eigen__0 ) ),
    introduced(definition,[new_symbols(definition,[sP8])]) ).

thf(sP9,plain,
    ( sP9
  <=> eigen__0 ),
    introduced(definition,[new_symbols(definition,[sP9])]) ).

thf(sP10,plain,
    ( sP10
  <=> ( sP4 = sP9 ) ),
    introduced(definition,[new_symbols(definition,[sP10])]) ).

thf(sP11,plain,
    ( sP11
  <=> ( sP2
     => ~ sP6 ) ),
    introduced(definition,[new_symbols(definition,[sP11])]) ).

thf(thm,conjecture,
    !! @ ( says @ peter ) ).

thf(h1,negated_conjecture,
    ~ ( !! @ ( says @ peter ) ),
    inference(assume_negation,[status(cth)],[thm]) ).

thf(h2,assumption,
    ~ sP8,
    introduced(assumption,[]) ).

thf(1,plain,
    ( sP5
    | ~ sP6
    | ~ sP9 ),
    inference(prop_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP2
    | sP8
    | ~ sP7
    | ~ sP5 ),
    inference(mating_rule,[status(thm)],]) ).

thf(3,plain,
    ( sP11
    | sP6 ),
    inference(prop_rule,[status(thm)],]) ).

thf(4,plain,
    ( sP11
    | sP2 ),
    inference(prop_rule,[status(thm)],]) ).

thf(5,plain,
    ( sP4
    | ~ sP11 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1]) ).

thf(6,plain,
    ( ~ sP4
    | sP3 ),
    inference(all_rule,[status(thm)],]) ).

thf(7,plain,
    ( ~ sP3
    | ~ sP1
    | ~ sP4 ),
    inference(prop_rule,[status(thm)],]) ).

thf(8,plain,
    ( sP10
    | sP4
    | sP9 ),
    inference(prop_rule,[status(thm)],]) ).

thf(9,plain,
    sP7,
    inference(prop_rule,[status(thm)],]) ).

thf(10,plain,
    ( ~ sP1
    | sP8
    | ~ sP7
    | ~ sP10 ),
    inference(mating_rule,[status(thm)],]) ).

thf(ax1,axiom,
    sP1 ).

thf(11,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,ax1,h2]) ).

thf(12,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__0)],[h1,11,h2]) ).

thf(13,plain,
    $false,
    inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[12,h0]) ).

thf(0,theorem,
    !! @ ( says @ peter ),
    inference(contra,[status(thm),contra(discharge,[h1])],[12,h1]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11  % Problem  : PUZ137^1 : TPTP v8.1.0. Released v5.3.0.
% 0.06/0.12  % Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.11/0.32  % Computer : n022.cluster.edu
% 0.11/0.32  % Model    : x86_64 x86_64
% 0.11/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32  % Memory   : 8042.1875MB
% 0.11/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32  % CPULimit : 300
% 0.11/0.32  % WCLimit  : 600
% 0.11/0.32  % DateTime : Sat May 28 21:27:38 EDT 2022
% 0.11/0.33  % CPUTime  : 
% 0.11/0.35  % SZS status Theorem
% 0.11/0.35  % Mode: mode213
% 0.11/0.35  % Inferences: 46
% 0.11/0.35  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------