%------------------------------------------------------------------------------
% File     : Satallax---3.5
% Problem  : SEV406^5 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s

% Computer : n008.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 : Tue Jul 19 18:06:15 EDT 2022

% Result   : Theorem 0.12s 0.36s
% Output   : Proof 0.12s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :   28
% Syntax   : Number of formulae    :   34 (   7 unt;   4 typ;   1 def)
%            Number of atoms       :   81 (   5 equ;   0 cnn)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :   92 (  26   ~;  16   |;   0   &;  26   @)
%                                         (   9 <=>;  15  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    5 (   5   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   16 (  14 usr;  12 con; 0-2 aty)
%            Number of variables   :    8 (   5   ^   3   !;   0   ?;   8   :)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_cP,type,
    cP: ( $i > $o ) > $o ).

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

thf(ty_cB,type,
    cB: $i > $o ).

thf(ty_cA,type,
    cA: $i > $o ).

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

thf(eigendef_eigen__0,definition,
    ( eigen__0
    = ( eps__0
      @ ^ [X1: $i] :
          ( ( ~ ( cA @ X1 )
           => ( cB @ X1 ) )
         != ( ~ ( cB @ X1 )
           => ( cA @ X1 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__0])]) ).

thf(sP1,plain,
    ( sP1
  <=> ( cP
      @ ^ [X1: $i] :
          ( ~ ( cA @ X1 )
         => ( cB @ X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ( cA @ eigen__0 ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ! [X1: $i] :
        ( ( ~ ( cA @ X1 )
         => ( cB @ X1 ) )
        = ( ~ ( cB @ X1 )
         => ( cA @ X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ( ~ ( cB @ eigen__0 )
     => sP2 ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> ( ( ~ sP2
       => ( cB @ eigen__0 ) )
      = sP4 ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
    ( sP6
  <=> ( cB @ eigen__0 ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
    ( sP7
  <=> ( ( ^ [X1: $i] :
            ( ~ ( cA @ X1 )
           => ( cB @ X1 ) ) )
      = ( ^ [X1: $i] :
            ( ~ ( cB @ X1 )
           => ( cA @ X1 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(sP8,plain,
    ( sP8
  <=> ( cP
      @ ^ [X1: $i] :
          ( ~ ( cB @ X1 )
         => ( cA @ X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP8])]) ).

thf(sP9,plain,
    ( sP9
  <=> ( ~ sP2
     => sP6 ) ),
    introduced(definition,[new_symbols(definition,[sP9])]) ).

thf(cTRIVEXT2_pme,conjecture,
    ( sP1
   => sP8 ) ).

thf(h1,negated_conjecture,
    ~ ( sP1
     => sP8 ),
    inference(assume_negation,[status(cth)],[cTRIVEXT2_pme]) ).

thf(h2,assumption,
    sP1,
    introduced(assumption,[]) ).

thf(h3,assumption,
    ~ sP8,
    introduced(assumption,[]) ).

thf(1,plain,
    ( sP4
    | ~ sP2 ),
    inference(prop_rule,[status(thm)],]) ).

thf(2,plain,
    ( sP4
    | ~ sP6 ),
    inference(prop_rule,[status(thm)],]) ).

thf(3,plain,
    ( sP9
    | ~ sP6 ),
    inference(prop_rule,[status(thm)],]) ).

thf(4,plain,
    ( sP9
    | ~ sP2 ),
    inference(prop_rule,[status(thm)],]) ).

thf(5,plain,
    ( ~ sP4
    | sP6
    | sP2 ),
    inference(prop_rule,[status(thm)],]) ).

thf(6,plain,
    ( ~ sP9
    | sP2
    | sP6 ),
    inference(prop_rule,[status(thm)],]) ).

thf(7,plain,
    ( sP5
    | ~ sP9
    | ~ sP4 ),
    inference(prop_rule,[status(thm)],]) ).

thf(8,plain,
    ( sP5
    | sP9
    | sP4 ),
    inference(prop_rule,[status(thm)],]) ).

thf(9,plain,
    ( sP3
    | ~ sP5 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__0]) ).

thf(10,plain,
    ( sP7
    | ~ sP3 ),
    inference(prop_rule,[status(thm)],]) ).

thf(11,plain,
    ( ~ sP1
    | sP8
    | ~ sP7 ),
    inference(mating_rule,[status(thm)],]) ).

thf(12,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h2,h3,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,h2,h3]) ).

thf(13,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,12,h2,h3]) ).

thf(14,plain,
    $false,
    inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[13,h0]) ).

thf(0,theorem,
    ( sP1
   => sP8 ),
    inference(contra,[status(thm),contra(discharge,[h1])],[13,h1]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : SEV406^5 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.12  % Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33  % Computer : n008.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  : 600
% 0.12/0.33  % DateTime : Mon Jun 27 20:15:38 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.12/0.36  % SZS status Theorem
% 0.12/0.36  % Mode: mode213
% 0.12/0.36  % Inferences: 16
% 0.12/0.36  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------