%------------------------------------------------------------------------------
% File     : Satallax---3.5
% Problem  : SEU885^5 : 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 : n018.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 14:10:41 EDT 2022

% Result   : Theorem 0.19s 0.36s
% Output   : Proof 0.19s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_a,type,
    a: $tType ).

thf(ty_b,type,
    b: $tType ).

thf(ty_eigen__1,type,
    eigen__1: b ).

thf(ty_cV,type,
    cV: b > $o ).

thf(ty_eigen__0,type,
    eigen__0: a ).

thf(ty_cF,type,
    cF: b > a ).

thf(ty_cU,type,
    cU: b > $o ).

thf(sP1,plain,
    ( sP1
  <=> ( eigen__0
      = ( cF @ eigen__1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

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

thf(sP3,plain,
    ( sP3
  <=> ( cV @ eigen__1 ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ( cU @ eigen__1 ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> ! [X1: b] :
        ( ( cV @ X1 )
       => ( eigen__0
         != ( cF @ X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
    ( sP6
  <=> ( sP3
     => ~ sP1 ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
    ( sP7
  <=> ! [X1: b] :
        ( ( cU @ X1 )
       => ( cV @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(cTHM30A_pme,conjecture,
    ( sP7
   => ! [X1: a] :
        ( ~ ! [X2: b] :
              ( ( cU @ X2 )
             => ( X1
               != ( cF @ X2 ) ) )
       => ~ ! [X2: b] :
              ( ( cV @ X2 )
             => ( X1
               != ( cF @ X2 ) ) ) ) ) ).

thf(h0,negated_conjecture,
    ~ ( sP7
     => ! [X1: a] :
          ( ~ ! [X2: b] :
                ( ( cU @ X2 )
               => ( X1
                 != ( cF @ X2 ) ) )
         => ~ ! [X2: b] :
                ( ( cV @ X2 )
               => ( X1
                 != ( cF @ X2 ) ) ) ) ),
    inference(assume_negation,[status(cth)],[cTHM30A_pme]) ).

thf(h1,assumption,
    sP7,
    introduced(assumption,[]) ).

thf(h2,assumption,
    ~ ! [X1: a] :
        ( ~ ! [X2: b] :
              ( ( cU @ X2 )
             => ( X1
               != ( cF @ X2 ) ) )
       => ~ ! [X2: b] :
              ( ( cV @ X2 )
             => ( X1
               != ( cF @ X2 ) ) ) ),
    introduced(assumption,[]) ).

thf(h3,assumption,
    ~ ( ~ ! [X1: b] :
            ( ( cU @ X1 )
           => ( eigen__0
             != ( cF @ X1 ) ) )
     => ~ sP5 ),
    introduced(assumption,[]) ).

thf(h4,assumption,
    ~ ! [X1: b] :
        ( ( cU @ X1 )
       => ( eigen__0
         != ( cF @ X1 ) ) ),
    introduced(assumption,[]) ).

thf(h5,assumption,
    sP5,
    introduced(assumption,[]) ).

thf(h6,assumption,
    ~ ( sP4
     => ~ sP1 ),
    introduced(assumption,[]) ).

thf(h7,assumption,
    sP4,
    introduced(assumption,[]) ).

thf(h8,assumption,
    sP1,
    introduced(assumption,[]) ).

thf(1,plain,
    ( ~ sP7
    | sP2 ),
    inference(all_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP2
    | ~ sP4
    | sP3 ),
    inference(prop_rule,[status(thm)],]) ).

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

thf(4,plain,
    ( ~ sP6
    | ~ sP3
    | ~ sP1 ),
    inference(prop_rule,[status(thm)],]) ).

thf(5,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h7,h8,h6,h4,h5,h3,h1,h2,h0])],[1,2,3,4,h1,h7,h8,h5]) ).

thf(6,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h6,h4,h5,h3,h1,h2,h0]),tab_negimp(discharge,[h7,h8])],[h6,5,h7,h8]) ).

thf(7,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h4,h5,h3,h1,h2,h0]),tab_negall(discharge,[h6]),tab_negall(eigenvar,eigen__1)],[h4,6,h6]) ).

thf(8,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h3,h1,h2,h0]),tab_negimp(discharge,[h4,h5])],[h3,7,h4,h5]) ).

thf(9,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h1,h2,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__0)],[h2,8,h3]) ).

thf(10,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,9,h1,h2]) ).

thf(0,theorem,
    ( sP7
   => ! [X1: a] :
        ( ~ ! [X2: b] :
              ( ( cU @ X2 )
             => ( X1
               != ( cF @ X2 ) ) )
       => ~ ! [X2: b] :
              ( ( cV @ X2 )
             => ( X1
               != ( cF @ X2 ) ) ) ) ),
    inference(contra,[status(thm),contra(discharge,[h0])],[10,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SEU885^5 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.12  % Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33  % Computer : n018.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 : Sat Jun 18 23:07:33 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.19/0.36  % SZS status Theorem
% 0.19/0.36  % Mode: mode213
% 0.19/0.36  % Inferences: 4
% 0.19/0.36  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------