%------------------------------------------------------------------------------
% File     : Satallax---3.5
% Problem  : SEU956^5 : 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 : n004.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 14:11:01 EDT 2022

% Result   : Theorem 0.13s 0.35s
% Output   : Proof 0.13s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_eigen__1,type,
    eigen__1: $i ).

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

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

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

thf(sP3,plain,
    ( sP3
  <=> ! [X1: $i] :
        ( ( eigen__1 = X1 )
       => ( eigen__0 = X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ! [X1: $i > $o] :
        ( ( ( (=) @ eigen__0 )
          = X1 )
       => ! [X2: $i] :
            ( ( X1 @ X2 )
           => ( eigen__0 = X2 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> ( sP2
     => ( eigen__0 = eigen__1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
    ( sP6
  <=> ! [X1: $i > $o,X2: $i > $o] :
        ( ( X1 = X2 )
       => ! [X3: $i] :
            ( ( X2 @ X3 )
           => ( X1 @ X3 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
    ( sP7
  <=> ( eigen__0 = eigen__1 ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(sP8,plain,
    ( sP8
  <=> ( sP1
     => sP3 ) ),
    introduced(definition,[new_symbols(definition,[sP8])]) ).

thf(cTHM13_pme,conjecture,
    ( sP6
   => ! [X1: $i,X2: $i] :
        ( ( ( (=) @ X1 )
          = ( (=) @ X2 ) )
       => ( X1 = X2 ) ) ) ).

thf(h0,negated_conjecture,
    ~ ( sP6
     => ! [X1: $i,X2: $i] :
          ( ( ( (=) @ X1 )
            = ( (=) @ X2 ) )
         => ( X1 = X2 ) ) ),
    inference(assume_negation,[status(cth)],[cTHM13_pme]) ).

thf(h1,assumption,
    sP6,
    introduced(assumption,[]) ).

thf(h2,assumption,
    ~ ! [X1: $i,X2: $i] :
        ( ( ( (=) @ X1 )
          = ( (=) @ X2 ) )
       => ( X1 = X2 ) ),
    introduced(assumption,[]) ).

thf(h3,assumption,
    ~ ! [X1: $i] :
        ( ( ( (=) @ eigen__0 )
          = ( (=) @ X1 ) )
       => ( eigen__0 = X1 ) ),
    introduced(assumption,[]) ).

thf(h4,assumption,
    ~ ( sP1
     => sP7 ),
    introduced(assumption,[]) ).

thf(h5,assumption,
    sP1,
    introduced(assumption,[]) ).

thf(h6,assumption,
    ~ sP7,
    introduced(assumption,[]) ).

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

thf(2,plain,
    ( ~ sP3
    | sP5 ),
    inference(all_rule,[status(thm)],]) ).

thf(3,plain,
    ( ~ sP5
    | ~ sP2
    | sP7 ),
    inference(prop_rule,[status(thm)],]) ).

thf(4,plain,
    ( ~ sP6
    | sP4 ),
    inference(all_rule,[status(thm)],]) ).

thf(5,plain,
    ( ~ sP4
    | sP8 ),
    inference(all_rule,[status(thm)],]) ).

thf(6,plain,
    ( ~ sP8
    | ~ sP1
    | sP3 ),
    inference(prop_rule,[status(thm)],]) ).

thf(7,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h5,h6,h4,h3,h1,h2,h0])],[1,2,3,4,5,6,h1,h5,h6]) ).

thf(8,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h4,h3,h1,h2,h0]),tab_negimp(discharge,[h5,h6])],[h4,7,h5,h6]) ).

thf(9,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h3,h1,h2,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__1)],[h3,8,h4]) ).

thf(10,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h1,h2,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__0)],[h2,9,h3]) ).

thf(11,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,10,h1,h2]) ).

thf(0,theorem,
    ( sP6
   => ! [X1: $i,X2: $i] :
        ( ( ( (=) @ X1 )
          = ( (=) @ X2 ) )
       => ( X1 = X2 ) ) ),
    inference(contra,[status(thm),contra(discharge,[h0])],[11,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SEU956^5 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.12  % Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.32  % Computer : n004.cluster.edu
% 0.13/0.32  % Model    : x86_64 x86_64
% 0.13/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32  % Memory   : 8042.1875MB
% 0.13/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32  % CPULimit : 300
% 0.13/0.32  % WCLimit  : 600
% 0.13/0.32  % DateTime : Mon Jun 20 10:22:08 EDT 2022
% 0.13/0.32  % CPUTime  : 
% 0.13/0.35  % SZS status Theorem
% 0.13/0.35  % Mode: mode213
% 0.13/0.35  % Inferences: 7
% 0.13/0.35  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------