%------------------------------------------------------------------------------
% File     : Satallax---3.5
% Problem  : SYO351^5 : 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 : n016.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 : Thu Jul 21 19:31:35 EDT 2022

% Result   : Theorem 0.12s 0.36s
% Output   : Proof 0.12s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

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

thf(ty_eigen__2,type,
    eigen__2: a ).

thf(ty_eigen__1,type,
    eigen__1: a ).

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

thf(sP1,plain,
    ( sP1
  <=> ! [X1: a] :
        ~ ( eigen__0 @ X1 ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ( $false
      = ( eigen__0 @ eigen__2 ) ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> $false ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ! [X1: a] :
        ( sP3
        = ( eigen__0 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> ( ( ^ [X1: a] : sP3 )
      = eigen__0 ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
    ( sP6
  <=> ( eigen__0 @ eigen__1 ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
    ( sP7
  <=> ( eigen__0 @ eigen__2 ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(cE6EXT_pme,conjecture,
    ( ( ^ [X1: a > $o] :
        ! [X2: a] :
          ~ ( X1 @ X2 ) )
    = ( (=)
      @ ^ [X1: a] : sP3 ) ) ).

thf(h0,negated_conjecture,
    ( ^ [X1: a > $o] :
      ! [X2: a] :
        ~ ( X1 @ X2 ) )
 != ( (=)
    @ ^ [X1: a] : sP3 ),
    inference(assume_negation,[status(cth)],[cE6EXT_pme]) ).

thf(h1,assumption,
    ~ ! [X1: a > $o] :
        ( ( ! [X2: a] :
              ~ ( X1 @ X2 ) )
        = ( ( ^ [X2: a] : sP3 )
          = X1 ) ),
    introduced(assumption,[]) ).

thf(h2,assumption,
    sP1 != sP5,
    introduced(assumption,[]) ).

thf(h3,assumption,
    sP1,
    introduced(assumption,[]) ).

thf(h4,assumption,
    sP5,
    introduced(assumption,[]) ).

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

thf(h6,assumption,
    ~ sP5,
    introduced(assumption,[]) ).

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

thf(h8,assumption,
    sP3 != sP6,
    introduced(assumption,[]) ).

thf(h9,assumption,
    sP3,
    introduced(assumption,[]) ).

thf(h10,assumption,
    sP6,
    introduced(assumption,[]) ).

thf(h11,assumption,
    ~ sP3,
    introduced(assumption,[]) ).

thf(h12,assumption,
    ~ sP6,
    introduced(assumption,[]) ).

thf(1,plain,
    $false,
    inference(tab_false,[status(thm),assumptions([h9,h10,h8,h7,h3,h4,h2,h1,h0])],[h9]) ).

thf(2,plain,
    ( ~ sP1
    | ~ sP6 ),
    inference(all_rule,[status(thm)],]) ).

thf(3,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h11,h12,h8,h7,h3,h4,h2,h1,h0])],[2,h3,h12]) ).

thf(4,plain,
    $false,
    inference(tab_be,[status(thm),assumptions([h8,h7,h3,h4,h2,h1,h0]),tab_be(discharge,[h9,h10]),tab_be(discharge,[h11,h12])],[h8,1,3,h9,h10,h11,h12]) ).

thf(5,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h7,h3,h4,h2,h1,h0]),tab_negall(discharge,[h8]),tab_negall(eigenvar,eigen__1)],[h7,4,h8]) ).

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

thf(h13,assumption,
    sP7,
    introduced(assumption,[]) ).

thf(7,plain,
    ( ~ sP2
    | sP3
    | ~ sP7 ),
    inference(prop_rule,[status(thm)],]) ).

thf(8,plain,
    ( ~ sP4
    | sP2 ),
    inference(all_rule,[status(thm)],]) ).

thf(9,plain,
    ~ sP3,
    inference(prop_rule,[status(thm)],]) ).

thf(10,plain,
    ( ~ sP5
    | sP4 ),
    inference(prop_rule,[status(thm)],]) ).

thf(11,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h13,h5,h6,h2,h1,h0])],[7,8,9,10,h13,h6]) ).

thf(12,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h5,h6,h2,h1,h0]),tab_negall(discharge,[h13]),tab_negall(eigenvar,eigen__2)],[h5,11,h13]) ).

thf(13,plain,
    $false,
    inference(tab_be,[status(thm),assumptions([h2,h1,h0]),tab_be(discharge,[h3,h4]),tab_be(discharge,[h5,h6])],[h2,6,12,h3,h4,h5,h6]) ).

thf(14,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__0)],[h1,13,h2]) ).

thf(15,plain,
    $false,
    inference(tab_fe,[status(thm),assumptions([h0]),tab_fe(discharge,[h1])],[h0,14,h1]) ).

thf(0,theorem,
    ( ( ^ [X1: a > $o] :
        ! [X2: a] :
          ~ ( X1 @ X2 ) )
    = ( (=)
      @ ^ [X1: a] : sP3 ) ),
    inference(contra,[status(thm),contra(discharge,[h0])],[15,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : SYO351^5 : 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 : n016.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 Jul  9 04:21:39 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: 15
% 0.12/0.36  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------