TSTP Solution File: SEV070^5 by Satallax---3.5

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%------------------------------------------------------------------------------
% File     : Satallax---3.5
% Problem  : SEV070^5 : TPTP v7.5.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s

% Computer : n014.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
% DateTime : Tue Mar 30 22:04:54 EDT 2021

% Result   : Theorem 0.12s
% Output   : Proof 0.12s
% Verified : 
% SZS Type : None (MakeTreeStats fails)
% Syntax   : Number of formulae    : 45

% Comments : 
%------------------------------------------------------------------------------
thf(ty_cS,type,
    cS: $i > $i ).

thf(ty_eigen__2,type,
    eigen__2: $i ).

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

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

thf(ty_eigen__3,type,
    eigen__3: $i > $o ).

thf(sP1,plain,
    ( sP1
  <=> ! [X1: $i] :
        ( ( eigen__3 @ X1 )
       => ( eigen__3 @ ( cS @ X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ( ~ ( ( eigen__3 @ eigen__1 )
         => ~ sP1 )
     => ( eigen__3 @ eigen__2 ) ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ! [X1: $i > $o] :
        ( ~ ( ( X1 @ eigen__0 )
           => ~ ! [X2: $i] :
                  ( ( X1 @ X2 )
                 => ( X1 @ ( cS @ X2 ) ) ) )
       => ( X1 @ eigen__1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ( ( eigen__3 @ eigen__1 )
     => ~ sP1 ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> ( ( eigen__3 @ eigen__0 )
     => ~ sP1 ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
    ( sP6
  <=> ( eigen__3 @ eigen__0 ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
    ( sP7
  <=> ( eigen__3 @ eigen__2 ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(sP8,plain,
    ( sP8
  <=> ( eigen__3 @ eigen__1 ) ),
    introduced(definition,[new_symbols(definition,[sP8])]) ).

thf(sP9,plain,
    ( sP9
  <=> ( ~ sP5
     => sP8 ) ),
    introduced(definition,[new_symbols(definition,[sP9])]) ).

thf(sP10,plain,
    ( sP10
  <=> ! [X1: $i > $o] :
        ( ~ ( ( X1 @ eigen__1 )
           => ~ ! [X2: $i] :
                  ( ( X1 @ X2 )
                 => ( X1 @ ( cS @ X2 ) ) ) )
       => ( X1 @ eigen__2 ) ) ),
    introduced(definition,[new_symbols(definition,[sP10])]) ).

thf(cTHM577_pme,conjecture,
    ! [X1: $i,X2: $i,X3: $i] :
      ( ~ ( ! [X4: $i > $o] :
              ( ~ ( ( X4 @ X1 )
                 => ~ ! [X5: $i] :
                        ( ( X4 @ X5 )
                       => ( X4 @ ( cS @ X5 ) ) ) )
             => ( X4 @ X2 ) )
         => ~ ! [X4: $i > $o] :
                ( ~ ( ( X4 @ X2 )
                   => ~ ! [X5: $i] :
                          ( ( X4 @ X5 )
                         => ( X4 @ ( cS @ X5 ) ) ) )
               => ( X4 @ X3 ) ) )
     => ! [X4: $i > $o] :
          ( ~ ( ( X4 @ X1 )
             => ~ ! [X5: $i] :
                    ( ( X4 @ X5 )
                   => ( X4 @ ( cS @ X5 ) ) ) )
         => ( X4 @ X3 ) ) ) ).

thf(h0,negated_conjecture,
    ~ ! [X1: $i,X2: $i,X3: $i] :
        ( ~ ( ! [X4: $i > $o] :
                ( ~ ( ( X4 @ X1 )
                   => ~ ! [X5: $i] :
                          ( ( X4 @ X5 )
                         => ( X4 @ ( cS @ X5 ) ) ) )
               => ( X4 @ X2 ) )
           => ~ ! [X4: $i > $o] :
                  ( ~ ( ( X4 @ X2 )
                     => ~ ! [X5: $i] :
                            ( ( X4 @ X5 )
                           => ( X4 @ ( cS @ X5 ) ) ) )
                 => ( X4 @ X3 ) ) )
       => ! [X4: $i > $o] :
            ( ~ ( ( X4 @ X1 )
               => ~ ! [X5: $i] :
                      ( ( X4 @ X5 )
                     => ( X4 @ ( cS @ X5 ) ) ) )
           => ( X4 @ X3 ) ) ),
    inference(assume_negation,[status(cth)],[cTHM577_pme]) ).

thf(h1,assumption,
    ~ ! [X1: $i,X2: $i] :
        ( ~ ( ! [X3: $i > $o] :
                ( ~ ( ( X3 @ eigen__0 )
                   => ~ ! [X4: $i] :
                          ( ( X3 @ X4 )
                         => ( X3 @ ( cS @ X4 ) ) ) )
               => ( X3 @ X1 ) )
           => ~ ! [X3: $i > $o] :
                  ( ~ ( ( X3 @ X1 )
                     => ~ ! [X4: $i] :
                            ( ( X3 @ X4 )
                           => ( X3 @ ( cS @ X4 ) ) ) )
                 => ( X3 @ X2 ) ) )
       => ! [X3: $i > $o] :
            ( ~ ( ( X3 @ eigen__0 )
               => ~ ! [X4: $i] :
                      ( ( X3 @ X4 )
                     => ( X3 @ ( cS @ X4 ) ) ) )
           => ( X3 @ X2 ) ) ),
    introduced(assumption,[]) ).

thf(h2,assumption,
    ~ ! [X1: $i] :
        ( ~ ( sP3
           => ~ ! [X2: $i > $o] :
                  ( ~ ( ( X2 @ eigen__1 )
                     => ~ ! [X3: $i] :
                            ( ( X2 @ X3 )
                           => ( X2 @ ( cS @ X3 ) ) ) )
                 => ( X2 @ X1 ) ) )
       => ! [X2: $i > $o] :
            ( ~ ( ( X2 @ eigen__0 )
               => ~ ! [X3: $i] :
                      ( ( X2 @ X3 )
                     => ( X2 @ ( cS @ X3 ) ) ) )
           => ( X2 @ X1 ) ) ),
    introduced(assumption,[]) ).

thf(h3,assumption,
    ~ ( ~ ( sP3
         => ~ sP10 )
     => ! [X1: $i > $o] :
          ( ~ ( ( X1 @ eigen__0 )
             => ~ ! [X2: $i] :
                    ( ( X1 @ X2 )
                   => ( X1 @ ( cS @ X2 ) ) ) )
         => ( X1 @ eigen__2 ) ) ),
    introduced(assumption,[]) ).

thf(h4,assumption,
    ~ ( sP3
     => ~ sP10 ),
    introduced(assumption,[]) ).

thf(h5,assumption,
    ~ ! [X1: $i > $o] :
        ( ~ ( ( X1 @ eigen__0 )
           => ~ ! [X2: $i] :
                  ( ( X1 @ X2 )
                 => ( X1 @ ( cS @ X2 ) ) ) )
       => ( X1 @ eigen__2 ) ),
    introduced(assumption,[]) ).

thf(h6,assumption,
    sP3,
    introduced(assumption,[]) ).

thf(h7,assumption,
    sP10,
    introduced(assumption,[]) ).

thf(h8,assumption,
    ~ ( ~ sP5
     => sP7 ),
    introduced(assumption,[]) ).

thf(h9,assumption,
    ~ sP5,
    introduced(assumption,[]) ).

thf(h10,assumption,
    ~ sP7,
    introduced(assumption,[]) ).

thf(h11,assumption,
    sP6,
    introduced(assumption,[]) ).

thf(h12,assumption,
    sP1,
    introduced(assumption,[]) ).

thf(1,plain,
    ( ~ sP3
    | sP9 ),
    inference(all_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP9
    | sP5
    | sP8 ),
    inference(prop_rule,[status(thm)],]) ).

thf(3,plain,
    ( ~ sP5
    | ~ sP6
    | ~ sP1 ),
    inference(prop_rule,[status(thm)],]) ).

thf(4,plain,
    ( ~ sP10
    | sP2 ),
    inference(all_rule,[status(thm)],]) ).

thf(5,plain,
    ( ~ sP2
    | sP4
    | sP7 ),
    inference(prop_rule,[status(thm)],]) ).

thf(6,plain,
    ( ~ sP4
    | ~ sP8
    | ~ sP1 ),
    inference(prop_rule,[status(thm)],]) ).

thf(7,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h11,h12,h9,h10,h8,h6,h7,h4,h5,h3,h2,h1,h0])],[1,2,3,4,5,6,h6,h7,h11,h12,h10]) ).

thf(8,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h9,h10,h8,h6,h7,h4,h5,h3,h2,h1,h0]),tab_negimp(discharge,[h11,h12])],[h9,7,h11,h12]) ).

thf(9,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h8,h6,h7,h4,h5,h3,h2,h1,h0]),tab_negimp(discharge,[h9,h10])],[h8,8,h9,h10]) ).

thf(10,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h6,h7,h4,h5,h3,h2,h1,h0]),tab_negall(discharge,[h8]),tab_negall(eigenvar,eigen__3)],[h5,9,h8]) ).

thf(11,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h4,h5,h3,h2,h1,h0]),tab_negimp(discharge,[h6,h7])],[h4,10,h6,h7]) ).

thf(12,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h3,h2,h1,h0]),tab_negimp(discharge,[h4,h5])],[h3,11,h4,h5]) ).

thf(13,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__2)],[h2,12,h3]) ).

thf(14,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__1)],[h1,13,h2]) ).

thf(15,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,14,h1]) ).

thf(0,theorem,
    ! [X1: $i,X2: $i,X3: $i] :
      ( ~ ( ! [X4: $i > $o] :
              ( ~ ( ( X4 @ X1 )
                 => ~ ! [X5: $i] :
                        ( ( X4 @ X5 )
                       => ( X4 @ ( cS @ X5 ) ) ) )
             => ( X4 @ X2 ) )
         => ~ ! [X4: $i > $o] :
                ( ~ ( ( X4 @ X2 )
                   => ~ ! [X5: $i] :
                          ( ( X4 @ X5 )
                         => ( X4 @ ( cS @ X5 ) ) ) )
               => ( X4 @ X3 ) ) )
     => ! [X4: $i > $o] :
          ( ~ ( ( X4 @ X1 )
             => ~ ! [X5: $i] :
                    ( ( X4 @ X5 )
                   => ( X4 @ ( cS @ X5 ) ) ) )
         => ( X4 @ X3 ) ) ),
    inference(contra,[status(thm),contra(discharge,[h0])],[15,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem  : SEV070^5 : TPTP v7.5.0. Released v4.0.0.
% 0.03/0.12  % Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33  % Computer : n014.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 : Fri Mar 26 14:06:37 EDT 2021
% 0.12/0.33  % CPUTime  : 
% 0.12/0.35  % SZS status Theorem
% 0.12/0.35  % Mode: mode213
% 0.12/0.35  % Inferences: 5
% 0.12/0.35  % SZS output start Proof
% See solution above
% 0.12/0.35  % SZS output end Proof
%------------------------------------------------------------------------------