TSTP Solution File: PUZ104^5 by Satallax---3.5

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%------------------------------------------------------------------------------
% File     : Satallax---3.5
% Problem  : PUZ104^5 : TPTP v8.1.0. Bugfixed v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s

% Computer : n028.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 : Mon Jul 18 18:26:03 EDT 2022

% Result   : Theorem 0.20s 0.35s
% Output   : Proof 0.20s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_s,type,
    s: $i > $i ).

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

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

thf(ty_c1,type,
    c1: $i ).

thf(sP1,plain,
    ( sP1
  <=> ! [X1: $i] :
        ( ( eigen__1 @ X1 )
       => ( eigen__1 @ ( s @ X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ( ( eigen__1 @ c1 )
     => ~ sP1 ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ( eigen__1 @ ( s @ eigen__0 ) ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ( sP3
     => ( eigen__1 @ ( s @ ( s @ eigen__0 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

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

thf(sP6,plain,
    ( sP6
  <=> ( ~ sP2
     => sP5 ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
    ( sP7
  <=> ( eigen__1 @ c1 ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(sP8,plain,
    ( sP8
  <=> ( eigen__1 @ ( s @ ( s @ eigen__0 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP8])]) ).

thf(sP9,plain,
    ( sP9
  <=> ( sP5
     => sP3 ) ),
    introduced(definition,[new_symbols(definition,[sP9])]) ).

thf(sP10,plain,
    ( sP10
  <=> ! [X1: $i > $o] :
        ( ~ ( ( X1 @ c1 )
           => ~ ! [X2: $i] :
                  ( ( X1 @ X2 )
                 => ( X1 @ ( s @ X2 ) ) ) )
       => ( X1 @ eigen__0 ) ) ),
    introduced(definition,[new_symbols(definition,[sP10])]) ).

thf(def_cCKB6_NUM,definition,
    ( cCKB6_NUM
    = ( ^ [X1: $i] :
        ! [X2: $i > $o] :
          ( ~ ( ( X2 @ c1 )
             => ~ ! [X3: $i] :
                    ( ( X2 @ X3 )
                   => ( X2 @ ( s @ X3 ) ) ) )
         => ( X2 @ X1 ) ) ) ) ).

thf(cCKB6_L4000,conjecture,
    ! [X1: $i] :
      ( ! [X2: $i > $o] :
          ( ~ ( ( X2 @ c1 )
             => ~ ! [X3: $i] :
                    ( ( X2 @ X3 )
                   => ( X2 @ ( s @ X3 ) ) ) )
         => ( X2 @ X1 ) )
     => ! [X2: $i > $o] :
          ( ~ ( ( X2 @ c1 )
             => ~ ! [X3: $i] :
                    ( ( X2 @ X3 )
                   => ( X2 @ ( s @ X3 ) ) ) )
         => ( X2 @ ( s @ ( s @ X1 ) ) ) ) ) ).

thf(h0,negated_conjecture,
    ~ ! [X1: $i] :
        ( ! [X2: $i > $o] :
            ( ~ ( ( X2 @ c1 )
               => ~ ! [X3: $i] :
                      ( ( X2 @ X3 )
                     => ( X2 @ ( s @ X3 ) ) ) )
           => ( X2 @ X1 ) )
       => ! [X2: $i > $o] :
            ( ~ ( ( X2 @ c1 )
               => ~ ! [X3: $i] :
                      ( ( X2 @ X3 )
                     => ( X2 @ ( s @ X3 ) ) ) )
           => ( X2 @ ( s @ ( s @ X1 ) ) ) ) ),
    inference(assume_negation,[status(cth)],[cCKB6_L4000]) ).

thf(h1,assumption,
    ~ ( sP10
     => ! [X1: $i > $o] :
          ( ~ ( ( X1 @ c1 )
             => ~ ! [X2: $i] :
                    ( ( X1 @ X2 )
                   => ( X1 @ ( s @ X2 ) ) ) )
         => ( X1 @ ( s @ ( s @ eigen__0 ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h2,assumption,
    sP10,
    introduced(assumption,[]) ).

thf(h3,assumption,
    ~ ! [X1: $i > $o] :
        ( ~ ( ( X1 @ c1 )
           => ~ ! [X2: $i] :
                  ( ( X1 @ X2 )
                 => ( X1 @ ( s @ X2 ) ) ) )
       => ( X1 @ ( s @ ( s @ eigen__0 ) ) ) ),
    introduced(assumption,[]) ).

thf(h4,assumption,
    ~ ( ~ sP2
     => sP8 ),
    introduced(assumption,[]) ).

thf(h5,assumption,
    ~ sP2,
    introduced(assumption,[]) ).

thf(h6,assumption,
    ~ sP8,
    introduced(assumption,[]) ).

thf(h7,assumption,
    sP7,
    introduced(assumption,[]) ).

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

thf(1,plain,
    ( ~ sP1
    | sP9 ),
    inference(all_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP9
    | ~ sP5
    | sP3 ),
    inference(prop_rule,[status(thm)],]) ).

thf(3,plain,
    ( ~ sP10
    | sP6 ),
    inference(all_rule,[status(thm)],]) ).

thf(4,plain,
    ( ~ sP6
    | sP2
    | sP5 ),
    inference(prop_rule,[status(thm)],]) ).

thf(5,plain,
    ( ~ sP2
    | ~ sP7
    | ~ sP1 ),
    inference(prop_rule,[status(thm)],]) ).

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

thf(7,plain,
    ( ~ sP4
    | ~ sP3
    | sP8 ),
    inference(prop_rule,[status(thm)],]) ).

thf(8,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h7,h8,h5,h6,h4,h2,h3,h1,h0])],[1,2,3,4,5,6,7,h2,h7,h8,h6]) ).

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

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

thf(11,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h2,h3,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__1)],[h3,10,h4]) ).

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

thf(13,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,12,h1]) ).

thf(0,theorem,
    ! [X1: $i] :
      ( ! [X2: $i > $o] :
          ( ~ ( ( X2 @ c1 )
             => ~ ! [X3: $i] :
                    ( ( X2 @ X3 )
                   => ( X2 @ ( s @ X3 ) ) ) )
         => ( X2 @ X1 ) )
     => ! [X2: $i > $o] :
          ( ~ ( ( X2 @ c1 )
             => ~ ! [X3: $i] :
                    ( ( X2 @ X3 )
                   => ( X2 @ ( s @ X3 ) ) ) )
         => ( X2 @ ( s @ ( s @ X1 ) ) ) ) ),
    inference(contra,[status(thm),contra(discharge,[h0])],[13,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : PUZ104^5 : TPTP v8.1.0. Bugfixed v5.2.0.
% 0.00/0.12  % Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.33  % Computer : n028.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 600
% 0.13/0.33  % DateTime : Sat May 28 23:11:02 EDT 2022
% 0.13/0.33  % CPUTime  : 
% 0.20/0.35  % SZS status Theorem
% 0.20/0.35  % Mode: mode213
% 0.20/0.35  % Inferences: 6
% 0.20/0.35  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------