TSTP Solution File: SEV229^5 by Satallax---3.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Satallax---3.5
% Problem  : SEV229^5 : 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 : 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 : Tue Jul 19 18:05:28 EDT 2022

% Result   : Theorem 0.12s 0.37s
% 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(ty_eigen__3,type,
    eigen__3: a ).

thf(ty_cE,type,
    cE: a > $o ).

thf(ty_cD,type,
    cD: a > $o ).

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

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

thf(sP3,plain,
    ( sP3
  <=> ( cE @ eigen__2 ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ( ( eigen__0 @ eigen__2 )
     => ~ ( ( cD @ eigen__2 )
         => ~ sP3 ) ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> ( sP2
     => ~ ( ( cD @ eigen__1 )
         => ~ ( cE @ eigen__1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

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

thf(sP7,plain,
    ( sP7
  <=> ! [X1: a] :
        ( ( eigen__0 @ X1 )
       => ( cD @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(sP8,plain,
    ( sP8
  <=> ( ( cD @ eigen__2 )
     => ~ sP3 ) ),
    introduced(definition,[new_symbols(definition,[sP8])]) ).

thf(sP9,plain,
    ( sP9
  <=> ( cE @ eigen__3 ) ),
    introduced(definition,[new_symbols(definition,[sP9])]) ).

thf(sP10,plain,
    ( sP10
  <=> ! [X1: a] :
        ( ( eigen__0 @ X1 )
       => ~ ( ( cD @ X1 )
           => ~ ( cE @ X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP10])]) ).

thf(sP11,plain,
    ( sP11
  <=> ( cD @ eigen__1 ) ),
    introduced(definition,[new_symbols(definition,[sP11])]) ).

thf(sP12,plain,
    ( sP12
  <=> ( eigen__0 @ eigen__2 ) ),
    introduced(definition,[new_symbols(definition,[sP12])]) ).

thf(sP13,plain,
    ( sP13
  <=> ! [X1: a] :
        ( ( eigen__0 @ X1 )
       => ( cE @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP13])]) ).

thf(sP14,plain,
    ( sP14
  <=> ( eigen__0 @ eigen__3 ) ),
    introduced(definition,[new_symbols(definition,[sP14])]) ).

thf(sP15,plain,
    ( sP15
  <=> ( cD @ eigen__3 ) ),
    introduced(definition,[new_symbols(definition,[sP15])]) ).

thf(sP16,plain,
    ( sP16
  <=> ( sP11
     => ~ ( cE @ eigen__1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP16])]) ).

thf(cX5209_pme,conjecture,
    ( ( ^ [X1: a > $o] :
        ! [X2: a] :
          ( ( X1 @ X2 )
         => ~ ( ( cD @ X2 )
             => ~ ( cE @ X2 ) ) ) )
    = ( ^ [X1: a > $o] :
          ~ ( ! [X2: a] :
                ( ( X1 @ X2 )
               => ( cD @ X2 ) )
           => ~ ! [X2: a] :
                  ( ( X1 @ X2 )
                 => ( cE @ X2 ) ) ) ) ) ).

thf(h0,negated_conjecture,
    ( ^ [X1: a > $o] :
      ! [X2: a] :
        ( ( X1 @ X2 )
       => ~ ( ( cD @ X2 )
           => ~ ( cE @ X2 ) ) ) )
 != ( ^ [X1: a > $o] :
        ~ ( ! [X2: a] :
              ( ( X1 @ X2 )
             => ( cD @ X2 ) )
         => ~ ! [X2: a] :
                ( ( X1 @ X2 )
               => ( cE @ X2 ) ) ) ),
    inference(assume_negation,[status(cth)],[cX5209_pme]) ).

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

thf(h2,assumption,
    sP10
 != ( ~ ( sP7
       => ~ sP13 ) ),
    introduced(assumption,[]) ).

thf(h3,assumption,
    sP10,
    introduced(assumption,[]) ).

thf(h4,assumption,
    ~ ( sP7
     => ~ sP13 ),
    introduced(assumption,[]) ).

thf(h5,assumption,
    ~ sP10,
    introduced(assumption,[]) ).

thf(h6,assumption,
    ( sP7
   => ~ sP13 ),
    introduced(assumption,[]) ).

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

thf(h8,assumption,
    ~ sP13,
    introduced(assumption,[]) ).

thf(h9,assumption,
    ~ ( sP2
     => sP11 ),
    introduced(assumption,[]) ).

thf(h10,assumption,
    sP2,
    introduced(assumption,[]) ).

thf(h11,assumption,
    ~ sP11,
    introduced(assumption,[]) ).

thf(1,plain,
    ( sP16
    | sP11 ),
    inference(prop_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP10
    | sP5 ),
    inference(all_rule,[status(thm)],]) ).

thf(3,plain,
    ( ~ sP5
    | ~ sP2
    | ~ sP16 ),
    inference(prop_rule,[status(thm)],]) ).

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

thf(5,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h9,h7,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h10,h11])],[h9,4,h10,h11]) ).

thf(6,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h7,h3,h4,h2,h1,h0]),tab_negall(discharge,[h9]),tab_negall(eigenvar,eigen__1)],[h7,5,h9]) ).

thf(h12,assumption,
    ~ ( sP12
     => sP3 ),
    introduced(assumption,[]) ).

thf(h13,assumption,
    sP12,
    introduced(assumption,[]) ).

thf(h14,assumption,
    ~ sP3,
    introduced(assumption,[]) ).

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

thf(8,plain,
    ( ~ sP10
    | sP4 ),
    inference(all_rule,[status(thm)],]) ).

thf(9,plain,
    ( ~ sP4
    | ~ sP12
    | ~ sP8 ),
    inference(prop_rule,[status(thm)],]) ).

thf(10,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h13,h14,h12,h8,h3,h4,h2,h1,h0])],[7,8,9,h3,h13,h14]) ).

thf(11,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h12,h8,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h13,h14])],[h12,10,h13,h14]) ).

thf(12,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h8,h3,h4,h2,h1,h0]),tab_negall(discharge,[h12]),tab_negall(eigenvar,eigen__2)],[h8,11,h12]) ).

thf(13,plain,
    $false,
    inference(tab_imp,[status(thm),assumptions([h3,h4,h2,h1,h0]),tab_imp(discharge,[h7]),tab_imp(discharge,[h8])],[h4,6,12,h7,h8]) ).

thf(h15,assumption,
    ~ ( sP14
     => ~ ( sP15
         => ~ sP9 ) ),
    introduced(assumption,[]) ).

thf(h16,assumption,
    sP14,
    introduced(assumption,[]) ).

thf(h17,assumption,
    ( sP15
   => ~ sP9 ),
    introduced(assumption,[]) ).

thf(h18,assumption,
    ~ sP15,
    introduced(assumption,[]) ).

thf(h19,assumption,
    ~ sP9,
    introduced(assumption,[]) ).

thf(h20,assumption,
    sP7,
    introduced(assumption,[]) ).

thf(h21,assumption,
    sP13,
    introduced(assumption,[]) ).

thf(14,plain,
    ( ~ sP7
    | sP1 ),
    inference(all_rule,[status(thm)],]) ).

thf(15,plain,
    ( ~ sP1
    | ~ sP14
    | sP15 ),
    inference(prop_rule,[status(thm)],]) ).

thf(16,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h20,h21,h18,h16,h17,h15,h5,h6,h2,h1,h0])],[14,15,h16,h18,h20]) ).

thf(17,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h18,h16,h17,h15,h5,h6,h2,h1,h0]),tab_negimp(discharge,[h20,h21])],[h6,16,h20,h21]) ).

thf(18,plain,
    ( ~ sP13
    | sP6 ),
    inference(all_rule,[status(thm)],]) ).

thf(19,plain,
    ( ~ sP6
    | ~ sP14
    | sP9 ),
    inference(prop_rule,[status(thm)],]) ).

thf(20,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h20,h21,h19,h16,h17,h15,h5,h6,h2,h1,h0])],[18,19,h16,h19,h21]) ).

thf(21,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h19,h16,h17,h15,h5,h6,h2,h1,h0]),tab_negimp(discharge,[h20,h21])],[h6,20,h20,h21]) ).

thf(22,plain,
    $false,
    inference(tab_imp,[status(thm),assumptions([h16,h17,h15,h5,h6,h2,h1,h0]),tab_imp(discharge,[h18]),tab_imp(discharge,[h19])],[h17,17,21,h18,h19]) ).

thf(23,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h15,h5,h6,h2,h1,h0]),tab_negimp(discharge,[h16,h17])],[h15,22,h16,h17]) ).

thf(24,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h5,h6,h2,h1,h0]),tab_negall(discharge,[h15]),tab_negall(eigenvar,eigen__3)],[h5,23,h15]) ).

thf(25,plain,
    $false,
    inference(tab_be,[status(thm),assumptions([h2,h1,h0]),tab_be(discharge,[h3,h4]),tab_be(discharge,[h5,h6])],[h2,13,24,h3,h4,h5,h6]) ).

thf(26,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__0)],[h1,25,h2]) ).

thf(27,plain,
    $false,
    inference(tab_fe,[status(thm),assumptions([h0]),tab_fe(discharge,[h1])],[h0,26,h1]) ).

thf(0,theorem,
    ( ( ^ [X1: a > $o] :
        ! [X2: a] :
          ( ( X1 @ X2 )
         => ~ ( ( cD @ X2 )
             => ~ ( cE @ X2 ) ) ) )
    = ( ^ [X1: a > $o] :
          ~ ( ! [X2: a] :
                ( ( X1 @ X2 )
               => ( cD @ X2 ) )
           => ~ ! [X2: a] :
                  ( ( X1 @ X2 )
                 => ( cE @ X2 ) ) ) ) ),
    inference(contra,[status(thm),contra(discharge,[h0])],[27,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : SEV229^5 : 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 : n028.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 : Tue Jun 28 14:10:27 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.12/0.37  % SZS status Theorem
% 0.12/0.37  % Mode: mode213
% 0.12/0.37  % Inferences: 15
% 0.12/0.37  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------