TSTP Solution File: SEV222^5 by Lash---1.13

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Lash---1.13
% Problem  : SEV222^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : lash -P picomus -M modes -p tstp -t %d %s

% Computer : n003.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  : 300s
% DateTime : Thu Aug 31 19:33:01 EDT 2023

% Result   : Theorem 0.20s 0.55s
% Output   : Proof 0.20s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

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

thf(ty_cZ,type,
    cZ: a > $o ).

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

thf(ty_eigen__2,type,
    eigen__2: a > $o ).

thf(ty_eigen__5,type,
    eigen__5: a > $o ).

thf(ty_cW,type,
    cW: ( a > $o ) > $o ).

thf(ty_eigen__0,type,
    eigen__0: a ).

thf(sP1,plain,
    ( sP1
  <=> ( eigen__1
      = ( ^ [X1: a] :
            ( ~ ( cZ @ X1 )
           => ( eigen__2 @ X1 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

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

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

thf(sP4,plain,
    ( sP4
  <=> ! [X1: a] :
        ( ( eigen__1 @ X1 )
        = ( ~ ( cZ @ X1 )
         => ( eigen__2 @ X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> ! [X1: a > $o] :
        ( ( cW @ X1 )
       => ( ( ^ [X2: a] :
                ( ~ ( cZ @ X2 )
               => ( eigen__5 @ X2 ) ) )
         != ( ^ [X2: a] :
                ( ~ ( cZ @ X2 )
               => ( X1 @ X2 ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
    ( sP6
  <=> ( ~ sP3
     => ( eigen__5 @ eigen__0 ) ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

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

thf(sP8,plain,
    ( sP8
  <=> ( ~ sP3
     => ( eigen__2 @ eigen__0 ) ) ),
    introduced(definition,[new_symbols(definition,[sP8])]) ).

thf(sP9,plain,
    ( sP9
  <=> ( cW @ eigen__5 ) ),
    introduced(definition,[new_symbols(definition,[sP9])]) ).

thf(sP10,plain,
    ( sP10
  <=> ( ( eigen__1 @ eigen__0 )
      = sP8 ) ),
    introduced(definition,[new_symbols(definition,[sP10])]) ).

thf(sP11,plain,
    ( sP11
  <=> ( cW @ eigen__2 ) ),
    introduced(definition,[new_symbols(definition,[sP11])]) ).

thf(sP12,plain,
    ( sP12
  <=> ( eigen__1 @ eigen__0 ) ),
    introduced(definition,[new_symbols(definition,[sP12])]) ).

thf(sP13,plain,
    ( sP13
  <=> ( eigen__5 @ eigen__0 ) ),
    introduced(definition,[new_symbols(definition,[sP13])]) ).

thf(sP14,plain,
    ( sP14
  <=> ( ~ sP5
     => sP6 ) ),
    introduced(definition,[new_symbols(definition,[sP14])]) ).

thf(sP15,plain,
    ( sP15
  <=> ! [X1: a > $o] :
        ( ~ ! [X2: a > $o] :
              ( ( cW @ X2 )
             => ( X1
               != ( ^ [X3: a] :
                      ( ~ ( cZ @ X3 )
                     => ( X2 @ X3 ) ) ) ) )
       => ( X1 @ eigen__0 ) ) ),
    introduced(definition,[new_symbols(definition,[sP15])]) ).

thf(sP16,plain,
    ( sP16
  <=> ( ~ sP7
     => sP3 ) ),
    introduced(definition,[new_symbols(definition,[sP16])]) ).

thf(sP17,plain,
    ( sP17
  <=> ( eigen__2 @ eigen__0 ) ),
    introduced(definition,[new_symbols(definition,[sP17])]) ).

thf(cTHM60_pme,conjecture,
    ! [X1: a] :
      ( ( ~ ! [X2: a > $o] :
              ( ( cW @ X2 )
             => ( X2 @ X1 ) )
       => ( cZ @ X1 ) )
      = ( ! [X2: a > $o] :
            ( ~ ! [X3: a > $o] :
                  ( ( cW @ X3 )
                 => ( X2
                   != ( ^ [X4: a] :
                          ( ~ ( cZ @ X4 )
                         => ( X3 @ X4 ) ) ) ) )
           => ( X2 @ X1 ) ) ) ) ).

thf(h0,negated_conjecture,
    ~ ! [X1: a] :
        ( ( ~ ! [X2: a > $o] :
                ( ( cW @ X2 )
               => ( X2 @ X1 ) )
         => ( cZ @ X1 ) )
        = ( ! [X2: a > $o] :
              ( ~ ! [X3: a > $o] :
                    ( ( cW @ X3 )
                   => ( X2
                     != ( ^ [X4: a] :
                            ( ~ ( cZ @ X4 )
                           => ( X3 @ X4 ) ) ) ) )
             => ( X2 @ X1 ) ) ) ),
    inference(assume_negation,[status(cth)],[cTHM60_pme]) ).

thf(h1,assumption,
    sP16 != sP15,
    introduced(assumption,[]) ).

thf(h2,assumption,
    sP16,
    introduced(assumption,[]) ).

thf(h3,assumption,
    sP15,
    introduced(assumption,[]) ).

thf(h4,assumption,
    ~ sP16,
    introduced(assumption,[]) ).

thf(h5,assumption,
    ~ sP15,
    introduced(assumption,[]) ).

thf(h6,assumption,
    ~ ( ~ ! [X1: a > $o] :
            ( ( cW @ X1 )
           => ( eigen__1
             != ( ^ [X2: a] :
                    ( ~ ( cZ @ X2 )
                   => ( X1 @ X2 ) ) ) ) )
     => sP12 ),
    introduced(assumption,[]) ).

thf(h7,assumption,
    ~ ! [X1: a > $o] :
        ( ( cW @ X1 )
       => ( eigen__1
         != ( ^ [X2: a] :
                ( ~ ( cZ @ X2 )
               => ( X1 @ X2 ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h8,assumption,
    ~ sP12,
    introduced(assumption,[]) ).

thf(h9,assumption,
    ~ ( sP11
     => ~ sP1 ),
    introduced(assumption,[]) ).

thf(h10,assumption,
    sP11,
    introduced(assumption,[]) ).

thf(h11,assumption,
    sP1,
    introduced(assumption,[]) ).

thf(1,plain,
    ( ~ sP2
    | ~ sP11
    | sP17 ),
    inference(prop_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP7
    | sP2 ),
    inference(all_rule,[status(thm)],]) ).

thf(3,plain,
    ( sP8
    | ~ sP17 ),
    inference(prop_rule,[status(thm)],]) ).

thf(4,plain,
    ( sP8
    | ~ sP3 ),
    inference(prop_rule,[status(thm)],]) ).

thf(5,plain,
    ( ~ sP10
    | sP12
    | ~ sP8 ),
    inference(prop_rule,[status(thm)],]) ).

thf(6,plain,
    ( ~ sP4
    | sP10 ),
    inference(all_rule,[status(thm)],]) ).

thf(7,plain,
    ( ~ sP16
    | sP7
    | sP3 ),
    inference(prop_rule,[status(thm)],]) ).

thf(8,plain,
    ( ~ sP1
    | sP4 ),
    inference(prop_rule,[status(thm)],]) ).

thf(9,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h10,h11,h9,h7,h8,h6,h2,h3,h1,h0])],[1,2,3,4,5,6,7,8,h2,h10,h11,h8]) ).

thf(10,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h9,h7,h8,h6,h2,h3,h1,h0]),tab_negimp(discharge,[h10,h11])],[h9,9,h10,h11]) ).

thf(11,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h7,h8,h6,h2,h3,h1,h0]),tab_negall(discharge,[h9]),tab_negall(eigenvar,eigen__2)],[h7,10,h9]) ).

thf(12,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h6,h2,h3,h1,h0]),tab_negimp(discharge,[h7,h8])],[h6,11,h7,h8]) ).

thf(13,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h2,h3,h1,h0]),tab_negall(discharge,[h6]),tab_negall(eigenvar,eigen__1)],[h3,12,h6]) ).

thf(h12,assumption,
    ~ sP7,
    introduced(assumption,[]) ).

thf(h13,assumption,
    ~ sP3,
    introduced(assumption,[]) ).

thf(h14,assumption,
    ~ ( sP9
     => sP13 ),
    introduced(assumption,[]) ).

thf(h15,assumption,
    sP9,
    introduced(assumption,[]) ).

thf(h16,assumption,
    ~ sP13,
    introduced(assumption,[]) ).

thf(14,plain,
    ( ~ sP5
    | ~ sP9 ),
    inference(all_rule,[status(thm)],]) ).

thf(15,plain,
    ( ~ sP6
    | sP3
    | sP13 ),
    inference(prop_rule,[status(thm)],]) ).

thf(16,plain,
    ( ~ sP14
    | sP5
    | sP6 ),
    inference(prop_rule,[status(thm)],]) ).

thf(17,plain,
    ( ~ sP15
    | sP14 ),
    inference(all_rule,[status(thm)],]) ).

thf(18,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h15,h16,h14,h12,h13,h4,h5,h1,h0])],[14,15,16,17,h15,h16,h13,h5]) ).

thf(19,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h14,h12,h13,h4,h5,h1,h0]),tab_negimp(discharge,[h15,h16])],[h14,18,h15,h16]) ).

thf(20,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h12,h13,h4,h5,h1,h0]),tab_negall(discharge,[h14]),tab_negall(eigenvar,eigen__5)],[h12,19,h14]) ).

thf(21,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h4,h5,h1,h0]),tab_negimp(discharge,[h12,h13])],[h4,20,h12,h13]) ).

thf(22,plain,
    $false,
    inference(tab_be,[status(thm),assumptions([h1,h0]),tab_be(discharge,[h2,h3]),tab_be(discharge,[h4,h5])],[h1,13,21,h2,h3,h4,h5]) ).

thf(23,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,22,h1]) ).

thf(0,theorem,
    ! [X1: a] :
      ( ( ~ ! [X2: a > $o] :
              ( ( cW @ X2 )
             => ( X2 @ X1 ) )
       => ( cZ @ X1 ) )
      = ( ! [X2: a > $o] :
            ( ~ ! [X3: a > $o] :
                  ( ( cW @ X3 )
                 => ( X2
                   != ( ^ [X4: a] :
                          ( ~ ( cZ @ X4 )
                         => ( X3 @ X4 ) ) ) ) )
           => ( X2 @ X1 ) ) ) ),
    inference(contra,[status(thm),contra(discharge,[h0])],[23,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SEV222^5 : TPTP v8.1.2. Released v4.0.0.
% 0.13/0.13  % Command  : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.35  % Computer : n003.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Thu Aug 24 02:35:22 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.20/0.55  % SZS status Theorem
% 0.20/0.55  % Mode: cade22grackle2xfee4
% 0.20/0.55  % Steps: 3393
% 0.20/0.55  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------