TSTP Solution File: SEV221^5 by Lash---1.13

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Lash---1.13
% Problem  : SEV221^5 : 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 : 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
% WCLimit  : 300s
% DateTime : Thu Aug 31 19:33:01 EDT 2023

% Result   : Theorem 0.19s 0.43s
% Output   : Proof 0.19s
% 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__12,type,
    eigen__12: a > $o ).

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

thf(ty_eigen__11,type,
    eigen__11: a > $o ).

thf(ty_eigen__0,type,
    eigen__0: a ).

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

thf(sP2,plain,
    ( sP2
  <=> ! [X1: a > $o] :
        ( ( cW @ X1 )
       => ( ( ^ [X2: a] :
                ~ ( ( cZ @ X2 )
                 => ~ ( eigen__1 @ X2 ) ) )
         != ( ^ [X2: a] :
                ~ ( ( cZ @ X2 )
                 => ~ ( X1 @ X2 ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ( eigen__12 @ eigen__0 ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ( sP1
     => ~ ( eigen__1 @ eigen__0 ) ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> ( ~ ! [X1: a > $o] :
            ( ( cW @ X1 )
           => ~ ( X1 @ eigen__0 ) )
     => ~ sP1 ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
    ( sP6
  <=> ( ~ sP2
     => sP4 ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
    ( sP7
  <=> ( cW @ eigen__12 ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(sP8,plain,
    ( sP8
  <=> ( ( eigen__11 @ eigen__0 )
      = ( ~ ( sP1
           => ~ sP3 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP8])]) ).

thf(sP9,plain,
    ( sP9
  <=> ( sP7
     => ~ sP3 ) ),
    introduced(definition,[new_symbols(definition,[sP9])]) ).

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

thf(sP11,plain,
    ( sP11
  <=> ( eigen__11 @ eigen__0 ) ),
    introduced(definition,[new_symbols(definition,[sP11])]) ).

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

thf(sP13,plain,
    ( sP13
  <=> ! [X1: a > $o] :
        ( ~ ! [X2: a > $o] :
              ( ( cW @ X2 )
             => ( X1
               != ( ^ [X3: a] :
                      ~ ( ( cZ @ X3 )
                       => ~ ( X2 @ X3 ) ) ) ) )
       => ~ ( X1 @ eigen__0 ) ) ),
    introduced(definition,[new_symbols(definition,[sP13])]) ).

thf(sP14,plain,
    ( sP14
  <=> ! [X1: a] :
        ( ( eigen__11 @ X1 )
        = ( ~ ( ( cZ @ X1 )
             => ~ ( eigen__12 @ X1 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP14])]) ).

thf(sP15,plain,
    ( sP15
  <=> ( sP1
     => ~ sP3 ) ),
    introduced(definition,[new_symbols(definition,[sP15])]) ).

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

thf(sP17,plain,
    ( sP17
  <=> ( eigen__11
      = ( ^ [X1: a] :
            ~ ( ( cZ @ X1 )
             => ~ ( eigen__12 @ X1 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP17])]) ).

thf(cTHM61_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)],[cTHM61_pme]) ).

thf(h1,assumption,
    ( ~ sP5 != ~ sP13 ),
    introduced(assumption,[]) ).

thf(h2,assumption,
    ~ sP5,
    introduced(assumption,[]) ).

thf(h3,assumption,
    ~ sP13,
    introduced(assumption,[]) ).

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

thf(h5,assumption,
    sP13,
    introduced(assumption,[]) ).

thf(h6,assumption,
    ~ sP10,
    introduced(assumption,[]) ).

thf(h7,assumption,
    sP1,
    introduced(assumption,[]) ).

thf(h8,assumption,
    ~ ( sP16
     => ~ sP12 ),
    introduced(assumption,[]) ).

thf(h9,assumption,
    sP16,
    introduced(assumption,[]) ).

thf(h10,assumption,
    sP12,
    introduced(assumption,[]) ).

thf(1,plain,
    ( ~ sP2
    | ~ sP16 ),
    inference(all_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP4
    | ~ sP1
    | ~ sP12 ),
    inference(prop_rule,[status(thm)],]) ).

thf(3,plain,
    ( ~ sP6
    | sP2
    | sP4 ),
    inference(prop_rule,[status(thm)],]) ).

thf(4,plain,
    ( ~ sP13
    | sP6 ),
    inference(all_rule,[status(thm)],]) ).

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

thf(6,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h8,h6,h7,h2,h3,h1,h0]),tab_negimp(discharge,[h9,h10])],[h8,5,h9,h10]) ).

thf(7,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h6,h7,h2,h3,h1,h0]),tab_negall(discharge,[h8]),tab_negall(eigenvar,eigen__1)],[h6,6,h8]) ).

thf(8,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h2,h3,h1,h0]),tab_negimp(discharge,[h6,h7])],[h2,7,h6,h7]) ).

thf(h11,assumption,
    ~ ( ~ ! [X1: a > $o] :
            ( ( cW @ X1 )
           => ( eigen__11
             != ( ^ [X2: a] :
                    ~ ( ( cZ @ X2 )
                     => ~ ( X1 @ X2 ) ) ) ) )
     => ~ sP11 ),
    introduced(assumption,[]) ).

thf(h12,assumption,
    ~ ! [X1: a > $o] :
        ( ( cW @ X1 )
       => ( eigen__11
         != ( ^ [X2: a] :
                ~ ( ( cZ @ X2 )
                 => ~ ( X1 @ X2 ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h13,assumption,
    sP11,
    introduced(assumption,[]) ).

thf(h14,assumption,
    ~ ( sP7
     => ~ sP17 ),
    introduced(assumption,[]) ).

thf(h15,assumption,
    sP7,
    introduced(assumption,[]) ).

thf(h16,assumption,
    sP17,
    introduced(assumption,[]) ).

thf(9,plain,
    ( ~ sP9
    | ~ sP7
    | ~ sP3 ),
    inference(prop_rule,[status(thm)],]) ).

thf(10,plain,
    ( ~ sP10
    | sP9 ),
    inference(all_rule,[status(thm)],]) ).

thf(11,plain,
    ( sP15
    | sP3 ),
    inference(prop_rule,[status(thm)],]) ).

thf(12,plain,
    ( sP15
    | sP1 ),
    inference(prop_rule,[status(thm)],]) ).

thf(13,plain,
    ( ~ sP8
    | ~ sP11
    | ~ sP15 ),
    inference(prop_rule,[status(thm)],]) ).

thf(14,plain,
    ( ~ sP14
    | sP8 ),
    inference(all_rule,[status(thm)],]) ).

thf(15,plain,
    ( ~ sP5
    | sP10
    | ~ sP1 ),
    inference(prop_rule,[status(thm)],]) ).

thf(16,plain,
    ( ~ sP17
    | sP14 ),
    inference(prop_rule,[status(thm)],]) ).

thf(17,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h15,h16,h14,h12,h13,h11,h4,h5,h1,h0])],[9,10,11,12,13,14,15,16,h4,h15,h16,h13]) ).

thf(18,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h14,h12,h13,h11,h4,h5,h1,h0]),tab_negimp(discharge,[h15,h16])],[h14,17,h15,h16]) ).

thf(19,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h12,h13,h11,h4,h5,h1,h0]),tab_negall(discharge,[h14]),tab_negall(eigenvar,eigen__12)],[h12,18,h14]) ).

thf(20,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h11,h4,h5,h1,h0]),tab_negimp(discharge,[h12,h13])],[h11,19,h12,h13]) ).

thf(21,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h4,h5,h1,h0]),tab_negall(discharge,[h11]),tab_negall(eigenvar,eigen__11)],[h5,20,h11]) ).

thf(22,plain,
    $false,
    inference(tab_be,[status(thm),assumptions([h1,h0]),tab_be(discharge,[h2,h3]),tab_be(discharge,[h4,h5])],[h1,8,21,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
% 0.00/0.12  % Problem  : SEV221^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.12  % Command  : lash -P picomus -M modes -p tstp -t %d %s
% 0.12/0.34  % Computer : n014.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 300
% 0.12/0.34  % DateTime : Thu Aug 24 03:04:19 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 0.19/0.43  % SZS status Theorem
% 0.19/0.43  % Mode: cade22grackle2xfee4
% 0.19/0.43  % Steps: 581
% 0.19/0.43  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------