TSTP Solution File: SYN057^5 by Lash---1.13

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%------------------------------------------------------------------------------
% File     : Lash---1.13
% Problem  : SYN057^5 : 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 : n009.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 : Fri Sep  1 03:19:41 EDT 2023

% Result   : Theorem 0.12s 0.39s
% Output   : Proof 0.12s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_cJ,type,
    cJ: $i > $o ).

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

thf(ty_cF,type,
    cF: $i > $o ).

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

thf(ty_cH,type,
    cH: $i > $o ).

thf(ty_cI,type,
    cI: $i > $o ).

thf(ty_cG,type,
    cG: $i > $o ).

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

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

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

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

thf(sP5,plain,
    ( sP5
  <=> ! [X1: $i] :
        ( ( cF @ X1 )
       => ( cH @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

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

thf(sP7,plain,
    ( sP7
  <=> ( sP1
     => ~ ( cI @ eigen__1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(sP8,plain,
    ( sP8
  <=> ( ~ sP7
     => ( cF @ eigen__1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP8])]) ).

thf(sP9,plain,
    ( sP9
  <=> ! [X1: $i] :
        ( ( cI @ X1 )
       => ~ ( cH @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP9])]) ).

thf(sP10,plain,
    ( sP10
  <=> ( sP3
     => ( cH @ eigen__0 ) ) ),
    introduced(definition,[new_symbols(definition,[sP10])]) ).

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

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

thf(sP13,plain,
    ( sP13
  <=> ( ~ ! [X1: $i] :
            ( ( cH @ X1 )
           => ( cG @ X1 ) )
     => sP9 ) ),
    introduced(definition,[new_symbols(definition,[sP13])]) ).

thf(sP14,plain,
    ( sP14
  <=> ( cI @ eigen__1 ) ),
    introduced(definition,[new_symbols(definition,[sP14])]) ).

thf(sP15,plain,
    ( sP15
  <=> ! [X1: $i] :
        ( ( cH @ X1 )
       => ( cG @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP15])]) ).

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

thf(sP17,plain,
    ( sP17
  <=> ( cH @ eigen__1 ) ),
    introduced(definition,[new_symbols(definition,[sP17])]) ).

thf(sP18,plain,
    ( sP18
  <=> ! [X1: $i] :
        ( ~ ( ( cJ @ X1 )
           => ~ ( cI @ X1 ) )
       => ( cF @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP18])]) ).

thf(cPELL27,conjecture,
    ( ~ ( ~ ( ~ ( ~ ! [X1: $i] :
                      ( ( cF @ X1 )
                     => ( cG @ X1 ) )
               => ~ sP5 )
           => ~ sP18 )
       => ~ sP13 )
   => ! [X1: $i] :
        ( ( cJ @ X1 )
       => ~ ( cI @ X1 ) ) ) ).

thf(h0,negated_conjecture,
    ~ ( ~ ( ~ ( ~ ( ~ ! [X1: $i] :
                        ( ( cF @ X1 )
                       => ( cG @ X1 ) )
                 => ~ sP5 )
             => ~ sP18 )
         => ~ sP13 )
     => ! [X1: $i] :
          ( ( cJ @ X1 )
         => ~ ( cI @ X1 ) ) ),
    inference(assume_negation,[status(cth)],[cPELL27]) ).

thf(h1,assumption,
    ~ ( ~ ( ~ ( ~ ! [X1: $i] :
                    ( ( cF @ X1 )
                   => ( cG @ X1 ) )
             => ~ sP5 )
         => ~ sP18 )
     => ~ sP13 ),
    introduced(assumption,[]) ).

thf(h2,assumption,
    ~ ! [X1: $i] :
        ( ( cJ @ X1 )
       => ~ ( cI @ X1 ) ),
    introduced(assumption,[]) ).

thf(h3,assumption,
    ~ ( ~ ( ~ ! [X1: $i] :
                ( ( cF @ X1 )
               => ( cG @ X1 ) )
         => ~ sP5 )
     => ~ sP18 ),
    introduced(assumption,[]) ).

thf(h4,assumption,
    sP13,
    introduced(assumption,[]) ).

thf(h5,assumption,
    ~ ( ~ ! [X1: $i] :
            ( ( cF @ X1 )
           => ( cG @ X1 ) )
     => ~ sP5 ),
    introduced(assumption,[]) ).

thf(h6,assumption,
    sP18,
    introduced(assumption,[]) ).

thf(h7,assumption,
    ~ ! [X1: $i] :
        ( ( cF @ X1 )
       => ( cG @ X1 ) ),
    introduced(assumption,[]) ).

thf(h8,assumption,
    sP5,
    introduced(assumption,[]) ).

thf(h9,assumption,
    ~ ( sP3
     => sP6 ),
    introduced(assumption,[]) ).

thf(h10,assumption,
    sP3,
    introduced(assumption,[]) ).

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

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

thf(h13,assumption,
    sP1,
    introduced(assumption,[]) ).

thf(h14,assumption,
    sP14,
    introduced(assumption,[]) ).

thf(1,plain,
    ( ~ sP10
    | ~ sP3
    | sP12 ),
    inference(prop_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP2
    | ~ sP12
    | sP6 ),
    inference(prop_rule,[status(thm)],]) ).

thf(3,plain,
    ( ~ sP5
    | sP10 ),
    inference(all_rule,[status(thm)],]) ).

thf(4,plain,
    ( ~ sP15
    | sP2 ),
    inference(all_rule,[status(thm)],]) ).

thf(5,plain,
    ( ~ sP7
    | ~ sP1
    | ~ sP14 ),
    inference(prop_rule,[status(thm)],]) ).

thf(6,plain,
    ( ~ sP8
    | sP7
    | sP11 ),
    inference(prop_rule,[status(thm)],]) ).

thf(7,plain,
    ( ~ sP16
    | ~ sP11
    | sP17 ),
    inference(prop_rule,[status(thm)],]) ).

thf(8,plain,
    ( ~ sP4
    | ~ sP14
    | ~ sP17 ),
    inference(prop_rule,[status(thm)],]) ).

thf(9,plain,
    ( ~ sP18
    | sP8 ),
    inference(all_rule,[status(thm)],]) ).

thf(10,plain,
    ( ~ sP5
    | sP16 ),
    inference(all_rule,[status(thm)],]) ).

thf(11,plain,
    ( ~ sP9
    | sP4 ),
    inference(all_rule,[status(thm)],]) ).

thf(12,plain,
    ( ~ sP13
    | sP15
    | sP9 ),
    inference(prop_rule,[status(thm)],]) ).

thf(13,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h13,h14,h12,h10,h11,h9,h7,h8,h5,h6,h3,h4,h1,h2,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,h10,h11,h8,h6,h4,h13,h14]) ).

thf(14,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h12,h10,h11,h9,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h13,h14])],[h12,13,h13,h14]) ).

thf(15,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h10,h11,h9,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h12]),tab_negall(eigenvar,eigen__1)],[h2,14,h12]) ).

thf(16,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h9,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h10,h11])],[h9,15,h10,h11]) ).

thf(17,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h9]),tab_negall(eigenvar,eigen__0)],[h7,16,h9]) ).

thf(18,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h7,h8])],[h5,17,h7,h8]) ).

thf(19,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h3,h4,h1,h2,h0]),tab_negimp(discharge,[h5,h6])],[h3,18,h5,h6]) ).

thf(20,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h1,h2,h0]),tab_negimp(discharge,[h3,h4])],[h1,19,h3,h4]) ).

thf(21,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,20,h1,h2]) ).

thf(0,theorem,
    ( ~ ( ~ ( ~ ( ~ ! [X1: $i] :
                      ( ( cF @ X1 )
                     => ( cG @ X1 ) )
               => ~ sP5 )
           => ~ sP18 )
       => ~ sP13 )
   => ! [X1: $i] :
        ( ( cJ @ X1 )
       => ~ ( cI @ X1 ) ) ),
    inference(contra,[status(thm),contra(discharge,[h0])],[21,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : SYN057^5 : TPTP v8.1.2. Released v4.0.0.
% 0.06/0.12  % Command  : lash -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33  % Computer : n009.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  : 300
% 0.12/0.33  % DateTime : Sat Aug 26 21:09:20 EDT 2023
% 0.12/0.33  % CPUTime  : 
% 0.12/0.39  % SZS status Theorem
% 0.12/0.39  % Mode: cade22grackle2xfee4
% 0.12/0.39  % Steps: 40
% 0.12/0.39  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------