%------------------------------------------------------------------------------
% File     : Satallax---3.5
% Problem  : SYO899^8 : TPTP v8.1.0. Released v8.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : satallax -E eprover-ho -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  : 600s
% DateTime : Thu Jul 21 19:35:14 EDT 2022

% Result   : Theorem 0.12s 0.36s
% Output   : Proof 0.12s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_mworld,type,
    mworld: $tType ).

thf(ty_p,type,
    p: mworld > $o ).

thf(ty_q,type,
    q: mworld > $o ).

thf(ty_eigen__0,type,
    eigen__0: mworld ).

thf(ty_mrel,type,
    mrel: mworld > mworld > $o ).

thf(ty_mactual,type,
    mactual: mworld ).

thf(sP1,plain,
    ( sP1
  <=> ! [X1: mworld] :
        ( ( mrel @ mactual @ X1 )
       => ( p @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ! [X1: mworld] :
        ( ( mrel @ eigen__0 @ X1 )
       => ( q @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

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

thf(sP4,plain,
    ( sP4
  <=> ! [X1: mworld] : ( mrel @ X1 @ X1 ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

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

thf(sP6,plain,
    ( sP6
  <=> ( ( mrel @ mactual @ eigen__0 )
     => ~ ( q @ eigen__0 ) ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
    ( sP7
  <=> ( sP3
     => ( q @ eigen__0 ) ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

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

thf(sP9,plain,
    ( sP9
  <=> ! [X1: mworld] :
        ( ( mrel @ mactual @ X1 )
       => ~ ( q @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP9])]) ).

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

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

thf(def_mlocal,definition,
    ( mlocal
    = ( ^ [X1: mworld > $o] : ( X1 @ mactual ) ) ) ).

thf(def_mnot,definition,
    ( mnot
    = ( ^ [X1: mworld > $o,X2: mworld] :
          ~ ( X1 @ X2 ) ) ) ).

thf(def_mand,definition,
    ( mand
    = ( ^ [X1: mworld > $o,X2: mworld > $o,X3: mworld] :
          ~ ( ( X1 @ X3 )
           => ~ ( X2 @ X3 ) ) ) ) ).

thf(def_mor,definition,
    ( mor
    = ( ^ [X1: mworld > $o,X2: mworld > $o,X3: mworld] :
          ( ~ ( X1 @ X3 )
         => ( X2 @ X3 ) ) ) ) ).

thf(def_mimplies,definition,
    ( mimplies
    = ( ^ [X1: mworld > $o,X2: mworld > $o,X3: mworld] :
          ( ( X1 @ X3 )
         => ( X2 @ X3 ) ) ) ) ).

thf(def_mequiv,definition,
    ( mequiv
    = ( ^ [X1: mworld > $o,X2: mworld > $o,X3: mworld] :
          ( ( X1 @ X3 )
          = ( X2 @ X3 ) ) ) ) ).

thf(def_mbox,definition,
    ( mbox
    = ( ^ [X1: mworld > $o,X2: mworld] :
        ! [X3: mworld] :
          ( ( mrel @ X2 @ X3 )
         => ( X1 @ X3 ) ) ) ) ).

thf(def_mdia,definition,
    ( mdia
    = ( ^ [X1: mworld > $o,X2: mworld] :
          ~ ! [X3: mworld] :
              ( ( mrel @ X2 @ X3 )
             => ~ ( X1 @ X3 ) ) ) ) ).

thf(con,conjecture,
    ( ~ ! [X1: mworld] :
          ( ( mrel @ mactual @ X1 )
         => ~ ( ( p @ X1 )
             => ! [X2: mworld] :
                  ( ( mrel @ X1 @ X2 )
                 => ( q @ X2 ) ) ) )
   => ( sP1
     => ~ sP9 ) ) ).

thf(h0,negated_conjecture,
    ~ ( ~ ! [X1: mworld] :
            ( ( mrel @ mactual @ X1 )
           => ~ ( ( p @ X1 )
               => ! [X2: mworld] :
                    ( ( mrel @ X1 @ X2 )
                   => ( q @ X2 ) ) ) )
     => ( sP1
       => ~ sP9 ) ),
    inference(assume_negation,[status(cth)],[con]) ).

thf(h1,assumption,
    ~ ! [X1: mworld] :
        ( ( mrel @ mactual @ X1 )
       => ~ ( ( p @ X1 )
           => ! [X2: mworld] :
                ( ( mrel @ X1 @ X2 )
               => ( q @ X2 ) ) ) ),
    introduced(assumption,[]) ).

thf(h2,assumption,
    ~ ( sP1
     => ~ sP9 ),
    introduced(assumption,[]) ).

thf(h3,assumption,
    ~ ( sP11
     => ~ ( sP8
         => sP2 ) ),
    introduced(assumption,[]) ).

thf(h4,assumption,
    sP11,
    introduced(assumption,[]) ).

thf(h5,assumption,
    ( sP8
   => sP2 ),
    introduced(assumption,[]) ).

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

thf(h7,assumption,
    sP2,
    introduced(assumption,[]) ).

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

thf(h9,assumption,
    sP9,
    introduced(assumption,[]) ).

thf(1,plain,
    ( ~ sP1
    | sP5 ),
    inference(all_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP5
    | ~ sP11
    | sP8 ),
    inference(prop_rule,[status(thm)],]) ).

thf(3,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h8,h9,h6,h4,h5,h3,h1,h2,h0])],[1,2,h4,h6,h8]) ).

thf(4,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h6,h4,h5,h3,h1,h2,h0]),tab_negimp(discharge,[h8,h9])],[h2,3,h8,h9]) ).

thf(5,plain,
    ( ~ sP4
    | sP3 ),
    inference(all_rule,[status(thm)],]) ).

thf(6,plain,
    ( ~ sP2
    | sP7 ),
    inference(all_rule,[status(thm)],]) ).

thf(7,plain,
    ( ~ sP7
    | ~ sP3
    | sP10 ),
    inference(prop_rule,[status(thm)],]) ).

thf(8,plain,
    ( ~ sP9
    | sP6 ),
    inference(all_rule,[status(thm)],]) ).

thf(9,plain,
    ( ~ sP6
    | ~ sP11
    | ~ sP10 ),
    inference(prop_rule,[status(thm)],]) ).

thf(mrel_reflexive,axiom,
    sP4 ).

thf(10,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h8,h9,h7,h4,h5,h3,h1,h2,h0])],[5,6,7,8,9,mrel_reflexive,h4,h7,h9]) ).

thf(11,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h7,h4,h5,h3,h1,h2,h0]),tab_negimp(discharge,[h8,h9])],[h2,10,h8,h9]) ).

thf(12,plain,
    $false,
    inference(tab_imp,[status(thm),assumptions([h4,h5,h3,h1,h2,h0]),tab_imp(discharge,[h6]),tab_imp(discharge,[h7])],[h5,4,11,h6,h7]) ).

thf(13,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h3,h1,h2,h0]),tab_negimp(discharge,[h4,h5])],[h3,12,h4,h5]) ).

thf(14,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h1,h2,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__0)],[h1,13,h3]) ).

thf(15,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,14,h1,h2]) ).

thf(0,theorem,
    ( ~ ! [X1: mworld] :
          ( ( mrel @ mactual @ X1 )
         => ~ ( ( p @ X1 )
             => ! [X2: mworld] :
                  ( ( mrel @ X1 @ X2 )
                 => ( q @ X2 ) ) ) )
   => ( sP1
     => ~ sP9 ) ),
    inference(contra,[status(thm),contra(discharge,[h0])],[15,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : SYO899^8 : TPTP v8.1.0. Released v8.1.0.
% 0.11/0.12  % Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33  % Computer : n014.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 : Sat Jul  9 11:55:35 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.12/0.36  % SZS status Theorem
% 0.12/0.36  % Mode: mode213
% 0.12/0.36  % Inferences: 18
% 0.12/0.36  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------