%------------------------------------------------------------------------------
% File     : Satallax---3.5
% Problem  : SEV412^5 : 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 : n024.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 18:06:16 EDT 2022

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

% Comments : 
%------------------------------------------------------------------------------
thf(ty_cG,type,
    cG: $o ).

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

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

thf(ty_cB,type,
    cB: $i > $o ).

thf(ty_cA,type,
    cA: $i > $o ).

thf(sP1,plain,
    ( sP1
  <=> ! [X1: $i] :
        ( ( cA @ X1 )
       => ( cB @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

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

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

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

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

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

thf(sP7,plain,
    ( sP7
  <=> ( sP2
     => sP4 ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

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

thf(cDUAL_EG2_pme,conjecture,
    ( ( ~ ( sP1
         => sP6 )
     => ( sP1
       => sP6 ) )
   => ( sP1
     => sP6 ) ) ).

thf(h0,negated_conjecture,
    ~ ( ( ~ ( sP1
           => sP6 )
       => ( sP1
         => sP6 ) )
     => ( sP1
       => sP6 ) ),
    inference(assume_negation,[status(cth)],[cDUAL_EG2_pme]) ).

thf(h1,assumption,
    ( ~ ( sP1
       => sP6 )
   => ( sP1
     => sP6 ) ),
    introduced(assumption,[]) ).

thf(h2,assumption,
    ~ ( sP1
     => sP6 ),
    introduced(assumption,[]) ).

thf(h3,assumption,
    ( sP1
   => sP6 ),
    introduced(assumption,[]) ).

thf(h4,assumption,
    ~ sP1,
    introduced(assumption,[]) ).

thf(h5,assumption,
    sP6,
    introduced(assumption,[]) ).

thf(h6,assumption,
    ~ sP3,
    introduced(assumption,[]) ).

thf(h7,assumption,
    sP8,
    introduced(assumption,[]) ).

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

thf(h9,assumption,
    sP1,
    introduced(assumption,[]) ).

thf(h10,assumption,
    ~ sP6,
    introduced(assumption,[]) ).

thf(1,plain,
    ( ~ sP1
    | sP3 ),
    inference(all_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP3
    | ~ sP8
    | sP5 ),
    inference(prop_rule,[status(thm)],]) ).

thf(3,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h9,h10,h7,h8,h6,h4,h3,h1,h2,h0])],[1,2,h7,h8,h9]) ).

thf(4,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h7,h8,h6,h4,h3,h1,h2,h0]),tab_negimp(discharge,[h9,h10])],[h2,3,h9,h10]) ).

thf(5,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h6,h4,h3,h1,h2,h0]),tab_negimp(discharge,[h7,h8])],[h6,4,h7,h8]) ).

thf(6,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h4,h3,h1,h2,h0]),tab_negall(discharge,[h6]),tab_negall(eigenvar,eigen__0)],[h4,5,h6]) ).

thf(7,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h9,h10,h5,h3,h1,h2,h0])],[h5,h10]) ).

thf(8,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h5,h3,h1,h2,h0]),tab_negimp(discharge,[h9,h10])],[h2,7,h9,h10]) ).

thf(9,plain,
    $false,
    inference(tab_imp,[status(thm),assumptions([h3,h1,h2,h0]),tab_imp(discharge,[h4]),tab_imp(discharge,[h5])],[h3,6,8,h4,h5]) ).

thf(h11,assumption,
    ~ sP7,
    introduced(assumption,[]) ).

thf(h12,assumption,
    sP2,
    introduced(assumption,[]) ).

thf(h13,assumption,
    ~ sP4,
    introduced(assumption,[]) ).

thf(10,plain,
    ( ~ sP1
    | sP7 ),
    inference(all_rule,[status(thm)],]) ).

thf(11,plain,
    ( ~ sP7
    | ~ sP2
    | sP4 ),
    inference(prop_rule,[status(thm)],]) ).

thf(12,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h9,h10,h12,h13,h11,h4,h3,h1,h2,h0])],[10,11,h12,h13,h9]) ).

thf(13,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h12,h13,h11,h4,h3,h1,h2,h0]),tab_negimp(discharge,[h9,h10])],[h2,12,h9,h10]) ).

thf(14,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h11,h4,h3,h1,h2,h0]),tab_negimp(discharge,[h12,h13])],[h11,13,h12,h13]) ).

thf(15,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h4,h3,h1,h2,h0]),tab_negall(discharge,[h11]),tab_negall(eigenvar,eigen__1)],[h4,14,h11]) ).

thf(16,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h9,h10,h5,h3,h1,h2,h0])],[h5,h10]) ).

thf(17,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h5,h3,h1,h2,h0]),tab_negimp(discharge,[h9,h10])],[h2,16,h9,h10]) ).

thf(18,plain,
    $false,
    inference(tab_imp,[status(thm),assumptions([h3,h1,h2,h0]),tab_imp(discharge,[h4]),tab_imp(discharge,[h5])],[h3,15,17,h4,h5]) ).

thf(19,plain,
    $false,
    inference(tab_imp,[status(thm),assumptions([h1,h2,h0]),tab_imp(discharge,[h3]),tab_imp(discharge,[h3])],[h1,9,18,h3,h3]) ).

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

thf(0,theorem,
    ( ( ~ ( sP1
         => sP6 )
     => ( sP1
       => sP6 ) )
   => ( sP1
     => sP6 ) ),
    inference(contra,[status(thm),contra(discharge,[h0])],[20,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : SEV412^5 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.13  % Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.34  % Computer : n024.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  : 600
% 0.12/0.34  % DateTime : Mon Jun 27 23:42:31 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.12/0.36  % SZS status Theorem
% 0.12/0.36  % Mode: mode213
% 0.12/0.36  % Inferences: 6
% 0.12/0.36  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------