%------------------------------------------------------------------------------
% File     : Lash---1.13
% Problem  : SYN375^5 : 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 : n019.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 03:20:42 EDT 2023

% Result   : Theorem 0.20s 0.39s
% Output   : Proof 0.20s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_eigen__0,type,
    eigen__0: $i ).

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

thf(ty_cP,type,
    cP: $i > $o ).

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

thf(sP2,plain,
    ( sP2
  <=> ! [X1: $i] :
        ~ ( cP @ X1 ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ! [X1: $i] : ( cP @ X1 ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ( ~ sP2
     => sP3 ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> ( cP @ eigen__1 ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(cX2126_BUG,conjecture,
    ( ~ ( ( sP3
         => ~ sP2 )
       => ~ sP4 )
   => ( ~ sP2 = sP3 ) ) ).

thf(h0,negated_conjecture,
    ~ ( ~ ( ( sP3
           => ~ sP2 )
         => ~ sP4 )
     => ( ~ sP2 = sP3 ) ),
    inference(assume_negation,[status(cth)],[cX2126_BUG]) ).

thf(h1,assumption,
    ~ ( ( sP3
       => ~ sP2 )
     => ~ sP4 ),
    introduced(assumption,[]) ).

thf(h2,assumption,
    ( ~ sP2 != sP3 ),
    introduced(assumption,[]) ).

thf(h3,assumption,
    ( sP3
   => ~ sP2 ),
    introduced(assumption,[]) ).

thf(h4,assumption,
    sP4,
    introduced(assumption,[]) ).

thf(h5,assumption,
    ~ sP2,
    introduced(assumption,[]) ).

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

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

thf(h8,assumption,
    ~ sP3,
    introduced(assumption,[]) ).

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

thf(h10,assumption,
    ~ sP5,
    introduced(assumption,[]) ).

thf(1,plain,
    ( ~ sP2
    | ~ sP1 ),
    inference(all_rule,[status(thm)],]) ).

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

thf(3,plain,
    ( ~ sP4
    | sP2
    | sP3 ),
    inference(prop_rule,[status(thm)],]) ).

thf(4,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h10,h9,h5,h6,h3,h4,h1,h2,h0])],[1,2,3,h4,h9,h10]) ).

thf(5,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h9,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h10]),tab_negall(eigenvar,eigen__1)],[h6,4,h10]) ).

thf(6,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h9]),tab_negall(eigenvar,eigen__0)],[h5,5,h9]) ).

thf(7,plain,
    ( ~ sP2
    | ~ sP1 ),
    inference(all_rule,[status(thm)],]) ).

thf(8,plain,
    ( ~ sP3
    | sP1 ),
    inference(all_rule,[status(thm)],]) ).

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

thf(10,plain,
    $false,
    inference(tab_be,[status(thm),assumptions([h3,h4,h1,h2,h0]),tab_be(discharge,[h5,h6]),tab_be(discharge,[h7,h8])],[h2,6,9,h5,h6,h7,h8]) ).

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

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

thf(0,theorem,
    ( ~ ( ( sP3
         => ~ sP2 )
       => ~ sP4 )
   => ( ~ sP2 = sP3 ) ),
    inference(contra,[status(thm),contra(discharge,[h0])],[12,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SYN375^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.12  % Command  : lash -P picomus -M modes -p tstp -t %d %s
% 0.15/0.34  % Computer : n019.cluster.edu
% 0.15/0.34  % Model    : x86_64 x86_64
% 0.15/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34  % Memory   : 8042.1875MB
% 0.15/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34  % CPULimit : 300
% 0.15/0.34  % WCLimit  : 300
% 0.15/0.34  % DateTime : Sat Aug 26 20:50:58 EDT 2023
% 0.15/0.34  % CPUTime  : 
% 0.20/0.39  % SZS status Theorem
% 0.20/0.39  % Mode: cade22grackle2xfee4
% 0.20/0.39  % Steps: 19
% 0.20/0.39  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------