%------------------------------------------------------------------------------
% File     : Lash---1.13
% Problem  : SYO353^5 : 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 : n017.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 04:46:23 EDT 2023

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

% Comments : 
%------------------------------------------------------------------------------
thf(ty_a,type,
    a: $tType ).

thf(ty_v,type,
    v: a ).

thf(ty_u,type,
    u: a ).

thf(ty_eigen__0,type,
    eigen__0: a > a > $o ).

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

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

thf(sP3,plain,
    ( sP3
  <=> ! [X1: a > $o] :
        ( ( X1 @ u )
       => ( X1 @ v ) ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ( eigen__0 @ u @ v ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

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

thf(cE1LEIBEQ1_pme,conjecture,
    ( sP3
   => ! [X1: a > a > $o] :
        ( ! [X2: a] : ( X1 @ X2 @ X2 )
       => ( X1 @ u @ v ) ) ) ).

thf(h0,negated_conjecture,
    ~ ( sP3
     => ! [X1: a > a > $o] :
          ( ! [X2: a] : ( X1 @ X2 @ X2 )
         => ( X1 @ u @ v ) ) ),
    inference(assume_negation,[status(cth)],[cE1LEIBEQ1_pme]) ).

thf(h1,assumption,
    sP3,
    introduced(assumption,[]) ).

thf(h2,assumption,
    ~ ! [X1: a > a > $o] :
        ( ! [X2: a] : ( X1 @ X2 @ X2 )
       => ( X1 @ u @ v ) ),
    introduced(assumption,[]) ).

thf(h3,assumption,
    ~ ( sP1
     => sP4 ),
    introduced(assumption,[]) ).

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

thf(h5,assumption,
    ~ sP4,
    introduced(assumption,[]) ).

thf(1,plain,
    ( ~ sP2
    | ~ sP5
    | sP4 ),
    inference(prop_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP3
    | sP2 ),
    inference(all_rule,[status(thm)],]) ).

thf(3,plain,
    ( ~ sP1
    | sP5 ),
    inference(all_rule,[status(thm)],]) ).

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

thf(5,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h3,h1,h2,h0]),tab_negimp(discharge,[h4,h5])],[h3,4,h4,h5]) ).

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

thf(7,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,6,h1,h2]) ).

thf(0,theorem,
    ( sP3
   => ! [X1: a > a > $o] :
        ( ! [X2: a] : ( X1 @ X2 @ X2 )
       => ( X1 @ u @ v ) ) ),
    inference(contra,[status(thm),contra(discharge,[h0])],[7,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SYO353^5 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.13  % Command  : lash -P picomus -M modes -p tstp -t %d %s
% 0.12/0.34  % Computer : n017.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
% 0.12/0.35  % DateTime : Sat Aug 26 03:28:40 EDT 2023
% 0.12/0.35  % CPUTime  : 
% 0.12/0.39  % SZS status Theorem
% 0.12/0.39  % Mode: cade22grackle2xfee4
% 0.12/0.39  % Steps: 16
% 0.12/0.39  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------