%------------------------------------------------------------------------------
% File     : Lash---1.13
% Problem  : SEU541^2 : TPTP v8.1.2. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : lash -P picomus -M modes -p tstp -t %d %s

% Computer : n027.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 : Thu Aug 31 17:18:28 EDT 2023

% Result   : Theorem 0.18s 0.36s
% Output   : Proof 0.18s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

% Comments : 
%------------------------------------------------------------------------------
thf(sP1,plain,
    ( sP1
  <=> $false ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(def_prop2setI,definition,
    ( prop2setI
    = ( ! [X1: $o] :
          ( ^ [X2: $o,X3: $o] :
              ( X2
             => X3 )
          @ X1
          @ ( in @ emptyset @ ( prop2set @ X1 ) ) ) ) ) ).

thf(def_set2prop,definition,
    ( set2prop
    = ( ^ [X1: $i] : ( in @ emptyset @ X1 ) ) ) ).

thf(prop2set2propI,conjecture,
    ~ sP1 ).

thf(h0,negated_conjecture,
    sP1,
    inference(assume_negation,[status(cth)],[prop2set2propI]) ).

thf(1,plain,
    ~ sP1,
    inference(prop_rule,[status(thm)],]) ).

thf(2,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h0])],[1,h0]) ).

thf(0,theorem,
    ~ sP1,
    inference(contra,[status(thm),contra(discharge,[h0])],[2,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SEU541^2 : TPTP v8.1.2. Released v3.7.0.
% 0.00/0.12  % Command  : lash -P picomus -M modes -p tstp -t %d %s
% 0.12/0.32  % Computer : n027.cluster.edu
% 0.12/0.32  % Model    : x86_64 x86_64
% 0.12/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32  % Memory   : 8042.1875MB
% 0.12/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32  % CPULimit : 300
% 0.12/0.32  % WCLimit  : 300
% 0.12/0.32  % DateTime : Wed Aug 23 21:43:01 EDT 2023
% 0.12/0.32  % CPUTime  : 
% 0.18/0.36  % SZS status Theorem
% 0.18/0.36  % Mode: cade22grackle2xfee4
% 0.18/0.36  % Steps: 1
% 0.18/0.36  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------