%------------------------------------------------------------------------------
% File     : Lash---1.13
% Problem  : SEV413^5 : 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 : n012.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 19:34:30 EDT 2023

% Result   : Theorem 0.20s 0.38s
% Output   : Proof 0.20s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

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

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

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

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

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

thf(cDUAL_EG5_pme,conjecture,
    ( sP1
   => ~ sP3 ) ).

thf(h0,negated_conjecture,
    ~ ( sP1
     => ~ sP3 ),
    inference(assume_negation,[status(cth)],[cDUAL_EG5_pme]) ).

thf(h1,assumption,
    sP1,
    introduced(assumption,[]) ).

thf(h2,assumption,
    sP3,
    introduced(assumption,[]) ).

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

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

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

thf(4,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,3,h1,h2]) ).

thf(0,theorem,
    ( sP1
   => ~ sP3 ),
    inference(contra,[status(thm),contra(discharge,[h0])],[4,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SEV413^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13  % Command  : lash -P picomus -M modes -p tstp -t %d %s
% 0.12/0.34  % Computer : n012.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
% 0.12/0.34  % DateTime : Thu Aug 24 03:59:27 EDT 2023
% 0.12/0.35  % CPUTime  : 
% 0.20/0.38  % SZS status Theorem
% 0.20/0.38  % Mode: cade22grackle2xfee4
% 0.20/0.38  % Steps: 2
% 0.20/0.38  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------