%------------------------------------------------------------------------------
% File     : Lash---1.13
% Problem  : SYO142^5 : 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 04:45:26 EDT 2023

% Result   : Theorem 0.13s 0.40s
% Output   : Proof 0.13s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_f,type,
    f: $i > $i ).

thf(ty_p,type,
    p: $i > $o ).

thf(ty_a,type,
    a: $i ).

thf(sP1,plain,
    ( sP1
  <=> ( p @ ( f @ ( f @ a ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ! [X1: $i] :
        ( ( sP1
         => ( p @ ( f @ ( f @ X1 ) ) ) )
       => ~ ( ( p @ X1 )
           => sP1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ! [X1: $i,X2: $i] :
        ( ( ( p @ X1 )
         => ( p @ ( f @ ( f @ X2 ) ) ) )
       => ~ ( ( p @ X2 )
           => sP1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ( ( p @ a )
     => sP1 ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> ( sP1
     => ( p @ ( f @ ( f @ ( f @ ( f @ a ) ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(cTEST4,conjecture,
    ~ sP3 ).

thf(h0,negated_conjecture,
    sP3,
    inference(assume_negation,[status(cth)],[cTEST4]) ).

thf(1,plain,
    ( sP5
    | sP1 ),
    inference(prop_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP2
    | ~ sP4 ),
    inference(all_rule,[status(thm)],]) ).

thf(3,plain,
    ( ~ sP2
    | ~ sP5 ),
    inference(all_rule,[status(thm)],]) ).

thf(4,plain,
    ( ~ sP3
    | sP2 ),
    inference(all_rule,[status(thm)],]) ).

thf(5,plain,
    ( sP4
    | ~ sP1 ),
    inference(prop_rule,[status(thm)],]) ).

thf(6,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h0])],[1,2,3,4,5,h0]) ).

thf(0,theorem,
    ~ sP3,
    inference(contra,[status(thm),contra(discharge,[h0])],[6,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : SYO142^5 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.13  % Command  : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.35  % Computer : n017.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Sat Aug 26 04:50:10 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.13/0.40  % SZS status Theorem
% 0.13/0.40  % Mode: cade22grackle2xfee4
% 0.13/0.40  % Steps: 36
% 0.13/0.40  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------