%------------------------------------------------------------------------------
% File     : Lash---1.13
% Problem  : SYO378^5 : TPTP v8.1.2. Bugfixed v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : lash -P picomus -M modes -p tstp -t %d %s

% Computer : n009.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 04:46:29 EDT 2023

% Result   : Theorem 0.19s 0.39s
% Output   : Proof 0.19s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_c,type,
    c: $i ).

thf(sP1,plain,
    ( sP1
  <=> ! [X1: $i > $o] :
        ( ( X1
          = ( ^ [X2: $i] : ( X2 = c ) ) )
       => ! [X2: $i] :
            ~ ( X1 @ X2 ) ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

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

thf(sP3,plain,
    ( sP3
  <=> ! [X1: ( $i > $o ) > $o] :
        ( ( X1
          = ( ^ [X2: $i > $o] :
                ~ ( ( X2
                    = ( ^ [X3: $i] : ( X3 = c ) ) )
                 => ! [X3: $i] :
                      ~ ( X2 @ X3 ) ) ) )
       => ! [X2: $i > $o] :
            ~ ( X1 @ X2 ) ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> $false ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(def_cQDP0,definition,
    ( cQDP0
    = ( ^ [X1: $i] : ( X1 = c ) ) ) ).

thf(def_cQDP1,definition,
    ( cQDP1
    = ( ^ [X1: $i > $o] :
          ( ( X1 = cQDP0 )
          & ? [X2: $i] : ( X1 @ X2 ) ) ) ) ).

thf(def_cQDP2,definition,
    ( cQDP2
    = ( ^ [X1: ( $i > $o ) > $o] :
          ( ( X1 = cQDP1 )
          & ? [X2: $i > $o] : ( X1 @ X2 ) ) ) ) ).

thf(cQDTHM2,conjecture,
    ~ sP3 ).

thf(h0,negated_conjecture,
    sP3,
    inference(assume_negation,[status(cth)],[cQDTHM2]) ).

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

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

thf(3,plain,
    ( ~ sP1
    | sP2 ),
    inference(all_rule,[status(thm)],]) ).

thf(4,plain,
    ( ~ sP3
    | sP1 ),
    inference(all_rule,[status(thm)],]) ).

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

thf(0,theorem,
    ~ sP3,
    inference(contra,[status(thm),contra(discharge,[h0])],[5,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12  % Problem  : SYO378^5 : TPTP v8.1.2. Bugfixed v5.2.0.
% 0.08/0.13  % Command  : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34  % Computer : n009.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Sat Aug 26 06:21:35 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.19/0.39  % SZS status Theorem
% 0.19/0.39  % Mode: cade22grackle2xfee4
% 0.19/0.39  % Steps: 7
% 0.19/0.39  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------