%------------------------------------------------------------------------------
% File     : Lash---1.13
% Problem  : NUM417^1 : TPTP v8.1.2. Released v3.6.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : lash -P picomus -M modes -p tstp -t %d %s

% Computer : n024.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 11:39:00 EDT 2023

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

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

thf(def_zero,definition,
    ( zero
    = ( ^ [X1: $i > $i,X2: $i] : X2 ) ) ).

thf(def_one,definition,
    ( one
    = ( ^ [X1: $i > $i,X2: $i] : ( X1 @ X2 ) ) ) ).

thf(def_two,definition,
    ( two
    = ( ^ [X1: $i > $i,X2: $i] : ( X1 @ ( X1 @ X2 ) ) ) ) ).

thf(def_three,definition,
    ( three
    = ( ^ [X1: $i > $i,X2: $i] : ( X1 @ ( X1 @ ( X1 @ X2 ) ) ) ) ) ).

thf(def_four,definition,
    ( four
    = ( ^ [X1: $i > $i,X2: $i] : ( X1 @ ( X1 @ ( X1 @ ( X1 @ X2 ) ) ) ) ) ) ).

thf(def_five,definition,
    ( five
    = ( ^ [X1: $i > $i,X2: $i] : ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ X2 ) ) ) ) ) ) ) ).

thf(def_six,definition,
    ( six
    = ( ^ [X1: $i > $i,X2: $i] : ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ X2 ) ) ) ) ) ) ) ) ).

thf(def_seven,definition,
    ( seven
    = ( ^ [X1: $i > $i,X2: $i] : ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ X2 ) ) ) ) ) ) ) ) ) ).

thf(def_eight,definition,
    ( eight
    = ( ^ [X1: $i > $i,X2: $i] : ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ X2 ) ) ) ) ) ) ) ) ) ) ).

thf(def_nine,definition,
    ( nine
    = ( ^ [X1: $i > $i,X2: $i] : ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ X2 ) ) ) ) ) ) ) ) ) ) ) ).

thf(def_ten,definition,
    ( ten
    = ( ^ [X1: $i > $i,X2: $i] : ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ).

thf(def_succ,definition,
    ( succ
    = ( ^ [X1: ( $i > $i ) > $i > $i,X2: $i > $i,X3: $i] : ( X2 @ ( X1 @ X2 @ X3 ) ) ) ) ).

thf(def_plus,definition,
    ( plus
    = ( ^ [X1: ( $i > $i ) > $i > $i,X2: ( $i > $i ) > $i > $i,X3: $i > $i,X4: $i] : ( X1 @ X3 @ ( X2 @ X3 @ X4 ) ) ) ) ).

thf(def_mult,definition,
    ( mult
    = ( ^ [X1: ( $i > $i ) > $i > $i,X2: ( $i > $i ) > $i > $i,X3: $i > $i,X4: $i] : ( X1 @ ( X2 @ X3 ) @ X4 ) ) ) ).

thf(thm,conjecture,
    ~ sP1 ).

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

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
% 0.03/0.12  % Problem  : NUM417^1 : TPTP v8.1.2. Released v3.6.0.
% 0.03/0.12  % Command  : lash -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33  % Computer : n024.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Fri Aug 25 10:06:39 EDT 2023
% 0.12/0.33  % CPUTime  : 
% 0.19/0.39  % SZS status Theorem
% 0.19/0.39  % Mode: cade22grackle2xfee4
% 0.19/0.39  % Steps: 1
% 0.19/0.39  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------