%------------------------------------------------------------------------------
% File     : Satallax---3.5
% Problem  : NUM020^1 : TPTP v8.1.0. Released v3.6.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s

% Computer : n029.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  : 600s
% DateTime : Mon Jul 18 13:49:53 EDT 2022

% Result   : Theorem 202.46s 202.59s
% Output   : Proof 202.46s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

% Comments : 
%------------------------------------------------------------------------------
thf(sP1,plain,
    ( sP1
  <=> ( ( ^ [X1: $i > $i,X2: $i] : ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ X2 ) ) ) ) ) ) )
      = ( ^ [X1: $i > $i,X2: $i] : ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ X2 ) ) ) ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ! [X1: ( $i > $i ) > $i > $i] :
        ( ( ^ [X2: $i > $i] :
              ( X1
              @ ^ [X3: $i] : ( X2 @ ( X2 @ ( X2 @ X3 ) ) ) ) )
       != ( ^ [X2: $i > $i,X3: $i] : ( X2 @ ( X2 @ ( X2 @ ( X2 @ ( X2 @ ( X2 @ X3 ) ) ) ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

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

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

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] : ( X1 @ ( X2 @ X3 ) ) ) ) ).

thf(thm,conjecture,
    ~ sP2 ).

thf(h0,negated_conjecture,
    sP2,
    inference(assume_negation,[status(cth)],[thm]) ).

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

thf(2,plain,
    ( ~ sP2
    | ~ sP1 ),
    inference(all_rule,[status(thm)],]) ).

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

thf(0,theorem,
    ~ sP2,
    inference(contra,[status(thm),contra(discharge,[h0])],[3,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13  % Problem  : NUM020^1 : TPTP v8.1.0. Released v3.6.0.
% 0.04/0.13  % Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34  % Computer : n029.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  : 600
% 0.13/0.34  % DateTime : Tue Jul  5 07:30:57 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 202.46/202.59  % SZS status Theorem
% 202.46/202.59  % Mode: mode492
% 202.46/202.59  % Inferences: 55063
% 202.46/202.59  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------