%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : NUM343+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n019.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 12:26:03 EDT 2022

% Result   : Theorem 0.47s 0.64s
% Output   : CNFRefutation 0.47s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    3
% Syntax   : Number of formulae    :   19 (   8 unt;   0 def)
%            Number of atoms       :   42 (   9 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :   41 (  18   ~;   9   |;   8   &)
%                                         (   3 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    5 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :    3 (   3 usr;   3 con; 0-0 aty)
%            Number of variables   :   24 (   1 sgn  15   !;   3   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(less_property,axiom,
    ! [X,Y] :
      ( less(X,Y)
    <=> ( ~ less(Y,X)
        & Y != X ) ) ).

fof(sum_something_n0_samething,conjecture,
    ? [X] :
      ( ( less(nn1,X)
        & less(X,n1) )
     => sum(n21,X,n21) ) ).

fof(subgoal_0,plain,
    ? [X] :
      ( ( less(nn1,X)
        & less(X,n1) )
     => sum(n21,X,n21) ),
    inference(strip,[],[sum_something_n0_samething]) ).

fof(negate_0_0,plain,
    ~ ? [X] :
        ( ( less(nn1,X)
          & less(X,n1) )
       => sum(n21,X,n21) ),
    inference(negate,[],[subgoal_0]) ).

fof(normalize_0_0,plain,
    ( ! [X] : ~ sum(n21,X,n21)
    & ! [X] : less(X,n1)
    & ! [X] : less(nn1,X) ),
    inference(canonicalize,[],[negate_0_0]) ).

fof(normalize_0_1,plain,
    ! [X] : less(nn1,X),
    inference(conjunct,[],[normalize_0_0]) ).

fof(normalize_0_2,plain,
    ! [X] : less(nn1,X),
    inference(specialize,[],[normalize_0_1]) ).

fof(normalize_0_3,plain,
    ! [X,Y] :
      ( ~ less(X,Y)
    <=> ( Y = X
        | less(Y,X) ) ),
    inference(canonicalize,[],[less_property]) ).

fof(normalize_0_4,plain,
    ! [X,Y] :
      ( ~ less(X,Y)
    <=> ( Y = X
        | less(Y,X) ) ),
    inference(specialize,[],[normalize_0_3]) ).

fof(normalize_0_5,plain,
    ! [X,Y] :
      ( ( Y != X
        | ~ less(X,Y) )
      & ( ~ less(X,Y)
        | ~ less(Y,X) )
      & ( Y = X
        | less(X,Y)
        | less(Y,X) ) ),
    inference(clausify,[],[normalize_0_4]) ).

fof(normalize_0_6,plain,
    ! [X,Y] :
      ( Y != X
      | ~ less(X,Y) ),
    inference(conjunct,[],[normalize_0_5]) ).

cnf(refute_0_0,plain,
    less(nn1,X),
    inference(canonicalize,[],[normalize_0_2]) ).

cnf(refute_0_1,plain,
    less(nn1,nn1),
    inference(subst,[],[refute_0_0:[bind(X,$fot(nn1))]]) ).

cnf(refute_0_2,plain,
    ( Y != X
    | ~ less(X,Y) ),
    inference(canonicalize,[],[normalize_0_6]) ).

cnf(refute_0_3,plain,
    ( X != X
    | ~ less(X,X) ),
    inference(subst,[],[refute_0_2:[bind(Y,$fot(X))]]) ).

cnf(refute_0_4,plain,
    X = X,
    introduced(tautology,[refl,[$fot(X)]]) ).

cnf(refute_0_5,plain,
    ~ less(X,X),
    inference(resolve,[$cnf( $equal(X,X) )],[refute_0_4,refute_0_3]) ).

cnf(refute_0_6,plain,
    ~ less(nn1,nn1),
    inference(subst,[],[refute_0_5:[bind(X,$fot(nn1))]]) ).

cnf(refute_0_7,plain,
    $false,
    inference(resolve,[$cnf( less(nn1,nn1) )],[refute_0_1,refute_0_6]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : NUM343+1 : TPTP v8.1.0. Released v3.1.0.
% 0.07/0.13  % Command  : metis --show proof --show saturation %s
% 0.13/0.34  % Computer : n019.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 : Wed Jul  6 06:47:08 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.13/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.47/0.64  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.47/0.64  
% 0.47/0.64  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.47/0.64  
%------------------------------------------------------------------------------