%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : NUM300+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n026.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 12:25:49 EDT 2022

% Result   : Theorem 0.62s 0.79s
% Output   : CNFRefutation 0.62s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   23 (  16 unt;   0 def)
%            Number of atoms       :   36 (   0 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   31 (  18   ~;  11   |;   1   &)
%                                         (   0 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   3 con; 0-1 aty)
%            Number of variables   :   33 (   8 sgn  18   !;   3   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(rdn0,axiom,
    rdn_translate(n0,rdn_pos(rdnn(n0))) ).

fof(rdnn1,axiom,
    rdn_translate(nn1,rdn_neg(rdnn(n1))) ).

fof(less_entry_point_neg_pos,axiom,
    ! [X,Y,RDN_X,RDN_Y] :
      ( ( rdn_translate(X,rdn_neg(RDN_X))
        & rdn_translate(Y,rdn_pos(RDN_Y)) )
     => less(X,Y) ) ).

fof(something_less_n0,conjecture,
    ? [X] : less(X,n0) ).

fof(subgoal_0,plain,
    ? [X] : less(X,n0),
    inference(strip,[],[something_less_n0]) ).

fof(negate_0_0,plain,
    ~ ? [X] : less(X,n0),
    inference(negate,[],[subgoal_0]) ).

fof(normalize_0_0,plain,
    rdn_translate(nn1,rdn_neg(rdnn(n1))),
    inference(canonicalize,[],[rdnn1]) ).

fof(normalize_0_1,plain,
    rdn_translate(n0,rdn_pos(rdnn(n0))),
    inference(canonicalize,[],[rdn0]) ).

fof(normalize_0_2,plain,
    ! [X,Y] :
      ( less(X,Y)
      | ! [RDN_X] : ~ rdn_translate(X,rdn_neg(RDN_X))
      | ! [RDN_Y] : ~ rdn_translate(Y,rdn_pos(RDN_Y)) ),
    inference(canonicalize,[],[less_entry_point_neg_pos]) ).

fof(normalize_0_3,plain,
    ! [X,Y] :
      ( less(X,Y)
      | ! [RDN_X] : ~ rdn_translate(X,rdn_neg(RDN_X))
      | ! [RDN_Y] : ~ rdn_translate(Y,rdn_pos(RDN_Y)) ),
    inference(specialize,[],[normalize_0_2]) ).

fof(normalize_0_4,plain,
    ! [RDN_X,RDN_Y,X,Y] :
      ( ~ rdn_translate(X,rdn_neg(RDN_X))
      | ~ rdn_translate(Y,rdn_pos(RDN_Y))
      | less(X,Y) ),
    inference(clausify,[],[normalize_0_3]) ).

fof(normalize_0_5,plain,
    ! [X] : ~ less(X,n0),
    inference(canonicalize,[],[negate_0_0]) ).

fof(normalize_0_6,plain,
    ! [X] : ~ less(X,n0),
    inference(specialize,[],[normalize_0_5]) ).

cnf(refute_0_0,plain,
    rdn_translate(nn1,rdn_neg(rdnn(n1))),
    inference(canonicalize,[],[normalize_0_0]) ).

cnf(refute_0_1,plain,
    rdn_translate(n0,rdn_pos(rdnn(n0))),
    inference(canonicalize,[],[normalize_0_1]) ).

cnf(refute_0_2,plain,
    ( ~ rdn_translate(X,rdn_neg(RDN_X))
    | ~ rdn_translate(Y,rdn_pos(RDN_Y))
    | less(X,Y) ),
    inference(canonicalize,[],[normalize_0_4]) ).

cnf(refute_0_3,plain,
    ( ~ rdn_translate(X_709,rdn_neg(X_707))
    | ~ rdn_translate(n0,rdn_pos(rdnn(n0)))
    | less(X_709,n0) ),
    inference(subst,[],[refute_0_2:[bind(RDN_X,$fot(X_707)),bind(RDN_Y,$fot(rdnn(n0))),bind(X,$fot(X_709)),bind(Y,$fot(n0))]]) ).

cnf(refute_0_4,plain,
    ( ~ rdn_translate(X_709,rdn_neg(X_707))
    | less(X_709,n0) ),
    inference(resolve,[$cnf( rdn_translate(n0,rdn_pos(rdnn(n0))) )],[refute_0_1,refute_0_3]) ).

cnf(refute_0_5,plain,
    ~ less(X,n0),
    inference(canonicalize,[],[normalize_0_6]) ).

cnf(refute_0_6,plain,
    ~ less(X_709,n0),
    inference(subst,[],[refute_0_5:[bind(X,$fot(X_709))]]) ).

cnf(refute_0_7,plain,
    ~ rdn_translate(X_709,rdn_neg(X_707)),
    inference(resolve,[$cnf( less(X_709,n0) )],[refute_0_4,refute_0_6]) ).

cnf(refute_0_8,plain,
    ~ rdn_translate(nn1,rdn_neg(rdnn(n1))),
    inference(subst,[],[refute_0_7:[bind(X_707,$fot(rdnn(n1))),bind(X_709,$fot(nn1))]]) ).

cnf(refute_0_9,plain,
    $false,
    inference(resolve,[$cnf( rdn_translate(nn1,rdn_neg(rdnn(n1))) )],[refute_0_0,refute_0_8]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : NUM300+1 : TPTP v8.1.0. Released v3.1.0.
% 0.06/0.13  % Command  : metis --show proof --show saturation %s
% 0.13/0.34  % Computer : n026.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 : Thu Jul  7 08:59:24 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.13/0.35  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.62/0.79  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.62/0.79  
% 0.62/0.79  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.62/0.79  
%------------------------------------------------------------------------------