%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : NUM302+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 12:25:49 EDT 2022

% Result   : Theorem 0.61s 0.79s
% Output   : CNFRefutation 0.61s
% 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(rdnn2,axiom,
    rdn_translate(nn2,rdn_neg(rdnn(n2))) ).

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(nn2_less_something,conjecture,
    ? [X] : less(nn2,X) ).

fof(subgoal_0,plain,
    ? [X] : less(nn2,X),
    inference(strip,[],[nn2_less_something]) ).

fof(negate_0_0,plain,
    ~ ? [X] : less(nn2,X),
    inference(negate,[],[subgoal_0]) ).

fof(normalize_0_0,plain,
    rdn_translate(n0,rdn_pos(rdnn(n0))),
    inference(canonicalize,[],[rdn0]) ).

fof(normalize_0_1,plain,
    rdn_translate(nn2,rdn_neg(rdnn(n2))),
    inference(canonicalize,[],[rdnn2]) ).

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(nn2,X),
    inference(canonicalize,[],[negate_0_0]) ).

fof(normalize_0_6,plain,
    ! [X] : ~ less(nn2,X),
    inference(specialize,[],[normalize_0_5]) ).

cnf(refute_0_0,plain,
    rdn_translate(n0,rdn_pos(rdnn(n0))),
    inference(canonicalize,[],[normalize_0_0]) ).

cnf(refute_0_1,plain,
    rdn_translate(nn2,rdn_neg(rdnn(n2))),
    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_950,rdn_pos(X_948))
    | ~ rdn_translate(nn2,rdn_neg(rdnn(n2)))
    | less(nn2,X_950) ),
    inference(subst,[],[refute_0_2:[bind(RDN_X,$fot(rdnn(n2))),bind(RDN_Y,$fot(X_948)),bind(X,$fot(nn2)),bind(Y,$fot(X_950))]]) ).

cnf(refute_0_4,plain,
    ( ~ rdn_translate(X_950,rdn_pos(X_948))
    | less(nn2,X_950) ),
    inference(resolve,[$cnf( rdn_translate(nn2,rdn_neg(rdnn(n2))) )],[refute_0_1,refute_0_3]) ).

cnf(refute_0_5,plain,
    ~ less(nn2,X),
    inference(canonicalize,[],[normalize_0_6]) ).

cnf(refute_0_6,plain,
    ~ less(nn2,X_950),
    inference(subst,[],[refute_0_5:[bind(X,$fot(X_950))]]) ).

cnf(refute_0_7,plain,
    ~ rdn_translate(X_950,rdn_pos(X_948)),
    inference(resolve,[$cnf( less(nn2,X_950) )],[refute_0_4,refute_0_6]) ).

cnf(refute_0_8,plain,
    ~ rdn_translate(n0,rdn_pos(rdnn(n0))),
    inference(subst,[],[refute_0_7:[bind(X_948,$fot(rdnn(n0))),bind(X_950,$fot(n0))]]) ).

cnf(refute_0_9,plain,
    $false,
    inference(resolve,[$cnf( rdn_translate(n0,rdn_pos(rdnn(n0))) )],[refute_0_0,refute_0_8]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11  % Problem  : NUM302+1 : TPTP v8.1.0. Released v3.1.0.
% 0.00/0.12  % Command  : metis --show proof --show saturation %s
% 0.12/0.33  % Computer : n019.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  : 600
% 0.12/0.33  % DateTime : Wed Jul  6 01:48:23 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.12/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.61/0.79  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.61/0.79  
% 0.61/0.79  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.61/0.79  
%------------------------------------------------------------------------------