%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : NUM318+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n007.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 12:25:54 EDT 2022

% Result   : Theorem 0.61s 0.79s
% Output   : CNFRefutation 0.61s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   20 (  13 unt;   0 def)
%            Number of atoms       :   32 (   0 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   25 (  13   ~;  10   |;   1   &)
%                                         (   0 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :    6 (   6 usr;   3 con; 0-1 aty)
%            Number of variables   :   14 (   0 sgn   9   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(rdn5,axiom,
    rdn_translate(n5,rdn_pos(rdnn(n5))) ).

fof(rdnn5,axiom,
    rdn_translate(nn5,rdn_neg(rdnn(n5))) ).

fof(sum_entry_point_posx_negx,axiom,
    ! [POS_X,NEG_X,RDN_X] :
      ( ( rdn_translate(POS_X,rdn_pos(RDN_X))
        & rdn_translate(NEG_X,rdn_neg(RDN_X)) )
     => sum(POS_X,NEG_X,n0) ) ).

fof(sum_n5_nn5_n0,conjecture,
    sum(n5,nn5,n0) ).

fof(subgoal_0,plain,
    sum(n5,nn5,n0),
    inference(strip,[],[sum_n5_nn5_n0]) ).

fof(negate_0_0,plain,
    ~ sum(n5,nn5,n0),
    inference(negate,[],[subgoal_0]) ).

fof(normalize_0_0,plain,
    rdn_translate(n5,rdn_pos(rdnn(n5))),
    inference(canonicalize,[],[rdn5]) ).

fof(normalize_0_1,plain,
    rdn_translate(nn5,rdn_neg(rdnn(n5))),
    inference(canonicalize,[],[rdnn5]) ).

fof(normalize_0_2,plain,
    ! [NEG_X,POS_X,RDN_X] :
      ( ~ rdn_translate(NEG_X,rdn_neg(RDN_X))
      | ~ rdn_translate(POS_X,rdn_pos(RDN_X))
      | sum(POS_X,NEG_X,n0) ),
    inference(canonicalize,[],[sum_entry_point_posx_negx]) ).

fof(normalize_0_3,plain,
    ! [NEG_X,POS_X,RDN_X] :
      ( ~ rdn_translate(NEG_X,rdn_neg(RDN_X))
      | ~ rdn_translate(POS_X,rdn_pos(RDN_X))
      | sum(POS_X,NEG_X,n0) ),
    inference(specialize,[],[normalize_0_2]) ).

fof(normalize_0_4,plain,
    ~ sum(n5,nn5,n0),
    inference(canonicalize,[],[negate_0_0]) ).

cnf(refute_0_0,plain,
    rdn_translate(n5,rdn_pos(rdnn(n5))),
    inference(canonicalize,[],[normalize_0_0]) ).

cnf(refute_0_1,plain,
    rdn_translate(nn5,rdn_neg(rdnn(n5))),
    inference(canonicalize,[],[normalize_0_1]) ).

cnf(refute_0_2,plain,
    ( ~ rdn_translate(NEG_X,rdn_neg(RDN_X))
    | ~ rdn_translate(POS_X,rdn_pos(RDN_X))
    | sum(POS_X,NEG_X,n0) ),
    inference(canonicalize,[],[normalize_0_3]) ).

cnf(refute_0_3,plain,
    ( ~ rdn_translate(X_380,rdn_pos(rdnn(n5)))
    | ~ rdn_translate(nn5,rdn_neg(rdnn(n5)))
    | sum(X_380,nn5,n0) ),
    inference(subst,[],[refute_0_2:[bind(NEG_X,$fot(nn5)),bind(POS_X,$fot(X_380)),bind(RDN_X,$fot(rdnn(n5)))]]) ).

cnf(refute_0_4,plain,
    ( ~ rdn_translate(X_380,rdn_pos(rdnn(n5)))
    | sum(X_380,nn5,n0) ),
    inference(resolve,[$cnf( rdn_translate(nn5,rdn_neg(rdnn(n5))) )],[refute_0_1,refute_0_3]) ).

cnf(refute_0_5,plain,
    ( ~ rdn_translate(n5,rdn_pos(rdnn(n5)))
    | sum(n5,nn5,n0) ),
    inference(subst,[],[refute_0_4:[bind(X_380,$fot(n5))]]) ).

cnf(refute_0_6,plain,
    sum(n5,nn5,n0),
    inference(resolve,[$cnf( rdn_translate(n5,rdn_pos(rdnn(n5))) )],[refute_0_0,refute_0_5]) ).

cnf(refute_0_7,plain,
    ~ sum(n5,nn5,n0),
    inference(canonicalize,[],[normalize_0_4]) ).

cnf(refute_0_8,plain,
    $false,
    inference(resolve,[$cnf( sum(n5,nn5,n0) )],[refute_0_6,refute_0_7]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.14  % Problem  : NUM318+1 : TPTP v8.1.0. Released v3.1.0.
% 0.13/0.15  % Command  : metis --show proof --show saturation %s
% 0.15/0.35  % Computer : n007.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit : 300
% 0.15/0.35  % WCLimit  : 600
% 0.15/0.35  % DateTime : Thu Jul  7 06:35:29 EDT 2022
% 0.15/0.35  % CPUTime  : 
% 0.15/0.35  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.61/0.79  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.61/0.79  
% 0.61/0.79  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.61/0.79  
%------------------------------------------------------------------------------