TSTP Solution File: NUM475+1 by Drodi---3.6.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : NUM475+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n005.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  : 300s
% DateTime : Tue Apr 30 20:34:49 EDT 2024

% Result   : Theorem 0.14s 0.40s
% Output   : CNFRefutation 0.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   28
% Syntax   : Number of formulae    :   99 (  29 unt;   2 def)
%            Number of atoms       :  273 (  60 equ)
%            Maximal formula atoms :   10 (   2 avg)
%            Number of connectives :  291 ( 117   ~; 125   |;  23   &)
%                                         (  18 <=>;   8  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :   19 (  17 usr;  15 prp; 0-2 aty)
%            Number of functors    :   11 (  11 usr;   7 con; 0-2 aty)
%            Number of variables   :   57 (  57   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f4,axiom,
    ! [W0,W1] :
      ( ( aNaturalNumber0(W0)
        & aNaturalNumber0(W1) )
     => aNaturalNumber0(sdtpldt0(W0,W1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f5,axiom,
    ! [W0,W1] :
      ( ( aNaturalNumber0(W0)
        & aNaturalNumber0(W1) )
     => aNaturalNumber0(sdtasdt0(W0,W1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f14,axiom,
    ! [W0,W1,W2] :
      ( ( aNaturalNumber0(W0)
        & aNaturalNumber0(W1)
        & aNaturalNumber0(W2) )
     => ( ( sdtpldt0(W0,W1) = sdtpldt0(W0,W2)
          | sdtpldt0(W1,W0) = sdtpldt0(W2,W0) )
       => W1 = W2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f19,definition,
    ! [W0,W1] :
      ( ( aNaturalNumber0(W0)
        & aNaturalNumber0(W1) )
     => ( sdtlseqdt0(W0,W1)
       => ! [W2] :
            ( W2 = sdtmndt0(W1,W0)
          <=> ( aNaturalNumber0(W2)
              & sdtpldt0(W0,W2) = W1 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f31,definition,
    ! [W0,W1] :
      ( ( aNaturalNumber0(W0)
        & aNaturalNumber0(W1) )
     => ( ( W0 != sz00
          & doDivides0(W0,W1) )
       => ! [W2] :
            ( W2 = sdtsldt0(W1,W0)
          <=> ( aNaturalNumber0(W2)
              & W1 = sdtasdt0(W0,W2) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f34,hypothesis,
    ( aNaturalNumber0(xl)
    & aNaturalNumber0(xm)
    & aNaturalNumber0(xn) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f35,hypothesis,
    ( doDivides0(xl,xm)
    & doDivides0(xl,sdtpldt0(xm,xn)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f36,hypothesis,
    xl != sz00,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f37,hypothesis,
    xp = sdtsldt0(xm,xl),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f38,hypothesis,
    xq = sdtsldt0(sdtpldt0(xm,xn),xl),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f39,hypothesis,
    sdtlseqdt0(xp,xq),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f40,hypothesis,
    xr = sdtmndt0(xq,xp),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f41,hypothesis,
    sdtpldt0(sdtasdt0(xl,xp),sdtasdt0(xl,xr)) = sdtpldt0(sdtasdt0(xl,xp),xn),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f42,conjecture,
    xn = sdtasdt0(xl,xr),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f43,negated_conjecture,
    xn != sdtasdt0(xl,xr),
    inference(negated_conjecture,[status(cth)],[f42]) ).

fof(f50,plain,
    ! [W0,W1] :
      ( ~ aNaturalNumber0(W0)
      | ~ aNaturalNumber0(W1)
      | aNaturalNumber0(sdtpldt0(W0,W1)) ),
    inference(pre_NNF_transformation,[status(esa)],[f4]) ).

fof(f51,plain,
    ! [X0,X1] :
      ( ~ aNaturalNumber0(X0)
      | ~ aNaturalNumber0(X1)
      | aNaturalNumber0(sdtpldt0(X0,X1)) ),
    inference(cnf_transformation,[status(esa)],[f50]) ).

fof(f52,plain,
    ! [W0,W1] :
      ( ~ aNaturalNumber0(W0)
      | ~ aNaturalNumber0(W1)
      | aNaturalNumber0(sdtasdt0(W0,W1)) ),
    inference(pre_NNF_transformation,[status(esa)],[f5]) ).

fof(f53,plain,
    ! [X0,X1] :
      ( ~ aNaturalNumber0(X0)
      | ~ aNaturalNumber0(X1)
      | aNaturalNumber0(sdtasdt0(X0,X1)) ),
    inference(cnf_transformation,[status(esa)],[f52]) ).

fof(f74,plain,
    ! [W0,W1,W2] :
      ( ~ aNaturalNumber0(W0)
      | ~ aNaturalNumber0(W1)
      | ~ aNaturalNumber0(W2)
      | ( sdtpldt0(W0,W1) != sdtpldt0(W0,W2)
        & sdtpldt0(W1,W0) != sdtpldt0(W2,W0) )
      | W1 = W2 ),
    inference(pre_NNF_transformation,[status(esa)],[f14]) ).

fof(f75,plain,
    ! [X0,X1,X2] :
      ( ~ aNaturalNumber0(X0)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X2)
      | sdtpldt0(X0,X1) != sdtpldt0(X0,X2)
      | X1 = X2 ),
    inference(cnf_transformation,[status(esa)],[f74]) ).

fof(f91,plain,
    ! [W0,W1] :
      ( ~ aNaturalNumber0(W0)
      | ~ aNaturalNumber0(W1)
      | ~ sdtlseqdt0(W0,W1)
      | ! [W2] :
          ( W2 = sdtmndt0(W1,W0)
        <=> ( aNaturalNumber0(W2)
            & sdtpldt0(W0,W2) = W1 ) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f19]) ).

fof(f92,plain,
    ! [W0,W1] :
      ( ~ aNaturalNumber0(W0)
      | ~ aNaturalNumber0(W1)
      | ~ sdtlseqdt0(W0,W1)
      | ! [W2] :
          ( ( W2 != sdtmndt0(W1,W0)
            | ( aNaturalNumber0(W2)
              & sdtpldt0(W0,W2) = W1 ) )
          & ( W2 = sdtmndt0(W1,W0)
            | ~ aNaturalNumber0(W2)
            | sdtpldt0(W0,W2) != W1 ) ) ),
    inference(NNF_transformation,[status(esa)],[f91]) ).

fof(f93,plain,
    ! [W0,W1] :
      ( ~ aNaturalNumber0(W0)
      | ~ aNaturalNumber0(W1)
      | ~ sdtlseqdt0(W0,W1)
      | ( ! [W2] :
            ( W2 != sdtmndt0(W1,W0)
            | ( aNaturalNumber0(W2)
              & sdtpldt0(W0,W2) = W1 ) )
        & ! [W2] :
            ( W2 = sdtmndt0(W1,W0)
            | ~ aNaturalNumber0(W2)
            | sdtpldt0(W0,W2) != W1 ) ) ),
    inference(miniscoping,[status(esa)],[f92]) ).

fof(f94,plain,
    ! [X0,X1,X2] :
      ( ~ aNaturalNumber0(X0)
      | ~ aNaturalNumber0(X1)
      | ~ sdtlseqdt0(X0,X1)
      | X2 != sdtmndt0(X1,X0)
      | aNaturalNumber0(X2) ),
    inference(cnf_transformation,[status(esa)],[f93]) ).

fof(f131,plain,
    ! [W0,W1] :
      ( ~ aNaturalNumber0(W0)
      | ~ aNaturalNumber0(W1)
      | W0 = sz00
      | ~ doDivides0(W0,W1)
      | ! [W2] :
          ( W2 = sdtsldt0(W1,W0)
        <=> ( aNaturalNumber0(W2)
            & W1 = sdtasdt0(W0,W2) ) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f31]) ).

fof(f132,plain,
    ! [W0,W1] :
      ( ~ aNaturalNumber0(W0)
      | ~ aNaturalNumber0(W1)
      | W0 = sz00
      | ~ doDivides0(W0,W1)
      | ! [W2] :
          ( ( W2 != sdtsldt0(W1,W0)
            | ( aNaturalNumber0(W2)
              & W1 = sdtasdt0(W0,W2) ) )
          & ( W2 = sdtsldt0(W1,W0)
            | ~ aNaturalNumber0(W2)
            | W1 != sdtasdt0(W0,W2) ) ) ),
    inference(NNF_transformation,[status(esa)],[f131]) ).

fof(f133,plain,
    ! [W0,W1] :
      ( ~ aNaturalNumber0(W0)
      | ~ aNaturalNumber0(W1)
      | W0 = sz00
      | ~ doDivides0(W0,W1)
      | ( ! [W2] :
            ( W2 != sdtsldt0(W1,W0)
            | ( aNaturalNumber0(W2)
              & W1 = sdtasdt0(W0,W2) ) )
        & ! [W2] :
            ( W2 = sdtsldt0(W1,W0)
            | ~ aNaturalNumber0(W2)
            | W1 != sdtasdt0(W0,W2) ) ) ),
    inference(miniscoping,[status(esa)],[f132]) ).

fof(f134,plain,
    ! [X0,X1,X2] :
      ( ~ aNaturalNumber0(X0)
      | ~ aNaturalNumber0(X1)
      | X0 = sz00
      | ~ doDivides0(X0,X1)
      | X2 != sdtsldt0(X1,X0)
      | aNaturalNumber0(X2) ),
    inference(cnf_transformation,[status(esa)],[f133]) ).

fof(f141,plain,
    aNaturalNumber0(xl),
    inference(cnf_transformation,[status(esa)],[f34]) ).

fof(f142,plain,
    aNaturalNumber0(xm),
    inference(cnf_transformation,[status(esa)],[f34]) ).

fof(f143,plain,
    aNaturalNumber0(xn),
    inference(cnf_transformation,[status(esa)],[f34]) ).

fof(f144,plain,
    doDivides0(xl,xm),
    inference(cnf_transformation,[status(esa)],[f35]) ).

fof(f145,plain,
    doDivides0(xl,sdtpldt0(xm,xn)),
    inference(cnf_transformation,[status(esa)],[f35]) ).

fof(f146,plain,
    xl != sz00,
    inference(cnf_transformation,[status(esa)],[f36]) ).

fof(f147,plain,
    xp = sdtsldt0(xm,xl),
    inference(cnf_transformation,[status(esa)],[f37]) ).

fof(f148,plain,
    xq = sdtsldt0(sdtpldt0(xm,xn),xl),
    inference(cnf_transformation,[status(esa)],[f38]) ).

fof(f149,plain,
    sdtlseqdt0(xp,xq),
    inference(cnf_transformation,[status(esa)],[f39]) ).

fof(f150,plain,
    xr = sdtmndt0(xq,xp),
    inference(cnf_transformation,[status(esa)],[f40]) ).

fof(f151,plain,
    sdtpldt0(sdtasdt0(xl,xp),sdtasdt0(xl,xr)) = sdtpldt0(sdtasdt0(xl,xp),xn),
    inference(cnf_transformation,[status(esa)],[f41]) ).

fof(f152,plain,
    xn != sdtasdt0(xl,xr),
    inference(cnf_transformation,[status(esa)],[f43]) ).

fof(f154,plain,
    ! [X0,X1] :
      ( ~ aNaturalNumber0(X0)
      | ~ aNaturalNumber0(X1)
      | ~ sdtlseqdt0(X0,X1)
      | aNaturalNumber0(sdtmndt0(X1,X0)) ),
    inference(destructive_equality_resolution,[status(esa)],[f94]) ).

fof(f160,plain,
    ! [X0,X1] :
      ( ~ aNaturalNumber0(X0)
      | ~ aNaturalNumber0(X1)
      | X0 = sz00
      | ~ doDivides0(X0,X1)
      | aNaturalNumber0(sdtsldt0(X1,X0)) ),
    inference(destructive_equality_resolution,[status(esa)],[f134]) ).

fof(f163,plain,
    ( spl0_0
  <=> aNaturalNumber0(sdtasdt0(xl,xp)) ),
    introduced(split_symbol_definition) ).

fof(f165,plain,
    ( ~ aNaturalNumber0(sdtasdt0(xl,xp))
    | spl0_0 ),
    inference(component_clause,[status(thm)],[f163]) ).

fof(f166,plain,
    ( spl0_1
  <=> aNaturalNumber0(sdtasdt0(xl,xr)) ),
    introduced(split_symbol_definition) ).

fof(f168,plain,
    ( ~ aNaturalNumber0(sdtasdt0(xl,xr))
    | spl0_1 ),
    inference(component_clause,[status(thm)],[f166]) ).

fof(f174,plain,
    ( spl0_3
  <=> aNaturalNumber0(xl) ),
    introduced(split_symbol_definition) ).

fof(f176,plain,
    ( ~ aNaturalNumber0(xl)
    | spl0_3 ),
    inference(component_clause,[status(thm)],[f174]) ).

fof(f177,plain,
    ( spl0_4
  <=> aNaturalNumber0(xr) ),
    introduced(split_symbol_definition) ).

fof(f180,plain,
    ( ~ aNaturalNumber0(xl)
    | ~ aNaturalNumber0(xr)
    | spl0_1 ),
    inference(resolution,[status(thm)],[f168,f53]) ).

fof(f181,plain,
    ( ~ spl0_3
    | ~ spl0_4
    | spl0_1 ),
    inference(split_clause,[status(thm)],[f180,f174,f177,f166]) ).

fof(f182,plain,
    ( $false
    | spl0_3 ),
    inference(forward_subsumption_resolution,[status(thm)],[f176,f141]) ).

fof(f183,plain,
    spl0_3,
    inference(contradiction_clause,[status(thm)],[f182]) ).

fof(f184,plain,
    ( spl0_5
  <=> aNaturalNumber0(xp) ),
    introduced(split_symbol_definition) ).

fof(f187,plain,
    ( ~ aNaturalNumber0(xl)
    | ~ aNaturalNumber0(xp)
    | spl0_0 ),
    inference(resolution,[status(thm)],[f165,f53]) ).

fof(f188,plain,
    ( ~ spl0_3
    | ~ spl0_5
    | spl0_0 ),
    inference(split_clause,[status(thm)],[f187,f174,f184,f163]) ).

fof(f189,plain,
    ( spl0_6
  <=> aNaturalNumber0(xn) ),
    introduced(split_symbol_definition) ).

fof(f191,plain,
    ( ~ aNaturalNumber0(xn)
    | spl0_6 ),
    inference(component_clause,[status(thm)],[f189]) ).

fof(f192,plain,
    ( spl0_7
  <=> sdtasdt0(xl,xr) = xn ),
    introduced(split_symbol_definition) ).

fof(f193,plain,
    ( sdtasdt0(xl,xr) = xn
    | ~ spl0_7 ),
    inference(component_clause,[status(thm)],[f192]) ).

fof(f195,plain,
    ( ~ aNaturalNumber0(sdtasdt0(xl,xp))
    | ~ aNaturalNumber0(sdtasdt0(xl,xr))
    | ~ aNaturalNumber0(xn)
    | sdtasdt0(xl,xr) = xn ),
    inference(resolution,[status(thm)],[f75,f151]) ).

fof(f196,plain,
    ( ~ spl0_0
    | ~ spl0_1
    | ~ spl0_6
    | spl0_7 ),
    inference(split_clause,[status(thm)],[f195,f163,f166,f189,f192]) ).

fof(f226,plain,
    ( $false
    | spl0_6 ),
    inference(forward_subsumption_resolution,[status(thm)],[f191,f143]) ).

fof(f227,plain,
    spl0_6,
    inference(contradiction_clause,[status(thm)],[f226]) ).

fof(f229,plain,
    ( $false
    | ~ spl0_7 ),
    inference(forward_subsumption_resolution,[status(thm)],[f193,f152]) ).

fof(f230,plain,
    ~ spl0_7,
    inference(contradiction_clause,[status(thm)],[f229]) ).

fof(f269,plain,
    ( spl0_15
  <=> aNaturalNumber0(xq) ),
    introduced(split_symbol_definition) ).

fof(f353,plain,
    ( spl0_30
  <=> sdtlseqdt0(xp,xq) ),
    introduced(split_symbol_definition) ).

fof(f355,plain,
    ( ~ sdtlseqdt0(xp,xq)
    | spl0_30 ),
    inference(component_clause,[status(thm)],[f353]) ).

fof(f356,plain,
    ( ~ aNaturalNumber0(xp)
    | ~ aNaturalNumber0(xq)
    | ~ sdtlseqdt0(xp,xq)
    | aNaturalNumber0(xr) ),
    inference(paramodulation,[status(thm)],[f150,f154]) ).

fof(f357,plain,
    ( ~ spl0_5
    | ~ spl0_15
    | ~ spl0_30
    | spl0_4 ),
    inference(split_clause,[status(thm)],[f356,f184,f269,f353,f177]) ).

fof(f482,plain,
    ( spl0_46
  <=> aNaturalNumber0(sdtpldt0(xm,xn)) ),
    introduced(split_symbol_definition) ).

fof(f484,plain,
    ( ~ aNaturalNumber0(sdtpldt0(xm,xn))
    | spl0_46 ),
    inference(component_clause,[status(thm)],[f482]) ).

fof(f485,plain,
    ( spl0_47
  <=> xl = sz00 ),
    introduced(split_symbol_definition) ).

fof(f486,plain,
    ( xl = sz00
    | ~ spl0_47 ),
    inference(component_clause,[status(thm)],[f485]) ).

fof(f488,plain,
    ( spl0_48
  <=> doDivides0(xl,sdtpldt0(xm,xn)) ),
    introduced(split_symbol_definition) ).

fof(f490,plain,
    ( ~ doDivides0(xl,sdtpldt0(xm,xn))
    | spl0_48 ),
    inference(component_clause,[status(thm)],[f488]) ).

fof(f491,plain,
    ( ~ aNaturalNumber0(xl)
    | ~ aNaturalNumber0(sdtpldt0(xm,xn))
    | xl = sz00
    | ~ doDivides0(xl,sdtpldt0(xm,xn))
    | aNaturalNumber0(xq) ),
    inference(paramodulation,[status(thm)],[f148,f160]) ).

fof(f492,plain,
    ( ~ spl0_3
    | ~ spl0_46
    | spl0_47
    | ~ spl0_48
    | spl0_15 ),
    inference(split_clause,[status(thm)],[f491,f174,f482,f485,f488,f269]) ).

fof(f493,plain,
    ( spl0_49
  <=> aNaturalNumber0(xm) ),
    introduced(split_symbol_definition) ).

fof(f495,plain,
    ( ~ aNaturalNumber0(xm)
    | spl0_49 ),
    inference(component_clause,[status(thm)],[f493]) ).

fof(f496,plain,
    ( spl0_50
  <=> doDivides0(xl,xm) ),
    introduced(split_symbol_definition) ).

fof(f498,plain,
    ( ~ doDivides0(xl,xm)
    | spl0_50 ),
    inference(component_clause,[status(thm)],[f496]) ).

fof(f499,plain,
    ( ~ aNaturalNumber0(xl)
    | ~ aNaturalNumber0(xm)
    | xl = sz00
    | ~ doDivides0(xl,xm)
    | aNaturalNumber0(xp) ),
    inference(paramodulation,[status(thm)],[f147,f160]) ).

fof(f500,plain,
    ( ~ spl0_3
    | ~ spl0_49
    | spl0_47
    | ~ spl0_50
    | spl0_5 ),
    inference(split_clause,[status(thm)],[f499,f174,f493,f485,f496,f184]) ).

fof(f501,plain,
    ( $false
    | spl0_50 ),
    inference(forward_subsumption_resolution,[status(thm)],[f498,f144]) ).

fof(f502,plain,
    spl0_50,
    inference(contradiction_clause,[status(thm)],[f501]) ).

fof(f503,plain,
    ( $false
    | spl0_49 ),
    inference(forward_subsumption_resolution,[status(thm)],[f495,f142]) ).

fof(f504,plain,
    spl0_49,
    inference(contradiction_clause,[status(thm)],[f503]) ).

fof(f505,plain,
    ( $false
    | ~ spl0_47 ),
    inference(forward_subsumption_resolution,[status(thm)],[f486,f146]) ).

fof(f506,plain,
    ~ spl0_47,
    inference(contradiction_clause,[status(thm)],[f505]) ).

fof(f507,plain,
    ( $false
    | spl0_48 ),
    inference(forward_subsumption_resolution,[status(thm)],[f490,f145]) ).

fof(f508,plain,
    spl0_48,
    inference(contradiction_clause,[status(thm)],[f507]) ).

fof(f509,plain,
    ( $false
    | spl0_30 ),
    inference(forward_subsumption_resolution,[status(thm)],[f355,f149]) ).

fof(f510,plain,
    spl0_30,
    inference(contradiction_clause,[status(thm)],[f509]) ).

fof(f513,plain,
    ( ~ aNaturalNumber0(xm)
    | ~ aNaturalNumber0(xn)
    | spl0_46 ),
    inference(resolution,[status(thm)],[f484,f51]) ).

fof(f514,plain,
    ( ~ spl0_49
    | ~ spl0_6
    | spl0_46 ),
    inference(split_clause,[status(thm)],[f513,f493,f189,f482]) ).

fof(f515,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f181,f183,f188,f196,f227,f230,f357,f492,f500,f502,f504,f506,f508,f510,f514]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13  % Problem  : NUM475+1 : TPTP v8.1.2. Released v4.0.0.
% 0.13/0.14  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.14/0.35  % Computer : n005.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Mon Apr 29 20:38:41 EDT 2024
% 0.14/0.35  % CPUTime  : 
% 0.14/0.36  % Drodi V3.6.0
% 0.14/0.40  % Refutation found
% 0.14/0.40  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.40  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.20/0.43  % Elapsed time: 0.062456 seconds
% 0.20/0.43  % CPU time: 0.353121 seconds
% 0.20/0.43  % Total memory used: 63.989 MB
% 0.20/0.43  % Net memory used: 63.721 MB
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