TSTP Solution File: NUM523+1 by Drodi---3.6.0

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%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : NUM523+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n017.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 20:35:00 EDT 2024

% Result   : Theorem 16.61s 2.44s
% Output   : CNFRefutation 16.61s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   54 (  12 unt;   1 def)
%            Number of atoms       :  153 (  12 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :  166 (  67   ~;  68   |;  18   &)
%                                         (   9 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :   12 (  10 usr;   8 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   4 con; 0-2 aty)
%            Number of variables   :   35 (  32   !;   3   ?)

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

fof(f30,definition,
    ! [W0,W1] :
      ( ( aNaturalNumber0(W0)
        & aNaturalNumber0(W1) )
     => ( doDivides0(W0,W1)
      <=> ? [W2] :
            ( aNaturalNumber0(W2)
            & W1 = sdtasdt0(W0,W2) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f39,axiom,
    ! [W0,W1,W2] :
      ( ( aNaturalNumber0(W0)
        & aNaturalNumber0(W1)
        & aNaturalNumber0(W2) )
     => ( ( isPrime0(W2)
          & doDivides0(W2,sdtasdt0(W0,W1)) )
       => ( doDivides0(W2,W0)
          | doDivides0(W2,W1) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f40,hypothesis,
    ( aNaturalNumber0(xn)
    & aNaturalNumber0(xm)
    & aNaturalNumber0(xp)
    & xn != sz00
    & xm != sz00
    & xp != sz00 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f42,hypothesis,
    sdtasdt0(xp,sdtasdt0(xm,xm)) = sdtasdt0(xn,xn),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f43,hypothesis,
    isPrime0(xp),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f44,conjecture,
    ( doDivides0(xp,sdtasdt0(xn,xn))
    & doDivides0(xp,xn) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f45,negated_conjecture,
    ~ ( doDivides0(xp,sdtasdt0(xn,xn))
      & doDivides0(xp,xn) ),
    inference(negated_conjecture,[status(cth)],[f44]) ).

fof(f54,plain,
    ! [W0,W1] :
      ( ~ aNaturalNumber0(W0)
      | ~ aNaturalNumber0(W1)
      | aNaturalNumber0(sdtasdt0(W0,W1)) ),
    inference(pre_NNF_transformation,[status(esa)],[f5]) ).

fof(f55,plain,
    ! [X0,X1] :
      ( ~ aNaturalNumber0(X0)
      | ~ aNaturalNumber0(X1)
      | aNaturalNumber0(sdtasdt0(X0,X1)) ),
    inference(cnf_transformation,[status(esa)],[f54]) ).

fof(f127,plain,
    ! [W0,W1] :
      ( ~ aNaturalNumber0(W0)
      | ~ aNaturalNumber0(W1)
      | ( doDivides0(W0,W1)
      <=> ? [W2] :
            ( aNaturalNumber0(W2)
            & W1 = sdtasdt0(W0,W2) ) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f30]) ).

fof(f128,plain,
    ! [W0,W1] :
      ( ~ aNaturalNumber0(W0)
      | ~ aNaturalNumber0(W1)
      | ( ( ~ doDivides0(W0,W1)
          | ? [W2] :
              ( aNaturalNumber0(W2)
              & W1 = sdtasdt0(W0,W2) ) )
        & ( doDivides0(W0,W1)
          | ! [W2] :
              ( ~ aNaturalNumber0(W2)
              | W1 != sdtasdt0(W0,W2) ) ) ) ),
    inference(NNF_transformation,[status(esa)],[f127]) ).

fof(f129,plain,
    ! [W0,W1] :
      ( ~ aNaturalNumber0(W0)
      | ~ aNaturalNumber0(W1)
      | ( ( ~ doDivides0(W0,W1)
          | ( aNaturalNumber0(sk0_1(W1,W0))
            & W1 = sdtasdt0(W0,sk0_1(W1,W0)) ) )
        & ( doDivides0(W0,W1)
          | ! [W2] :
              ( ~ aNaturalNumber0(W2)
              | W1 != sdtasdt0(W0,W2) ) ) ) ),
    inference(skolemization,[status(esa)],[f128]) ).

fof(f132,plain,
    ! [X0,X1,X2] :
      ( ~ aNaturalNumber0(X0)
      | ~ aNaturalNumber0(X1)
      | doDivides0(X0,X1)
      | ~ aNaturalNumber0(X2)
      | X1 != sdtasdt0(X0,X2) ),
    inference(cnf_transformation,[status(esa)],[f129]) ).

fof(f164,plain,
    ! [W0,W1,W2] :
      ( ~ aNaturalNumber0(W0)
      | ~ aNaturalNumber0(W1)
      | ~ aNaturalNumber0(W2)
      | ~ isPrime0(W2)
      | ~ doDivides0(W2,sdtasdt0(W0,W1))
      | doDivides0(W2,W0)
      | doDivides0(W2,W1) ),
    inference(pre_NNF_transformation,[status(esa)],[f39]) ).

fof(f165,plain,
    ! [X0,X1,X2] :
      ( ~ aNaturalNumber0(X0)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X2)
      | ~ isPrime0(X2)
      | ~ doDivides0(X2,sdtasdt0(X0,X1))
      | doDivides0(X2,X0)
      | doDivides0(X2,X1) ),
    inference(cnf_transformation,[status(esa)],[f164]) ).

fof(f166,plain,
    aNaturalNumber0(xn),
    inference(cnf_transformation,[status(esa)],[f40]) ).

fof(f167,plain,
    aNaturalNumber0(xm),
    inference(cnf_transformation,[status(esa)],[f40]) ).

fof(f168,plain,
    aNaturalNumber0(xp),
    inference(cnf_transformation,[status(esa)],[f40]) ).

fof(f174,plain,
    sdtasdt0(xp,sdtasdt0(xm,xm)) = sdtasdt0(xn,xn),
    inference(cnf_transformation,[status(esa)],[f42]) ).

fof(f175,plain,
    isPrime0(xp),
    inference(cnf_transformation,[status(esa)],[f43]) ).

fof(f176,plain,
    ( ~ doDivides0(xp,sdtasdt0(xn,xn))
    | ~ doDivides0(xp,xn) ),
    inference(pre_NNF_transformation,[status(esa)],[f45]) ).

fof(f177,plain,
    ( ~ doDivides0(xp,sdtasdt0(xn,xn))
    | ~ doDivides0(xp,xn) ),
    inference(cnf_transformation,[status(esa)],[f176]) ).

fof(f178,plain,
    ( spl0_0
  <=> doDivides0(xp,sdtasdt0(xn,xn)) ),
    introduced(split_symbol_definition) ).

fof(f179,plain,
    ( doDivides0(xp,sdtasdt0(xn,xn))
    | ~ spl0_0 ),
    inference(component_clause,[status(thm)],[f178]) ).

fof(f181,plain,
    ( spl0_1
  <=> doDivides0(xp,xn) ),
    introduced(split_symbol_definition) ).

fof(f184,plain,
    ( ~ spl0_0
    | ~ spl0_1 ),
    inference(split_clause,[status(thm)],[f177,f178,f181]) ).

fof(f191,plain,
    ! [X0,X1] :
      ( ~ aNaturalNumber0(X0)
      | ~ aNaturalNumber0(sdtasdt0(X0,X1))
      | doDivides0(X0,sdtasdt0(X0,X1))
      | ~ aNaturalNumber0(X1) ),
    inference(destructive_equality_resolution,[status(esa)],[f132]) ).

fof(f197,plain,
    ! [X0,X1] :
      ( ~ aNaturalNumber0(X0)
      | doDivides0(X0,sdtasdt0(X0,X1))
      | ~ aNaturalNumber0(X1) ),
    inference(forward_subsumption_resolution,[status(thm)],[f191,f55]) ).

fof(f270,plain,
    ( spl0_2
  <=> aNaturalNumber0(xp) ),
    introduced(split_symbol_definition) ).

fof(f272,plain,
    ( ~ aNaturalNumber0(xp)
    | spl0_2 ),
    inference(component_clause,[status(thm)],[f270]) ).

fof(f273,plain,
    ( spl0_3
  <=> aNaturalNumber0(xn) ),
    introduced(split_symbol_definition) ).

fof(f275,plain,
    ( ~ aNaturalNumber0(xn)
    | spl0_3 ),
    inference(component_clause,[status(thm)],[f273]) ).

fof(f291,plain,
    ( $false
    | spl0_3 ),
    inference(forward_subsumption_resolution,[status(thm)],[f275,f166]) ).

fof(f292,plain,
    spl0_3,
    inference(contradiction_clause,[status(thm)],[f291]) ).

fof(f303,plain,
    ( $false
    | spl0_2 ),
    inference(forward_subsumption_resolution,[status(thm)],[f272,f168]) ).

fof(f304,plain,
    spl0_2,
    inference(contradiction_clause,[status(thm)],[f303]) ).

fof(f2036,plain,
    ( spl0_197
  <=> aNaturalNumber0(sdtasdt0(xm,xm)) ),
    introduced(split_symbol_definition) ).

fof(f2038,plain,
    ( ~ aNaturalNumber0(sdtasdt0(xm,xm))
    | spl0_197 ),
    inference(component_clause,[status(thm)],[f2036]) ).

fof(f2085,plain,
    ( ~ aNaturalNumber0(xp)
    | doDivides0(xp,sdtasdt0(xn,xn))
    | ~ aNaturalNumber0(sdtasdt0(xm,xm)) ),
    inference(paramodulation,[status(thm)],[f174,f197]) ).

fof(f2086,plain,
    ( ~ spl0_2
    | spl0_0
    | ~ spl0_197 ),
    inference(split_clause,[status(thm)],[f2085,f270,f178,f2036]) ).

fof(f2219,plain,
    ( spl0_213
  <=> aNaturalNumber0(xm) ),
    introduced(split_symbol_definition) ).

fof(f2221,plain,
    ( ~ aNaturalNumber0(xm)
    | spl0_213 ),
    inference(component_clause,[status(thm)],[f2219]) ).

fof(f2222,plain,
    ( ~ aNaturalNumber0(xm)
    | ~ aNaturalNumber0(xm)
    | spl0_197 ),
    inference(resolution,[status(thm)],[f2038,f55]) ).

fof(f2223,plain,
    ( ~ spl0_213
    | spl0_197 ),
    inference(split_clause,[status(thm)],[f2222,f2219,f2036]) ).

fof(f2224,plain,
    ( $false
    | spl0_213 ),
    inference(forward_subsumption_resolution,[status(thm)],[f2221,f167]) ).

fof(f2225,plain,
    spl0_213,
    inference(contradiction_clause,[status(thm)],[f2224]) ).

fof(f2840,plain,
    ( spl0_252
  <=> isPrime0(xp) ),
    introduced(split_symbol_definition) ).

fof(f2842,plain,
    ( ~ isPrime0(xp)
    | spl0_252 ),
    inference(component_clause,[status(thm)],[f2840]) ).

fof(f2869,plain,
    ( $false
    | spl0_252 ),
    inference(forward_subsumption_resolution,[status(thm)],[f2842,f175]) ).

fof(f2870,plain,
    spl0_252,
    inference(contradiction_clause,[status(thm)],[f2869]) ).

fof(f5831,plain,
    ( ~ aNaturalNumber0(xn)
    | ~ aNaturalNumber0(xn)
    | ~ aNaturalNumber0(xp)
    | ~ isPrime0(xp)
    | doDivides0(xp,xn)
    | doDivides0(xp,xn)
    | ~ spl0_0 ),
    inference(resolution,[status(thm)],[f179,f165]) ).

fof(f5832,plain,
    ( ~ spl0_3
    | ~ spl0_2
    | ~ spl0_252
    | spl0_1
    | ~ spl0_0 ),
    inference(split_clause,[status(thm)],[f5831,f273,f270,f2840,f181,f178]) ).

fof(f5859,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f184,f292,f304,f2086,f2223,f2225,f2870,f5832]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.11  % Problem  : NUM523+1 : TPTP v8.1.2. Released v4.0.0.
% 0.09/0.11  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.09/0.32  % Computer : n017.cluster.edu
% 0.09/0.32  % Model    : x86_64 x86_64
% 0.09/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.32  % Memory   : 8042.1875MB
% 0.09/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.09/0.32  % CPULimit : 300
% 0.09/0.32  % WCLimit  : 300
% 0.09/0.32  % DateTime : Mon Apr 29 20:19:03 EDT 2024
% 0.09/0.32  % CPUTime  : 
% 0.09/0.33  % Drodi V3.6.0
% 16.61/2.44  % Refutation found
% 16.61/2.44  % SZS status Theorem for theBenchmark: Theorem is valid
% 16.61/2.44  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 16.61/2.47  % Elapsed time: 2.132294 seconds
% 16.61/2.47  % CPU time: 16.758839 seconds
% 16.61/2.47  % Total memory used: 144.996 MB
% 16.61/2.47  % Net memory used: 140.920 MB
%------------------------------------------------------------------------------