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Drodi---4.1.1.THM-CRf.s

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%------------------------------------------------------------------------------
% File     : Drodi---4.1.1
% Problem  : NUM584+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p

% Computer : n018.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8046.5625MB
% OS       : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Thu Sep 24 01:41:05 PM UTC 2026

% Result   : Theorem 0.15s 0.44s
% Output   : CNFRefutation 0.15s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   28 (   5 unt;   2 def)
%            Number of atoms       :  209 (  36 equ)
%            Maximal formula atoms :   17 (   7 avg)
%            Number of connectives :  246 (  65   ~;  63   |;  98   &)
%                                         (   9 <=>;  11  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   6 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :    9 (   7 usr;   3 prp; 0-2 aty)
%            Number of functors    :   11 (  11 usr;   6 con; 0-2 aty)
%            Number of variables   :   41 (  38   !;   3   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f87,hypothesis,
    ( sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) = xK
    & ! [W0] :
        ( aElementOf0(W0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
      <=> ( ( W0 = szmzizndt0(sdtlpdtrp0(xN,xi))
            | aElementOf0(W0,xQ) )
          & aElement0(W0) ) )
    & aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
    & ! [W0] :
        ( aElementOf0(W0,sdtlpdtrp0(xN,xi))
       => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W0) )
    & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f88,hypothesis,
    ( aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS)
    & ! [W0] :
        ( aElementOf0(W0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
       => aElementOf0(W0,xS) )
    & ! [W0] :
        ( aElementOf0(W0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
      <=> ( ( W0 = szmzizndt0(sdtlpdtrp0(xN,xi))
            | aElementOf0(W0,xQ) )
          & aElement0(W0) ) )
    & aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
    & ! [W0] :
        ( aElementOf0(W0,sdtlpdtrp0(xN,xi))
       => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W0) )
    & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f89,conjecture,
    ( ( ! [W0] :
          ( aElementOf0(W0,sdtlpdtrp0(xN,xi))
         => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W0) )
      & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi)) )
   => ( ( ! [W0] :
            ( aElementOf0(W0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
          <=> ( ( W0 = szmzizndt0(sdtlpdtrp0(xN,xi))
                | aElementOf0(W0,xQ) )
              & aElement0(W0) ) )
        & aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) )
     => ( aElementOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),slbdtsldtrb0(xS,xK))
        | ( sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) = xK
          & ( aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS)
            | ! [W0] :
                ( aElementOf0(W0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
               => aElementOf0(W0,xS) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f90,negated_conjecture,
    ~ ( ( ! [W0] :
            ( aElementOf0(W0,sdtlpdtrp0(xN,xi))
           => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W0) )
        & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi)) )
     => ( ( ! [W0] :
              ( aElementOf0(W0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
            <=> ( ( W0 = szmzizndt0(sdtlpdtrp0(xN,xi))
                  | aElementOf0(W0,xQ) )
                & aElement0(W0) ) )
          & aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) )
       => ( aElementOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),slbdtsldtrb0(xS,xK))
          | ( sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) = xK
            & ( aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS)
              | ! [W0] :
                  ( aElementOf0(W0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
                 => aElementOf0(W0,xS) ) ) ) ) ) ),
    inference(negated_conjecture,[status(cth)],[f89]) ).

fof(f437,plain,
    ( sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) = xK
    & ! [W0] :
        ( aElementOf0(W0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
      <=> ( ( W0 = szmzizndt0(sdtlpdtrp0(xN,xi))
            | aElementOf0(W0,xQ) )
          & aElement0(W0) ) )
    & aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
    & ! [W0] :
        ( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W0)
        | ~ aElementOf0(W0,sdtlpdtrp0(xN,xi)) )
    & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi)) ),
    inference(pre_NNF_transformation,[status(thm)],[f87]) ).

fof(f438,plain,
    ( sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) = xK
    & ! [W0] :
        ( ( ( W0 != szmzizndt0(sdtlpdtrp0(xN,xi))
            & ~ aElementOf0(W0,xQ) )
          | ~ aElement0(W0)
          | aElementOf0(W0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) )
        & ( ( ( W0 = szmzizndt0(sdtlpdtrp0(xN,xi))
              | aElementOf0(W0,xQ) )
            & aElement0(W0) )
          | ~ aElementOf0(W0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) ) )
    & aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
    & ! [W0] :
        ( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W0)
        | ~ aElementOf0(W0,sdtlpdtrp0(xN,xi)) )
    & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi)) ),
    inference(NNF_transformation,[status(thm)],[f437]) ).

fof(f439,plain,
    ( sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) = xK
    & ! [W0] :
        ( ( W0 != szmzizndt0(sdtlpdtrp0(xN,xi))
          & ~ aElementOf0(W0,xQ) )
        | ~ aElement0(W0)
        | aElementOf0(W0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) )
    & ! [W0] :
        ( ( ( W0 = szmzizndt0(sdtlpdtrp0(xN,xi))
            | aElementOf0(W0,xQ) )
          & aElement0(W0) )
        | ~ aElementOf0(W0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) )
    & aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
    & ! [W0] :
        ( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W0)
        | ~ aElementOf0(W0,sdtlpdtrp0(xN,xi)) )
    & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi)) ),
    inference(miniscoping,[status(thm)],[f438]) ).

fof(f447,plain,
    sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) = xK,
    inference(cnf_transformation,[status(thm)],[f439]) ).

fof(f448,plain,
    ( aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS)
    & ! [W0] :
        ( aElementOf0(W0,xS)
        | ~ aElementOf0(W0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) )
    & ! [W0] :
        ( aElementOf0(W0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
      <=> ( ( W0 = szmzizndt0(sdtlpdtrp0(xN,xi))
            | aElementOf0(W0,xQ) )
          & aElement0(W0) ) )
    & aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
    & ! [W0] :
        ( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W0)
        | ~ aElementOf0(W0,sdtlpdtrp0(xN,xi)) )
    & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi)) ),
    inference(pre_NNF_transformation,[status(thm)],[f88]) ).

fof(f449,plain,
    ( aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS)
    & ! [W0] :
        ( aElementOf0(W0,xS)
        | ~ aElementOf0(W0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) )
    & ! [W0] :
        ( ( ( W0 != szmzizndt0(sdtlpdtrp0(xN,xi))
            & ~ aElementOf0(W0,xQ) )
          | ~ aElement0(W0)
          | aElementOf0(W0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) )
        & ( ( ( W0 = szmzizndt0(sdtlpdtrp0(xN,xi))
              | aElementOf0(W0,xQ) )
            & aElement0(W0) )
          | ~ aElementOf0(W0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) ) )
    & aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
    & ! [W0] :
        ( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W0)
        | ~ aElementOf0(W0,sdtlpdtrp0(xN,xi)) )
    & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi)) ),
    inference(NNF_transformation,[status(thm)],[f448]) ).

fof(f450,plain,
    ( aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS)
    & ! [W0] :
        ( aElementOf0(W0,xS)
        | ~ aElementOf0(W0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) )
    & ! [W0] :
        ( ( W0 != szmzizndt0(sdtlpdtrp0(xN,xi))
          & ~ aElementOf0(W0,xQ) )
        | ~ aElement0(W0)
        | aElementOf0(W0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) )
    & ! [W0] :
        ( ( ( W0 = szmzizndt0(sdtlpdtrp0(xN,xi))
            | aElementOf0(W0,xQ) )
          & aElement0(W0) )
        | ~ aElementOf0(W0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) )
    & aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
    & ! [W0] :
        ( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W0)
        | ~ aElementOf0(W0,sdtlpdtrp0(xN,xi)) )
    & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi)) ),
    inference(miniscoping,[status(thm)],[f449]) ).

fof(f459,plain,
    aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS),
    inference(cnf_transformation,[status(thm)],[f450]) ).

fof(f460,plain,
    ( ~ aElementOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),slbdtsldtrb0(xS,xK))
    & ( sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) != xK
      | ( ~ aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS)
        & ? [W0] :
            ( ~ aElementOf0(W0,xS)
            & aElementOf0(W0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) ) ) )
    & ! [W0] :
        ( aElementOf0(W0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
      <=> ( ( W0 = szmzizndt0(sdtlpdtrp0(xN,xi))
            | aElementOf0(W0,xQ) )
          & aElement0(W0) ) )
    & aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
    & ! [W0] :
        ( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W0)
        | ~ aElementOf0(W0,sdtlpdtrp0(xN,xi)) )
    & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi)) ),
    inference(pre_NNF_transformation,[status(thm)],[f90]) ).

fof(f461,plain,
    ( ~ aElementOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),slbdtsldtrb0(xS,xK))
    & ( sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) != xK
      | ( ~ aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS)
        & ? [W0] :
            ( ~ aElementOf0(W0,xS)
            & aElementOf0(W0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) ) ) )
    & ! [W0] :
        ( ( ( W0 != szmzizndt0(sdtlpdtrp0(xN,xi))
            & ~ aElementOf0(W0,xQ) )
          | ~ aElement0(W0)
          | aElementOf0(W0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) )
        & ( ( ( W0 = szmzizndt0(sdtlpdtrp0(xN,xi))
              | aElementOf0(W0,xQ) )
            & aElement0(W0) )
          | ~ aElementOf0(W0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) ) )
    & aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
    & ! [W0] :
        ( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W0)
        | ~ aElementOf0(W0,sdtlpdtrp0(xN,xi)) )
    & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi)) ),
    inference(NNF_transformation,[status(thm)],[f460]) ).

fof(f462,plain,
    ( ~ aElementOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),slbdtsldtrb0(xS,xK))
    & ( sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) != xK
      | ( ~ aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS)
        & ? [W0] :
            ( ~ aElementOf0(W0,xS)
            & aElementOf0(W0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) ) ) )
    & ! [W0] :
        ( ( W0 != szmzizndt0(sdtlpdtrp0(xN,xi))
          & ~ aElementOf0(W0,xQ) )
        | ~ aElement0(W0)
        | aElementOf0(W0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) )
    & ! [W0] :
        ( ( ( W0 = szmzizndt0(sdtlpdtrp0(xN,xi))
            | aElementOf0(W0,xQ) )
          & aElement0(W0) )
        | ~ aElementOf0(W0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) )
    & aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
    & ! [W0] :
        ( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W0)
        | ~ aElementOf0(W0,sdtlpdtrp0(xN,xi)) )
    & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi)) ),
    inference(miniscoping,[status(thm)],[f461]) ).

fof(f463,plain,
    ( ~ aElementOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),slbdtsldtrb0(xS,xK))
    & ( sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) != xK
      | ( ~ aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS)
        & ~ aElementOf0(sK24_skl,xS)
        & aElementOf0(sK24_skl,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) ) )
    & ! [W0] :
        ( ( W0 != szmzizndt0(sdtlpdtrp0(xN,xi))
          & ~ aElementOf0(W0,xQ) )
        | ~ aElement0(W0)
        | aElementOf0(W0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) )
    & ! [W0] :
        ( ( ( W0 = szmzizndt0(sdtlpdtrp0(xN,xi))
            | aElementOf0(W0,xQ) )
          & aElement0(W0) )
        | ~ aElementOf0(W0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) )
    & aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
    & ! [W0] :
        ( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W0)
        | ~ aElementOf0(W0,sdtlpdtrp0(xN,xi)) )
    & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK24_skl]),skolemize(W0,sK24_skl)],[f462]) ).

fof(f473,plain,
    ( sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) != xK
    | ~ aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS) ),
    inference(cnf_transformation,[status(thm)],[f463]) ).

fof(f553,definition,
    ( sQ1_spl
  <=> sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) = xK ),
    introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).

fof(f555,plain,
    ( sQ1_spl
    | sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) != xK ),
    inference(component_clause,[status(thm)],[f553]) ).

fof(f561,definition,
    ( sQ3_spl
  <=> aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS) ),
    introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).

fof(f563,plain,
    ( sQ3_spl
    | ~ aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS) ),
    inference(component_clause,[status(thm)],[f561]) ).

fof(f564,plain,
    ( ~ sQ1_spl
    | ~ sQ3_spl ),
    inference(split_clause,[status(thm)],[f473,f561,f553]) ).

fof(f634,plain,
    ( sQ1_spl
    | xK != xK ),
    inference(forward_demodulation,[status(thm)],[f447,f555]) ).

fof(f635,plain,
    ( sQ1_spl
    | $false ),
    inference(trivial_equality_resolution,[status(thm)],[f634]) ).

fof(f636,plain,
    sQ1_spl,
    inference(contradiction_clause,[status(thm)],[f635]) ).

fof(f637,plain,
    ( sQ3_spl
    | $false ),
    inference(forward_subsumption_resolution,[status(thm)],[f563,f459]) ).

fof(f638,plain,
    sQ3_spl,
    inference(contradiction_clause,[status(thm)],[f637]) ).

fof(f639,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f564,f636,f638]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : NUM584+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04  % Command  : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36  % Computer : n018.cluster.edu
% 0.10/0.36  % Model    : x86_64 x86_64
% 0.10/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36  % Memory   : 8046.5625MB
% 0.10/0.36  % OS       : Linux 6.8.0-71-generic
% 0.10/0.36  % CPULimit : 300
% 0.10/0.36  % WCLimit  : 300
% 0.10/0.36  % DateTime : Mon Sep 21 02:44:31 UTC 2026
% 0.10/0.37  % CPUTime  : 
% 0.15/0.39  % Drodi V4.1.1
% 0.15/0.44  % Refutation found
% 0.15/0.44  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.15/0.44  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.46  % Elapsed time: 0.087624 seconds
% 0.15/0.46  % CPU time: 0.317000 seconds
% 0.15/0.46  % Total memory used: 119.278 MB
% 0.15/0.46  % Net memory used: 118.835 MB
%------------------------------------------------------------------------------