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Drodi---4.1.1.THM-CRf.s

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%------------------------------------------------------------------------------
% File     : Drodi---4.1.1
% Problem  : NUM564+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p

% Computer : n001.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 01:41:01 PM UTC 2026

% Result   : Theorem 0.12s 5.82s
% Output   : CNFRefutation 0.12s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   19
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   79 (  22 unt;   3 def)
%            Number of atoms       :  279 (  70 equ)
%            Maximal formula atoms :   18 (   3 avg)
%            Number of connectives :  340 ( 140   ~; 134   |;  49   &)
%                                         (  10 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   5 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    8 (   6 usr;   1 prp; 0-2 aty)
%            Number of functors    :   14 (  14 usr;   7 con; 0-3 aty)
%            Number of variables   :  100 (  93   !;   7   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f5,definition,
    ! [W0] :
      ( W0 = slcrc0
    <=> ( ~ ? [W1] : aElementOf0(W1,W0)
        & aSet0(W0) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f8,axiom,
    ! [W0] :
      ( ( isCountable0(W0)
        & aSet0(W0) )
     => ~ isFinite0(W0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f10,definition,
    ! [W0] :
      ( aSet0(W0)
     => ! [W1] :
          ( aSubsetOf0(W1,W0)
        <=> ( ! [W2] :
                ( aElementOf0(W2,W1)
               => aElementOf0(W2,W0) )
            & aSet0(W1) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f23,axiom,
    ( isCountable0(szNzAzT0)
    & aSet0(szNzAzT0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f24,axiom,
    aElementOf0(sz00,szNzAzT0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f42,axiom,
    ! [W0] :
      ( aSet0(W0)
     => ( sbrdtbr0(W0) = sz00
      <=> W0 = slcrc0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f57,definition,
    ! [W0,W1] :
      ( ( aElementOf0(W1,szNzAzT0)
        & aSet0(W0) )
     => ! [W2] :
          ( W2 = slbdtsldtrb0(W0,W1)
        <=> ( ! [W3] :
                ( aElementOf0(W3,W2)
              <=> ( sbrdtbr0(W3) = W1
                  & aSubsetOf0(W3,W0) ) )
            & aSet0(W2) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f59,axiom,
    ! [W0] :
      ( ( ~ isFinite0(W0)
        & aSet0(W0) )
     => ! [W1] :
          ( aElementOf0(W1,szNzAzT0)
         => slbdtsldtrb0(W0,W1) != slcrc0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f75,hypothesis,
    ( isCountable0(xS)
    & aSubsetOf0(xS,szNzAzT0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f76,hypothesis,
    ( aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
    & szDzozmdt0(xc) = slbdtsldtrb0(xS,xK)
    & aFunction0(xc) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f78,hypothesis,
    xK = sz00,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f79,conjecture,
    aElementOf0(slcrc0,slbdtsldtrb0(xS,sz00)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f80,negated_conjecture,
    ~ aElementOf0(slcrc0,slbdtsldtrb0(xS,sz00)),
    inference(negated_conjecture,[status(cth)],[f79]) ).

fof(f91,plain,
    ! [W0] :
      ( W0 = slcrc0
    <=> ( ! [W1] : ~ aElementOf0(W1,W0)
        & aSet0(W0) ) ),
    inference(pre_NNF_transformation,[status(thm)],[f5]) ).

fof(f92,plain,
    ! [W0] :
      ( ( ? [W1] : aElementOf0(W1,W0)
        | ~ aSet0(W0)
        | W0 = slcrc0 )
      & ( ( ! [W1] : ~ aElementOf0(W1,W0)
          & aSet0(W0) )
        | W0 != slcrc0 ) ),
    inference(NNF_transformation,[status(thm)],[f91]) ).

fof(f93,plain,
    ( ! [W0] :
        ( ? [W1] : aElementOf0(W1,W0)
        | ~ aSet0(W0)
        | W0 = slcrc0 )
    & ! [W0] :
        ( ( ! [W1] : ~ aElementOf0(W1,W0)
          & aSet0(W0) )
        | W0 != slcrc0 ) ),
    inference(miniscoping,[status(thm)],[f92]) ).

fof(f94,plain,
    ( ! [W0] :
        ( aElementOf0(sK0_skl(W0),W0)
        | ~ aSet0(W0)
        | W0 = slcrc0 )
    & ! [W0] :
        ( ( ! [W1] : ~ aElementOf0(W1,W0)
          & aSet0(W0) )
        | W0 != slcrc0 ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(W1,sK0_skl(W0))],[f93]) ).

fof(f97,plain,
    ! [X0] :
      ( aElementOf0(sK0_skl(X0),X0)
      | ~ aSet0(X0)
      | X0 = slcrc0 ),
    inference(cnf_transformation,[status(thm)],[f94]) ).

fof(f101,plain,
    ! [W0] :
      ( ~ isFinite0(W0)
      | ~ isCountable0(W0)
      | ~ aSet0(W0) ),
    inference(pre_NNF_transformation,[status(thm)],[f8]) ).

fof(f102,plain,
    ! [X0] :
      ( ~ isFinite0(X0)
      | ~ isCountable0(X0)
      | ~ aSet0(X0) ),
    inference(cnf_transformation,[status(thm)],[f101]) ).

fof(f105,plain,
    ! [W0] :
      ( ! [W1] :
          ( aSubsetOf0(W1,W0)
        <=> ( ! [W2] :
                ( aElementOf0(W2,W0)
                | ~ aElementOf0(W2,W1) )
            & aSet0(W1) ) )
      | ~ aSet0(W0) ),
    inference(pre_NNF_transformation,[status(thm)],[f10]) ).

fof(f106,plain,
    ! [W0] :
      ( ! [W1] :
          ( ( ? [W2] :
                ( ~ aElementOf0(W2,W0)
                & aElementOf0(W2,W1) )
            | ~ aSet0(W1)
            | aSubsetOf0(W1,W0) )
          & ( ( ! [W2] :
                  ( aElementOf0(W2,W0)
                  | ~ aElementOf0(W2,W1) )
              & aSet0(W1) )
            | ~ aSubsetOf0(W1,W0) ) )
      | ~ aSet0(W0) ),
    inference(NNF_transformation,[status(thm)],[f105]) ).

fof(f107,plain,
    ! [W0] :
      ( ( ! [W1] :
            ( ? [W2] :
                ( ~ aElementOf0(W2,W0)
                & aElementOf0(W2,W1) )
            | ~ aSet0(W1)
            | aSubsetOf0(W1,W0) )
        & ! [W1] :
            ( ( ! [W2] :
                  ( aElementOf0(W2,W0)
                  | ~ aElementOf0(W2,W1) )
              & aSet0(W1) )
            | ~ aSubsetOf0(W1,W0) ) )
      | ~ aSet0(W0) ),
    inference(miniscoping,[status(thm)],[f106]) ).

fof(f108,plain,
    ! [W0] :
      ( ( ! [W1] :
            ( ( ~ aElementOf0(sK1_skl(W1,W0),W0)
              & aElementOf0(sK1_skl(W1,W0),W1) )
            | ~ aSet0(W1)
            | aSubsetOf0(W1,W0) )
        & ! [W1] :
            ( ( ! [W2] :
                  ( aElementOf0(W2,W0)
                  | ~ aElementOf0(W2,W1) )
              & aSet0(W1) )
            | ~ aSubsetOf0(W1,W0) ) )
      | ~ aSet0(W0) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(W2,sK1_skl(W1,W0))],[f107]) ).

fof(f109,plain,
    ! [X0,X1] :
      ( aSet0(X1)
      | ~ aSubsetOf0(X1,X0)
      | ~ aSet0(X0) ),
    inference(cnf_transformation,[status(thm)],[f108]) ).

fof(f157,plain,
    aSet0(szNzAzT0),
    inference(cnf_transformation,[status(thm)],[f23]) ).

fof(f159,plain,
    aElementOf0(sz00,szNzAzT0),
    inference(cnf_transformation,[status(thm)],[f24]) ).

fof(f201,plain,
    ! [W0] :
      ( ( sbrdtbr0(W0) = sz00
      <=> W0 = slcrc0 )
      | ~ aSet0(W0) ),
    inference(pre_NNF_transformation,[status(thm)],[f42]) ).

fof(f202,plain,
    ! [W0] :
      ( ( ( W0 != slcrc0
          | sbrdtbr0(W0) = sz00 )
        & ( W0 = slcrc0
          | sbrdtbr0(W0) != sz00 ) )
      | ~ aSet0(W0) ),
    inference(NNF_transformation,[status(thm)],[f201]) ).

fof(f203,plain,
    ! [X0] :
      ( X0 = slcrc0
      | sbrdtbr0(X0) != sz00
      | ~ aSet0(X0) ),
    inference(cnf_transformation,[status(thm)],[f202]) ).

fof(f262,plain,
    ! [W0,W1] :
      ( ! [W2] :
          ( W2 = slbdtsldtrb0(W0,W1)
        <=> ( ! [W3] :
                ( aElementOf0(W3,W2)
              <=> ( sbrdtbr0(W3) = W1
                  & aSubsetOf0(W3,W0) ) )
            & aSet0(W2) ) )
      | ~ aElementOf0(W1,szNzAzT0)
      | ~ aSet0(W0) ),
    inference(pre_NNF_transformation,[status(thm)],[f57]) ).

fof(f263,plain,
    ! [W0,W1] :
      ( ! [W2] :
          ( ( ? [W3] :
                ( ( ( sbrdtbr0(W3) = W1
                    & aSubsetOf0(W3,W0) )
                  | aElementOf0(W3,W2) )
                & ( sbrdtbr0(W3) != W1
                  | ~ aSubsetOf0(W3,W0)
                  | ~ aElementOf0(W3,W2) ) )
            | ~ aSet0(W2)
            | W2 = slbdtsldtrb0(W0,W1) )
          & ( ( ! [W3] :
                  ( ( sbrdtbr0(W3) != W1
                    | ~ aSubsetOf0(W3,W0)
                    | aElementOf0(W3,W2) )
                  & ( ( sbrdtbr0(W3) = W1
                      & aSubsetOf0(W3,W0) )
                    | ~ aElementOf0(W3,W2) ) )
              & aSet0(W2) )
            | W2 != slbdtsldtrb0(W0,W1) ) )
      | ~ aElementOf0(W1,szNzAzT0)
      | ~ aSet0(W0) ),
    inference(NNF_transformation,[status(thm)],[f262]) ).

fof(f264,plain,
    ! [W0,W1] :
      ( ( ! [W2] :
            ( ? [W3] :
                ( ( ( sbrdtbr0(W3) = W1
                    & aSubsetOf0(W3,W0) )
                  | aElementOf0(W3,W2) )
                & ( sbrdtbr0(W3) != W1
                  | ~ aSubsetOf0(W3,W0)
                  | ~ aElementOf0(W3,W2) ) )
            | ~ aSet0(W2)
            | W2 = slbdtsldtrb0(W0,W1) )
        & ! [W2] :
            ( ( ! [W3] :
                  ( sbrdtbr0(W3) != W1
                  | ~ aSubsetOf0(W3,W0)
                  | aElementOf0(W3,W2) )
              & ! [W3] :
                  ( ( sbrdtbr0(W3) = W1
                    & aSubsetOf0(W3,W0) )
                  | ~ aElementOf0(W3,W2) )
              & aSet0(W2) )
            | W2 != slbdtsldtrb0(W0,W1) ) )
      | ~ aElementOf0(W1,szNzAzT0)
      | ~ aSet0(W0) ),
    inference(miniscoping,[status(thm)],[f263]) ).

fof(f265,plain,
    ! [W0,W1] :
      ( ( ! [W2] :
            ( ( ( ( sbrdtbr0(sK10_skl(W2,W1,W0)) = W1
                  & aSubsetOf0(sK10_skl(W2,W1,W0),W0) )
                | aElementOf0(sK10_skl(W2,W1,W0),W2) )
              & ( sbrdtbr0(sK10_skl(W2,W1,W0)) != W1
                | ~ aSubsetOf0(sK10_skl(W2,W1,W0),W0)
                | ~ aElementOf0(sK10_skl(W2,W1,W0),W2) ) )
            | ~ aSet0(W2)
            | W2 = slbdtsldtrb0(W0,W1) )
        & ! [W2] :
            ( ( ! [W3] :
                  ( sbrdtbr0(W3) != W1
                  | ~ aSubsetOf0(W3,W0)
                  | aElementOf0(W3,W2) )
              & ! [W3] :
                  ( ( sbrdtbr0(W3) = W1
                    & aSubsetOf0(W3,W0) )
                  | ~ aElementOf0(W3,W2) )
              & aSet0(W2) )
            | W2 != slbdtsldtrb0(W0,W1) ) )
      | ~ aElementOf0(W1,szNzAzT0)
      | ~ aSet0(W0) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK10_skl]),skolemize(W3,sK10_skl(W2,W1,W0))],[f264]) ).

fof(f266,plain,
    ! [X0,X1,X2] :
      ( aSet0(X2)
      | X2 != slbdtsldtrb0(X0,X1)
      | ~ aElementOf0(X1,szNzAzT0)
      | ~ aSet0(X0) ),
    inference(cnf_transformation,[status(thm)],[f265]) ).

fof(f267,plain,
    ! [X0,X1,X2,X3] :
      ( aSubsetOf0(X3,X0)
      | ~ aElementOf0(X3,X2)
      | X2 != slbdtsldtrb0(X0,X1)
      | ~ aElementOf0(X1,szNzAzT0)
      | ~ aSet0(X0) ),
    inference(cnf_transformation,[status(thm)],[f265]) ).

fof(f268,plain,
    ! [X0,X1,X2,X3] :
      ( sbrdtbr0(X3) = X1
      | ~ aElementOf0(X3,X2)
      | X2 != slbdtsldtrb0(X0,X1)
      | ~ aElementOf0(X1,szNzAzT0)
      | ~ aSet0(X0) ),
    inference(cnf_transformation,[status(thm)],[f265]) ).

fof(f275,plain,
    ! [W0] :
      ( ! [W1] :
          ( slbdtsldtrb0(W0,W1) != slcrc0
          | ~ aElementOf0(W1,szNzAzT0) )
      | isFinite0(W0)
      | ~ aSet0(W0) ),
    inference(pre_NNF_transformation,[status(thm)],[f59]) ).

fof(f276,plain,
    ! [X0,X1] :
      ( slbdtsldtrb0(X0,X1) != slcrc0
      | ~ aElementOf0(X1,szNzAzT0)
      | isFinite0(X0)
      | ~ aSet0(X0) ),
    inference(cnf_transformation,[status(thm)],[f275]) ).

fof(f340,plain,
    aSubsetOf0(xS,szNzAzT0),
    inference(cnf_transformation,[status(thm)],[f75]) ).

fof(f341,plain,
    isCountable0(xS),
    inference(cnf_transformation,[status(thm)],[f75]) ).

fof(f343,plain,
    szDzozmdt0(xc) = slbdtsldtrb0(xS,xK),
    inference(cnf_transformation,[status(thm)],[f76]) ).

fof(f351,plain,
    xK = sz00,
    inference(cnf_transformation,[status(thm)],[f78]) ).

fof(f352,plain,
    ~ aElementOf0(slcrc0,slbdtsldtrb0(xS,sz00)),
    inference(cnf_transformation,[status(thm)],[f80]) ).

fof(f382,plain,
    ! [X0,X1] :
      ( aSet0(slbdtsldtrb0(X0,X1))
      | ~ aElementOf0(X1,szNzAzT0)
      | ~ aSet0(X0) ),
    inference(destructive_equality_resolution,[status(thm)],[f266]) ).

fof(f383,plain,
    ! [X0,X1,X2] :
      ( aSubsetOf0(X2,X0)
      | ~ aElementOf0(X2,slbdtsldtrb0(X0,X1))
      | ~ aElementOf0(X1,szNzAzT0)
      | ~ aSet0(X0) ),
    inference(destructive_equality_resolution,[status(thm)],[f267]) ).

fof(f384,plain,
    ! [X0,X1,X2] :
      ( sbrdtbr0(X2) = X1
      | ~ aElementOf0(X2,slbdtsldtrb0(X0,X1))
      | ~ aElementOf0(X1,szNzAzT0)
      | ~ aSet0(X0) ),
    inference(destructive_equality_resolution,[status(thm)],[f268]) ).

fof(f411,plain,
    ( ~ isFinite0(xS)
    | ~ aSet0(xS) ),
    inference(resolution,[status(thm)],[f102,f341]) ).

fof(f419,plain,
    ~ aElementOf0(slcrc0,szDzozmdt0(xc)),
    inference(backward_demodulation,[status(thm)],[f420,f352]) ).

fof(f420,plain,
    szDzozmdt0(xc) = slbdtsldtrb0(xS,sz00),
    inference(forward_demodulation,[status(thm)],[f351,f343]) ).

fof(f421,plain,
    ( aSet0(szDzozmdt0(xc))
    | ~ aElementOf0(sz00,szNzAzT0)
    | ~ aSet0(xS) ),
    inference(paramodulation,[status(thm)],[f420,f382]) ).

fof(f422,plain,
    ( aSet0(szDzozmdt0(xc))
    | ~ aSet0(xS) ),
    inference(forward_subsumption_resolution,[status(thm)],[f421,f159]) ).

fof(f427,plain,
    ! [X0] :
      ( aSubsetOf0(X0,xS)
      | ~ aElementOf0(X0,szDzozmdt0(xc))
      | ~ aElementOf0(sz00,szNzAzT0)
      | ~ aSet0(xS) ),
    inference(paramodulation,[status(thm)],[f420,f383]) ).

fof(f429,plain,
    ! [X0] :
      ( aSubsetOf0(X0,xS)
      | ~ aElementOf0(X0,szDzozmdt0(xc))
      | ~ aSet0(xS) ),
    inference(forward_subsumption_resolution,[status(thm)],[f427,f159]) ).

fof(f430,plain,
    ( szDzozmdt0(xc) != slcrc0
    | ~ aElementOf0(sz00,szNzAzT0)
    | isFinite0(xS)
    | ~ aSet0(xS) ),
    inference(paramodulation,[status(thm)],[f420,f276]) ).

fof(f431,plain,
    ( szDzozmdt0(xc) != slcrc0
    | ~ aElementOf0(sz00,szNzAzT0)
    | ~ aSet0(xS) ),
    inference(forward_subsumption_resolution,[status(thm)],[f430,f411]) ).

fof(f436,plain,
    ( aSet0(xS)
    | ~ aSet0(szNzAzT0) ),
    inference(resolution,[status(thm)],[f109,f340]) ).

fof(f438,plain,
    aSet0(xS),
    inference(forward_subsumption_resolution,[status(thm)],[f436,f157]) ).

fof(f452,plain,
    aSet0(szDzozmdt0(xc)),
    inference(backward_subsumption_resolution,[status(thm)],[f422,f438]) ).

fof(f498,plain,
    ! [X0] :
      ( aSubsetOf0(X0,xS)
      | ~ aElementOf0(X0,szDzozmdt0(xc)) ),
    inference(forward_subsumption_resolution,[status(thm)],[f429,f438]) ).

fof(f500,plain,
    ( ~ aSet0(szDzozmdt0(xc))
    | szDzozmdt0(xc) = slcrc0
    | aSubsetOf0(sK0_skl(szDzozmdt0(xc)),xS) ),
    inference(resolution,[status(thm)],[f498,f97]) ).

fof(f502,plain,
    ( szDzozmdt0(xc) = slcrc0
    | aSubsetOf0(sK0_skl(szDzozmdt0(xc)),xS) ),
    inference(forward_subsumption_resolution,[status(thm)],[f500,f452]) ).

fof(f516,plain,
    ( szDzozmdt0(xc) != slcrc0
    | ~ aElementOf0(sz00,szNzAzT0) ),
    inference(forward_subsumption_resolution,[status(thm)],[f431,f438]) ).

fof(f517,plain,
    szDzozmdt0(xc) != slcrc0,
    inference(resolution,[status(thm)],[f516,f159]) ).

fof(f518,plain,
    aSubsetOf0(sK0_skl(szDzozmdt0(xc)),xS),
    inference(forward_subsumption_resolution,[status(thm)],[f502,f517]) ).

fof(f522,plain,
    ( aSet0(sK0_skl(szDzozmdt0(xc)))
    | ~ aSet0(xS) ),
    inference(resolution,[status(thm)],[f518,f109]) ).

fof(f525,plain,
    aSet0(sK0_skl(szDzozmdt0(xc))),
    inference(forward_subsumption_resolution,[status(thm)],[f522,f438]) ).

fof(f2582,plain,
    ! [X0] :
      ( sbrdtbr0(X0) = sz00
      | ~ aElementOf0(X0,szDzozmdt0(xc))
      | ~ aElementOf0(sz00,szNzAzT0)
      | ~ aSet0(xS) ),
    inference(paramodulation,[status(thm)],[f420,f384]) ).

fof(f2588,plain,
    ! [X0] :
      ( sbrdtbr0(X0) = sz00
      | ~ aElementOf0(X0,szDzozmdt0(xc))
      | ~ aElementOf0(sz00,szNzAzT0) ),
    inference(forward_subsumption_resolution,[status(thm)],[f2582,f438]) ).

fof(f2589,plain,
    ! [X0] :
      ( sbrdtbr0(X0) = sz00
      | ~ aElementOf0(X0,szDzozmdt0(xc)) ),
    inference(forward_subsumption_resolution,[status(thm)],[f2588,f159]) ).

fof(f2596,plain,
    ( ~ aSet0(szDzozmdt0(xc))
    | szDzozmdt0(xc) = slcrc0
    | sbrdtbr0(sK0_skl(szDzozmdt0(xc))) = sz00 ),
    inference(resolution,[status(thm)],[f2589,f97]) ).

fof(f2603,plain,
    ( ~ aSet0(szDzozmdt0(xc))
    | sbrdtbr0(sK0_skl(szDzozmdt0(xc))) = sz00 ),
    inference(forward_subsumption_resolution,[status(thm)],[f2596,f517]) ).

fof(f2604,plain,
    sbrdtbr0(sK0_skl(szDzozmdt0(xc))) = sz00,
    inference(forward_subsumption_resolution,[status(thm)],[f2603,f452]) ).

fof(f2605,plain,
    ( sK0_skl(szDzozmdt0(xc)) = slcrc0
    | ~ aSet0(sK0_skl(szDzozmdt0(xc))) ),
    inference(resolution,[status(thm)],[f2604,f203]) ).

fof(f2620,plain,
    sK0_skl(szDzozmdt0(xc)) = slcrc0,
    inference(forward_subsumption_resolution,[status(thm)],[f2605,f525]) ).

fof(f2645,plain,
    ( aElementOf0(slcrc0,szDzozmdt0(xc))
    | ~ aSet0(szDzozmdt0(xc))
    | szDzozmdt0(xc) = slcrc0 ),
    inference(paramodulation,[status(thm)],[f2620,f97]) ).

fof(f2648,plain,
    ( aElementOf0(slcrc0,szDzozmdt0(xc))
    | ~ aSet0(szDzozmdt0(xc)) ),
    inference(forward_subsumption_resolution,[status(thm)],[f2645,f517]) ).

fof(f2791,plain,
    aElementOf0(slcrc0,szDzozmdt0(xc)),
    inference(forward_subsumption_resolution,[status(thm)],[f2648,f452]) ).

fof(f2792,plain,
    $false,
    inference(backward_subsumption_resolution,[status(thm)],[f419,f2791]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02  % Problem  : NUM564+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04  % Command  : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/5.35  % Computer : n001.cluster.edu
% 0.07/5.35  % Model    : x86_64 x86_64
% 0.07/5.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/5.35  % Memory   : 8046.5625MB
% 0.07/5.35  % OS       : Linux 6.8.0-71-generic
% 0.07/5.36  % CPULimit : 300
% 0.07/5.36  % WCLimit  : 300
% 0.07/5.36  % DateTime : Mon Sep 21 02:45:50 UTC 2026
% 0.07/5.36  % CPUTime  : 
% 0.07/5.38  % Drodi V4.1.1
% 0.12/5.82  % Refutation found
% 0.12/5.82  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/5.82  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/5.84  % Elapsed time: 0.474489 seconds
% 0.12/5.84  % CPU time: 3.515651 seconds
% 0.12/5.84  % Total memory used: 151.058 MB
% 0.12/5.84  % Net memory used: 146.932 MB
%------------------------------------------------------------------------------