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Drodi---4.1.1.THM-CRf.s

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%------------------------------------------------------------------------------
% File     : Drodi---4.1.1
% Problem  : NUM611+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n004.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 01:41:11 PM UTC 2026

% Result   : Theorem 1.07s 0.66s
% Output   : CNFRefutation 1.07s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   19
%            Number of leaves      :   19
% Syntax   : Number of formulae    :   83 (  30 unt;   2 def)
%            Number of atoms       :  271 (  64 equ)
%            Maximal formula atoms :   18 (   3 avg)
%            Number of connectives :  314 ( 126   ~; 124   |;  46   &)
%                                         (   8 <=>;  10  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   4 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    8 (   6 usr;   1 prp; 0-2 aty)
%            Number of functors    :   24 (  24 usr;  13 con; 0-3 aty)
%            Number of variables   :   83 (  79   !;   4   ?)

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

fof(f11,axiom,
    ! [W0] :
      ( ( isFinite0(W0)
        & aSet0(W0) )
     => ! [W1] :
          ( aSubsetOf0(W1,W0)
         => isFinite0(W1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

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

fof(f26,axiom,
    ! [W0,W1] :
      ( ( aElementOf0(W1,szNzAzT0)
        & aElementOf0(W0,szNzAzT0) )
     => ( szszuzczcdt0(W0) = szszuzczcdt0(W1)
       => W0 = W1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f41,axiom,
    ! [W0] :
      ( aSet0(W0)
     => ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
      <=> isFinite0(W0) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f44,axiom,
    ! [W0] :
      ( aSet0(W0)
     => ! [W1] :
          ( ( aElementOf0(W1,W0)
            & isFinite0(W0) )
         => szszuzczcdt0(sbrdtbr0(sdtmndt0(W0,W1))) = sbrdtbr0(W0) ) ),
    file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p') ).

fof(f74,hypothesis,
    aElementOf0(xK,szNzAzT0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

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

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

fof(f80,hypothesis,
    ( szszuzczcdt0(xk) = xK
    & aElementOf0(xk,szNzAzT0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f95,hypothesis,
    ( xO = sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))
    & aSet0(xO) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f100,hypothesis,
    ( xQ != slcrc0
    & aSubsetOf0(xQ,xO) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f102,hypothesis,
    aElementOf0(xQ,szDzozmdt0(xc)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f103,hypothesis,
    xp = szmzizndt0(xQ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f104,hypothesis,
    ( xP = sdtmndt0(xQ,szmzizndt0(xQ))
    & aSet0(xP) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f105,hypothesis,
    aElementOf0(xp,xQ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f107,hypothesis,
    aSubsetOf0(xP,xQ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f109,conjecture,
    sbrdtbr0(xP) = xk,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f110,negated_conjecture,
    sbrdtbr0(xP) != xk,
    inference(negated_conjecture,[status(cth)],[f109]) ).

fof(f135,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(f136,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)],[f135]) ).

fof(f137,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)],[f136]) ).

fof(f138,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))],[f137]) ).

fof(f139,plain,
    ! [X0,X1] :
      ( aSet0(X1)
      | ~ aSubsetOf0(X1,X0)
      | ~ aSet0(X0) ),
    inference(cnf_transformation,[status(thm)],[f138]) ).

fof(f143,plain,
    ! [W0] :
      ( ! [W1] :
          ( isFinite0(W1)
          | ~ aSubsetOf0(W1,W0) )
      | ~ isFinite0(W0)
      | ~ aSet0(W0) ),
    inference(pre_NNF_transformation,[status(thm)],[f11]) ).

fof(f144,plain,
    ! [X0,X1] :
      ( isFinite0(X1)
      | ~ aSubsetOf0(X1,X0)
      | ~ isFinite0(X0)
      | ~ aSet0(X0) ),
    inference(cnf_transformation,[status(thm)],[f143]) ).

fof(f187,plain,
    aSet0(szNzAzT0),
    inference(cnf_transformation,[status(thm)],[f23]) ).

fof(f193,plain,
    ! [W0,W1] :
      ( W0 = W1
      | szszuzczcdt0(W0) != szszuzczcdt0(W1)
      | ~ aElementOf0(W1,szNzAzT0)
      | ~ aElementOf0(W0,szNzAzT0) ),
    inference(pre_NNF_transformation,[status(thm)],[f26]) ).

fof(f194,plain,
    ! [X0,X1] :
      ( X0 = X1
      | szszuzczcdt0(X0) != szszuzczcdt0(X1)
      | ~ aElementOf0(X1,szNzAzT0)
      | ~ aElementOf0(X0,szNzAzT0) ),
    inference(cnf_transformation,[status(thm)],[f193]) ).

fof(f227,plain,
    ! [W0] :
      ( ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
      <=> isFinite0(W0) )
      | ~ aSet0(W0) ),
    inference(pre_NNF_transformation,[status(thm)],[f41]) ).

fof(f228,plain,
    ! [W0] :
      ( ( ( ~ isFinite0(W0)
          | aElementOf0(sbrdtbr0(W0),szNzAzT0) )
        & ( isFinite0(W0)
          | ~ aElementOf0(sbrdtbr0(W0),szNzAzT0) ) )
      | ~ aSet0(W0) ),
    inference(NNF_transformation,[status(thm)],[f227]) ).

fof(f229,plain,
    ! [X0] :
      ( isFinite0(X0)
      | ~ aElementOf0(sbrdtbr0(X0),szNzAzT0)
      | ~ aSet0(X0) ),
    inference(cnf_transformation,[status(thm)],[f228]) ).

fof(f230,plain,
    ! [X0] :
      ( ~ isFinite0(X0)
      | aElementOf0(sbrdtbr0(X0),szNzAzT0)
      | ~ aSet0(X0) ),
    inference(cnf_transformation,[status(thm)],[f228]) ).

fof(f237,plain,
    ! [W0] :
      ( ! [W1] :
          ( szszuzczcdt0(sbrdtbr0(sdtmndt0(W0,W1))) = sbrdtbr0(W0)
          | ~ aElementOf0(W1,W0)
          | ~ isFinite0(W0) )
      | ~ aSet0(W0) ),
    inference(pre_NNF_transformation,[status(thm)],[f44]) ).

fof(f238,plain,
    ! [X0,X1] :
      ( szszuzczcdt0(sbrdtbr0(sdtmndt0(X0,X1))) = sbrdtbr0(X0)
      | ~ aElementOf0(X1,X0)
      | ~ isFinite0(X0)
      | ~ aSet0(X0) ),
    inference(cnf_transformation,[status(thm)],[f237]) ).

fof(f292,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(f293,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)],[f292]) ).

fof(f294,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)],[f293]) ).

fof(f295,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))],[f294]) ).

fof(f298,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)],[f295]) ).

fof(f369,plain,
    aElementOf0(xK,szNzAzT0),
    inference(cnf_transformation,[status(thm)],[f74]) ).

fof(f370,plain,
    aSubsetOf0(xS,szNzAzT0),
    inference(cnf_transformation,[status(thm)],[f75]) ).

fof(f373,plain,
    szDzozmdt0(xc) = slbdtsldtrb0(xS,xK),
    inference(cnf_transformation,[status(thm)],[f76]) ).

fof(f383,plain,
    aElementOf0(xk,szNzAzT0),
    inference(cnf_transformation,[status(thm)],[f80]) ).

fof(f384,plain,
    szszuzczcdt0(xk) = xK,
    inference(cnf_transformation,[status(thm)],[f80]) ).

fof(f431,plain,
    aSet0(xO),
    inference(cnf_transformation,[status(thm)],[f95]) ).

fof(f442,plain,
    aSubsetOf0(xQ,xO),
    inference(cnf_transformation,[status(thm)],[f100]) ).

fof(f445,plain,
    aElementOf0(xQ,szDzozmdt0(xc)),
    inference(cnf_transformation,[status(thm)],[f102]) ).

fof(f446,plain,
    xp = szmzizndt0(xQ),
    inference(cnf_transformation,[status(thm)],[f103]) ).

fof(f447,plain,
    aSet0(xP),
    inference(cnf_transformation,[status(thm)],[f104]) ).

fof(f448,plain,
    xP = sdtmndt0(xQ,szmzizndt0(xQ)),
    inference(cnf_transformation,[status(thm)],[f104]) ).

fof(f449,plain,
    aElementOf0(xp,xQ),
    inference(cnf_transformation,[status(thm)],[f105]) ).

fof(f451,plain,
    aSubsetOf0(xP,xQ),
    inference(cnf_transformation,[status(thm)],[f107]) ).

fof(f453,plain,
    sbrdtbr0(xP) != xk,
    inference(cnf_transformation,[status(thm)],[f110]) ).

fof(f485,plain,
    ! [X0,X1,X2] :
      ( sbrdtbr0(X2) = X1
      | ~ aElementOf0(X2,slbdtsldtrb0(X0,X1))
      | ~ aElementOf0(X1,szNzAzT0)
      | ~ aSet0(X0) ),
    inference(destructive_equality_resolution,[status(thm)],[f298]) ).

fof(f568,plain,
    ( aSet0(xS)
    | ~ aSet0(szNzAzT0) ),
    inference(resolution,[status(thm)],[f370,f139]) ).

fof(f570,plain,
    aSet0(xS),
    inference(forward_subsumption_resolution,[status(thm)],[f568,f187]) ).

fof(f573,plain,
    ( isFinite0(xP)
    | ~ isFinite0(xQ)
    | ~ aSet0(xQ) ),
    inference(resolution,[status(thm)],[f144,f451]) ).

fof(f617,plain,
    ( aSet0(xQ)
    | ~ aSet0(xO) ),
    inference(resolution,[status(thm)],[f442,f139]) ).

fof(f620,plain,
    aSet0(xQ),
    inference(forward_subsumption_resolution,[status(thm)],[f617,f431]) ).

fof(f623,plain,
    ( isFinite0(xP)
    | ~ isFinite0(xQ) ),
    inference(backward_subsumption_resolution,[status(thm)],[f573,f620]) ).

fof(f633,plain,
    xP = sdtmndt0(xQ,xp),
    inference(backward_demodulation,[status(thm)],[f446,f448]) ).

fof(f1009,plain,
    ! [X0] :
      ( sbrdtbr0(X0) = xK
      | ~ aElementOf0(X0,szDzozmdt0(xc))
      | ~ aElementOf0(xK,szNzAzT0)
      | ~ aSet0(xS) ),
    inference(paramodulation,[status(thm)],[f373,f485]) ).

fof(f1016,plain,
    ! [X0] :
      ( sbrdtbr0(X0) = xK
      | ~ aElementOf0(X0,szDzozmdt0(xc))
      | ~ aElementOf0(xK,szNzAzT0) ),
    inference(forward_subsumption_resolution,[status(thm)],[f1009,f570]) ).

fof(f1053,plain,
    ! [X0] :
      ( sbrdtbr0(X0) = xK
      | ~ aElementOf0(X0,szDzozmdt0(xc)) ),
    inference(forward_subsumption_resolution,[status(thm)],[f1016,f369]) ).

fof(f1055,plain,
    sbrdtbr0(xQ) = xK,
    inference(resolution,[status(thm)],[f1053,f445]) ).

fof(f1067,plain,
    ( isFinite0(xQ)
    | ~ aElementOf0(xK,szNzAzT0)
    | ~ aSet0(xQ) ),
    inference(paramodulation,[status(thm)],[f1055,f229]) ).

fof(f1076,plain,
    ( isFinite0(xQ)
    | ~ aElementOf0(xK,szNzAzT0) ),
    inference(forward_subsumption_resolution,[status(thm)],[f1067,f620]) ).

fof(f1081,plain,
    isFinite0(xP),
    inference(backward_subsumption_resolution,[status(thm)],[f623,f1083]) ).

fof(f1083,plain,
    isFinite0(xQ),
    inference(forward_subsumption_resolution,[status(thm)],[f1076,f369]) ).

fof(f1386,plain,
    ! [X0] :
      ( xk = X0
      | xK != szszuzczcdt0(X0)
      | ~ aElementOf0(X0,szNzAzT0)
      | ~ aElementOf0(xk,szNzAzT0) ),
    inference(paramodulation,[status(thm)],[f384,f194]) ).

fof(f1389,plain,
    ! [X0] :
      ( xk = X0
      | xK != szszuzczcdt0(X0)
      | ~ aElementOf0(X0,szNzAzT0) ),
    inference(forward_subsumption_resolution,[status(thm)],[f1386,f383]) ).

fof(f1410,plain,
    ! [X0] :
      ( ~ isFinite0(X0)
      | ~ aSet0(X0)
      | xk = sbrdtbr0(X0)
      | xK != szszuzczcdt0(sbrdtbr0(X0)) ),
    inference(resolution,[status(thm)],[f1389,f230]) ).

fof(f1936,plain,
    ( szszuzczcdt0(sbrdtbr0(xP)) = sbrdtbr0(xQ)
    | ~ aElementOf0(xp,xQ)
    | ~ isFinite0(xQ)
    | ~ aSet0(xQ) ),
    inference(paramodulation,[status(thm)],[f633,f238]) ).

fof(f1937,plain,
    ( szszuzczcdt0(sbrdtbr0(xP)) = xK
    | ~ aElementOf0(xp,xQ)
    | ~ isFinite0(xQ)
    | ~ aSet0(xQ) ),
    inference(forward_demodulation,[status(thm)],[f1055,f1936]) ).

fof(f1938,plain,
    ( szszuzczcdt0(sbrdtbr0(xP)) = xK
    | ~ aElementOf0(xp,xQ)
    | ~ isFinite0(xQ) ),
    inference(forward_subsumption_resolution,[status(thm)],[f1937,f620]) ).

fof(f2999,plain,
    ( szszuzczcdt0(sbrdtbr0(xP)) = xK
    | ~ aElementOf0(xp,xQ) ),
    inference(forward_subsumption_resolution,[status(thm)],[f1938,f1083]) ).

fof(f3000,plain,
    ( ~ isFinite0(xP)
    | ~ aSet0(xP)
    | xk = sbrdtbr0(xP)
    | ~ aElementOf0(xp,xQ) ),
    inference(resolution,[status(thm)],[f2999,f1410]) ).

fof(f3001,plain,
    ( ~ isFinite0(xP)
    | ~ aSet0(xP)
    | xk = sbrdtbr0(xP) ),
    inference(forward_subsumption_resolution,[status(thm)],[f3000,f449]) ).

fof(f3179,plain,
    ( ~ isFinite0(xP)
    | ~ aSet0(xP) ),
    inference(forward_subsumption_resolution,[status(thm)],[f3001,f453]) ).

fof(f3180,plain,
    ~ aSet0(xP),
    inference(resolution,[status(thm)],[f3179,f1081]) ).

fof(f3181,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[f3180,f447]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : NUM611+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04  % Command  : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36  % Computer : n004.cluster.edu
% 0.09/0.36  % Model    : x86_64 x86_64
% 0.09/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36  % Memory   : 8046.5625MB
% 0.09/0.36  % OS       : Linux 6.8.0-71-generic
% 0.09/0.36  % CPULimit : 300
% 0.09/0.36  % WCLimit  : 300
% 0.09/0.36  % DateTime : Mon Sep 21 02:44:19 UTC 2026
% 0.09/0.37  % CPUTime  : 
% 0.09/0.38  % Drodi V4.1.1
% 1.07/0.66  % Refutation found
% 1.07/0.66  % SZS status Theorem for theBenchmark: Theorem is valid
% 1.07/0.66  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.07/0.69  % Elapsed time: 0.309441 seconds
% 1.07/0.69  % CPU time: 2.070560 seconds
% 1.07/0.69  % Total memory used: 143.603 MB
% 1.07/0.69  % Net memory used: 140.523 MB
%------------------------------------------------------------------------------