TSTP Solution File: NUM581+3 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : NUM581+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s

% Computer : n003.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 Aug 22 10:52:12 EDT 2023

% Result   : Theorem 86.86s 64.69s
% Output   : CNFRefutation 87.07s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :   85
% Syntax   : Number of formulae    :  140 (  30 unt;  73 typ;   2 def)
%            Number of atoms       :  196 (  12 equ)
%            Maximal formula atoms :   22 (   2 avg)
%            Number of connectives :  198 (  69   ~;  60   |;  40   &)
%                                         (   6 <=>;  23  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   16 (   4 avg)
%            Maximal term depth    :    5 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  129 (  61   >;  68   *;   0   +;   0  <<)
%            Number of predicates  :   11 (   9 usr;   1 prp; 0-2 aty)
%            Number of functors    :   64 (  64 usr;  12 con; 0-4 aty)
%            Number of variables   :   55 (;  55   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ sdtlseqdt0 > iLess0 > aSubsetOf0 > aElementOf0 > isFinite0 > isCountable0 > aSet0 > aFunction0 > aElement0 > slbdtsldtrb0 > sdtpldt0 > sdtmndt0 > sdtlpdtrp0 > sdtlcdtrc0 > sdtlbdtrb0 > sdtexdt0 > #nlpp > szszuzczcdt0 > szmzizndt0 > szmzazxdt0 > szDzozmdt0 > szDzizrdt0 > slbdtrb0 > sbrdtbr0 > xk > xi > xc > xT > xS > xQ > xN > xK > szNzAzT0 > sz00 > slcrc0 > #skF_7 > #skF_11 > #skF_17 > #skF_31 > #skF_33 > #skF_6 > #skF_1 > #skF_18 > #skF_37 > #skF_38 > #skF_4 > #skF_29 > #skF_12 > #skF_30 > #skF_32 > #skF_23 > #skF_39 > #skF_35 > #skF_5 > #skF_19 > #skF_10 > #skF_8 > #skF_20 > #skF_28 > #skF_26 > #skF_24 > #skF_34 > #skF_15 > #skF_13 > #skF_14 > #skF_25 > #skF_3 > #skF_2 > #skF_27 > #skF_36 > #skF_21 > #skF_9 > #skF_22 > #skF_16

%Foreground sorts:

%Background operators:

%Foreground operators:
tff(xk,type,
    xk: $i ).

tff('#skF_7',type,
    '#skF_7': $i > $i ).

tff('#skF_11',type,
    '#skF_11': ( $i * $i ) > $i ).

tff(sbrdtbr0,type,
    sbrdtbr0: $i > $i ).

tff('#skF_17',type,
    '#skF_17': ( $i * $i * $i ) > $i ).

tff('#skF_31',type,
    '#skF_31': ( $i * $i * $i ) > $i ).

tff('#skF_33',type,
    '#skF_33': ( $i * $i * $i ) > $i ).

tff(aSet0,type,
    aSet0: $i > $o ).

tff(szszuzczcdt0,type,
    szszuzczcdt0: $i > $i ).

tff(sdtlbdtrb0,type,
    sdtlbdtrb0: ( $i * $i ) > $i ).

tff(szDzozmdt0,type,
    szDzozmdt0: $i > $i ).

tff('#skF_6',type,
    '#skF_6': ( $i * $i * $i ) > $i ).

tff(sdtmndt0,type,
    sdtmndt0: ( $i * $i ) > $i ).

tff('#skF_1',type,
    '#skF_1': $i > $i ).

tff('#skF_18',type,
    '#skF_18': ( $i * $i * $i ) > $i ).

tff(aElement0,type,
    aElement0: $i > $o ).

tff(sdtexdt0,type,
    sdtexdt0: ( $i * $i ) > $i ).

tff('#skF_37',type,
    '#skF_37': $i > $i ).

tff(xi,type,
    xi: $i ).

tff(szNzAzT0,type,
    szNzAzT0: $i ).

tff(sdtlseqdt0,type,
    sdtlseqdt0: ( $i * $i ) > $o ).

tff(xS,type,
    xS: $i ).

tff(sz00,type,
    sz00: $i ).

tff(sdtlpdtrp0,type,
    sdtlpdtrp0: ( $i * $i ) > $i ).

tff('#skF_38',type,
    '#skF_38': ( $i * $i ) > $i ).

tff('#skF_4',type,
    '#skF_4': ( $i * $i * $i ) > $i ).

tff(xc,type,
    xc: $i ).

tff('#skF_29',type,
    '#skF_29': ( $i * $i * $i ) > $i ).

tff('#skF_12',type,
    '#skF_12': ( $i * $i ) > $i ).

tff(sdtpldt0,type,
    sdtpldt0: ( $i * $i ) > $i ).

tff('#skF_30',type,
    '#skF_30': ( $i * $i * $i ) > $i ).

tff(slbdtsldtrb0,type,
    slbdtsldtrb0: ( $i * $i ) > $i ).

tff('#skF_32',type,
    '#skF_32': ( $i * $i * $i * $i ) > $i ).

tff('#skF_23',type,
    '#skF_23': ( $i * $i * $i ) > $i ).

tff('#skF_39',type,
    '#skF_39': $i ).

tff('#skF_35',type,
    '#skF_35': ( $i * $i * $i ) > $i ).

tff(aSubsetOf0,type,
    aSubsetOf0: ( $i * $i ) > $o ).

tff('#skF_5',type,
    '#skF_5': ( $i * $i * $i ) > $i ).

tff('#skF_19',type,
    '#skF_19': ( $i * $i * $i ) > $i ).

tff(isCountable0,type,
    isCountable0: $i > $o ).

tff('#skF_10',type,
    '#skF_10': ( $i * $i ) > $i ).

tff('#skF_8',type,
    '#skF_8': ( $i * $i ) > $i ).

tff(xT,type,
    xT: $i ).

tff(xN,type,
    xN: $i ).

tff(aElementOf0,type,
    aElementOf0: ( $i * $i ) > $o ).

tff('#skF_20',type,
    '#skF_20': ( $i * $i * $i ) > $i ).

tff(szDzizrdt0,type,
    szDzizrdt0: $i > $i ).

tff('#skF_28',type,
    '#skF_28': ( $i * $i ) > $i ).

tff('#skF_26',type,
    '#skF_26': $i > $i ).

tff('#skF_24',type,
    '#skF_24': ( $i * $i ) > $i ).

tff('#skF_34',type,
    '#skF_34': ( $i * $i * $i ) > $i ).

tff('#skF_15',type,
    '#skF_15': ( $i * $i * $i ) > $i ).

tff('#skF_13',type,
    '#skF_13': $i > $i ).

tff('#skF_14',type,
    '#skF_14': ( $i * $i * $i ) > $i ).

tff(slcrc0,type,
    slcrc0: $i ).

tff(aFunction0,type,
    aFunction0: $i > $o ).

tff(isFinite0,type,
    isFinite0: $i > $o ).

tff(xQ,type,
    xQ: $i ).

tff('#skF_25',type,
    '#skF_25': ( $i * $i ) > $i ).

tff('#skF_3',type,
    '#skF_3': ( $i * $i * $i ) > $i ).

tff(sdtlcdtrc0,type,
    sdtlcdtrc0: ( $i * $i ) > $i ).

tff('#skF_2',type,
    '#skF_2': ( $i * $i ) > $i ).

tff(iLess0,type,
    iLess0: ( $i * $i ) > $o ).

tff('#skF_27',type,
    '#skF_27': $i > $i ).

tff(szmzizndt0,type,
    szmzizndt0: $i > $i ).

tff('#skF_36',type,
    '#skF_36': ( $i * $i * $i * $i ) > $i ).

tff(szmzazxdt0,type,
    szmzazxdt0: $i > $i ).

tff('#skF_21',type,
    '#skF_21': ( $i * $i * $i ) > $i ).

tff(xK,type,
    xK: $i ).

tff('#skF_9',type,
    '#skF_9': ( $i * $i ) > $i ).

tff(slbdtrb0,type,
    slbdtrb0: $i > $i ).

tff('#skF_22',type,
    '#skF_22': ( $i * $i * $i * $i ) > $i ).

tff('#skF_16',type,
    '#skF_16': ( $i * $i * $i ) > $i ).

tff(f_924,hypothesis,
    aElementOf0(xi,szNzAzT0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3989) ).

tff(f_252,axiom,
    ! [W0] :
      ( aElementOf0(W0,szNzAzT0)
     => sdtlseqdt0(sz00,W0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mZeroLess) ).

tff(f_999,negated_conjecture,
    ~ ( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
        & ! [W0] :
            ( aElementOf0(W0,sdtlpdtrp0(xN,xi))
           => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W0) ) )
     => ( ( aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
          & ! [W0] :
              ( aElementOf0(W0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
            <=> ( aElement0(W0)
                & ( aElementOf0(W0,xQ)
                  | ( W0 = szmzizndt0(sdtlpdtrp0(xN,xi)) ) ) ) ) )
       => ( ! [W0] :
              ( aElementOf0(W0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
             => aElementOf0(W0,xS) )
          | aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).

tff(f_212,axiom,
    aElementOf0(sz00,szNzAzT0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mZeroNum) ).

tff(f_674,hypothesis,
    ( aSet0(xS)
    & ! [W0] :
        ( aElementOf0(W0,xS)
       => aElementOf0(W0,szNzAzT0) )
    & aSubsetOf0(xS,szNzAzT0)
    & isCountable0(xS) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3435) ).

tff(f_873,hypothesis,
    ( aFunction0(xN)
    & ( szDzozmdt0(xN) = szNzAzT0 )
    & ( sdtlpdtrp0(xN,sz00) = xS )
    & ! [W0] :
        ( aElementOf0(W0,szNzAzT0)
       => ( ( ( ( aSet0(sdtlpdtrp0(xN,W0))
                & ! [W1] :
                    ( aElementOf0(W1,sdtlpdtrp0(xN,W0))
                   => aElementOf0(W1,szNzAzT0) ) )
              | aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0) )
            & isCountable0(sdtlpdtrp0(xN,W0)) )
         => ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
            & ! [W1] :
                ( aElementOf0(W1,sdtlpdtrp0(xN,W0))
               => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
            & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
            & ! [W1] :
                ( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
              <=> ( aElement0(W1)
                  & aElementOf0(W1,sdtlpdtrp0(xN,W0))
                  & ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
            & aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
            & ! [W1] :
                ( aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
               => aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
            & aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
            & isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3623) ).

tff(f_899,hypothesis,
    ! [W0,W1] :
      ( ( aElementOf0(W0,szNzAzT0)
        & aElementOf0(W1,szNzAzT0) )
     => ( sdtlseqdt0(W1,W0)
       => ( ! [W2] :
              ( aElementOf0(W2,sdtlpdtrp0(xN,W0))
             => aElementOf0(W2,sdtlpdtrp0(xN,W1)) )
          & aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3754) ).

tff(f_886,hypothesis,
    ! [W0] :
      ( aElementOf0(W0,szNzAzT0)
     => ( aSet0(sdtlpdtrp0(xN,W0))
        & ! [W1] :
            ( aElementOf0(W1,sdtlpdtrp0(xN,W0))
           => aElementOf0(W1,szNzAzT0) )
        & aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
        & isCountable0(sdtlpdtrp0(xN,W0)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3671) ).

tff(f_39,axiom,
    ! [W0] :
      ( aSet0(W0)
     => ! [W1] :
          ( aElementOf0(W1,W0)
         => aElement0(W1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEOfElem) ).

tff(f_955,hypothesis,
    ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
    & ! [W0] :
        ( aElementOf0(W0,sdtlpdtrp0(xN,xi))
       => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W0) )
    & aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
    & ! [W0] :
        ( aElementOf0(W0,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
      <=> ( aElement0(W0)
          & aElementOf0(W0,sdtlpdtrp0(xN,xi))
          & ( W0 != szmzizndt0(sdtlpdtrp0(xN,xi)) ) ) )
    & aSet0(xQ)
    & ! [W0] :
        ( aElementOf0(W0,xQ)
       => aElementOf0(W0,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
    & aSubsetOf0(xQ,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
    & ( sbrdtbr0(xQ) = xk )
    & aElementOf0(xQ,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3989_02) ).

tff(f_84,definition,
    ! [W0] :
      ( aSet0(W0)
     => ! [W1] :
          ( aSubsetOf0(W1,W0)
        <=> ( aSet0(W1)
            & ! [W2] :
                ( aElementOf0(W2,W1)
               => aElementOf0(W2,W0) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSub) ).

tff(f_156,definition,
    ! [W0,W1] :
      ( ( aSet0(W0)
        & aElement0(W1) )
     => ! [W2] :
          ( ( W2 = sdtmndt0(W0,W1) )
        <=> ( aSet0(W2)
            & ! [W3] :
                ( aElementOf0(W3,W2)
              <=> ( aElement0(W3)
                  & aElementOf0(W3,W0)
                  & ( W3 != W1 ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefDiff) ).

tff(c_8416,plain,
    aElementOf0(xi,szNzAzT0),
    inference(cnfTransformation,[status(thm)],[f_924]) ).

tff(c_126,plain,
    ! [W0_80] :
      ( sdtlseqdt0(sz00,W0_80)
      | ~ aElementOf0(W0_80,szNzAzT0) ),
    inference(cnfTransformation,[status(thm)],[f_252]) ).

tff(c_8460,plain,
    ~ aElementOf0('#skF_39',xS),
    inference(cnfTransformation,[status(thm)],[f_999]) ).

tff(c_110,plain,
    aElementOf0(sz00,szNzAzT0),
    inference(cnfTransformation,[status(thm)],[f_212]) ).

tff(c_344,plain,
    aSet0(xS),
    inference(cnfTransformation,[status(thm)],[f_674]) ).

tff(c_8322,plain,
    sdtlpdtrp0(xN,sz00) = xS,
    inference(cnfTransformation,[status(thm)],[f_873]) ).

tff(c_45267,plain,
    ! [W0_1755,W1_1756] :
      ( aSubsetOf0(sdtlpdtrp0(xN,W0_1755),sdtlpdtrp0(xN,W1_1756))
      | ~ sdtlseqdt0(W1_1756,W0_1755)
      | ~ aElementOf0(W1_1756,szNzAzT0)
      | ~ aElementOf0(W0_1755,szNzAzT0) ),
    inference(cnfTransformation,[status(thm)],[f_899]) ).

tff(c_20161,plain,
    ! [W0_992,W1_993] :
      ( aSubsetOf0(sdtlpdtrp0(xN,W0_992),sdtlpdtrp0(xN,W1_993))
      | ~ sdtlseqdt0(W1_993,W0_992)
      | ~ aElementOf0(W1_993,szNzAzT0)
      | ~ aElementOf0(W0_992,szNzAzT0) ),
    inference(cnfTransformation,[status(thm)],[f_899]) ).

tff(c_20191,plain,
    ! [W0_992] :
      ( aSubsetOf0(sdtlpdtrp0(xN,W0_992),xS)
      | ~ sdtlseqdt0(sz00,W0_992)
      | ~ aElementOf0(sz00,szNzAzT0)
      | ~ aElementOf0(W0_992,szNzAzT0) ),
    inference(superposition,[status(thm),theory(equality)],[c_8322,c_20161]) ).

tff(c_20424,plain,
    ! [W0_996] :
      ( aSubsetOf0(sdtlpdtrp0(xN,W0_996),xS)
      | ~ sdtlseqdt0(sz00,W0_996)
      | ~ aElementOf0(W0_996,szNzAzT0) ),
    inference(demodulation,[status(thm),theory(equality)],[c_110,c_20191]) ).

tff(c_8400,plain,
    ! [W0_581] :
      ( aSet0(sdtlpdtrp0(xN,W0_581))
      | ~ aElementOf0(W0_581,szNzAzT0) ),
    inference(cnfTransformation,[status(thm)],[f_886]) ).

tff(c_8474,plain,
    ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
    | ~ aElement0(szmzizndt0(sdtlpdtrp0(xN,xi))) ),
    inference(cnfTransformation,[status(thm)],[f_999]) ).

tff(c_8876,plain,
    ~ aElement0(szmzizndt0(sdtlpdtrp0(xN,xi))),
    inference(splitLeft,[status(thm)],[c_8474]) ).

tff(c_8468,plain,
    aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi)),
    inference(cnfTransformation,[status(thm)],[f_999]) ).

tff(c_8606,plain,
    ! [W1_614,W0_615] :
      ( aElement0(W1_614)
      | ~ aElementOf0(W1_614,W0_615)
      | ~ aSet0(W0_615) ),
    inference(cnfTransformation,[status(thm)],[f_39]) ).

tff(c_8628,plain,
    ( aElement0(szmzizndt0(sdtlpdtrp0(xN,xi)))
    | ~ aSet0(sdtlpdtrp0(xN,xi)) ),
    inference(resolution,[status(thm)],[c_8468,c_8606]) ).

tff(c_9102,plain,
    ~ aSet0(sdtlpdtrp0(xN,xi)),
    inference(negUnitSimplification,[status(thm)],[c_8876,c_8628]) ).

tff(c_9105,plain,
    ~ aElementOf0(xi,szNzAzT0),
    inference(resolution,[status(thm)],[c_8400,c_9102]) ).

tff(c_9109,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_8416,c_9105]) ).

tff(c_9111,plain,
    aElement0(szmzizndt0(sdtlpdtrp0(xN,xi))),
    inference(splitRight,[status(thm)],[c_8474]) ).

tff(c_8430,plain,
    aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))),
    inference(cnfTransformation,[status(thm)],[f_955]) ).

tff(c_8422,plain,
    aSubsetOf0(xQ,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))),
    inference(cnfTransformation,[status(thm)],[f_955]) ).

tff(c_8462,plain,
    aElementOf0('#skF_39',sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))),
    inference(cnfTransformation,[status(thm)],[f_999]) ).

tff(c_9147,plain,
    ! [W0_650] :
      ( ( szmzizndt0(sdtlpdtrp0(xN,xi)) = W0_650 )
      | aElementOf0(W0_650,xQ)
      | ~ aElementOf0(W0_650,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) ),
    inference(cnfTransformation,[status(thm)],[f_999]) ).

tff(c_9162,plain,
    ( ( szmzizndt0(sdtlpdtrp0(xN,xi)) = '#skF_39' )
    | aElementOf0('#skF_39',xQ) ),
    inference(resolution,[status(thm)],[c_8462,c_9147]) ).

tff(c_9225,plain,
    aElementOf0('#skF_39',xQ),
    inference(splitLeft,[status(thm)],[c_9162]) ).

tff(c_10677,plain,
    ! [W2_752,W0_753,W1_754] :
      ( aElementOf0(W2_752,W0_753)
      | ~ aElementOf0(W2_752,W1_754)
      | ~ aSubsetOf0(W1_754,W0_753)
      | ~ aSet0(W0_753) ),
    inference(cnfTransformation,[status(thm)],[f_84]) ).

tff(c_10837,plain,
    ! [W0_759] :
      ( aElementOf0('#skF_39',W0_759)
      | ~ aSubsetOf0(xQ,W0_759)
      | ~ aSet0(W0_759) ),
    inference(resolution,[status(thm)],[c_9225,c_10677]) ).

tff(c_10844,plain,
    ( aElementOf0('#skF_39',sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
    | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ),
    inference(resolution,[status(thm)],[c_8422,c_10837]) ).

tff(c_10854,plain,
    aElementOf0('#skF_39',sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))),
    inference(demodulation,[status(thm),theory(equality)],[c_8430,c_10844]) ).

tff(c_12892,plain,
    ! [W3_814,W0_815,W1_816] :
      ( aElementOf0(W3_814,W0_815)
      | ~ aElementOf0(W3_814,sdtmndt0(W0_815,W1_816))
      | ~ aElement0(W1_816)
      | ~ aSet0(W0_815) ),
    inference(cnfTransformation,[status(thm)],[f_156]) ).

tff(c_12899,plain,
    ( aElementOf0('#skF_39',sdtlpdtrp0(xN,xi))
    | ~ aElement0(szmzizndt0(sdtlpdtrp0(xN,xi)))
    | ~ aSet0(sdtlpdtrp0(xN,xi)) ),
    inference(resolution,[status(thm)],[c_10854,c_12892]) ).

tff(c_12927,plain,
    ( aElementOf0('#skF_39',sdtlpdtrp0(xN,xi))
    | ~ aSet0(sdtlpdtrp0(xN,xi)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_9111,c_12899]) ).

tff(c_12935,plain,
    ~ aSet0(sdtlpdtrp0(xN,xi)),
    inference(splitLeft,[status(thm)],[c_12927]) ).

tff(c_12938,plain,
    ~ aElementOf0(xi,szNzAzT0),
    inference(resolution,[status(thm)],[c_8400,c_12935]) ).

tff(c_12942,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_8416,c_12938]) ).

tff(c_12943,plain,
    aElementOf0('#skF_39',sdtlpdtrp0(xN,xi)),
    inference(splitRight,[status(thm)],[c_12927]) ).

tff(c_24,plain,
    ! [W2_23,W0_14,W1_20] :
      ( aElementOf0(W2_23,W0_14)
      | ~ aElementOf0(W2_23,W1_20)
      | ~ aSubsetOf0(W1_20,W0_14)
      | ~ aSet0(W0_14) ),
    inference(cnfTransformation,[status(thm)],[f_84]) ).

tff(c_12959,plain,
    ! [W0_14] :
      ( aElementOf0('#skF_39',W0_14)
      | ~ aSubsetOf0(sdtlpdtrp0(xN,xi),W0_14)
      | ~ aSet0(W0_14) ),
    inference(resolution,[status(thm)],[c_12943,c_24]) ).

tff(c_20441,plain,
    ( aElementOf0('#skF_39',xS)
    | ~ aSet0(xS)
    | ~ sdtlseqdt0(sz00,xi)
    | ~ aElementOf0(xi,szNzAzT0) ),
    inference(resolution,[status(thm)],[c_20424,c_12959]) ).

tff(c_20473,plain,
    ( aElementOf0('#skF_39',xS)
    | ~ sdtlseqdt0(sz00,xi) ),
    inference(demodulation,[status(thm),theory(equality)],[c_8416,c_344,c_20441]) ).

tff(c_20474,plain,
    ~ sdtlseqdt0(sz00,xi),
    inference(negUnitSimplification,[status(thm)],[c_8460,c_20473]) ).

tff(c_20543,plain,
    ~ aElementOf0(xi,szNzAzT0),
    inference(resolution,[status(thm)],[c_126,c_20474]) ).

tff(c_20547,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_8416,c_20543]) ).

tff(c_20548,plain,
    szmzizndt0(sdtlpdtrp0(xN,xi)) = '#skF_39',
    inference(splitRight,[status(thm)],[c_9162]) ).

tff(c_20562,plain,
    aElementOf0('#skF_39',sdtlpdtrp0(xN,xi)),
    inference(demodulation,[status(thm),theory(equality)],[c_20548,c_8468]) ).

tff(c_34487,plain,
    ! [W2_1492,W0_1493,W1_1494] :
      ( aElementOf0(W2_1492,W0_1493)
      | ~ aElementOf0(W2_1492,W1_1494)
      | ~ aSubsetOf0(W1_1494,W0_1493)
      | ~ aSet0(W0_1493) ),
    inference(cnfTransformation,[status(thm)],[f_84]) ).

tff(c_34539,plain,
    ! [W0_1493] :
      ( aElementOf0('#skF_39',W0_1493)
      | ~ aSubsetOf0(sdtlpdtrp0(xN,xi),W0_1493)
      | ~ aSet0(W0_1493) ),
    inference(resolution,[status(thm)],[c_20562,c_34487]) ).

tff(c_45281,plain,
    ! [W1_1756] :
      ( aElementOf0('#skF_39',sdtlpdtrp0(xN,W1_1756))
      | ~ aSet0(sdtlpdtrp0(xN,W1_1756))
      | ~ sdtlseqdt0(W1_1756,xi)
      | ~ aElementOf0(W1_1756,szNzAzT0)
      | ~ aElementOf0(xi,szNzAzT0) ),
    inference(resolution,[status(thm)],[c_45267,c_34539]) ).

tff(c_45393,plain,
    ! [W1_1760] :
      ( aElementOf0('#skF_39',sdtlpdtrp0(xN,W1_1760))
      | ~ aSet0(sdtlpdtrp0(xN,W1_1760))
      | ~ sdtlseqdt0(W1_1760,xi)
      | ~ aElementOf0(W1_1760,szNzAzT0) ),
    inference(demodulation,[status(thm),theory(equality)],[c_8416,c_45281]) ).

tff(c_45410,plain,
    ( aElementOf0('#skF_39',xS)
    | ~ aSet0(sdtlpdtrp0(xN,sz00))
    | ~ sdtlseqdt0(sz00,xi)
    | ~ aElementOf0(sz00,szNzAzT0) ),
    inference(superposition,[status(thm),theory(equality)],[c_8322,c_45393]) ).

tff(c_45423,plain,
    ( aElementOf0('#skF_39',xS)
    | ~ sdtlseqdt0(sz00,xi) ),
    inference(demodulation,[status(thm),theory(equality)],[c_110,c_344,c_8322,c_45410]) ).

tff(c_45424,plain,
    ~ sdtlseqdt0(sz00,xi),
    inference(negUnitSimplification,[status(thm)],[c_8460,c_45423]) ).

tff(c_45427,plain,
    ~ aElementOf0(xi,szNzAzT0),
    inference(resolution,[status(thm)],[c_126,c_45424]) ).

tff(c_45431,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_8416,c_45427]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : NUM581+3 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14  % Command  : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.15/0.35  % Computer : n003.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit : 300
% 0.15/0.35  % WCLimit  : 300
% 0.15/0.35  % DateTime : Thu Aug  3 14:52:38 EDT 2023
% 0.15/0.36  % CPUTime  : 
% 86.86/64.69  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 86.86/64.70  
% 86.86/64.70  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 87.07/64.73  
% 87.07/64.73  Inference rules
% 87.07/64.73  ----------------------
% 87.07/64.73  #Ref     : 5
% 87.07/64.73  #Sup     : 6709
% 87.07/64.73  #Fact    : 0
% 87.07/64.73  #Define  : 0
% 87.07/64.73  #Split   : 330
% 87.07/64.73  #Chain   : 0
% 87.07/64.73  #Close   : 0
% 87.07/64.73  
% 87.07/64.73  Ordering : KBO
% 87.07/64.73  
% 87.07/64.73  Simplification rules
% 87.07/64.73  ----------------------
% 87.07/64.73  #Subsume      : 2356
% 87.07/64.73  #Demod        : 6978
% 87.07/64.73  #Tautology    : 1567
% 87.07/64.73  #SimpNegUnit  : 423
% 87.07/64.73  #BackRed      : 576
% 87.07/64.73  
% 87.07/64.73  #Partial instantiations: 0
% 87.07/64.73  #Strategies tried      : 1
% 87.07/64.73  
% 87.07/64.73  Timing (in seconds)
% 87.07/64.73  ----------------------
% 87.07/64.73  Preprocessing        : 2.41
% 87.07/64.73  Parsing              : 0.51
% 87.07/64.73  CNF conversion       : 0.19
% 87.07/64.73  Main loop            : 61.22
% 87.07/64.73  Inferencing          : 1.76
% 87.07/64.73  Reduction            : 44.46
% 87.07/64.73  Demodulation         : 37.51
% 87.07/64.73  BG Simplification    : 0.87
% 87.07/64.73  Subsumption          : 11.75
% 87.07/64.73  Abstraction          : 0.50
% 87.07/64.73  MUC search           : 0.00
% 87.07/64.73  Cooper               : 0.00
% 87.07/64.73  Total                : 63.69
% 87.07/64.73  Index Insertion      : 0.00
% 87.07/64.73  Index Deletion       : 0.00
% 87.07/64.73  Index Matching       : 0.00
% 87.07/64.73  BG Taut test         : 0.00
%------------------------------------------------------------------------------