TSTP Solution File: NUM554+1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : NUM554+1 : 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 10:52:05 EDT 2023

% Result   : Theorem 239.29s 210.89s
% Output   : CNFRefutation 239.40s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   22
%            Number of leaves      :   62
% Syntax   : Number of formulae    :  154 (  44 unt;  41 typ;   4 def)
%            Number of atoms       :  300 (  36 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :  322 ( 135   ~; 136   |;  24   &)
%                                         (   7 <=>;  20  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   4 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   56 (  31   >;  25   *;   0   +;   0  <<)
%            Number of predicates  :   10 (   8 usr;   1 prp; 0-2 aty)
%            Number of functors    :   33 (  33 usr;  10 con; 0-3 aty)
%            Number of variables   :   90 (;  90   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ sdtlseqdt0 > iLess0 > aSubsetOf0 > aElementOf0 > isFinite0 > isCountable0 > aSet0 > aElement0 > slbdtsldtrb0 > sdtpldt0 > sdtmndt0 > #nlpp > szszuzczcdt0 > szmzizndt0 > szmzazxdt0 > slbdtrb0 > sbrdtbr0 > xy > xx > xk > xT > xS > xQ > xP > szNzAzT0 > sz00 > slcrc0 > #skF_7 > #skF_11 > #skF_6 > #skF_1 > #skF_4 > #skF_12 > #skF_5 > #skF_10 > #skF_8 > #skF_15 > #skF_13 > #skF_14 > #skF_3 > #skF_2 > #skF_9

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

tff(szszuzczcdt0,type,
    szszuzczcdt0: $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(aElement0,type,
    aElement0: $i > $o ).

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

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

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

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

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

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

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

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

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

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

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

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

tff('#skF_5',type,
    '#skF_5': ( $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(aElementOf0,type,
    aElementOf0: ( $i * $i ) > $o ).

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

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

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

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

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

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

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

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

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

tff(f_526,hypothesis,
    ( aSet0(xS)
    & aSet0(xT)
    & ( xk != sz00 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2202_02) ).

tff(f_520,hypothesis,
    aElementOf0(xk,szNzAzT0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2202) ).

tff(f_537,hypothesis,
    ( aSet0(xQ)
    & isFinite0(xQ)
    & ( sbrdtbr0(xQ) = xk ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2291) ).

tff(f_540,hypothesis,
    ( aElement0(xy)
    & aElementOf0(xy,xQ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2304) ).

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(f_531,hypothesis,
    aElementOf0(xx,xS),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2256) ).

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

tff(f_545,hypothesis,
    xP = sdtpldt0(sdtmndt0(xQ,xy),xx),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2357) ).

tff(f_137,definition,
    ! [W0,W1] :
      ( ( aSet0(W0)
        & aElement0(W1) )
     => ! [W2] :
          ( ( W2 = sdtpldt0(W0,W1) )
        <=> ( aSet0(W2)
            & ! [W3] :
                ( aElementOf0(W3,W2)
              <=> ( aElement0(W3)
                  & ( aElementOf0(W3,W0)
                    | ( W3 = W1 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefCons) ).

tff(f_208,axiom,
    ! [W0] :
      ( aElement0(W0)
     => ! [W1] :
          ( ( aSet0(W1)
            & isFinite0(W1) )
         => isFinite0(sdtmndt0(W1,W0)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mFDiffSet) ).

tff(f_199,axiom,
    ! [W0] :
      ( aElement0(W0)
     => ! [W1] :
          ( ( aSet0(W1)
            & isFinite0(W1) )
         => isFinite0(sdtpldt0(W1,W0)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mFConsSet) ).

tff(f_544,hypothesis,
    ~ aElementOf0(xx,xQ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2338) ).

tff(f_172,axiom,
    ! [W0,W1] :
      ( ( aElement0(W0)
        & aSet0(W1) )
     => ( ~ aElementOf0(W0,W1)
       => ( sdtmndt0(sdtpldt0(W1,W0),W0) = W1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDiffCons) ).

tff(f_351,axiom,
    ! [W0] :
      ( aSet0(W0)
     => ! [W1] :
          ( ( isFinite0(W0)
            & aElementOf0(W1,W0) )
         => ( szszuzczcdt0(sbrdtbr0(sdtmndt0(W0,W1))) = sbrdtbr0(W0) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCardDiff) ).

tff(f_487,definition,
    ! [W0,W1] :
      ( ( aSet0(W0)
        & aElementOf0(W1,szNzAzT0) )
     => ! [W2] :
          ( ( W2 = slbdtsldtrb0(W0,W1) )
        <=> ( aSet0(W2)
            & ! [W3] :
                ( aElementOf0(W3,W2)
              <=> ( aSubsetOf0(W3,W0)
                  & ( sbrdtbr0(W3) = W1 ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSel) ).

tff(f_547,negated_conjecture,
    ~ aElementOf0(xP,slbdtsldtrb0(xS,xk)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).

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_97,axiom,
    ! [W0] :
      ( aSet0(W0)
     => aSubsetOf0(W0,W0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSubRefl) ).

tff(f_360,axiom,
    ! [W0] :
      ( aSet0(W0)
     => ! [W1] :
          ( ( isFinite0(W0)
            & aSubsetOf0(W1,W0) )
         => sdtlseqdt0(sbrdtbr0(W1),sbrdtbr0(W0)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCardSub) ).

tff(f_532,hypothesis,
    aElementOf0(xQ,slbdtsldtrb0(xS,xk)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2270) ).

tff(f_119,axiom,
    ! [W0,W1,W2] :
      ( ( aSet0(W0)
        & aSet0(W1)
        & aSet0(W2) )
     => ( ( aSubsetOf0(W0,W1)
          & aSubsetOf0(W1,W2) )
       => aSubsetOf0(W0,W2) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSubTrans) ).

tff(c_258,plain,
    aSet0(xS),
    inference(cnfTransformation,[status(thm)],[f_526]) ).

tff(c_252,plain,
    aElementOf0(xk,szNzAzT0),
    inference(cnfTransformation,[status(thm)],[f_520]) ).

tff(c_272,plain,
    aSet0(xQ),
    inference(cnfTransformation,[status(thm)],[f_537]) ).

tff(c_276,plain,
    aElement0(xy),
    inference(cnfTransformation,[status(thm)],[f_540]) ).

tff(c_923,plain,
    ! [W0_231,W1_232] :
      ( aSet0(sdtmndt0(W0_231,W1_232))
      | ~ aElement0(W1_232)
      | ~ aSet0(W0_231) ),
    inference(cnfTransformation,[status(thm)],[f_156]) ).

tff(c_264,plain,
    aElementOf0(xx,xS),
    inference(cnfTransformation,[status(thm)],[f_531]) ).

tff(c_407,plain,
    ! [W1_184,W0_185] :
      ( aElement0(W1_184)
      | ~ aElementOf0(W1_184,W0_185)
      | ~ aSet0(W0_185) ),
    inference(cnfTransformation,[status(thm)],[f_39]) ).

tff(c_422,plain,
    ( aElement0(xx)
    | ~ aSet0(xS) ),
    inference(resolution,[status(thm)],[c_264,c_407]) ).

tff(c_435,plain,
    aElement0(xx),
    inference(demodulation,[status(thm),theory(equality)],[c_258,c_422]) ).

tff(c_282,plain,
    sdtpldt0(sdtmndt0(xQ,xy),xx) = xP,
    inference(cnfTransformation,[status(thm)],[f_545]) ).

tff(c_878,plain,
    ! [W0_227,W1_228] :
      ( aSet0(sdtpldt0(W0_227,W1_228))
      | ~ aElement0(W1_228)
      | ~ aSet0(W0_227) ),
    inference(cnfTransformation,[status(thm)],[f_137]) ).

tff(c_884,plain,
    ( aSet0(xP)
    | ~ aElement0(xx)
    | ~ aSet0(sdtmndt0(xQ,xy)) ),
    inference(superposition,[status(thm),theory(equality)],[c_282,c_878]) ).

tff(c_887,plain,
    ( aSet0(xP)
    | ~ aSet0(sdtmndt0(xQ,xy)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_435,c_884]) ).

tff(c_888,plain,
    ~ aSet0(sdtmndt0(xQ,xy)),
    inference(splitLeft,[status(thm)],[c_887]) ).

tff(c_926,plain,
    ( ~ aElement0(xy)
    | ~ aSet0(xQ) ),
    inference(resolution,[status(thm)],[c_923,c_888]) ).

tff(c_933,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_272,c_276,c_926]) ).

tff(c_934,plain,
    aSet0(xP),
    inference(splitRight,[status(thm)],[c_887]) ).

tff(c_270,plain,
    isFinite0(xQ),
    inference(cnfTransformation,[status(thm)],[f_537]) ).

tff(c_1312,plain,
    ! [W1_265,W0_266] :
      ( isFinite0(sdtmndt0(W1_265,W0_266))
      | ~ isFinite0(W1_265)
      | ~ aSet0(W1_265)
      | ~ aElement0(W0_266) ),
    inference(cnfTransformation,[status(thm)],[f_208]) ).

tff(c_935,plain,
    aSet0(sdtmndt0(xQ,xy)),
    inference(splitRight,[status(thm)],[c_887]) ).

tff(c_1258,plain,
    ! [W1_258,W0_259] :
      ( isFinite0(sdtpldt0(W1_258,W0_259))
      | ~ isFinite0(W1_258)
      | ~ aSet0(W1_258)
      | ~ aElement0(W0_259) ),
    inference(cnfTransformation,[status(thm)],[f_199]) ).

tff(c_1264,plain,
    ( isFinite0(xP)
    | ~ isFinite0(sdtmndt0(xQ,xy))
    | ~ aSet0(sdtmndt0(xQ,xy))
    | ~ aElement0(xx) ),
    inference(superposition,[status(thm),theory(equality)],[c_282,c_1258]) ).

tff(c_1267,plain,
    ( isFinite0(xP)
    | ~ isFinite0(sdtmndt0(xQ,xy)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_435,c_935,c_1264]) ).

tff(c_1268,plain,
    ~ isFinite0(sdtmndt0(xQ,xy)),
    inference(splitLeft,[status(thm)],[c_1267]) ).

tff(c_1315,plain,
    ( ~ isFinite0(xQ)
    | ~ aSet0(xQ)
    | ~ aElement0(xy) ),
    inference(resolution,[status(thm)],[c_1312,c_1268]) ).

tff(c_1322,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_276,c_272,c_270,c_1315]) ).

tff(c_1323,plain,
    isFinite0(xP),
    inference(splitRight,[status(thm)],[c_1267]) ).

tff(c_1179,plain,
    ! [W3_254,W0_255] :
      ( aElementOf0(W3_254,sdtpldt0(W0_255,W3_254))
      | ~ aElement0(W3_254)
      | ~ aSet0(W0_255) ),
    inference(cnfTransformation,[status(thm)],[f_137]) ).

tff(c_1185,plain,
    ( aElementOf0(xx,xP)
    | ~ aElement0(xx)
    | ~ aSet0(sdtmndt0(xQ,xy)) ),
    inference(superposition,[status(thm),theory(equality)],[c_282,c_1179]) ).

tff(c_1188,plain,
    aElementOf0(xx,xP),
    inference(demodulation,[status(thm),theory(equality)],[c_935,c_435,c_1185]) ).

tff(c_274,plain,
    aElementOf0(xy,xQ),
    inference(cnfTransformation,[status(thm)],[f_540]) ).

tff(c_268,plain,
    sbrdtbr0(xQ) = xk,
    inference(cnfTransformation,[status(thm)],[f_537]) ).

tff(c_280,plain,
    ~ aElementOf0(xx,xQ),
    inference(cnfTransformation,[status(thm)],[f_544]) ).

tff(c_2220,plain,
    ! [W1_348,W0_349] :
      ( ( sdtmndt0(sdtpldt0(W1_348,W0_349),W0_349) = W1_348 )
      | aElementOf0(W0_349,W1_348)
      | ~ aSet0(W1_348)
      | ~ aElement0(W0_349) ),
    inference(cnfTransformation,[status(thm)],[f_172]) ).

tff(c_2253,plain,
    ( ( sdtmndt0(xQ,xy) = sdtmndt0(xP,xx) )
    | aElementOf0(xx,sdtmndt0(xQ,xy))
    | ~ aSet0(sdtmndt0(xQ,xy))
    | ~ aElement0(xx) ),
    inference(superposition,[status(thm),theory(equality)],[c_282,c_2220]) ).

tff(c_2259,plain,
    ( ( sdtmndt0(xQ,xy) = sdtmndt0(xP,xx) )
    | aElementOf0(xx,sdtmndt0(xQ,xy)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_435,c_935,c_2253]) ).

tff(c_2260,plain,
    aElementOf0(xx,sdtmndt0(xQ,xy)),
    inference(splitLeft,[status(thm)],[c_2259]) ).

tff(c_74,plain,
    ! [W3_54,W0_44,W1_45] :
      ( aElementOf0(W3_54,W0_44)
      | ~ aElementOf0(W3_54,sdtmndt0(W0_44,W1_45))
      | ~ aElement0(W1_45)
      | ~ aSet0(W0_44) ),
    inference(cnfTransformation,[status(thm)],[f_156]) ).

tff(c_2263,plain,
    ( aElementOf0(xx,xQ)
    | ~ aElement0(xy)
    | ~ aSet0(xQ) ),
    inference(resolution,[status(thm)],[c_2260,c_74]) ).

tff(c_2274,plain,
    aElementOf0(xx,xQ),
    inference(demodulation,[status(thm),theory(equality)],[c_272,c_276,c_2263]) ).

tff(c_2276,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_280,c_2274]) ).

tff(c_2277,plain,
    sdtmndt0(xQ,xy) = sdtmndt0(xP,xx),
    inference(splitRight,[status(thm)],[c_2259]) ).

tff(c_2964,plain,
    ! [W0_377,W1_378] :
      ( ( szszuzczcdt0(sbrdtbr0(sdtmndt0(W0_377,W1_378))) = sbrdtbr0(W0_377) )
      | ~ aElementOf0(W1_378,W0_377)
      | ~ isFinite0(W0_377)
      | ~ aSet0(W0_377) ),
    inference(cnfTransformation,[status(thm)],[f_351]) ).

tff(c_3022,plain,
    ( ( szszuzczcdt0(sbrdtbr0(sdtmndt0(xP,xx))) = sbrdtbr0(xQ) )
    | ~ aElementOf0(xy,xQ)
    | ~ isFinite0(xQ)
    | ~ aSet0(xQ) ),
    inference(superposition,[status(thm),theory(equality)],[c_2277,c_2964]) ).

tff(c_3029,plain,
    szszuzczcdt0(sbrdtbr0(sdtmndt0(xP,xx))) = xk,
    inference(demodulation,[status(thm),theory(equality)],[c_272,c_270,c_274,c_268,c_3022]) ).

tff(c_160,plain,
    ! [W0_102,W1_104] :
      ( ( szszuzczcdt0(sbrdtbr0(sdtmndt0(W0_102,W1_104))) = sbrdtbr0(W0_102) )
      | ~ aElementOf0(W1_104,W0_102)
      | ~ isFinite0(W0_102)
      | ~ aSet0(W0_102) ),
    inference(cnfTransformation,[status(thm)],[f_351]) ).

tff(c_3033,plain,
    ( ( sbrdtbr0(xP) = xk )
    | ~ aElementOf0(xx,xP)
    | ~ isFinite0(xP)
    | ~ aSet0(xP) ),
    inference(superposition,[status(thm),theory(equality)],[c_3029,c_160]) ).

tff(c_3089,plain,
    sbrdtbr0(xP) = xk,
    inference(demodulation,[status(thm),theory(equality)],[c_934,c_1323,c_1188,c_3033]) ).

tff(c_3444,plain,
    ! [W3_392,W0_393] :
      ( aElementOf0(W3_392,slbdtsldtrb0(W0_393,sbrdtbr0(W3_392)))
      | ~ aSubsetOf0(W3_392,W0_393)
      | ~ aElementOf0(sbrdtbr0(W3_392),szNzAzT0)
      | ~ aSet0(W0_393) ),
    inference(cnfTransformation,[status(thm)],[f_487]) ).

tff(c_3458,plain,
    ! [W0_393] :
      ( aElementOf0(xP,slbdtsldtrb0(W0_393,xk))
      | ~ aSubsetOf0(xP,W0_393)
      | ~ aElementOf0(sbrdtbr0(xP),szNzAzT0)
      | ~ aSet0(W0_393) ),
    inference(superposition,[status(thm),theory(equality)],[c_3089,c_3444]) ).

tff(c_5182,plain,
    ! [W0_439] :
      ( aElementOf0(xP,slbdtsldtrb0(W0_439,xk))
      | ~ aSubsetOf0(xP,W0_439)
      | ~ aSet0(W0_439) ),
    inference(demodulation,[status(thm),theory(equality)],[c_252,c_3089,c_3458]) ).

tff(c_284,plain,
    ~ aElementOf0(xP,slbdtsldtrb0(xS,xk)),
    inference(cnfTransformation,[status(thm)],[f_547]) ).

tff(c_5196,plain,
    ( ~ aSubsetOf0(xP,xS)
    | ~ aSet0(xS) ),
    inference(resolution,[status(thm)],[c_5182,c_284]) ).

tff(c_5207,plain,
    ~ aSubsetOf0(xP,xS),
    inference(demodulation,[status(thm),theory(equality)],[c_258,c_5196]) ).

tff(c_30,plain,
    ! [W0_14,W1_20] :
      ( aElementOf0('#skF_2'(W0_14,W1_20),W1_20)
      | aSubsetOf0(W1_20,W0_14)
      | ~ aSet0(W1_20)
      | ~ aSet0(W0_14) ),
    inference(cnfTransformation,[status(thm)],[f_84]) ).

tff(c_34,plain,
    ! [W0_27] :
      ( aSubsetOf0(W0_27,W0_27)
      | ~ aSet0(W0_27) ),
    inference(cnfTransformation,[status(thm)],[f_97]) ).

tff(c_1762,plain,
    ! [W1_311,W0_312] :
      ( sdtlseqdt0(sbrdtbr0(W1_311),sbrdtbr0(W0_312))
      | ~ aSubsetOf0(W1_311,W0_312)
      | ~ isFinite0(W0_312)
      | ~ aSet0(W0_312) ),
    inference(cnfTransformation,[status(thm)],[f_360]) ).

tff(c_1780,plain,
    ! [W1_311] :
      ( sdtlseqdt0(sbrdtbr0(W1_311),xk)
      | ~ aSubsetOf0(W1_311,xQ)
      | ~ isFinite0(xQ)
      | ~ aSet0(xQ) ),
    inference(superposition,[status(thm),theory(equality)],[c_268,c_1762]) ).

tff(c_1914,plain,
    ! [W1_319] :
      ( sdtlseqdt0(sbrdtbr0(W1_319),xk)
      | ~ aSubsetOf0(W1_319,xQ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_272,c_270,c_1780]) ).

tff(c_1923,plain,
    ( sdtlseqdt0(xk,xk)
    | ~ aSubsetOf0(xQ,xQ) ),
    inference(superposition,[status(thm),theory(equality)],[c_268,c_1914]) ).

tff(c_1952,plain,
    ~ aSubsetOf0(xQ,xQ),
    inference(splitLeft,[status(thm)],[c_1923]) ).

tff(c_1956,plain,
    ~ aSet0(xQ),
    inference(resolution,[status(thm)],[c_34,c_1952]) ).

tff(c_1960,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_272,c_1956]) ).

tff(c_1962,plain,
    aSubsetOf0(xQ,xQ),
    inference(splitRight,[status(thm)],[c_1923]) ).

tff(c_266,plain,
    aElementOf0(xQ,slbdtsldtrb0(xS,xk)),
    inference(cnfTransformation,[status(thm)],[f_532]) ).

tff(c_2345,plain,
    ! [W3_352,W0_353,W1_354] :
      ( aSubsetOf0(W3_352,W0_353)
      | ~ aElementOf0(W3_352,slbdtsldtrb0(W0_353,W1_354))
      | ~ aElementOf0(W1_354,szNzAzT0)
      | ~ aSet0(W0_353) ),
    inference(cnfTransformation,[status(thm)],[f_487]) ).

tff(c_2367,plain,
    ( aSubsetOf0(xQ,xS)
    | ~ aElementOf0(xk,szNzAzT0)
    | ~ aSet0(xS) ),
    inference(resolution,[status(thm)],[c_266,c_2345]) ).

tff(c_2377,plain,
    aSubsetOf0(xQ,xS),
    inference(demodulation,[status(thm),theory(equality)],[c_258,c_252,c_2367]) ).

tff(c_3527,plain,
    ! [W0_396,W2_397,W1_398] :
      ( aSubsetOf0(W0_396,W2_397)
      | ~ aSubsetOf0(W1_398,W2_397)
      | ~ aSubsetOf0(W0_396,W1_398)
      | ~ aSet0(W2_397)
      | ~ aSet0(W1_398)
      | ~ aSet0(W0_396) ),
    inference(cnfTransformation,[status(thm)],[f_119]) ).

tff(c_3537,plain,
    ! [W0_396] :
      ( aSubsetOf0(W0_396,xS)
      | ~ aSubsetOf0(W0_396,xQ)
      | ~ aSet0(xS)
      | ~ aSet0(xQ)
      | ~ aSet0(W0_396) ),
    inference(resolution,[status(thm)],[c_2377,c_3527]) ).

tff(c_3566,plain,
    ! [W0_396] :
      ( aSubsetOf0(W0_396,xS)
      | ~ aSubsetOf0(W0_396,xQ)
      | ~ aSet0(W0_396) ),
    inference(demodulation,[status(thm),theory(equality)],[c_272,c_258,c_3537]) ).

tff(c_2294,plain,
    aSet0(sdtmndt0(xP,xx)),
    inference(demodulation,[status(thm),theory(equality)],[c_2277,c_935]) ).

tff(c_2295,plain,
    sdtpldt0(sdtmndt0(xP,xx),xx) = xP,
    inference(demodulation,[status(thm),theory(equality)],[c_2277,c_282]) ).

tff(c_2890,plain,
    ! [W3_373,W1_374,W0_375] :
      ( ( W3_373 = W1_374 )
      | aElementOf0(W3_373,W0_375)
      | ~ aElementOf0(W3_373,sdtpldt0(W0_375,W1_374))
      | ~ aElement0(W1_374)
      | ~ aSet0(W0_375) ),
    inference(cnfTransformation,[status(thm)],[f_137]) ).

tff(c_2899,plain,
    ! [W3_373] :
      ( ( xx = W3_373 )
      | aElementOf0(W3_373,sdtmndt0(xP,xx))
      | ~ aElementOf0(W3_373,xP)
      | ~ aElement0(xx)
      | ~ aSet0(sdtmndt0(xP,xx)) ),
    inference(superposition,[status(thm),theory(equality)],[c_2295,c_2890]) ).

tff(c_3383,plain,
    ! [W3_391] :
      ( ( xx = W3_391 )
      | aElementOf0(W3_391,sdtmndt0(xP,xx))
      | ~ aElementOf0(W3_391,xP) ),
    inference(demodulation,[status(thm),theory(equality)],[c_2294,c_435,c_2899]) ).

tff(c_2299,plain,
    ! [W3_54] :
      ( aElementOf0(W3_54,xQ)
      | ~ aElementOf0(W3_54,sdtmndt0(xP,xx))
      | ~ aElement0(xy)
      | ~ aSet0(xQ) ),
    inference(superposition,[status(thm),theory(equality)],[c_2277,c_74]) ).

tff(c_2321,plain,
    ! [W3_54] :
      ( aElementOf0(W3_54,xQ)
      | ~ aElementOf0(W3_54,sdtmndt0(xP,xx)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_272,c_276,c_2299]) ).

tff(c_3479,plain,
    ! [W3_394] :
      ( aElementOf0(W3_394,xQ)
      | ( xx = W3_394 )
      | ~ aElementOf0(W3_394,xP) ),
    inference(resolution,[status(thm)],[c_3383,c_2321]) ).

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_38952,plain,
    ! [W3_981,W0_982] :
      ( aElementOf0(W3_981,W0_982)
      | ~ aSubsetOf0(xQ,W0_982)
      | ~ aSet0(W0_982)
      | ( xx = W3_981 )
      | ~ aElementOf0(W3_981,xP) ),
    inference(resolution,[status(thm)],[c_3479,c_24]) ).

tff(c_38970,plain,
    ! [W3_981] :
      ( aElementOf0(W3_981,xS)
      | ~ aSet0(xS)
      | ( xx = W3_981 )
      | ~ aElementOf0(W3_981,xP)
      | ~ aSubsetOf0(xQ,xQ)
      | ~ aSet0(xQ) ),
    inference(resolution,[status(thm)],[c_3566,c_38952]) ).

tff(c_39110,plain,
    ! [W3_984] :
      ( aElementOf0(W3_984,xS)
      | ( xx = W3_984 )
      | ~ aElementOf0(W3_984,xP) ),
    inference(demodulation,[status(thm),theory(equality)],[c_272,c_1962,c_258,c_38970]) ).

tff(c_28,plain,
    ! [W0_14,W1_20] :
      ( ~ aElementOf0('#skF_2'(W0_14,W1_20),W0_14)
      | aSubsetOf0(W1_20,W0_14)
      | ~ aSet0(W1_20)
      | ~ aSet0(W0_14) ),
    inference(cnfTransformation,[status(thm)],[f_84]) ).

tff(c_39157,plain,
    ! [W1_20] :
      ( aSubsetOf0(W1_20,xS)
      | ~ aSet0(W1_20)
      | ~ aSet0(xS)
      | ( '#skF_2'(xS,W1_20) = xx )
      | ~ aElementOf0('#skF_2'(xS,W1_20),xP) ),
    inference(resolution,[status(thm)],[c_39110,c_28]) ).

tff(c_422224,plain,
    ! [W1_3076] :
      ( aSubsetOf0(W1_3076,xS)
      | ~ aSet0(W1_3076)
      | ( '#skF_2'(xS,W1_3076) = xx )
      | ~ aElementOf0('#skF_2'(xS,W1_3076),xP) ),
    inference(demodulation,[status(thm),theory(equality)],[c_258,c_39157]) ).

tff(c_422251,plain,
    ( ( '#skF_2'(xS,xP) = xx )
    | aSubsetOf0(xP,xS)
    | ~ aSet0(xP)
    | ~ aSet0(xS) ),
    inference(resolution,[status(thm)],[c_30,c_422224]) ).

tff(c_422272,plain,
    ( ( '#skF_2'(xS,xP) = xx )
    | aSubsetOf0(xP,xS) ),
    inference(demodulation,[status(thm),theory(equality)],[c_258,c_934,c_422251]) ).

tff(c_422273,plain,
    '#skF_2'(xS,xP) = xx,
    inference(negUnitSimplification,[status(thm)],[c_5207,c_422272]) ).

tff(c_422298,plain,
    ( ~ aElementOf0(xx,xS)
    | aSubsetOf0(xP,xS)
    | ~ aSet0(xP)
    | ~ aSet0(xS) ),
    inference(superposition,[status(thm),theory(equality)],[c_422273,c_28]) ).

tff(c_422326,plain,
    aSubsetOf0(xP,xS),
    inference(demodulation,[status(thm),theory(equality)],[c_258,c_934,c_264,c_422298]) ).

tff(c_422328,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_5207,c_422326]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.14/0.13  % Problem  : NUM554+1 : TPTP v8.1.2. Released v4.0.0.
% 0.14/0.14  % 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
% 0.14/0.35  % Computer : n003.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Thu Aug  3 14:48:08 EDT 2023
% 0.14/0.36  % CPUTime  : 
% 239.29/210.89  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 239.30/210.90  
% 239.30/210.90  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 239.40/210.94  
% 239.40/210.94  Inference rules
% 239.40/210.94  ----------------------
% 239.40/210.94  #Ref     : 2
% 239.40/210.94  #Sup     : 75668
% 239.40/210.94  #Fact    : 14
% 239.40/210.94  #Define  : 0
% 239.40/210.94  #Split   : 576
% 239.40/210.95  #Chain   : 0
% 239.40/210.95  #Close   : 0
% 239.40/210.95  
% 239.40/210.95  Ordering : KBO
% 239.40/210.95  
% 239.40/210.95  Simplification rules
% 239.40/210.95  ----------------------
% 239.40/210.95  #Subsume      : 27297
% 239.40/210.95  #Demod        : 145697
% 239.40/210.95  #Tautology    : 14675
% 239.40/210.95  #SimpNegUnit  : 11691
% 239.40/210.95  #BackRed      : 1504
% 239.40/210.95  
% 239.40/210.95  #Partial instantiations: 0
% 239.40/210.95  #Strategies tried      : 1
% 239.40/210.95  
% 239.40/210.95  Timing (in seconds)
% 239.40/210.95  ----------------------
% 239.40/210.95  Preprocessing        : 0.75
% 239.40/210.95  Parsing              : 0.38
% 239.40/210.95  CNF conversion       : 0.07
% 239.40/210.95  Main loop            : 208.99
% 239.40/210.95  Inferencing          : 18.33
% 239.40/210.95  Reduction            : 133.96
% 239.40/210.95  Demodulation         : 111.83
% 239.40/210.95  BG Simplification    : 0.57
% 239.40/210.95  Subsumption          : 46.96
% 239.40/210.95  Abstraction          : 1.28
% 239.40/210.95  MUC search           : 0.00
% 239.40/210.95  Cooper               : 0.00
% 239.40/210.95  Total                : 209.81
% 239.40/210.95  Index Insertion      : 0.00
% 239.40/210.95  Index Deletion       : 0.00
% 239.40/210.95  Index Matching       : 0.00
% 239.40/210.95  BG Taut test         : 0.00
%------------------------------------------------------------------------------