TSTP Solution File: NUM536+2 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : NUM536+2 : 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 : n021.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 10:52:01 EDT 2023

% Result   : Theorem 20.25s 9.42s
% Output   : CNFRefutation 20.52s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :   25
% Syntax   : Number of formulae    :  113 (  31 unt;  17 typ;   2 def)
%            Number of atoms       :  267 (  34 equ)
%            Maximal formula atoms :   11 (   2 avg)
%            Number of connectives :  299 ( 128   ~; 148   |;  10   &)
%                                         (   4 <=>;   9  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   4 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   27 (  14   >;  13   *;   0   +;   0  <<)
%            Number of predicates  :    8 (   6 usr;   1 prp; 0-2 aty)
%            Number of functors    :   11 (  11 usr;   3 con; 0-3 aty)
%            Number of variables   :   63 (;  62   !;   1   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ aSubsetOf0 > aElementOf0 > isFinite0 > isCountable0 > aSet0 > aElement0 > sdtpldt0 > sdtmndt0 > #nlpp > xx > xS > slcrc0 > #skF_6 > #skF_1 > #skF_4 > #skF_5 > #skF_3 > #skF_2

%Foreground sorts:

%Background operators:

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

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(xS,type,
    xS: $i ).

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

tff(sdtpldt0,type,
    sdtpldt0: ( $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(aElementOf0,type,
    aElementOf0: ( $i * $i ) > $o ).

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

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

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

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

tff(f_193,negated_conjecture,
    ~ ( ( aSet0(sdtpldt0(xS,xx))
        & ! [W0] :
            ( aElementOf0(W0,sdtpldt0(xS,xx))
          <=> ( aElement0(W0)
              & ( aElementOf0(W0,xS)
                | ( W0 = xx ) ) ) ) )
     => ( ( aSet0(sdtmndt0(sdtpldt0(xS,xx),xx))
          & ! [W0] :
              ( aElementOf0(W0,sdtmndt0(sdtpldt0(xS,xx),xx))
            <=> ( aElement0(W0)
                & aElementOf0(W0,sdtpldt0(xS,xx))
                & ( W0 != xx ) ) ) )
       => ( sdtmndt0(sdtpldt0(xS,xx),xx) = xS ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).

tff(f_166,hypothesis,
    ( aElement0(xx)
    & aSet0(xS) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__679) ).

tff(f_52,definition,
    ! [W0] :
      ( ( W0 = slcrc0 )
    <=> ( aSet0(W0)
        & ~ ? [W1] : aElementOf0(W1,W0) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefEmp) ).

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_168,hypothesis,
    ~ aElementOf0(xx,xS),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__679_02) ).

tff(f_97,axiom,
    ! [W0] :
      ( aSet0(W0)
     => aSubsetOf0(W0,W0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSubRefl) ).

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

tff(f_107,axiom,
    ! [W0,W1] :
      ( ( aSet0(W0)
        & aSet0(W1) )
     => ( ( aSubsetOf0(W0,W1)
          & aSubsetOf0(W1,W0) )
       => ( W0 = W1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSubASymm) ).

tff(c_102,plain,
    sdtmndt0(sdtpldt0(xS,xx),xx) != xS,
    inference(cnfTransformation,[status(thm)],[f_193]) ).

tff(c_106,plain,
    aSet0(sdtmndt0(sdtpldt0(xS,xx),xx)),
    inference(cnfTransformation,[status(thm)],[f_193]) ).

tff(c_96,plain,
    aSet0(xS),
    inference(cnfTransformation,[status(thm)],[f_166]) ).

tff(c_12,plain,
    ! [W1_10] : ~ aElementOf0(W1_10,slcrc0),
    inference(cnfTransformation,[status(thm)],[f_52]) ).

tff(c_108,plain,
    aSet0(sdtpldt0(xS,xx)),
    inference(cnfTransformation,[status(thm)],[f_193]) ).

tff(c_154,plain,
    ! [W0_68] :
      ( ( slcrc0 = W0_68 )
      | aElementOf0('#skF_1'(W0_68),W0_68)
      | ~ aSet0(W0_68) ),
    inference(cnfTransformation,[status(thm)],[f_52]) ).

tff(c_118,plain,
    ! [W0_58] :
      ( aElement0(W0_58)
      | ~ aElementOf0(W0_58,sdtpldt0(xS,xx)) ),
    inference(cnfTransformation,[status(thm)],[f_193]) ).

tff(c_161,plain,
    ( aElement0('#skF_1'(sdtpldt0(xS,xx)))
    | ( sdtpldt0(xS,xx) = slcrc0 )
    | ~ aSet0(sdtpldt0(xS,xx)) ),
    inference(resolution,[status(thm)],[c_154,c_118]) ).

tff(c_169,plain,
    ( aElement0('#skF_1'(sdtpldt0(xS,xx)))
    | ( sdtpldt0(xS,xx) = slcrc0 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_108,c_161]) ).

tff(c_214,plain,
    sdtpldt0(xS,xx) = slcrc0,
    inference(splitLeft,[status(thm)],[c_169]) ).

tff(c_98,plain,
    aElement0(xx),
    inference(cnfTransformation,[status(thm)],[f_166]) ).

tff(c_120,plain,
    ( aElementOf0(xx,sdtpldt0(xS,xx))
    | ~ aElement0(xx) ),
    inference(cnfTransformation,[status(thm)],[f_193]) ).

tff(c_124,plain,
    aElementOf0(xx,sdtpldt0(xS,xx)),
    inference(demodulation,[status(thm),theory(equality)],[c_98,c_120]) ).

tff(c_221,plain,
    aElementOf0(xx,slcrc0),
    inference(demodulation,[status(thm),theory(equality)],[c_214,c_124]) ).

tff(c_225,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_12,c_221]) ).

tff(c_227,plain,
    sdtpldt0(xS,xx) != slcrc0,
    inference(splitRight,[status(thm)],[c_169]) ).

tff(c_10,plain,
    ! [W0_7] :
      ( ( slcrc0 = W0_7 )
      | aElementOf0('#skF_1'(W0_7),W0_7)
      | ~ aSet0(W0_7) ),
    inference(cnfTransformation,[status(thm)],[f_52]) ).

tff(c_228,plain,
    ! [W0_82] :
      ( ( xx = W0_82 )
      | aElementOf0(W0_82,xS)
      | ~ aElementOf0(W0_82,sdtpldt0(xS,xx)) ),
    inference(cnfTransformation,[status(thm)],[f_193]) ).

tff(c_239,plain,
    ( ( '#skF_1'(sdtpldt0(xS,xx)) = xx )
    | aElementOf0('#skF_1'(sdtpldt0(xS,xx)),xS)
    | ( sdtpldt0(xS,xx) = slcrc0 )
    | ~ aSet0(sdtpldt0(xS,xx)) ),
    inference(resolution,[status(thm)],[c_10,c_228]) ).

tff(c_251,plain,
    ( ( '#skF_1'(sdtpldt0(xS,xx)) = xx )
    | aElementOf0('#skF_1'(sdtpldt0(xS,xx)),xS)
    | ( sdtpldt0(xS,xx) = slcrc0 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_108,c_239]) ).

tff(c_252,plain,
    ( ( '#skF_1'(sdtpldt0(xS,xx)) = xx )
    | aElementOf0('#skF_1'(sdtpldt0(xS,xx)),xS) ),
    inference(negUnitSimplification,[status(thm)],[c_227,c_251]) ).

tff(c_324,plain,
    aElementOf0('#skF_1'(sdtpldt0(xS,xx)),xS),
    inference(splitLeft,[status(thm)],[c_252]) ).

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_330,plain,
    ! [W0_14] :
      ( aElementOf0('#skF_1'(sdtpldt0(xS,xx)),W0_14)
      | ~ aSubsetOf0(xS,W0_14)
      | ~ aSet0(W0_14) ),
    inference(resolution,[status(thm)],[c_324,c_24]) ).

tff(c_390,plain,
    ! [W0_96] :
      ( aElementOf0(W0_96,sdtpldt0(xS,xx))
      | ~ aElementOf0(W0_96,sdtmndt0(sdtpldt0(xS,xx),xx)) ),
    inference(cnfTransformation,[status(thm)],[f_193]) ).

tff(c_394,plain,
    ( aElementOf0('#skF_1'(sdtpldt0(xS,xx)),sdtpldt0(xS,xx))
    | ~ aSubsetOf0(xS,sdtmndt0(sdtpldt0(xS,xx),xx))
    | ~ aSet0(sdtmndt0(sdtpldt0(xS,xx),xx)) ),
    inference(resolution,[status(thm)],[c_330,c_390]) ).

tff(c_401,plain,
    ( aElementOf0('#skF_1'(sdtpldt0(xS,xx)),sdtpldt0(xS,xx))
    | ~ aSubsetOf0(xS,sdtmndt0(sdtpldt0(xS,xx),xx)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_106,c_394]) ).

tff(c_1092,plain,
    ~ aSubsetOf0(xS,sdtmndt0(sdtpldt0(xS,xx),xx)),
    inference(splitLeft,[status(thm)],[c_401]) ).

tff(c_100,plain,
    ~ aElementOf0(xx,xS),
    inference(cnfTransformation,[status(thm)],[f_168]) ).

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

tff(c_413,plain,
    ! [W0_99,W1_100] :
      ( aElementOf0('#skF_2'(W0_99,W1_100),W1_100)
      | aSubsetOf0(W1_100,W0_99)
      | ~ aSet0(W1_100)
      | ~ aSet0(W0_99) ),
    inference(cnfTransformation,[status(thm)],[f_84]) ).

tff(c_6,plain,
    ! [W1_5,W0_3] :
      ( aElement0(W1_5)
      | ~ aElementOf0(W1_5,W0_3)
      | ~ aSet0(W0_3) ),
    inference(cnfTransformation,[status(thm)],[f_39]) ).

tff(c_464,plain,
    ! [W0_99,W1_100] :
      ( aElement0('#skF_2'(W0_99,W1_100))
      | aSubsetOf0(W1_100,W0_99)
      | ~ aSet0(W1_100)
      | ~ aSet0(W0_99) ),
    inference(resolution,[status(thm)],[c_413,c_6]) ).

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_122,plain,
    ! [W0_58] :
      ( ~ aElementOf0(W0_58,xS)
      | aElementOf0(W0_58,sdtpldt0(xS,xx))
      | ~ aElement0(W0_58) ),
    inference(cnfTransformation,[status(thm)],[f_193]) ).

tff(c_405,plain,
    ! [W0_97,W1_98] :
      ( ~ aElementOf0('#skF_2'(W0_97,W1_98),W0_97)
      | aSubsetOf0(W1_98,W0_97)
      | ~ aSet0(W1_98)
      | ~ aSet0(W0_97) ),
    inference(cnfTransformation,[status(thm)],[f_84]) ).

tff(c_409,plain,
    ! [W1_98] :
      ( aSubsetOf0(W1_98,sdtpldt0(xS,xx))
      | ~ aSet0(W1_98)
      | ~ aSet0(sdtpldt0(xS,xx))
      | ~ aElementOf0('#skF_2'(sdtpldt0(xS,xx),W1_98),xS)
      | ~ aElement0('#skF_2'(sdtpldt0(xS,xx),W1_98)) ),
    inference(resolution,[status(thm)],[c_122,c_405]) ).

tff(c_3384,plain,
    ! [W1_220] :
      ( aSubsetOf0(W1_220,sdtpldt0(xS,xx))
      | ~ aSet0(W1_220)
      | ~ aElementOf0('#skF_2'(sdtpldt0(xS,xx),W1_220),xS)
      | ~ aElement0('#skF_2'(sdtpldt0(xS,xx),W1_220)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_108,c_409]) ).

tff(c_3400,plain,
    ( ~ aElement0('#skF_2'(sdtpldt0(xS,xx),xS))
    | aSubsetOf0(xS,sdtpldt0(xS,xx))
    | ~ aSet0(xS)
    | ~ aSet0(sdtpldt0(xS,xx)) ),
    inference(resolution,[status(thm)],[c_30,c_3384]) ).

tff(c_3412,plain,
    ( ~ aElement0('#skF_2'(sdtpldt0(xS,xx),xS))
    | aSubsetOf0(xS,sdtpldt0(xS,xx)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_108,c_96,c_3400]) ).

tff(c_3413,plain,
    ~ aElement0('#skF_2'(sdtpldt0(xS,xx),xS)),
    inference(splitLeft,[status(thm)],[c_3412]) ).

tff(c_3416,plain,
    ( aSubsetOf0(xS,sdtpldt0(xS,xx))
    | ~ aSet0(xS)
    | ~ aSet0(sdtpldt0(xS,xx)) ),
    inference(resolution,[status(thm)],[c_464,c_3413]) ).

tff(c_3419,plain,
    aSubsetOf0(xS,sdtpldt0(xS,xx)),
    inference(demodulation,[status(thm),theory(equality)],[c_108,c_96,c_3416]) ).

tff(c_334,plain,
    ! [W0_95] :
      ( aElementOf0('#skF_1'(sdtpldt0(xS,xx)),W0_95)
      | ~ aSubsetOf0(xS,W0_95)
      | ~ aSet0(W0_95) ),
    inference(resolution,[status(thm)],[c_324,c_24]) ).

tff(c_372,plain,
    ! [W0_14,W0_95] :
      ( aElementOf0('#skF_1'(sdtpldt0(xS,xx)),W0_14)
      | ~ aSubsetOf0(W0_95,W0_14)
      | ~ aSet0(W0_14)
      | ~ aSubsetOf0(xS,W0_95)
      | ~ aSet0(W0_95) ),
    inference(resolution,[status(thm)],[c_334,c_24]) ).

tff(c_3427,plain,
    ( aElementOf0('#skF_1'(sdtpldt0(xS,xx)),sdtpldt0(xS,xx))
    | ~ aSet0(sdtpldt0(xS,xx))
    | ~ aSubsetOf0(xS,xS)
    | ~ aSet0(xS) ),
    inference(resolution,[status(thm)],[c_3419,c_372]) ).

tff(c_3452,plain,
    ( aElementOf0('#skF_1'(sdtpldt0(xS,xx)),sdtpldt0(xS,xx))
    | ~ aSubsetOf0(xS,xS) ),
    inference(demodulation,[status(thm),theory(equality)],[c_96,c_108,c_3427]) ).

tff(c_3882,plain,
    ~ aSubsetOf0(xS,xS),
    inference(splitLeft,[status(thm)],[c_3452]) ).

tff(c_3888,plain,
    ~ aSet0(xS),
    inference(resolution,[status(thm)],[c_34,c_3882]) ).

tff(c_3895,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_96,c_3888]) ).

tff(c_3897,plain,
    aSubsetOf0(xS,xS),
    inference(splitRight,[status(thm)],[c_3452]) ).

tff(c_589,plain,
    ! [W0_112] :
      ( aElementOf0(W0_112,sdtmndt0(sdtpldt0(xS,xx),xx))
      | ( xx = W0_112 )
      | ~ aElementOf0(W0_112,sdtpldt0(xS,xx))
      | ~ aElement0(W0_112) ),
    inference(cnfTransformation,[status(thm)],[f_193]) ).

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_596,plain,
    ! [W1_20] :
      ( aSubsetOf0(W1_20,sdtmndt0(sdtpldt0(xS,xx),xx))
      | ~ aSet0(W1_20)
      | ~ aSet0(sdtmndt0(sdtpldt0(xS,xx),xx))
      | ( '#skF_2'(sdtmndt0(sdtpldt0(xS,xx),xx),W1_20) = xx )
      | ~ aElementOf0('#skF_2'(sdtmndt0(sdtpldt0(xS,xx),xx),W1_20),sdtpldt0(xS,xx))
      | ~ aElement0('#skF_2'(sdtmndt0(sdtpldt0(xS,xx),xx),W1_20)) ),
    inference(resolution,[status(thm)],[c_589,c_28]) ).

tff(c_50985,plain,
    ! [W1_1086] :
      ( aSubsetOf0(W1_1086,sdtmndt0(sdtpldt0(xS,xx),xx))
      | ~ aSet0(W1_1086)
      | ( '#skF_2'(sdtmndt0(sdtpldt0(xS,xx),xx),W1_1086) = xx )
      | ~ aElementOf0('#skF_2'(sdtmndt0(sdtpldt0(xS,xx),xx),W1_1086),sdtpldt0(xS,xx))
      | ~ aElement0('#skF_2'(sdtmndt0(sdtpldt0(xS,xx),xx),W1_1086)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_106,c_596]) ).

tff(c_52798,plain,
    ! [W1_1096] :
      ( aSubsetOf0(W1_1096,sdtmndt0(sdtpldt0(xS,xx),xx))
      | ~ aSet0(W1_1096)
      | ( '#skF_2'(sdtmndt0(sdtpldt0(xS,xx),xx),W1_1096) = xx )
      | ~ aElementOf0('#skF_2'(sdtmndt0(sdtpldt0(xS,xx),xx),W1_1096),xS)
      | ~ aElement0('#skF_2'(sdtmndt0(sdtpldt0(xS,xx),xx),W1_1096)) ),
    inference(resolution,[status(thm)],[c_122,c_50985]) ).

tff(c_52876,plain,
    ( ( '#skF_2'(sdtmndt0(sdtpldt0(xS,xx),xx),xS) = xx )
    | ~ aElement0('#skF_2'(sdtmndt0(sdtpldt0(xS,xx),xx),xS))
    | aSubsetOf0(xS,sdtmndt0(sdtpldt0(xS,xx),xx))
    | ~ aSet0(xS)
    | ~ aSet0(sdtmndt0(sdtpldt0(xS,xx),xx)) ),
    inference(resolution,[status(thm)],[c_30,c_52798]) ).

tff(c_52929,plain,
    ( ( '#skF_2'(sdtmndt0(sdtpldt0(xS,xx),xx),xS) = xx )
    | ~ aElement0('#skF_2'(sdtmndt0(sdtpldt0(xS,xx),xx),xS))
    | aSubsetOf0(xS,sdtmndt0(sdtpldt0(xS,xx),xx)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_106,c_96,c_52876]) ).

tff(c_52930,plain,
    ( ( '#skF_2'(sdtmndt0(sdtpldt0(xS,xx),xx),xS) = xx )
    | ~ aElement0('#skF_2'(sdtmndt0(sdtpldt0(xS,xx),xx),xS)) ),
    inference(negUnitSimplification,[status(thm)],[c_1092,c_52929]) ).

tff(c_53079,plain,
    ~ aElement0('#skF_2'(sdtmndt0(sdtpldt0(xS,xx),xx),xS)),
    inference(splitLeft,[status(thm)],[c_52930]) ).

tff(c_53177,plain,
    ( aSubsetOf0(xS,sdtmndt0(sdtpldt0(xS,xx),xx))
    | ~ aSet0(xS)
    | ~ aSet0(sdtmndt0(sdtpldt0(xS,xx),xx)) ),
    inference(resolution,[status(thm)],[c_464,c_53079]) ).

tff(c_53186,plain,
    aSubsetOf0(xS,sdtmndt0(sdtpldt0(xS,xx),xx)),
    inference(demodulation,[status(thm),theory(equality)],[c_106,c_96,c_53177]) ).

tff(c_53188,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_1092,c_53186]) ).

tff(c_53189,plain,
    '#skF_2'(sdtmndt0(sdtpldt0(xS,xx),xx),xS) = xx,
    inference(splitRight,[status(thm)],[c_52930]) ).

tff(c_1419,plain,
    ! [W0_154,W1_155,W0_156] :
      ( aElementOf0('#skF_2'(W0_154,W1_155),W0_156)
      | ~ aSubsetOf0(W1_155,W0_156)
      | ~ aSet0(W0_156)
      | aSubsetOf0(W1_155,W0_154)
      | ~ aSet0(W1_155)
      | ~ aSet0(W0_154) ),
    inference(resolution,[status(thm)],[c_413,c_24]) ).

tff(c_47873,plain,
    ! [W0_1048,W1_1049,W0_1050,W0_1051] :
      ( aElementOf0('#skF_2'(W0_1048,W1_1049),W0_1050)
      | ~ aSubsetOf0(W0_1051,W0_1050)
      | ~ aSet0(W0_1050)
      | ~ aSubsetOf0(W1_1049,W0_1051)
      | ~ aSet0(W0_1051)
      | aSubsetOf0(W1_1049,W0_1048)
      | ~ aSet0(W1_1049)
      | ~ aSet0(W0_1048) ),
    inference(resolution,[status(thm)],[c_1419,c_24]) ).

tff(c_47919,plain,
    ! [W0_1048,W1_1049] :
      ( aElementOf0('#skF_2'(W0_1048,W1_1049),xS)
      | ~ aSubsetOf0(W1_1049,xS)
      | ~ aSet0(xS)
      | aSubsetOf0(W1_1049,W0_1048)
      | ~ aSet0(W1_1049)
      | ~ aSet0(W0_1048) ),
    inference(resolution,[status(thm)],[c_3897,c_47873]) ).

tff(c_47995,plain,
    ! [W0_1048,W1_1049] :
      ( aElementOf0('#skF_2'(W0_1048,W1_1049),xS)
      | ~ aSubsetOf0(W1_1049,xS)
      | aSubsetOf0(W1_1049,W0_1048)
      | ~ aSet0(W1_1049)
      | ~ aSet0(W0_1048) ),
    inference(demodulation,[status(thm),theory(equality)],[c_96,c_47919]) ).

tff(c_53206,plain,
    ( aElementOf0(xx,xS)
    | ~ aSubsetOf0(xS,xS)
    | aSubsetOf0(xS,sdtmndt0(sdtpldt0(xS,xx),xx))
    | ~ aSet0(xS)
    | ~ aSet0(sdtmndt0(sdtpldt0(xS,xx),xx)) ),
    inference(superposition,[status(thm),theory(equality)],[c_53189,c_47995]) ).

tff(c_53276,plain,
    ( aElementOf0(xx,xS)
    | aSubsetOf0(xS,sdtmndt0(sdtpldt0(xS,xx),xx)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_106,c_96,c_3897,c_53206]) ).

tff(c_53278,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_1092,c_100,c_53276]) ).

tff(c_53280,plain,
    aSubsetOf0(xS,sdtmndt0(sdtpldt0(xS,xx),xx)),
    inference(splitRight,[status(thm)],[c_401]) ).

tff(c_36,plain,
    ! [W1_29,W0_28] :
      ( ( W1_29 = W0_28 )
      | ~ aSubsetOf0(W1_29,W0_28)
      | ~ aSubsetOf0(W0_28,W1_29)
      | ~ aSet0(W1_29)
      | ~ aSet0(W0_28) ),
    inference(cnfTransformation,[status(thm)],[f_107]) ).

tff(c_53284,plain,
    ( ( sdtmndt0(sdtpldt0(xS,xx),xx) = xS )
    | ~ aSubsetOf0(sdtmndt0(sdtpldt0(xS,xx),xx),xS)
    | ~ aSet0(xS)
    | ~ aSet0(sdtmndt0(sdtpldt0(xS,xx),xx)) ),
    inference(resolution,[status(thm)],[c_53280,c_36]) ).

tff(c_53296,plain,
    ( ( sdtmndt0(sdtpldt0(xS,xx),xx) = xS )
    | ~ aSubsetOf0(sdtmndt0(sdtpldt0(xS,xx),xx),xS) ),
    inference(demodulation,[status(thm),theory(equality)],[c_106,c_96,c_53284]) ).

tff(c_53297,plain,
    ~ aSubsetOf0(sdtmndt0(sdtpldt0(xS,xx),xx),xS),
    inference(negUnitSimplification,[status(thm)],[c_102,c_53296]) ).

tff(c_110,plain,
    ~ aElementOf0(xx,sdtmndt0(sdtpldt0(xS,xx),xx)),
    inference(cnfTransformation,[status(thm)],[f_193]) ).

tff(c_112,plain,
    ! [W0_59] :
      ( aElementOf0(W0_59,sdtpldt0(xS,xx))
      | ~ aElementOf0(W0_59,sdtmndt0(sdtpldt0(xS,xx),xx)) ),
    inference(cnfTransformation,[status(thm)],[f_193]) ).

tff(c_421,plain,
    ! [W0_99] :
      ( aElementOf0('#skF_2'(W0_99,sdtmndt0(sdtpldt0(xS,xx),xx)),sdtpldt0(xS,xx))
      | aSubsetOf0(sdtmndt0(sdtpldt0(xS,xx),xx),W0_99)
      | ~ aSet0(sdtmndt0(sdtpldt0(xS,xx),xx))
      | ~ aSet0(W0_99) ),
    inference(resolution,[status(thm)],[c_413,c_112]) ).

tff(c_56100,plain,
    ! [W0_1187] :
      ( aElementOf0('#skF_2'(W0_1187,sdtmndt0(sdtpldt0(xS,xx),xx)),sdtpldt0(xS,xx))
      | aSubsetOf0(sdtmndt0(sdtpldt0(xS,xx),xx),W0_1187)
      | ~ aSet0(W0_1187) ),
    inference(demodulation,[status(thm),theory(equality)],[c_106,c_421]) ).

tff(c_116,plain,
    ! [W0_58] :
      ( ( xx = W0_58 )
      | aElementOf0(W0_58,xS)
      | ~ aElementOf0(W0_58,sdtpldt0(xS,xx)) ),
    inference(cnfTransformation,[status(thm)],[f_193]) ).

tff(c_56501,plain,
    ! [W0_1198] :
      ( ( '#skF_2'(W0_1198,sdtmndt0(sdtpldt0(xS,xx),xx)) = xx )
      | aElementOf0('#skF_2'(W0_1198,sdtmndt0(sdtpldt0(xS,xx),xx)),xS)
      | aSubsetOf0(sdtmndt0(sdtpldt0(xS,xx),xx),W0_1198)
      | ~ aSet0(W0_1198) ),
    inference(resolution,[status(thm)],[c_56100,c_116]) ).

tff(c_56509,plain,
    ( ~ aSet0(sdtmndt0(sdtpldt0(xS,xx),xx))
    | ( '#skF_2'(xS,sdtmndt0(sdtpldt0(xS,xx),xx)) = xx )
    | aSubsetOf0(sdtmndt0(sdtpldt0(xS,xx),xx),xS)
    | ~ aSet0(xS) ),
    inference(resolution,[status(thm)],[c_56501,c_28]) ).

tff(c_56523,plain,
    ( ( '#skF_2'(xS,sdtmndt0(sdtpldt0(xS,xx),xx)) = xx )
    | aSubsetOf0(sdtmndt0(sdtpldt0(xS,xx),xx),xS) ),
    inference(demodulation,[status(thm),theory(equality)],[c_96,c_106,c_56509]) ).

tff(c_56524,plain,
    '#skF_2'(xS,sdtmndt0(sdtpldt0(xS,xx),xx)) = xx,
    inference(negUnitSimplification,[status(thm)],[c_53297,c_56523]) ).

tff(c_56552,plain,
    ( aElementOf0(xx,sdtmndt0(sdtpldt0(xS,xx),xx))
    | aSubsetOf0(sdtmndt0(sdtpldt0(xS,xx),xx),xS)
    | ~ aSet0(sdtmndt0(sdtpldt0(xS,xx),xx))
    | ~ aSet0(xS) ),
    inference(superposition,[status(thm),theory(equality)],[c_56524,c_30]) ).

tff(c_56580,plain,
    ( aElementOf0(xx,sdtmndt0(sdtpldt0(xS,xx),xx))
    | aSubsetOf0(sdtmndt0(sdtpldt0(xS,xx),xx),xS) ),
    inference(demodulation,[status(thm),theory(equality)],[c_96,c_106,c_56552]) ).

tff(c_56582,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_53297,c_110,c_56580]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : NUM536+2 : 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
% 0.13/0.35  % Computer : n021.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Thu Aug  3 14:39:51 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 20.25/9.42  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 20.52/9.43  
% 20.52/9.43  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 20.52/9.47  
% 20.52/9.47  Inference rules
% 20.52/9.47  ----------------------
% 20.52/9.47  #Ref     : 0
% 20.52/9.47  #Sup     : 11322
% 20.52/9.47  #Fact    : 0
% 20.52/9.47  #Define  : 0
% 20.52/9.47  #Split   : 69
% 20.52/9.47  #Chain   : 0
% 20.52/9.47  #Close   : 0
% 20.52/9.47  
% 20.52/9.47  Ordering : KBO
% 20.52/9.47  
% 20.52/9.47  Simplification rules
% 20.52/9.47  ----------------------
% 20.52/9.47  #Subsume      : 5087
% 20.52/9.47  #Demod        : 12246
% 20.52/9.47  #Tautology    : 2086
% 20.52/9.47  #SimpNegUnit  : 1566
% 20.52/9.47  #BackRed      : 145
% 20.52/9.47  
% 20.52/9.47  #Partial instantiations: 0
% 20.52/9.47  #Strategies tried      : 1
% 20.52/9.47  
% 20.52/9.47  Timing (in seconds)
% 20.52/9.47  ----------------------
% 20.52/9.47  Preprocessing        : 0.59
% 20.52/9.47  Parsing              : 0.30
% 20.52/9.47  CNF conversion       : 0.05
% 20.52/9.47  Main loop            : 7.82
% 20.52/9.47  Inferencing          : 1.85
% 20.52/9.47  Reduction            : 2.81
% 20.52/9.47  Demodulation         : 2.00
% 20.52/9.47  BG Simplification    : 0.13
% 20.52/9.47  Subsumption          : 2.60
% 20.52/9.47  Abstraction          : 0.23
% 20.52/9.47  MUC search           : 0.00
% 20.52/9.47  Cooper               : 0.00
% 20.52/9.47  Total                : 8.47
% 20.52/9.47  Index Insertion      : 0.00
% 20.52/9.47  Index Deletion       : 0.00
% 20.52/9.47  Index Matching       : 0.00
% 20.52/9.47  BG Taut test         : 0.00
%------------------------------------------------------------------------------