TSTP Solution File: NUM534+2 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : NUM534+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/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s

% Computer : n025.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 18.48s 7.45s
% Output   : CNFRefutation 18.64s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   24
%            Number of leaves      :   24
% Syntax   : Number of formulae    :  130 (  40 unt;  17 typ;   2 def)
%            Number of atoms       :  298 (  70 equ)
%            Maximal formula atoms :   11 (   2 avg)
%            Number of connectives :  317 ( 132   ~; 164   |;   9   &)
%                                         (   4 <=>;   8  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   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   :   60 (;  59   !;   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_183,negated_conjecture,
    ~ ( ( aSet0(sdtmndt0(xS,xx))
        & ! [W0] :
            ( aElementOf0(W0,sdtmndt0(xS,xx))
          <=> ( aElement0(W0)
              & aElementOf0(W0,xS)
              & ( W0 != xx ) ) ) )
     => ( ( aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
          & ! [W0] :
              ( aElementOf0(W0,sdtpldt0(sdtmndt0(xS,xx),xx))
            <=> ( aElement0(W0)
                & ( aElementOf0(W0,sdtmndt0(xS,xx))
                  | ( W0 = xx ) ) ) ) )
       => ( sdtpldt0(sdtmndt0(xS,xx),xx) = xS ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).

tff(f_157,hypothesis,
    aSet0(xS),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__617) ).

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

tff(f_158,hypothesis,
    aElementOf0(xx,xS),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__617_02) ).

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

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

tff(c_98,plain,
    sdtpldt0(sdtmndt0(xS,xx),xx) != xS,
    inference(cnfTransformation,[status(thm)],[f_183]) ).

tff(c_100,plain,
    aSet0(sdtpldt0(sdtmndt0(xS,xx),xx)),
    inference(cnfTransformation,[status(thm)],[f_183]) ).

tff(c_94,plain,
    aSet0(xS),
    inference(cnfTransformation,[status(thm)],[f_157]) ).

tff(c_104,plain,
    aSet0(sdtmndt0(xS,xx)),
    inference(cnfTransformation,[status(thm)],[f_183]) ).

tff(c_144,plain,
    ! [W0_66] :
      ( ( slcrc0 = W0_66 )
      | aElementOf0('#skF_1'(W0_66),W0_66)
      | ~ aSet0(W0_66) ),
    inference(cnfTransformation,[status(thm)],[f_52]) ).

tff(c_118,plain,
    ! [W0_55] :
      ( aElement0(W0_55)
      | ~ aElementOf0(W0_55,sdtmndt0(xS,xx)) ),
    inference(cnfTransformation,[status(thm)],[f_183]) ).

tff(c_155,plain,
    ( aElement0('#skF_1'(sdtmndt0(xS,xx)))
    | ( sdtmndt0(xS,xx) = slcrc0 )
    | ~ aSet0(sdtmndt0(xS,xx)) ),
    inference(resolution,[status(thm)],[c_144,c_118]) ).

tff(c_166,plain,
    ( aElement0('#skF_1'(sdtmndt0(xS,xx)))
    | ( sdtmndt0(xS,xx) = slcrc0 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_104,c_155]) ).

tff(c_213,plain,
    sdtmndt0(xS,xx) = slcrc0,
    inference(splitLeft,[status(thm)],[c_166]) ).

tff(c_219,plain,
    sdtpldt0(slcrc0,xx) != xS,
    inference(demodulation,[status(thm),theory(equality)],[c_213,c_98]) ).

tff(c_218,plain,
    aSet0(sdtpldt0(slcrc0,xx)),
    inference(demodulation,[status(thm),theory(equality)],[c_213,c_100]) ).

tff(c_96,plain,
    aElementOf0(xx,xS),
    inference(cnfTransformation,[status(thm)],[f_158]) ).

tff(c_439,plain,
    ! [W0_96,W1_97] :
      ( aElementOf0('#skF_2'(W0_96,W1_97),W1_97)
      | aSubsetOf0(W1_97,W0_96)
      | ~ aSet0(W1_97)
      | ~ aSet0(W0_96) ),
    inference(cnfTransformation,[status(thm)],[f_84]) ).

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

tff(c_106,plain,
    ! [W0_56] :
      ( ( xx = W0_56 )
      | aElementOf0(W0_56,sdtmndt0(xS,xx))
      | ~ aElementOf0(W0_56,sdtpldt0(sdtmndt0(xS,xx),xx)) ),
    inference(cnfTransformation,[status(thm)],[f_183]) ).

tff(c_381,plain,
    ! [W0_56] :
      ( ( xx = W0_56 )
      | aElementOf0(W0_56,slcrc0)
      | ~ aElementOf0(W0_56,sdtpldt0(slcrc0,xx)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_213,c_213,c_106]) ).

tff(c_382,plain,
    ! [W0_56] :
      ( ( xx = W0_56 )
      | ~ aElementOf0(W0_56,sdtpldt0(slcrc0,xx)) ),
    inference(negUnitSimplification,[status(thm)],[c_12,c_381]) ).

tff(c_443,plain,
    ! [W0_96] :
      ( ( '#skF_2'(W0_96,sdtpldt0(slcrc0,xx)) = xx )
      | aSubsetOf0(sdtpldt0(slcrc0,xx),W0_96)
      | ~ aSet0(sdtpldt0(slcrc0,xx))
      | ~ aSet0(W0_96) ),
    inference(resolution,[status(thm)],[c_439,c_382]) ).

tff(c_899,plain,
    ! [W0_125] :
      ( ( '#skF_2'(W0_125,sdtpldt0(slcrc0,xx)) = xx )
      | aSubsetOf0(sdtpldt0(slcrc0,xx),W0_125)
      | ~ aSet0(W0_125) ),
    inference(demodulation,[status(thm),theory(equality)],[c_218,c_443]) ).

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_481,plain,
    ! [W0_96,W1_97] :
      ( aElement0('#skF_2'(W0_96,W1_97))
      | aSubsetOf0(W1_97,W0_96)
      | ~ aSet0(W1_97)
      | ~ aSet0(W0_96) ),
    inference(resolution,[status(thm)],[c_439,c_6]) ).

tff(c_102,plain,
    ! [W0_55] :
      ( aElementOf0(W0_55,sdtmndt0(xS,xx))
      | ( xx = W0_55 )
      | ~ aElementOf0(W0_55,xS)
      | ~ aElement0(W0_55) ),
    inference(cnfTransformation,[status(thm)],[f_183]) ).

tff(c_237,plain,
    ! [W0_55] :
      ( aElementOf0(W0_55,slcrc0)
      | ( xx = W0_55 )
      | ~ aElementOf0(W0_55,xS)
      | ~ aElement0(W0_55) ),
    inference(demodulation,[status(thm),theory(equality)],[c_213,c_102]) ).

tff(c_238,plain,
    ! [W0_55] :
      ( ( xx = W0_55 )
      | ~ aElementOf0(W0_55,xS)
      | ~ aElement0(W0_55) ),
    inference(negUnitSimplification,[status(thm)],[c_12,c_237]) ).

tff(c_461,plain,
    ! [W0_96] :
      ( ( '#skF_2'(W0_96,xS) = xx )
      | ~ aElement0('#skF_2'(W0_96,xS))
      | aSubsetOf0(xS,W0_96)
      | ~ aSet0(xS)
      | ~ aSet0(W0_96) ),
    inference(resolution,[status(thm)],[c_439,c_238]) ).

tff(c_632,plain,
    ! [W0_112] :
      ( ( '#skF_2'(W0_112,xS) = xx )
      | ~ aElement0('#skF_2'(W0_112,xS))
      | aSubsetOf0(xS,W0_112)
      | ~ aSet0(W0_112) ),
    inference(demodulation,[status(thm),theory(equality)],[c_94,c_461]) ).

tff(c_636,plain,
    ! [W0_96] :
      ( ( '#skF_2'(W0_96,xS) = xx )
      | aSubsetOf0(xS,W0_96)
      | ~ aSet0(xS)
      | ~ aSet0(W0_96) ),
    inference(resolution,[status(thm)],[c_481,c_632]) ).

tff(c_640,plain,
    ! [W0_113] :
      ( ( '#skF_2'(W0_113,xS) = xx )
      | aSubsetOf0(xS,W0_113)
      | ~ aSet0(W0_113) ),
    inference(demodulation,[status(thm),theory(equality)],[c_94,c_636]) ).

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_650,plain,
    ! [W0_113] :
      ( ( xS = W0_113 )
      | ~ aSubsetOf0(W0_113,xS)
      | ~ aSet0(xS)
      | ( '#skF_2'(W0_113,xS) = xx )
      | ~ aSet0(W0_113) ),
    inference(resolution,[status(thm)],[c_640,c_36]) ).

tff(c_668,plain,
    ! [W0_113] :
      ( ( xS = W0_113 )
      | ~ aSubsetOf0(W0_113,xS)
      | ( '#skF_2'(W0_113,xS) = xx )
      | ~ aSet0(W0_113) ),
    inference(demodulation,[status(thm),theory(equality)],[c_94,c_650]) ).

tff(c_903,plain,
    ( ( sdtpldt0(slcrc0,xx) = xS )
    | ( '#skF_2'(sdtpldt0(slcrc0,xx),xS) = xx )
    | ~ aSet0(sdtpldt0(slcrc0,xx))
    | ( '#skF_2'(xS,sdtpldt0(slcrc0,xx)) = xx )
    | ~ aSet0(xS) ),
    inference(resolution,[status(thm)],[c_899,c_668]) ).

tff(c_925,plain,
    ( ( sdtpldt0(slcrc0,xx) = xS )
    | ( '#skF_2'(sdtpldt0(slcrc0,xx),xS) = xx )
    | ( '#skF_2'(xS,sdtpldt0(slcrc0,xx)) = xx ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_94,c_218,c_903]) ).

tff(c_926,plain,
    ( ( '#skF_2'(sdtpldt0(slcrc0,xx),xS) = xx )
    | ( '#skF_2'(xS,sdtpldt0(slcrc0,xx)) = xx ) ),
    inference(negUnitSimplification,[status(thm)],[c_219,c_925]) ).

tff(c_966,plain,
    '#skF_2'(xS,sdtpldt0(slcrc0,xx)) = xx,
    inference(splitLeft,[status(thm)],[c_926]) ).

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_973,plain,
    ( ~ aElementOf0(xx,xS)
    | aSubsetOf0(sdtpldt0(slcrc0,xx),xS)
    | ~ aSet0(sdtpldt0(slcrc0,xx))
    | ~ aSet0(xS) ),
    inference(superposition,[status(thm),theory(equality)],[c_966,c_28]) ).

tff(c_985,plain,
    aSubsetOf0(sdtpldt0(slcrc0,xx),xS),
    inference(demodulation,[status(thm),theory(equality)],[c_94,c_218,c_96,c_973]) ).

tff(c_995,plain,
    ( ( sdtpldt0(slcrc0,xx) = xS )
    | ~ aSubsetOf0(xS,sdtpldt0(slcrc0,xx))
    | ~ aSet0(sdtpldt0(slcrc0,xx))
    | ~ aSet0(xS) ),
    inference(resolution,[status(thm)],[c_985,c_36]) ).

tff(c_1011,plain,
    ( ( sdtpldt0(slcrc0,xx) = xS )
    | ~ aSubsetOf0(xS,sdtpldt0(slcrc0,xx)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_94,c_218,c_995]) ).

tff(c_1012,plain,
    ~ aSubsetOf0(xS,sdtpldt0(slcrc0,xx)),
    inference(negUnitSimplification,[status(thm)],[c_219,c_1011]) ).

tff(c_136,plain,
    ! [W1_63,W0_64] :
      ( aElement0(W1_63)
      | ~ aElementOf0(W1_63,W0_64)
      | ~ aSet0(W0_64) ),
    inference(cnfTransformation,[status(thm)],[f_39]) ).

tff(c_139,plain,
    ( aElement0(xx)
    | ~ aSet0(xS) ),
    inference(resolution,[status(thm)],[c_96,c_136]) ).

tff(c_142,plain,
    aElement0(xx),
    inference(demodulation,[status(thm),theory(equality)],[c_94,c_139]) ).

tff(c_110,plain,
    ( aElementOf0(xx,sdtpldt0(sdtmndt0(xS,xx),xx))
    | ~ aElement0(xx) ),
    inference(cnfTransformation,[status(thm)],[f_183]) ).

tff(c_195,plain,
    aElementOf0(xx,sdtpldt0(sdtmndt0(xS,xx),xx)),
    inference(demodulation,[status(thm),theory(equality)],[c_142,c_110]) ).

tff(c_214,plain,
    aElementOf0(xx,sdtpldt0(slcrc0,xx)),
    inference(demodulation,[status(thm),theory(equality)],[c_213,c_195]) ).

tff(c_993,plain,
    ( ( sdtpldt0(slcrc0,xx) = xS )
    | ( '#skF_2'(sdtpldt0(slcrc0,xx),xS) = xx )
    | ~ aSet0(sdtpldt0(slcrc0,xx)) ),
    inference(resolution,[status(thm)],[c_985,c_668]) ).

tff(c_1007,plain,
    ( ( sdtpldt0(slcrc0,xx) = xS )
    | ( '#skF_2'(sdtpldt0(slcrc0,xx),xS) = xx ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_218,c_993]) ).

tff(c_1008,plain,
    '#skF_2'(sdtpldt0(slcrc0,xx),xS) = xx,
    inference(negUnitSimplification,[status(thm)],[c_219,c_1007]) ).

tff(c_1061,plain,
    ( ~ aElementOf0(xx,sdtpldt0(slcrc0,xx))
    | aSubsetOf0(xS,sdtpldt0(slcrc0,xx))
    | ~ aSet0(xS)
    | ~ aSet0(sdtpldt0(slcrc0,xx)) ),
    inference(superposition,[status(thm),theory(equality)],[c_1008,c_28]) ).

tff(c_1071,plain,
    aSubsetOf0(xS,sdtpldt0(slcrc0,xx)),
    inference(demodulation,[status(thm),theory(equality)],[c_218,c_94,c_214,c_1061]) ).

tff(c_1073,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_1012,c_1071]) ).

tff(c_1075,plain,
    '#skF_2'(xS,sdtpldt0(slcrc0,xx)) != xx,
    inference(splitRight,[status(thm)],[c_926]) ).

tff(c_471,plain,
    ! [W0_96] :
      ( ( '#skF_2'(W0_96,sdtpldt0(slcrc0,xx)) = xx )
      | aSubsetOf0(sdtpldt0(slcrc0,xx),W0_96)
      | ~ aSet0(W0_96) ),
    inference(demodulation,[status(thm),theory(equality)],[c_218,c_443]) ).

tff(c_1074,plain,
    '#skF_2'(sdtpldt0(slcrc0,xx),xS) = xx,
    inference(splitRight,[status(thm)],[c_926]) ).

tff(c_1079,plain,
    ( ~ aElementOf0(xx,sdtpldt0(slcrc0,xx))
    | aSubsetOf0(xS,sdtpldt0(slcrc0,xx))
    | ~ aSet0(xS)
    | ~ aSet0(sdtpldt0(slcrc0,xx)) ),
    inference(superposition,[status(thm),theory(equality)],[c_1074,c_28]) ).

tff(c_1089,plain,
    aSubsetOf0(xS,sdtpldt0(slcrc0,xx)),
    inference(demodulation,[status(thm),theory(equality)],[c_218,c_94,c_214,c_1079]) ).

tff(c_1099,plain,
    ( ( sdtpldt0(slcrc0,xx) = xS )
    | ~ aSubsetOf0(sdtpldt0(slcrc0,xx),xS)
    | ~ aSet0(xS)
    | ~ aSet0(sdtpldt0(slcrc0,xx)) ),
    inference(resolution,[status(thm)],[c_1089,c_36]) ).

tff(c_1114,plain,
    ( ( sdtpldt0(slcrc0,xx) = xS )
    | ~ aSubsetOf0(sdtpldt0(slcrc0,xx),xS) ),
    inference(demodulation,[status(thm),theory(equality)],[c_218,c_94,c_1099]) ).

tff(c_1115,plain,
    ~ aSubsetOf0(sdtpldt0(slcrc0,xx),xS),
    inference(negUnitSimplification,[status(thm)],[c_219,c_1114]) ).

tff(c_1127,plain,
    ( ( '#skF_2'(xS,sdtpldt0(slcrc0,xx)) = xx )
    | ~ aSet0(xS) ),
    inference(resolution,[status(thm)],[c_471,c_1115]) ).

tff(c_1130,plain,
    '#skF_2'(xS,sdtpldt0(slcrc0,xx)) = xx,
    inference(demodulation,[status(thm),theory(equality)],[c_94,c_1127]) ).

tff(c_1131,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_1075,c_1130]) ).

tff(c_1133,plain,
    sdtmndt0(xS,xx) != slcrc0,
    inference(splitRight,[status(thm)],[c_166]) ).

tff(c_116,plain,
    ! [W0_55] :
      ( aElementOf0(W0_55,xS)
      | ~ aElementOf0(W0_55,sdtmndt0(xS,xx)) ),
    inference(cnfTransformation,[status(thm)],[f_183]) ).

tff(c_148,plain,
    ( aElementOf0('#skF_1'(sdtmndt0(xS,xx)),xS)
    | ( sdtmndt0(xS,xx) = slcrc0 )
    | ~ aSet0(sdtmndt0(xS,xx)) ),
    inference(resolution,[status(thm)],[c_144,c_116]) ).

tff(c_162,plain,
    ( aElementOf0('#skF_1'(sdtmndt0(xS,xx)),xS)
    | ( sdtmndt0(xS,xx) = slcrc0 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_104,c_148]) ).

tff(c_1134,plain,
    aElementOf0('#skF_1'(sdtmndt0(xS,xx)),xS),
    inference(negUnitSimplification,[status(thm)],[c_1133,c_162]) ).

tff(c_1157,plain,
    ! [W2_132,W0_133,W1_134] :
      ( aElementOf0(W2_132,W0_133)
      | ~ aElementOf0(W2_132,W1_134)
      | ~ aSubsetOf0(W1_134,W0_133)
      | ~ aSet0(W0_133) ),
    inference(cnfTransformation,[status(thm)],[f_84]) ).

tff(c_1168,plain,
    ! [W0_133] :
      ( aElementOf0('#skF_1'(sdtmndt0(xS,xx)),W0_133)
      | ~ aSubsetOf0(xS,W0_133)
      | ~ aSet0(W0_133) ),
    inference(resolution,[status(thm)],[c_1134,c_1157]) ).

tff(c_1506,plain,
    ! [W0_159] :
      ( ( xx = W0_159 )
      | aElementOf0(W0_159,sdtmndt0(xS,xx))
      | ~ aElementOf0(W0_159,sdtpldt0(sdtmndt0(xS,xx),xx)) ),
    inference(cnfTransformation,[status(thm)],[f_183]) ).

tff(c_1521,plain,
    ( ( '#skF_1'(sdtmndt0(xS,xx)) = xx )
    | aElementOf0('#skF_1'(sdtmndt0(xS,xx)),sdtmndt0(xS,xx))
    | ~ aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx))
    | ~ aSet0(sdtpldt0(sdtmndt0(xS,xx),xx)) ),
    inference(resolution,[status(thm)],[c_1168,c_1506]) ).

tff(c_1542,plain,
    ( ( '#skF_1'(sdtmndt0(xS,xx)) = xx )
    | aElementOf0('#skF_1'(sdtmndt0(xS,xx)),sdtmndt0(xS,xx))
    | ~ aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_100,c_1521]) ).

tff(c_3184,plain,
    ~ aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx)),
    inference(splitLeft,[status(thm)],[c_1542]) ).

tff(c_1312,plain,
    ! [W0_148,W1_149] :
      ( aElementOf0('#skF_2'(W0_148,W1_149),W1_149)
      | aSubsetOf0(W1_149,W0_148)
      | ~ aSet0(W1_149)
      | ~ aSet0(W0_148) ),
    inference(cnfTransformation,[status(thm)],[f_84]) ).

tff(c_1361,plain,
    ! [W0_148,W1_149] :
      ( aElement0('#skF_2'(W0_148,W1_149))
      | aSubsetOf0(W1_149,W0_148)
      | ~ aSet0(W1_149)
      | ~ aSet0(W0_148) ),
    inference(resolution,[status(thm)],[c_1312,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_1402,plain,
    ! [W0_154] :
      ( ~ aElementOf0(W0_154,sdtmndt0(xS,xx))
      | aElementOf0(W0_154,sdtpldt0(sdtmndt0(xS,xx),xx))
      | ~ aElement0(W0_154) ),
    inference(cnfTransformation,[status(thm)],[f_183]) ).

tff(c_1406,plain,
    ! [W1_20] :
      ( aSubsetOf0(W1_20,sdtpldt0(sdtmndt0(xS,xx),xx))
      | ~ aSet0(W1_20)
      | ~ aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
      | ~ aElementOf0('#skF_2'(sdtpldt0(sdtmndt0(xS,xx),xx),W1_20),sdtmndt0(xS,xx))
      | ~ aElement0('#skF_2'(sdtpldt0(sdtmndt0(xS,xx),xx),W1_20)) ),
    inference(resolution,[status(thm)],[c_1402,c_28]) ).

tff(c_24586,plain,
    ! [W1_760] :
      ( aSubsetOf0(W1_760,sdtpldt0(sdtmndt0(xS,xx),xx))
      | ~ aSet0(W1_760)
      | ~ aElementOf0('#skF_2'(sdtpldt0(sdtmndt0(xS,xx),xx),W1_760),sdtmndt0(xS,xx))
      | ~ aElement0('#skF_2'(sdtpldt0(sdtmndt0(xS,xx),xx),W1_760)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_100,c_1406]) ).

tff(c_25058,plain,
    ! [W1_767] :
      ( aSubsetOf0(W1_767,sdtpldt0(sdtmndt0(xS,xx),xx))
      | ~ aSet0(W1_767)
      | ( '#skF_2'(sdtpldt0(sdtmndt0(xS,xx),xx),W1_767) = xx )
      | ~ aElementOf0('#skF_2'(sdtpldt0(sdtmndt0(xS,xx),xx),W1_767),xS)
      | ~ aElement0('#skF_2'(sdtpldt0(sdtmndt0(xS,xx),xx),W1_767)) ),
    inference(resolution,[status(thm)],[c_102,c_24586]) ).

tff(c_25086,plain,
    ( ( '#skF_2'(sdtpldt0(sdtmndt0(xS,xx),xx),xS) = xx )
    | ~ aElement0('#skF_2'(sdtpldt0(sdtmndt0(xS,xx),xx),xS))
    | aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx))
    | ~ aSet0(xS)
    | ~ aSet0(sdtpldt0(sdtmndt0(xS,xx),xx)) ),
    inference(resolution,[status(thm)],[c_30,c_25058]) ).

tff(c_25107,plain,
    ( ( '#skF_2'(sdtpldt0(sdtmndt0(xS,xx),xx),xS) = xx )
    | ~ aElement0('#skF_2'(sdtpldt0(sdtmndt0(xS,xx),xx),xS))
    | aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_100,c_94,c_25086]) ).

tff(c_25108,plain,
    ( ( '#skF_2'(sdtpldt0(sdtmndt0(xS,xx),xx),xS) = xx )
    | ~ aElement0('#skF_2'(sdtpldt0(sdtmndt0(xS,xx),xx),xS)) ),
    inference(negUnitSimplification,[status(thm)],[c_3184,c_25107]) ).

tff(c_25109,plain,
    ~ aElement0('#skF_2'(sdtpldt0(sdtmndt0(xS,xx),xx),xS)),
    inference(splitLeft,[status(thm)],[c_25108]) ).

tff(c_25112,plain,
    ( aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx))
    | ~ aSet0(xS)
    | ~ aSet0(sdtpldt0(sdtmndt0(xS,xx),xx)) ),
    inference(resolution,[status(thm)],[c_1361,c_25109]) ).

tff(c_25115,plain,
    aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx)),
    inference(demodulation,[status(thm),theory(equality)],[c_100,c_94,c_25112]) ).

tff(c_25117,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_3184,c_25115]) ).

tff(c_25118,plain,
    '#skF_2'(sdtpldt0(sdtmndt0(xS,xx),xx),xS) = xx,
    inference(splitRight,[status(thm)],[c_25108]) ).

tff(c_25165,plain,
    ( ~ aElementOf0(xx,sdtpldt0(sdtmndt0(xS,xx),xx))
    | aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx))
    | ~ aSet0(xS)
    | ~ aSet0(sdtpldt0(sdtmndt0(xS,xx),xx)) ),
    inference(superposition,[status(thm),theory(equality)],[c_25118,c_28]) ).

tff(c_25211,plain,
    aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx)),
    inference(demodulation,[status(thm),theory(equality)],[c_100,c_94,c_195,c_25165]) ).

tff(c_25213,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_3184,c_25211]) ).

tff(c_25215,plain,
    aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx)),
    inference(splitRight,[status(thm)],[c_1542]) ).

tff(c_25230,plain,
    ( ( sdtpldt0(sdtmndt0(xS,xx),xx) = xS )
    | ~ aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),xS)
    | ~ aSet0(xS)
    | ~ aSet0(sdtpldt0(sdtmndt0(xS,xx),xx)) ),
    inference(resolution,[status(thm)],[c_25215,c_36]) ).

tff(c_25261,plain,
    ( ( sdtpldt0(sdtmndt0(xS,xx),xx) = xS )
    | ~ aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),xS) ),
    inference(demodulation,[status(thm),theory(equality)],[c_100,c_94,c_25230]) ).

tff(c_25262,plain,
    ~ aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),xS),
    inference(negUnitSimplification,[status(thm)],[c_98,c_25261]) ).

tff(c_1517,plain,
    ! [W0_14] :
      ( ( '#skF_2'(W0_14,sdtpldt0(sdtmndt0(xS,xx),xx)) = xx )
      | aElementOf0('#skF_2'(W0_14,sdtpldt0(sdtmndt0(xS,xx),xx)),sdtmndt0(xS,xx))
      | aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),W0_14)
      | ~ aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
      | ~ aSet0(W0_14) ),
    inference(resolution,[status(thm)],[c_30,c_1506]) ).

tff(c_49179,plain,
    ! [W0_1302] :
      ( ( '#skF_2'(W0_1302,sdtpldt0(sdtmndt0(xS,xx),xx)) = xx )
      | aElementOf0('#skF_2'(W0_1302,sdtpldt0(sdtmndt0(xS,xx),xx)),sdtmndt0(xS,xx))
      | aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),W0_1302)
      | ~ aSet0(W0_1302) ),
    inference(demodulation,[status(thm),theory(equality)],[c_100,c_1517]) ).

tff(c_49360,plain,
    ! [W0_1303] :
      ( aElementOf0('#skF_2'(W0_1303,sdtpldt0(sdtmndt0(xS,xx),xx)),xS)
      | ( '#skF_2'(W0_1303,sdtpldt0(sdtmndt0(xS,xx),xx)) = xx )
      | aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),W0_1303)
      | ~ aSet0(W0_1303) ),
    inference(resolution,[status(thm)],[c_49179,c_116]) ).

tff(c_49374,plain,
    ( ~ aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
    | ( '#skF_2'(xS,sdtpldt0(sdtmndt0(xS,xx),xx)) = xx )
    | aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),xS)
    | ~ aSet0(xS) ),
    inference(resolution,[status(thm)],[c_49360,c_28]) ).

tff(c_49399,plain,
    ( ( '#skF_2'(xS,sdtpldt0(sdtmndt0(xS,xx),xx)) = xx )
    | aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),xS) ),
    inference(demodulation,[status(thm),theory(equality)],[c_94,c_100,c_49374]) ).

tff(c_49400,plain,
    '#skF_2'(xS,sdtpldt0(sdtmndt0(xS,xx),xx)) = xx,
    inference(negUnitSimplification,[status(thm)],[c_25262,c_49399]) ).

tff(c_49465,plain,
    ( ~ aElementOf0(xx,xS)
    | aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),xS)
    | ~ aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
    | ~ aSet0(xS) ),
    inference(superposition,[status(thm),theory(equality)],[c_49400,c_28]) ).

tff(c_49520,plain,
    aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),xS),
    inference(demodulation,[status(thm),theory(equality)],[c_94,c_100,c_96,c_49465]) ).

tff(c_49522,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_25262,c_49520]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : NUM534+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/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.17/0.35  % Computer : n025.cluster.edu
% 0.17/0.35  % Model    : x86_64 x86_64
% 0.17/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.35  % Memory   : 8042.1875MB
% 0.17/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.17/0.35  % CPULimit : 300
% 0.17/0.35  % WCLimit  : 300
% 0.17/0.35  % DateTime : Thu Aug  3 15:20:19 EDT 2023
% 0.17/0.36  % CPUTime  : 
% 18.48/7.45  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 18.48/7.47  
% 18.48/7.47  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 18.64/7.51  
% 18.64/7.51  Inference rules
% 18.64/7.51  ----------------------
% 18.64/7.51  #Ref     : 0
% 18.64/7.51  #Sup     : 10256
% 18.64/7.51  #Fact    : 0
% 18.64/7.51  #Define  : 0
% 18.64/7.51  #Split   : 63
% 18.64/7.51  #Chain   : 0
% 18.64/7.51  #Close   : 0
% 18.64/7.51  
% 18.64/7.51  Ordering : KBO
% 18.64/7.51  
% 18.64/7.51  Simplification rules
% 18.64/7.51  ----------------------
% 18.64/7.51  #Subsume      : 4674
% 18.64/7.51  #Demod        : 10609
% 18.64/7.51  #Tautology    : 2005
% 18.64/7.51  #SimpNegUnit  : 1060
% 18.64/7.51  #BackRed      : 88
% 18.64/7.51  
% 18.64/7.51  #Partial instantiations: 0
% 18.64/7.51  #Strategies tried      : 1
% 18.64/7.51  
% 18.64/7.51  Timing (in seconds)
% 18.64/7.51  ----------------------
% 18.64/7.51  Preprocessing        : 0.58
% 18.64/7.51  Parsing              : 0.29
% 18.64/7.51  CNF conversion       : 0.05
% 18.64/7.51  Main loop            : 5.83
% 18.64/7.51  Inferencing          : 1.57
% 18.64/7.51  Reduction            : 2.04
% 18.64/7.51  Demodulation         : 1.43
% 18.64/7.51  BG Simplification    : 0.11
% 18.64/7.51  Subsumption          : 1.81
% 18.64/7.51  Abstraction          : 0.20
% 18.64/7.51  MUC search           : 0.00
% 18.64/7.51  Cooper               : 0.00
% 18.64/7.51  Total                : 6.48
% 18.64/7.51  Index Insertion      : 0.00
% 18.64/7.51  Index Deletion       : 0.00
% 18.64/7.51  Index Matching       : 0.00
% 18.64/7.51  BG Taut test         : 0.00
%------------------------------------------------------------------------------