TSTP Solution File: RNG109+1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : RNG109+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 : n010.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 10:54:59 EDT 2023

% Result   : Theorem 35.61s 21.31s
% Output   : CNFRefutation 35.61s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :   64
% Syntax   : Number of formulae    :  179 (  63 unt;  47 typ;   4 def)
%            Number of atoms       :  268 (  66 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :  253 ( 117   ~;  97   |;  21   &)
%                                         (   6 <=>;  12  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   88 (  41   >;  47   *;   0   +;   0  <<)
%            Number of predicates  :   13 (  11 usr;   1 prp; 0-3 aty)
%            Number of functors    :   36 (  36 usr;   6 con; 0-4 aty)
%            Number of variables   :   86 (;  81   !;   5   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ sdteqdtlpzmzozddtrp0 > aGcdOfAnd0 > misRelativelyPrime0 > iLess0 > doDivides0 > aElementOf0 > aDivisorOf0 > aSet0 > aNaturalNumber0 > aIdeal0 > aElement0 > sdtpldt1 > sdtpldt0 > sdtasdt0 > sdtasasdt0 > #nlpp > smndt0 > slsdtgt0 > sbrdtbr0 > xc > xb > xa > xI > sz10 > sz00 > #skF_22 > #skF_6 > #skF_17 > #skF_20 > #skF_4 > #skF_8 > #skF_14 > #skF_15 > #skF_18 > #skF_23 > #skF_5 > #skF_19 > #skF_7 > #skF_9 > #skF_13 > #skF_11 > #skF_3 > #skF_2 > #skF_12 > #skF_1 > #skF_16 > #skF_21 > #skF_10

%Foreground sorts:

%Background operators:

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

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

tff(sdtasdt0,type,
    sdtasdt0: ( $i * $i ) > $i ).

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

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

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

tff(sz10,type,
    sz10: $i ).

tff(sdtpldt1,type,
    sdtpldt1: ( $i * $i ) > $i ).

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

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

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

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

tff(misRelativelyPrime0,type,
    misRelativelyPrime0: ( $i * $i ) > $o ).

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

tff(aIdeal0,type,
    aIdeal0: $i > $o ).

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

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

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

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

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

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

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

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

tff(aNaturalNumber0,type,
    aNaturalNumber0: $i > $o ).

tff(slsdtgt0,type,
    slsdtgt0: $i > $i ).

tff(smndt0,type,
    smndt0: $i > $i ).

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

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

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

tff(doDivides0,type,
    doDivides0: ( $i * $i ) > $o ).

tff(aGcdOfAnd0,type,
    aGcdOfAnd0: ( $i * $i * $i ) > $o ).

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

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

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

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

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

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

tff(aDivisorOf0,type,
    aDivisorOf0: ( $i * $i ) > $o ).

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

tff(sdtasasdt0,type,
    sdtasasdt0: ( $i * $i ) > $i ).

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

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

tff(sdteqdtlpzmzozddtrp0,type,
    sdteqdtlpzmzozddtrp0: ( $i * $i * $i ) > $o ).

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

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

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

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

tff(f_357,hypothesis,
    ( ( xa != sz00 )
    | ( xb != sz00 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2110) ).

tff(f_352,hypothesis,
    ( aElement0(xa)
    & aElement0(xb) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2091) ).

tff(f_67,axiom,
    ! [W0] :
      ( aElement0(W0)
     => ( ( sdtpldt0(W0,sz00) = W0 )
        & ( W0 = sdtpldt0(sz00,W0) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddZero) ).

tff(f_31,axiom,
    aElement0(sz10),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC_01) ).

tff(f_35,axiom,
    ! [W0] :
      ( aElement0(W0)
     => aElement0(smndt0(W0)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsU) ).

tff(f_79,axiom,
    ! [W0,W1] :
      ( ( aElement0(W0)
        & aElement0(W1) )
     => ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulComm) ).

tff(f_109,axiom,
    ! [W0] :
      ( aElement0(W0)
     => ( ( sdtasdt0(smndt0(sz10),W0) = smndt0(W0) )
        & ( smndt0(W0) = sdtasdt0(W0,smndt0(sz10)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulMnOne) ).

tff(f_295,definition,
    ! [W0,W1] :
      ( ( aElement0(W0)
        & aElement0(W1) )
     => ( doDivides0(W0,W1)
      <=> ? [W2] :
            ( aElement0(W2)
            & ( sdtasdt0(W0,W2) = W1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefDiv) ).

tff(f_361,hypothesis,
    ( aIdeal0(xI)
    & ( xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2174) ).

tff(f_205,definition,
    ! [W0] :
      ( aIdeal0(W0)
    <=> ( aSet0(W0)
        & ! [W1] :
            ( aElementOf0(W1,W0)
           => ( ! [W2] :
                  ( aElementOf0(W2,W0)
                 => aElementOf0(sdtpldt0(W1,W2),W0) )
              & ! [W2] :
                  ( aElement0(W2)
                 => aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefIdeal) ).

tff(f_374,negated_conjecture,
    ~ ? [W0] :
        ( aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
        & ( W0 != sz00 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).

tff(f_368,hypothesis,
    ( aElementOf0(sz00,slsdtgt0(xa))
    & aElementOf0(xa,slsdtgt0(xa))
    & aElementOf0(sz00,slsdtgt0(xb))
    & aElementOf0(xb,slsdtgt0(xb)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2203) ).

tff(f_345,definition,
    ! [W0] :
      ( aElement0(W0)
     => ! [W1] :
          ( ( W1 = slsdtgt0(W0) )
        <=> ( aSet0(W1)
            & ! [W2] :
                ( aElementOf0(W2,W1)
              <=> ? [W3] :
                    ( aElement0(W3)
                    & ( sdtasdt0(W0,W3) = W2 ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefPrIdeal) ).

tff(f_172,definition,
    ! [W0,W1] :
      ( ( aSet0(W0)
        & aSet0(W1) )
     => ! [W2] :
          ( ( W2 = sdtpldt1(W0,W1) )
        <=> ( aSet0(W2)
            & ! [W3] :
                ( aElementOf0(W3,W2)
              <=> ? [W4,W5] :
                    ( aElementOf0(W4,W0)
                    & aElementOf0(W5,W1)
                    & ( sdtpldt0(W4,W5) = W3 ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSSum) ).

tff(f_73,axiom,
    ! [W0] :
      ( aElement0(W0)
     => ( ( sdtpldt0(W0,smndt0(W0)) = sz00 )
        & ( sz00 = sdtpldt0(smndt0(W0),W0) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddInvr) ).

tff(f_47,axiom,
    ! [W0,W1] :
      ( ( aElement0(W0)
        & aElement0(W1) )
     => aElement0(sdtasdt0(W0,W1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB_02) ).

tff(f_30,axiom,
    aElement0(sz00),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC) ).

tff(c_212,plain,
    ( ( xb != sz00 )
    | ( xa != sz00 ) ),
    inference(cnfTransformation,[status(thm)],[f_357]) ).

tff(c_232,plain,
    xa != sz00,
    inference(splitLeft,[status(thm)],[c_212]) ).

tff(c_210,plain,
    aElement0(xa),
    inference(cnfTransformation,[status(thm)],[f_352]) ).

tff(c_236,plain,
    ! [W0_228] :
      ( ( sdtpldt0(sz00,W0_228) = W0_228 )
      | ~ aElement0(W0_228) ),
    inference(cnfTransformation,[status(thm)],[f_67]) ).

tff(c_256,plain,
    sdtpldt0(sz00,xa) = xa,
    inference(resolution,[status(thm)],[c_210,c_236]) ).

tff(c_6,plain,
    aElement0(sz10),
    inference(cnfTransformation,[status(thm)],[f_31]) ).

tff(c_8,plain,
    ! [W0_2] :
      ( aElement0(smndt0(W0_2))
      | ~ aElement0(W0_2) ),
    inference(cnfTransformation,[status(thm)],[f_35]) ).

tff(c_999,plain,
    ! [W1_270,W0_271] :
      ( ( sdtasdt0(W1_270,W0_271) = sdtasdt0(W0_271,W1_270) )
      | ~ aElement0(W1_270)
      | ~ aElement0(W0_271) ),
    inference(cnfTransformation,[status(thm)],[f_79]) ).

tff(c_1505,plain,
    ! [W0_284] :
      ( ( sdtasdt0(sz10,W0_284) = sdtasdt0(W0_284,sz10) )
      | ~ aElement0(W0_284) ),
    inference(resolution,[status(thm)],[c_6,c_999]) ).

tff(c_14832,plain,
    ! [W0_460] :
      ( ( sdtasdt0(smndt0(W0_460),sz10) = sdtasdt0(sz10,smndt0(W0_460)) )
      | ~ aElement0(W0_460) ),
    inference(resolution,[status(thm)],[c_8,c_1505]) ).

tff(c_40,plain,
    ! [W0_23] :
      ( ( sdtasdt0(smndt0(sz10),W0_23) = smndt0(W0_23) )
      | ~ aElement0(W0_23) ),
    inference(cnfTransformation,[status(thm)],[f_109]) ).

tff(c_14882,plain,
    ( ( sdtasdt0(sz10,smndt0(sz10)) = smndt0(sz10) )
    | ~ aElement0(sz10)
    | ~ aElement0(sz10) ),
    inference(superposition,[status(thm),theory(equality)],[c_14832,c_40]) ).

tff(c_14930,plain,
    sdtasdt0(sz10,smndt0(sz10)) = smndt0(sz10),
    inference(demodulation,[status(thm),theory(equality)],[c_6,c_6,c_14882]) ).

tff(c_158,plain,
    ! [W0_160,W2_164] :
      ( doDivides0(W0_160,sdtasdt0(W0_160,W2_164))
      | ~ aElement0(W2_164)
      | ~ aElement0(sdtasdt0(W0_160,W2_164))
      | ~ aElement0(W0_160) ),
    inference(cnfTransformation,[status(thm)],[f_295]) ).

tff(c_14967,plain,
    ( doDivides0(sz10,smndt0(sz10))
    | ~ aElement0(smndt0(sz10))
    | ~ aElement0(sdtasdt0(sz10,smndt0(sz10)))
    | ~ aElement0(sz10) ),
    inference(superposition,[status(thm),theory(equality)],[c_14930,c_158]) ).

tff(c_15012,plain,
    ( doDivides0(sz10,smndt0(sz10))
    | ~ aElement0(smndt0(sz10)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_6,c_14930,c_14967]) ).

tff(c_15202,plain,
    ~ aElement0(smndt0(sz10)),
    inference(splitLeft,[status(thm)],[c_15012]) ).

tff(c_15205,plain,
    ~ aElement0(sz10),
    inference(resolution,[status(thm)],[c_8,c_15202]) ).

tff(c_15209,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_6,c_15205]) ).

tff(c_15211,plain,
    aElement0(smndt0(sz10)),
    inference(splitRight,[status(thm)],[c_15012]) ).

tff(c_1026,plain,
    ! [W0_271] :
      ( ( sdtasdt0(xa,W0_271) = sdtasdt0(W0_271,xa) )
      | ~ aElement0(W0_271) ),
    inference(resolution,[status(thm)],[c_210,c_999]) ).

tff(c_15271,plain,
    sdtasdt0(smndt0(sz10),xa) = sdtasdt0(xa,smndt0(sz10)),
    inference(resolution,[status(thm)],[c_15211,c_1026]) ).

tff(c_19240,plain,
    ( ( sdtasdt0(xa,smndt0(sz10)) = smndt0(xa) )
    | ~ aElement0(xa) ),
    inference(superposition,[status(thm),theory(equality)],[c_15271,c_40]) ).

tff(c_19285,plain,
    sdtasdt0(xa,smndt0(sz10)) = smndt0(xa),
    inference(demodulation,[status(thm),theory(equality)],[c_210,c_19240]) ).

tff(c_19847,plain,
    sdtasdt0(smndt0(sz10),xa) = smndt0(xa),
    inference(demodulation,[status(thm),theory(equality)],[c_19285,c_15271]) ).

tff(c_218,plain,
    aIdeal0(xI),
    inference(cnfTransformation,[status(thm)],[f_361]) ).

tff(c_2107,plain,
    ! [W2_299,W1_300,W0_301] :
      ( aElementOf0(sdtasdt0(W2_299,W1_300),W0_301)
      | ~ aElement0(W2_299)
      | ~ aElementOf0(W1_300,W0_301)
      | ~ aIdeal0(W0_301) ),
    inference(cnfTransformation,[status(thm)],[f_205]) ).

tff(c_216,plain,
    sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)) = xI,
    inference(cnfTransformation,[status(thm)],[f_361]) ).

tff(c_228,plain,
    ! [W0_222] :
      ( ( sz00 = W0_222 )
      | ~ aElementOf0(W0_222,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ),
    inference(cnfTransformation,[status(thm)],[f_374]) ).

tff(c_229,plain,
    ! [W0_222] :
      ( ( sz00 = W0_222 )
      | ~ aElementOf0(W0_222,xI) ),
    inference(demodulation,[status(thm),theory(equality)],[c_216,c_228]) ).

tff(c_2118,plain,
    ! [W2_299,W1_300] :
      ( ( sdtasdt0(W2_299,W1_300) = sz00 )
      | ~ aElement0(W2_299)
      | ~ aElementOf0(W1_300,xI)
      | ~ aIdeal0(xI) ),
    inference(resolution,[status(thm)],[c_2107,c_229]) ).

tff(c_2207,plain,
    ! [W2_299,W1_300] :
      ( ( sdtasdt0(W2_299,W1_300) = sz00 )
      | ~ aElement0(W2_299)
      | ~ aElementOf0(W1_300,xI) ),
    inference(demodulation,[status(thm),theory(equality)],[c_218,c_2118]) ).

tff(c_15272,plain,
    ! [W1_300] :
      ( ( sdtasdt0(smndt0(sz10),W1_300) = sz00 )
      | ~ aElementOf0(W1_300,xI) ),
    inference(resolution,[status(thm)],[c_15211,c_2207]) ).

tff(c_20081,plain,
    ( ( smndt0(xa) = sz00 )
    | ~ aElementOf0(xa,xI) ),
    inference(superposition,[status(thm),theory(equality)],[c_19847,c_15272]) ).

tff(c_20225,plain,
    ~ aElementOf0(xa,xI),
    inference(splitLeft,[status(thm)],[c_20081]) ).

tff(c_224,plain,
    aElementOf0(xa,slsdtgt0(xa)),
    inference(cnfTransformation,[status(thm)],[f_368]) ).

tff(c_222,plain,
    aElementOf0(sz00,slsdtgt0(xb)),
    inference(cnfTransformation,[status(thm)],[f_368]) ).

tff(c_257,plain,
    ! [W0_229] :
      ( ( sdtpldt0(W0_229,sz00) = W0_229 )
      | ~ aElement0(W0_229) ),
    inference(cnfTransformation,[status(thm)],[f_67]) ).

tff(c_277,plain,
    sdtpldt0(xa,sz00) = xa,
    inference(resolution,[status(thm)],[c_210,c_257]) ).

tff(c_188,plain,
    ! [W0_181] :
      ( aSet0(slsdtgt0(W0_181))
      | ~ aElement0(W0_181) ),
    inference(cnfTransformation,[status(thm)],[f_345]) ).

tff(c_513,plain,
    ! [W0_249,W1_250] :
      ( aSet0(sdtpldt1(W0_249,W1_250))
      | ~ aSet0(W1_250)
      | ~ aSet0(W0_249) ),
    inference(cnfTransformation,[status(thm)],[f_172]) ).

tff(c_516,plain,
    ( aSet0(xI)
    | ~ aSet0(slsdtgt0(xb))
    | ~ aSet0(slsdtgt0(xa)) ),
    inference(superposition,[status(thm),theory(equality)],[c_216,c_513]) ).

tff(c_810,plain,
    ~ aSet0(slsdtgt0(xa)),
    inference(splitLeft,[status(thm)],[c_516]) ).

tff(c_813,plain,
    ~ aElement0(xa),
    inference(resolution,[status(thm)],[c_188,c_810]) ).

tff(c_820,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_210,c_813]) ).

tff(c_822,plain,
    aSet0(slsdtgt0(xa)),
    inference(splitRight,[status(thm)],[c_516]) ).

tff(c_208,plain,
    aElement0(xb),
    inference(cnfTransformation,[status(thm)],[f_352]) ).

tff(c_821,plain,
    ( ~ aSet0(slsdtgt0(xb))
    | aSet0(xI) ),
    inference(splitRight,[status(thm)],[c_516]) ).

tff(c_848,plain,
    ~ aSet0(slsdtgt0(xb)),
    inference(splitLeft,[status(thm)],[c_821]) ).

tff(c_851,plain,
    ~ aElement0(xb),
    inference(resolution,[status(thm)],[c_188,c_848]) ).

tff(c_858,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_208,c_851]) ).

tff(c_860,plain,
    aSet0(slsdtgt0(xb)),
    inference(splitRight,[status(thm)],[c_821]) ).

tff(c_7898,plain,
    ! [W4_390,W5_391,W0_392,W1_393] :
      ( aElementOf0(sdtpldt0(W4_390,W5_391),sdtpldt1(W0_392,W1_393))
      | ~ aElementOf0(W5_391,W1_393)
      | ~ aElementOf0(W4_390,W0_392)
      | ~ aSet0(W1_393)
      | ~ aSet0(W0_392) ),
    inference(cnfTransformation,[status(thm)],[f_172]) ).

tff(c_7987,plain,
    ! [W4_390,W5_391] :
      ( aElementOf0(sdtpldt0(W4_390,W5_391),xI)
      | ~ aElementOf0(W5_391,slsdtgt0(xb))
      | ~ aElementOf0(W4_390,slsdtgt0(xa))
      | ~ aSet0(slsdtgt0(xb))
      | ~ aSet0(slsdtgt0(xa)) ),
    inference(superposition,[status(thm),theory(equality)],[c_216,c_7898]) ).

tff(c_41292,plain,
    ! [W4_630,W5_631] :
      ( aElementOf0(sdtpldt0(W4_630,W5_631),xI)
      | ~ aElementOf0(W5_631,slsdtgt0(xb))
      | ~ aElementOf0(W4_630,slsdtgt0(xa)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_822,c_860,c_7987]) ).

tff(c_41549,plain,
    ( aElementOf0(xa,xI)
    | ~ aElementOf0(sz00,slsdtgt0(xb))
    | ~ aElementOf0(xa,slsdtgt0(xa)) ),
    inference(superposition,[status(thm),theory(equality)],[c_277,c_41292]) ).

tff(c_41685,plain,
    aElementOf0(xa,xI),
    inference(demodulation,[status(thm),theory(equality)],[c_224,c_222,c_41549]) ).

tff(c_41687,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_20225,c_41685]) ).

tff(c_41688,plain,
    smndt0(xa) = sz00,
    inference(splitRight,[status(thm)],[c_20081]) ).

tff(c_22,plain,
    ! [W0_13] :
      ( ( sdtpldt0(smndt0(W0_13),W0_13) = sz00 )
      | ~ aElement0(W0_13) ),
    inference(cnfTransformation,[status(thm)],[f_73]) ).

tff(c_41750,plain,
    ( ( sdtpldt0(sz00,xa) = sz00 )
    | ~ aElement0(xa) ),
    inference(superposition,[status(thm),theory(equality)],[c_41688,c_22]) ).

tff(c_41782,plain,
    xa = sz00,
    inference(demodulation,[status(thm),theory(equality)],[c_210,c_256,c_41750]) ).

tff(c_41784,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_232,c_41782]) ).

tff(c_41785,plain,
    xb != sz00,
    inference(splitRight,[status(thm)],[c_212]) ).

tff(c_41800,plain,
    ! [W0_635] :
      ( ( sdtpldt0(sz00,W0_635) = W0_635 )
      | ~ aElement0(W0_635) ),
    inference(cnfTransformation,[status(thm)],[f_67]) ).

tff(c_41816,plain,
    sdtpldt0(sz00,xb) = xb,
    inference(resolution,[status(thm)],[c_208,c_41800]) ).

tff(c_43478,plain,
    ! [W2_705,W1_706,W0_707] :
      ( aElementOf0(sdtasdt0(W2_705,W1_706),W0_707)
      | ~ aElement0(W2_705)
      | ~ aElementOf0(W1_706,W0_707)
      | ~ aIdeal0(W0_707) ),
    inference(cnfTransformation,[status(thm)],[f_205]) ).

tff(c_43485,plain,
    ! [W2_705,W1_706] :
      ( ( sdtasdt0(W2_705,W1_706) = sz00 )
      | ~ aElement0(W2_705)
      | ~ aElementOf0(W1_706,xI)
      | ~ aIdeal0(xI) ),
    inference(resolution,[status(thm)],[c_43478,c_229]) ).

tff(c_43720,plain,
    ! [W2_712,W1_713] :
      ( ( sdtasdt0(W2_712,W1_713) = sz00 )
      | ~ aElement0(W2_712)
      | ~ aElementOf0(W1_713,xI) ),
    inference(demodulation,[status(thm),theory(equality)],[c_218,c_43485]) ).

tff(c_43762,plain,
    ! [W0_2,W1_713] :
      ( ( sdtasdt0(smndt0(W0_2),W1_713) = sz00 )
      | ~ aElementOf0(W1_713,xI)
      | ~ aElement0(W0_2) ),
    inference(resolution,[status(thm)],[c_8,c_43720]) ).

tff(c_42449,plain,
    ! [W1_677,W0_678] :
      ( ( sdtasdt0(W1_677,W0_678) = sdtasdt0(W0_678,W1_677) )
      | ~ aElement0(W1_677)
      | ~ aElement0(W0_678) ),
    inference(cnfTransformation,[status(thm)],[f_79]) ).

tff(c_42935,plain,
    ! [W0_691] :
      ( ( sdtasdt0(xb,W0_691) = sdtasdt0(W0_691,xb) )
      | ~ aElement0(W0_691) ),
    inference(resolution,[status(thm)],[c_208,c_42449]) ).

tff(c_49873,plain,
    ! [W0_813] :
      ( ( sdtasdt0(smndt0(W0_813),xb) = sdtasdt0(xb,smndt0(W0_813)) )
      | ~ aElement0(W0_813) ),
    inference(resolution,[status(thm)],[c_8,c_42935]) ).

tff(c_49906,plain,
    ( ( sdtasdt0(xb,smndt0(sz10)) = smndt0(xb) )
    | ~ aElement0(xb)
    | ~ aElement0(sz10) ),
    inference(superposition,[status(thm),theory(equality)],[c_49873,c_40]) ).

tff(c_49941,plain,
    sdtasdt0(xb,smndt0(sz10)) = smndt0(xb),
    inference(demodulation,[status(thm),theory(equality)],[c_6,c_208,c_49906]) ).

tff(c_12,plain,
    ! [W0_5,W1_6] :
      ( aElement0(sdtasdt0(W0_5,W1_6))
      | ~ aElement0(W1_6)
      | ~ aElement0(W0_5) ),
    inference(cnfTransformation,[status(thm)],[f_47]) ).

tff(c_49984,plain,
    ( aElement0(smndt0(xb))
    | ~ aElement0(smndt0(sz10))
    | ~ aElement0(xb) ),
    inference(superposition,[status(thm),theory(equality)],[c_49941,c_12]) ).

tff(c_50012,plain,
    ( aElement0(smndt0(xb))
    | ~ aElement0(smndt0(sz10)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_208,c_49984]) ).

tff(c_50030,plain,
    ~ aElement0(smndt0(sz10)),
    inference(splitLeft,[status(thm)],[c_50012]) ).

tff(c_50033,plain,
    ~ aElement0(sz10),
    inference(resolution,[status(thm)],[c_8,c_50030]) ).

tff(c_50037,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_6,c_50033]) ).

tff(c_50039,plain,
    aElement0(smndt0(sz10)),
    inference(splitRight,[status(thm)],[c_50012]) ).

tff(c_42470,plain,
    ! [W0_678] :
      ( ( sdtasdt0(xb,W0_678) = sdtasdt0(W0_678,xb) )
      | ~ aElement0(W0_678) ),
    inference(resolution,[status(thm)],[c_208,c_42449]) ).

tff(c_50274,plain,
    sdtasdt0(smndt0(sz10),xb) = sdtasdt0(xb,smndt0(sz10)),
    inference(resolution,[status(thm)],[c_50039,c_42470]) ).

tff(c_50316,plain,
    sdtasdt0(smndt0(sz10),xb) = smndt0(xb),
    inference(demodulation,[status(thm),theory(equality)],[c_49941,c_50274]) ).

tff(c_51946,plain,
    ( ( smndt0(xb) = sz00 )
    | ~ aElementOf0(xb,xI)
    | ~ aElement0(sz10) ),
    inference(superposition,[status(thm),theory(equality)],[c_43762,c_50316]) ).

tff(c_51981,plain,
    ( ( smndt0(xb) = sz00 )
    | ~ aElementOf0(xb,xI) ),
    inference(demodulation,[status(thm),theory(equality)],[c_6,c_51946]) ).

tff(c_52141,plain,
    ~ aElementOf0(xb,xI),
    inference(splitLeft,[status(thm)],[c_51981]) ).

tff(c_41786,plain,
    xa = sz00,
    inference(splitRight,[status(thm)],[c_212]) ).

tff(c_226,plain,
    aElementOf0(sz00,slsdtgt0(xa)),
    inference(cnfTransformation,[status(thm)],[f_368]) ).

tff(c_41789,plain,
    aElementOf0(sz00,slsdtgt0(sz00)),
    inference(demodulation,[status(thm),theory(equality)],[c_41786,c_226]) ).

tff(c_220,plain,
    aElementOf0(xb,slsdtgt0(xb)),
    inference(cnfTransformation,[status(thm)],[f_368]) ).

tff(c_4,plain,
    aElement0(sz00),
    inference(cnfTransformation,[status(thm)],[f_30]) ).

tff(c_41936,plain,
    sdtpldt1(slsdtgt0(sz00),slsdtgt0(xb)) = xI,
    inference(demodulation,[status(thm),theory(equality)],[c_41786,c_216]) ).

tff(c_42137,plain,
    ! [W0_662,W1_663] :
      ( aSet0(sdtpldt1(W0_662,W1_663))
      | ~ aSet0(W1_663)
      | ~ aSet0(W0_662) ),
    inference(cnfTransformation,[status(thm)],[f_172]) ).

tff(c_42140,plain,
    ( aSet0(xI)
    | ~ aSet0(slsdtgt0(xb))
    | ~ aSet0(slsdtgt0(sz00)) ),
    inference(superposition,[status(thm),theory(equality)],[c_41936,c_42137]) ).

tff(c_42373,plain,
    ~ aSet0(slsdtgt0(sz00)),
    inference(splitLeft,[status(thm)],[c_42140]) ).

tff(c_42381,plain,
    ~ aElement0(sz00),
    inference(resolution,[status(thm)],[c_188,c_42373]) ).

tff(c_42388,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_4,c_42381]) ).

tff(c_42390,plain,
    aSet0(slsdtgt0(sz00)),
    inference(splitRight,[status(thm)],[c_42140]) ).

tff(c_42389,plain,
    ( ~ aSet0(slsdtgt0(xb))
    | aSet0(xI) ),
    inference(splitRight,[status(thm)],[c_42140]) ).

tff(c_42391,plain,
    ~ aSet0(slsdtgt0(xb)),
    inference(splitLeft,[status(thm)],[c_42389]) ).

tff(c_42394,plain,
    ~ aElement0(xb),
    inference(resolution,[status(thm)],[c_188,c_42391]) ).

tff(c_42401,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_208,c_42394]) ).

tff(c_42403,plain,
    aSet0(slsdtgt0(xb)),
    inference(splitRight,[status(thm)],[c_42389]) ).

tff(c_52369,plain,
    ! [W4_837,W5_838,W0_839,W1_840] :
      ( aElementOf0(sdtpldt0(W4_837,W5_838),sdtpldt1(W0_839,W1_840))
      | ~ aElementOf0(W5_838,W1_840)
      | ~ aElementOf0(W4_837,W0_839)
      | ~ aSet0(W1_840)
      | ~ aSet0(W0_839) ),
    inference(cnfTransformation,[status(thm)],[f_172]) ).

tff(c_52461,plain,
    ! [W4_837,W5_838] :
      ( aElementOf0(sdtpldt0(W4_837,W5_838),xI)
      | ~ aElementOf0(W5_838,slsdtgt0(xb))
      | ~ aElementOf0(W4_837,slsdtgt0(sz00))
      | ~ aSet0(slsdtgt0(xb))
      | ~ aSet0(slsdtgt0(sz00)) ),
    inference(superposition,[status(thm),theory(equality)],[c_41936,c_52369]) ).

tff(c_94423,plain,
    ! [W4_1127,W5_1128] :
      ( aElementOf0(sdtpldt0(W4_1127,W5_1128),xI)
      | ~ aElementOf0(W5_1128,slsdtgt0(xb))
      | ~ aElementOf0(W4_1127,slsdtgt0(sz00)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_42390,c_42403,c_52461]) ).

tff(c_94692,plain,
    ( aElementOf0(xb,xI)
    | ~ aElementOf0(xb,slsdtgt0(xb))
    | ~ aElementOf0(sz00,slsdtgt0(sz00)) ),
    inference(superposition,[status(thm),theory(equality)],[c_41816,c_94423]) ).

tff(c_94817,plain,
    aElementOf0(xb,xI),
    inference(demodulation,[status(thm),theory(equality)],[c_41789,c_220,c_94692]) ).

tff(c_94819,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_52141,c_94817]) ).

tff(c_94820,plain,
    smndt0(xb) = sz00,
    inference(splitRight,[status(thm)],[c_51981]) ).

tff(c_94901,plain,
    ( ( sdtpldt0(sz00,xb) = sz00 )
    | ~ aElement0(xb) ),
    inference(superposition,[status(thm),theory(equality)],[c_94820,c_22]) ).

tff(c_94937,plain,
    xb = sz00,
    inference(demodulation,[status(thm),theory(equality)],[c_208,c_41816,c_94901]) ).

tff(c_94939,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_41785,c_94937]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : RNG109+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 : n010.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 17:47:43 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 35.61/21.31  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 35.61/21.32  
% 35.61/21.32  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 35.61/21.36  
% 35.61/21.36  Inference rules
% 35.61/21.36  ----------------------
% 35.61/21.36  #Ref     : 0
% 35.61/21.36  #Sup     : 20130
% 35.61/21.36  #Fact    : 0
% 35.61/21.36  #Define  : 0
% 35.61/21.36  #Split   : 38
% 35.61/21.36  #Chain   : 0
% 35.61/21.36  #Close   : 0
% 35.61/21.36  
% 35.61/21.36  Ordering : KBO
% 35.61/21.36  
% 35.61/21.36  Simplification rules
% 35.61/21.36  ----------------------
% 35.61/21.36  #Subsume      : 3317
% 35.61/21.36  #Demod        : 26904
% 35.61/21.36  #Tautology    : 7169
% 35.61/21.36  #SimpNegUnit  : 277
% 35.61/21.36  #BackRed      : 69
% 35.61/21.36  
% 35.61/21.36  #Partial instantiations: 0
% 35.61/21.36  #Strategies tried      : 1
% 35.61/21.36  
% 35.61/21.36  Timing (in seconds)
% 35.61/21.36  ----------------------
% 35.61/21.37  Preprocessing        : 0.70
% 35.61/21.37  Parsing              : 0.35
% 35.61/21.37  CNF conversion       : 0.06
% 35.61/21.37  Main loop            : 19.52
% 35.61/21.37  Inferencing          : 2.91
% 35.61/21.37  Reduction            : 11.89
% 35.61/21.37  Demodulation         : 10.60
% 35.61/21.37  BG Simplification    : 0.18
% 35.61/21.37  Subsumption          : 3.93
% 35.61/21.37  Abstraction          : 0.26
% 35.61/21.37  MUC search           : 0.00
% 35.61/21.37  Cooper               : 0.00
% 35.61/21.37  Total                : 20.29
% 35.61/21.37  Index Insertion      : 0.00
% 35.61/21.37  Index Deletion       : 0.00
% 35.61/21.37  Index Matching       : 0.00
% 35.61/21.37  BG Taut test         : 0.00
%------------------------------------------------------------------------------