TSTP Solution File: RNG119+1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : RNG119+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 : n016.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 10:55:01 EDT 2023

% Result   : Theorem 7.91s 2.88s
% Output   : CNFRefutation 7.91s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   68
% Syntax   : Number of formulae    :  109 (  29 unt;  53 typ;   3 def)
%            Number of atoms       :  115 (  20 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :   99 (  40   ~;  28   |;  17   &)
%                                         (   3 <=>;  11  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   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    :   42 (  42 usr;  12 con; 0-4 aty)
%            Number of variables   :   32 (;  31   !;   1   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ sdteqdtlpzmzozddtrp0 > aGcdOfAnd0 > misRelativelyPrime0 > iLess0 > doDivides0 > aElementOf0 > aDivisorOf0 > aSet0 > aNaturalNumber0 > aIdeal0 > aElement0 > sdtpldt1 > sdtpldt0 > sdtasdt0 > sdtasasdt0 > #nlpp > smndt0 > slsdtgt0 > sbrdtbr0 > xu > xr > xq > xc > xb > xa > xI > sz10 > sz00 > #skF_22 > #skF_6 > #skF_17 > #skF_25 > #skF_20 > #skF_4 > #skF_8 > #skF_14 > #skF_15 > #skF_26 > #skF_18 > #skF_23 > #skF_5 > #skF_19 > #skF_7 > #skF_9 > #skF_13 > #skF_11 > #skF_3 > #skF_2 > #skF_24 > #skF_12 > #skF_1 > #skF_16 > #skF_21 > #skF_10

%Foreground sorts:

%Background operators:

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

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

tff(xr,type,
    xr: $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_25',type,
    '#skF_25': $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(xu,type,
    xu: $i ).

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('#skF_26',type,
    '#skF_26': $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('#skF_24',type,
    '#skF_24': $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_401,hypothesis,
    ~ doDivides0(xu,xb),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2612) ).

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

tff(f_390,hypothesis,
    ~ ( aDivisorOf0(xu,xa)
      & aDivisorOf0(xu,xb) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2383) ).

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_386,hypothesis,
    ( aElementOf0(xu,xI)
    & ( xu != sz00 )
    & ! [W0] :
        ( ( aElementOf0(W0,xI)
          & ( W0 != sz00 ) )
       => ~ iLess0(sbrdtbr0(W0),sbrdtbr0(xu)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2273) ).

tff(f_137,axiom,
    ! [W0] :
      ( aSet0(W0)
     => ! [W1] :
          ( aElementOf0(W1,W0)
         => aElement0(W1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEOfElem) ).

tff(f_399,hypothesis,
    ~ ~ doDivides0(xu,xa),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2479) ).

tff(f_304,definition,
    ! [W0] :
      ( aElement0(W0)
     => ! [W1] :
          ( aDivisorOf0(W1,W0)
        <=> ( aElement0(W1)
            & doDivides0(W1,W0) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefDvs) ).

tff(f_413,negated_conjecture,
    xr != sz00,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).

tff(f_410,hypothesis,
    ( aElement0(xq)
    & aElement0(xr)
    & ( xb = sdtpldt0(sdtasdt0(xq,xu),xr) )
    & ( ( xr = sz00 )
      | iLess0(sbrdtbr0(xr),sbrdtbr0(xu)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2666) ).

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_47,axiom,
    ! [W0,W1] :
      ( ( aElement0(W0)
        & aElement0(W1) )
     => aElement0(sdtasdt0(W0,W1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB_02) ).

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_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(c_248,plain,
    ~ doDivides0(xu,xb),
    inference(cnfTransformation,[status(thm)],[f_401]) ).

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

tff(c_238,plain,
    ( ~ aDivisorOf0(xu,xb)
    | ~ aDivisorOf0(xu,xa) ),
    inference(cnfTransformation,[status(thm)],[f_390]) ).

tff(c_463,plain,
    ~ aDivisorOf0(xu,xa),
    inference(splitLeft,[status(thm)],[c_238]) ).

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

tff(c_108,plain,
    ! [W0_117] :
      ( aSet0(W0_117)
      | ~ aIdeal0(W0_117) ),
    inference(cnfTransformation,[status(thm)],[f_205]) ).

tff(c_236,plain,
    aElementOf0(xu,xI),
    inference(cnfTransformation,[status(thm)],[f_386]) ).

tff(c_653,plain,
    ! [W1_238,W0_239] :
      ( aElement0(W1_238)
      | ~ aElementOf0(W1_238,W0_239)
      | ~ aSet0(W0_239) ),
    inference(cnfTransformation,[status(thm)],[f_137]) ).

tff(c_680,plain,
    ( aElement0(xu)
    | ~ aSet0(xI) ),
    inference(resolution,[status(thm)],[c_236,c_653]) ).

tff(c_682,plain,
    ~ aSet0(xI),
    inference(splitLeft,[status(thm)],[c_680]) ).

tff(c_685,plain,
    ~ aIdeal0(xI),
    inference(resolution,[status(thm)],[c_108,c_682]) ).

tff(c_689,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_218,c_685]) ).

tff(c_690,plain,
    aElement0(xu),
    inference(splitRight,[status(thm)],[c_680]) ).

tff(c_246,plain,
    doDivides0(xu,xa),
    inference(cnfTransformation,[status(thm)],[f_399]) ).

tff(c_1829,plain,
    ! [W1_272,W0_273] :
      ( aDivisorOf0(W1_272,W0_273)
      | ~ doDivides0(W1_272,W0_273)
      | ~ aElement0(W1_272)
      | ~ aElement0(W0_273) ),
    inference(cnfTransformation,[status(thm)],[f_304]) ).

tff(c_1835,plain,
    ( aDivisorOf0(xu,xa)
    | ~ aElement0(xu)
    | ~ aElement0(xa) ),
    inference(resolution,[status(thm)],[c_246,c_1829]) ).

tff(c_1839,plain,
    aDivisorOf0(xu,xa),
    inference(demodulation,[status(thm),theory(equality)],[c_210,c_690,c_1835]) ).

tff(c_1841,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_463,c_1839]) ).

tff(c_1843,plain,
    aDivisorOf0(xu,xa),
    inference(splitRight,[status(thm)],[c_238]) ).

tff(c_1967,plain,
    ! [W1_276,W0_277] :
      ( aElement0(W1_276)
      | ~ aDivisorOf0(W1_276,W0_277)
      | ~ aElement0(W0_277) ),
    inference(cnfTransformation,[status(thm)],[f_304]) ).

tff(c_1970,plain,
    ( aElement0(xu)
    | ~ aElement0(xa) ),
    inference(resolution,[status(thm)],[c_1843,c_1967]) ).

tff(c_1973,plain,
    aElement0(xu),
    inference(demodulation,[status(thm),theory(equality)],[c_210,c_1970]) ).

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

tff(c_258,plain,
    xr = sz00,
    inference(cnfTransformation,[status(thm)],[f_413]) ).

tff(c_252,plain,
    sdtpldt0(sdtasdt0(xq,xu),xr) = xb,
    inference(cnfTransformation,[status(thm)],[f_410]) ).

tff(c_260,plain,
    sdtpldt0(sdtasdt0(xq,xu),sz00) = xb,
    inference(demodulation,[status(thm),theory(equality)],[c_258,c_252]) ).

tff(c_256,plain,
    aElement0(xq),
    inference(cnfTransformation,[status(thm)],[f_410]) ).

tff(c_2753,plain,
    ! [W1_306,W0_307] :
      ( ( sdtasdt0(W1_306,W0_307) = sdtasdt0(W0_307,W1_306) )
      | ~ aElement0(W1_306)
      | ~ aElement0(W0_307) ),
    inference(cnfTransformation,[status(thm)],[f_79]) ).

tff(c_2824,plain,
    ! [W0_309] :
      ( ( sdtasdt0(xq,W0_309) = sdtasdt0(W0_309,xq) )
      | ~ aElement0(W0_309) ),
    inference(resolution,[status(thm)],[c_256,c_2753]) ).

tff(c_2868,plain,
    sdtasdt0(xu,xq) = sdtasdt0(xq,xu),
    inference(resolution,[status(thm)],[c_1973,c_2824]) ).

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_2923,plain,
    ( aElement0(sdtasdt0(xq,xu))
    | ~ aElement0(xq)
    | ~ aElement0(xu) ),
    inference(superposition,[status(thm),theory(equality)],[c_2868,c_12]) ).

tff(c_2927,plain,
    aElement0(sdtasdt0(xq,xu)),
    inference(demodulation,[status(thm),theory(equality)],[c_1973,c_256,c_2923]) ).

tff(c_20,plain,
    ! [W0_12] :
      ( ( sdtpldt0(W0_12,sz00) = W0_12 )
      | ~ aElement0(W0_12) ),
    inference(cnfTransformation,[status(thm)],[f_67]) ).

tff(c_2946,plain,
    sdtpldt0(sdtasdt0(xq,xu),sz00) = sdtasdt0(xq,xu),
    inference(resolution,[status(thm)],[c_2927,c_20]) ).

tff(c_2959,plain,
    sdtasdt0(xq,xu) = xb,
    inference(demodulation,[status(thm),theory(equality)],[c_260,c_2946]) ).

tff(c_2963,plain,
    sdtasdt0(xu,xq) = xb,
    inference(demodulation,[status(thm),theory(equality)],[c_2959,c_2868]) ).

tff(c_4488,plain,
    ! [W0_347,W2_348] :
      ( doDivides0(W0_347,sdtasdt0(W0_347,W2_348))
      | ~ aElement0(W2_348)
      | ~ aElement0(sdtasdt0(W0_347,W2_348))
      | ~ aElement0(W0_347) ),
    inference(cnfTransformation,[status(thm)],[f_295]) ).

tff(c_4521,plain,
    ( doDivides0(xu,xb)
    | ~ aElement0(xq)
    | ~ aElement0(sdtasdt0(xu,xq))
    | ~ aElement0(xu) ),
    inference(superposition,[status(thm),theory(equality)],[c_2963,c_4488]) ).

tff(c_4662,plain,
    doDivides0(xu,xb),
    inference(demodulation,[status(thm),theory(equality)],[c_1973,c_208,c_2963,c_256,c_4521]) ).

tff(c_4664,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_248,c_4662]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : RNG119+1 : 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
% 0.14/0.35  % Computer : n016.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 18:24:38 EDT 2023
% 0.14/0.36  % CPUTime  : 
% 7.91/2.88  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.91/2.89  
% 7.91/2.89  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 7.91/2.92  
% 7.91/2.92  Inference rules
% 7.91/2.92  ----------------------
% 7.91/2.92  #Ref     : 0
% 7.91/2.92  #Sup     : 1086
% 7.91/2.92  #Fact    : 0
% 7.91/2.92  #Define  : 0
% 7.91/2.92  #Split   : 7
% 7.91/2.92  #Chain   : 0
% 7.91/2.92  #Close   : 0
% 7.91/2.92  
% 7.91/2.92  Ordering : KBO
% 7.91/2.92  
% 7.91/2.92  Simplification rules
% 7.91/2.92  ----------------------
% 7.91/2.92  #Subsume      : 23
% 7.91/2.92  #Demod        : 923
% 7.91/2.92  #Tautology    : 571
% 7.91/2.92  #SimpNegUnit  : 33
% 7.91/2.92  #BackRed      : 3
% 7.91/2.92  
% 7.91/2.92  #Partial instantiations: 0
% 7.91/2.92  #Strategies tried      : 1
% 7.91/2.92  
% 7.91/2.92  Timing (in seconds)
% 7.91/2.92  ----------------------
% 7.91/2.93  Preprocessing        : 0.76
% 7.91/2.93  Parsing              : 0.37
% 7.91/2.93  CNF conversion       : 0.07
% 7.91/2.93  Main loop            : 1.09
% 7.91/2.93  Inferencing          : 0.36
% 7.91/2.93  Reduction            : 0.38
% 7.91/2.93  Demodulation         : 0.28
% 7.91/2.93  BG Simplification    : 0.06
% 7.91/2.93  Subsumption          : 0.20
% 7.91/2.93  Abstraction          : 0.04
% 7.91/2.93  MUC search           : 0.00
% 7.91/2.93  Cooper               : 0.00
% 7.91/2.93  Total                : 1.91
% 7.91/2.93  Index Insertion      : 0.00
% 7.91/2.93  Index Deletion       : 0.00
% 7.91/2.93  Index Matching       : 0.00
% 7.91/2.93  BG Taut test         : 0.00
%------------------------------------------------------------------------------