TSTP Solution File: RNG108+4 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : RNG108+4 : 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 : n029.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 7.06s 2.62s
% Output   : CNFRefutation 7.26s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   61
% Syntax   : Number of formulae    :   99 (  25 unt;  54 typ;   0 def)
%            Number of atoms       :  107 (  30 equ)
%            Maximal formula atoms :   18 (   2 avg)
%            Number of connectives :  104 (  42   ~;  33   |;  21   &)
%                                         (   3 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   93 (  46   >;  47   *;   0   +;   0  <<)
%            Number of predicates  :   13 (  11 usr;   1 prp; 0-3 aty)
%            Number of functors    :   43 (  43 usr;   8 con; 0-4 aty)
%            Number of variables   :   30 (;  22   !;   8   ?;   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_24 > #skF_6 > #skF_17 > #skF_25 > #skF_20 > #skF_4 > #skF_8 > #skF_14 > #skF_15 > #skF_29 > #skF_26 > #skF_18 > #skF_23 > #skF_28 > #skF_5 > #skF_19 > #skF_7 > #skF_9 > #skF_13 > #skF_11 > #skF_3 > #skF_2 > #skF_27 > #skF_12 > #skF_1 > #skF_16 > #skF_21 > #skF_30 > #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('#skF_24',type,
    '#skF_24': $i > $i ).

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('#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_29',type,
    '#skF_29': $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('#skF_28',type,
    '#skF_28': $i > $i ).

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_27',type,
    '#skF_27': $i > $i ).

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_30',type,
    '#skF_30': $i > $i ).

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

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

tff(f_115,axiom,
    ! [W0] :
      ( aElement0(W0)
     => ( ( sdtasdt0(W0,sz00) = sz00 )
        & ( sz00 = sdtasdt0(sz00,W0) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulZero) ).

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

tff(f_93,axiom,
    ! [W0] :
      ( aElement0(W0)
     => ( ( sdtasdt0(W0,sz10) = W0 )
        & ( W0 = sdtasdt0(sz10,W0) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulUnit) ).

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

tff(f_480,negated_conjecture,
    ~ ( ( ? [W0] :
            ( aElement0(W0)
            & ( sdtasdt0(xa,W0) = sz00 ) )
        | aElementOf0(sz00,slsdtgt0(xa)) )
      & ( ? [W0] :
            ( aElement0(W0)
            & ( sdtasdt0(xa,W0) = xa ) )
        | aElementOf0(xa,slsdtgt0(xa)) )
      & ( ? [W0] :
            ( aElement0(W0)
            & ( sdtasdt0(xb,W0) = sz00 ) )
        | aElementOf0(sz00,slsdtgt0(xb)) )
      & ( ? [W0] :
            ( aElement0(W0)
            & ( sdtasdt0(xb,W0) = xb ) )
        | aElementOf0(xb,slsdtgt0(xb)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).

tff(f_452,hypothesis,
    ( aSet0(xI)
    & ! [W0] :
        ( aElementOf0(W0,xI)
       => ( ! [W1] :
              ( aElementOf0(W1,xI)
             => aElementOf0(sdtpldt0(W0,W1),xI) )
          & ! [W1] :
              ( aElement0(W1)
             => aElementOf0(sdtasdt0(W1,W0),xI) ) ) )
    & aIdeal0(xI)
    & ! [W0] :
        ( aElementOf0(W0,slsdtgt0(xa))
      <=> ? [W1] :
            ( aElement0(W1)
            & ( sdtasdt0(xa,W1) = W0 ) ) )
    & ! [W0] :
        ( aElementOf0(W0,slsdtgt0(xb))
      <=> ? [W1] :
            ( aElement0(W1)
            & ( sdtasdt0(xb,W1) = W0 ) ) )
    & ! [W0] :
        ( aElementOf0(W0,xI)
      <=> ? [W1,W2] :
            ( aElementOf0(W1,slsdtgt0(xa))
            & aElementOf0(W2,slsdtgt0(xb))
            & ( sdtpldt0(W1,W2) = W0 ) ) )
    & ( xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2174) ).

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

tff(c_2607,plain,
    ! [W0_334] :
      ( ( sdtasdt0(W0_334,sz00) = sz00 )
      | ~ aElement0(W0_334) ),
    inference(cnfTransformation,[status(thm)],[f_115]) ).

tff(c_2638,plain,
    sdtasdt0(xa,sz00) = sz00,
    inference(resolution,[status(thm)],[c_210,c_2607]) ).

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

tff(c_2671,plain,
    ! [W0_335] :
      ( ( sdtasdt0(W0_335,sz10) = W0_335 )
      | ~ aElement0(W0_335) ),
    inference(cnfTransformation,[status(thm)],[f_93]) ).

tff(c_2704,plain,
    sdtasdt0(xa,sz10) = xa,
    inference(resolution,[status(thm)],[c_210,c_2671]) ).

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

tff(c_322,plain,
    ! [W0_248] :
      ( ( sdtasdt0(xa,W0_248) != sz00 )
      | ~ aElement0(W0_248)
      | ~ aElementOf0(xa,slsdtgt0(xa))
      | ~ aElementOf0(sz00,slsdtgt0(xb))
      | ~ aElementOf0(xb,slsdtgt0(xb)) ),
    inference(cnfTransformation,[status(thm)],[f_480]) ).

tff(c_362,plain,
    ~ aElementOf0(xb,slsdtgt0(xb)),
    inference(splitLeft,[status(thm)],[c_322]) ).

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

tff(c_976,plain,
    ! [W0_277] :
      ( ( sdtasdt0(W0_277,sz10) = W0_277 )
      | ~ aElement0(W0_277) ),
    inference(cnfTransformation,[status(thm)],[f_93]) ).

tff(c_1006,plain,
    sdtasdt0(xb,sz10) = xb,
    inference(resolution,[status(thm)],[c_208,c_976]) ).

tff(c_1480,plain,
    ! [W1_296] :
      ( aElementOf0(sdtasdt0(xb,W1_296),slsdtgt0(xb))
      | ~ aElement0(W1_296) ),
    inference(cnfTransformation,[status(thm)],[f_452]) ).

tff(c_1492,plain,
    ( aElementOf0(xb,slsdtgt0(xb))
    | ~ aElement0(sz10) ),
    inference(superposition,[status(thm),theory(equality)],[c_1006,c_1480]) ).

tff(c_1498,plain,
    aElementOf0(xb,slsdtgt0(xb)),
    inference(demodulation,[status(thm),theory(equality)],[c_6,c_1492]) ).

tff(c_1500,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_362,c_1498]) ).

tff(c_1502,plain,
    aElementOf0(xb,slsdtgt0(xb)),
    inference(splitRight,[status(thm)],[c_322]) ).

tff(c_320,plain,
    ( ~ aElementOf0(sz00,slsdtgt0(xa))
    | ~ aElementOf0(xa,slsdtgt0(xa))
    | ~ aElementOf0(sz00,slsdtgt0(xb))
    | ~ aElementOf0(xb,slsdtgt0(xb)) ),
    inference(cnfTransformation,[status(thm)],[f_480]) ).

tff(c_352,plain,
    ~ aElementOf0(xb,slsdtgt0(xb)),
    inference(splitLeft,[status(thm)],[c_320]) ).

tff(c_1505,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_1502,c_352]) ).

tff(c_1507,plain,
    aElementOf0(xb,slsdtgt0(xb)),
    inference(splitRight,[status(thm)],[c_320]) ).

tff(c_336,plain,
    ! [W0_251] :
      ( ~ aElementOf0(sz00,slsdtgt0(xa))
      | ~ aElementOf0(xa,slsdtgt0(xa))
      | ~ aElementOf0(sz00,slsdtgt0(xb))
      | ( sdtasdt0(xb,W0_251) != xb )
      | ~ aElement0(W0_251) ),
    inference(cnfTransformation,[status(thm)],[f_480]) ).

tff(c_1508,plain,
    ~ aElementOf0(sz00,slsdtgt0(xb)),
    inference(splitLeft,[status(thm)],[c_336]) ).

tff(c_1525,plain,
    ! [W0_301] :
      ( ( sdtasdt0(W0_301,sz00) = sz00 )
      | ~ aElement0(W0_301) ),
    inference(cnfTransformation,[status(thm)],[f_115]) ).

tff(c_1555,plain,
    sdtasdt0(xb,sz00) = sz00,
    inference(resolution,[status(thm)],[c_208,c_1525]) ).

tff(c_2384,plain,
    ! [W1_326] :
      ( aElementOf0(sdtasdt0(xb,W1_326),slsdtgt0(xb))
      | ~ aElement0(W1_326) ),
    inference(cnfTransformation,[status(thm)],[f_452]) ).

tff(c_2400,plain,
    ( aElementOf0(sz00,slsdtgt0(xb))
    | ~ aElement0(sz00) ),
    inference(superposition,[status(thm),theory(equality)],[c_1555,c_2384]) ).

tff(c_2408,plain,
    aElementOf0(sz00,slsdtgt0(xb)),
    inference(demodulation,[status(thm),theory(equality)],[c_4,c_2400]) ).

tff(c_2410,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_1508,c_2408]) ).

tff(c_2412,plain,
    aElementOf0(sz00,slsdtgt0(xb)),
    inference(splitRight,[status(thm)],[c_336]) ).

tff(c_326,plain,
    ! [W0_248,W0_249] :
      ( ( sdtasdt0(xa,W0_248) != sz00 )
      | ~ aElement0(W0_248)
      | ( sdtasdt0(xa,W0_249) != xa )
      | ~ aElement0(W0_249)
      | ~ aElementOf0(sz00,slsdtgt0(xb))
      | ~ aElementOf0(xb,slsdtgt0(xb)) ),
    inference(cnfTransformation,[status(thm)],[f_480]) ).

tff(c_2917,plain,
    ! [W0_248,W0_249] :
      ( ( sdtasdt0(xa,W0_248) != sz00 )
      | ~ aElement0(W0_248)
      | ( sdtasdt0(xa,W0_249) != xa )
      | ~ aElement0(W0_249) ),
    inference(demodulation,[status(thm),theory(equality)],[c_1507,c_2412,c_326]) ).

tff(c_2919,plain,
    ! [W0_341] :
      ( ( sdtasdt0(xa,W0_341) != xa )
      | ~ aElement0(W0_341) ),
    inference(splitLeft,[status(thm)],[c_2917]) ).

tff(c_2940,plain,
    sdtasdt0(xa,sz10) != xa,
    inference(resolution,[status(thm)],[c_6,c_2919]) ).

tff(c_2960,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_2704,c_2940]) ).

tff(c_2962,plain,
    ! [W0_342] :
      ( ( sdtasdt0(xa,W0_342) != sz00 )
      | ~ aElement0(W0_342) ),
    inference(splitRight,[status(thm)],[c_2917]) ).

tff(c_2974,plain,
    sdtasdt0(xa,sz00) != sz00,
    inference(resolution,[status(thm)],[c_4,c_2962]) ).

tff(c_2999,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_2638,c_2974]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : RNG108+4 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13  % 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
% 0.14/0.34  % Computer : n029.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 300
% 0.14/0.34  % DateTime : Thu Aug  3 18:13:07 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 7.06/2.62  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.06/2.63  
% 7.06/2.63  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 7.26/2.66  
% 7.26/2.66  Inference rules
% 7.26/2.66  ----------------------
% 7.26/2.66  #Ref     : 0
% 7.26/2.66  #Sup     : 772
% 7.26/2.66  #Fact    : 0
% 7.26/2.66  #Define  : 0
% 7.26/2.66  #Split   : 17
% 7.26/2.66  #Chain   : 0
% 7.26/2.66  #Close   : 0
% 7.26/2.66  
% 7.26/2.66  Ordering : KBO
% 7.26/2.66  
% 7.26/2.66  Simplification rules
% 7.26/2.66  ----------------------
% 7.26/2.66  #Subsume      : 27
% 7.26/2.66  #Demod        : 321
% 7.26/2.66  #Tautology    : 518
% 7.26/2.66  #SimpNegUnit  : 3
% 7.26/2.66  #BackRed      : 0
% 7.26/2.66  
% 7.26/2.66  #Partial instantiations: 0
% 7.26/2.66  #Strategies tried      : 1
% 7.26/2.66  
% 7.26/2.66  Timing (in seconds)
% 7.26/2.66  ----------------------
% 7.26/2.66  Preprocessing        : 0.75
% 7.26/2.66  Parsing              : 0.36
% 7.26/2.66  CNF conversion       : 0.07
% 7.26/2.67  Main loop            : 0.84
% 7.26/2.67  Inferencing          : 0.25
% 7.26/2.67  Reduction            : 0.28
% 7.26/2.67  Demodulation         : 0.20
% 7.26/2.67  BG Simplification    : 0.06
% 7.26/2.67  Subsumption          : 0.18
% 7.26/2.67  Abstraction          : 0.03
% 7.26/2.67  MUC search           : 0.00
% 7.26/2.67  Cooper               : 0.00
% 7.26/2.67  Total                : 1.65
% 7.26/2.67  Index Insertion      : 0.00
% 7.26/2.67  Index Deletion       : 0.00
% 7.26/2.67  Index Matching       : 0.00
% 7.26/2.67  BG Taut test         : 0.00
%------------------------------------------------------------------------------