TSTP Solution File: RNG103+1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : RNG103+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 : n002.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 10:54:58 EDT 2023

% Result   : Theorem 16.61s 6.89s
% Output   : CNFRefutation 16.61s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   58
% Syntax   : Number of formulae    :   87 (  20 unt;  49 typ;   1 def)
%            Number of atoms       :   72 (  21 equ)
%            Maximal formula atoms :    6 (   1 avg)
%            Number of connectives :   55 (  21   ~;  17   |;  10   &)
%                                         (   2 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   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    :   38 (  38 usr;   8 con; 0-4 aty)
%            Number of variables   :   23 (;  22   !;   1   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ sdteqdtlpzmzozddtrp0 > aGcdOfAnd0 > misRelativelyPrime0 > iLess0 > doDivides0 > aElementOf0 > aDivisorOf0 > aSet0 > aNaturalNumber0 > aIdeal0 > aElement0 > sdtpldt1 > sdtpldt0 > sdtasdt0 > sdtasasdt0 > #nlpp > smndt0 > slsdtgt0 > sbrdtbr0 > xz > xy > xx > xv > xu > xc > 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('#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(xu,type,
    xu: $i ).

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

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

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(xy,type,
    xy: $i ).

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

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

tff(xx,type,
    xx: $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(xz,type,
    xz: $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(xv,type,
    xv: $i ).

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

tff(f_359,negated_conjecture,
    sdtpldt0(xx,xy) != sdtasdt0(xc,sdtpldt0(xu,xv)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).

tff(f_354,hypothesis,
    ( aElement0(xu)
    & ( sdtasdt0(xc,xu) = xx ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1956) ).

tff(f_346,hypothesis,
    aElement0(xc),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1905) ).

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_351,hypothesis,
    ( aElementOf0(xx,slsdtgt0(xc))
    & aElementOf0(xy,slsdtgt0(xc))
    & aElement0(xz) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1933) ).

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

tff(f_53,axiom,
    ! [W0,W1] :
      ( ( aElement0(W0)
        & aElement0(W1) )
     => ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddComm) ).

tff(f_357,hypothesis,
    ( aElement0(xv)
    & ( sdtasdt0(xc,xv) = xy ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1979) ).

tff(f_103,axiom,
    ! [W0,W1,W2] :
      ( ( aElement0(W0)
        & aElement0(W1)
        & aElement0(W2) )
     => ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
        & ( sdtasdt0(sdtpldt0(W1,W2),W0) = sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAMDistr) ).

tff(c_222,plain,
    sdtasdt0(xc,sdtpldt0(xu,xv)) != sdtpldt0(xx,xy),
    inference(cnfTransformation,[status(thm)],[f_359]) ).

tff(c_216,plain,
    aElement0(xu),
    inference(cnfTransformation,[status(thm)],[f_354]) ).

tff(c_206,plain,
    aElement0(xc),
    inference(cnfTransformation,[status(thm)],[f_346]) ).

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

tff(c_212,plain,
    aElementOf0(xx,slsdtgt0(xc)),
    inference(cnfTransformation,[status(thm)],[f_351]) ).

tff(c_535,plain,
    ! [W1_233,W0_234] :
      ( aElement0(W1_233)
      | ~ aElementOf0(W1_233,W0_234)
      | ~ aSet0(W0_234) ),
    inference(cnfTransformation,[status(thm)],[f_137]) ).

tff(c_542,plain,
    ( aElement0(xx)
    | ~ aSet0(slsdtgt0(xc)) ),
    inference(resolution,[status(thm)],[c_212,c_535]) ).

tff(c_548,plain,
    ~ aSet0(slsdtgt0(xc)),
    inference(splitLeft,[status(thm)],[c_542]) ).

tff(c_551,plain,
    ~ aElement0(xc),
    inference(resolution,[status(thm)],[c_188,c_548]) ).

tff(c_558,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_206,c_551]) ).

tff(c_560,plain,
    aSet0(slsdtgt0(xc)),
    inference(splitRight,[status(thm)],[c_542]) ).

tff(c_210,plain,
    aElementOf0(xy,slsdtgt0(xc)),
    inference(cnfTransformation,[status(thm)],[f_351]) ).

tff(c_543,plain,
    ( aElement0(xy)
    | ~ aSet0(slsdtgt0(xc)) ),
    inference(resolution,[status(thm)],[c_210,c_535]) ).

tff(c_629,plain,
    aElement0(xy),
    inference(demodulation,[status(thm),theory(equality)],[c_560,c_543]) ).

tff(c_559,plain,
    aElement0(xx),
    inference(splitRight,[status(thm)],[c_542]) ).

tff(c_1297,plain,
    ! [W1_267,W0_268] :
      ( ( sdtpldt0(W1_267,W0_268) = sdtpldt0(W0_268,W1_267) )
      | ~ aElement0(W1_267)
      | ~ aElement0(W0_268) ),
    inference(cnfTransformation,[status(thm)],[f_53]) ).

tff(c_15275,plain,
    ! [W0_478] :
      ( ( sdtpldt0(xx,W0_478) = sdtpldt0(W0_478,xx) )
      | ~ aElement0(W0_478) ),
    inference(resolution,[status(thm)],[c_559,c_1297]) ).

tff(c_15467,plain,
    sdtpldt0(xy,xx) = sdtpldt0(xx,xy),
    inference(resolution,[status(thm)],[c_629,c_15275]) ).

tff(c_220,plain,
    aElement0(xv),
    inference(cnfTransformation,[status(thm)],[f_357]) ).

tff(c_7088,plain,
    ! [W0_374] :
      ( ( sdtpldt0(xu,W0_374) = sdtpldt0(W0_374,xu) )
      | ~ aElement0(W0_374) ),
    inference(resolution,[status(thm)],[c_216,c_1297]) ).

tff(c_7199,plain,
    sdtpldt0(xv,xu) = sdtpldt0(xu,xv),
    inference(resolution,[status(thm)],[c_220,c_7088]) ).

tff(c_214,plain,
    sdtasdt0(xc,xu) = xx,
    inference(cnfTransformation,[status(thm)],[f_354]) ).

tff(c_218,plain,
    sdtasdt0(xc,xv) = xy,
    inference(cnfTransformation,[status(thm)],[f_357]) ).

tff(c_5303,plain,
    ! [W0_365,W1_366,W2_367] :
      ( ( sdtpldt0(sdtasdt0(W0_365,W1_366),sdtasdt0(W0_365,W2_367)) = sdtasdt0(W0_365,sdtpldt0(W1_366,W2_367)) )
      | ~ aElement0(W2_367)
      | ~ aElement0(W1_366)
      | ~ aElement0(W0_365) ),
    inference(cnfTransformation,[status(thm)],[f_103]) ).

tff(c_5666,plain,
    ! [W2_367] :
      ( ( sdtpldt0(xy,sdtasdt0(xc,W2_367)) = sdtasdt0(xc,sdtpldt0(xv,W2_367)) )
      | ~ aElement0(W2_367)
      | ~ aElement0(xv)
      | ~ aElement0(xc) ),
    inference(superposition,[status(thm),theory(equality)],[c_218,c_5303]) ).

tff(c_23126,plain,
    ! [W2_517] :
      ( ( sdtpldt0(xy,sdtasdt0(xc,W2_517)) = sdtasdt0(xc,sdtpldt0(xv,W2_517)) )
      | ~ aElement0(W2_517) ),
    inference(demodulation,[status(thm),theory(equality)],[c_206,c_220,c_5666]) ).

tff(c_23194,plain,
    ( ( sdtasdt0(xc,sdtpldt0(xv,xu)) = sdtpldt0(xy,xx) )
    | ~ aElement0(xu) ),
    inference(superposition,[status(thm),theory(equality)],[c_214,c_23126]) ).

tff(c_23222,plain,
    sdtasdt0(xc,sdtpldt0(xu,xv)) = sdtpldt0(xx,xy),
    inference(demodulation,[status(thm),theory(equality)],[c_216,c_15467,c_7199,c_23194]) ).

tff(c_23224,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_222,c_23222]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : RNG103+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
% 0.13/0.35  % Computer : n002.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 18:19:16 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 16.61/6.89  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 16.61/6.90  
% 16.61/6.90  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 16.61/6.93  
% 16.61/6.93  Inference rules
% 16.61/6.93  ----------------------
% 16.61/6.93  #Ref     : 0
% 16.61/6.93  #Sup     : 5253
% 16.61/6.93  #Fact    : 0
% 16.61/6.93  #Define  : 0
% 16.61/6.93  #Split   : 15
% 16.61/6.93  #Chain   : 0
% 16.61/6.93  #Close   : 0
% 16.61/6.93  
% 16.61/6.93  Ordering : KBO
% 16.61/6.93  
% 16.61/6.93  Simplification rules
% 16.61/6.93  ----------------------
% 16.61/6.93  #Subsume      : 103
% 16.61/6.93  #Demod        : 6694
% 16.61/6.93  #Tautology    : 1938
% 16.61/6.93  #SimpNegUnit  : 55
% 16.61/6.93  #BackRed      : 9
% 16.61/6.93  
% 16.61/6.93  #Partial instantiations: 0
% 16.61/6.93  #Strategies tried      : 1
% 16.61/6.93  
% 16.61/6.93  Timing (in seconds)
% 16.61/6.93  ----------------------
% 16.61/6.93  Preprocessing        : 0.65
% 16.61/6.93  Parsing              : 0.31
% 16.61/6.93  CNF conversion       : 0.06
% 16.61/6.93  Main loop            : 5.26
% 16.61/6.93  Inferencing          : 1.15
% 16.61/6.93  Reduction            : 2.79
% 16.61/6.93  Demodulation         : 2.40
% 16.61/6.93  BG Simplification    : 0.10
% 16.61/6.93  Subsumption          : 0.98
% 16.61/6.93  Abstraction          : 0.11
% 16.61/6.93  MUC search           : 0.00
% 16.61/6.93  Cooper               : 0.00
% 16.61/6.93  Total                : 5.96
% 16.61/6.93  Index Insertion      : 0.00
% 16.61/6.93  Index Deletion       : 0.00
% 16.61/6.93  Index Matching       : 0.00
% 16.61/6.93  BG Taut test         : 0.00
%------------------------------------------------------------------------------