TSTP Solution File: RNG121+1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : RNG121+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 : n022.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 10:55:02 EDT 2023

% Result   : Theorem 54.78s 40.04s
% Output   : CNFRefutation 54.78s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   60
% Syntax   : Number of formulae    :   87 (  18 unt;  53 typ;   2 def)
%            Number of atoms       :   78 (  10 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :   75 (  31   ~;  25   |;  12   &)
%                                         (   4 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   4 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   :   27 (;  24   !;   3   ?;   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_415,negated_conjecture,
    ~ aElementOf0(xb,xI),
    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_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_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_361,hypothesis,
    ( aIdeal0(xI)
    & ( xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2174) ).

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(c_262,plain,
    ~ aElementOf0(xb,xI),
    inference(cnfTransformation,[status(thm)],[f_415]) ).

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

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

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

tff(c_1683,plain,
    ! [W0_267] :
      ( ( sdtpldt0(sz00,W0_267) = W0_267 )
      | ~ aElement0(W0_267) ),
    inference(cnfTransformation,[status(thm)],[f_67]) ).

tff(c_1713,plain,
    sdtpldt0(sz00,xb) = xb,
    inference(resolution,[status(thm)],[c_208,c_1683]) ).

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

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

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

tff(c_6392,plain,
    ! [W0_391,W1_392,W3_393] :
      ( aElementOf0('#skF_7'(W0_391,W1_392,sdtpldt1(W0_391,W1_392),W3_393),W0_391)
      | ~ aElementOf0(W3_393,sdtpldt1(W0_391,W1_392))
      | ~ aSet0(W1_392)
      | ~ aSet0(W0_391) ),
    inference(cnfTransformation,[status(thm)],[f_172]) ).

tff(c_6406,plain,
    ! [W3_393] :
      ( aElementOf0('#skF_7'(slsdtgt0(xa),slsdtgt0(xb),xI,W3_393),slsdtgt0(xa))
      | ~ aElementOf0(W3_393,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
      | ~ aSet0(slsdtgt0(xb))
      | ~ aSet0(slsdtgt0(xa)) ),
    inference(superposition,[status(thm),theory(equality)],[c_216,c_6392]) ).

tff(c_6410,plain,
    ! [W3_393] :
      ( aElementOf0('#skF_7'(slsdtgt0(xa),slsdtgt0(xb),xI,W3_393),slsdtgt0(xa))
      | ~ aElementOf0(W3_393,xI)
      | ~ aSet0(slsdtgt0(xb))
      | ~ aSet0(slsdtgt0(xa)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_216,c_6406]) ).

tff(c_80575,plain,
    ~ aSet0(slsdtgt0(xa)),
    inference(splitLeft,[status(thm)],[c_6410]) ).

tff(c_80578,plain,
    ~ aElement0(xa),
    inference(resolution,[status(thm)],[c_188,c_80575]) ).

tff(c_80585,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_210,c_80578]) ).

tff(c_80587,plain,
    aSet0(slsdtgt0(xa)),
    inference(splitRight,[status(thm)],[c_6410]) ).

tff(c_80586,plain,
    ! [W3_393] :
      ( ~ aSet0(slsdtgt0(xb))
      | aElementOf0('#skF_7'(slsdtgt0(xa),slsdtgt0(xb),xI,W3_393),slsdtgt0(xa))
      | ~ aElementOf0(W3_393,xI) ),
    inference(splitRight,[status(thm)],[c_6410]) ).

tff(c_80901,plain,
    ~ aSet0(slsdtgt0(xb)),
    inference(splitLeft,[status(thm)],[c_80586]) ).

tff(c_80904,plain,
    ~ aElement0(xb),
    inference(resolution,[status(thm)],[c_188,c_80901]) ).

tff(c_80911,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_208,c_80904]) ).

tff(c_80913,plain,
    aSet0(slsdtgt0(xb)),
    inference(splitRight,[status(thm)],[c_80586]) ).

tff(c_6250,plain,
    ! [W4_387,W5_388,W0_389,W1_390] :
      ( aElementOf0(sdtpldt0(W4_387,W5_388),sdtpldt1(W0_389,W1_390))
      | ~ aElementOf0(W5_388,W1_390)
      | ~ aElementOf0(W4_387,W0_389)
      | ~ aSet0(W1_390)
      | ~ aSet0(W0_389) ),
    inference(cnfTransformation,[status(thm)],[f_172]) ).

tff(c_6348,plain,
    ! [W4_387,W5_388] :
      ( aElementOf0(sdtpldt0(W4_387,W5_388),xI)
      | ~ aElementOf0(W5_388,slsdtgt0(xb))
      | ~ aElementOf0(W4_387,slsdtgt0(xa))
      | ~ aSet0(slsdtgt0(xb))
      | ~ aSet0(slsdtgt0(xa)) ),
    inference(superposition,[status(thm),theory(equality)],[c_216,c_6250]) ).

tff(c_90859,plain,
    ! [W4_751,W5_752] :
      ( aElementOf0(sdtpldt0(W4_751,W5_752),xI)
      | ~ aElementOf0(W5_752,slsdtgt0(xb))
      | ~ aElementOf0(W4_751,slsdtgt0(xa)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_80587,c_80913,c_6348]) ).

tff(c_91243,plain,
    ( aElementOf0(xb,xI)
    | ~ aElementOf0(xb,slsdtgt0(xb))
    | ~ aElementOf0(sz00,slsdtgt0(xa)) ),
    inference(superposition,[status(thm),theory(equality)],[c_1713,c_90859]) ).

tff(c_91406,plain,
    aElementOf0(xb,xI),
    inference(demodulation,[status(thm),theory(equality)],[c_226,c_220,c_91243]) ).

tff(c_91408,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_262,c_91406]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : RNG121+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
% 0.16/0.35  % Computer : n022.cluster.edu
% 0.16/0.35  % Model    : x86_64 x86_64
% 0.16/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.35  % Memory   : 8042.1875MB
% 0.16/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.35  % CPULimit : 300
% 0.16/0.35  % WCLimit  : 300
% 0.16/0.35  % DateTime : Thu Aug  3 17:57:48 EDT 2023
% 0.16/0.35  % CPUTime  : 
% 54.78/40.04  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 54.78/40.05  
% 54.78/40.05  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 54.78/40.08  
% 54.78/40.08  Inference rules
% 54.78/40.08  ----------------------
% 54.78/40.08  #Ref     : 0
% 54.78/40.08  #Sup     : 20234
% 54.78/40.08  #Fact    : 0
% 54.78/40.08  #Define  : 0
% 54.78/40.08  #Split   : 36
% 54.78/40.08  #Chain   : 0
% 54.78/40.08  #Close   : 0
% 54.78/40.08  
% 54.78/40.08  Ordering : KBO
% 54.78/40.08  
% 54.78/40.08  Simplification rules
% 54.78/40.08  ----------------------
% 54.78/40.08  #Subsume      : 1662
% 54.78/40.08  #Demod        : 32144
% 54.78/40.08  #Tautology    : 6953
% 54.78/40.08  #SimpNegUnit  : 222
% 54.78/40.08  #BackRed      : 29
% 54.78/40.08  
% 54.78/40.08  #Partial instantiations: 0
% 54.78/40.08  #Strategies tried      : 1
% 54.78/40.08  
% 54.78/40.08  Timing (in seconds)
% 54.78/40.08  ----------------------
% 54.78/40.08  Preprocessing        : 0.72
% 54.78/40.08  Parsing              : 0.34
% 54.78/40.08  CNF conversion       : 0.07
% 54.78/40.08  Main loop            : 38.24
% 54.78/40.08  Inferencing          : 4.01
% 54.78/40.08  Reduction            : 26.02
% 54.78/40.08  Demodulation         : 23.84
% 54.78/40.08  BG Simplification    : 0.20
% 54.78/40.08  Subsumption          : 6.65
% 54.78/40.08  Abstraction          : 0.29
% 54.78/40.08  MUC search           : 0.00
% 54.78/40.08  Cooper               : 0.00
% 54.78/40.08  Total                : 39.01
% 54.78/40.08  Index Insertion      : 0.00
% 54.78/40.08  Index Deletion       : 0.00
% 54.78/40.08  Index Matching       : 0.00
% 54.78/40.08  BG Taut test         : 0.00
%------------------------------------------------------------------------------