TSTP Solution File: RNG126+4 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : RNG126+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 : 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 10:55:03 EDT 2023

% Result   : Theorem 68.50s 49.98s
% Output   : CNFRefutation 68.50s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   77
% Syntax   : Number of formulae    :   95 (  12 unt;  71 typ;   0 def)
%            Number of atoms       :   75 (  19 equ)
%            Maximal formula atoms :   18 (   3 avg)
%            Number of connectives :   67 (  16   ~;  12   |;  25   &)
%                                         (   5 <=>;   9  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   97 (  50   >;  47   *;   0   +;   0  <<)
%            Number of predicates  :   13 (  11 usr;   1 prp; 0-3 aty)
%            Number of functors    :   60 (  60 usr;  21 con; 0-4 aty)
%            Number of variables   :   33 (;  20   !;  13   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ sdteqdtlpzmzozddtrp0 > aGcdOfAnd0 > misRelativelyPrime0 > iLess0 > doDivides0 > aElementOf0 > aDivisorOf0 > aSet0 > aNaturalNumber0 > aIdeal0 > aElement0 > sdtpldt1 > sdtpldt0 > sdtasdt0 > sdtasasdt0 > #nlpp > smndt0 > slsdtgt0 > sbrdtbr0 > xu > xc > xb > xa > xI > sz10 > sz00 > #skF_33 > #skF_41 > #skF_22 > #skF_24 > #skF_6 > #skF_31 > #skF_17 > #skF_25 > #skF_20 > #skF_36 > #skF_43 > #skF_40 > #skF_4 > #skF_37 > #skF_8 > #skF_14 > #skF_15 > #skF_29 > #skF_26 > #skF_18 > #skF_23 > #skF_28 > #skF_5 > #skF_19 > #skF_38 > #skF_7 > #skF_32 > #skF_39 > #skF_9 > #skF_13 > #skF_42 > #skF_11 > #skF_3 > #skF_2 > #skF_35 > #skF_27 > #skF_44 > #skF_12 > #skF_46 > #skF_1 > #skF_16 > #skF_21 > #skF_45 > #skF_30 > #skF_10 > #skF_34

%Foreground sorts:

%Background operators:

%Foreground operators:
tff('#skF_33',type,
    '#skF_33': $i ).

tff('#skF_41',type,
    '#skF_41': $i ).

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('#skF_31',type,
    '#skF_31': $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('#skF_36',type,
    '#skF_36': $i ).

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

tff('#skF_43',type,
    '#skF_43': $i ).

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

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

tff('#skF_40',type,
    '#skF_40': $i ).

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

tff('#skF_37',type,
    '#skF_37': $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_38',type,
    '#skF_38': $i > $i ).

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

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

tff('#skF_32',type,
    '#skF_32': $i ).

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

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

tff('#skF_39',type,
    '#skF_39': $i > $i ).

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_42',type,
    '#skF_42': $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_35',type,
    '#skF_35': $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_44',type,
    '#skF_44': $i ).

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

tff('#skF_46',type,
    '#skF_46': $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_45',type,
    '#skF_45': $i > $i ).

tff('#skF_30',type,
    '#skF_30': $i > $i ).

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

tff('#skF_34',type,
    '#skF_34': $i ).

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(f_580,negated_conjecture,
    ~ ( ! [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,W1] :
              ( aElementOf0(W0,slsdtgt0(xa))
              & aElementOf0(W1,slsdtgt0(xb))
              & ( sdtpldt0(W0,W1) = xc ) )
          | aElementOf0(xc,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).

tff(f_534,hypothesis,
    ( ? [W0,W1] :
        ( aElementOf0(W0,slsdtgt0(xa))
        & aElementOf0(W1,slsdtgt0(xb))
        & ( sdtpldt0(W0,W1) = xu ) )
    & aElementOf0(xu,xI)
    & ( xu != sz00 )
    & ! [W0] :
        ( ( ( ? [W1,W2] :
                ( aElementOf0(W1,slsdtgt0(xa))
                & aElementOf0(W2,slsdtgt0(xb))
                & ( sdtpldt0(W1,W2) = W0 ) )
            | aElementOf0(W0,xI) )
          & ( W0 != sz00 ) )
       => ~ iLess0(sbrdtbr0(W0),sbrdtbr0(xu)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2273) ).

tff(f_555,hypothesis,
    ? [W0] :
      ( aElement0(W0)
      & ( sdtasdt0(xu,W0) = xc ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2744) ).

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

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(c_290,plain,
    sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)) = xI,
    inference(cnfTransformation,[status(thm)],[f_452]) ).

tff(c_400,plain,
    ~ aElementOf0(xc,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))),
    inference(cnfTransformation,[status(thm)],[f_580]) ).

tff(c_416,plain,
    ~ aElementOf0(xc,xI),
    inference(demodulation,[status(thm),theory(equality)],[c_290,c_400]) ).

tff(c_368,plain,
    aElementOf0(xu,xI),
    inference(cnfTransformation,[status(thm)],[f_534]) ).

tff(c_398,plain,
    aElement0('#skF_44'),
    inference(cnfTransformation,[status(thm)],[f_555]) ).

tff(c_396,plain,
    sdtasdt0(xu,'#skF_44') = xc,
    inference(cnfTransformation,[status(thm)],[f_555]) ).

tff(c_300,plain,
    aSet0(xI),
    inference(cnfTransformation,[status(thm)],[f_452]) ).

tff(c_2653,plain,
    ! [W1_315,W0_316] :
      ( aElement0(W1_315)
      | ~ aElementOf0(W1_315,W0_316)
      | ~ aSet0(W0_316) ),
    inference(cnfTransformation,[status(thm)],[f_137]) ).

tff(c_2683,plain,
    ( aElement0(xu)
    | ~ aSet0(xI) ),
    inference(resolution,[status(thm)],[c_368,c_2653]) ).

tff(c_2705,plain,
    aElement0(xu),
    inference(demodulation,[status(thm),theory(equality)],[c_300,c_2683]) ).

tff(c_29864,plain,
    ! [W1_496,W0_497] :
      ( ( sdtasdt0(W1_496,W0_497) = sdtasdt0(W0_497,W1_496) )
      | ~ aElement0(W1_496)
      | ~ aElement0(W0_497) ),
    inference(cnfTransformation,[status(thm)],[f_79]) ).

tff(c_136536,plain,
    ! [W0_918] :
      ( ( sdtasdt0(W0_918,'#skF_44') = sdtasdt0('#skF_44',W0_918) )
      | ~ aElement0(W0_918) ),
    inference(resolution,[status(thm)],[c_398,c_29864]) ).

tff(c_137034,plain,
    sdtasdt0(xu,'#skF_44') = sdtasdt0('#skF_44',xu),
    inference(resolution,[status(thm)],[c_2705,c_136536]) ).

tff(c_137312,plain,
    sdtasdt0('#skF_44',xu) = xc,
    inference(demodulation,[status(thm),theory(equality)],[c_396,c_137034]) ).

tff(c_316,plain,
    ! [W1_247,W0_243] :
      ( aElementOf0(sdtasdt0(W1_247,W0_243),xI)
      | ~ aElement0(W1_247)
      | ~ aElementOf0(W0_243,xI) ),
    inference(cnfTransformation,[status(thm)],[f_452]) ).

tff(c_137428,plain,
    ( aElementOf0(xc,xI)
    | ~ aElement0('#skF_44')
    | ~ aElementOf0(xu,xI) ),
    inference(superposition,[status(thm),theory(equality)],[c_137312,c_316]) ).

tff(c_137495,plain,
    aElementOf0(xc,xI),
    inference(demodulation,[status(thm),theory(equality)],[c_368,c_398,c_137428]) ).

tff(c_137497,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_416,c_137495]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : RNG126+4 : 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 : n016.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 18:25:53 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 68.50/49.98  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 68.50/49.99  
% 68.50/49.99  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 68.50/50.02  
% 68.50/50.02  Inference rules
% 68.50/50.02  ----------------------
% 68.50/50.02  #Ref     : 0
% 68.50/50.02  #Sup     : 31297
% 68.50/50.02  #Fact    : 0
% 68.50/50.02  #Define  : 0
% 68.50/50.02  #Split   : 139
% 68.50/50.02  #Chain   : 0
% 68.50/50.02  #Close   : 0
% 68.50/50.02  
% 68.50/50.02  Ordering : KBO
% 68.50/50.02  
% 68.50/50.02  Simplification rules
% 68.50/50.02  ----------------------
% 68.50/50.02  #Subsume      : 4514
% 68.50/50.02  #Demod        : 43496
% 68.50/50.02  #Tautology    : 9209
% 68.50/50.02  #SimpNegUnit  : 884
% 68.50/50.02  #BackRed      : 1304
% 68.50/50.02  
% 68.50/50.02  #Partial instantiations: 0
% 68.50/50.02  #Strategies tried      : 1
% 68.50/50.02  
% 68.50/50.02  Timing (in seconds)
% 68.50/50.02  ----------------------
% 68.50/50.02  Preprocessing        : 0.78
% 68.50/50.02  Parsing              : 0.37
% 68.50/50.02  CNF conversion       : 0.08
% 68.50/50.02  Main loop            : 48.15
% 68.50/50.02  Inferencing          : 5.27
% 68.50/50.02  Reduction            : 31.54
% 68.50/50.02  Demodulation         : 28.13
% 68.50/50.02  BG Simplification    : 0.23
% 68.50/50.02  Subsumption          : 9.31
% 68.50/50.02  Abstraction          : 0.33
% 68.50/50.02  MUC search           : 0.00
% 68.50/50.02  Cooper               : 0.00
% 68.50/50.02  Total                : 48.99
% 68.50/50.02  Index Insertion      : 0.00
% 68.50/50.02  Index Deletion       : 0.00
% 68.50/50.02  Index Matching       : 0.00
% 68.50/50.02  BG Taut test         : 0.00
%------------------------------------------------------------------------------