TSTP Solution File: RNG125+1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : RNG125+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 : n021.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 7.11s 2.63s
% Output   : CNFRefutation 7.11s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   60
% Syntax   : Number of formulae    :   88 (  20 unt;  51 typ;   2 def)
%            Number of atoms       :   73 (   3 equ)
%            Maximal formula atoms :    7 (   1 avg)
%            Number of connectives :   67 (  31   ~;  18   |;   9   &)
%                                         (   2 <=>;   7  =>;   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    :   40 (  40 usr;  10 con; 0-4 aty)
%            Number of variables   :   18 (;  18   !;   0   ?;   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_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('#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(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_390,hypothesis,
    ~ ( aDivisorOf0(xu,xa)
      & aDivisorOf0(xu,xb) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2383) ).

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

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_402,hypothesis,
    ~ ~ doDivides0(xu,xb),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2612) ).

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

tff(c_347,plain,
    ~ aDivisorOf0(xu,xa),
    inference(splitLeft,[status(thm)],[c_238]) ).

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

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_584,plain,
    ! [W1_237,W0_238] :
      ( aElement0(W1_237)
      | ~ aElementOf0(W1_237,W0_238)
      | ~ aSet0(W0_238) ),
    inference(cnfTransformation,[status(thm)],[f_137]) ).

tff(c_611,plain,
    ( aElement0(xu)
    | ~ aSet0(xI) ),
    inference(resolution,[status(thm)],[c_236,c_584]) ).

tff(c_613,plain,
    ~ aSet0(xI),
    inference(splitLeft,[status(thm)],[c_611]) ).

tff(c_616,plain,
    ~ aIdeal0(xI),
    inference(resolution,[status(thm)],[c_108,c_613]) ).

tff(c_620,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_218,c_616]) ).

tff(c_621,plain,
    aElement0(xu),
    inference(splitRight,[status(thm)],[c_611]) ).

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

tff(c_1780,plain,
    ! [W1_276,W0_277] :
      ( aDivisorOf0(W1_276,W0_277)
      | ~ doDivides0(W1_276,W0_277)
      | ~ aElement0(W1_276)
      | ~ aElement0(W0_277) ),
    inference(cnfTransformation,[status(thm)],[f_304]) ).

tff(c_1786,plain,
    ( aDivisorOf0(xu,xa)
    | ~ aElement0(xu)
    | ~ aElement0(xa) ),
    inference(resolution,[status(thm)],[c_246,c_1780]) ).

tff(c_1793,plain,
    aDivisorOf0(xu,xa),
    inference(demodulation,[status(thm),theory(equality)],[c_210,c_621,c_1786]) ).

tff(c_1795,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_347,c_1793]) ).

tff(c_1796,plain,
    ~ aDivisorOf0(xu,xb),
    inference(splitRight,[status(thm)],[c_238]) ).

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

tff(c_1797,plain,
    aDivisorOf0(xu,xa),
    inference(splitRight,[status(thm)],[c_238]) ).

tff(c_2009,plain,
    ! [W1_283,W0_284] :
      ( aElement0(W1_283)
      | ~ aDivisorOf0(W1_283,W0_284)
      | ~ aElement0(W0_284) ),
    inference(cnfTransformation,[status(thm)],[f_304]) ).

tff(c_2012,plain,
    ( aElement0(xu)
    | ~ aElement0(xa) ),
    inference(resolution,[status(thm)],[c_1797,c_2009]) ).

tff(c_2015,plain,
    aElement0(xu),
    inference(demodulation,[status(thm),theory(equality)],[c_210,c_2012]) ).

tff(c_248,plain,
    doDivides0(xu,xb),
    inference(cnfTransformation,[status(thm)],[f_402]) ).

tff(c_3198,plain,
    ! [W1_325,W0_326] :
      ( aDivisorOf0(W1_325,W0_326)
      | ~ doDivides0(W1_325,W0_326)
      | ~ aElement0(W1_325)
      | ~ aElement0(W0_326) ),
    inference(cnfTransformation,[status(thm)],[f_304]) ).

tff(c_3207,plain,
    ( aDivisorOf0(xu,xb)
    | ~ aElement0(xu)
    | ~ aElement0(xb) ),
    inference(resolution,[status(thm)],[c_248,c_3198]) ).

tff(c_3214,plain,
    aDivisorOf0(xu,xb),
    inference(demodulation,[status(thm),theory(equality)],[c_208,c_2015,c_3207]) ).

tff(c_3216,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_1796,c_3214]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : RNG125+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 : n021.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 17:53:21 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 7.11/2.63  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.11/2.64  
% 7.11/2.64  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 7.11/2.67  
% 7.11/2.67  Inference rules
% 7.11/2.67  ----------------------
% 7.11/2.67  #Ref     : 0
% 7.11/2.67  #Sup     : 742
% 7.11/2.67  #Fact    : 0
% 7.11/2.67  #Define  : 0
% 7.11/2.67  #Split   : 4
% 7.11/2.67  #Chain   : 0
% 7.11/2.67  #Close   : 0
% 7.11/2.67  
% 7.11/2.67  Ordering : KBO
% 7.11/2.67  
% 7.11/2.67  Simplification rules
% 7.11/2.67  ----------------------
% 7.11/2.67  #Subsume      : 14
% 7.11/2.67  #Demod        : 599
% 7.11/2.67  #Tautology    : 437
% 7.11/2.67  #SimpNegUnit  : 2
% 7.11/2.67  #BackRed      : 0
% 7.11/2.67  
% 7.11/2.67  #Partial instantiations: 0
% 7.11/2.67  #Strategies tried      : 1
% 7.11/2.67  
% 7.11/2.67  Timing (in seconds)
% 7.11/2.67  ----------------------
% 7.11/2.67  Preprocessing        : 0.72
% 7.11/2.67  Parsing              : 0.34
% 7.11/2.67  CNF conversion       : 0.07
% 7.11/2.67  Main loop            : 0.87
% 7.11/2.67  Inferencing          : 0.28
% 7.11/2.67  Reduction            : 0.28
% 7.11/2.67  Demodulation         : 0.20
% 7.11/2.67  BG Simplification    : 0.06
% 7.11/2.67  Subsumption          : 0.18
% 7.11/2.67  Abstraction          : 0.04
% 7.11/2.67  MUC search           : 0.00
% 7.11/2.67  Cooper               : 0.00
% 7.11/2.67  Total                : 1.64
% 7.11/2.67  Index Insertion      : 0.00
% 7.11/2.67  Index Deletion       : 0.00
% 7.11/2.67  Index Matching       : 0.00
% 7.11/2.67  BG Taut test         : 0.00
%------------------------------------------------------------------------------