TSTP Solution File: RNG105+1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : RNG105+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 : n015.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 7.04s 2.64s
% Output   : CNFRefutation 7.04s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   59
% Syntax   : Number of formulae    :   92 (  21 unt;  49 typ;   1 def)
%            Number of atoms       :   82 (   8 equ)
%            Maximal formula atoms :    6 (   1 avg)
%            Number of connectives :   72 (  33   ~;  25   |;   9   &)
%                                         (   2 <=>;   3  =>;   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   :   20 (;  19   !;   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_363,negated_conjecture,
    ~ ( aElementOf0(sdtpldt0(xx,xy),slsdtgt0(xc))
      & aElementOf0(sdtasdt0(xz,xx),slsdtgt0(xc)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).

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

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

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

tff(f_41,axiom,
    ! [W0,W1] :
      ( ( aElement0(W0)
        & aElement0(W1) )
     => aElement0(sdtpldt0(W0,W1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB) ).

tff(f_358,hypothesis,
    sdtpldt0(xx,xy) = sdtasdt0(xc,sdtpldt0(xu,xv)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2010) ).

tff(f_47,axiom,
    ! [W0,W1] :
      ( ( aElement0(W0)
        & aElement0(W1) )
     => aElement0(sdtasdt0(W0,W1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB_02) ).

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_359,hypothesis,
    sdtasdt0(xz,xx) = sdtasdt0(xc,sdtasdt0(xu,xz)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2043) ).

tff(c_226,plain,
    ( ~ aElementOf0(sdtasdt0(xz,xx),slsdtgt0(xc))
    | ~ aElementOf0(sdtpldt0(xx,xy),slsdtgt0(xc)) ),
    inference(cnfTransformation,[status(thm)],[f_363]) ).

tff(c_232,plain,
    ~ aElementOf0(sdtpldt0(xx,xy),slsdtgt0(xc)),
    inference(splitLeft,[status(thm)],[c_226]) ).

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

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

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

tff(c_10,plain,
    ! [W0_3,W1_4] :
      ( aElement0(sdtpldt0(W0_3,W1_4))
      | ~ aElement0(W1_4)
      | ~ aElement0(W0_3) ),
    inference(cnfTransformation,[status(thm)],[f_41]) ).

tff(c_222,plain,
    sdtasdt0(xc,sdtpldt0(xu,xv)) = sdtpldt0(xx,xy),
    inference(cnfTransformation,[status(thm)],[f_358]) ).

tff(c_896,plain,
    ! [W0_247,W1_248] :
      ( aElement0(sdtasdt0(W0_247,W1_248))
      | ~ aElement0(W1_248)
      | ~ aElement0(W0_247) ),
    inference(cnfTransformation,[status(thm)],[f_47]) ).

tff(c_917,plain,
    ( aElement0(sdtpldt0(xx,xy))
    | ~ aElement0(sdtpldt0(xu,xv))
    | ~ aElement0(xc) ),
    inference(superposition,[status(thm),theory(equality)],[c_222,c_896]) ).

tff(c_1027,plain,
    ( aElement0(sdtpldt0(xx,xy))
    | ~ aElement0(sdtpldt0(xu,xv)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_206,c_917]) ).

tff(c_1368,plain,
    ~ aElement0(sdtpldt0(xu,xv)),
    inference(splitLeft,[status(thm)],[c_1027]) ).

tff(c_1371,plain,
    ( ~ aElement0(xv)
    | ~ aElement0(xu) ),
    inference(resolution,[status(thm)],[c_10,c_1368]) ).

tff(c_1375,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_216,c_220,c_1371]) ).

tff(c_1377,plain,
    aElement0(sdtpldt0(xu,xv)),
    inference(splitRight,[status(thm)],[c_1027]) ).

tff(c_1669,plain,
    ! [W0_270,W3_271] :
      ( aElementOf0(sdtasdt0(W0_270,W3_271),slsdtgt0(W0_270))
      | ~ aElement0(W3_271)
      | ~ aElement0(W0_270) ),
    inference(cnfTransformation,[status(thm)],[f_345]) ).

tff(c_1705,plain,
    ( aElementOf0(sdtpldt0(xx,xy),slsdtgt0(xc))
    | ~ aElement0(sdtpldt0(xu,xv))
    | ~ aElement0(xc) ),
    inference(superposition,[status(thm),theory(equality)],[c_222,c_1669]) ).

tff(c_1830,plain,
    aElementOf0(sdtpldt0(xx,xy),slsdtgt0(xc)),
    inference(demodulation,[status(thm),theory(equality)],[c_206,c_1377,c_1705]) ).

tff(c_1832,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_232,c_1830]) ).

tff(c_1833,plain,
    ~ aElementOf0(sdtasdt0(xz,xx),slsdtgt0(xc)),
    inference(splitRight,[status(thm)],[c_226]) ).

tff(c_208,plain,
    aElement0(xz),
    inference(cnfTransformation,[status(thm)],[f_351]) ).

tff(c_12,plain,
    ! [W0_5,W1_6] :
      ( aElement0(sdtasdt0(W0_5,W1_6))
      | ~ aElement0(W1_6)
      | ~ aElement0(W0_5) ),
    inference(cnfTransformation,[status(thm)],[f_47]) ).

tff(c_224,plain,
    sdtasdt0(xc,sdtasdt0(xu,xz)) = sdtasdt0(xz,xx),
    inference(cnfTransformation,[status(thm)],[f_359]) ).

tff(c_2454,plain,
    ! [W0_295,W1_296] :
      ( aElement0(sdtasdt0(W0_295,W1_296))
      | ~ aElement0(W1_296)
      | ~ aElement0(W0_295) ),
    inference(cnfTransformation,[status(thm)],[f_47]) ).

tff(c_2475,plain,
    ( aElement0(sdtasdt0(xz,xx))
    | ~ aElement0(sdtasdt0(xu,xz))
    | ~ aElement0(xc) ),
    inference(superposition,[status(thm),theory(equality)],[c_224,c_2454]) ).

tff(c_2585,plain,
    ( aElement0(sdtasdt0(xz,xx))
    | ~ aElement0(sdtasdt0(xu,xz)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_206,c_2475]) ).

tff(c_2802,plain,
    ~ aElement0(sdtasdt0(xu,xz)),
    inference(splitLeft,[status(thm)],[c_2585]) ).

tff(c_2805,plain,
    ( ~ aElement0(xz)
    | ~ aElement0(xu) ),
    inference(resolution,[status(thm)],[c_12,c_2802]) ).

tff(c_2809,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_216,c_208,c_2805]) ).

tff(c_2811,plain,
    aElement0(sdtasdt0(xu,xz)),
    inference(splitRight,[status(thm)],[c_2585]) ).

tff(c_3554,plain,
    ! [W0_321,W3_322] :
      ( aElementOf0(sdtasdt0(W0_321,W3_322),slsdtgt0(W0_321))
      | ~ aElement0(W3_322)
      | ~ aElement0(W0_321) ),
    inference(cnfTransformation,[status(thm)],[f_345]) ).

tff(c_3599,plain,
    ( aElementOf0(sdtasdt0(xz,xx),slsdtgt0(xc))
    | ~ aElement0(sdtasdt0(xu,xz))
    | ~ aElement0(xc) ),
    inference(superposition,[status(thm),theory(equality)],[c_224,c_3554]) ).

tff(c_3726,plain,
    aElementOf0(sdtasdt0(xz,xx),slsdtgt0(xc)),
    inference(demodulation,[status(thm),theory(equality)],[c_206,c_2811,c_3599]) ).

tff(c_3728,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_1833,c_3726]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : RNG105+1 : TPTP v8.1.2. Released v4.0.0.
% 0.13/0.14  % 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
% 0.13/0.36  % Computer : n015.cluster.edu
% 0.13/0.36  % Model    : x86_64 x86_64
% 0.13/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.36  % Memory   : 8042.1875MB
% 0.13/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.36  % CPULimit : 300
% 0.13/0.36  % WCLimit  : 300
% 0.13/0.36  % DateTime : Thu Aug  3 18:17:59 EDT 2023
% 0.13/0.36  % CPUTime  : 
% 7.04/2.64  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.04/2.64  
% 7.04/2.64  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 7.04/2.67  
% 7.04/2.67  Inference rules
% 7.04/2.67  ----------------------
% 7.04/2.67  #Ref     : 0
% 7.04/2.67  #Sup     : 942
% 7.04/2.67  #Fact    : 0
% 7.04/2.67  #Define  : 0
% 7.04/2.67  #Split   : 6
% 7.04/2.67  #Chain   : 0
% 7.04/2.67  #Close   : 0
% 7.04/2.67  
% 7.04/2.67  Ordering : KBO
% 7.04/2.67  
% 7.04/2.67  Simplification rules
% 7.04/2.67  ----------------------
% 7.04/2.67  #Subsume      : 12
% 7.04/2.67  #Demod        : 545
% 7.04/2.67  #Tautology    : 469
% 7.04/2.67  #SimpNegUnit  : 2
% 7.04/2.67  #BackRed      : 0
% 7.04/2.67  
% 7.04/2.67  #Partial instantiations: 0
% 7.04/2.67  #Strategies tried      : 1
% 7.04/2.67  
% 7.04/2.67  Timing (in seconds)
% 7.04/2.67  ----------------------
% 7.04/2.68  Preprocessing        : 0.70
% 7.04/2.68  Parsing              : 0.35
% 7.04/2.68  CNF conversion       : 0.06
% 7.04/2.68  Main loop            : 0.89
% 7.04/2.68  Inferencing          : 0.31
% 7.04/2.68  Reduction            : 0.28
% 7.04/2.68  Demodulation         : 0.20
% 7.04/2.68  BG Simplification    : 0.06
% 7.04/2.68  Subsumption          : 0.18
% 7.04/2.68  Abstraction          : 0.04
% 7.04/2.68  MUC search           : 0.00
% 7.04/2.68  Cooper               : 0.00
% 7.04/2.68  Total                : 1.64
% 7.04/2.68  Index Insertion      : 0.00
% 7.04/2.68  Index Deletion       : 0.00
% 7.04/2.68  Index Matching       : 0.00
% 7.04/2.68  BG Taut test         : 0.00
%------------------------------------------------------------------------------