TSTP Solution File: RNG072+2 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : RNG072+2 : 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 10:54:52 EDT 2023

% Result   : Theorem 13.40s 4.87s
% Output   : CNFRefutation 13.40s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   45
% Syntax   : Number of formulae    :   93 (  31 unt;  33 typ;   0 def)
%            Number of atoms       :  131 (  18 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :  129 (  58   ~;  47   |;  18   &)
%                                         (   0 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   3 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   22 (  15   >;   7   *;   0   +;   0  <<)
%            Number of predicates  :    7 (   5 usr;   1 prp; 0-2 aty)
%            Number of functors    :   28 (  28 usr;  18 con; 0-2 aty)
%            Number of variables   :   41 (;  41   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ sdtlseqdt0 > iLess0 > aVector0 > aScalar0 > aNaturalNumber0 > sdtpldt0 > sdtlbdtrb0 > sdtasdt0 > sdtasasdt0 > #nlpp > szszuzczcdt0 > sziznziztdt0 > smndt0 > aDimensionOf0 > xt > xs > xq > xp > xS > xR > xP > xN > xH > xG > xF > xE > xD > xC > xB > xA > sz0z00 > sz00 > #skF_1 > #skF_2

%Foreground sorts:

%Background operators:

%Foreground operators:
tff(xq,type,
    xq: $i ).

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

tff(sdtasdt0,type,
    sdtasdt0: ( $i * $i ) > $i ).

tff(szszuzczcdt0,type,
    szszuzczcdt0: $i > $i ).

tff(sdtlbdtrb0,type,
    sdtlbdtrb0: ( $i * $i ) > $i ).

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

tff('#skF_1',type,
    '#skF_1': $i > $i ).

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

tff(sziznziztdt0,type,
    sziznziztdt0: $i > $i ).

tff(sdtlseqdt0,type,
    sdtlseqdt0: ( $i * $i ) > $o ).

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

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

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

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

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

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

tff(aDimensionOf0,type,
    aDimensionOf0: $i > $i ).

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

tff(aNaturalNumber0,type,
    aNaturalNumber0: $i > $o ).

tff(sz0z00,type,
    sz0z00: $i ).

tff(smndt0,type,
    smndt0: $i > $i ).

tff(aScalar0,type,
    aScalar0: $i > $o ).

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

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

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

tff('#skF_2',type,
    '#skF_2': ( $i * $i ) > $i ).

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

tff(sdtasasdt0,type,
    sdtasasdt0: ( $i * $i ) > $i ).

tff(iLess0,type,
    iLess0: ( $i * $i ) > $o ).

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

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

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

tff(aVector0,type,
    aVector0: $i > $o ).

tff(f_394,hypothesis,
    ( aScalar0(xS)
    & ( xS = sdtasdt0(xF,xD) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1930) ).

tff(f_388,hypothesis,
    ( aScalar0(xR)
    & ( xR = sdtasdt0(xC,xG) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1892) ).

tff(f_118,axiom,
    ! [W0,W1,W2] :
      ( ( aScalar0(W0)
        & aScalar0(W1)
        & aScalar0(W2) )
     => ( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
        & ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
        & ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) )
        & ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mArith) ).

tff(f_76,axiom,
    ! [W0,W1] :
      ( ( aScalar0(W0)
        & aScalar0(W1) )
     => aScalar0(sdtpldt0(W0,W1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSumSc) ).

tff(f_82,axiom,
    ! [W0,W1] :
      ( ( aScalar0(W0)
        & aScalar0(W1) )
     => aScalar0(sdtasdt0(W0,W1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulSc) ).

tff(f_391,hypothesis,
    ( aScalar0(xP)
    & ( xP = sdtasdt0(xE,xH) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1911) ).

tff(f_223,axiom,
    ! [W0,W1] :
      ( ( aScalar0(W0)
        & aScalar0(W1) )
     => ( sdtlseqdt0(W0,W1)
        | sdtlseqdt0(W1,W0) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLETot) ).

tff(f_409,negated_conjecture,
    ~ sdtlseqdt0(sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS)),sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).

tff(f_379,hypothesis,
    ( aScalar0(xF)
    & ( xF = sdtasdt0(xA,xA) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1837) ).

tff(f_404,hypothesis,
    sdtlseqdt0(sdtpldt0(xR,xS),sdtpldt0(xP,xP)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2610) ).

tff(f_407,hypothesis,
    ( sdtlseqdt0(sz0z00,sdtpldt0(xR,xS))
    & sdtlseqdt0(sz0z00,sdtpldt0(xP,xP)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2628) ).

tff(f_215,axiom,
    ! [W0,W1,W2,W3] :
      ( ( aScalar0(W0)
        & aScalar0(W1)
        & aScalar0(W2)
        & aScalar0(W3) )
     => ( ( sdtlseqdt0(W0,W1)
          & sdtlseqdt0(sz0z00,W2)
          & sdtlseqdt0(W2,W3) )
       => sdtlseqdt0(sdtasdt0(W0,W2),sdtasdt0(W1,W3)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLEMonM) ).

tff(c_182,plain,
    aScalar0(xS),
    inference(cnfTransformation,[status(thm)],[f_394]) ).

tff(c_174,plain,
    aScalar0(xR),
    inference(cnfTransformation,[status(thm)],[f_388]) ).

tff(c_50,plain,
    ! [W1_18,W0_17,W2_19] :
      ( ( sdtpldt0(W1_18,W0_17) = sdtpldt0(W0_17,W1_18) )
      | ~ aScalar0(W2_19)
      | ~ aScalar0(W1_18)
      | ~ aScalar0(W0_17) ),
    inference(cnfTransformation,[status(thm)],[f_118]) ).

tff(c_1948,plain,
    ! [W2_19] : ~ aScalar0(W2_19),
    inference(splitLeft,[status(thm)],[c_50]) ).

tff(c_24,plain,
    ! [W0_11,W1_12] :
      ( aScalar0(sdtpldt0(W0_11,W1_12))
      | ~ aScalar0(W1_12)
      | ~ aScalar0(W0_11) ),
    inference(cnfTransformation,[status(thm)],[f_76]) ).

tff(c_26,plain,
    ! [W0_13,W1_14] :
      ( aScalar0(sdtasdt0(W0_13,W1_14))
      | ~ aScalar0(W1_14)
      | ~ aScalar0(W0_13) ),
    inference(cnfTransformation,[status(thm)],[f_82]) ).

tff(c_178,plain,
    aScalar0(xP),
    inference(cnfTransformation,[status(thm)],[f_391]) ).

tff(c_1603,plain,
    ! [W1_117,W0_118] :
      ( sdtlseqdt0(W1_117,W0_118)
      | sdtlseqdt0(W0_118,W1_117)
      | ~ aScalar0(W1_117)
      | ~ aScalar0(W0_118) ),
    inference(cnfTransformation,[status(thm)],[f_223]) ).

tff(c_204,plain,
    ~ sdtlseqdt0(sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS)),sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP))),
    inference(cnfTransformation,[status(thm)],[f_409]) ).

tff(c_1612,plain,
    ( sdtlseqdt0(sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP)),sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS)))
    | ~ aScalar0(sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS)))
    | ~ aScalar0(sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP))) ),
    inference(resolution,[status(thm)],[c_1603,c_204]) ).

tff(c_1673,plain,
    ~ aScalar0(sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP))),
    inference(splitLeft,[status(thm)],[c_1612]) ).

tff(c_1695,plain,
    ~ aScalar0(sdtpldt0(xP,xP)),
    inference(resolution,[status(thm)],[c_26,c_1673]) ).

tff(c_1698,plain,
    ~ aScalar0(xP),
    inference(resolution,[status(thm)],[c_24,c_1695]) ).

tff(c_1702,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_178,c_1698]) ).

tff(c_1704,plain,
    aScalar0(sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP))),
    inference(splitRight,[status(thm)],[c_1612]) ).

tff(c_1613,plain,
    ( sdtlseqdt0(sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP)),sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS)))
    | ~ aScalar0(sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP)))
    | ~ aScalar0(sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS))) ),
    inference(resolution,[status(thm)],[c_1603,c_204]) ).

tff(c_1786,plain,
    ( sdtlseqdt0(sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP)),sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS)))
    | ~ aScalar0(sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS))) ),
    inference(demodulation,[status(thm),theory(equality)],[c_1704,c_1613]) ).

tff(c_1787,plain,
    ~ aScalar0(sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS))),
    inference(splitLeft,[status(thm)],[c_1786]) ).

tff(c_1825,plain,
    ~ aScalar0(sdtpldt0(xR,xS)),
    inference(resolution,[status(thm)],[c_26,c_1787]) ).

tff(c_1828,plain,
    ( ~ aScalar0(xS)
    | ~ aScalar0(xR) ),
    inference(resolution,[status(thm)],[c_24,c_1825]) ).

tff(c_1832,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_174,c_182,c_1828]) ).

tff(c_1834,plain,
    aScalar0(sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS))),
    inference(splitRight,[status(thm)],[c_1786]) ).

tff(c_1972,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_1948,c_1834]) ).

tff(c_2060,plain,
    ! [W1_123,W0_124] :
      ( ( sdtpldt0(W1_123,W0_124) = sdtpldt0(W0_124,W1_123) )
      | ~ aScalar0(W1_123)
      | ~ aScalar0(W0_124) ),
    inference(splitRight,[status(thm)],[c_50]) ).

tff(c_2136,plain,
    ! [W0_125] :
      ( ( sdtpldt0(xS,W0_125) = sdtpldt0(W0_125,xS) )
      | ~ aScalar0(W0_125) ),
    inference(resolution,[status(thm)],[c_182,c_2060]) ).

tff(c_2237,plain,
    sdtpldt0(xS,xR) = sdtpldt0(xR,xS),
    inference(resolution,[status(thm)],[c_174,c_2136]) ).

tff(c_2617,plain,
    ( aScalar0(sdtpldt0(xR,xS))
    | ~ aScalar0(xR)
    | ~ aScalar0(xS) ),
    inference(superposition,[status(thm),theory(equality)],[c_2237,c_24]) ).

tff(c_2621,plain,
    aScalar0(sdtpldt0(xR,xS)),
    inference(demodulation,[status(thm),theory(equality)],[c_182,c_174,c_2617]) ).

tff(c_5972,plain,
    ! [W0_153,W1_154,W2_155] :
      ( ( sdtasdt0(sdtasdt0(W0_153,W1_154),W2_155) = sdtasdt0(W0_153,sdtasdt0(W1_154,W2_155)) )
      | ~ aScalar0(W2_155)
      | ~ aScalar0(W1_154)
      | ~ aScalar0(W0_153) ),
    inference(cnfTransformation,[status(thm)],[f_118]) ).

tff(c_46,plain,
    ! [W1_18,W0_17,W2_19] :
      ( ( sdtasdt0(W1_18,W0_17) = sdtasdt0(W0_17,W1_18) )
      | ~ aScalar0(W2_19)
      | ~ aScalar0(W1_18)
      | ~ aScalar0(W0_17) ),
    inference(cnfTransformation,[status(thm)],[f_118]) ).

tff(c_2523,plain,
    ! [W2_19] : ~ aScalar0(W2_19),
    inference(splitLeft,[status(thm)],[c_46]) ).

tff(c_162,plain,
    aScalar0(xF),
    inference(cnfTransformation,[status(thm)],[f_379]) ).

tff(c_2229,plain,
    sdtpldt0(xS,xF) = sdtpldt0(xF,xS),
    inference(resolution,[status(thm)],[c_162,c_2136]) ).

tff(c_2485,plain,
    ( aScalar0(sdtpldt0(xF,xS))
    | ~ aScalar0(xF)
    | ~ aScalar0(xS) ),
    inference(superposition,[status(thm),theory(equality)],[c_2229,c_24]) ).

tff(c_2489,plain,
    aScalar0(sdtpldt0(xF,xS)),
    inference(demodulation,[status(thm),theory(equality)],[c_182,c_162,c_2485]) ).

tff(c_2556,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_2523,c_2489]) ).

tff(c_2678,plain,
    ! [W1_128,W0_129] :
      ( ( sdtasdt0(W1_128,W0_129) = sdtasdt0(W0_129,W1_128) )
      | ~ aScalar0(W1_128)
      | ~ aScalar0(W0_129) ),
    inference(splitRight,[status(thm)],[c_46]) ).

tff(c_2766,plain,
    ! [W0_129] :
      ( ( sdtasdt0(sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP)),W0_129) = sdtasdt0(W0_129,sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP))) )
      | ~ aScalar0(W0_129) ),
    inference(resolution,[status(thm)],[c_1704,c_2678]) ).

tff(c_6024,plain,
    ! [W2_155] :
      ( ( sdtasdt0(sdtpldt0(xP,xP),sdtasdt0(sdtpldt0(xP,xP),W2_155)) = sdtasdt0(W2_155,sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP))) )
      | ~ aScalar0(W2_155)
      | ~ aScalar0(W2_155)
      | ~ aScalar0(sdtpldt0(xP,xP))
      | ~ aScalar0(sdtpldt0(xP,xP)) ),
    inference(superposition,[status(thm),theory(equality)],[c_5972,c_2766]) ).

tff(c_12987,plain,
    ~ aScalar0(sdtpldt0(xP,xP)),
    inference(splitLeft,[status(thm)],[c_6024]) ).

tff(c_12990,plain,
    ~ aScalar0(xP),
    inference(resolution,[status(thm)],[c_24,c_12987]) ).

tff(c_12994,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_178,c_12990]) ).

tff(c_12996,plain,
    aScalar0(sdtpldt0(xP,xP)),
    inference(splitRight,[status(thm)],[c_6024]) ).

tff(c_198,plain,
    sdtlseqdt0(sdtpldt0(xR,xS),sdtpldt0(xP,xP)),
    inference(cnfTransformation,[status(thm)],[f_404]) ).

tff(c_202,plain,
    sdtlseqdt0(sz0z00,sdtpldt0(xR,xS)),
    inference(cnfTransformation,[status(thm)],[f_407]) ).

tff(c_13122,plain,
    ! [W0_178,W2_179,W1_180,W3_181] :
      ( sdtlseqdt0(sdtasdt0(W0_178,W2_179),sdtasdt0(W1_180,W3_181))
      | ~ sdtlseqdt0(W2_179,W3_181)
      | ~ sdtlseqdt0(sz0z00,W2_179)
      | ~ sdtlseqdt0(W0_178,W1_180)
      | ~ aScalar0(W3_181)
      | ~ aScalar0(W2_179)
      | ~ aScalar0(W1_180)
      | ~ aScalar0(W0_178) ),
    inference(cnfTransformation,[status(thm)],[f_215]) ).

tff(c_13129,plain,
    ( ~ sdtlseqdt0(sz0z00,sdtpldt0(xR,xS))
    | ~ sdtlseqdt0(sdtpldt0(xR,xS),sdtpldt0(xP,xP))
    | ~ aScalar0(sdtpldt0(xP,xP))
    | ~ aScalar0(sdtpldt0(xR,xS)) ),
    inference(resolution,[status(thm)],[c_13122,c_204]) ).

tff(c_14071,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_2621,c_12996,c_198,c_202,c_13129]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : RNG072+2 : 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
% 0.14/0.35  % Computer : n016.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Thu Aug  3 18:25:38 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 13.40/4.87  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 13.40/4.88  
% 13.40/4.88  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 13.40/4.91  
% 13.40/4.91  Inference rules
% 13.40/4.91  ----------------------
% 13.40/4.91  #Ref     : 2
% 13.40/4.91  #Sup     : 3326
% 13.40/4.91  #Fact    : 4
% 13.40/4.91  #Define  : 0
% 13.40/4.91  #Split   : 17
% 13.40/4.91  #Chain   : 0
% 13.40/4.91  #Close   : 0
% 13.40/4.91  
% 13.40/4.91  Ordering : KBO
% 13.40/4.91  
% 13.40/4.91  Simplification rules
% 13.40/4.91  ----------------------
% 13.40/4.91  #Subsume      : 77
% 13.40/4.91  #Demod        : 3825
% 13.40/4.91  #Tautology    : 1026
% 13.40/4.91  #SimpNegUnit  : 76
% 13.40/4.91  #BackRed      : 62
% 13.40/4.91  
% 13.40/4.91  #Partial instantiations: 0
% 13.40/4.91  #Strategies tried      : 1
% 13.40/4.91  
% 13.40/4.91  Timing (in seconds)
% 13.40/4.91  ----------------------
% 13.40/4.91  Preprocessing        : 0.68
% 13.40/4.91  Parsing              : 0.35
% 13.40/4.91  CNF conversion       : 0.05
% 13.40/4.91  Main loop            : 3.14
% 13.40/4.91  Inferencing          : 0.74
% 13.40/4.91  Reduction            : 1.62
% 13.40/4.91  Demodulation         : 1.40
% 13.40/4.92  BG Simplification    : 0.08
% 13.40/4.92  Subsumption          : 0.56
% 13.40/4.92  Abstraction          : 0.08
% 13.40/4.92  MUC search           : 0.00
% 13.40/4.92  Cooper               : 0.00
% 13.40/4.92  Total                : 3.88
% 13.40/4.92  Index Insertion      : 0.00
% 13.40/4.92  Index Deletion       : 0.00
% 13.40/4.92  Index Matching       : 0.00
% 13.40/4.92  BG Taut test         : 0.00
%------------------------------------------------------------------------------