TSTP Solution File: RNG061+2 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : RNG061+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 : n032.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 10:54:50 EDT 2023

% Result   : Theorem 33.92s 21.92s
% Output   : CNFRefutation 34.05s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   48
% Syntax   : Number of formulae    :   88 (  26 unt;  33 typ;   0 def)
%            Number of atoms       :  109 (  29 equ)
%            Maximal formula atoms :    7 (   1 avg)
%            Number of connectives :   89 (  35   ~;  27   |;  19   &)
%                                         (   0 <=>;   8  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Maximal term depth    :    4 (   2 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   :   30 (;  30   !;   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_397,hypothesis,
    ( aScalar0(xN)
    & ( xN = sdtasdt0(xR,xS) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1949) ).

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

tff(f_86,axiom,
    ! [W0] :
      ( aScalar0(W0)
     => aScalar0(smndt0(W0)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNegSc) ).

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

tff(f_404,hypothesis,
    ( ( sdtasdt0(xR,smndt0(xS)) = smndt0(xN) )
    & ( sdtasdt0(smndt0(xS),xR) = smndt0(xN) )
    & ( sdtasdt0(smndt0(xS),smndt0(xS)) = sdtasdt0(xS,xS) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2144) ).

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

tff(f_405,hypothesis,
    sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))) = sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),smndt0(xN)),sdtpldt0(smndt0(xN),sdtasdt0(xS,xS))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2180) ).

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_328,hypothesis,
    ( aVector0(xs)
    & aVector0(xt) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1678) ).

tff(f_351,hypothesis,
    ( aVector0(xp)
    & ( szszuzczcdt0(aDimensionOf0(xp)) = aDimensionOf0(xs) )
    & ! [W0] :
        ( aNaturalNumber0(W0)
       => ( sdtlbdtrb0(xp,W0) = sdtlbdtrb0(xs,W0) ) )
    & ( xp = sziznziztdt0(xs) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1709) ).

tff(f_258,axiom,
    ! [W0] :
      ( aVector0(W0)
     => aNaturalNumber0(aDimensionOf0(W0)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDimNat) ).

tff(f_66,axiom,
    ! [W0] :
      ( aNaturalNumber0(W0)
     => iLess0(W0,szszuzczcdt0(W0)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIH) ).

tff(f_361,hypothesis,
    ( aVector0(xq)
    & ( szszuzczcdt0(aDimensionOf0(xq)) = aDimensionOf0(xt) )
    & ! [W0] :
        ( aNaturalNumber0(W0)
       => ( sdtlbdtrb0(xq,W0) = sdtlbdtrb0(xt,W0) ) )
    & ( xq = sziznziztdt0(xt) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1726) ).

tff(f_264,axiom,
    ! [W0,W1] :
      ( ( aVector0(W0)
        & aNaturalNumber0(W1) )
     => aScalar0(sdtlbdtrb0(W0,W1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mElmSc) ).

tff(f_407,negated_conjecture,
    sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))) != sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),smndt0(xN)),sdtpldt0(sdtasdt0(xS,xS),smndt0(xN))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).

tff(c_186,plain,
    aScalar0(xN),
    inference(cnfTransformation,[status(thm)],[f_397]) ).

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

tff(c_28,plain,
    ! [W0_15] :
      ( aScalar0(smndt0(W0_15))
      | ~ aScalar0(W0_15) ),
    inference(cnfTransformation,[status(thm)],[f_86]) ).

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

tff(c_196,plain,
    sdtasdt0(xR,smndt0(xS)) = smndt0(xN),
    inference(cnfTransformation,[status(thm)],[f_404]) ).

tff(c_864,plain,
    ! [W0_97,W1_98] :
      ( aScalar0(sdtasdt0(W0_97,W1_98))
      | ~ aScalar0(W1_98)
      | ~ aScalar0(W0_97) ),
    inference(cnfTransformation,[status(thm)],[f_82]) ).

tff(c_912,plain,
    ( aScalar0(smndt0(xN))
    | ~ aScalar0(smndt0(xS))
    | ~ aScalar0(xR) ),
    inference(superposition,[status(thm),theory(equality)],[c_196,c_864]) ).

tff(c_1006,plain,
    ( aScalar0(smndt0(xN))
    | ~ aScalar0(smndt0(xS)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_174,c_912]) ).

tff(c_1104,plain,
    ~ aScalar0(smndt0(xS)),
    inference(splitLeft,[status(thm)],[c_1006]) ).

tff(c_1107,plain,
    ~ aScalar0(xS),
    inference(resolution,[status(thm)],[c_28,c_1104]) ).

tff(c_1111,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_182,c_1107]) ).

tff(c_1113,plain,
    aScalar0(smndt0(xS)),
    inference(splitRight,[status(thm)],[c_1006]) ).

tff(c_192,plain,
    sdtasdt0(smndt0(xS),smndt0(xS)) = sdtasdt0(xS,xS),
    inference(cnfTransformation,[status(thm)],[f_404]) ).

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_1504,plain,
    ( aScalar0(sdtasdt0(xS,xS))
    | ~ aScalar0(smndt0(xS))
    | ~ aScalar0(smndt0(xS)) ),
    inference(superposition,[status(thm),theory(equality)],[c_192,c_26]) ).

tff(c_1511,plain,
    aScalar0(sdtasdt0(xS,xS)),
    inference(demodulation,[status(thm),theory(equality)],[c_1113,c_1113,c_1504]) ).

tff(c_198,plain,
    sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),smndt0(xN)),sdtpldt0(smndt0(xN),sdtasdt0(xS,xS))) = sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))),
    inference(cnfTransformation,[status(thm)],[f_405]) ).

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_2755,plain,
    ! [W2_19] : ~ aScalar0(W2_19),
    inference(splitLeft,[status(thm)],[c_50]) ).

tff(c_114,plain,
    aVector0(xt),
    inference(cnfTransformation,[status(thm)],[f_328]) ).

tff(c_130,plain,
    aVector0(xp),
    inference(cnfTransformation,[status(thm)],[f_351]) ).

tff(c_90,plain,
    ! [W0_55] :
      ( aNaturalNumber0(aDimensionOf0(W0_55))
      | ~ aVector0(W0_55) ),
    inference(cnfTransformation,[status(thm)],[f_258]) ).

tff(c_128,plain,
    szszuzczcdt0(aDimensionOf0(xp)) = aDimensionOf0(xs),
    inference(cnfTransformation,[status(thm)],[f_351]) ).

tff(c_621,plain,
    ! [W0_90] :
      ( iLess0(W0_90,szszuzczcdt0(W0_90))
      | ~ aNaturalNumber0(W0_90) ),
    inference(cnfTransformation,[status(thm)],[f_66]) ).

tff(c_627,plain,
    ( iLess0(aDimensionOf0(xp),aDimensionOf0(xs))
    | ~ aNaturalNumber0(aDimensionOf0(xp)) ),
    inference(superposition,[status(thm),theory(equality)],[c_128,c_621]) ).

tff(c_1749,plain,
    ~ aNaturalNumber0(aDimensionOf0(xp)),
    inference(splitLeft,[status(thm)],[c_627]) ).

tff(c_1789,plain,
    ~ aVector0(xp),
    inference(resolution,[status(thm)],[c_90,c_1749]) ).

tff(c_1793,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_130,c_1789]) ).

tff(c_1795,plain,
    aNaturalNumber0(aDimensionOf0(xp)),
    inference(splitRight,[status(thm)],[c_627]) ).

tff(c_134,plain,
    ! [W0_80] :
      ( ( sdtlbdtrb0(xt,W0_80) = sdtlbdtrb0(xq,W0_80) )
      | ~ aNaturalNumber0(W0_80) ),
    inference(cnfTransformation,[status(thm)],[f_361]) ).

tff(c_1806,plain,
    sdtlbdtrb0(xt,aDimensionOf0(xp)) = sdtlbdtrb0(xq,aDimensionOf0(xp)),
    inference(resolution,[status(thm)],[c_1795,c_134]) ).

tff(c_92,plain,
    ! [W0_56,W1_57] :
      ( aScalar0(sdtlbdtrb0(W0_56,W1_57))
      | ~ aNaturalNumber0(W1_57)
      | ~ aVector0(W0_56) ),
    inference(cnfTransformation,[status(thm)],[f_264]) ).

tff(c_1965,plain,
    ( aScalar0(sdtlbdtrb0(xq,aDimensionOf0(xp)))
    | ~ aNaturalNumber0(aDimensionOf0(xp))
    | ~ aVector0(xt) ),
    inference(superposition,[status(thm),theory(equality)],[c_1806,c_92]) ).

tff(c_1969,plain,
    aScalar0(sdtlbdtrb0(xq,aDimensionOf0(xp))),
    inference(demodulation,[status(thm),theory(equality)],[c_114,c_1795,c_1965]) ).

tff(c_2779,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_2755,c_1969]) ).

tff(c_2842,plain,
    ! [W1_130,W0_131] :
      ( ( sdtpldt0(W1_130,W0_131) = sdtpldt0(W0_131,W1_130) )
      | ~ aScalar0(W1_130)
      | ~ aScalar0(W0_131) ),
    inference(splitRight,[status(thm)],[c_50]) ).

tff(c_75578,plain,
    ! [W0_256,W0_257] :
      ( ( sdtpldt0(smndt0(W0_256),W0_257) = sdtpldt0(W0_257,smndt0(W0_256)) )
      | ~ aScalar0(W0_257)
      | ~ aScalar0(W0_256) ),
    inference(resolution,[status(thm)],[c_28,c_2842]) ).

tff(c_200,plain,
    sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),smndt0(xN)),sdtpldt0(sdtasdt0(xS,xS),smndt0(xN))) != sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))),
    inference(cnfTransformation,[status(thm)],[f_407]) ).

tff(c_75693,plain,
    ( ( sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),smndt0(xN)),sdtpldt0(smndt0(xN),sdtasdt0(xS,xS))) != sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))) )
    | ~ aScalar0(sdtasdt0(xS,xS))
    | ~ aScalar0(xN) ),
    inference(superposition,[status(thm),theory(equality)],[c_75578,c_200]) ).

tff(c_75818,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_186,c_1511,c_198,c_75693]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10  % Problem  : RNG061+2 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.11  % 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
% 0.09/0.31  % Computer : n032.cluster.edu
% 0.09/0.31  % Model    : x86_64 x86_64
% 0.09/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.31  % Memory   : 8042.1875MB
% 0.09/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.09/0.31  % CPULimit : 300
% 0.09/0.31  % WCLimit  : 300
% 0.09/0.31  % DateTime : Thu Aug  3 18:02:51 EDT 2023
% 0.09/0.31  % CPUTime  : 
% 33.92/21.92  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 33.98/21.93  
% 33.98/21.93  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 34.05/21.96  
% 34.05/21.96  Inference rules
% 34.05/21.96  ----------------------
% 34.05/21.96  #Ref     : 3
% 34.05/21.96  #Sup     : 16903
% 34.05/21.96  #Fact    : 2
% 34.05/21.96  #Define  : 0
% 34.05/21.96  #Split   : 19
% 34.05/21.96  #Chain   : 0
% 34.05/21.96  #Close   : 0
% 34.05/21.96  
% 34.05/21.96  Ordering : KBO
% 34.05/21.96  
% 34.05/21.96  Simplification rules
% 34.05/21.96  ----------------------
% 34.05/21.96  #Subsume      : 169
% 34.05/21.96  #Demod        : 22618
% 34.05/21.96  #Tautology    : 4609
% 34.05/21.96  #SimpNegUnit  : 80
% 34.05/21.96  #BackRed      : 65
% 34.05/21.96  
% 34.05/21.96  #Partial instantiations: 0
% 34.05/21.96  #Strategies tried      : 1
% 34.05/21.96  
% 34.05/21.96  Timing (in seconds)
% 34.05/21.96  ----------------------
% 34.05/21.96  Preprocessing        : 0.67
% 34.05/21.96  Parsing              : 0.34
% 34.05/21.96  CNF conversion       : 0.05
% 34.05/21.96  Main loop            : 20.36
% 34.05/21.96  Inferencing          : 2.22
% 34.05/21.96  Reduction            : 13.33
% 34.05/21.96  Demodulation         : 12.14
% 34.05/21.96  BG Simplification    : 0.19
% 34.05/21.96  Subsumption          : 3.87
% 34.05/21.96  Abstraction          : 0.31
% 34.05/21.96  MUC search           : 0.00
% 34.05/21.96  Cooper               : 0.00
% 34.05/21.96  Total                : 21.08
% 34.05/21.96  Index Insertion      : 0.00
% 34.05/21.96  Index Deletion       : 0.00
% 34.05/21.96  Index Matching       : 0.00
% 34.05/21.96  BG Taut test         : 0.00
%------------------------------------------------------------------------------