TSTP Solution File: NUM459+2 by Beagle---0.9.51

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%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : NUM459+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/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s

% Computer : n004.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 10:51:44 EDT 2023

% Result   : Theorem 9.31s 3.25s
% Output   : CNFRefutation 9.56s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   22
% Syntax   : Number of formulae    :   62 (  23 unt;  12 typ;   2 def)
%            Number of atoms       :  124 (  43 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :  122 (  48   ~;  45   |;  17   &)
%                                         (   2 <=>;  10  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   11 (   6   >;   5   *;   0   +;   0  <<)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :   10 (  10 usr;   6 con; 0-2 aty)
%            Number of variables   :   37 (;  34   !;   3   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ sdtlseqdt0 > aNaturalNumber0 > sdtpldt0 > sdtmndt0 > sdtasdt0 > #nlpp > xn > xm > sz10 > sz00 > #skF_2 > #skF_3 > #skF_1

%Foreground sorts:

%Background operators:

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

tff(sz10,type,
    sz10: $i ).

tff(sdtmndt0,type,
    sdtmndt0: ( $i * $i ) > $i ).

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

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

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

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

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

tff('#skF_3',type,
    '#skF_3': $i ).

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

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

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

tff(f_198,negated_conjecture,
    ~ ( ( ? [W0] :
            ( aNaturalNumber0(W0)
            & ( sdtpldt0(xm,W0) = xn ) )
        & sdtlseqdt0(xm,xn)
        & ? [W0] :
            ( aNaturalNumber0(W0)
            & ( sdtpldt0(xn,W0) = xm ) )
        & sdtlseqdt0(xn,xm) )
     => ( xm = xn ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).

tff(f_53,axiom,
    ! [W0,W1] :
      ( ( aNaturalNumber0(W0)
        & aNaturalNumber0(W1) )
     => ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddComm) ).

tff(f_141,axiom,
    ! [W0,W1] :
      ( ( aNaturalNumber0(W0)
        & aNaturalNumber0(W1) )
     => ( ( sdtpldt0(W0,W1) = sz00 )
       => ( ( W0 = sz00 )
          & ( W1 = sz00 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mZeroAdd) ).

tff(f_182,hypothesis,
    ( aNaturalNumber0(xm)
    & aNaturalNumber0(xn) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__745) ).

tff(f_61,axiom,
    ! [W0,W1,W2] :
      ( ( aNaturalNumber0(W0)
        & aNaturalNumber0(W1)
        & aNaturalNumber0(W2) )
     => ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddAsso) ).

tff(f_67,axiom,
    ! [W0] :
      ( aNaturalNumber0(W0)
     => ( ( sdtpldt0(W0,sz00) = W0 )
        & ( W0 = sdtpldt0(sz00,W0) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_AddZero) ).

tff(f_31,axiom,
    aNaturalNumber0(sz00),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC) ).

tff(f_162,definition,
    ! [W0,W1] :
      ( ( aNaturalNumber0(W0)
        & aNaturalNumber0(W1) )
     => ( sdtlseqdt0(W0,W1)
      <=> ? [W2] :
            ( aNaturalNumber0(W2)
            & ( sdtpldt0(W0,W2) = W1 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefLE) ).

tff(f_41,axiom,
    ! [W0,W1] :
      ( ( aNaturalNumber0(W0)
        & aNaturalNumber0(W1) )
     => aNaturalNumber0(sdtpldt0(W0,W1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB) ).

tff(f_175,definition,
    ! [W0,W1] :
      ( ( aNaturalNumber0(W0)
        & aNaturalNumber0(W1) )
     => ( sdtlseqdt0(W0,W1)
       => ! [W2] :
            ( ( W2 = sdtmndt0(W1,W0) )
          <=> ( aNaturalNumber0(W2)
              & ( sdtpldt0(W0,W2) = W1 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefDiff) ).

tff(c_70,plain,
    xn != xm,
    inference(cnfTransformation,[status(thm)],[f_198]) ).

tff(c_74,plain,
    sdtpldt0(xn,'#skF_3') = xm,
    inference(cnfTransformation,[status(thm)],[f_198]) ).

tff(c_82,plain,
    aNaturalNumber0('#skF_2'),
    inference(cnfTransformation,[status(thm)],[f_198]) ).

tff(c_76,plain,
    aNaturalNumber0('#skF_3'),
    inference(cnfTransformation,[status(thm)],[f_198]) ).

tff(c_586,plain,
    ! [W1_55,W0_56] :
      ( ( sdtpldt0(W1_55,W0_56) = sdtpldt0(W0_56,W1_55) )
      | ~ aNaturalNumber0(W1_55)
      | ~ aNaturalNumber0(W0_56) ),
    inference(cnfTransformation,[status(thm)],[f_53]) ).

tff(c_906,plain,
    ! [W0_61] :
      ( ( sdtpldt0(W0_61,'#skF_3') = sdtpldt0('#skF_3',W0_61) )
      | ~ aNaturalNumber0(W0_61) ),
    inference(resolution,[status(thm)],[c_76,c_586]) ).

tff(c_954,plain,
    sdtpldt0('#skF_2','#skF_3') = sdtpldt0('#skF_3','#skF_2'),
    inference(resolution,[status(thm)],[c_82,c_906]) ).

tff(c_46,plain,
    ! [W1_31,W0_30] :
      ( ( sz00 = W1_31 )
      | ( sdtpldt0(W0_30,W1_31) != sz00 )
      | ~ aNaturalNumber0(W1_31)
      | ~ aNaturalNumber0(W0_30) ),
    inference(cnfTransformation,[status(thm)],[f_141]) ).

tff(c_1116,plain,
    ( ( sz00 = '#skF_3' )
    | ( sdtpldt0('#skF_3','#skF_2') != sz00 )
    | ~ aNaturalNumber0('#skF_3')
    | ~ aNaturalNumber0('#skF_2') ),
    inference(superposition,[status(thm),theory(equality)],[c_954,c_46]) ).

tff(c_1125,plain,
    ( ( sz00 = '#skF_3' )
    | ( sdtpldt0('#skF_3','#skF_2') != sz00 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_82,c_76,c_1116]) ).

tff(c_1207,plain,
    sdtpldt0('#skF_3','#skF_2') != sz00,
    inference(splitLeft,[status(thm)],[c_1125]) ).

tff(c_68,plain,
    aNaturalNumber0(xm),
    inference(cnfTransformation,[status(thm)],[f_182]) ).

tff(c_80,plain,
    sdtpldt0(xm,'#skF_2') = xn,
    inference(cnfTransformation,[status(thm)],[f_198]) ).

tff(c_3098,plain,
    ! [W0_88,W1_89,W2_90] :
      ( ( sdtpldt0(sdtpldt0(W0_88,W1_89),W2_90) = sdtpldt0(W0_88,sdtpldt0(W1_89,W2_90)) )
      | ~ aNaturalNumber0(W2_90)
      | ~ aNaturalNumber0(W1_89)
      | ~ aNaturalNumber0(W0_88) ),
    inference(cnfTransformation,[status(thm)],[f_61]) ).

tff(c_3228,plain,
    ! [W2_90] :
      ( ( sdtpldt0(xm,sdtpldt0('#skF_2',W2_90)) = sdtpldt0(xn,W2_90) )
      | ~ aNaturalNumber0(W2_90)
      | ~ aNaturalNumber0('#skF_2')
      | ~ aNaturalNumber0(xm) ),
    inference(superposition,[status(thm),theory(equality)],[c_80,c_3098]) ).

tff(c_7850,plain,
    ! [W2_117] :
      ( ( sdtpldt0(xm,sdtpldt0('#skF_2',W2_117)) = sdtpldt0(xn,W2_117) )
      | ~ aNaturalNumber0(W2_117) ),
    inference(demodulation,[status(thm),theory(equality)],[c_68,c_82,c_3228]) ).

tff(c_7894,plain,
    ( ( sdtpldt0(xm,sdtpldt0('#skF_3','#skF_2')) = sdtpldt0(xn,'#skF_3') )
    | ~ aNaturalNumber0('#skF_3') ),
    inference(superposition,[status(thm),theory(equality)],[c_954,c_7850]) ).

tff(c_7928,plain,
    sdtpldt0(xm,sdtpldt0('#skF_3','#skF_2')) = xm,
    inference(demodulation,[status(thm),theory(equality)],[c_76,c_74,c_7894]) ).

tff(c_302,plain,
    ! [W0_50] :
      ( ( sdtpldt0(W0_50,sz00) = W0_50 )
      | ~ aNaturalNumber0(W0_50) ),
    inference(cnfTransformation,[status(thm)],[f_67]) ).

tff(c_325,plain,
    sdtpldt0(xm,sz00) = xm,
    inference(resolution,[status(thm)],[c_68,c_302]) ).

tff(c_4,plain,
    aNaturalNumber0(sz00),
    inference(cnfTransformation,[status(thm)],[f_31]) ).

tff(c_2186,plain,
    ! [W0_75,W2_76] :
      ( sdtlseqdt0(W0_75,sdtpldt0(W0_75,W2_76))
      | ~ aNaturalNumber0(W2_76)
      | ~ aNaturalNumber0(sdtpldt0(W0_75,W2_76))
      | ~ aNaturalNumber0(W0_75) ),
    inference(cnfTransformation,[status(thm)],[f_162]) ).

tff(c_2228,plain,
    ( sdtlseqdt0(xm,xm)
    | ~ aNaturalNumber0(sz00)
    | ~ aNaturalNumber0(sdtpldt0(xm,sz00))
    | ~ aNaturalNumber0(xm) ),
    inference(superposition,[status(thm),theory(equality)],[c_325,c_2186]) ).

tff(c_2280,plain,
    sdtlseqdt0(xm,xm),
    inference(demodulation,[status(thm),theory(equality)],[c_68,c_68,c_325,c_4,c_2228]) ).

tff(c_10,plain,
    ! [W0_2,W1_3] :
      ( aNaturalNumber0(sdtpldt0(W0_2,W1_3))
      | ~ aNaturalNumber0(W1_3)
      | ~ aNaturalNumber0(W0_2) ),
    inference(cnfTransformation,[status(thm)],[f_41]) ).

tff(c_1119,plain,
    ( aNaturalNumber0(sdtpldt0('#skF_3','#skF_2'))
    | ~ aNaturalNumber0('#skF_3')
    | ~ aNaturalNumber0('#skF_2') ),
    inference(superposition,[status(thm),theory(equality)],[c_954,c_10]) ).

tff(c_1127,plain,
    aNaturalNumber0(sdtpldt0('#skF_3','#skF_2')),
    inference(demodulation,[status(thm),theory(equality)],[c_82,c_76,c_1119]) ).

tff(c_7082,plain,
    ! [W0_112,W2_113] :
      ( ( sdtmndt0(sdtpldt0(W0_112,W2_113),W0_112) = W2_113 )
      | ~ aNaturalNumber0(W2_113)
      | ~ sdtlseqdt0(W0_112,sdtpldt0(W0_112,W2_113))
      | ~ aNaturalNumber0(sdtpldt0(W0_112,W2_113))
      | ~ aNaturalNumber0(W0_112) ),
    inference(cnfTransformation,[status(thm)],[f_175]) ).

tff(c_7151,plain,
    ( ( sdtmndt0(sdtpldt0(xm,sz00),xm) = sz00 )
    | ~ aNaturalNumber0(sz00)
    | ~ sdtlseqdt0(xm,xm)
    | ~ aNaturalNumber0(sdtpldt0(xm,sz00))
    | ~ aNaturalNumber0(xm) ),
    inference(superposition,[status(thm),theory(equality)],[c_325,c_7082]) ).

tff(c_7210,plain,
    sdtmndt0(xm,xm) = sz00,
    inference(demodulation,[status(thm),theory(equality)],[c_68,c_68,c_325,c_2280,c_4,c_325,c_7151]) ).

tff(c_58,plain,
    ! [W0_39,W2_42] :
      ( ( sdtmndt0(sdtpldt0(W0_39,W2_42),W0_39) = W2_42 )
      | ~ aNaturalNumber0(W2_42)
      | ~ sdtlseqdt0(W0_39,sdtpldt0(W0_39,W2_42))
      | ~ aNaturalNumber0(sdtpldt0(W0_39,W2_42))
      | ~ aNaturalNumber0(W0_39) ),
    inference(cnfTransformation,[status(thm)],[f_175]) ).

tff(c_8151,plain,
    ( ( sdtmndt0(sdtpldt0(xm,sdtpldt0('#skF_3','#skF_2')),xm) = sdtpldt0('#skF_3','#skF_2') )
    | ~ aNaturalNumber0(sdtpldt0('#skF_3','#skF_2'))
    | ~ sdtlseqdt0(xm,xm)
    | ~ aNaturalNumber0(sdtpldt0(xm,sdtpldt0('#skF_3','#skF_2')))
    | ~ aNaturalNumber0(xm) ),
    inference(superposition,[status(thm),theory(equality)],[c_7928,c_58]) ).

tff(c_8176,plain,
    sdtpldt0('#skF_3','#skF_2') = sz00,
    inference(demodulation,[status(thm),theory(equality)],[c_68,c_68,c_7928,c_2280,c_1127,c_7210,c_7928,c_8151]) ).

tff(c_8178,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_1207,c_8176]) ).

tff(c_8179,plain,
    sz00 = '#skF_3',
    inference(splitRight,[status(thm)],[c_1125]) ).

tff(c_66,plain,
    aNaturalNumber0(xn),
    inference(cnfTransformation,[status(thm)],[f_182]) ).

tff(c_324,plain,
    sdtpldt0(xn,sz00) = xn,
    inference(resolution,[status(thm)],[c_66,c_302]) ).

tff(c_8256,plain,
    sdtpldt0(xn,'#skF_3') = xn,
    inference(demodulation,[status(thm),theory(equality)],[c_8179,c_324]) ).

tff(c_8282,plain,
    xn = xm,
    inference(demodulation,[status(thm),theory(equality)],[c_74,c_8256]) ).

tff(c_8284,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_70,c_8282]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : NUM459+2 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13  % Command  : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.12/0.34  % Computer : n004.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 300
% 0.12/0.34  % DateTime : Thu Aug  3 14:51:11 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 9.31/3.25  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.56/3.26  
% 9.56/3.26  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 9.56/3.29  
% 9.56/3.29  Inference rules
% 9.56/3.29  ----------------------
% 9.56/3.29  #Ref     : 4
% 9.56/3.29  #Sup     : 1922
% 9.56/3.29  #Fact    : 0
% 9.56/3.29  #Define  : 0
% 9.56/3.29  #Split   : 19
% 9.56/3.29  #Chain   : 0
% 9.56/3.29  #Close   : 0
% 9.56/3.29  
% 9.56/3.29  Ordering : KBO
% 9.56/3.29  
% 9.56/3.29  Simplification rules
% 9.56/3.29  ----------------------
% 9.56/3.29  #Subsume      : 35
% 9.56/3.29  #Demod        : 2393
% 9.56/3.29  #Tautology    : 567
% 9.56/3.29  #SimpNegUnit  : 181
% 9.56/3.29  #BackRed      : 39
% 9.56/3.29  
% 9.56/3.29  #Partial instantiations: 0
% 9.56/3.29  #Strategies tried      : 1
% 9.56/3.29  
% 9.56/3.29  Timing (in seconds)
% 9.56/3.29  ----------------------
% 9.56/3.29  Preprocessing        : 0.58
% 9.56/3.29  Parsing              : 0.30
% 9.56/3.29  CNF conversion       : 0.04
% 9.56/3.29  Main loop            : 1.64
% 9.56/3.29  Inferencing          : 0.42
% 9.56/3.29  Reduction            : 0.67
% 9.56/3.29  Demodulation         : 0.51
% 9.56/3.29  BG Simplification    : 0.06
% 9.56/3.29  Subsumption          : 0.37
% 9.56/3.29  Abstraction          : 0.06
% 9.56/3.29  MUC search           : 0.00
% 9.56/3.29  Cooper               : 0.00
% 9.56/3.29  Total                : 2.27
% 9.56/3.29  Index Insertion      : 0.00
% 9.56/3.29  Index Deletion       : 0.00
% 9.56/3.29  Index Matching       : 0.00
% 9.56/3.29  BG Taut test         : 0.00
%------------------------------------------------------------------------------