TSTP Solution File: NUM468+2 by Beagle---0.9.51

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%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : NUM468+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 : n003.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 10:51:47 EDT 2023

% Result   : Theorem 20.80s 7.96s
% Output   : CNFRefutation 20.80s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   22
% Syntax   : Number of formulae    :   52 (  17 unt;  17 typ;   0 def)
%            Number of atoms       :   92 (  50 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :   94 (  37   ~;  36   |;  13   &)
%                                         (   0 <=>;   8  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   4 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   19 (  10   >;   9   *;   0   +;   0  <<)
%            Number of predicates  :    6 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :   13 (  13 usr;   7 con; 0-2 aty)
%            Number of variables   :   22 (;  20   !;   2   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ sdtlseqdt0 > iLess0 > doDivides0 > aNaturalNumber0 > sdtsldt0 > sdtpldt0 > sdtmndt0 > sdtasdt0 > #nlpp > xn > xm > xl > sz10 > sz00 > #skF_3 > #skF_4 > #skF_2 > #skF_1

%Foreground sorts:

%Background operators:

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

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_3',type,
    '#skF_3': $i ).

tff(doDivides0,type,
    doDivides0: ( $i * $i ) > $o ).

tff('#skF_4',type,
    '#skF_4': $i ).

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

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

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

tff(sdtsldt0,type,
    sdtsldt0: ( $i * $i ) > $i ).

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

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

tff(f_366,negated_conjecture,
    ~ ( ( xl != sz00 )
     => ( ( aNaturalNumber0(sdtsldt0(xm,xl))
          & ( xm = sdtasdt0(xl,sdtsldt0(xm,xl)) ) )
       => ( ( aNaturalNumber0(sdtsldt0(xn,xl))
            & ( xn = sdtasdt0(xl,sdtsldt0(xn,xl)) ) )
         => ( sdtpldt0(xm,xn) = sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).

tff(f_340,hypothesis,
    ( aNaturalNumber0(xl)
    & aNaturalNumber0(xm)
    & aNaturalNumber0(xn) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1240) ).

tff(f_353,hypothesis,
    ( ? [W0] :
        ( aNaturalNumber0(W0)
        & ( xm = sdtasdt0(xl,W0) ) )
    & doDivides0(xl,xm)
    & ? [W0] :
        ( aNaturalNumber0(W0)
        & ( xn = sdtasdt0(xl,W0) ) )
    & doDivides0(xl,xn) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1240_04) ).

tff(f_131,axiom,
    ! [W0] :
      ( aNaturalNumber0(W0)
     => ( ( W0 != sz00 )
       => ! [W1,W2] :
            ( ( aNaturalNumber0(W1)
              & aNaturalNumber0(W2) )
           => ( ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
                | ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
             => ( W1 = W2 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulCanc) ).

tff(f_103,axiom,
    ! [W0,W1,W2] :
      ( ( aNaturalNumber0(W0)
        & aNaturalNumber0(W1)
        & aNaturalNumber0(W2) )
     => ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
        & ( sdtasdt0(sdtpldt0(W1,W2),W0) = sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAMDistr) ).

tff(c_139,plain,
    sdtasdt0(xl,sdtsldt0(xm,xl)) = xm,
    inference(cnfTransformation,[status(thm)],[f_366]) ).

tff(c_141,plain,
    aNaturalNumber0(sdtsldt0(xm,xl)),
    inference(cnfTransformation,[status(thm)],[f_366]) ).

tff(c_143,plain,
    xl != sz00,
    inference(cnfTransformation,[status(thm)],[f_366]) ).

tff(c_119,plain,
    aNaturalNumber0(xl),
    inference(cnfTransformation,[status(thm)],[f_340]) ).

tff(c_131,plain,
    aNaturalNumber0('#skF_4'),
    inference(cnfTransformation,[status(thm)],[f_353]) ).

tff(c_129,plain,
    sdtasdt0(xl,'#skF_4') = xm,
    inference(cnfTransformation,[status(thm)],[f_353]) ).

tff(c_17366,plain,
    ! [W0_374,W2_375,W1_376] :
      ( ( sdtasdt0(W0_374,W2_375) != sdtasdt0(W0_374,W1_376) )
      | ( W2_375 = W1_376 )
      | ~ aNaturalNumber0(W2_375)
      | ~ aNaturalNumber0(W1_376)
      | ( sz00 = W0_374 )
      | ~ aNaturalNumber0(W0_374) ),
    inference(cnfTransformation,[status(thm)],[f_131]) ).

tff(c_17638,plain,
    ! [W2_375] :
      ( ( sdtasdt0(xl,W2_375) != xm )
      | ( W2_375 = '#skF_4' )
      | ~ aNaturalNumber0(W2_375)
      | ~ aNaturalNumber0('#skF_4')
      | ( xl = sz00 )
      | ~ aNaturalNumber0(xl) ),
    inference(superposition,[status(thm),theory(equality)],[c_129,c_17366]) ).

tff(c_18007,plain,
    ! [W2_375] :
      ( ( sdtasdt0(xl,W2_375) != xm )
      | ( W2_375 = '#skF_4' )
      | ~ aNaturalNumber0(W2_375)
      | ( xl = sz00 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_119,c_131,c_17638]) ).

tff(c_18799,plain,
    ! [W2_381] :
      ( ( sdtasdt0(xl,W2_381) != xm )
      | ( W2_381 = '#skF_4' )
      | ~ aNaturalNumber0(W2_381) ),
    inference(negUnitSimplification,[status(thm)],[c_143,c_18007]) ).

tff(c_18853,plain,
    ( ( sdtasdt0(xl,sdtsldt0(xm,xl)) != xm )
    | ( sdtsldt0(xm,xl) = '#skF_4' ) ),
    inference(resolution,[status(thm)],[c_141,c_18799]) ).

tff(c_18894,plain,
    sdtsldt0(xm,xl) = '#skF_4',
    inference(demodulation,[status(thm),theory(equality)],[c_139,c_18853]) ).

tff(c_135,plain,
    sdtasdt0(xl,sdtsldt0(xn,xl)) = xn,
    inference(cnfTransformation,[status(thm)],[f_366]) ).

tff(c_137,plain,
    aNaturalNumber0(sdtsldt0(xn,xl)),
    inference(cnfTransformation,[status(thm)],[f_366]) ).

tff(c_125,plain,
    aNaturalNumber0('#skF_3'),
    inference(cnfTransformation,[status(thm)],[f_353]) ).

tff(c_123,plain,
    sdtasdt0(xl,'#skF_3') = xn,
    inference(cnfTransformation,[status(thm)],[f_353]) ).

tff(c_17632,plain,
    ! [W1_376] :
      ( ( sdtasdt0(xl,W1_376) != xn )
      | ( W1_376 = '#skF_3' )
      | ~ aNaturalNumber0('#skF_3')
      | ~ aNaturalNumber0(W1_376)
      | ( xl = sz00 )
      | ~ aNaturalNumber0(xl) ),
    inference(superposition,[status(thm),theory(equality)],[c_123,c_17366]) ).

tff(c_17998,plain,
    ! [W1_376] :
      ( ( sdtasdt0(xl,W1_376) != xn )
      | ( W1_376 = '#skF_3' )
      | ~ aNaturalNumber0(W1_376)
      | ( xl = sz00 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_119,c_125,c_17632]) ).

tff(c_18050,plain,
    ! [W1_377] :
      ( ( sdtasdt0(xl,W1_377) != xn )
      | ( W1_377 = '#skF_3' )
      | ~ aNaturalNumber0(W1_377) ),
    inference(negUnitSimplification,[status(thm)],[c_143,c_17998]) ).

tff(c_18113,plain,
    ( ( sdtasdt0(xl,sdtsldt0(xn,xl)) != xn )
    | ( sdtsldt0(xn,xl) = '#skF_3' ) ),
    inference(resolution,[status(thm)],[c_137,c_18050]) ).

tff(c_18158,plain,
    sdtsldt0(xn,xl) = '#skF_3',
    inference(demodulation,[status(thm),theory(equality)],[c_135,c_18113]) ).

tff(c_133,plain,
    sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))) != sdtpldt0(xm,xn),
    inference(cnfTransformation,[status(thm)],[f_366]) ).

tff(c_18193,plain,
    sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),'#skF_3')) != sdtpldt0(xm,xn),
    inference(demodulation,[status(thm),theory(equality)],[c_18158,c_133]) ).

tff(c_28077,plain,
    sdtasdt0(xl,sdtpldt0('#skF_4','#skF_3')) != sdtpldt0(xm,xn),
    inference(demodulation,[status(thm),theory(equality)],[c_18894,c_18193]) ).

tff(c_20375,plain,
    ! [W0_393,W1_394,W2_395] :
      ( ( sdtpldt0(sdtasdt0(W0_393,W1_394),sdtasdt0(W0_393,W2_395)) = sdtasdt0(W0_393,sdtpldt0(W1_394,W2_395)) )
      | ~ aNaturalNumber0(W2_395)
      | ~ aNaturalNumber0(W1_394)
      | ~ aNaturalNumber0(W0_393) ),
    inference(cnfTransformation,[status(thm)],[f_103]) ).

tff(c_20737,plain,
    ! [W2_395] :
      ( ( sdtpldt0(xm,sdtasdt0(xl,W2_395)) = sdtasdt0(xl,sdtpldt0('#skF_4',W2_395)) )
      | ~ aNaturalNumber0(W2_395)
      | ~ aNaturalNumber0('#skF_4')
      | ~ aNaturalNumber0(xl) ),
    inference(superposition,[status(thm),theory(equality)],[c_129,c_20375]) ).

tff(c_34722,plain,
    ! [W2_446] :
      ( ( sdtpldt0(xm,sdtasdt0(xl,W2_446)) = sdtasdt0(xl,sdtpldt0('#skF_4',W2_446)) )
      | ~ aNaturalNumber0(W2_446) ),
    inference(demodulation,[status(thm),theory(equality)],[c_119,c_131,c_20737]) ).

tff(c_34793,plain,
    ( ( sdtasdt0(xl,sdtpldt0('#skF_4','#skF_3')) = sdtpldt0(xm,xn) )
    | ~ aNaturalNumber0('#skF_3') ),
    inference(superposition,[status(thm),theory(equality)],[c_123,c_34722]) ).

tff(c_34842,plain,
    sdtasdt0(xl,sdtpldt0('#skF_4','#skF_3')) = sdtpldt0(xm,xn),
    inference(demodulation,[status(thm),theory(equality)],[c_125,c_34793]) ).

tff(c_34844,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_28077,c_34842]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13  % Problem  : NUM468+2 : TPTP v8.1.2. Released v4.0.0.
% 0.13/0.14  % 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
% 0.14/0.35  % Computer : n003.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 14:52:08 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 20.80/7.96  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 20.80/7.96  
% 20.80/7.96  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 20.80/7.99  
% 20.80/7.99  Inference rules
% 20.80/7.99  ----------------------
% 20.80/7.99  #Ref     : 12
% 20.80/7.99  #Sup     : 7248
% 20.80/7.99  #Fact    : 2
% 20.80/7.99  #Define  : 0
% 20.80/7.99  #Split   : 56
% 20.80/7.99  #Chain   : 0
% 20.80/7.99  #Close   : 0
% 20.80/7.99  
% 20.80/7.99  Ordering : KBO
% 20.80/7.99  
% 20.80/7.99  Simplification rules
% 20.80/7.99  ----------------------
% 20.80/7.99  #Subsume      : 236
% 20.80/7.99  #Demod        : 12506
% 20.80/7.99  #Tautology    : 3077
% 20.80/7.99  #SimpNegUnit  : 1103
% 20.80/7.99  #BackRed      : 1114
% 20.80/7.99  
% 20.80/7.99  #Partial instantiations: 0
% 20.80/7.99  #Strategies tried      : 1
% 20.80/7.99  
% 20.80/7.99  Timing (in seconds)
% 20.80/7.99  ----------------------
% 20.80/8.00  Preprocessing        : 0.69
% 20.80/8.00  Parsing              : 0.34
% 20.80/8.00  CNF conversion       : 0.05
% 20.80/8.00  Main loop            : 6.18
% 20.80/8.00  Inferencing          : 1.21
% 20.80/8.00  Reduction            : 3.20
% 20.80/8.00  Demodulation         : 2.60
% 20.80/8.00  BG Simplification    : 0.12
% 20.80/8.00  Subsumption          : 1.23
% 20.80/8.00  Abstraction          : 0.15
% 20.80/8.00  MUC search           : 0.00
% 20.80/8.00  Cooper               : 0.00
% 20.80/8.00  Total                : 6.92
% 20.97/8.00  Index Insertion      : 0.00
% 20.97/8.00  Index Deletion       : 0.00
% 20.97/8.00  Index Matching       : 0.00
% 20.97/8.00  BG Taut test         : 0.00
%------------------------------------------------------------------------------