TSTP Solution File: NUM469+2 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : NUM469+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 : n009.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 8.46s 3.06s
% Output   : CNFRefutation 8.46s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   24
% Syntax   : Number of formulae    :   60 (  25 unt;  17 typ;   0 def)
%            Number of atoms       :   76 (  38 equ)
%            Maximal formula atoms :    6 (   1 avg)
%            Number of connectives :   52 (  19   ~;  14   |;  15   &)
%                                         (   0 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   2 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   :   16 (;  13   !;   3   ?;   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_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_93,axiom,
    ! [W0] :
      ( aNaturalNumber0(W0)
     => ( ( sdtasdt0(W0,sz00) = sz00 )
        & ( sz00 = sdtasdt0(sz00,W0) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_MulZero) ).

tff(f_365,hypothesis,
    ( ( 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__1298) ).

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

tff(f_372,negated_conjecture,
    ~ ( ? [W0] :
          ( aNaturalNumber0(W0)
          & ( sdtpldt0(xm,xn) = sdtasdt0(xl,W0) ) )
      | doDivides0(xl,sdtpldt0(xm,xn)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).

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_41,axiom,
    ! [W0,W1] :
      ( ( aNaturalNumber0(W0)
        & aNaturalNumber0(W1) )
     => aNaturalNumber0(sdtpldt0(W0,W1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB) ).

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

tff(c_301,plain,
    ! [W0_82] :
      ( ( sdtasdt0(sz00,W0_82) = sz00 )
      | ~ aNaturalNumber0(W0_82) ),
    inference(cnfTransformation,[status(thm)],[f_93]) ).

tff(c_324,plain,
    sdtasdt0(sz00,'#skF_3') = sz00,
    inference(resolution,[status(thm)],[c_125,c_301]) ).

tff(c_137,plain,
    ( aNaturalNumber0(sdtsldt0(xn,xl))
    | ( xl = sz00 ) ),
    inference(cnfTransformation,[status(thm)],[f_365]) ).

tff(c_268,plain,
    xl = sz00,
    inference(splitLeft,[status(thm)],[c_137]) ).

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

tff(c_270,plain,
    sdtasdt0(sz00,'#skF_3') = xn,
    inference(demodulation,[status(thm),theory(equality)],[c_268,c_123]) ).

tff(c_353,plain,
    xn = sz00,
    inference(demodulation,[status(thm),theory(equality)],[c_324,c_270]) ).

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

tff(c_325,plain,
    sdtasdt0(sz00,'#skF_4') = sz00,
    inference(resolution,[status(thm)],[c_131,c_301]) ).

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

tff(c_271,plain,
    sdtasdt0(sz00,'#skF_4') = xm,
    inference(demodulation,[status(thm),theory(equality)],[c_268,c_129]) ).

tff(c_335,plain,
    xm = sz00,
    inference(demodulation,[status(thm),theory(equality)],[c_325,c_271]) ).

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

tff(c_184,plain,
    ! [W0_80] :
      ( ( sdtasdt0(W0_80,sz00) = sz00 )
      | ~ aNaturalNumber0(W0_80) ),
    inference(cnfTransformation,[status(thm)],[f_93]) ).

tff(c_208,plain,
    sdtasdt0(xl,sz00) = sz00,
    inference(resolution,[status(thm)],[c_119,c_184]) ).

tff(c_326,plain,
    sdtasdt0(sz00,sz00) = sz00,
    inference(demodulation,[status(thm),theory(equality)],[c_268,c_208]) ).

tff(c_225,plain,
    ! [W0_81] :
      ( ( sdtpldt0(xm,xn) != sdtasdt0(xl,W0_81) )
      | ~ aNaturalNumber0(W0_81) ),
    inference(cnfTransformation,[status(thm)],[f_372]) ).

tff(c_249,plain,
    sdtpldt0(xm,xn) != sdtasdt0(xl,xl),
    inference(resolution,[status(thm)],[c_119,c_225]) ).

tff(c_399,plain,
    sdtpldt0(sz00,sz00) != sz00,
    inference(demodulation,[status(thm),theory(equality)],[c_353,c_335,c_326,c_268,c_268,c_249]) ).

tff(c_115,plain,
    aNaturalNumber0(xn),
    inference(cnfTransformation,[status(thm)],[f_340]) ).

tff(c_358,plain,
    ! [W0_83] :
      ( ( sdtpldt0(sz00,W0_83) = W0_83 )
      | ~ aNaturalNumber0(W0_83) ),
    inference(cnfTransformation,[status(thm)],[f_67]) ).

tff(c_376,plain,
    sdtpldt0(sz00,xn) = xn,
    inference(resolution,[status(thm)],[c_115,c_358]) ).

tff(c_404,plain,
    sdtpldt0(sz00,sz00) = sz00,
    inference(demodulation,[status(thm),theory(equality)],[c_353,c_353,c_376]) ).

tff(c_405,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_399,c_404]) ).

tff(c_407,plain,
    xl != sz00,
    inference(splitRight,[status(thm)],[c_137]) ).

tff(c_141,plain,
    ( aNaturalNumber0(sdtsldt0(xm,xl))
    | ( xl = sz00 ) ),
    inference(cnfTransformation,[status(thm)],[f_365]) ).

tff(c_551,plain,
    aNaturalNumber0(sdtsldt0(xm,xl)),
    inference(negUnitSimplification,[status(thm)],[c_407,c_141]) ).

tff(c_406,plain,
    aNaturalNumber0(sdtsldt0(xn,xl)),
    inference(splitRight,[status(thm)],[c_137]) ).

tff(c_133,plain,
    ( ( sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))) = sdtpldt0(xm,xn) )
    | ( xl = sz00 ) ),
    inference(cnfTransformation,[status(thm)],[f_365]) ).

tff(c_5647,plain,
    sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))) = sdtpldt0(xm,xn),
    inference(negUnitSimplification,[status(thm)],[c_407,c_133]) ).

tff(c_703,plain,
    ! [W0_88,W1_89] :
      ( aNaturalNumber0(sdtpldt0(W0_88,W1_89))
      | ~ aNaturalNumber0(W1_89)
      | ~ aNaturalNumber0(W0_88) ),
    inference(cnfTransformation,[status(thm)],[f_41]) ).

tff(c_145,plain,
    ! [W0_77] :
      ( ( sdtpldt0(xm,xn) != sdtasdt0(xl,W0_77) )
      | ~ aNaturalNumber0(W0_77) ),
    inference(cnfTransformation,[status(thm)],[f_372]) ).

tff(c_765,plain,
    ! [W0_88,W1_89] :
      ( ( sdtasdt0(xl,sdtpldt0(W0_88,W1_89)) != sdtpldt0(xm,xn) )
      | ~ aNaturalNumber0(W1_89)
      | ~ aNaturalNumber0(W0_88) ),
    inference(resolution,[status(thm)],[c_703,c_145]) ).

tff(c_5654,plain,
    ( ~ aNaturalNumber0(sdtsldt0(xn,xl))
    | ~ aNaturalNumber0(sdtsldt0(xm,xl)) ),
    inference(superposition,[status(thm),theory(equality)],[c_5647,c_765]) ).

tff(c_5674,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_551,c_406,c_5654]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : NUM469+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/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 : n009.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 14:21:08 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 8.46/3.06  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.46/3.06  
% 8.46/3.06  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 8.46/3.09  
% 8.46/3.09  Inference rules
% 8.46/3.09  ----------------------
% 8.46/3.09  #Ref     : 0
% 8.46/3.09  #Sup     : 1133
% 8.46/3.09  #Fact    : 2
% 8.46/3.09  #Define  : 0
% 8.46/3.09  #Split   : 15
% 8.46/3.09  #Chain   : 0
% 8.46/3.09  #Close   : 0
% 8.46/3.09  
% 8.46/3.09  Ordering : KBO
% 8.46/3.09  
% 8.46/3.09  Simplification rules
% 8.46/3.09  ----------------------
% 8.46/3.09  #Subsume      : 179
% 8.46/3.09  #Demod        : 2349
% 8.46/3.09  #Tautology    : 635
% 8.46/3.09  #SimpNegUnit  : 141
% 8.46/3.09  #BackRed      : 505
% 8.46/3.09  
% 8.46/3.09  #Partial instantiations: 0
% 8.46/3.09  #Strategies tried      : 1
% 8.46/3.09  
% 8.46/3.09  Timing (in seconds)
% 8.46/3.09  ----------------------
% 8.46/3.10  Preprocessing        : 0.68
% 8.46/3.10  Parsing              : 0.35
% 8.46/3.10  CNF conversion       : 0.05
% 8.46/3.10  Main loop            : 1.26
% 8.46/3.10  Inferencing          : 0.38
% 8.46/3.10  Reduction            : 0.47
% 8.46/3.10  Demodulation         : 0.35
% 8.46/3.10  BG Simplification    : 0.06
% 8.46/3.10  Subsumption          : 0.26
% 8.46/3.10  Abstraction          : 0.05
% 8.46/3.10  MUC search           : 0.00
% 8.46/3.10  Cooper               : 0.00
% 8.46/3.10  Total                : 1.98
% 8.46/3.10  Index Insertion      : 0.00
% 8.46/3.10  Index Deletion       : 0.00
% 8.46/3.10  Index Matching       : 0.00
% 8.46/3.10  BG Taut test         : 0.00
%------------------------------------------------------------------------------