TSTP Solution File: NUM469+1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : NUM469+1 : 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 : n010.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 14.98s 5.13s
% Output   : CNFRefutation 14.98s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :   29
% Syntax   : Number of formulae    :   87 (  34 unt;  15 typ;   2 def)
%            Number of atoms       :  158 (  47 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :  151 (  65   ~;  58   |;  15   &)
%                                         (   2 <=>;  11  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   3 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    :   11 (  11 usr;   5 con; 0-2 aty)
%            Number of variables   :   37 (;  36   !;   1   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ sdtlseqdt0 > iLess0 > doDivides0 > aNaturalNumber0 > sdtsldt0 > sdtpldt0 > sdtmndt0 > sdtasdt0 > #nlpp > xn > xm > xl > sz10 > sz00 > #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(doDivides0,type,
    doDivides0: ( $i * $i ) > $o ).

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_340,hypothesis,
    ( aNaturalNumber0(xl)
    & aNaturalNumber0(xm)
    & aNaturalNumber0(xn) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1240) ).

tff(f_35,axiom,
    ( aNaturalNumber0(sz10)
    & ( sz10 != sz00 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC_01) ).

tff(f_87,axiom,
    ! [W0] :
      ( aNaturalNumber0(W0)
     => ( ( sdtasdt0(W0,sz10) = W0 )
        & ( W0 = sdtasdt0(sz10,W0) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_MulUnit) ).

tff(f_278,axiom,
    ! [W0,W1] :
      ( ( aNaturalNumber0(W0)
        & aNaturalNumber0(W1) )
     => ( ( W0 != sz00 )
       => sdtlseqdt0(W1,sdtasdt0(W1,W0)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMonMul2) ).

tff(f_343,hypothesis,
    ( doDivides0(xl,xm)
    & doDivides0(xl,xn) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1240_04) ).

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_349,negated_conjecture,
    ~ doDivides0(xl,sdtpldt0(xm,xn)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).

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

tff(f_307,definition,
    ! [W0,W1] :
      ( ( aNaturalNumber0(W0)
        & aNaturalNumber0(W1) )
     => ( doDivides0(W0,W1)
      <=> ? [W2] :
            ( aNaturalNumber0(W2)
            & ( W1 = sdtasdt0(W0,W2) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefDiv) ).

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_323,definition,
    ! [W0,W1] :
      ( ( aNaturalNumber0(W0)
        & aNaturalNumber0(W1) )
     => ( ( ( W0 != sz00 )
          & doDivides0(W0,W1) )
       => ! [W2] :
            ( ( W2 = sdtsldt0(W1,W0) )
          <=> ( aNaturalNumber0(W2)
              & ( W1 = sdtasdt0(W0,W2) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefQuot) ).

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

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_347,hypothesis,
    ( ( xl != sz00 )
   => ( sdtpldt0(xm,xn) = sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1298) ).

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

tff(c_8,plain,
    aNaturalNumber0(sz10),
    inference(cnfTransformation,[status(thm)],[f_35]) ).

tff(c_241,plain,
    ! [W0_81] :
      ( ( sdtasdt0(sz10,W0_81) = W0_81 )
      | ~ aNaturalNumber0(W0_81) ),
    inference(cnfTransformation,[status(thm)],[f_87]) ).

tff(c_262,plain,
    sdtasdt0(sz10,xl) = xl,
    inference(resolution,[status(thm)],[c_119,c_241]) ).

tff(c_1092,plain,
    ! [W1_107,W0_108] :
      ( sdtlseqdt0(W1_107,sdtasdt0(W1_107,W0_108))
      | ( sz00 = W0_108 )
      | ~ aNaturalNumber0(W1_107)
      | ~ aNaturalNumber0(W0_108) ),
    inference(cnfTransformation,[status(thm)],[f_278]) ).

tff(c_1134,plain,
    ( sdtlseqdt0(sz10,xl)
    | ( xl = sz00 )
    | ~ aNaturalNumber0(sz10)
    | ~ aNaturalNumber0(xl) ),
    inference(superposition,[status(thm),theory(equality)],[c_262,c_1092]) ).

tff(c_1199,plain,
    ( sdtlseqdt0(sz10,xl)
    | ( xl = sz00 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_119,c_8,c_1134]) ).

tff(c_1576,plain,
    xl = sz00,
    inference(splitLeft,[status(thm)],[c_1199]) ).

tff(c_121,plain,
    doDivides0(xl,xn),
    inference(cnfTransformation,[status(thm)],[f_343]) ).

tff(c_1594,plain,
    doDivides0(sz00,xn),
    inference(demodulation,[status(thm),theory(equality)],[c_1576,c_121]) ).

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

tff(c_200,plain,
    ! [W0_80] :
      ( ( sdtpldt0(sz00,W0_80) = W0_80 )
      | ~ aNaturalNumber0(W0_80) ),
    inference(cnfTransformation,[status(thm)],[f_67]) ).

tff(c_216,plain,
    sdtpldt0(sz00,xn) = xn,
    inference(resolution,[status(thm)],[c_115,c_200]) ).

tff(c_117,plain,
    aNaturalNumber0(xm),
    inference(cnfTransformation,[status(thm)],[f_340]) ).

tff(c_261,plain,
    sdtasdt0(sz10,xm) = xm,
    inference(resolution,[status(thm)],[c_117,c_241]) ).

tff(c_1128,plain,
    ( sdtlseqdt0(sz10,xm)
    | ( xm = sz00 )
    | ~ aNaturalNumber0(sz10)
    | ~ aNaturalNumber0(xm) ),
    inference(superposition,[status(thm),theory(equality)],[c_261,c_1092]) ).

tff(c_1195,plain,
    ( sdtlseqdt0(sz10,xm)
    | ( xm = sz00 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_117,c_8,c_1128]) ).

tff(c_1664,plain,
    xm = sz00,
    inference(splitLeft,[status(thm)],[c_1195]) ).

tff(c_127,plain,
    ~ doDivides0(xl,sdtpldt0(xm,xn)),
    inference(cnfTransformation,[status(thm)],[f_349]) ).

tff(c_1592,plain,
    ~ doDivides0(sz00,sdtpldt0(xm,xn)),
    inference(demodulation,[status(thm),theory(equality)],[c_1576,c_127]) ).

tff(c_1665,plain,
    ~ doDivides0(sz00,sdtpldt0(sz00,xn)),
    inference(demodulation,[status(thm),theory(equality)],[c_1664,c_1592]) ).

tff(c_1682,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_1594,c_216,c_1665]) ).

tff(c_1684,plain,
    xm != sz00,
    inference(splitRight,[status(thm)],[c_1195]) ).

tff(c_123,plain,
    doDivides0(xl,xm),
    inference(cnfTransformation,[status(thm)],[f_343]) ).

tff(c_1593,plain,
    doDivides0(sz00,xm),
    inference(demodulation,[status(thm),theory(equality)],[c_1576,c_123]) ).

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

tff(c_903,plain,
    ! [W0_102,W1_103] :
      ( aNaturalNumber0('#skF_2'(W0_102,W1_103))
      | ~ doDivides0(W0_102,W1_103)
      | ~ aNaturalNumber0(W1_103)
      | ~ aNaturalNumber0(W0_102) ),
    inference(cnfTransformation,[status(thm)],[f_307]) ).

tff(c_30,plain,
    ! [W0_18] :
      ( ( sdtasdt0(sz00,W0_18) = sz00 )
      | ~ aNaturalNumber0(W0_18) ),
    inference(cnfTransformation,[status(thm)],[f_93]) ).

tff(c_19364,plain,
    ! [W0_357,W1_358] :
      ( ( sdtasdt0(sz00,'#skF_2'(W0_357,W1_358)) = sz00 )
      | ~ doDivides0(W0_357,W1_358)
      | ~ aNaturalNumber0(W1_358)
      | ~ aNaturalNumber0(W0_357) ),
    inference(resolution,[status(thm)],[c_903,c_30]) ).

tff(c_103,plain,
    ! [W0_65,W1_66] :
      ( ( sdtasdt0(W0_65,'#skF_2'(W0_65,W1_66)) = W1_66 )
      | ~ doDivides0(W0_65,W1_66)
      | ~ aNaturalNumber0(W1_66)
      | ~ aNaturalNumber0(W0_65) ),
    inference(cnfTransformation,[status(thm)],[f_307]) ).

tff(c_19430,plain,
    ! [W1_358] :
      ( ( sz00 = W1_358 )
      | ~ doDivides0(sz00,W1_358)
      | ~ aNaturalNumber0(W1_358)
      | ~ aNaturalNumber0(sz00)
      | ~ doDivides0(sz00,W1_358)
      | ~ aNaturalNumber0(W1_358)
      | ~ aNaturalNumber0(sz00) ),
    inference(superposition,[status(thm),theory(equality)],[c_19364,c_103]) ).

tff(c_19507,plain,
    ! [W1_359] :
      ( ( sz00 = W1_359 )
      | ~ doDivides0(sz00,W1_359)
      | ~ aNaturalNumber0(W1_359) ),
    inference(demodulation,[status(thm),theory(equality)],[c_4,c_4,c_19430]) ).

tff(c_19517,plain,
    ( ( xm = sz00 )
    | ~ aNaturalNumber0(xm) ),
    inference(resolution,[status(thm)],[c_1593,c_19507]) ).

tff(c_19530,plain,
    xm = sz00,
    inference(demodulation,[status(thm),theory(equality)],[c_117,c_19517]) ).

tff(c_19532,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_1684,c_19530]) ).

tff(c_19534,plain,
    xl != sz00,
    inference(splitRight,[status(thm)],[c_1199]) ).

tff(c_111,plain,
    ! [W1_71,W0_70] :
      ( aNaturalNumber0(sdtsldt0(W1_71,W0_70))
      | ~ doDivides0(W0_70,W1_71)
      | ( sz00 = W0_70 )
      | ~ aNaturalNumber0(W1_71)
      | ~ aNaturalNumber0(W0_70) ),
    inference(cnfTransformation,[status(thm)],[f_323]) ).

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_622,plain,
    ! [W1_93,W0_94] :
      ( ( sdtpldt0(W1_93,W0_94) = sdtpldt0(W0_94,W1_93) )
      | ~ aNaturalNumber0(W1_93)
      | ~ aNaturalNumber0(W0_94) ),
    inference(cnfTransformation,[status(thm)],[f_53]) ).

tff(c_644,plain,
    ! [W0_95] :
      ( ( sdtpldt0(xn,W0_95) = sdtpldt0(W0_95,xn) )
      | ~ aNaturalNumber0(W0_95) ),
    inference(resolution,[status(thm)],[c_115,c_622]) ).

tff(c_673,plain,
    sdtpldt0(xn,xm) = sdtpldt0(xm,xn),
    inference(resolution,[status(thm)],[c_117,c_644]) ).

tff(c_807,plain,
    ( aNaturalNumber0(sdtpldt0(xm,xn))
    | ~ aNaturalNumber0(xm)
    | ~ aNaturalNumber0(xn) ),
    inference(superposition,[status(thm),theory(equality)],[c_673,c_10]) ).

tff(c_815,plain,
    aNaturalNumber0(sdtpldt0(xm,xn)),
    inference(demodulation,[status(thm),theory(equality)],[c_115,c_117,c_807]) ).

tff(c_125,plain,
    ( ( sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))) = sdtpldt0(xm,xn) )
    | ( xl = sz00 ) ),
    inference(cnfTransformation,[status(thm)],[f_347]) ).

tff(c_23972,plain,
    sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))) = sdtpldt0(xm,xn),
    inference(negUnitSimplification,[status(thm)],[c_19534,c_125]) ).

tff(c_101,plain,
    ! [W0_65,W2_69] :
      ( doDivides0(W0_65,sdtasdt0(W0_65,W2_69))
      | ~ aNaturalNumber0(W2_69)
      | ~ aNaturalNumber0(sdtasdt0(W0_65,W2_69))
      | ~ aNaturalNumber0(W0_65) ),
    inference(cnfTransformation,[status(thm)],[f_307]) ).

tff(c_23976,plain,
    ( doDivides0(xl,sdtpldt0(xm,xn))
    | ~ aNaturalNumber0(sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl)))
    | ~ aNaturalNumber0(sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))))
    | ~ aNaturalNumber0(xl) ),
    inference(superposition,[status(thm),theory(equality)],[c_23972,c_101]) ).

tff(c_23988,plain,
    ( doDivides0(xl,sdtpldt0(xm,xn))
    | ~ aNaturalNumber0(sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))) ),
    inference(demodulation,[status(thm),theory(equality)],[c_119,c_815,c_23972,c_23976]) ).

tff(c_23989,plain,
    ~ aNaturalNumber0(sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))),
    inference(negUnitSimplification,[status(thm)],[c_127,c_23988]) ).

tff(c_24003,plain,
    ( ~ aNaturalNumber0(sdtsldt0(xn,xl))
    | ~ aNaturalNumber0(sdtsldt0(xm,xl)) ),
    inference(resolution,[status(thm)],[c_10,c_23989]) ).

tff(c_24152,plain,
    ~ aNaturalNumber0(sdtsldt0(xm,xl)),
    inference(splitLeft,[status(thm)],[c_24003]) ).

tff(c_24155,plain,
    ( ~ doDivides0(xl,xm)
    | ( xl = sz00 )
    | ~ aNaturalNumber0(xm)
    | ~ aNaturalNumber0(xl) ),
    inference(resolution,[status(thm)],[c_111,c_24152]) ).

tff(c_24158,plain,
    xl = sz00,
    inference(demodulation,[status(thm),theory(equality)],[c_119,c_117,c_123,c_24155]) ).

tff(c_24160,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_19534,c_24158]) ).

tff(c_24161,plain,
    ~ aNaturalNumber0(sdtsldt0(xn,xl)),
    inference(splitRight,[status(thm)],[c_24003]) ).

tff(c_24165,plain,
    ( ~ doDivides0(xl,xn)
    | ( xl = sz00 )
    | ~ aNaturalNumber0(xn)
    | ~ aNaturalNumber0(xl) ),
    inference(resolution,[status(thm)],[c_111,c_24161]) ).

tff(c_24168,plain,
    xl = sz00,
    inference(demodulation,[status(thm),theory(equality)],[c_119,c_115,c_121,c_24165]) ).

tff(c_24170,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_19534,c_24168]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : NUM469+1 : 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
% 0.14/0.36  % Computer : n010.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit : 300
% 0.14/0.36  % WCLimit  : 300
% 0.14/0.36  % DateTime : Thu Aug  3 14:18:28 EDT 2023
% 0.14/0.36  % CPUTime  : 
% 14.98/5.13  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 14.98/5.14  
% 14.98/5.14  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 14.98/5.17  
% 14.98/5.17  Inference rules
% 14.98/5.17  ----------------------
% 14.98/5.17  #Ref     : 19
% 14.98/5.17  #Sup     : 5044
% 14.98/5.17  #Fact    : 2
% 14.98/5.17  #Define  : 0
% 14.98/5.17  #Split   : 22
% 14.98/5.17  #Chain   : 0
% 14.98/5.17  #Close   : 0
% 14.98/5.17  
% 14.98/5.17  Ordering : KBO
% 14.98/5.17  
% 14.98/5.17  Simplification rules
% 14.98/5.17  ----------------------
% 14.98/5.17  #Subsume      : 444
% 14.98/5.17  #Demod        : 7935
% 14.98/5.17  #Tautology    : 1885
% 14.98/5.17  #SimpNegUnit  : 751
% 14.98/5.17  #BackRed      : 304
% 14.98/5.17  
% 14.98/5.17  #Partial instantiations: 0
% 14.98/5.17  #Strategies tried      : 1
% 14.98/5.17  
% 14.98/5.17  Timing (in seconds)
% 14.98/5.17  ----------------------
% 14.98/5.18  Preprocessing        : 0.67
% 14.98/5.18  Parsing              : 0.34
% 14.98/5.18  CNF conversion       : 0.05
% 14.98/5.18  Main loop            : 3.37
% 14.98/5.18  Inferencing          : 0.86
% 14.98/5.18  Reduction            : 1.44
% 14.98/5.18  Demodulation         : 1.08
% 14.98/5.18  BG Simplification    : 0.10
% 14.98/5.18  Subsumption          : 0.74
% 14.98/5.18  Abstraction          : 0.10
% 14.98/5.18  MUC search           : 0.00
% 14.98/5.18  Cooper               : 0.00
% 14.98/5.18  Total                : 4.10
% 14.98/5.18  Index Insertion      : 0.00
% 14.98/5.18  Index Deletion       : 0.00
% 14.98/5.18  Index Matching       : 0.00
% 14.98/5.18  BG Taut test         : 0.00
%------------------------------------------------------------------------------