TSTP Solution File: NUM478+2 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : NUM478+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 : n014.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 10:51:49 EDT 2023

% Result   : Theorem 21.10s 9.99s
% Output   : CNFRefutation 21.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   23
% Syntax   : Number of formulae    :   51 (  18 unt;  16 typ;   0 def)
%            Number of atoms       :   80 (  40 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :   78 (  33   ~;  29   |;   9   &)
%                                         (   0 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   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    :   12 (  12 usr;   6 con; 0-2 aty)
%            Number of variables   :   24 (;  23   !;   1   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ sdtlseqdt0 > iLess0 > doDivides0 > aNaturalNumber0 > sdtsldt0 > sdtpldt0 > sdtmndt0 > sdtasdt0 > #nlpp > xn > xm > xl > sz10 > sz00 > #skF_3 > #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_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_383,hypothesis,
    aNaturalNumber0(xn),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1553) ).

tff(f_373,hypothesis,
    ( aNaturalNumber0(xl)
    & aNaturalNumber0(xm) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1524) ).

tff(f_382,hypothesis,
    ( ( xl != sz00 )
    & ? [W0] :
        ( aNaturalNumber0(W0)
        & ( xm = sdtasdt0(xl,W0) ) )
    & doDivides0(xl,xm) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1524_04) ).

tff(f_81,axiom,
    ! [W0,W1,W2] :
      ( ( aNaturalNumber0(W0)
        & aNaturalNumber0(W1)
        & aNaturalNumber0(W2) )
     => ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulAsso) ).

tff(f_73,axiom,
    ! [W0,W1] :
      ( ( aNaturalNumber0(W0)
        & aNaturalNumber0(W1) )
     => ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulComm) ).

tff(f_391,negated_conjecture,
    ~ ( ( aNaturalNumber0(sdtsldt0(xm,xl))
        & ( xm = sdtasdt0(xl,sdtsldt0(xm,xl)) ) )
     => ( ( sdtasdt0(xn,xm) = sdtasdt0(xl,sdtasdt0(xn,sdtsldt0(xm,xl))) )
        | ( sdtasdt0(xn,sdtsldt0(xm,xl)) = sdtsldt0(sdtasdt0(xn,xm),xl) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).

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(c_133,plain,
    aNaturalNumber0(xn),
    inference(cnfTransformation,[status(thm)],[f_383]) ).

tff(c_123,plain,
    aNaturalNumber0(xl),
    inference(cnfTransformation,[status(thm)],[f_373]) ).

tff(c_129,plain,
    aNaturalNumber0('#skF_3'),
    inference(cnfTransformation,[status(thm)],[f_382]) ).

tff(c_127,plain,
    sdtasdt0(xl,'#skF_3') = xm,
    inference(cnfTransformation,[status(thm)],[f_382]) ).

tff(c_58323,plain,
    ! [W0_739,W1_740,W2_741] :
      ( ( sdtasdt0(sdtasdt0(W0_739,W1_740),W2_741) = sdtasdt0(W0_739,sdtasdt0(W1_740,W2_741)) )
      | ~ aNaturalNumber0(W2_741)
      | ~ aNaturalNumber0(W1_740)
      | ~ aNaturalNumber0(W0_739) ),
    inference(cnfTransformation,[status(thm)],[f_81]) ).

tff(c_58544,plain,
    ! [W2_741] :
      ( ( sdtasdt0(xl,sdtasdt0('#skF_3',W2_741)) = sdtasdt0(xm,W2_741) )
      | ~ aNaturalNumber0(W2_741)
      | ~ aNaturalNumber0('#skF_3')
      | ~ aNaturalNumber0(xl) ),
    inference(superposition,[status(thm),theory(equality)],[c_127,c_58323]) ).

tff(c_66154,plain,
    ! [W2_785] :
      ( ( sdtasdt0(xl,sdtasdt0('#skF_3',W2_785)) = sdtasdt0(xm,W2_785) )
      | ~ aNaturalNumber0(W2_785) ),
    inference(demodulation,[status(thm),theory(equality)],[c_123,c_129,c_58544]) ).

tff(c_739,plain,
    ! [W1_99,W0_100] :
      ( ( sdtasdt0(W1_99,W0_100) = sdtasdt0(W0_100,W1_99) )
      | ~ aNaturalNumber0(W1_99)
      | ~ aNaturalNumber0(W0_100) ),
    inference(cnfTransformation,[status(thm)],[f_73]) ).

tff(c_1700,plain,
    ! [W0_116] :
      ( ( sdtasdt0(W0_116,'#skF_3') = sdtasdt0('#skF_3',W0_116) )
      | ~ aNaturalNumber0(W0_116) ),
    inference(resolution,[status(thm)],[c_129,c_739]) ).

tff(c_1768,plain,
    sdtasdt0(xn,'#skF_3') = sdtasdt0('#skF_3',xn),
    inference(resolution,[status(thm)],[c_133,c_1700]) ).

tff(c_139,plain,
    sdtasdt0(xl,sdtsldt0(xm,xl)) = xm,
    inference(cnfTransformation,[status(thm)],[f_391]) ).

tff(c_141,plain,
    aNaturalNumber0(sdtsldt0(xm,xl)),
    inference(cnfTransformation,[status(thm)],[f_391]) ).

tff(c_131,plain,
    xl != sz00,
    inference(cnfTransformation,[status(thm)],[f_382]) ).

tff(c_57351,plain,
    ! [W0_735,W2_736,W1_737] :
      ( ( sdtasdt0(W0_735,W2_736) != sdtasdt0(W0_735,W1_737) )
      | ( W2_736 = W1_737 )
      | ~ aNaturalNumber0(W2_736)
      | ~ aNaturalNumber0(W1_737)
      | ( sz00 = W0_735 )
      | ~ aNaturalNumber0(W0_735) ),
    inference(cnfTransformation,[status(thm)],[f_131]) ).

tff(c_57571,plain,
    ! [W2_736] :
      ( ( sdtasdt0(xl,W2_736) != xm )
      | ( W2_736 = '#skF_3' )
      | ~ aNaturalNumber0(W2_736)
      | ~ aNaturalNumber0('#skF_3')
      | ( xl = sz00 )
      | ~ aNaturalNumber0(xl) ),
    inference(superposition,[status(thm),theory(equality)],[c_127,c_57351]) ).

tff(c_57886,plain,
    ! [W2_736] :
      ( ( sdtasdt0(xl,W2_736) != xm )
      | ( W2_736 = '#skF_3' )
      | ~ aNaturalNumber0(W2_736)
      | ( xl = sz00 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_123,c_129,c_57571]) ).

tff(c_58102,plain,
    ! [W2_738] :
      ( ( sdtasdt0(xl,W2_738) != xm )
      | ( W2_738 = '#skF_3' )
      | ~ aNaturalNumber0(W2_738) ),
    inference(negUnitSimplification,[status(thm)],[c_131,c_57886]) ).

tff(c_58180,plain,
    ( ( sdtasdt0(xl,sdtsldt0(xm,xl)) != xm )
    | ( sdtsldt0(xm,xl) = '#skF_3' ) ),
    inference(resolution,[status(thm)],[c_141,c_58102]) ).

tff(c_58226,plain,
    sdtsldt0(xm,xl) = '#skF_3',
    inference(demodulation,[status(thm),theory(equality)],[c_139,c_58180]) ).

tff(c_121,plain,
    aNaturalNumber0(xm),
    inference(cnfTransformation,[status(thm)],[f_373]) ).

tff(c_55316,plain,
    ! [W0_721] :
      ( ( sdtasdt0(xm,W0_721) = sdtasdt0(W0_721,xm) )
      | ~ aNaturalNumber0(W0_721) ),
    inference(resolution,[status(thm)],[c_121,c_739]) ).

tff(c_55420,plain,
    sdtasdt0(xn,xm) = sdtasdt0(xm,xn),
    inference(resolution,[status(thm)],[c_133,c_55316]) ).

tff(c_137,plain,
    sdtasdt0(xl,sdtasdt0(xn,sdtsldt0(xm,xl))) != sdtasdt0(xn,xm),
    inference(cnfTransformation,[status(thm)],[f_391]) ).

tff(c_55559,plain,
    sdtasdt0(xl,sdtasdt0(xn,sdtsldt0(xm,xl))) != sdtasdt0(xm,xn),
    inference(demodulation,[status(thm),theory(equality)],[c_55420,c_137]) ).

tff(c_58249,plain,
    sdtasdt0(xl,sdtasdt0(xn,'#skF_3')) != sdtasdt0(xm,xn),
    inference(demodulation,[status(thm),theory(equality)],[c_58226,c_55559]) ).

tff(c_58287,plain,
    sdtasdt0(xl,sdtasdt0('#skF_3',xn)) != sdtasdt0(xm,xn),
    inference(demodulation,[status(thm),theory(equality)],[c_1768,c_58249]) ).

tff(c_66187,plain,
    ~ aNaturalNumber0(xn),
    inference(superposition,[status(thm),theory(equality)],[c_66154,c_58287]) ).

tff(c_66255,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_133,c_66187]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : NUM478+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
% 0.16/0.34  % Computer : n014.cluster.edu
% 0.16/0.34  % Model    : x86_64 x86_64
% 0.16/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34  % Memory   : 8042.1875MB
% 0.16/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34  % CPULimit : 300
% 0.16/0.34  % WCLimit  : 300
% 0.16/0.34  % DateTime : Thu Aug  3 14:26:03 EDT 2023
% 0.16/0.35  % CPUTime  : 
% 21.10/9.99  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 21.21/10.00  
% 21.21/10.00  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 21.21/10.03  
% 21.21/10.03  Inference rules
% 21.21/10.03  ----------------------
% 21.21/10.03  #Ref     : 26
% 21.21/10.03  #Sup     : 13901
% 21.21/10.03  #Fact    : 2
% 21.21/10.03  #Define  : 0
% 21.21/10.03  #Split   : 31
% 21.21/10.03  #Chain   : 0
% 21.21/10.03  #Close   : 0
% 21.21/10.03  
% 21.21/10.03  Ordering : KBO
% 21.21/10.03  
% 21.21/10.03  Simplification rules
% 21.21/10.03  ----------------------
% 21.21/10.03  #Subsume      : 861
% 21.21/10.03  #Demod        : 21140
% 21.21/10.03  #Tautology    : 4404
% 21.21/10.03  #SimpNegUnit  : 2562
% 21.21/10.03  #BackRed      : 1056
% 21.21/10.03  
% 21.21/10.03  #Partial instantiations: 0
% 21.21/10.03  #Strategies tried      : 1
% 21.21/10.03  
% 21.21/10.03  Timing (in seconds)
% 21.21/10.03  ----------------------
% 21.21/10.03  Preprocessing        : 0.68
% 21.21/10.03  Parsing              : 0.34
% 21.21/10.03  CNF conversion       : 0.05
% 21.21/10.03  Main loop            : 8.30
% 21.21/10.03  Inferencing          : 1.60
% 21.21/10.03  Reduction            : 4.14
% 21.21/10.03  Demodulation         : 3.25
% 21.21/10.03  BG Simplification    : 0.16
% 21.21/10.03  Subsumption          : 1.91
% 21.21/10.03  Abstraction          : 0.21
% 21.21/10.03  MUC search           : 0.00
% 21.21/10.03  Cooper               : 0.00
% 21.21/10.03  Total                : 9.02
% 21.21/10.03  Index Insertion      : 0.00
% 21.21/10.03  Index Deletion       : 0.00
% 21.21/10.03  Index Matching       : 0.00
% 21.21/10.03  BG Taut test         : 0.00
%------------------------------------------------------------------------------