TSTP Solution File: COM018+4 by Beagle---0.9.51

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%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : COM018+4 : 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 10:35:19 EDT 2023

% Result   : Theorem 9.58s 3.38s
% Output   : CNFRefutation 9.94s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   48
% Syntax   : Number of formulae    :   55 (   6 unt;  43 typ;   0 def)
%            Number of atoms       :   72 (   5 equ)
%            Maximal formula atoms :   30 (   6 avg)
%            Number of connectives :   69 (   9   ~;  20   |;  35   &)
%                                         (   0 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   17 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   62 (  30   >;  32   *;   0   +;   0  <<)
%            Number of predicates  :   12 (  10 usr;   1 prp; 0-3 aty)
%            Number of functors    :   33 (  33 usr;  13 con; 0-4 aty)
%            Number of variables   :   20 (;  10   !;  10   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ sdtmndtplgtdt0 > sdtmndtasgtdt0 > aReductOfIn0 > aNormalFormOfIn0 > iLess0 > isTerminating0 > isLocallyConfluent0 > isConfluent0 > aRewritingSystem0 > aElement0 > #nlpp > xw > xv > xu > xc > xb > xa > xR > #skF_9 > #skF_7 > #skF_5 > #skF_17 > #skF_1 > #skF_20 > #skF_4 > #skF_25 > #skF_18 > #skF_12 > #skF_8 > #skF_13 > #skF_10 > #skF_2 > #skF_19 > #skF_6 > #skF_21 > #skF_26 > #skF_15 > #skF_14 > #skF_3 > #skF_11 > #skF_22 > #skF_24 > #skF_23 > #skF_16

%Foreground sorts:

%Background operators:

%Foreground operators:
tff('#skF_9',type,
    '#skF_9': $i > $i ).

tff('#skF_7',type,
    '#skF_7': $i > $i ).

tff(sdtmndtplgtdt0,type,
    sdtmndtplgtdt0: ( $i * $i * $i ) > $o ).

tff('#skF_5',type,
    '#skF_5': $i > $i ).

tff('#skF_17',type,
    '#skF_17': ( $i * $i * $i ) > $i ).

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

tff('#skF_20',type,
    '#skF_20': $i ).

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

tff(aReductOfIn0,type,
    aReductOfIn0: ( $i * $i * $i ) > $o ).

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

tff('#skF_25',type,
    '#skF_25': $i ).

tff('#skF_18',type,
    '#skF_18': ( $i * $i * $i ) > $i ).

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

tff(aElement0,type,
    aElement0: $i > $o ).

tff('#skF_12',type,
    '#skF_12': ( $i * $i * $i ) > $i ).

tff('#skF_8',type,
    '#skF_8': $i > $i ).

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

tff(isTerminating0,type,
    isTerminating0: $i > $o ).

tff(aNormalFormOfIn0,type,
    aNormalFormOfIn0: ( $i * $i * $i ) > $o ).

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

tff('#skF_13',type,
    '#skF_13': ( $i * $i ) > $i ).

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

tff('#skF_10',type,
    '#skF_10': $i > $i ).

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

tff('#skF_19',type,
    '#skF_19': ( $i * $i * $i ) > $i ).

tff('#skF_6',type,
    '#skF_6': ( $i * $i * $i * $i ) > $i ).

tff('#skF_21',type,
    '#skF_21': $i ).

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

tff('#skF_26',type,
    '#skF_26': $i > $i ).

tff('#skF_15',type,
    '#skF_15': ( $i * $i * $i ) > $i ).

tff('#skF_14',type,
    '#skF_14': ( $i * $i * $i ) > $i ).

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

tff('#skF_11',type,
    '#skF_11': $i > $i ).

tff('#skF_22',type,
    '#skF_22': $i ).

tff(aRewritingSystem0,type,
    aRewritingSystem0: $i > $o ).

tff('#skF_24',type,
    '#skF_24': $i ).

tff('#skF_23',type,
    '#skF_23': $i ).

tff(isConfluent0,type,
    isConfluent0: $i > $o ).

tff(isLocallyConfluent0,type,
    isLocallyConfluent0: $i > $o ).

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

tff(sdtmndtasgtdt0,type,
    sdtmndtasgtdt0: ( $i * $i * $i ) > $o ).

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

tff('#skF_16',type,
    '#skF_16': ( $i * $i * $i ) > $i ).

tff(f_198,hypothesis,
    aRewritingSystem0(xR),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__656) ).

tff(f_263,hypothesis,
    ( ! [W0,W1,W2] :
        ( ( aElement0(W0)
          & aElement0(W1)
          & aElement0(W2)
          & aReductOfIn0(W1,W0,xR)
          & aReductOfIn0(W2,W0,xR) )
       => ? [W3] :
            ( aElement0(W3)
            & ( ( W1 = W3 )
              | ( ( aReductOfIn0(W3,W1,xR)
                  | ? [W4] :
                      ( aElement0(W4)
                      & aReductOfIn0(W4,W1,xR)
                      & sdtmndtplgtdt0(W4,xR,W3) ) )
                & sdtmndtplgtdt0(W1,xR,W3) ) )
            & sdtmndtasgtdt0(W1,xR,W3)
            & ( ( W2 = W3 )
              | ( ( aReductOfIn0(W3,W2,xR)
                  | ? [W4] :
                      ( aElement0(W4)
                      & aReductOfIn0(W4,W2,xR)
                      & sdtmndtplgtdt0(W4,xR,W3) ) )
                & sdtmndtplgtdt0(W2,xR,W3) ) )
            & sdtmndtasgtdt0(W2,xR,W3) ) )
    & isLocallyConfluent0(xR)
    & ! [W0,W1] :
        ( ( aElement0(W0)
          & aElement0(W1) )
       => ( ( aReductOfIn0(W1,W0,xR)
            | ? [W2] :
                ( aElement0(W2)
                & aReductOfIn0(W2,W0,xR)
                & sdtmndtplgtdt0(W2,xR,W1) )
            | sdtmndtplgtdt0(W0,xR,W1) )
         => iLess0(W1,W0) ) )
    & isTerminating0(xR) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__656_01) ).

tff(f_427,hypothesis,
    ( aElement0(xw)
    & ( ( xu = xw )
      | ( ( aReductOfIn0(xw,xu,xR)
          | ? [W0] :
              ( aElement0(W0)
              & aReductOfIn0(W0,xu,xR)
              & sdtmndtplgtdt0(W0,xR,xw) ) )
        & sdtmndtplgtdt0(xu,xR,xw) ) )
    & sdtmndtasgtdt0(xu,xR,xw)
    & ( ( xv = xw )
      | ( ( aReductOfIn0(xw,xv,xR)
          | ? [W0] :
              ( aElement0(W0)
              & aReductOfIn0(W0,xv,xR)
              & sdtmndtplgtdt0(W0,xR,xw) ) )
        & sdtmndtplgtdt0(xv,xR,xw) ) )
    & sdtmndtasgtdt0(xv,xR,xw) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__799) ).

tff(f_197,axiom,
    ! [W0] :
      ( ( aRewritingSystem0(W0)
        & isTerminating0(W0) )
     => ! [W1] :
          ( aElement0(W1)
         => ? [W2] : aNormalFormOfIn0(W2,W1,W0) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mTermNF) ).

tff(f_451,negated_conjecture,
    ~ ? [W0] :
        ( ( aElement0(W0)
          & ( ( xw = W0 )
            | aReductOfIn0(W0,xw,xR)
            | ? [W1] :
                ( aElement0(W1)
                & aReductOfIn0(W1,xw,xR)
                & sdtmndtplgtdt0(W1,xR,W0) )
            | sdtmndtplgtdt0(xw,xR,W0)
            | sdtmndtasgtdt0(xw,xR,W0) )
          & ~ ? [W1] : aReductOfIn0(W1,W0,xR) )
        | aNormalFormOfIn0(W0,xw,xR) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).

tff(c_88,plain,
    aRewritingSystem0(xR),
    inference(cnfTransformation,[status(thm)],[f_198]) ).

tff(c_90,plain,
    isTerminating0(xR),
    inference(cnfTransformation,[status(thm)],[f_263]) ).

tff(c_726,plain,
    aElement0(xw),
    inference(cnfTransformation,[status(thm)],[f_427]) ).

tff(c_3081,plain,
    ! [W0_483,W1_484] :
      ( aNormalFormOfIn0('#skF_13'(W0_483,W1_484),W1_484,W0_483)
      | ~ aElement0(W1_484)
      | ~ isTerminating0(W0_483)
      | ~ aRewritingSystem0(W0_483) ),
    inference(cnfTransformation,[status(thm)],[f_197]) ).

tff(c_744,plain,
    ! [W0_115] : ~ aNormalFormOfIn0(W0_115,xw,xR),
    inference(cnfTransformation,[status(thm)],[f_451]) ).

tff(c_3088,plain,
    ( ~ aElement0(xw)
    | ~ isTerminating0(xR)
    | ~ aRewritingSystem0(xR) ),
    inference(resolution,[status(thm)],[c_3081,c_744]) ).

tff(c_3093,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_88,c_90,c_726,c_3088]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : COM018+4 : TPTP v8.1.2. Released v4.0.0.
% 0.13/0.13  % 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
% 0.14/0.35  % Computer : n004.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 23:26:56 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 9.58/3.38  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.58/3.39  
% 9.58/3.39  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 9.94/3.41  
% 9.94/3.41  Inference rules
% 9.94/3.41  ----------------------
% 9.94/3.41  #Ref     : 0
% 9.94/3.41  #Sup     : 331
% 9.94/3.41  #Fact    : 0
% 9.94/3.41  #Define  : 0
% 9.94/3.41  #Split   : 40
% 9.94/3.41  #Chain   : 0
% 9.94/3.41  #Close   : 0
% 9.94/3.41  
% 9.94/3.41  Ordering : KBO
% 9.94/3.41  
% 9.94/3.41  Simplification rules
% 9.94/3.41  ----------------------
% 9.94/3.41  #Subsume      : 40
% 9.94/3.41  #Demod        : 1005
% 9.94/3.41  #Tautology    : 290
% 9.94/3.41  #SimpNegUnit  : 46
% 9.94/3.41  #BackRed      : 104
% 9.94/3.41  
% 9.94/3.41  #Partial instantiations: 0
% 9.94/3.41  #Strategies tried      : 1
% 9.94/3.41  
% 9.94/3.41  Timing (in seconds)
% 9.94/3.41  ----------------------
% 9.94/3.42  Preprocessing        : 0.86
% 9.94/3.42  Parsing              : 0.36
% 9.94/3.42  CNF conversion       : 0.08
% 9.94/3.42  Main loop            : 1.49
% 9.94/3.42  Inferencing          : 0.35
% 9.94/3.42  Reduction            : 0.42
% 9.94/3.42  Demodulation         : 0.29
% 9.94/3.42  BG Simplification    : 0.12
% 9.94/3.42  Subsumption          : 0.53
% 9.94/3.42  Abstraction          : 0.03
% 9.94/3.42  MUC search           : 0.00
% 9.94/3.42  Cooper               : 0.00
% 9.94/3.42  Total                : 2.40
% 9.94/3.42  Index Insertion      : 0.00
% 9.94/3.42  Index Deletion       : 0.00
% 9.94/3.42  Index Matching       : 0.00
% 9.94/3.42  BG Taut test         : 0.00
%------------------------------------------------------------------------------