TSTP Solution File: COM013+1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : COM013+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/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s

% Computer : n022.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 10:35:18 EDT 2023

% Result   : Theorem 9.92s 3.36s
% Output   : CNFRefutation 10.25s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   18
%            Number of leaves      :   33
% Syntax   : Number of formulae    :   76 (   6 unt;  25 typ;   4 def)
%            Number of atoms       :  243 (   1 equ)
%            Maximal formula atoms :    8 (   4 avg)
%            Number of connectives :  351 ( 159   ~; 158   |;  16   &)
%                                         (   4 <=>;  14  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   7 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   42 (  23   >;  19   *;   0   +;   0  <<)
%            Number of predicates  :   12 (  10 usr;   1 prp; 0-3 aty)
%            Number of functors    :   15 (  15 usr;   2 con; 0-4 aty)
%            Number of variables   :  109 (; 105   !;   4   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ sdtmndtplgtdt0 > sdtmndtasgtdt0 > aReductOfIn0 > aNormalFormOfIn0 > iLess0 > isTerminating0 > isLocallyConfluent0 > isConfluent0 > aRewritingSystem0 > aElement0 > #nlpp > xR > #skF_9 > #skF_7 > #skF_5 > #skF_1 > #skF_4 > #skF_12 > #skF_8 > #skF_10 > #skF_2 > #skF_13 > #skF_6 > #skF_3 > #skF_11 > #skF_14

%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_1',type,
    '#skF_1': ( $i * $i * $i ) > $i ).

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

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

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

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

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

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

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

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

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

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

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

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

tff('#skF_14',type,
    '#skF_14': $i > $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(f_204,negated_conjecture,
    ~ ! [W0] :
        ( aElement0(W0)
       => ( ! [W1] :
              ( aElement0(W1)
             => ( iLess0(W1,W0)
               => ? [W2] : aNormalFormOfIn0(W2,W1,xR) ) )
         => ? [W1] : aNormalFormOfIn0(W1,W0,xR) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).

tff(f_190,hypothesis,
    ( aRewritingSystem0(xR)
    & isTerminating0(xR) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__587) ).

tff(f_101,definition,
    ! [W0,W1,W2] :
      ( ( aElement0(W0)
        & aRewritingSystem0(W1)
        & aElement0(W2) )
     => ( sdtmndtasgtdt0(W0,W1,W2)
      <=> ( ( W0 = W2 )
          | sdtmndtplgtdt0(W0,W1,W2) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mTCRDef) ).

tff(f_187,definition,
    ! [W0,W1] :
      ( ( aElement0(W0)
        & aRewritingSystem0(W1) )
     => ! [W2] :
          ( aNormalFormOfIn0(W2,W0,W1)
        <=> ( aElement0(W2)
            & sdtmndtasgtdt0(W0,W1,W2)
            & ~ ? [W3] : aReductOfIn0(W3,W2,W1) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNFRDef) ).

tff(f_42,axiom,
    ! [W0,W1] :
      ( ( aElement0(W0)
        & aRewritingSystem0(W1) )
     => ! [W2] :
          ( aReductOfIn0(W2,W0,W1)
         => aElement0(W2) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mReduct) ).

tff(f_75,definition,
    ! [W0,W1,W2] :
      ( ( aElement0(W0)
        & aRewritingSystem0(W1)
        & aElement0(W2) )
     => ( sdtmndtplgtdt0(W0,W1,W2)
      <=> ( aReductOfIn0(W2,W0,W1)
          | ? [W3] :
              ( aElement0(W3)
              & aReductOfIn0(W3,W0,W1)
              & sdtmndtplgtdt0(W3,W1,W2) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mTCDef) ).

tff(f_172,definition,
    ! [W0] :
      ( aRewritingSystem0(W0)
     => ( isTerminating0(W0)
      <=> ! [W1,W2] :
            ( ( aElement0(W1)
              & aElement0(W2) )
           => ( sdtmndtplgtdt0(W1,W0,W2)
             => iLess0(W2,W1) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mTermin) ).

tff(f_115,axiom,
    ! [W0,W1,W2,W3] :
      ( ( aElement0(W0)
        & aRewritingSystem0(W1)
        & aElement0(W2)
        & aElement0(W3) )
     => ( ( sdtmndtasgtdt0(W0,W1,W2)
          & sdtmndtasgtdt0(W2,W1,W3) )
       => sdtmndtasgtdt0(W0,W1,W3) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mTCRTrans) ).

tff(c_90,plain,
    ! [W1_87] : ~ aNormalFormOfIn0(W1_87,'#skF_13',xR),
    inference(cnfTransformation,[status(thm)],[f_204]) ).

tff(c_94,plain,
    aElement0('#skF_13'),
    inference(cnfTransformation,[status(thm)],[f_204]) ).

tff(c_88,plain,
    aRewritingSystem0(xR),
    inference(cnfTransformation,[status(thm)],[f_190]) ).

tff(c_28,plain,
    ! [W2_24,W1_23] :
      ( sdtmndtasgtdt0(W2_24,W1_23,W2_24)
      | ~ aRewritingSystem0(W1_23)
      | ~ aElement0(W2_24) ),
    inference(cnfTransformation,[status(thm)],[f_101]) ).

tff(c_688,plain,
    ! [W2_237,W0_238,W1_239] :
      ( aNormalFormOfIn0(W2_237,W0_238,W1_239)
      | aReductOfIn0('#skF_12'(W0_238,W1_239,W2_237),W2_237,W1_239)
      | ~ sdtmndtasgtdt0(W0_238,W1_239,W2_237)
      | ~ aElement0(W2_237)
      | ~ aRewritingSystem0(W1_239)
      | ~ aElement0(W0_238) ),
    inference(cnfTransformation,[status(thm)],[f_187]) ).

tff(c_6,plain,
    ! [W2_6,W0_3,W1_4] :
      ( aElement0(W2_6)
      | ~ aReductOfIn0(W2_6,W0_3,W1_4)
      | ~ aRewritingSystem0(W1_4)
      | ~ aElement0(W0_3) ),
    inference(cnfTransformation,[status(thm)],[f_42]) ).

tff(c_705,plain,
    ! [W0_238,W1_239,W2_237] :
      ( aElement0('#skF_12'(W0_238,W1_239,W2_237))
      | aNormalFormOfIn0(W2_237,W0_238,W1_239)
      | ~ sdtmndtasgtdt0(W0_238,W1_239,W2_237)
      | ~ aElement0(W2_237)
      | ~ aRewritingSystem0(W1_239)
      | ~ aElement0(W0_238) ),
    inference(resolution,[status(thm)],[c_688,c_6]) ).

tff(c_86,plain,
    isTerminating0(xR),
    inference(cnfTransformation,[status(thm)],[f_190]) ).

tff(c_14,plain,
    ! [W2_14,W0_12,W1_13] :
      ( ~ aReductOfIn0(W2_14,W0_12,W1_13)
      | sdtmndtplgtdt0(W0_12,W1_13,W2_14)
      | ~ aElement0(W2_14)
      | ~ aRewritingSystem0(W1_13)
      | ~ aElement0(W0_12) ),
    inference(cnfTransformation,[status(thm)],[f_75]) ).

tff(c_156,plain,
    ! [W2_131,W1_132,W0_133] :
      ( iLess0(W2_131,W1_132)
      | ~ sdtmndtplgtdt0(W1_132,W0_133,W2_131)
      | ~ aElement0(W2_131)
      | ~ aElement0(W1_132)
      | ~ isTerminating0(W0_133)
      | ~ aRewritingSystem0(W0_133) ),
    inference(cnfTransformation,[status(thm)],[f_172]) ).

tff(c_163,plain,
    ! [W2_14,W0_12,W1_13] :
      ( iLess0(W2_14,W0_12)
      | ~ isTerminating0(W1_13)
      | ~ aReductOfIn0(W2_14,W0_12,W1_13)
      | ~ aElement0(W2_14)
      | ~ aRewritingSystem0(W1_13)
      | ~ aElement0(W0_12) ),
    inference(resolution,[status(thm)],[c_14,c_156]) ).

tff(c_6375,plain,
    ! [W0_604,W1_605,W2_606] :
      ( iLess0('#skF_12'(W0_604,W1_605,W2_606),W2_606)
      | ~ isTerminating0(W1_605)
      | ~ aElement0('#skF_12'(W0_604,W1_605,W2_606))
      | aNormalFormOfIn0(W2_606,W0_604,W1_605)
      | ~ sdtmndtasgtdt0(W0_604,W1_605,W2_606)
      | ~ aElement0(W2_606)
      | ~ aRewritingSystem0(W1_605)
      | ~ aElement0(W0_604) ),
    inference(resolution,[status(thm)],[c_688,c_163]) ).

tff(c_78,plain,
    ! [W2_77,W0_70,W1_71] :
      ( aNormalFormOfIn0(W2_77,W0_70,W1_71)
      | aReductOfIn0('#skF_12'(W0_70,W1_71,W2_77),W2_77,W1_71)
      | ~ sdtmndtasgtdt0(W0_70,W1_71,W2_77)
      | ~ aElement0(W2_77)
      | ~ aRewritingSystem0(W1_71)
      | ~ aElement0(W0_70) ),
    inference(cnfTransformation,[status(thm)],[f_187]) ).

tff(c_92,plain,
    ! [W1_85] :
      ( aNormalFormOfIn0('#skF_14'(W1_85),W1_85,xR)
      | ~ iLess0(W1_85,'#skF_13')
      | ~ aElement0(W1_85) ),
    inference(cnfTransformation,[status(thm)],[f_204]) ).

tff(c_117,plain,
    ! [W2_104,W0_105,W1_106] :
      ( aElement0(W2_104)
      | ~ aNormalFormOfIn0(W2_104,W0_105,W1_106)
      | ~ aRewritingSystem0(W1_106)
      | ~ aElement0(W0_105) ),
    inference(cnfTransformation,[status(thm)],[f_187]) ).

tff(c_120,plain,
    ! [W1_85] :
      ( aElement0('#skF_14'(W1_85))
      | ~ aRewritingSystem0(xR)
      | ~ iLess0(W1_85,'#skF_13')
      | ~ aElement0(W1_85) ),
    inference(resolution,[status(thm)],[c_92,c_117]) ).

tff(c_123,plain,
    ! [W1_85] :
      ( aElement0('#skF_14'(W1_85))
      | ~ iLess0(W1_85,'#skF_13')
      | ~ aElement0(W1_85) ),
    inference(demodulation,[status(thm),theory(equality)],[c_88,c_120]) ).

tff(c_150,plain,
    ! [W2_125,W0_126,W1_127] :
      ( ~ aReductOfIn0(W2_125,W0_126,W1_127)
      | sdtmndtplgtdt0(W0_126,W1_127,W2_125)
      | ~ aElement0(W2_125)
      | ~ aRewritingSystem0(W1_127)
      | ~ aElement0(W0_126) ),
    inference(cnfTransformation,[status(thm)],[f_75]) ).

tff(c_26,plain,
    ! [W0_22,W1_23,W2_24] :
      ( ~ sdtmndtplgtdt0(W0_22,W1_23,W2_24)
      | sdtmndtasgtdt0(W0_22,W1_23,W2_24)
      | ~ aElement0(W2_24)
      | ~ aRewritingSystem0(W1_23)
      | ~ aElement0(W0_22) ),
    inference(cnfTransformation,[status(thm)],[f_101]) ).

tff(c_154,plain,
    ! [W0_126,W1_127,W2_125] :
      ( sdtmndtasgtdt0(W0_126,W1_127,W2_125)
      | ~ aReductOfIn0(W2_125,W0_126,W1_127)
      | ~ aElement0(W2_125)
      | ~ aRewritingSystem0(W1_127)
      | ~ aElement0(W0_126) ),
    inference(resolution,[status(thm)],[c_150,c_26]) ).

tff(c_82,plain,
    ! [W0_70,W1_71,W2_77] :
      ( sdtmndtasgtdt0(W0_70,W1_71,W2_77)
      | ~ aNormalFormOfIn0(W2_77,W0_70,W1_71)
      | ~ aRewritingSystem0(W1_71)
      | ~ aElement0(W0_70) ),
    inference(cnfTransformation,[status(thm)],[f_187]) ).

tff(c_269,plain,
    ! [W0_157,W1_158,W3_159,W2_160] :
      ( sdtmndtasgtdt0(W0_157,W1_158,W3_159)
      | ~ sdtmndtasgtdt0(W2_160,W1_158,W3_159)
      | ~ sdtmndtasgtdt0(W0_157,W1_158,W2_160)
      | ~ aElement0(W3_159)
      | ~ aElement0(W2_160)
      | ~ aRewritingSystem0(W1_158)
      | ~ aElement0(W0_157) ),
    inference(cnfTransformation,[status(thm)],[f_115]) ).

tff(c_424,plain,
    ! [W0_202,W1_203,W2_204,W0_205] :
      ( sdtmndtasgtdt0(W0_202,W1_203,W2_204)
      | ~ sdtmndtasgtdt0(W0_202,W1_203,W0_205)
      | ~ aElement0(W2_204)
      | ~ aElement0(W0_202)
      | ~ aNormalFormOfIn0(W2_204,W0_205,W1_203)
      | ~ aRewritingSystem0(W1_203)
      | ~ aElement0(W0_205) ),
    inference(resolution,[status(thm)],[c_82,c_269]) ).

tff(c_603,plain,
    ! [W0_227,W1_228,W2_229,W2_230] :
      ( sdtmndtasgtdt0(W0_227,W1_228,W2_229)
      | ~ aElement0(W2_229)
      | ~ aNormalFormOfIn0(W2_229,W2_230,W1_228)
      | ~ aReductOfIn0(W2_230,W0_227,W1_228)
      | ~ aElement0(W2_230)
      | ~ aRewritingSystem0(W1_228)
      | ~ aElement0(W0_227) ),
    inference(resolution,[status(thm)],[c_154,c_424]) ).

tff(c_605,plain,
    ! [W0_227,W1_85] :
      ( sdtmndtasgtdt0(W0_227,xR,'#skF_14'(W1_85))
      | ~ aElement0('#skF_14'(W1_85))
      | ~ aReductOfIn0(W1_85,W0_227,xR)
      | ~ aRewritingSystem0(xR)
      | ~ aElement0(W0_227)
      | ~ iLess0(W1_85,'#skF_13')
      | ~ aElement0(W1_85) ),
    inference(resolution,[status(thm)],[c_92,c_603]) ).

tff(c_608,plain,
    ! [W0_227,W1_85] :
      ( sdtmndtasgtdt0(W0_227,xR,'#skF_14'(W1_85))
      | ~ aElement0('#skF_14'(W1_85))
      | ~ aReductOfIn0(W1_85,W0_227,xR)
      | ~ aElement0(W0_227)
      | ~ iLess0(W1_85,'#skF_13')
      | ~ aElement0(W1_85) ),
    inference(demodulation,[status(thm),theory(equality)],[c_88,c_605]) ).

tff(c_80,plain,
    ! [W3_80,W2_77,W1_71,W0_70] :
      ( ~ aReductOfIn0(W3_80,W2_77,W1_71)
      | ~ aNormalFormOfIn0(W2_77,W0_70,W1_71)
      | ~ aRewritingSystem0(W1_71)
      | ~ aElement0(W0_70) ),
    inference(cnfTransformation,[status(thm)],[f_187]) ).

tff(c_707,plain,
    ! [W2_243,W0_244,W1_245,W0_246] :
      ( ~ aNormalFormOfIn0(W2_243,W0_244,W1_245)
      | ~ aElement0(W0_244)
      | aNormalFormOfIn0(W2_243,W0_246,W1_245)
      | ~ sdtmndtasgtdt0(W0_246,W1_245,W2_243)
      | ~ aElement0(W2_243)
      | ~ aRewritingSystem0(W1_245)
      | ~ aElement0(W0_246) ),
    inference(resolution,[status(thm)],[c_688,c_80]) ).

tff(c_709,plain,
    ! [W1_85,W0_246] :
      ( aNormalFormOfIn0('#skF_14'(W1_85),W0_246,xR)
      | ~ sdtmndtasgtdt0(W0_246,xR,'#skF_14'(W1_85))
      | ~ aElement0('#skF_14'(W1_85))
      | ~ aRewritingSystem0(xR)
      | ~ aElement0(W0_246)
      | ~ iLess0(W1_85,'#skF_13')
      | ~ aElement0(W1_85) ),
    inference(resolution,[status(thm)],[c_92,c_707]) ).

tff(c_713,plain,
    ! [W1_247,W0_248] :
      ( aNormalFormOfIn0('#skF_14'(W1_247),W0_248,xR)
      | ~ sdtmndtasgtdt0(W0_248,xR,'#skF_14'(W1_247))
      | ~ aElement0('#skF_14'(W1_247))
      | ~ aElement0(W0_248)
      | ~ iLess0(W1_247,'#skF_13')
      | ~ aElement0(W1_247) ),
    inference(demodulation,[status(thm),theory(equality)],[c_88,c_709]) ).

tff(c_743,plain,
    ! [W1_249,W0_250] :
      ( aNormalFormOfIn0('#skF_14'(W1_249),W0_250,xR)
      | ~ aElement0('#skF_14'(W1_249))
      | ~ aReductOfIn0(W1_249,W0_250,xR)
      | ~ aElement0(W0_250)
      | ~ iLess0(W1_249,'#skF_13')
      | ~ aElement0(W1_249) ),
    inference(resolution,[status(thm)],[c_608,c_713]) ).

tff(c_761,plain,
    ! [W1_249] :
      ( ~ aElement0('#skF_14'(W1_249))
      | ~ aReductOfIn0(W1_249,'#skF_13',xR)
      | ~ aElement0('#skF_13')
      | ~ iLess0(W1_249,'#skF_13')
      | ~ aElement0(W1_249) ),
    inference(resolution,[status(thm)],[c_743,c_90]) ).

tff(c_783,plain,
    ! [W1_251] :
      ( ~ aElement0('#skF_14'(W1_251))
      | ~ aReductOfIn0(W1_251,'#skF_13',xR)
      | ~ iLess0(W1_251,'#skF_13')
      | ~ aElement0(W1_251) ),
    inference(demodulation,[status(thm),theory(equality)],[c_94,c_761]) ).

tff(c_788,plain,
    ! [W1_252] :
      ( ~ aReductOfIn0(W1_252,'#skF_13',xR)
      | ~ iLess0(W1_252,'#skF_13')
      | ~ aElement0(W1_252) ),
    inference(resolution,[status(thm)],[c_123,c_783]) ).

tff(c_792,plain,
    ! [W0_70] :
      ( ~ iLess0('#skF_12'(W0_70,xR,'#skF_13'),'#skF_13')
      | ~ aElement0('#skF_12'(W0_70,xR,'#skF_13'))
      | aNormalFormOfIn0('#skF_13',W0_70,xR)
      | ~ sdtmndtasgtdt0(W0_70,xR,'#skF_13')
      | ~ aElement0('#skF_13')
      | ~ aRewritingSystem0(xR)
      | ~ aElement0(W0_70) ),
    inference(resolution,[status(thm)],[c_78,c_788]) ).

tff(c_799,plain,
    ! [W0_70] :
      ( ~ iLess0('#skF_12'(W0_70,xR,'#skF_13'),'#skF_13')
      | ~ aElement0('#skF_12'(W0_70,xR,'#skF_13'))
      | aNormalFormOfIn0('#skF_13',W0_70,xR)
      | ~ sdtmndtasgtdt0(W0_70,xR,'#skF_13')
      | ~ aElement0(W0_70) ),
    inference(demodulation,[status(thm),theory(equality)],[c_88,c_94,c_792]) ).

tff(c_6379,plain,
    ! [W0_604] :
      ( ~ isTerminating0(xR)
      | ~ aElement0('#skF_12'(W0_604,xR,'#skF_13'))
      | aNormalFormOfIn0('#skF_13',W0_604,xR)
      | ~ sdtmndtasgtdt0(W0_604,xR,'#skF_13')
      | ~ aElement0('#skF_13')
      | ~ aRewritingSystem0(xR)
      | ~ aElement0(W0_604) ),
    inference(resolution,[status(thm)],[c_6375,c_799]) ).

tff(c_6383,plain,
    ! [W0_607] :
      ( ~ aElement0('#skF_12'(W0_607,xR,'#skF_13'))
      | aNormalFormOfIn0('#skF_13',W0_607,xR)
      | ~ sdtmndtasgtdt0(W0_607,xR,'#skF_13')
      | ~ aElement0(W0_607) ),
    inference(demodulation,[status(thm),theory(equality)],[c_88,c_94,c_86,c_6379]) ).

tff(c_6387,plain,
    ! [W0_238] :
      ( aNormalFormOfIn0('#skF_13',W0_238,xR)
      | ~ sdtmndtasgtdt0(W0_238,xR,'#skF_13')
      | ~ aElement0('#skF_13')
      | ~ aRewritingSystem0(xR)
      | ~ aElement0(W0_238) ),
    inference(resolution,[status(thm)],[c_705,c_6383]) ).

tff(c_6391,plain,
    ! [W0_608] :
      ( aNormalFormOfIn0('#skF_13',W0_608,xR)
      | ~ sdtmndtasgtdt0(W0_608,xR,'#skF_13')
      | ~ aElement0(W0_608) ),
    inference(demodulation,[status(thm),theory(equality)],[c_88,c_94,c_6387]) ).

tff(c_6451,plain,
    ( aNormalFormOfIn0('#skF_13','#skF_13',xR)
    | ~ aRewritingSystem0(xR)
    | ~ aElement0('#skF_13') ),
    inference(resolution,[status(thm)],[c_28,c_6391]) ).

tff(c_6496,plain,
    aNormalFormOfIn0('#skF_13','#skF_13',xR),
    inference(demodulation,[status(thm),theory(equality)],[c_94,c_88,c_6451]) ).

tff(c_6498,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_90,c_6496]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : COM013+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/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.15/0.35  % Computer : n022.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit : 300
% 0.15/0.35  % WCLimit  : 300
% 0.15/0.35  % DateTime : Thu Aug  3 23:29:48 EDT 2023
% 0.15/0.35  % CPUTime  : 
% 9.92/3.36  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.92/3.37  
% 9.92/3.37  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 10.25/3.40  
% 10.25/3.40  Inference rules
% 10.25/3.40  ----------------------
% 10.25/3.40  #Ref     : 0
% 10.25/3.40  #Sup     : 1275
% 10.25/3.40  #Fact    : 0
% 10.25/3.40  #Define  : 0
% 10.25/3.40  #Split   : 2
% 10.25/3.40  #Chain   : 0
% 10.25/3.40  #Close   : 0
% 10.25/3.40  
% 10.25/3.40  Ordering : KBO
% 10.25/3.40  
% 10.25/3.40  Simplification rules
% 10.25/3.40  ----------------------
% 10.25/3.40  #Subsume      : 333
% 10.25/3.40  #Demod        : 789
% 10.25/3.40  #Tautology    : 185
% 10.25/3.40  #SimpNegUnit  : 1
% 10.25/3.40  #BackRed      : 0
% 10.25/3.40  
% 10.25/3.40  #Partial instantiations: 0
% 10.25/3.40  #Strategies tried      : 1
% 10.25/3.40  
% 10.25/3.40  Timing (in seconds)
% 10.25/3.40  ----------------------
% 10.25/3.40  Preprocessing        : 0.59
% 10.25/3.40  Parsing              : 0.31
% 10.25/3.40  CNF conversion       : 0.05
% 10.25/3.40  Main loop            : 1.69
% 10.25/3.40  Inferencing          : 0.62
% 10.25/3.40  Reduction            : 0.36
% 10.25/3.40  Demodulation         : 0.22
% 10.25/3.40  BG Simplification    : 0.06
% 10.25/3.40  Subsumption          : 0.55
% 10.25/3.40  Abstraction          : 0.06
% 10.25/3.40  MUC search           : 0.00
% 10.25/3.40  Cooper               : 0.00
% 10.25/3.40  Total                : 2.33
% 10.25/3.40  Index Insertion      : 0.00
% 10.25/3.40  Index Deletion       : 0.00
% 10.25/3.40  Index Matching       : 0.00
% 10.25/3.40  BG Taut test         : 0.00
%------------------------------------------------------------------------------