TSTP Solution File: KRS143+1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : KRS143+1 : TPTP v8.1.2. Released v3.1.0.
% 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 : 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 10:45:17 EDT 2023

% Result   : Theorem 3.78s 1.90s
% Output   : CNFRefutation 4.06s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :   19
% Syntax   : Number of formulae    :  195 (  80 unt;  14 typ;   0 def)
%            Number of atoms       :  448 (  47 equ)
%            Maximal formula atoms :    9 (   2 avg)
%            Number of connectives :  495 ( 228   ~; 253   |;   7   &)
%                                         (   2 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    8 (   7   >;   1   *;   0   +;   0  <<)
%            Number of predicates  :    8 (   6 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   7 con; 0-1 aty)
%            Number of variables   :  112 (; 110   !;   2   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ rp > xsd_string > xsd_integer > cowlThing > cowlNothing > cc > #nlpp > #skF_1 > #skF_7 > #skF_5 > #skF_6 > #skF_2 > #skF_3 > #skF_8 > #skF_4

%Foreground sorts:

%Background operators:

%Foreground operators:
tff(cc,type,
    cc: $i > $o ).

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

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

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

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

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

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

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

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

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

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

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

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

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

tff(f_76,axiom,
    ! [X] :
      ( cowlThing(X)
      & ~ cowlNothing(X) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_0) ).

tff(f_126,negated_conjecture,
    ~ ( ! [X] :
          ( cowlThing(X)
          & ~ cowlNothing(X) )
      & ! [X] :
          ( xsd_string(X)
        <=> ~ xsd_integer(X) )
      & ! [X] :
          ( cc(X)
         => ( ? [Y0] : rp(X,Y0)
            & ! [Y0,Y1] :
                ( ( rp(X,Y0)
                  & rp(X,Y1) )
               => ( Y0 = Y1 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',the_axiom) ).

tff(f_82,axiom,
    ! [X] :
      ( xsd_string(X)
    <=> ~ xsd_integer(X) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1) ).

tff(f_88,axiom,
    ! [X] :
      ( cc(X)
     => ? [Y0] : rp(X,Y0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_2) ).

tff(f_98,axiom,
    ! [X] :
      ( cc(X)
     => ! [Y0,Y1] :
          ( ( rp(X,Y0)
            & rp(X,Y1) )
         => ( Y0 = Y1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_3) ).

tff(c_16,plain,
    ! [X_17] : cowlThing(X_17),
    inference(cnfTransformation,[status(thm)],[f_76]) ).

tff(c_18,plain,
    ! [X_17] : ~ cowlNothing(X_17),
    inference(cnfTransformation,[status(thm)],[f_76]) ).

tff(c_58,plain,
    ( ~ xsd_integer('#skF_4')
    | xsd_string('#skF_5')
    | cc('#skF_6')
    | ~ cowlThing('#skF_3')
    | cowlNothing('#skF_2') ),
    inference(cnfTransformation,[status(thm)],[f_126]) ).

tff(c_60,plain,
    ( ~ xsd_integer('#skF_4')
    | xsd_string('#skF_5')
    | cc('#skF_6')
    | ~ cowlThing('#skF_3') ),
    inference(negUnitSimplification,[status(thm)],[c_18,c_58]) ).

tff(c_78,plain,
    ( ~ xsd_integer('#skF_4')
    | xsd_string('#skF_5')
    | cc('#skF_6') ),
    inference(demodulation,[status(thm),theory(equality)],[c_16,c_60]) ).

tff(c_115,plain,
    ~ xsd_integer('#skF_4'),
    inference(splitLeft,[status(thm)],[c_78]) ).

tff(c_22,plain,
    ! [X_18] :
      ( xsd_string(X_18)
      | xsd_integer(X_18) ),
    inference(cnfTransformation,[status(thm)],[f_82]) ).

tff(c_56,plain,
    ( ~ xsd_string('#skF_4')
    | xsd_string('#skF_5')
    | cc('#skF_6')
    | ~ cowlThing('#skF_3')
    | cowlNothing('#skF_2') ),
    inference(cnfTransformation,[status(thm)],[f_126]) ).

tff(c_63,plain,
    ( ~ xsd_string('#skF_4')
    | xsd_string('#skF_5')
    | cc('#skF_6')
    | ~ cowlThing('#skF_3') ),
    inference(negUnitSimplification,[status(thm)],[c_18,c_56]) ).

tff(c_84,plain,
    ( ~ xsd_string('#skF_4')
    | xsd_string('#skF_5')
    | cc('#skF_6') ),
    inference(demodulation,[status(thm),theory(equality)],[c_16,c_63]) ).

tff(c_116,plain,
    ~ xsd_string('#skF_4'),
    inference(splitLeft,[status(thm)],[c_84]) ).

tff(c_119,plain,
    xsd_integer('#skF_4'),
    inference(resolution,[status(thm)],[c_22,c_116]) ).

tff(c_123,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_115,c_119]) ).

tff(c_125,plain,
    xsd_string('#skF_4'),
    inference(splitRight,[status(thm)],[c_84]) ).

tff(c_52,plain,
    ( ~ xsd_string('#skF_4')
    | xsd_integer('#skF_5')
    | cc('#skF_6')
    | ~ cowlThing('#skF_3')
    | cowlNothing('#skF_2') ),
    inference(cnfTransformation,[status(thm)],[f_126]) ).

tff(c_73,plain,
    ( ~ xsd_string('#skF_4')
    | xsd_integer('#skF_5')
    | cc('#skF_6')
    | ~ cowlThing('#skF_3') ),
    inference(negUnitSimplification,[status(thm)],[c_18,c_52]) ).

tff(c_104,plain,
    ( ~ xsd_string('#skF_4')
    | xsd_integer('#skF_5')
    | cc('#skF_6') ),
    inference(demodulation,[status(thm),theory(equality)],[c_16,c_73]) ).

tff(c_131,plain,
    ( xsd_integer('#skF_5')
    | cc('#skF_6') ),
    inference(demodulation,[status(thm),theory(equality)],[c_125,c_104]) ).

tff(c_132,plain,
    cc('#skF_6'),
    inference(splitLeft,[status(thm)],[c_131]) ).

tff(c_24,plain,
    ! [X_19] :
      ( rp(X_19,'#skF_1'(X_19))
      | ~ cc(X_19) ),
    inference(cnfTransformation,[status(thm)],[f_88]) ).

tff(c_28,plain,
    ! [Y0_29] :
      ( ~ xsd_string('#skF_4')
      | xsd_integer('#skF_5')
      | ( '#skF_7' != '#skF_8' )
      | ~ rp('#skF_6',Y0_29)
      | ~ cowlThing('#skF_3')
      | cowlNothing('#skF_2') ),
    inference(cnfTransformation,[status(thm)],[f_126]) ).

tff(c_71,plain,
    ! [Y0_29] :
      ( ~ xsd_string('#skF_4')
      | xsd_integer('#skF_5')
      | ( '#skF_7' != '#skF_8' )
      | ~ rp('#skF_6',Y0_29)
      | ~ cowlThing('#skF_3') ),
    inference(negUnitSimplification,[status(thm)],[c_18,c_28]) ).

tff(c_100,plain,
    ! [Y0_29] :
      ( ~ xsd_string('#skF_4')
      | xsd_integer('#skF_5')
      | ( '#skF_7' != '#skF_8' )
      | ~ rp('#skF_6',Y0_29) ),
    inference(demodulation,[status(thm),theory(equality)],[c_16,c_71]) ).

tff(c_137,plain,
    ! [Y0_29] :
      ( xsd_integer('#skF_5')
      | ( '#skF_7' != '#skF_8' )
      | ~ rp('#skF_6',Y0_29) ),
    inference(demodulation,[status(thm),theory(equality)],[c_125,c_100]) ).

tff(c_138,plain,
    '#skF_7' != '#skF_8',
    inference(splitLeft,[status(thm)],[c_137]) ).

tff(c_48,plain,
    ! [Y0_29] :
      ( ~ xsd_string('#skF_4')
      | xsd_string('#skF_5')
      | rp('#skF_6','#skF_7')
      | ~ rp('#skF_6',Y0_29)
      | ~ cowlThing('#skF_3')
      | cowlNothing('#skF_2') ),
    inference(cnfTransformation,[status(thm)],[f_126]) ).

tff(c_67,plain,
    ! [Y0_29] :
      ( ~ xsd_string('#skF_4')
      | xsd_string('#skF_5')
      | rp('#skF_6','#skF_7')
      | ~ rp('#skF_6',Y0_29)
      | ~ cowlThing('#skF_3') ),
    inference(negUnitSimplification,[status(thm)],[c_18,c_48]) ).

tff(c_92,plain,
    ! [Y0_29] :
      ( ~ xsd_string('#skF_4')
      | xsd_string('#skF_5')
      | rp('#skF_6','#skF_7')
      | ~ rp('#skF_6',Y0_29) ),
    inference(demodulation,[status(thm),theory(equality)],[c_16,c_67]) ).

tff(c_142,plain,
    ! [Y0_29] :
      ( xsd_string('#skF_5')
      | rp('#skF_6','#skF_7')
      | ~ rp('#skF_6',Y0_29) ),
    inference(demodulation,[status(thm),theory(equality)],[c_125,c_92]) ).

tff(c_144,plain,
    ! [Y0_35] : ~ rp('#skF_6',Y0_35),
    inference(splitLeft,[status(thm)],[c_142]) ).

tff(c_148,plain,
    ~ cc('#skF_6'),
    inference(resolution,[status(thm)],[c_24,c_144]) ).

tff(c_152,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_132,c_148]) ).

tff(c_153,plain,
    ( rp('#skF_6','#skF_7')
    | xsd_string('#skF_5') ),
    inference(splitRight,[status(thm)],[c_142]) ).

tff(c_154,plain,
    xsd_string('#skF_5'),
    inference(splitLeft,[status(thm)],[c_153]) ).

tff(c_20,plain,
    ! [X_18] :
      ( ~ xsd_integer(X_18)
      | ~ xsd_string(X_18) ),
    inference(cnfTransformation,[status(thm)],[f_82]) ).

tff(c_158,plain,
    ~ xsd_integer('#skF_5'),
    inference(resolution,[status(thm)],[c_154,c_20]) ).

tff(c_44,plain,
    ! [Y0_29] :
      ( ~ xsd_string('#skF_4')
      | xsd_integer('#skF_5')
      | rp('#skF_6','#skF_7')
      | ~ rp('#skF_6',Y0_29)
      | ~ cowlThing('#skF_3')
      | cowlNothing('#skF_2') ),
    inference(cnfTransformation,[status(thm)],[f_126]) ).

tff(c_70,plain,
    ! [Y0_29] :
      ( ~ xsd_string('#skF_4')
      | xsd_integer('#skF_5')
      | rp('#skF_6','#skF_7')
      | ~ rp('#skF_6',Y0_29)
      | ~ cowlThing('#skF_3') ),
    inference(negUnitSimplification,[status(thm)],[c_18,c_44]) ).

tff(c_98,plain,
    ! [Y0_29] :
      ( ~ xsd_string('#skF_4')
      | xsd_integer('#skF_5')
      | rp('#skF_6','#skF_7')
      | ~ rp('#skF_6',Y0_29) ),
    inference(demodulation,[status(thm),theory(equality)],[c_16,c_70]) ).

tff(c_221,plain,
    ! [Y0_29] :
      ( xsd_integer('#skF_5')
      | rp('#skF_6','#skF_7')
      | ~ rp('#skF_6',Y0_29) ),
    inference(demodulation,[status(thm),theory(equality)],[c_125,c_98]) ).

tff(c_222,plain,
    ! [Y0_29] :
      ( rp('#skF_6','#skF_7')
      | ~ rp('#skF_6',Y0_29) ),
    inference(negUnitSimplification,[status(thm)],[c_158,c_221]) ).

tff(c_223,plain,
    ! [Y0_29] : ~ rp('#skF_6',Y0_29),
    inference(splitLeft,[status(thm)],[c_222]) ).

tff(c_36,plain,
    ! [Y0_29] :
      ( ~ xsd_string('#skF_4')
      | xsd_integer('#skF_5')
      | rp('#skF_6','#skF_8')
      | ~ rp('#skF_6',Y0_29)
      | ~ cowlThing('#skF_3')
      | cowlNothing('#skF_2') ),
    inference(cnfTransformation,[status(thm)],[f_126]) ).

tff(c_66,plain,
    ! [Y0_29] :
      ( ~ xsd_string('#skF_4')
      | xsd_integer('#skF_5')
      | rp('#skF_6','#skF_8')
      | ~ rp('#skF_6',Y0_29)
      | ~ cowlThing('#skF_3') ),
    inference(negUnitSimplification,[status(thm)],[c_18,c_36]) ).

tff(c_90,plain,
    ! [Y0_29] :
      ( ~ xsd_string('#skF_4')
      | xsd_integer('#skF_5')
      | rp('#skF_6','#skF_8')
      | ~ rp('#skF_6',Y0_29) ),
    inference(demodulation,[status(thm),theory(equality)],[c_16,c_66]) ).

tff(c_170,plain,
    ! [Y0_29] :
      ( xsd_integer('#skF_5')
      | rp('#skF_6','#skF_8')
      | ~ rp('#skF_6',Y0_29) ),
    inference(demodulation,[status(thm),theory(equality)],[c_125,c_90]) ).

tff(c_171,plain,
    ! [Y0_29] :
      ( rp('#skF_6','#skF_8')
      | ~ rp('#skF_6',Y0_29) ),
    inference(negUnitSimplification,[status(thm)],[c_158,c_170]) ).

tff(c_173,plain,
    ! [Y0_41] : ~ rp('#skF_6',Y0_41),
    inference(splitLeft,[status(thm)],[c_171]) ).

tff(c_177,plain,
    ~ cc('#skF_6'),
    inference(resolution,[status(thm)],[c_24,c_173]) ).

tff(c_181,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_132,c_177]) ).

tff(c_182,plain,
    rp('#skF_6','#skF_8'),
    inference(splitRight,[status(thm)],[c_171]) ).

tff(c_225,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_223,c_182]) ).

tff(c_226,plain,
    rp('#skF_6','#skF_7'),
    inference(splitRight,[status(thm)],[c_222]) ).

tff(c_26,plain,
    ! [Y1_25,Y0_24,X_21] :
      ( ( Y1_25 = Y0_24 )
      | ~ rp(X_21,Y1_25)
      | ~ rp(X_21,Y0_24)
      | ~ cc(X_21) ),
    inference(cnfTransformation,[status(thm)],[f_98]) ).

tff(c_188,plain,
    ! [Y0_24] :
      ( ( Y0_24 = '#skF_8' )
      | ~ rp('#skF_6',Y0_24)
      | ~ cc('#skF_6') ),
    inference(resolution,[status(thm)],[c_182,c_26]) ).

tff(c_194,plain,
    ! [Y0_24] :
      ( ( Y0_24 = '#skF_8' )
      | ~ rp('#skF_6',Y0_24) ),
    inference(demodulation,[status(thm),theory(equality)],[c_132,c_188]) ).

tff(c_229,plain,
    '#skF_7' = '#skF_8',
    inference(resolution,[status(thm)],[c_226,c_194]) ).

tff(c_238,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_138,c_229]) ).

tff(c_239,plain,
    rp('#skF_6','#skF_7'),
    inference(splitRight,[status(thm)],[c_153]) ).

tff(c_246,plain,
    ! [Y1_43,Y0_44,X_45] :
      ( ( Y1_43 = Y0_44 )
      | ~ rp(X_45,Y1_43)
      | ~ rp(X_45,Y0_44)
      | ~ cc(X_45) ),
    inference(cnfTransformation,[status(thm)],[f_98]) ).

tff(c_248,plain,
    ! [Y0_44] :
      ( ( Y0_44 = '#skF_7' )
      | ~ rp('#skF_6',Y0_44)
      | ~ cc('#skF_6') ),
    inference(resolution,[status(thm)],[c_239,c_246]) ).

tff(c_255,plain,
    ! [Y0_46] :
      ( ( Y0_46 = '#skF_7' )
      | ~ rp('#skF_6',Y0_46) ),
    inference(demodulation,[status(thm),theory(equality)],[c_132,c_248]) ).

tff(c_262,plain,
    ( ( '#skF_1'('#skF_6') = '#skF_7' )
    | ~ cc('#skF_6') ),
    inference(resolution,[status(thm)],[c_24,c_255]) ).

tff(c_267,plain,
    '#skF_1'('#skF_6') = '#skF_7',
    inference(demodulation,[status(thm),theory(equality)],[c_132,c_262]) ).

tff(c_240,plain,
    ~ xsd_string('#skF_5'),
    inference(splitRight,[status(thm)],[c_153]) ).

tff(c_40,plain,
    ! [Y0_29] :
      ( ~ xsd_string('#skF_4')
      | xsd_string('#skF_5')
      | rp('#skF_6','#skF_8')
      | ~ rp('#skF_6',Y0_29)
      | ~ cowlThing('#skF_3')
      | cowlNothing('#skF_2') ),
    inference(cnfTransformation,[status(thm)],[f_126]) ).

tff(c_74,plain,
    ! [Y0_29] :
      ( ~ xsd_string('#skF_4')
      | xsd_string('#skF_5')
      | rp('#skF_6','#skF_8')
      | ~ rp('#skF_6',Y0_29)
      | ~ cowlThing('#skF_3') ),
    inference(negUnitSimplification,[status(thm)],[c_18,c_40]) ).

tff(c_106,plain,
    ! [Y0_29] :
      ( ~ xsd_string('#skF_4')
      | xsd_string('#skF_5')
      | rp('#skF_6','#skF_8')
      | ~ rp('#skF_6',Y0_29) ),
    inference(demodulation,[status(thm),theory(equality)],[c_16,c_74]) ).

tff(c_292,plain,
    ! [Y0_29] :
      ( xsd_string('#skF_5')
      | rp('#skF_6','#skF_8')
      | ~ rp('#skF_6',Y0_29) ),
    inference(demodulation,[status(thm),theory(equality)],[c_125,c_106]) ).

tff(c_293,plain,
    ! [Y0_29] :
      ( rp('#skF_6','#skF_8')
      | ~ rp('#skF_6',Y0_29) ),
    inference(negUnitSimplification,[status(thm)],[c_240,c_292]) ).

tff(c_294,plain,
    ! [Y0_29] : ~ rp('#skF_6',Y0_29),
    inference(splitLeft,[status(thm)],[c_293]) ).

tff(c_296,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_294,c_239]) ).

tff(c_297,plain,
    rp('#skF_6','#skF_8'),
    inference(splitRight,[status(thm)],[c_293]) ).

tff(c_254,plain,
    ! [Y0_44,X_19] :
      ( ( Y0_44 = '#skF_1'(X_19) )
      | ~ rp(X_19,Y0_44)
      | ~ cc(X_19) ),
    inference(resolution,[status(thm)],[c_24,c_246]) ).

tff(c_302,plain,
    ( ( '#skF_1'('#skF_6') = '#skF_8' )
    | ~ cc('#skF_6') ),
    inference(resolution,[status(thm)],[c_297,c_254]) ).

tff(c_310,plain,
    '#skF_7' = '#skF_8',
    inference(demodulation,[status(thm),theory(equality)],[c_132,c_267,c_302]) ).

tff(c_312,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_138,c_310]) ).

tff(c_313,plain,
    ! [Y0_29] :
      ( ~ rp('#skF_6',Y0_29)
      | xsd_integer('#skF_5') ),
    inference(splitRight,[status(thm)],[c_137]) ).

tff(c_320,plain,
    ! [Y0_49] : ~ rp('#skF_6',Y0_49),
    inference(splitLeft,[status(thm)],[c_313]) ).

tff(c_324,plain,
    ~ cc('#skF_6'),
    inference(resolution,[status(thm)],[c_24,c_320]) ).

tff(c_328,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_132,c_324]) ).

tff(c_329,plain,
    xsd_integer('#skF_5'),
    inference(splitRight,[status(thm)],[c_313]) ).

tff(c_314,plain,
    '#skF_7' = '#skF_8',
    inference(splitRight,[status(thm)],[c_137]) ).

tff(c_32,plain,
    ! [Y0_29] :
      ( ~ xsd_string('#skF_4')
      | xsd_string('#skF_5')
      | ( '#skF_7' != '#skF_8' )
      | ~ rp('#skF_6',Y0_29)
      | ~ cowlThing('#skF_3')
      | cowlNothing('#skF_2') ),
    inference(cnfTransformation,[status(thm)],[f_126]) ).

tff(c_62,plain,
    ! [Y0_29] :
      ( ~ xsd_string('#skF_4')
      | xsd_string('#skF_5')
      | ( '#skF_7' != '#skF_8' )
      | ~ rp('#skF_6',Y0_29)
      | ~ cowlThing('#skF_3') ),
    inference(negUnitSimplification,[status(thm)],[c_18,c_32]) ).

tff(c_82,plain,
    ! [Y0_29] :
      ( ~ xsd_string('#skF_4')
      | xsd_string('#skF_5')
      | ( '#skF_7' != '#skF_8' )
      | ~ rp('#skF_6',Y0_29) ),
    inference(demodulation,[status(thm),theory(equality)],[c_16,c_62]) ).

tff(c_331,plain,
    ! [Y0_29] :
      ( xsd_string('#skF_5')
      | ~ rp('#skF_6',Y0_29) ),
    inference(demodulation,[status(thm),theory(equality)],[c_314,c_125,c_82]) ).

tff(c_333,plain,
    ! [Y0_50] : ~ rp('#skF_6',Y0_50),
    inference(splitLeft,[status(thm)],[c_331]) ).

tff(c_337,plain,
    ~ cc('#skF_6'),
    inference(resolution,[status(thm)],[c_24,c_333]) ).

tff(c_341,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_132,c_337]) ).

tff(c_342,plain,
    xsd_string('#skF_5'),
    inference(splitRight,[status(thm)],[c_331]) ).

tff(c_345,plain,
    ~ xsd_integer('#skF_5'),
    inference(resolution,[status(thm)],[c_342,c_20]) ).

tff(c_349,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_329,c_345]) ).

tff(c_350,plain,
    xsd_integer('#skF_5'),
    inference(splitRight,[status(thm)],[c_131]) ).

tff(c_351,plain,
    ~ cc('#skF_6'),
    inference(splitRight,[status(thm)],[c_131]) ).

tff(c_124,plain,
    ( cc('#skF_6')
    | xsd_string('#skF_5') ),
    inference(splitRight,[status(thm)],[c_84]) ).

tff(c_353,plain,
    xsd_string('#skF_5'),
    inference(negUnitSimplification,[status(thm)],[c_351,c_124]) ).

tff(c_356,plain,
    ~ xsd_integer('#skF_5'),
    inference(resolution,[status(thm)],[c_353,c_20]) ).

tff(c_360,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_350,c_356]) ).

tff(c_361,plain,
    ( cc('#skF_6')
    | xsd_string('#skF_5') ),
    inference(splitRight,[status(thm)],[c_78]) ).

tff(c_363,plain,
    xsd_string('#skF_5'),
    inference(splitLeft,[status(thm)],[c_361]) ).

tff(c_367,plain,
    ~ xsd_integer('#skF_5'),
    inference(resolution,[status(thm)],[c_363,c_20]) ).

tff(c_362,plain,
    xsd_integer('#skF_4'),
    inference(splitRight,[status(thm)],[c_78]) ).

tff(c_54,plain,
    ( ~ xsd_integer('#skF_4')
    | xsd_integer('#skF_5')
    | cc('#skF_6')
    | ~ cowlThing('#skF_3')
    | cowlNothing('#skF_2') ),
    inference(cnfTransformation,[status(thm)],[f_126]) ).

tff(c_59,plain,
    ( ~ xsd_integer('#skF_4')
    | xsd_integer('#skF_5')
    | cc('#skF_6')
    | ~ cowlThing('#skF_3') ),
    inference(negUnitSimplification,[status(thm)],[c_18,c_54]) ).

tff(c_76,plain,
    ( ~ xsd_integer('#skF_4')
    | xsd_integer('#skF_5')
    | cc('#skF_6') ),
    inference(demodulation,[status(thm),theory(equality)],[c_16,c_59]) ).

tff(c_376,plain,
    ( xsd_integer('#skF_5')
    | cc('#skF_6') ),
    inference(demodulation,[status(thm),theory(equality)],[c_362,c_76]) ).

tff(c_377,plain,
    cc('#skF_6'),
    inference(negUnitSimplification,[status(thm)],[c_367,c_376]) ).

tff(c_30,plain,
    ! [Y0_29] :
      ( ~ xsd_integer('#skF_4')
      | xsd_integer('#skF_5')
      | ( '#skF_7' != '#skF_8' )
      | ~ rp('#skF_6',Y0_29)
      | ~ cowlThing('#skF_3')
      | cowlNothing('#skF_2') ),
    inference(cnfTransformation,[status(thm)],[f_126]) ).

tff(c_69,plain,
    ! [Y0_29] :
      ( ~ xsd_integer('#skF_4')
      | xsd_integer('#skF_5')
      | ( '#skF_7' != '#skF_8' )
      | ~ rp('#skF_6',Y0_29)
      | ~ cowlThing('#skF_3') ),
    inference(negUnitSimplification,[status(thm)],[c_18,c_30]) ).

tff(c_96,plain,
    ! [Y0_29] :
      ( ~ xsd_integer('#skF_4')
      | xsd_integer('#skF_5')
      | ( '#skF_7' != '#skF_8' )
      | ~ rp('#skF_6',Y0_29) ),
    inference(demodulation,[status(thm),theory(equality)],[c_16,c_69]) ).

tff(c_382,plain,
    ! [Y0_29] :
      ( xsd_integer('#skF_5')
      | ( '#skF_7' != '#skF_8' )
      | ~ rp('#skF_6',Y0_29) ),
    inference(demodulation,[status(thm),theory(equality)],[c_362,c_96]) ).

tff(c_383,plain,
    ! [Y0_29] :
      ( ( '#skF_7' != '#skF_8' )
      | ~ rp('#skF_6',Y0_29) ),
    inference(negUnitSimplification,[status(thm)],[c_367,c_382]) ).

tff(c_384,plain,
    '#skF_7' != '#skF_8',
    inference(splitLeft,[status(thm)],[c_383]) ).

tff(c_46,plain,
    ! [Y0_29] :
      ( ~ xsd_integer('#skF_4')
      | xsd_integer('#skF_5')
      | rp('#skF_6','#skF_7')
      | ~ rp('#skF_6',Y0_29)
      | ~ cowlThing('#skF_3')
      | cowlNothing('#skF_2') ),
    inference(cnfTransformation,[status(thm)],[f_126]) ).

tff(c_68,plain,
    ! [Y0_29] :
      ( ~ xsd_integer('#skF_4')
      | xsd_integer('#skF_5')
      | rp('#skF_6','#skF_7')
      | ~ rp('#skF_6',Y0_29)
      | ~ cowlThing('#skF_3') ),
    inference(negUnitSimplification,[status(thm)],[c_18,c_46]) ).

tff(c_94,plain,
    ! [Y0_29] :
      ( ~ xsd_integer('#skF_4')
      | xsd_integer('#skF_5')
      | rp('#skF_6','#skF_7')
      | ~ rp('#skF_6',Y0_29) ),
    inference(demodulation,[status(thm),theory(equality)],[c_16,c_68]) ).

tff(c_389,plain,
    ! [Y0_29] :
      ( xsd_integer('#skF_5')
      | rp('#skF_6','#skF_7')
      | ~ rp('#skF_6',Y0_29) ),
    inference(demodulation,[status(thm),theory(equality)],[c_362,c_94]) ).

tff(c_390,plain,
    ! [Y0_29] :
      ( rp('#skF_6','#skF_7')
      | ~ rp('#skF_6',Y0_29) ),
    inference(negUnitSimplification,[status(thm)],[c_367,c_389]) ).

tff(c_392,plain,
    ! [Y0_52] : ~ rp('#skF_6',Y0_52),
    inference(splitLeft,[status(thm)],[c_390]) ).

tff(c_396,plain,
    ~ cc('#skF_6'),
    inference(resolution,[status(thm)],[c_24,c_392]) ).

tff(c_400,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_377,c_396]) ).

tff(c_401,plain,
    rp('#skF_6','#skF_7'),
    inference(splitRight,[status(thm)],[c_390]) ).

tff(c_403,plain,
    ! [Y1_53,Y0_54,X_55] :
      ( ( Y1_53 = Y0_54 )
      | ~ rp(X_55,Y1_53)
      | ~ rp(X_55,Y0_54)
      | ~ cc(X_55) ),
    inference(cnfTransformation,[status(thm)],[f_98]) ).

tff(c_405,plain,
    ! [Y0_54] :
      ( ( Y0_54 = '#skF_7' )
      | ~ rp('#skF_6',Y0_54)
      | ~ cc('#skF_6') ),
    inference(resolution,[status(thm)],[c_401,c_403]) ).

tff(c_412,plain,
    ! [Y0_56] :
      ( ( Y0_56 = '#skF_7' )
      | ~ rp('#skF_6',Y0_56) ),
    inference(demodulation,[status(thm),theory(equality)],[c_377,c_405]) ).

tff(c_419,plain,
    ( ( '#skF_1'('#skF_6') = '#skF_7' )
    | ~ cc('#skF_6') ),
    inference(resolution,[status(thm)],[c_24,c_412]) ).

tff(c_424,plain,
    '#skF_1'('#skF_6') = '#skF_7',
    inference(demodulation,[status(thm),theory(equality)],[c_377,c_419]) ).

tff(c_38,plain,
    ! [Y0_29] :
      ( ~ xsd_integer('#skF_4')
      | xsd_integer('#skF_5')
      | rp('#skF_6','#skF_8')
      | ~ rp('#skF_6',Y0_29)
      | ~ cowlThing('#skF_3')
      | cowlNothing('#skF_2') ),
    inference(cnfTransformation,[status(thm)],[f_126]) ).

tff(c_65,plain,
    ! [Y0_29] :
      ( ~ xsd_integer('#skF_4')
      | xsd_integer('#skF_5')
      | rp('#skF_6','#skF_8')
      | ~ rp('#skF_6',Y0_29)
      | ~ cowlThing('#skF_3') ),
    inference(negUnitSimplification,[status(thm)],[c_18,c_38]) ).

tff(c_88,plain,
    ! [Y0_29] :
      ( ~ xsd_integer('#skF_4')
      | xsd_integer('#skF_5')
      | rp('#skF_6','#skF_8')
      | ~ rp('#skF_6',Y0_29) ),
    inference(demodulation,[status(thm),theory(equality)],[c_16,c_65]) ).

tff(c_454,plain,
    ! [Y0_29] :
      ( xsd_integer('#skF_5')
      | rp('#skF_6','#skF_8')
      | ~ rp('#skF_6',Y0_29) ),
    inference(demodulation,[status(thm),theory(equality)],[c_362,c_88]) ).

tff(c_455,plain,
    ! [Y0_29] :
      ( rp('#skF_6','#skF_8')
      | ~ rp('#skF_6',Y0_29) ),
    inference(negUnitSimplification,[status(thm)],[c_367,c_454]) ).

tff(c_456,plain,
    ! [Y0_29] : ~ rp('#skF_6',Y0_29),
    inference(splitLeft,[status(thm)],[c_455]) ).

tff(c_458,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_456,c_401]) ).

tff(c_459,plain,
    rp('#skF_6','#skF_8'),
    inference(splitRight,[status(thm)],[c_455]) ).

tff(c_411,plain,
    ! [Y0_54,X_19] :
      ( ( Y0_54 = '#skF_1'(X_19) )
      | ~ rp(X_19,Y0_54)
      | ~ cc(X_19) ),
    inference(resolution,[status(thm)],[c_24,c_403]) ).

tff(c_462,plain,
    ( ( '#skF_1'('#skF_6') = '#skF_8' )
    | ~ cc('#skF_6') ),
    inference(resolution,[status(thm)],[c_459,c_411]) ).

tff(c_470,plain,
    '#skF_7' = '#skF_8',
    inference(demodulation,[status(thm),theory(equality)],[c_377,c_424,c_462]) ).

tff(c_472,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_384,c_470]) ).

tff(c_479,plain,
    ! [Y0_59] : ~ rp('#skF_6',Y0_59),
    inference(splitRight,[status(thm)],[c_383]) ).

tff(c_483,plain,
    ~ cc('#skF_6'),
    inference(resolution,[status(thm)],[c_24,c_479]) ).

tff(c_487,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_377,c_483]) ).

tff(c_488,plain,
    cc('#skF_6'),
    inference(splitRight,[status(thm)],[c_361]) ).

tff(c_489,plain,
    ~ xsd_string('#skF_5'),
    inference(splitRight,[status(thm)],[c_361]) ).

tff(c_34,plain,
    ! [Y0_29] :
      ( ~ xsd_integer('#skF_4')
      | xsd_string('#skF_5')
      | ( '#skF_7' != '#skF_8' )
      | ~ rp('#skF_6',Y0_29)
      | ~ cowlThing('#skF_3')
      | cowlNothing('#skF_2') ),
    inference(cnfTransformation,[status(thm)],[f_126]) ).

tff(c_61,plain,
    ! [Y0_29] :
      ( ~ xsd_integer('#skF_4')
      | xsd_string('#skF_5')
      | ( '#skF_7' != '#skF_8' )
      | ~ rp('#skF_6',Y0_29)
      | ~ cowlThing('#skF_3') ),
    inference(negUnitSimplification,[status(thm)],[c_18,c_34]) ).

tff(c_80,plain,
    ! [Y0_29] :
      ( ~ xsd_integer('#skF_4')
      | xsd_string('#skF_5')
      | ( '#skF_7' != '#skF_8' )
      | ~ rp('#skF_6',Y0_29) ),
    inference(demodulation,[status(thm),theory(equality)],[c_16,c_61]) ).

tff(c_503,plain,
    ! [Y0_29] :
      ( xsd_string('#skF_5')
      | ( '#skF_7' != '#skF_8' )
      | ~ rp('#skF_6',Y0_29) ),
    inference(demodulation,[status(thm),theory(equality)],[c_362,c_80]) ).

tff(c_504,plain,
    ! [Y0_29] :
      ( ( '#skF_7' != '#skF_8' )
      | ~ rp('#skF_6',Y0_29) ),
    inference(negUnitSimplification,[status(thm)],[c_489,c_503]) ).

tff(c_505,plain,
    '#skF_7' != '#skF_8',
    inference(splitLeft,[status(thm)],[c_504]) ).

tff(c_50,plain,
    ! [Y0_29] :
      ( ~ xsd_integer('#skF_4')
      | xsd_string('#skF_5')
      | rp('#skF_6','#skF_7')
      | ~ rp('#skF_6',Y0_29)
      | ~ cowlThing('#skF_3')
      | cowlNothing('#skF_2') ),
    inference(cnfTransformation,[status(thm)],[f_126]) ).

tff(c_64,plain,
    ! [Y0_29] :
      ( ~ xsd_integer('#skF_4')
      | xsd_string('#skF_5')
      | rp('#skF_6','#skF_7')
      | ~ rp('#skF_6',Y0_29)
      | ~ cowlThing('#skF_3') ),
    inference(negUnitSimplification,[status(thm)],[c_18,c_50]) ).

tff(c_86,plain,
    ! [Y0_29] :
      ( ~ xsd_integer('#skF_4')
      | xsd_string('#skF_5')
      | rp('#skF_6','#skF_7')
      | ~ rp('#skF_6',Y0_29) ),
    inference(demodulation,[status(thm),theory(equality)],[c_16,c_64]) ).

tff(c_564,plain,
    ! [Y0_29] :
      ( xsd_string('#skF_5')
      | rp('#skF_6','#skF_7')
      | ~ rp('#skF_6',Y0_29) ),
    inference(demodulation,[status(thm),theory(equality)],[c_362,c_86]) ).

tff(c_565,plain,
    ! [Y0_29] :
      ( rp('#skF_6','#skF_7')
      | ~ rp('#skF_6',Y0_29) ),
    inference(negUnitSimplification,[status(thm)],[c_489,c_564]) ).

tff(c_566,plain,
    ! [Y0_29] : ~ rp('#skF_6',Y0_29),
    inference(splitLeft,[status(thm)],[c_565]) ).

tff(c_42,plain,
    ! [Y0_29] :
      ( ~ xsd_integer('#skF_4')
      | xsd_string('#skF_5')
      | rp('#skF_6','#skF_8')
      | ~ rp('#skF_6',Y0_29)
      | ~ cowlThing('#skF_3')
      | cowlNothing('#skF_2') ),
    inference(cnfTransformation,[status(thm)],[f_126]) ).

tff(c_72,plain,
    ! [Y0_29] :
      ( ~ xsd_integer('#skF_4')
      | xsd_string('#skF_5')
      | rp('#skF_6','#skF_8')
      | ~ rp('#skF_6',Y0_29)
      | ~ cowlThing('#skF_3') ),
    inference(negUnitSimplification,[status(thm)],[c_18,c_42]) ).

tff(c_102,plain,
    ! [Y0_29] :
      ( ~ xsd_integer('#skF_4')
      | xsd_string('#skF_5')
      | rp('#skF_6','#skF_8')
      | ~ rp('#skF_6',Y0_29) ),
    inference(demodulation,[status(thm),theory(equality)],[c_16,c_72]) ).

tff(c_514,plain,
    ! [Y0_29] :
      ( xsd_string('#skF_5')
      | rp('#skF_6','#skF_8')
      | ~ rp('#skF_6',Y0_29) ),
    inference(demodulation,[status(thm),theory(equality)],[c_362,c_102]) ).

tff(c_515,plain,
    ! [Y0_29] :
      ( rp('#skF_6','#skF_8')
      | ~ rp('#skF_6',Y0_29) ),
    inference(negUnitSimplification,[status(thm)],[c_489,c_514]) ).

tff(c_522,plain,
    ! [Y0_61] : ~ rp('#skF_6',Y0_61),
    inference(splitLeft,[status(thm)],[c_515]) ).

tff(c_526,plain,
    ~ cc('#skF_6'),
    inference(resolution,[status(thm)],[c_24,c_522]) ).

tff(c_530,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_488,c_526]) ).

tff(c_531,plain,
    rp('#skF_6','#skF_8'),
    inference(splitRight,[status(thm)],[c_515]) ).

tff(c_568,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_566,c_531]) ).

tff(c_569,plain,
    rp('#skF_6','#skF_7'),
    inference(splitRight,[status(thm)],[c_565]) ).

tff(c_541,plain,
    ! [Y1_62,Y0_63,X_64] :
      ( ( Y1_62 = Y0_63 )
      | ~ rp(X_64,Y1_62)
      | ~ rp(X_64,Y0_63)
      | ~ cc(X_64) ),
    inference(cnfTransformation,[status(thm)],[f_98]) ).

tff(c_543,plain,
    ! [Y0_63] :
      ( ( Y0_63 = '#skF_8' )
      | ~ rp('#skF_6',Y0_63)
      | ~ cc('#skF_6') ),
    inference(resolution,[status(thm)],[c_531,c_541]) ).

tff(c_548,plain,
    ! [Y0_63] :
      ( ( Y0_63 = '#skF_8' )
      | ~ rp('#skF_6',Y0_63) ),
    inference(demodulation,[status(thm),theory(equality)],[c_488,c_543]) ).

tff(c_572,plain,
    '#skF_7' = '#skF_8',
    inference(resolution,[status(thm)],[c_569,c_548]) ).

tff(c_578,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_505,c_572]) ).

tff(c_585,plain,
    ! [Y0_66] : ~ rp('#skF_6',Y0_66),
    inference(splitRight,[status(thm)],[c_504]) ).

tff(c_589,plain,
    ~ cc('#skF_6'),
    inference(resolution,[status(thm)],[c_24,c_585]) ).

tff(c_593,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_488,c_589]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : KRS143+1 : TPTP v8.1.2. Released v3.1.0.
% 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
% 0.14/0.36  % 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 19:52:13 EDT 2023
% 0.14/0.36  % CPUTime  : 
% 3.78/1.90  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.93/1.92  
% 3.93/1.92  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.06/1.97  
% 4.06/1.97  Inference rules
% 4.06/1.97  ----------------------
% 4.06/1.97  #Ref     : 0
% 4.06/1.97  #Sup     : 68
% 4.06/1.97  #Fact    : 0
% 4.06/1.97  #Define  : 0
% 4.06/1.97  #Split   : 20
% 4.06/1.97  #Chain   : 0
% 4.06/1.97  #Close   : 0
% 4.06/1.97  
% 4.06/1.97  Ordering : KBO
% 4.06/1.97  
% 4.06/1.97  Simplification rules
% 4.06/1.97  ----------------------
% 4.06/1.97  #Subsume      : 26
% 4.06/1.97  #Demod        : 108
% 4.06/1.97  #Tautology    : 49
% 4.06/1.97  #SimpNegUnit  : 45
% 4.06/1.97  #BackRed      : 4
% 4.06/1.97  
% 4.06/1.97  #Partial instantiations: 0
% 4.06/1.97  #Strategies tried      : 1
% 4.06/1.97  
% 4.06/1.97  Timing (in seconds)
% 4.06/1.97  ----------------------
% 4.06/1.97  Preprocessing        : 0.52
% 4.06/1.97  Parsing              : 0.26
% 4.06/1.97  CNF conversion       : 0.04
% 4.06/1.97  Main loop            : 0.36
% 4.06/1.97  Inferencing          : 0.11
% 4.06/1.97  Reduction            : 0.10
% 4.06/1.97  Demodulation         : 0.06
% 4.06/1.97  BG Simplification    : 0.03
% 4.06/1.97  Subsumption          : 0.09
% 4.06/1.97  Abstraction          : 0.02
% 4.06/1.97  MUC search           : 0.00
% 4.06/1.97  Cooper               : 0.00
% 4.06/1.97  Total                : 0.96
% 4.06/1.97  Index Insertion      : 0.00
% 4.06/1.97  Index Deletion       : 0.00
% 4.06/1.97  Index Matching       : 0.00
% 4.06/1.97  BG Taut test         : 0.00
%------------------------------------------------------------------------------