TSTP Solution File: SWW616_2 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SWW616_2 : TPTP v8.1.2. Released v6.1.0.
% 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 : n032.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 11:07:49 EDT 2023

% Result   : Theorem 12.99s 3.96s
% Output   : CNFRefutation 12.99s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   23
%            Number of leaves      :   70
% Syntax   : Number of formulae    :  134 (  48 unt;  69 typ;   0 def)
%            Number of atoms       :  121 (  31 equ)
%            Maximal formula atoms :   26 (   1 avg)
%            Number of connectives :  110 (  54   ~;  31   |;  13   &)
%                                         (   0 <=>;  12  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   27 (   3 avg)
%            Maximal term depth    :    8 (   2 avg)
%            Number arithmetic     :  397 (  88 atm; 209 fun;  75 num;  25 var)
%            Number of types       :    8 (   6 usr;   1 ari)
%            Number of type conns  :   80 (  35   >;  45   *;   0   +;   0  <<)
%            Number of predicates  :    7 (   3 usr;   1 prp; 0-3 aty)
%            Number of functors    :   66 (  60 usr;  31 con; 0-5 aty)
%            Number of variables   :   26 (;  26   !;   0   ?;  26   :)

% Comments : 
%------------------------------------------------------------------------------
%$ maxsublo > sort > maxsub > set > set1 > match_bool > get > sum1 > sum > mk_array > make > get1 > const > mod > mk_ref > map > length > elts > div > contents > #nlpp > witness > tb2t2 > tb2t1 > tb2t > t2tb2 > t2tb1 > t2tb > ref > array > abs > tuple02 > tuple01 > true > real > qtmark > int > false > bool1 > #skF_4 > #skF_1 > #skF_5 > #skF_3 > #skF_2 > #skF_7

%Foreground sorts:
tff(map_int_int,type,
    map_int_int: $tType ).

tff(bool,type,
    bool: $tType ).

tff(tuple0,type,
    tuple0: $tType ).

tff(array_int,type,
    array_int: $tType ).

tff(ty,type,
    ty: $tType ).

tff(uni,type,
    uni: $tType ).

%Background operators:
tff('#skE_7',type,
    '#skE_7': $int ).

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

tff('#skF_14',type,
    '#skF_14': $int ).

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

tff('#skE_2',type,
    '#skE_2': $int ).

tff('#skE_1',type,
    '#skE_1': $int ).

tff('#skF_11',type,
    '#skF_11': $int ).

tff('#skF_16',type,
    '#skF_16': $int ).

tff('#skE_6',type,
    '#skE_6': $int ).

tff('#skF_15',type,
    '#skF_15': $int ).

tff('#skF_17',type,
    '#skF_17': $int ).

tff('#skE_5',type,
    '#skE_5': $int ).

tff('#skE_8',type,
    '#skE_8': $int ).

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

tff('#skE_4',type,
    '#skE_4': $int ).

tff('#skF_10',type,
    '#skF_10': $int ).

tff('#skF_12',type,
    '#skF_12': $int ).

tff('#skE_3',type,
    '#skE_3': $int ).

tff('#skF_9',type,
    '#skF_9': $int ).

%Foreground operators:
tff(tb2t1,type,
    tb2t1: uni > map_int_int ).

tff(maxsub,type,
    maxsub: ( array_int * $int ) > $o ).

tff(tuple02,type,
    tuple02: tuple0 ).

tff('#skF_4',type,
    '#skF_4': ( array_int * $int ) > $int ).

tff(const,type,
    const: ( ty * ty * uni ) > uni ).

tff(get1,type,
    get1: ( ty * uni * $int ) > uni ).

tff(elts,type,
    elts: ( ty * uni ) > uni ).

tff(div,type,
    div: ( $int * $int ) > $int ).

tff(tuple01,type,
    tuple01: ty ).

tff(int,type,
    int: ty ).

tff(tb2t,type,
    tb2t: uni > $int ).

tff(tb2t2,type,
    tb2t2: uni > array_int ).

tff(abs,type,
    abs: $int > $int ).

tff(contents,type,
    contents: ( ty * uni ) > uni ).

tff(t2tb,type,
    t2tb: $int > uni ).

tff(real,type,
    real: ty ).

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

tff('#skF_5',type,
    '#skF_5': ( array_int * $int ) > $int ).

tff(match_bool,type,
    match_bool: ( ty * bool * uni * uni ) > uni ).

tff(false,type,
    false: bool ).

tff(t2tb2,type,
    t2tb2: array_int > uni ).

tff(set,type,
    set: ( ty * ty * uni * uni * uni ) > uni ).

tff(array,type,
    array: ty > ty ).

tff(mod,type,
    mod: ( $int * $int ) > $int ).

tff(make,type,
    make: ( ty * $int * uni ) > uni ).

tff(sum,type,
    sum: ( map_int_int * $int * $int ) > $int ).

tff(maxsublo,type,
    maxsublo: ( array_int * $int * $int ) > $o ).

tff(length,type,
    length: ( ty * uni ) > $int ).

tff(qtmark,type,
    qtmark: ty ).

tff(set1,type,
    set1: ( ty * uni * $int * uni ) > uni ).

tff('#skF_3',type,
    '#skF_3': ( array_int * $int * $int ) > $int ).

tff(t2tb1,type,
    t2tb1: map_int_int > uni ).

tff(get,type,
    get: ( ty * ty * uni * uni ) > uni ).

tff(mk_array,type,
    mk_array: ( ty * $int * uni ) > uni ).

tff(bool1,type,
    bool1: ty ).

tff(map,type,
    map: ( ty * ty ) > ty ).

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

tff('#skF_7',type,
    '#skF_7': map_int_int ).

tff(sort,type,
    sort: ( ty * uni ) > $o ).

tff(true,type,
    true: bool ).

tff(ref,type,
    ref: ty > ty ).

tff(witness,type,
    witness: ty > uni ).

tff(sum1,type,
    sum1: ( array_int * $int * $int ) > $int ).

tff(mk_ref,type,
    mk_ref: ( ty * uni ) > uni ).

tff(f_348,negated_conjecture,
    ~ ! [Aa: $int,A1: map_int_int,La: $int,Ha: $int] :
        ( ( $lesseq(0,Aa)
          & $lesseq(0,La)
          & $lesseq(La,Ha)
          & $lesseq(Ha,Aa) )
       => ( ( Ha != La )
         => ! [Loa: $int] :
              ( ( Loa = $sum(La,div($difference(Ha,La),2)) )
             => ! [Hia: $int] :
                  ( ( Hia = $sum(La,div($difference(Ha,La),2)) )
                 => ( $lesseq(La,$difference($sum(La,div($difference(Ha,La),2)),1))
                   => ! [Sa: $int,Msa: $int,Lo1a: $int] :
                        ( ( $lesseq(La,Lo1a)
                          & $lesseq(Lo1a,$sum(La,div($difference(Ha,La),2)))
                          & ( $sum(La,div($difference(Ha,La),2)) = Hia )
                          & ( Msa = sum(A1,Lo1a,Hia) )
                          & ! [Lqta: $int] :
                              ( ( $less($difference(La,1),Lqta)
                                & $lesseq(Lqta,$sum(La,div($difference(Ha,La),2))) )
                             => $lesseq(sum(A1,Lqta,$sum(La,div($difference(Ha,La),2))),Msa) )
                          & ( Sa = sum(A1,$sum($difference(La,1),1),$sum(La,div($difference(Ha,La),2))) ) )
                       => ( ! [Lqta: $int] :
                              ( ( $lesseq(La,Lqta)
                                & $lesseq(Lqta,$sum(La,div($difference(Ha,La),2))) )
                             => $lesseq(sum(A1,Lqta,$sum(La,div($difference(Ha,La),2))),sum(A1,Lo1a,$sum(La,div($difference(Ha,La),2)))) )
                         => ! [S1a: $int] :
                              ( ( S1a = Msa )
                             => ( $lesseq($sum(La,div($difference(Ha,La),2)),$difference(Ha,1))
                               => ! [Lqta: $int,Hqta: $int] :
                                    ( ( $lesseq(La,Lqta)
                                      & $lesseq(Lqta,$sum(La,div($difference(Ha,La),2)))
                                      & $lesseq($sum(La,div($difference(Ha,La),2)),Hqta)
                                      & $lesseq(Hqta,$sum(La,div($difference(Ha,La),2))) )
                                   => $lesseq(sum(A1,Lqta,Hqta),Msa) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',wP_parameter_maximum_subarray_rec) ).

tff(c_210,plain,
    $sum('#skF_8',div($sum($uminus('#skF_8'),'#skF_9'),2)) = '#skF_10',
    inference(cnfTransformation,[status(thm)],[f_348]) ).

tff(c_250,plain,
    div($sum('#skF_9',$uminus('#skF_8')),2) = $sum('#skF_10',$uminus('#skF_8')),
    inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_210]) ).

tff(c_390,plain,
    div($sum($uminus('#skF_8'),'#skF_9'),2) = $sum('#skF_10',$uminus('#skF_8')),
    inference(backgroundSimplification,[status(thm),theory('LIA')],[c_250]) ).

tff(c_178,plain,
    $lesseq('#skF_16',$sum('#skF_8',div($sum($uminus('#skF_8'),'#skF_9'),2))),
    inference(cnfTransformation,[status(thm)],[f_348]) ).

tff(c_303,plain,
    ~ $less($sum('#skF_8',div($sum($uminus('#skF_8'),'#skF_9'),2)),'#skF_16'),
    inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_178]) ).

tff(c_432,plain,
    ~ $less($sum('#skF_8',$sum('#skF_10',$uminus('#skF_8'))),'#skF_16'),
    inference(demodulation,[status(thm),theory(equality)],[c_390,c_303]) ).

tff(c_434,plain,
    ~ $less('#skF_10','#skF_16'),
    inference(backgroundSimplification,[status(thm),theory('LIA')],[c_432]) ).

tff(c_169,plain,
    ~ $lesseq(sum('#skF_7','#skF_16','#skF_17'),'#skF_13'),
    inference(cnfTransformation,[status(thm)],[f_348]) ).

tff(c_315,plain,
    $less('#skF_13',sum('#skF_7','#skF_16','#skF_17')),
    inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_169]) ).

tff(c_492,plain,
    sum('#skF_7','#skF_16','#skF_17') = '#skE_1',
    inference(define,[status(thm),theory(equality)],[c_315]) ).

tff(c_444,plain,
    $less('#skF_13',sum('#skF_7','#skF_16','#skF_17')),
    inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_169]) ).

tff(c_499,plain,
    $less('#skF_13','#skE_1'),
    inference(demodulation,[status(thm),theory(equality)],[c_492,c_444]) ).

tff(c_498,plain,
    sum('#skF_7','#skF_16','#skF_17') = '#skE_1',
    inference(define,[status(thm),theory(equality)],[c_315]) ).

tff(c_204,plain,
    $lesseq('#skF_8',$difference($sum('#skF_8',div($sum('#skF_9',$uminus('#skF_8')),2)),1)),
    inference(cnfTransformation,[status(thm)],[f_348]) ).

tff(c_260,plain,
    ~ $less(div($sum($uminus('#skF_8'),'#skF_9'),2),1),
    inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_204]) ).

tff(c_263,plain,
    ~ $less(div($sum('#skF_9',$uminus('#skF_8')),2),1),
    inference(backgroundSimplification,[status(thm),theory('LIA')],[c_260]) ).

tff(c_691,plain,
    div($sum('#skF_9',$uminus('#skF_8')),2) = '#skE_2',
    inference(define,[status(thm),theory(equality)],[c_263]) ).

tff(c_1069,plain,
    div($sum($uminus('#skF_8'),'#skF_9'),2) = '#skE_2',
    inference(backgroundSimplification,[status(thm),theory('LIA')],[c_691]) ).

tff(c_253,plain,
    div($sum($uminus('#skF_8'),'#skF_9'),2) = $sum('#skF_10',$uminus('#skF_8')),
    inference(backgroundSimplification,[status(thm),theory('LIA')],[c_250]) ).

tff(c_1085,plain,
    $sum('#skF_10',$uminus('#skF_8')) = '#skE_2',
    inference(superposition,[status(thm),theory(equality)],[c_1069,c_253]) ).

tff(c_1086,plain,
    '#skF_8' = $sum('#skF_10',$uminus('#skE_2')),
    inference(backgroundSimplification,[status(thm),theory('LIA')],[c_1085]) ).

tff(c_1088,plain,
    '#skF_8' = $sum($uminus('#skE_2'),'#skF_10'),
    inference(backgroundSimplification,[status(thm),theory('LIA')],[c_1086]) ).

tff(c_191,plain,
    ! [Lqt_296a: $int] :
      ( $lesseq(sum('#skF_7',Lqt_296a,$sum('#skF_8',div($sum('#skF_9',$uminus('#skF_8')),2))),'#skF_13')
      | ~ $lesseq(Lqt_296a,$sum('#skF_8',div($sum($uminus('#skF_8'),'#skF_9'),2)))
      | ~ $less($difference('#skF_8',1),Lqt_296a) ),
    inference(cnfTransformation,[status(thm)],[f_348]) ).

tff(c_279,plain,
    ! [Lqt_296a: $int] :
      ( ~ $less('#skF_13',sum('#skF_7',Lqt_296a,$sum('#skF_8',div($sum($uminus('#skF_8'),'#skF_9'),2))))
      | $less($sum('#skF_8',div($sum($uminus('#skF_8'),'#skF_9'),2)),Lqt_296a)
      | ~ $less('#skF_8',$sum(1,Lqt_296a)) ),
    inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_191]) ).

tff(c_282,plain,
    ! [Lqt_296a: $int] :
      ( ~ $less('#skF_13',sum('#skF_7',Lqt_296a,$sum('#skF_8',div($sum('#skF_9',$uminus('#skF_8')),2))))
      | $less($sum('#skF_8',div($sum($uminus('#skF_8'),'#skF_9'),2)),Lqt_296a)
      | ~ $less('#skF_8',$sum(1,Lqt_296a)) ),
    inference(backgroundSimplification,[status(thm),theory('LIA')],[c_279]) ).

tff(c_410,plain,
    ! [Lqt_296a: $int] :
      ( ~ $less('#skF_13',sum('#skF_7',Lqt_296a,$sum('#skF_8',div($sum('#skF_9',$uminus('#skF_8')),2))))
      | $less($sum('#skF_8',$sum('#skF_10',$uminus('#skF_8'))),Lqt_296a)
      | ~ $less('#skF_8',$sum(1,Lqt_296a)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_390,c_282]) ).

tff(c_413,plain,
    ! [Lqt_296a: $int] :
      ( ~ $less('#skF_13',sum('#skF_7',Lqt_296a,$sum('#skF_8',div($sum($uminus('#skF_8'),'#skF_9'),2))))
      | $less('#skF_10',Lqt_296a)
      | ~ $less('#skF_8',$sum(1,Lqt_296a)) ),
    inference(backgroundSimplification,[status(thm),theory('LIA')],[c_410]) ).

tff(c_1472,plain,
    ! [Lqt_296a: $int] :
      ( ~ $less('#skF_13',sum('#skF_7',Lqt_296a,$sum($sum($uminus('#skE_2'),'#skF_10'),div($sum($uminus($sum($uminus('#skE_2'),'#skF_10')),'#skF_9'),2))))
      | $less('#skF_10',Lqt_296a)
      | ~ $less($sum($uminus('#skE_2'),'#skF_10'),$sum(1,Lqt_296a)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_1088,c_1088,c_1088,c_413]) ).

tff(c_1475,plain,
    ! [Lqt_296a: $int] :
      ( ~ $less('#skF_13',sum('#skF_7',Lqt_296a,$sum('#skF_10',$sum($uminus('#skE_2'),div($sum('#skF_9',$sum($uminus('#skF_10'),'#skE_2')),2)))))
      | $less('#skF_10',Lqt_296a)
      | ~ $less('#skF_10',$sum(1,$sum(Lqt_296a,'#skE_2'))) ),
    inference(backgroundSimplification,[status(thm),theory('LIA')],[c_1472]) ).

tff(c_1482,plain,
    div($sum('#skF_9',$sum($uminus('#skF_10'),'#skE_2')),2) = '#skE_5',
    inference(define,[status(thm),theory(equality)],[c_1475]) ).

tff(c_2077,plain,
    div($sum($uminus('#skF_10'),$sum('#skE_2','#skF_9')),2) = '#skE_5',
    inference(backgroundSimplification,[status(thm),theory('LIA')],[c_1482]) ).

tff(c_1104,plain,
    div($sum($uminus($sum($uminus('#skE_2'),'#skF_10')),'#skF_9'),2) = $sum('#skF_10',$uminus($sum($uminus('#skE_2'),'#skF_10'))),
    inference(demodulation,[status(thm),theory(equality)],[c_1088,c_1088,c_253]) ).

tff(c_1127,plain,
    div($sum('#skF_9',$sum($uminus('#skF_10'),'#skE_2')),2) = '#skE_2',
    inference(backgroundSimplification,[status(thm),theory('LIA')],[c_1104]) ).

tff(c_1130,plain,
    div($sum($uminus('#skF_10'),$sum('#skE_2','#skF_9')),2) = '#skE_2',
    inference(backgroundSimplification,[status(thm),theory('LIA')],[c_1127]) ).

tff(c_2107,plain,
    '#skE_5' = '#skE_2',
    inference(superposition,[status(thm),theory(equality)],[c_2077,c_1130]) ).

tff(c_2109,plain,
    '#skE_5' = '#skE_2',
    inference(backgroundSimplification,[status(thm),theory('LIA')],[c_2107]) ).

tff(c_1477,plain,
    div($sum('#skF_9',$sum($uminus('#skF_10'),'#skE_2')),2) = '#skE_5',
    inference(define,[status(thm),theory(equality)],[c_1475]) ).

tff(c_1476,plain,
    ! [Lqt_296a: $int] :
      ( ~ $less('#skF_13',sum('#skF_7',Lqt_296a,$sum('#skF_10',$sum($uminus('#skE_2'),div($sum('#skF_9',$sum($uminus('#skF_10'),'#skE_2')),2)))))
      | $less('#skF_10',Lqt_296a)
      | ~ $less('#skF_10',$sum(1,$sum(Lqt_296a,'#skE_2'))) ),
    inference(backgroundSimplification,[status(thm),theory('LIA')],[c_1472]) ).

tff(c_1486,plain,
    ! [Lqt_296a: $int] :
      ( ~ $less('#skF_13',sum('#skF_7',Lqt_296a,$sum('#skF_10',$sum($uminus('#skE_2'),'#skE_5'))))
      | $less('#skF_10',Lqt_296a)
      | ~ $less('#skF_10',$sum(1,$sum(Lqt_296a,'#skE_2'))) ),
    inference(demodulation,[status(thm),theory(equality)],[c_1477,c_1476]) ).

tff(c_1489,plain,
    ! [Lqt_296a: $int] :
      ( ~ $less('#skF_13',sum('#skF_7',Lqt_296a,$sum($uminus('#skE_2'),$sum('#skE_5','#skF_10'))))
      | $less('#skF_10',Lqt_296a)
      | ~ $less('#skF_10',$sum(1,$sum('#skE_2',Lqt_296a))) ),
    inference(backgroundSimplification,[status(thm),theory('LIA')],[c_1486]) ).

tff(c_4313,plain,
    ! [Lqt_296a: $int] :
      ( ~ $less('#skF_13',sum('#skF_7',Lqt_296a,$sum($uminus('#skE_2'),$sum('#skE_2','#skF_10'))))
      | $less('#skF_10',Lqt_296a)
      | ~ $less('#skF_10',$sum(1,$sum('#skE_2',Lqt_296a))) ),
    inference(demodulation,[status(thm),theory(equality)],[c_2109,c_1489]) ).

tff(c_4318,plain,
    ! [Lqt_1435a: $int] :
      ( ~ $less('#skF_13',sum('#skF_7',Lqt_1435a,'#skF_10'))
      | $less('#skF_10',Lqt_1435a)
      | ~ $less('#skF_10',$sum(1,$sum(Lqt_1435a,'#skE_2'))) ),
    inference(backgroundSimplification,[status(thm),theory('LIA')],[c_4313]) ).

tff(c_4331,plain,
    ( ~ $less('#skF_13','#skE_1')
    | $less('#skF_10','#skF_16')
    | ~ $less('#skF_10',$sum(1,$sum('#skF_16','#skE_2')))
    | ( '#skF_17' != '#skF_10' ) ),
    inference(superposition,[status(thm),theory(equality)],[c_498,c_4318]) ).

tff(c_4344,plain,
    ( $less('#skF_10','#skF_16')
    | ~ $less('#skF_10',$sum(1,$sum('#skF_16','#skE_2')))
    | ( '#skF_17' != '#skF_10' ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_499,c_4331]) ).

tff(c_4345,plain,
    ( ~ $less('#skF_10',$sum(1,$sum('#skF_16','#skE_2')))
    | ( '#skF_17' != '#skF_10' ) ),
    inference(negUnitSimplification,[status(thm)],[c_434,c_4344]) ).

tff(c_4347,plain,
    ( ~ $less('#skF_10',$sum(1,$sum('#skE_2','#skF_16')))
    | ( '#skF_17' != '#skF_10' ) ),
    inference(backgroundSimplification,[status(thm),theory('LIA')],[c_4345]) ).

tff(c_4483,plain,
    '#skF_17' != '#skF_10',
    inference(splitLeft,[status(thm)],[c_4347]) ).

tff(c_175,plain,
    $lesseq($sum('#skF_8',div($sum($uminus('#skF_8'),'#skF_9'),2)),'#skF_17'),
    inference(cnfTransformation,[status(thm)],[f_348]) ).

tff(c_307,plain,
    ~ $less('#skF_17',$sum('#skF_8',div($sum($uminus('#skF_8'),'#skF_9'),2))),
    inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_175]) ).

tff(c_436,plain,
    ~ $less('#skF_17',$sum('#skF_8',$sum('#skF_10',$uminus('#skF_8')))),
    inference(demodulation,[status(thm),theory(equality)],[c_390,c_307]) ).

tff(c_438,plain,
    ~ $less('#skF_17','#skF_10'),
    inference(backgroundSimplification,[status(thm),theory('LIA')],[c_436]) ).

tff(c_172,plain,
    $lesseq('#skF_17',$sum('#skF_8',div($sum($uminus('#skF_8'),'#skF_9'),2))),
    inference(cnfTransformation,[status(thm)],[f_348]) ).

tff(c_311,plain,
    ~ $less($sum('#skF_8',div($sum($uminus('#skF_8'),'#skF_9'),2)),'#skF_17'),
    inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_172]) ).

tff(c_440,plain,
    ~ $less($sum('#skF_8',$sum('#skF_10',$uminus('#skF_8'))),'#skF_17'),
    inference(demodulation,[status(thm),theory(equality)],[c_390,c_311]) ).

tff(c_442,plain,
    ~ $less('#skF_10','#skF_17'),
    inference(backgroundSimplification,[status(thm),theory('LIA')],[c_440]) ).

tff(c_4484,plain,
    $false,
    inference(close,[status(thm),theory('LIA')],[c_4483,c_438,c_442]) ).

tff(c_4485,plain,
    ~ $less('#skF_10',$sum(1,$sum('#skE_2','#skF_16'))),
    inference(splitRight,[status(thm)],[c_4347]) ).

tff(c_4488,plain,
    ~ $less('#skF_10',$sum(1,$sum('#skF_16','#skE_2'))),
    inference(backgroundSimplification,[status(thm),theory('LIA')],[c_4485]) ).

tff(c_180,plain,
    $lesseq('#skF_8','#skF_16'),
    inference(cnfTransformation,[status(thm)],[f_348]) ).

tff(c_299,plain,
    ~ $less('#skF_16','#skF_8'),
    inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_180]) ).

tff(c_1117,plain,
    ~ $less('#skF_16',$sum($uminus('#skE_2'),'#skF_10')),
    inference(demodulation,[status(thm),theory(equality)],[c_1088,c_299]) ).

tff(c_1119,plain,
    ~ $less($sum('#skE_2','#skF_16'),'#skF_10'),
    inference(backgroundSimplification,[status(thm),theory('LIA')],[c_1117]) ).

tff(c_1137,plain,
    ~ $less($sum('#skF_16','#skE_2'),'#skF_10'),
    inference(backgroundSimplification,[status(thm),theory('LIA')],[c_1119]) ).

tff(c_10053,plain,
    $false,
    inference(close,[status(thm),theory('LIA')],[c_4488,c_1137]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SWW616_2 : TPTP v8.1.2. Released v6.1.0.
% 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
% 0.13/0.33  % Computer : n032.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 300
% 0.13/0.33  % DateTime : Thu Aug  3 19:10:06 EDT 2023
% 0.13/0.33  % CPUTime  : 
% 12.99/3.96  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.99/3.97  
% 12.99/3.97  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 12.99/4.00  
% 12.99/4.00  Inference rules
% 12.99/4.00  ----------------------
% 12.99/4.00  #Ref     : 0
% 12.99/4.00  #Sup     : 1548
% 12.99/4.00  #Fact    : 3
% 12.99/4.00  #Define  : 9
% 12.99/4.00  #Split   : 29
% 12.99/4.00  #Chain   : 0
% 12.99/4.00  #Close   : 7
% 12.99/4.00  
% 12.99/4.00  Ordering : LPO
% 12.99/4.00  
% 12.99/4.00  Simplification rules
% 12.99/4.00  ----------------------
% 12.99/4.00  #Subsume      : 75
% 12.99/4.00  #Demod        : 443
% 12.99/4.00  #Tautology    : 834
% 12.99/4.00  #SimpNegUnit  : 17
% 12.99/4.00  #BackRed      : 29
% 12.99/4.00  
% 12.99/4.00  #Partial instantiations: 178
% 12.99/4.00  #Strategies tried      : 1
% 12.99/4.00  
% 12.99/4.00  Timing (in seconds)
% 12.99/4.00  ----------------------
% 12.99/4.01  Preprocessing        : 0.90
% 12.99/4.01  Parsing              : 0.45
% 12.99/4.01  CNF conversion       : 0.07
% 12.99/4.01  Main loop            : 2.10
% 12.99/4.01  Inferencing          : 0.44
% 12.99/4.01  Reduction            : 0.64
% 12.99/4.01  Demodulation         : 0.43
% 12.99/4.01  BG Simplification    : 0.20
% 12.99/4.01  Subsumption          : 0.37
% 12.99/4.01  Abstraction          : 0.07
% 12.99/4.01  MUC search           : 0.16
% 12.99/4.01  Cooper               : 0.34
% 12.99/4.01  Total                : 3.05
% 12.99/4.01  Index Insertion      : 0.00
% 12.99/4.01  Index Deletion       : 0.00
% 12.99/4.01  Index Matching       : 0.00
% 12.99/4.01  BG Taut test         : 0.00
%------------------------------------------------------------------------------