TSTP Solution File: SWW575_2 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SWW575_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/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 : n016.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 11:07:43 EDT 2023

% Result   : Theorem 55.84s 25.56s
% Output   : CNFRefutation 55.93s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   23
%            Number of leaves      :   86
% Syntax   : Number of formulae    :  300 ( 123 unt;  85 typ;   0 def)
%            Number of atoms       :  425 (  97 equ)
%            Maximal formula atoms :   54 (   1 avg)
%            Number of connectives :  323 ( 113   ~; 157   |;  33   &)
%                                         (   0 <=>;  20  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   29 (   2 avg)
%            Maximal term depth    :    5 (   1 avg)
%            Number arithmetic     :  693 ( 300 atm; 174 fun; 177 num;  42 var)
%            Number of types       :    8 (   6 usr;   1 ari)
%            Number of type conns  :  174 (  50   >; 124   *;   0   +;   0  <<)
%            Number of predicates  :   15 (  11 usr;   1 prp; 0-7 aty)
%            Number of functors    :   74 (  68 usr;  32 con; 0-7 aty)
%            Number of variables   :   45 (;  43   !;   2   ?;  45   :)

% Comments : 
%------------------------------------------------------------------------------
%$ exchange2 > permut_sub2 > permut3 > permut2 > map_eq_sub1 > exchange3 > array_eq_sub1 > permut_sub3 > permut_all > array_eq > sort1 > set > occ1 > set2 > match_bool1 > get > mk_array2 > make1 > get4 > const > mk_ref > mk_array3 > map > length1 > get3 > elts > contents > #nlpp > witness1 > tb2t2 > tb2t1 > tb2t > t2tb2 > t2tb1 > t2tb > ref > array > tuple03 > tuple0 > true1 > real > qtmark > int > false1 > bool > #skF_23 > #skF_10 > #skF_22 > #skF_6 > #skF_2 > #skF_8 > #skF_13 > #skF_5 > #skF_11 > #skF_1 > #skF_15 > #skF_9 > #skF_4 > #skF_7 > #skF_21 > #skF_12 > #skF_3

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

tff(tuple02,type,
    tuple02: $tType ).

tff(bool1,type,
    bool1: $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('#skE_11',type,
    '#skE_11': $int ).

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

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

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

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

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

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

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

tff('#skE_10',type,
    '#skE_10': $int ).

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

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

tff('#skF_18',type,
    '#skF_18': $int ).

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

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

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

tff('#skE_9',type,
    '#skE_9': $int ).

tff('#skF_19',type,
    '#skF_19': $int ).

%Foreground operators:
tff(length1,type,
    length1: ( ty * uni ) > $int ).

tff('#skF_23',type,
    '#skF_23': $int > $int ).

tff(t2tb1,type,
    t2tb1: $int > uni ).

tff(permut_sub2,type,
    permut_sub2: ( ty * uni * uni * $int * $int ) > $o ).

tff(true1,type,
    true1: bool1 ).

tff(get3,type,
    get3: ( map_int_int * $int ) > $int ).

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

tff(permut_sub3,type,
    permut_sub3: ( array_int * array_int * $int * $int ) > $o ).

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

tff(occ1,type,
    occ1: ( ty * uni * uni * $int * $int ) > $int ).

tff('#skF_22',type,
    '#skF_22': map_int_int ).

tff('#skF_6',type,
    '#skF_6': ( uni * $int * uni * ty * $int * uni ) > $int ).

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

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

tff(int,type,
    int: ty ).

tff(false1,type,
    false1: bool1 ).

tff(map_eq_sub1,type,
    map_eq_sub1: ( ty * uni * uni * $int * $int ) > $o ).

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

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

tff(sort1,type,
    sort1: ( ty * uni ) > $o ).

tff('#skF_13',type,
    '#skF_13': ( uni * $int * uni * $int * $int * $int * ty ) > $int ).

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

tff(tb2t1,type,
    tb2t1: uni > $int ).

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

tff(exchange3,type,
    exchange3: ( ty * uni * uni * $int * $int ) > $o ).

tff(witness1,type,
    witness1: ty > uni ).

tff(permut2,type,
    permut2: ( ty * uni * uni * $int * $int ) > $o ).

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

tff(real,type,
    real: ty ).

tff('#skF_11',type,
    '#skF_11': ( uni * ty * $int * uni * $int ) > $int ).

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

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

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

tff(match_bool1,type,
    match_bool1: ( ty * bool1 * uni * uni ) > uni ).

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

tff('#skF_15',type,
    '#skF_15': map_int_int ).

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

tff(make1,type,
    make1: ( ty * $int * uni ) > uni ).

tff(exchange2,type,
    exchange2: ( ty * uni * uni * $int * $int * $int * $int ) > $o ).

tff('#skF_9',type,
    '#skF_9': ( ty * $int * $int * uni * $int * uni ) > $int ).

tff(array_eq_sub1,type,
    array_eq_sub1: ( ty * uni * uni * $int * $int ) > $o ).

tff(tuple0,type,
    tuple0: ty ).

tff(qtmark,type,
    qtmark: ty ).

tff(mk_array2,type,
    mk_array2: ( ty * $int * uni ) > uni ).

tff(bool,type,
    bool: ty ).

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

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

tff(t2tb,type,
    t2tb: map_int_int > uni ).

tff(mk_array3,type,
    mk_array3: ( $int * map_int_int ) > array_int ).

tff(tuple03,type,
    tuple03: tuple02 ).

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

tff(permut3,type,
    permut3: ( ty * uni * uni * $int * $int ) > $o ).

tff(set2,type,
    set2: ( ty * uni * $int * uni ) > uni ).

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

tff(tb2t,type,
    tb2t: uni > map_int_int ).

tff('#skF_7',type,
    '#skF_7': ( uni * ty * $int * uni * $int ) > uni ).

tff('#skF_21',type,
    '#skF_21': map_int_int ).

tff(get4,type,
    get4: ( ty * uni * $int ) > uni ).

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

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

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

tff(f_653,negated_conjecture,
    ~ ! [Aa: $int,A1: map_int_int,Ma: $int,Na: $int,Ka: $int] :
        ( ( $lesseq(0,Aa)
          & $lesseq(0,Ma)
          & $lesseq(Ma,Ka)
          & $lesseq(Ka,Na)
          & $less(Na,Aa) )
       => ( $less(Ma,Na)
         => ( ( $lesseq(0,Ma)
              & $less(Ma,Na)
              & $less(Na,Aa) )
           => ! [Ja: $int,Ia: $int,A2: map_int_int] :
                ( ( $lesseq(0,Aa)
                  & $lesseq(Ma,Ja)
                  & $less(Ja,Ia)
                  & $lesseq(Ia,Na)
                  & permut_sub3(mk_array3(Aa,A1),mk_array3(Aa,A2),Ma,$sum(Na,1))
                  & ! [Ra: $int] :
                      ( ( $lesseq(Ma,Ra)
                        & $lesseq(Ra,Ja) )
                     => $lesseq(get3(A2,Ra),42) )
                  & ! [Ra: $int] :
                      ( ( $less(Ja,Ra)
                        & $less(Ra,Ia) )
                     => ( get3(A2,Ra) = 42 ) )
                  & ! [Ra: $int] :
                      ( ( $lesseq(Ia,Ra)
                        & $lesseq(Ra,Na) )
                     => $lesseq(42,get3(A2,Ra)) ) )
               => ( $lesseq(Ka,Ja)
                 => ( ( $lesseq(0,Ma)
                      & $lesseq(Ma,Ka)
                      & $lesseq(Ka,Ja)
                      & $less(Ja,Aa) )
                   => ! [A3: map_int_int] :
                        ( ( $lesseq(0,Aa)
                          & permut_sub3(mk_array3(Aa,A2),mk_array3(Aa,A3),Ma,$sum(Ja,1))
                          & ! [Ra: $int] :
                              ( ( $lesseq(Ma,Ra)
                                & $lesseq(Ra,Ka) )
                             => $lesseq(get3(A3,Ra),get3(A3,Ka)) )
                          & ! [Ra: $int] :
                              ( ( $lesseq(Ka,Ra)
                                & $lesseq(Ra,Ja) )
                             => $lesseq(get3(A3,Ka),get3(A3,Ra)) ) )
                       => ( permut_sub3(mk_array3(Aa,A2),mk_array3(Aa,A3),Ma,$sum(Na,1))
                         => ( ! [Ra: $int] :
                                ( ( $less(Ja,Ra)
                                  & $lesseq(Ra,Na) )
                               => ( get3(A3,Ra) = get3(A2,Ra) ) )
                           => ( ! [Ra: $int] :
                                  ( ( $lesseq(Ma,Ra)
                                    & $lesseq(Ra,Ja) )
                                 => ( ? [Sa: $int] :
                                        ( $lesseq(Ma,Sa)
                                        & $lesseq(Sa,Ja)
                                        & ( get3(A3,Ra) = get3(A2,Sa) ) )
                                    & $lesseq(get3(A3,Ra),get3(A3,$sum(Ja,1))) ) )
                             => ( ~ $lesseq(Ia,Ka)
                               => ( permut_sub3(mk_array3(Aa,A3),mk_array3(Aa,A3),Ma,$sum(Na,1))
                                 => ! [Ra: $int] :
                                      ( ( $lesseq(Ia,Ra)
                                        & $lesseq(Ra,Na) )
                                     => ( ? [Sa: $int] :
                                            ( $lesseq(Ia,Sa)
                                            & $lesseq(Sa,Na)
                                            & ( get3(A3,Ra) = get3(A3,Sa) ) )
                                        & $lesseq(get3(A3,$difference(Ia,1)),get3(A3,Ra)) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',wP_parameter_find) ).

tff(c_320,plain,
    $lesseq('#skF_24','#skF_17'),
    inference(cnfTransformation,[status(thm)],[f_653]) ).

tff(c_474,plain,
    ~ $less('#skF_17','#skF_24'),
    inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_320]) ).

tff(c_322,plain,
    $lesseq('#skF_20','#skF_24'),
    inference(cnfTransformation,[status(thm)],[f_653]) ).

tff(c_473,plain,
    ~ $less('#skF_24','#skF_20'),
    inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_322]) ).

tff(c_318,plain,
    ! [S_416a: $int] :
      ( ~ $lesseq(get3('#skF_22',$sum($uminus(1),'#skF_20')),get3('#skF_22','#skF_24'))
      | ( get3('#skF_22',S_416a) != get3('#skF_22','#skF_24') )
      | ~ $lesseq('#skF_20',S_416a)
      | ~ $lesseq(S_416a,'#skF_17') ),
    inference(cnfTransformation,[status(thm)],[f_653]) ).

tff(c_478,plain,
    ! [S_416a: $int] :
      ( $less(get3('#skF_22','#skF_24'),get3('#skF_22',$sum($uminus(1),'#skF_20')))
      | ( get3('#skF_22',S_416a) != get3('#skF_22','#skF_24') )
      | $less(S_416a,'#skF_20')
      | $less('#skF_17',S_416a) ),
    inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_318]) ).

tff(c_3099,plain,
    get3('#skF_22','#skF_24') = '#skE_3',
    inference(define,[status(thm),theory(equality)],[c_478]) ).

tff(c_329,plain,
    ! [R_412a: $int] :
      ( ( get3('#skF_22',R_412a) = get3('#skF_21',R_412a) )
      | ~ $less('#skF_19',R_412a)
      | ~ $lesseq(R_412a,'#skF_17') ),
    inference(cnfTransformation,[status(thm)],[f_653]) ).

tff(c_467,plain,
    ! [R_412a: $int] :
      ( ( get3('#skF_22',R_412a) = get3('#skF_21',R_412a) )
      | ~ $less('#skF_19',R_412a)
      | $less('#skF_17',R_412a) ),
    inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_329]) ).

tff(c_3106,plain,
    get3('#skF_22','#skF_24') = '#skE_3',
    inference(define,[status(thm),theory(equality)],[c_478]) ).

tff(c_3200,plain,
    ( ( get3('#skF_21','#skF_24') = '#skE_3' )
    | ~ $less('#skF_19','#skF_24')
    | $less('#skF_17','#skF_24') ),
    inference(superposition,[status(thm),theory(equality)],[c_467,c_3106]) ).

tff(c_3327,plain,
    ( ( get3('#skF_21','#skF_24') = '#skE_3' )
    | ~ $less('#skF_19','#skF_24') ),
    inference(negUnitSimplification,[status(thm)],[c_474,c_3200]) ).

tff(c_3329,plain,
    get3('#skF_21','#skF_24') = '#skE_5',
    inference(define,[status(thm),theory(equality)],[c_3327]) ).

tff(c_3328,plain,
    ( ( get3('#skF_21','#skF_24') = '#skE_3' )
    | ~ $less('#skF_19','#skF_24') ),
    inference(negUnitSimplification,[status(thm)],[c_474,c_3200]) ).

tff(c_3336,plain,
    ( ( '#skE_5' = '#skE_3' )
    | ~ $less('#skF_19','#skF_24') ),
    inference(demodulation,[status(thm),theory(equality)],[c_3329,c_3328]) ).

tff(c_3338,plain,
    ~ $less('#skF_19','#skF_24'),
    inference(splitLeft,[status(thm)],[c_3336]) ).

tff(c_436,plain,
    $less('#skF_19','#skF_20'),
    inference(cnfTransformation,[status(thm)],[f_653]) ).

tff(c_3339,plain,
    $false,
    inference(close,[status(thm),theory('LIA')],[c_3338,c_436,c_473]) ).

tff(c_3342,plain,
    '#skE_5' = '#skE_3',
    inference(splitRight,[status(thm)],[c_3336]) ).

tff(c_3335,plain,
    get3('#skF_21','#skF_24') = '#skE_5',
    inference(define,[status(thm),theory(equality)],[c_3327]) ).

tff(c_3351,plain,
    get3('#skF_21','#skF_24') = '#skE_3',
    inference(demodulation,[status(thm),theory(equality)],[c_3342,c_3335]) ).

tff(c_352,plain,
    ! [R_400a: $int] :
      ( $lesseq(42,get3('#skF_21',R_400a))
      | ~ $lesseq('#skF_20',R_400a)
      | ~ $lesseq(R_400a,'#skF_17') ),
    inference(cnfTransformation,[status(thm)],[f_653]) ).

tff(c_444,plain,
    ! [R_400a: $int] :
      ( ~ $less(get3('#skF_21',R_400a),42)
      | $less(R_400a,'#skF_20')
      | $less('#skF_17',R_400a) ),
    inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_352]) ).

tff(c_3397,plain,
    ( ~ $less('#skE_3',42)
    | $less('#skF_24','#skF_20')
    | $less('#skF_17','#skF_24') ),
    inference(superposition,[status(thm),theory(equality)],[c_3351,c_444]) ).

tff(c_3485,plain,
    ~ $less('#skE_3',42),
    inference(negUnitSimplification,[status(thm)],[c_474,c_473,c_3397]) ).

tff(c_443,plain,
    ! [R_399a: $int] :
      ( ( get3('#skF_21',R_399a) = 42 )
      | ~ $less('#skF_19',R_399a)
      | ~ $less(R_399a,'#skF_20') ),
    inference(cnfTransformation,[status(thm)],[f_653]) ).

tff(c_381,plain,
    ! [R_413a: $int] :
      ( $lesseq(get3('#skF_22',R_413a),get3('#skF_22',$sum(1,'#skF_19')))
      | ~ $lesseq('#skF_16',R_413a)
      | ~ $lesseq(R_413a,'#skF_19') ),
    inference(cnfTransformation,[status(thm)],[f_653]) ).

tff(c_424,plain,
    ! [R_413a: $int] :
      ( ~ $less(get3('#skF_22',$sum(1,'#skF_19')),get3('#skF_22',R_413a))
      | $less(R_413a,'#skF_16')
      | $less('#skF_19',R_413a) ),
    inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_381]) ).

tff(c_1995,plain,
    get3('#skF_22',$sum(1,'#skF_19')) = '#skE_2',
    inference(define,[status(thm),theory(equality)],[c_424]) ).

tff(c_2048,plain,
    ( ( get3('#skF_21',$sum(1,'#skF_19')) = '#skE_2' )
    | ~ $less('#skF_19',$sum(1,'#skF_19'))
    | $less('#skF_17',$sum(1,'#skF_19')) ),
    inference(superposition,[status(thm),theory(equality)],[c_467,c_1995]) ).

tff(c_2051,plain,
    ( ( get3('#skF_21',$sum(1,'#skF_19')) = '#skE_2' )
    | $less('#skF_17',$sum(1,'#skF_19')) ),
    inference(backgroundSimplification,[status(thm),theory('LIA')],[c_2048]) ).

tff(c_100589,plain,
    get3('#skF_21',$sum(1,'#skF_19')) = '#skE_7',
    inference(define,[status(thm),theory(equality)],[c_2051]) ).

tff(c_4539,plain,
    ( ( get3('#skF_21',$sum(1,'#skF_19')) = '#skE_2' )
    | $less('#skF_17',$sum(1,'#skF_19')) ),
    inference(backgroundSimplification,[status(thm),theory('LIA')],[c_2048]) ).

tff(c_100596,plain,
    ( ( '#skE_7' = '#skE_2' )
    | $less('#skF_17',$sum(1,'#skF_19')) ),
    inference(demodulation,[status(thm),theory(equality)],[c_100589,c_4539]) ).

tff(c_100598,plain,
    $less('#skF_17',$sum(1,'#skF_19')),
    inference(splitLeft,[status(thm)],[c_100596]) ).

tff(c_100682,plain,
    $false,
    inference(close,[status(thm),theory('LIA')],[c_100598,c_436,c_473,c_474]) ).

tff(c_100685,plain,
    '#skE_7' = '#skE_2',
    inference(splitRight,[status(thm)],[c_100596]) ).

tff(c_100595,plain,
    get3('#skF_21',$sum(1,'#skF_19')) = '#skE_7',
    inference(define,[status(thm),theory(equality)],[c_2051]) ).

tff(c_100698,plain,
    get3('#skF_21',$sum(1,'#skF_19')) = '#skE_2',
    inference(demodulation,[status(thm),theory(equality)],[c_100685,c_100595]) ).

tff(c_100776,plain,
    ( ( '#skE_2' = 42 )
    | ~ $less('#skF_19',$sum(1,'#skF_19'))
    | ~ $less($sum(1,'#skF_19'),'#skF_20') ),
    inference(superposition,[status(thm),theory(equality)],[c_443,c_100698]) ).

tff(c_100778,plain,
    ( ( '#skE_2' = 42 )
    | ~ $less($sum(1,'#skF_19'),'#skF_20') ),
    inference(backgroundSimplification,[status(thm),theory('LIA')],[c_100776]) ).

tff(c_100784,plain,
    ~ $less($sum(1,'#skF_19'),'#skF_20'),
    inference(splitLeft,[status(thm)],[c_100778]) ).

tff(c_3205,plain,
    get3('#skF_22',$sum($uminus(1),'#skF_20')) = '#skE_4',
    inference(define,[status(thm),theory(equality)],[c_478]) ).

tff(c_336,plain,
    ! [R_410a: $int] :
      ( $lesseq(get3('#skF_22',R_410a),get3('#skF_22','#skF_18'))
      | ~ $lesseq('#skF_16',R_410a)
      | ~ $lesseq(R_410a,'#skF_18') ),
    inference(cnfTransformation,[status(thm)],[f_653]) ).

tff(c_458,plain,
    ! [R_410a: $int] :
      ( ~ $less(get3('#skF_22','#skF_18'),get3('#skF_22',R_410a))
      | $less(R_410a,'#skF_16')
      | $less('#skF_18',R_410a) ),
    inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_336]) ).

tff(c_1724,plain,
    get3('#skF_22','#skF_18') = '#skE_1',
    inference(define,[status(thm),theory(equality)],[c_458]) ).

tff(c_647,plain,
    ! [R_410a: $int] :
      ( ~ $less(get3('#skF_22','#skF_18'),get3('#skF_22',R_410a))
      | $less(R_410a,'#skF_16')
      | $less('#skF_18',R_410a) ),
    inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_336]) ).

tff(c_1734,plain,
    ! [R_410a: $int] :
      ( ~ $less('#skE_1',get3('#skF_22',R_410a))
      | $less(R_410a,'#skF_16')
      | $less('#skF_18',R_410a) ),
    inference(demodulation,[status(thm),theory(equality)],[c_1724,c_647]) ).

tff(c_3277,plain,
    ( ~ $less('#skE_1','#skE_4')
    | $less($sum($uminus(1),'#skF_20'),'#skF_16')
    | $less('#skF_18',$sum($uminus(1),'#skF_20')) ),
    inference(superposition,[status(thm),theory(equality)],[c_3205,c_1734]) ).

tff(c_3279,plain,
    ( ~ $less('#skE_1','#skE_4')
    | $less('#skF_20',$sum(1,'#skF_16'))
    | $less($sum(1,'#skF_18'),'#skF_20') ),
    inference(backgroundSimplification,[status(thm),theory('LIA')],[c_3277]) ).

tff(c_101365,plain,
    ~ $less('#skE_1','#skE_4'),
    inference(splitLeft,[status(thm)],[c_3279]) ).

tff(c_350,plain,
    $lesseq('#skF_18','#skF_19'),
    inference(cnfTransformation,[status(thm)],[f_653]) ).

tff(c_445,plain,
    ~ $less('#skF_19','#skF_18'),
    inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_350]) ).

tff(c_375,plain,
    $lesseq('#skF_16','#skF_18'),
    inference(cnfTransformation,[status(thm)],[f_653]) ).

tff(c_427,plain,
    ~ $less('#skF_18','#skF_16'),
    inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_375]) ).

tff(c_4540,plain,
    get3('#skF_21',$sum(1,'#skF_19')) = '#skE_7',
    inference(define,[status(thm),theory(equality)],[c_2051]) ).

tff(c_4547,plain,
    ( ( '#skE_7' = '#skE_2' )
    | $less('#skF_17',$sum(1,'#skF_19')) ),
    inference(demodulation,[status(thm),theory(equality)],[c_4540,c_4539]) ).

tff(c_4549,plain,
    $less('#skF_17',$sum(1,'#skF_19')),
    inference(splitLeft,[status(thm)],[c_4547]) ).

tff(c_4550,plain,
    $false,
    inference(close,[status(thm),theory('LIA')],[c_4549,c_436,c_473,c_474]) ).

tff(c_4553,plain,
    '#skE_7' = '#skE_2',
    inference(splitRight,[status(thm)],[c_4547]) ).

tff(c_4546,plain,
    get3('#skF_21',$sum(1,'#skF_19')) = '#skE_7',
    inference(define,[status(thm),theory(equality)],[c_2051]) ).

tff(c_4562,plain,
    get3('#skF_21',$sum(1,'#skF_19')) = '#skE_2',
    inference(demodulation,[status(thm),theory(equality)],[c_4553,c_4546]) ).

tff(c_4629,plain,
    ( ( '#skE_2' = 42 )
    | ~ $less('#skF_19',$sum(1,'#skF_19'))
    | ~ $less($sum(1,'#skF_19'),'#skF_20') ),
    inference(superposition,[status(thm),theory(equality)],[c_4562,c_443]) ).

tff(c_4631,plain,
    ( ( '#skE_2' = 42 )
    | ~ $less($sum(1,'#skF_19'),'#skF_20') ),
    inference(backgroundSimplification,[status(thm),theory('LIA')],[c_4629]) ).

tff(c_4646,plain,
    ~ $less($sum(1,'#skF_19'),'#skF_20'),
    inference(splitLeft,[status(thm)],[c_4631]) ).

tff(c_5230,plain,
    ~ $less('#skE_1','#skE_4'),
    inference(splitLeft,[status(thm)],[c_3279]) ).

tff(c_383,plain,
    ! [R_413a: $int] :
      ( ( get3('#skF_22',R_413a) = get3('#skF_21','#skF_23'(R_413a)) )
      | ~ $lesseq('#skF_16',R_413a)
      | ~ $lesseq(R_413a,'#skF_19') ),
    inference(cnfTransformation,[status(thm)],[f_653]) ).

tff(c_420,plain,
    ! [R_413a: $int] :
      ( ( get3('#skF_22',R_413a) = get3('#skF_21','#skF_23'(R_413a)) )
      | $less(R_413a,'#skF_16')
      | $less('#skF_19',R_413a) ),
    inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_383]) ).

tff(c_1737,plain,
    get3('#skF_22','#skF_18') = '#skE_1',
    inference(define,[status(thm),theory(equality)],[c_458]) ).

tff(c_1770,plain,
    ( ( get3('#skF_21','#skF_23'('#skF_18')) = '#skE_1' )
    | $less('#skF_18','#skF_16')
    | $less('#skF_19','#skF_18') ),
    inference(superposition,[status(thm),theory(equality)],[c_420,c_1737]) ).

tff(c_3582,plain,
    get3('#skF_21','#skF_23'('#skF_18')) = '#skE_1',
    inference(negUnitSimplification,[status(thm)],[c_445,c_427,c_1770]) ).

tff(c_3597,plain,
    '#skF_23'('#skF_18') = '#skE_6',
    inference(define,[status(thm),theory(equality)],[c_3582]) ).

tff(c_385,plain,
    ! [R_413a: $int] :
      ( $lesseq('#skF_23'(R_413a),'#skF_19')
      | ~ $lesseq('#skF_16',R_413a)
      | ~ $lesseq(R_413a,'#skF_19') ),
    inference(cnfTransformation,[status(thm)],[f_653]) ).

tff(c_419,plain,
    ! [R_413a: $int] :
      ( ~ $less('#skF_19','#skF_23'(R_413a))
      | $less(R_413a,'#skF_16')
      | $less('#skF_19',R_413a) ),
    inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_385]) ).

tff(c_3616,plain,
    ( ~ $less('#skF_19','#skE_6')
    | $less('#skF_18','#skF_16')
    | $less('#skF_19','#skF_18') ),
    inference(superposition,[status(thm),theory(equality)],[c_3597,c_419]) ).

tff(c_3696,plain,
    ~ $less('#skF_19','#skE_6'),
    inference(negUnitSimplification,[status(thm)],[c_445,c_427,c_3616]) ).

tff(c_3584,plain,
    '#skF_23'('#skF_18') = '#skE_6',
    inference(define,[status(thm),theory(equality)],[c_3582]) ).

tff(c_3583,plain,
    get3('#skF_21','#skF_23'('#skF_18')) = '#skE_1',
    inference(negUnitSimplification,[status(thm)],[c_445,c_427,c_1770]) ).

tff(c_3622,plain,
    get3('#skF_21','#skE_6') = '#skE_1',
    inference(demodulation,[status(thm),theory(equality)],[c_3584,c_3583]) ).

tff(c_3687,plain,
    ( ( '#skE_1' = 42 )
    | ~ $less('#skF_19','#skE_6')
    | ~ $less('#skE_6','#skF_20') ),
    inference(superposition,[status(thm),theory(equality)],[c_443,c_3622]) ).

tff(c_3694,plain,
    ~ $less('#skE_6','#skF_20'),
    inference(splitLeft,[status(thm)],[c_3687]) ).

tff(c_3697,plain,
    $false,
    inference(close,[status(thm),theory('LIA')],[c_3696,c_3694,c_436]) ).

tff(c_3700,plain,
    ( ~ $less('#skF_19','#skE_6')
    | ( '#skE_1' = 42 ) ),
    inference(splitRight,[status(thm)],[c_3687]) ).

tff(c_3703,plain,
    ~ $less('#skF_19','#skE_6'),
    inference(splitLeft,[status(thm)],[c_3700]) ).

tff(c_387,plain,
    ! [R_413a: $int] :
      ( $lesseq('#skF_16','#skF_23'(R_413a))
      | ~ $lesseq('#skF_16',R_413a)
      | ~ $lesseq(R_413a,'#skF_19') ),
    inference(cnfTransformation,[status(thm)],[f_653]) ).

tff(c_415,plain,
    ! [R_413a: $int] :
      ( ~ $less('#skF_23'(R_413a),'#skF_16')
      | $less(R_413a,'#skF_16')
      | $less('#skF_19',R_413a) ),
    inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_387]) ).

tff(c_3614,plain,
    ( ~ $less('#skE_6','#skF_16')
    | $less('#skF_18','#skF_16')
    | $less('#skF_19','#skF_18') ),
    inference(superposition,[status(thm),theory(equality)],[c_3597,c_415]) ).

tff(c_3692,plain,
    ~ $less('#skE_6','#skF_16'),
    inference(negUnitSimplification,[status(thm)],[c_445,c_427,c_3614]) ).

tff(c_355,plain,
    ! [R_398a: $int] :
      ( $lesseq(get3('#skF_21',R_398a),42)
      | ~ $lesseq('#skF_16',R_398a)
      | ~ $lesseq(R_398a,'#skF_19') ),
    inference(cnfTransformation,[status(thm)],[f_653]) ).

tff(c_442,plain,
    ! [R_398a: $int] :
      ( ~ $less(42,get3('#skF_21',R_398a))
      | $less(R_398a,'#skF_16')
      | $less('#skF_19',R_398a) ),
    inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_355]) ).

tff(c_3678,plain,
    ( ~ $less(42,'#skE_1')
    | $less('#skE_6','#skF_16')
    | $less('#skF_19','#skE_6') ),
    inference(superposition,[status(thm),theory(equality)],[c_3622,c_442]) ).

tff(c_3709,plain,
    ~ $less(42,'#skE_1'),
    inference(negUnitSimplification,[status(thm)],[c_3703,c_3692,c_3678]) ).

tff(c_3091,plain,
    get3('#skF_22','#skF_24') = '#skE_3',
    inference(define,[status(thm),theory(equality)],[c_478]) ).

tff(c_3092,plain,
    get3('#skF_22',$sum($uminus(1),'#skF_20')) = '#skE_4',
    inference(define,[status(thm),theory(equality)],[c_478]) ).

tff(c_655,plain,
    ! [S_416a: $int] :
      ( $less(get3('#skF_22','#skF_24'),get3('#skF_22',$sum($uminus(1),'#skF_20')))
      | ( get3('#skF_22',S_416a) != get3('#skF_22','#skF_24') )
      | $less(S_416a,'#skF_20')
      | $less('#skF_17',S_416a) ),
    inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_318]) ).

tff(c_3103,plain,
    ! [S_416a: $int] :
      ( $less('#skE_3','#skE_4')
      | ( get3('#skF_22',S_416a) != '#skE_3' )
      | $less(S_416a,'#skF_20')
      | $less('#skF_17',S_416a) ),
    inference(demodulation,[status(thm),theory(equality)],[c_3091,c_3092,c_3091,c_655]) ).

tff(c_3520,plain,
    $less('#skE_3','#skE_4'),
    inference(splitLeft,[status(thm)],[c_3103]) ).

tff(c_5231,plain,
    $false,
    inference(close,[status(thm),theory('LIA')],[c_5230,c_3709,c_3520,c_3485]) ).

tff(c_5234,plain,
    ( $less($sum(1,'#skF_18'),'#skF_20')
    | $less('#skF_20',$sum(1,'#skF_16')) ),
    inference(splitRight,[status(thm)],[c_3279]) ).

tff(c_5283,plain,
    $less('#skF_20',$sum(1,'#skF_16')),
    inference(splitLeft,[status(thm)],[c_5234]) ).

tff(c_5284,plain,
    $false,
    inference(close,[status(thm),theory('LIA')],[c_5283,c_436,c_427,c_445]) ).

tff(c_5288,plain,
    ~ $less('#skF_20',$sum(1,'#skF_16')),
    inference(splitRight,[status(thm)],[c_5234]) ).

tff(c_3313,plain,
    ( ( get3('#skF_21','#skF_23'($sum($uminus(1),'#skF_20'))) = '#skE_4' )
    | $less($sum($uminus(1),'#skF_20'),'#skF_16')
    | $less('#skF_19',$sum($uminus(1),'#skF_20')) ),
    inference(superposition,[status(thm),theory(equality)],[c_420,c_3205]) ).

tff(c_3316,plain,
    ( ( get3('#skF_21','#skF_23'($sum($uminus(1),'#skF_20'))) = '#skE_4' )
    | $less('#skF_20',$sum(1,'#skF_16'))
    | $less($sum(1,'#skF_19'),'#skF_20') ),
    inference(backgroundSimplification,[status(thm),theory('LIA')],[c_3313]) ).

tff(c_30146,plain,
    get3('#skF_21','#skF_23'($sum($uminus(1),'#skF_20'))) = '#skE_4',
    inference(negUnitSimplification,[status(thm)],[c_4646,c_5288,c_3316]) ).

tff(c_30406,plain,
    '#skF_23'($sum($uminus(1),'#skF_20')) = '#skE_10',
    inference(define,[status(thm),theory(equality)],[c_30146]) ).

tff(c_30559,plain,
    ( ~ $less('#skF_19','#skE_10')
    | $less($sum($uminus(1),'#skF_20'),'#skF_16')
    | $less('#skF_19',$sum($uminus(1),'#skF_20')) ),
    inference(superposition,[status(thm),theory(equality)],[c_30406,c_419]) ).

tff(c_30561,plain,
    ( ~ $less('#skF_19','#skE_10')
    | $less('#skF_20',$sum(1,'#skF_16'))
    | $less($sum(1,'#skF_19'),'#skF_20') ),
    inference(backgroundSimplification,[status(thm),theory('LIA')],[c_30559]) ).

tff(c_31099,plain,
    ~ $less('#skF_19','#skE_10'),
    inference(negUnitSimplification,[status(thm)],[c_4646,c_5288,c_30561]) ).

tff(c_30556,plain,
    ( ~ $less('#skE_10','#skF_16')
    | $less($sum($uminus(1),'#skF_20'),'#skF_16')
    | $less('#skF_19',$sum($uminus(1),'#skF_20')) ),
    inference(superposition,[status(thm),theory(equality)],[c_30406,c_415]) ).

tff(c_30558,plain,
    ( ~ $less('#skE_10','#skF_16')
    | $less('#skF_20',$sum(1,'#skF_16'))
    | $less($sum(1,'#skF_19'),'#skF_20') ),
    inference(backgroundSimplification,[status(thm),theory('LIA')],[c_30556]) ).

tff(c_30572,plain,
    ~ $less('#skE_10','#skF_16'),
    inference(negUnitSimplification,[status(thm)],[c_4646,c_5288,c_30558]) ).

tff(c_30405,plain,
    '#skF_23'($sum($uminus(1),'#skF_20')) = '#skE_10',
    inference(define,[status(thm),theory(equality)],[c_30146]) ).

tff(c_3294,plain,
    ( ( get3('#skF_21','#skF_23'($sum($uminus(1),'#skF_20'))) = '#skE_4' )
    | $less($sum($uminus(1),'#skF_20'),'#skF_16')
    | $less('#skF_19',$sum($uminus(1),'#skF_20')) ),
    inference(superposition,[status(thm),theory(equality)],[c_3205,c_420]) ).

tff(c_3297,plain,
    ( ( get3('#skF_21','#skF_23'($sum($uminus(1),'#skF_20'))) = '#skE_4' )
    | $less('#skF_20',$sum(1,'#skF_16'))
    | $less($sum(1,'#skF_19'),'#skF_20') ),
    inference(backgroundSimplification,[status(thm),theory('LIA')],[c_3294]) ).

tff(c_31809,plain,
    ( ( get3('#skF_21','#skE_10') = '#skE_4' )
    | $less('#skF_20',$sum(1,'#skF_16'))
    | $less($sum(1,'#skF_19'),'#skF_20') ),
    inference(demodulation,[status(thm),theory(equality)],[c_30405,c_3297]) ).

tff(c_31815,plain,
    get3('#skF_21','#skE_10') = '#skE_4',
    inference(negUnitSimplification,[status(thm)],[c_4646,c_5288,c_31809]) ).

tff(c_31928,plain,
    ( ~ $less(42,'#skE_4')
    | $less('#skE_10','#skF_16')
    | $less('#skF_19','#skE_10') ),
    inference(superposition,[status(thm),theory(equality)],[c_31815,c_442]) ).

tff(c_33854,plain,
    ~ $less(42,'#skE_4'),
    inference(negUnitSimplification,[status(thm)],[c_31099,c_30572,c_31928]) ).

tff(c_33855,plain,
    $false,
    inference(close,[status(thm),theory('LIA')],[c_33854,c_3520,c_3485]) ).

tff(c_33858,plain,
    '#skE_2' = 42,
    inference(splitRight,[status(thm)],[c_4631]) ).

tff(c_1989,plain,
    get3('#skF_22',$sum(1,'#skF_19')) = '#skE_2',
    inference(define,[status(thm),theory(equality)],[c_424]) ).

tff(c_2751,plain,
    ! [R_1184a: $int] :
      ( ~ $less('#skE_1',get3('#skF_22',R_1184a))
      | $less(R_1184a,'#skF_16')
      | $less('#skF_18',R_1184a) ),
    inference(demodulation,[status(thm),theory(equality)],[c_1724,c_647]) ).

tff(c_2765,plain,
    ( ~ $less('#skE_1','#skE_2')
    | $less($sum(1,'#skF_19'),'#skF_16')
    | $less('#skF_18',$sum(1,'#skF_19')) ),
    inference(superposition,[status(thm),theory(equality)],[c_1989,c_2751]) ).

tff(c_34279,plain,
    ( ~ $less('#skE_1',42)
    | $less($sum(1,'#skF_19'),'#skF_16')
    | $less('#skF_18',$sum(1,'#skF_19')) ),
    inference(demodulation,[status(thm),theory(equality)],[c_33858,c_2765]) ).

tff(c_34281,plain,
    ~ $less('#skE_1',42),
    inference(splitLeft,[status(thm)],[c_34279]) ).

tff(c_33859,plain,
    $less($sum(1,'#skF_19'),'#skF_20'),
    inference(splitRight,[status(thm)],[c_4631]) ).

tff(c_3298,plain,
    ( ( get3('#skF_21',$sum($uminus(1),'#skF_20')) = '#skE_4' )
    | ~ $less('#skF_19',$sum($uminus(1),'#skF_20'))
    | $less('#skF_17',$sum($uminus(1),'#skF_20')) ),
    inference(superposition,[status(thm),theory(equality)],[c_3205,c_467]) ).

tff(c_3301,plain,
    ( ( get3('#skF_21',$sum($uminus(1),'#skF_20')) = '#skE_4' )
    | ~ $less($sum(1,'#skF_19'),'#skF_20')
    | $less($sum(1,'#skF_17'),'#skF_20') ),
    inference(backgroundSimplification,[status(thm),theory('LIA')],[c_3298]) ).

tff(c_50409,plain,
    ( ( get3('#skF_21',$sum($uminus(1),'#skF_20')) = '#skE_4' )
    | $less($sum(1,'#skF_17'),'#skF_20') ),
    inference(demodulation,[status(thm),theory(equality)],[c_33859,c_3301]) ).

tff(c_51133,plain,
    get3('#skF_21',$sum($uminus(1),'#skF_20')) = '#skE_11',
    inference(define,[status(thm),theory(equality)],[c_50409]) ).

tff(c_51252,plain,
    ( ( '#skE_11' = 42 )
    | ~ $less('#skF_19',$sum($uminus(1),'#skF_20'))
    | ~ $less($sum($uminus(1),'#skF_20'),'#skF_20') ),
    inference(superposition,[status(thm),theory(equality)],[c_51133,c_443]) ).

tff(c_51254,plain,
    ( ( '#skE_11' = 42 )
    | ~ $less($sum(1,'#skF_19'),'#skF_20') ),
    inference(backgroundSimplification,[status(thm),theory('LIA')],[c_51252]) ).

tff(c_51274,plain,
    '#skE_11' = 42,
    inference(demodulation,[status(thm),theory(equality)],[c_33859,c_51254]) ).

tff(c_50411,plain,
    get3('#skF_21',$sum($uminus(1),'#skF_20')) = '#skE_11',
    inference(define,[status(thm),theory(equality)],[c_50409]) ).

tff(c_50410,plain,
    ( ( get3('#skF_21',$sum($uminus(1),'#skF_20')) = '#skE_4' )
    | $less($sum(1,'#skF_17'),'#skF_20') ),
    inference(demodulation,[status(thm),theory(equality)],[c_33859,c_3301]) ).

tff(c_50418,plain,
    ( ( '#skE_4' = '#skE_11' )
    | $less($sum(1,'#skF_17'),'#skF_20') ),
    inference(demodulation,[status(thm),theory(equality)],[c_50411,c_50410]) ).

tff(c_66610,plain,
    ( ( '#skE_4' = 42 )
    | $less($sum(1,'#skF_17'),'#skF_20') ),
    inference(demodulation,[status(thm),theory(equality)],[c_51274,c_50418]) ).

tff(c_66612,plain,
    $less($sum(1,'#skF_17'),'#skF_20'),
    inference(splitLeft,[status(thm)],[c_66610]) ).

tff(c_66682,plain,
    $false,
    inference(close,[status(thm),theory('LIA')],[c_66612,c_473,c_474]) ).

tff(c_66685,plain,
    '#skE_4' = 42,
    inference(splitRight,[status(thm)],[c_66610]) ).

tff(c_34702,plain,
    ~ $less('#skE_1','#skE_4'),
    inference(splitLeft,[status(thm)],[c_3279]) ).

tff(c_34707,plain,
    $false,
    inference(close,[status(thm),theory('LIA')],[c_34702,c_3709,c_3520,c_3485]) ).

tff(c_34711,plain,
    $less('#skE_1','#skE_4'),
    inference(splitRight,[status(thm)],[c_3279]) ).

tff(c_66688,plain,
    $less('#skE_1',42),
    inference(demodulation,[status(thm),theory(equality)],[c_66685,c_34711]) ).

tff(c_66697,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_34281,c_66688]) ).

tff(c_66701,plain,
    $less('#skE_1',42),
    inference(splitRight,[status(thm)],[c_34279]) ).

tff(c_3171,plain,
    ( ~ $less('#skE_1','#skE_3')
    | $less('#skF_24','#skF_16')
    | $less('#skF_18','#skF_24') ),
    inference(superposition,[status(thm),theory(equality)],[c_3106,c_1734]) ).

tff(c_3518,plain,
    ~ $less('#skE_1','#skE_3'),
    inference(splitLeft,[status(thm)],[c_3171]) ).

tff(c_66726,plain,
    $false,
    inference(close,[status(thm),theory('LIA')],[c_66701,c_3518,c_3485]) ).

tff(c_66730,plain,
    $less('#skF_19','#skE_6'),
    inference(splitRight,[status(thm)],[c_3700]) ).

tff(c_66867,plain,
    ( $less('#skF_18','#skF_16')
    | $less('#skF_19','#skF_18') ),
    inference(demodulation,[status(thm),theory(equality)],[c_66730,c_3616]) ).

tff(c_66868,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_445,c_427,c_66867]) ).

tff(c_66881,plain,
    ! [S_6591a: $int] :
      ( ( get3('#skF_22',S_6591a) != '#skE_3' )
      | $less(S_6591a,'#skF_20')
      | $less('#skF_17',S_6591a) ),
    inference(splitRight,[status(thm)],[c_3103]) ).

tff(c_66904,plain,
    ( $less('#skF_24','#skF_20')
    | $less('#skF_17','#skF_24') ),
    inference(superposition,[status(thm),theory(equality)],[c_3099,c_66881]) ).

tff(c_66913,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_474,c_473,c_66904]) ).

tff(c_66917,plain,
    $less('#skE_1','#skE_3'),
    inference(splitRight,[status(thm)],[c_3171]) ).

tff(c_66919,plain,
    $less('#skE_3','#skE_4'),
    inference(splitLeft,[status(thm)],[c_3103]) ).

tff(c_101375,plain,
    $false,
    inference(close,[status(thm),theory('LIA')],[c_101365,c_66917,c_66919]) ).

tff(c_101378,plain,
    ( $less($sum(1,'#skF_18'),'#skF_20')
    | $less('#skF_20',$sum(1,'#skF_16')) ),
    inference(splitRight,[status(thm)],[c_3279]) ).

tff(c_101381,plain,
    $less('#skF_20',$sum(1,'#skF_16')),
    inference(splitLeft,[status(thm)],[c_101378]) ).

tff(c_101435,plain,
    $false,
    inference(close,[status(thm),theory('LIA')],[c_101381,c_436,c_427,c_445]) ).

tff(c_101439,plain,
    ~ $less('#skF_20',$sum(1,'#skF_16')),
    inference(splitRight,[status(thm)],[c_101378]) ).

tff(c_118518,plain,
    get3('#skF_21','#skF_23'($sum($uminus(1),'#skF_20'))) = '#skE_4',
    inference(negUnitSimplification,[status(thm)],[c_100784,c_101439,c_3316]) ).

tff(c_118520,plain,
    '#skF_23'($sum($uminus(1),'#skF_20')) = '#skE_10',
    inference(define,[status(thm),theory(equality)],[c_118518]) ).

tff(c_118519,plain,
    get3('#skF_21','#skF_23'($sum($uminus(1),'#skF_20'))) = '#skE_4',
    inference(negUnitSimplification,[status(thm)],[c_100784,c_101439,c_3316]) ).

tff(c_118533,plain,
    get3('#skF_21','#skE_10') = '#skE_4',
    inference(demodulation,[status(thm),theory(equality)],[c_118520,c_118519]) ).

tff(c_118658,plain,
    ( ~ $less(42,'#skE_4')
    | $less('#skE_10','#skF_16')
    | $less('#skF_19','#skE_10') ),
    inference(superposition,[status(thm),theory(equality)],[c_118533,c_442]) ).

tff(c_118843,plain,
    ~ $less(42,'#skE_4'),
    inference(splitLeft,[status(thm)],[c_118658]) ).

tff(c_118844,plain,
    $false,
    inference(close,[status(thm),theory('LIA')],[c_118843,c_66919,c_3485]) ).

tff(c_118847,plain,
    ( $less('#skF_19','#skE_10')
    | $less('#skE_10','#skF_16') ),
    inference(splitRight,[status(thm)],[c_118658]) ).

tff(c_118854,plain,
    $less('#skE_10','#skF_16'),
    inference(splitLeft,[status(thm)],[c_118847]) ).

tff(c_118672,plain,
    ( ( '#skE_4' = 42 )
    | ~ $less('#skF_19','#skE_10')
    | ~ $less('#skE_10','#skF_20') ),
    inference(superposition,[status(thm),theory(equality)],[c_443,c_118533]) ).

tff(c_118838,plain,
    ~ $less('#skE_10','#skF_20'),
    inference(splitLeft,[status(thm)],[c_118672]) ).

tff(c_118855,plain,
    $false,
    inference(close,[status(thm),theory('LIA')],[c_118854,c_118838,c_436,c_427,c_445]) ).

tff(c_118858,plain,
    $less('#skF_19','#skE_10'),
    inference(splitRight,[status(thm)],[c_118847]) ).

tff(c_118679,plain,
    '#skF_23'($sum($uminus(1),'#skF_20')) = '#skE_10',
    inference(define,[status(thm),theory(equality)],[c_118518]) ).

tff(c_118826,plain,
    ( ~ $less('#skF_19','#skE_10')
    | $less($sum($uminus(1),'#skF_20'),'#skF_16')
    | $less('#skF_19',$sum($uminus(1),'#skF_20')) ),
    inference(superposition,[status(thm),theory(equality)],[c_118679,c_419]) ).

tff(c_118828,plain,
    ( ~ $less('#skF_19','#skE_10')
    | $less('#skF_20',$sum(1,'#skF_16'))
    | $less($sum(1,'#skF_19'),'#skF_20') ),
    inference(backgroundSimplification,[status(thm),theory('LIA')],[c_118826]) ).

tff(c_119331,plain,
    ( $less('#skF_20',$sum(1,'#skF_16'))
    | $less($sum(1,'#skF_19'),'#skF_20') ),
    inference(demodulation,[status(thm),theory(equality)],[c_118858,c_118828]) ).

tff(c_119332,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_100784,c_101439,c_119331]) ).

tff(c_119336,plain,
    $less('#skE_10','#skF_20'),
    inference(splitRight,[status(thm)],[c_118672]) ).

tff(c_118660,plain,
    ( ( '#skE_4' = 42 )
    | ~ $less('#skF_19','#skE_10')
    | ~ $less('#skE_10','#skF_20') ),
    inference(superposition,[status(thm),theory(equality)],[c_118533,c_443]) ).

tff(c_119339,plain,
    ( ( '#skE_4' = 42 )
    | ~ $less('#skF_19','#skE_10') ),
    inference(demodulation,[status(thm),theory(equality)],[c_119336,c_118660]) ).

tff(c_119341,plain,
    ~ $less('#skF_19','#skE_10'),
    inference(splitLeft,[status(thm)],[c_119339]) ).

tff(c_119812,plain,
    ( ~ $less(42,'#skE_4')
    | $less('#skE_10','#skF_16') ),
    inference(negUnitSimplification,[status(thm)],[c_119341,c_118658]) ).

tff(c_119814,plain,
    ~ $less(42,'#skE_4'),
    inference(splitLeft,[status(thm)],[c_119812]) ).

tff(c_119953,plain,
    $false,
    inference(close,[status(thm),theory('LIA')],[c_119814,c_66919,c_3485]) ).

tff(c_119956,plain,
    $less('#skE_10','#skF_16'),
    inference(splitRight,[status(thm)],[c_119812]) ).

tff(c_118823,plain,
    ( ~ $less('#skE_10','#skF_16')
    | $less($sum($uminus(1),'#skF_20'),'#skF_16')
    | $less('#skF_19',$sum($uminus(1),'#skF_20')) ),
    inference(superposition,[status(thm),theory(equality)],[c_118679,c_415]) ).

tff(c_118825,plain,
    ( ~ $less('#skE_10','#skF_16')
    | $less('#skF_20',$sum(1,'#skF_16'))
    | $less($sum(1,'#skF_19'),'#skF_20') ),
    inference(backgroundSimplification,[status(thm),theory('LIA')],[c_118823]) ).

tff(c_119959,plain,
    ( $less('#skF_20',$sum(1,'#skF_16'))
    | $less($sum(1,'#skF_19'),'#skF_20') ),
    inference(demodulation,[status(thm),theory(equality)],[c_119956,c_118825]) ).

tff(c_119960,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_100784,c_101439,c_119959]) ).

tff(c_119963,plain,
    '#skE_4' = 42,
    inference(splitRight,[status(thm)],[c_119339]) ).

tff(c_119977,plain,
    $less('#skE_3',42),
    inference(demodulation,[status(thm),theory(equality)],[c_119963,c_66919]) ).

tff(c_119988,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_3485,c_119977]) ).

tff(c_119992,plain,
    $less($sum(1,'#skF_19'),'#skF_20'),
    inference(splitRight,[status(thm)],[c_100778]) ).

tff(c_135743,plain,
    ( ( get3('#skF_21',$sum($uminus(1),'#skF_20')) = '#skE_4' )
    | $less($sum(1,'#skF_17'),'#skF_20') ),
    inference(demodulation,[status(thm),theory(equality)],[c_119992,c_3301]) ).

tff(c_135776,plain,
    get3('#skF_21',$sum($uminus(1),'#skF_20')) = '#skE_11',
    inference(define,[status(thm),theory(equality)],[c_135743]) ).

tff(c_135909,plain,
    ( ( '#skE_11' = 42 )
    | ~ $less('#skF_19',$sum($uminus(1),'#skF_20'))
    | ~ $less($sum($uminus(1),'#skF_20'),'#skF_20') ),
    inference(superposition,[status(thm),theory(equality)],[c_135776,c_443]) ).

tff(c_135911,plain,
    ( ( '#skE_11' = 42 )
    | ~ $less($sum(1,'#skF_19'),'#skF_20') ),
    inference(backgroundSimplification,[status(thm),theory('LIA')],[c_135909]) ).

tff(c_135930,plain,
    '#skE_11' = 42,
    inference(demodulation,[status(thm),theory(equality)],[c_119992,c_135911]) ).

tff(c_135745,plain,
    get3('#skF_21',$sum($uminus(1),'#skF_20')) = '#skE_11',
    inference(define,[status(thm),theory(equality)],[c_135743]) ).

tff(c_135744,plain,
    ( ( get3('#skF_21',$sum($uminus(1),'#skF_20')) = '#skE_4' )
    | $less($sum(1,'#skF_17'),'#skF_20') ),
    inference(demodulation,[status(thm),theory(equality)],[c_119992,c_3301]) ).

tff(c_135752,plain,
    ( ( '#skE_4' = '#skE_11' )
    | $less($sum(1,'#skF_17'),'#skF_20') ),
    inference(demodulation,[status(thm),theory(equality)],[c_135745,c_135744]) ).

tff(c_135754,plain,
    $less($sum(1,'#skF_17'),'#skF_20'),
    inference(splitLeft,[status(thm)],[c_135752]) ).

tff(c_135755,plain,
    $false,
    inference(close,[status(thm),theory('LIA')],[c_135754,c_473,c_474]) ).

tff(c_135758,plain,
    '#skE_4' = '#skE_11',
    inference(splitRight,[status(thm)],[c_135752]) ).

tff(c_135770,plain,
    $less('#skE_3','#skE_11'),
    inference(demodulation,[status(thm),theory(equality)],[c_135758,c_66919]) ).

tff(c_135937,plain,
    $less('#skE_3',42),
    inference(demodulation,[status(thm),theory(equality)],[c_135930,c_135770]) ).

tff(c_135946,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_3485,c_135937]) ).

tff(c_135964,plain,
    ! [S_11526a: $int] :
      ( ( get3('#skF_22',S_11526a) != '#skE_3' )
      | $less(S_11526a,'#skF_20')
      | $less('#skF_17',S_11526a) ),
    inference(splitRight,[status(thm)],[c_3103]) ).

tff(c_135987,plain,
    ( $less('#skF_24','#skF_20')
    | $less('#skF_17','#skF_24') ),
    inference(superposition,[status(thm),theory(equality)],[c_3099,c_135964]) ).

tff(c_135996,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_474,c_473,c_135987]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14  % Problem  : SWW575_2 : TPTP v8.1.2. Released v6.1.0.
% 0.00/0.15  % 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
% 0.15/0.36  % Computer : n016.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit : 300
% 0.15/0.36  % WCLimit  : 300
% 0.15/0.36  % DateTime : Thu Aug  3 19:45:38 EDT 2023
% 0.15/0.36  % CPUTime  : 
% 55.84/25.56  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 55.93/25.59  
% 55.93/25.59  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 55.93/25.63  
% 55.93/25.63  Inference rules
% 55.93/25.63  ----------------------
% 55.93/25.63  #Ref     : 9
% 55.93/25.63  #Sup     : 26081
% 55.93/25.63  #Fact    : 21
% 55.93/25.63  #Define  : 25
% 55.93/25.63  #Split   : 89
% 55.93/25.63  #Chain   : 0
% 55.93/25.63  #Close   : 39
% 55.93/25.63  
% 55.93/25.63  Ordering : LPO
% 55.93/25.63  
% 55.93/25.63  Simplification rules
% 55.93/25.63  ----------------------
% 55.93/25.63  #Subsume      : 2554
% 55.93/25.63  #Demod        : 17033
% 55.93/25.63  #Tautology    : 12880
% 55.93/25.63  #SimpNegUnit  : 248
% 55.93/25.63  #BackRed      : 101
% 55.93/25.63  
% 55.93/25.63  #Partial instantiations: 1851
% 55.93/25.63  #Strategies tried      : 1
% 55.93/25.63  
% 55.93/25.63  Timing (in seconds)
% 55.93/25.63  ----------------------
% 55.93/25.64  Preprocessing        : 1.27
% 55.93/25.64  Parsing              : 0.55
% 55.93/25.64  CNF conversion       : 0.10
% 55.93/25.64  Main loop            : 23.25
% 55.93/25.64  Inferencing          : 3.86
% 55.93/25.64  Reduction            : 9.26
% 55.93/25.64  Demodulation         : 7.48
% 55.93/25.64  BG Simplification    : 0.86
% 55.93/25.64  Subsumption          : 6.34
% 55.93/25.64  Abstraction          : 0.48
% 55.93/25.64  MUC search           : 1.31
% 55.93/25.64  Cooper               : 1.79
% 55.93/25.64  Total                : 24.61
% 55.93/25.64  Index Insertion      : 0.00
% 55.93/25.64  Index Deletion       : 0.00
% 55.93/25.64  Index Matching       : 0.00
% 55.93/25.64  BG Taut test         : 0.00
%------------------------------------------------------------------------------