TSTP Solution File: SWW597_2 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SWW597_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 : n004.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Tue Aug 22 11:07:46 EDT 2023

% Result   : Theorem 18.01s 5.45s
% Output   : CNFRefutation 18.01s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :   85
% Syntax   : Number of formulae    :  157 (  59 unt;  72 typ;   0 def)
%            Number of atoms       :  145 (  71 equ)
%            Maximal formula atoms :   16 (   1 avg)
%            Number of connectives :   99 (  39   ~;  40   |;  10   &)
%                                         (   1 <=>;   9  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   17 (   3 avg)
%            Maximal term depth    :    7 (   2 avg)
%            Number arithmetic     :  122 (  44 atm;  15 fun;  20 num;  43 var)
%            Number of types       :    9 (   7 usr;   1 ari)
%            Number of type conns  :  152 (  45   >; 107   *;   0   +;   0  <<)
%            Number of predicates  :   15 (  11 usr;   1 prp; 0-7 aty)
%            Number of functors    :   57 (  54 usr;  22 con; 0-7 aty)
%            Number of variables   :   98 (;  98   !;   0   ?;  98   :)

% Comments : 
%------------------------------------------------------------------------------
%$ exchange > permut_sub > permut1 > permut > map_eq_sub > exchange1 > array_eq_sub > monochrome > permut_all > array_eq > sort > set > occ > match_color > set1 > match_bool > get > mk_array > make > get1 > const > mk_ref > map > length > elts > contents > #nlpp > witness > tb2t3 > tb2t2 > tb2t1 > tb2t > t2tb3 > t2tb2 > t2tb1 > t2tb > ref > array > white > tuple02 > tuple01 > true > red > real > qtmark > int > false > color1 > bool1 > blue > #skF_10 > #skF_6 > #skF_4 > #skF_8 > #skF_14 > #skF_1 > #skF_7 > #skF_2 > #skF_3 > #skF_5

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

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

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

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

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

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

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

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

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

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

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

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

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

%Foreground operators:
tff('#skF_10',type,
    '#skF_10': map_int_color ).

tff(tb2t3,type,
    tb2t3: uni > map_int_color ).

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

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

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

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

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

tff(tuple02,type,
    tuple02: tuple0 ).

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

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

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

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

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

tff(tuple01,type,
    tuple01: ty ).

tff(tb2t1,type,
    tb2t1: uni > array_color ).

tff(int,type,
    int: ty ).

tff(match_color,type,
    match_color: ( ty * color * uni * uni * uni ) > uni ).

tff(blue,type,
    blue: color ).

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

tff(exchange1,type,
    exchange1: ( ty * uni * uni * $int * $int ) > $o ).

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

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

tff(color1,type,
    color1: ty ).

tff(monochrome,type,
    monochrome: ( array_color * $int * $int * color ) > $o ).

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

tff(real,type,
    real: ty ).

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

tff(false,type,
    false: bool ).

tff(permut1,type,
    permut1: ( ty * uni * uni * $int * $int ) > $o ).

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

tff('#skF_14',type,
    '#skF_14': map_int_color ).

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

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

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

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

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

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

tff(qtmark,type,
    qtmark: ty ).

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

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

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

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

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

tff(t2tb3,type,
    t2tb3: map_int_color > uni ).

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

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

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

tff(true,type,
    true: bool ).

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

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

tff(red,type,
    red: color ).

tff(white,type,
    white: color ).

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

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

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

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

tff(f_374,axiom,
    white != red,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',white_Red) ).

tff(f_390,axiom,
    ! [I: color] : ( tb2t2(t2tb2(I)) = I ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',bridgeL2) ).

tff(f_405,axiom,
    ! [X: map_int_color] : sort(map(int,color1),t2tb3(X)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2tb_sort3) ).

tff(f_102,axiom,
    ! [A: ty,Ua: $int,U1: uni] :
      ( sort(map(int,A),U1)
     => ( elts(A,mk_array(A,Ua,U1)) = U1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',elts_def) ).

tff(f_114,axiom,
    ! [A: ty,A1: uni,Ia: $int] : ( get1(A,A1,Ia) = get(A,int,elts(A,A1),t2tb(Ia)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',get_def) ).

tff(f_446,negated_conjecture,
    ~ ! [Aa: $int,A1: map_int_color] :
        ( $lesseq(0,Aa)
       => ! [Ra: $int,Ia: $int,Ba: $int,A2: map_int_color] :
            ( ( $lesseq(0,Ba)
              & $lesseq(Ba,Ia)
              & $lesseq(Ia,Ra)
              & $lesseq(Ra,Aa)
              & monochrome(tb2t1(mk_array(color1,Aa,t2tb3(A2))),0,Ba,blue)
              & monochrome(tb2t1(mk_array(color1,Aa,t2tb3(A2))),Ba,Ia,white)
              & monochrome(tb2t1(mk_array(color1,Aa,t2tb3(A2))),Ra,Aa,red)
              & permut_all(color1,mk_array(color1,Aa,t2tb3(A1)),mk_array(color1,Aa,t2tb3(A2))) )
           => ( $less(Ia,Ra)
             => ( ( $lesseq(0,Aa)
                  & $lesseq(0,Ia)
                  & $less(Ia,Aa) )
               => ( ( tb2t2(get(color1,int,t2tb3(A2),t2tb(Ia))) = white )
                 => ! [I1a: $int] :
                      ( ( I1a = $sum(Ia,1) )
                     => monochrome(tb2t1(mk_array(color1,Aa,t2tb3(A2))),Ba,I1a,white) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',wP_parameter_dutch_flag) ).

tff(f_68,axiom,
    ! [A: ty,B: ty,X: uni,X1: uni] : sort(B,get(B,A,X,X1)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',get_sort) ).

tff(f_394,axiom,
    ! [J: uni] :
      ( sort(color1,J)
     => ( t2tb2(tb2t2(J)) = J ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',bridgeR2) ).

tff(f_370,axiom,
    blue != white,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',blue_White) ).

tff(f_380,axiom,
    ! [U: color] :
      ( ( U = blue )
      | ( U = white )
      | ( U = red ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',color_inversion) ).

tff(f_403,axiom,
    ! [A: array_color,Ia: $int,Ja: $int,C: color] :
      ( monochrome(A,Ia,Ja,C)
    <=> ! [Ka: $int] :
          ( ( $lesseq(Ia,Ka)
            & $less(Ka,Ja) )
         => ( tb2t2(get1(color1,t2tb1(A),Ka)) = C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',monochrome_def) ).

tff(f_386,axiom,
    ! [J: uni] : ( t2tb1(tb2t1(J)) = J ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',bridgeR1) ).

tff(f_106,axiom,
    ! [A: ty,X: uni,X1a: $int] : sort(A,get1(A,X,X1a)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',get_sort1) ).

tff(c_224,plain,
    white != red,
    inference(cnfTransformation,[status(thm)],[f_374]) ).

tff(c_236,plain,
    ! [I_252: color] : ( tb2t2(t2tb2(I_252)) = I_252 ),
    inference(cnfTransformation,[status(thm)],[f_390]) ).

tff(c_249,plain,
    ! [X_261: map_int_color] : sort(map(int,color1),t2tb3(X_261)),
    inference(cnfTransformation,[status(thm)],[f_405]) ).

tff(c_2597,plain,
    ! [A_943: ty,U_944a: $int,U1_945: uni] :
      ( ( elts(A_943,mk_array(A_943,U_944a,U1_945)) = U1_945 )
      | ~ sort(map(int,A_943),U1_945) ),
    inference(cnfTransformation,[status(thm)],[f_102]) ).

tff(c_2657,plain,
    ! [U_947a: $int,X_948: map_int_color] : ( elts(color1,mk_array(color1,U_947a,t2tb3(X_948))) = t2tb3(X_948) ),
    inference(resolution,[status(thm)],[c_249,c_2597]) ).

tff(c_425,plain,
    ! [A_73: ty,A1_74: uni,I_75a: $int] : ( get(A_73,int,elts(A_73,A1_74),t2tb(I_75a)) = get1(A_73,A1_74,I_75a) ),
    inference(cnfTransformation,[status(thm)],[f_114]) ).

tff(c_17581,plain,
    ! [X_4595: map_int_color,I_4596a: $int,U_4597a: $int] : ( get(color1,int,t2tb3(X_4595),t2tb(I_4596a)) = get1(color1,mk_array(color1,U_4597a,t2tb3(X_4595)),I_4596a) ),
    inference(superposition,[status(thm),theory(equality)],[c_2657,c_425]) ).

tff(c_335,plain,
    tb2t2(get(color1,int,t2tb3('#skF_14'),t2tb('#skF_12'))) = white,
    inference(cnfTransformation,[status(thm)],[f_446]) ).

tff(c_26,plain,
    ! [B_26: ty,A_25: ty,X_27: uni,X1_28: uni] : sort(B_26,get(B_26,A_25,X_27,X1_28)),
    inference(cnfTransformation,[status(thm)],[f_68]) ).

tff(c_650,plain,
    ! [J_536: uni] :
      ( ( t2tb2(tb2t2(J_536)) = J_536 )
      | ~ sort(color1,J_536) ),
    inference(cnfTransformation,[status(thm)],[f_394]) ).

tff(c_3323,plain,
    ! [A_1157: ty,X_1158: uni,X1_1159: uni] : ( t2tb2(tb2t2(get(color1,A_1157,X_1158,X1_1159))) = get(color1,A_1157,X_1158,X1_1159) ),
    inference(resolution,[status(thm)],[c_26,c_650]) ).

tff(c_3389,plain,
    get(color1,int,t2tb3('#skF_14'),t2tb('#skF_12')) = t2tb2(white),
    inference(superposition,[status(thm),theory(equality)],[c_335,c_3323]) ).

tff(c_17675,plain,
    ! [U_4601a: $int] : ( get1(color1,mk_array(color1,U_4601a,t2tb3('#skF_14')),'#skF_12') = t2tb2(white) ),
    inference(superposition,[status(thm),theory(equality)],[c_17581,c_3389]) ).

tff(c_220,plain,
    white != blue,
    inference(cnfTransformation,[status(thm)],[f_370]) ).

tff(c_13214,plain,
    ! [X_4094: map_int_color,I_4095a: $int,U_4096a: $int] : ( get(color1,int,t2tb3(X_4094),t2tb(I_4095a)) = get1(color1,mk_array(color1,U_4096a,t2tb3(X_4094)),I_4095a) ),
    inference(superposition,[status(thm),theory(equality)],[c_2657,c_425]) ).

tff(c_13308,plain,
    ! [U_4104a: $int] : ( get1(color1,mk_array(color1,U_4104a,t2tb3('#skF_14')),'#skF_12') = t2tb2(white) ),
    inference(superposition,[status(thm),theory(equality)],[c_13214,c_3389]) ).

tff(c_226,plain,
    ! [U_247: color] :
      ( ( red = U_247 )
      | ( white = U_247 )
      | ( blue = U_247 ) ),
    inference(cnfTransformation,[status(thm)],[f_380]) ).

tff(c_246,plain,
    ! [I_255a: $int,A_254: array_color,J_256a: $int,C_257: color] :
      ( $lesseq(I_255a,'#skF_8'(A_254,I_255a,J_256a,C_257))
      | monochrome(A_254,I_255a,J_256a,C_257) ),
    inference(cnfTransformation,[status(thm)],[f_403]) ).

tff(c_2697,plain,
    ! [A_950: array_color,I_951a: $int,J_952a: $int,C_953: color] :
      ( ~ $less('#skF_8'(A_950,I_951a,J_952a,C_953),I_951a)
      | monochrome(A_950,I_951a,J_952a,C_953) ),
    inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_246]) ).

tff(c_256,plain,
    '#skF_15' = $sum('#skF_12',1),
    inference(cnfTransformation,[status(thm)],[f_446]) ).

tff(c_336,plain,
    '#skF_15' = $sum(1,'#skF_12'),
    inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_256]) ).

tff(c_340,plain,
    ~ monochrome(tb2t1(mk_array(color1,'#skF_9',t2tb3('#skF_14'))),'#skF_13','#skF_15',white),
    inference(cnfTransformation,[status(thm)],[f_446]) ).

tff(c_463,plain,
    ~ monochrome(tb2t1(mk_array(color1,'#skF_9',t2tb3('#skF_14'))),'#skF_13',$sum(1,'#skF_12'),white),
    inference(demodulation,[status(thm),theory(equality)],[c_336,c_340]) ).

tff(c_2711,plain,
    ~ $less('#skF_8'(tb2t1(mk_array(color1,'#skF_9',t2tb3('#skF_14'))),'#skF_13',$sum(1,'#skF_12'),white),'#skF_13'),
    inference(resolution,[status(thm)],[c_2697,c_463]) ).

tff(c_3665,plain,
    '#skF_8'(tb2t1(mk_array(color1,'#skF_9',t2tb3('#skF_14'))),'#skF_13',$sum(1,'#skF_12'),white) = '#skE_1',
    inference(define,[status(thm),theory(equality)],[c_2711]) ).

tff(c_232,plain,
    ! [J_250: uni] : ( t2tb1(tb2t1(J_250)) = J_250 ),
    inference(cnfTransformation,[status(thm)],[f_386]) ).

tff(c_4667,plain,
    ! [A_1327: array_color,I_1328a: $int,J_1329a: $int,C_1330: color] :
      ( ( tb2t2(get1(color1,t2tb1(A_1327),'#skF_8'(A_1327,I_1328a,J_1329a,C_1330))) != C_1330 )
      | monochrome(A_1327,I_1328a,J_1329a,C_1330) ),
    inference(cnfTransformation,[status(thm)],[f_403]) ).

tff(c_4675,plain,
    tb2t2(get1(color1,t2tb1(tb2t1(mk_array(color1,'#skF_9',t2tb3('#skF_14')))),'#skF_8'(tb2t1(mk_array(color1,'#skF_9',t2tb3('#skF_14'))),'#skF_13',$sum(1,'#skF_12'),white))) != white,
    inference(resolution,[status(thm)],[c_4667,c_463]) ).

tff(c_4796,plain,
    tb2t2(get1(color1,mk_array(color1,'#skF_9',t2tb3('#skF_14')),'#skE_1')) != white,
    inference(demodulation,[status(thm),theory(equality)],[c_3665,c_232,c_4675]) ).

tff(c_4802,plain,
    ( ( tb2t2(get1(color1,mk_array(color1,'#skF_9',t2tb3('#skF_14')),'#skE_1')) = red )
    | ( tb2t2(get1(color1,mk_array(color1,'#skF_9',t2tb3('#skF_14')),'#skE_1')) = blue ) ),
    inference(superposition,[status(thm),theory(equality)],[c_226,c_4796]) ).

tff(c_5215,plain,
    tb2t2(get1(color1,mk_array(color1,'#skF_9',t2tb3('#skF_14')),'#skE_1')) = blue,
    inference(splitLeft,[status(thm)],[c_4802]) ).

tff(c_429,plain,
    ! [A_67: ty,X_68: uni,X1_69a: $int] : sort(A_67,get1(A_67,X_68,X1_69a)),
    inference(cnfTransformation,[status(thm)],[f_106]) ).

tff(c_672,plain,
    ! [X_68: uni,X1_69a: $int] : ( t2tb2(tb2t2(get1(color1,X_68,X1_69a))) = get1(color1,X_68,X1_69a) ),
    inference(resolution,[status(thm)],[c_429,c_650]) ).

tff(c_5233,plain,
    get1(color1,mk_array(color1,'#skF_9',t2tb3('#skF_14')),'#skE_1') = t2tb2(blue),
    inference(superposition,[status(thm),theory(equality)],[c_5215,c_672]) ).

tff(c_13411,plain,
    ( ( t2tb2(white) = t2tb2(blue) )
    | ( '#skF_12' != '#skE_1' ) ),
    inference(superposition,[status(thm),theory(equality)],[c_13308,c_5233]) ).

tff(c_13442,plain,
    '#skF_12' != '#skE_1',
    inference(splitLeft,[status(thm)],[c_13411]) ).

tff(c_2784,plain,
    '#skF_8'(tb2t1(mk_array(color1,'#skF_9',t2tb3('#skF_14'))),'#skF_13',$sum(1,'#skF_12'),white) = '#skE_1',
    inference(define,[status(thm),theory(equality)],[c_2711]) ).

tff(c_2783,plain,
    ~ $less('#skF_8'(tb2t1(mk_array(color1,'#skF_9',t2tb3('#skF_14'))),'#skF_13',$sum(1,'#skF_12'),white),'#skF_13'),
    inference(resolution,[status(thm)],[c_2697,c_463]) ).

tff(c_2791,plain,
    ~ $less('#skE_1','#skF_13'),
    inference(demodulation,[status(thm),theory(equality)],[c_2784,c_2783]) ).

tff(c_319,plain,
    monochrome(tb2t1(mk_array(color1,'#skF_9',t2tb3('#skF_14'))),'#skF_13','#skF_12',white),
    inference(cnfTransformation,[status(thm)],[f_446]) ).

tff(c_239,plain,
    ! [A_254: array_color,I_255a: $int,C_257: color,K_260a: $int,J_256a: $int] :
      ( ( tb2t2(get1(color1,t2tb1(A_254),K_260a)) = C_257 )
      | ~ monochrome(A_254,I_255a,J_256a,C_257)
      | ~ $lesseq(I_255a,K_260a)
      | ~ $less(K_260a,J_256a) ),
    inference(cnfTransformation,[status(thm)],[f_403]) ).

tff(c_6802,plain,
    ! [K_1582a: $int,J_1579a: $int,A_1580: array_color,I_1581a: $int,C_1583: color] :
      ( ( tb2t2(get1(color1,t2tb1(A_1580),K_1582a)) = C_1583 )
      | ~ monochrome(A_1580,I_1581a,J_1579a,C_1583)
      | $less(K_1582a,I_1581a)
      | ~ $less(K_1582a,J_1579a) ),
    inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_239]) ).

tff(c_6817,plain,
    ! [K_1582a: $int] :
      ( ( tb2t2(get1(color1,t2tb1(tb2t1(mk_array(color1,'#skF_9',t2tb3('#skF_14')))),K_1582a)) = white )
      | $less(K_1582a,'#skF_13')
      | ~ $less(K_1582a,'#skF_12') ),
    inference(resolution,[status(thm)],[c_319,c_6802]) ).

tff(c_7029,plain,
    ! [K_1612a: $int] :
      ( ( tb2t2(get1(color1,mk_array(color1,'#skF_9',t2tb3('#skF_14')),K_1612a)) = white )
      | $less(K_1612a,'#skF_13')
      | ~ $less(K_1612a,'#skF_12') ),
    inference(demodulation,[status(thm),theory(equality)],[c_232,c_6817]) ).

tff(c_7053,plain,
    ( ( tb2t2(t2tb2(blue)) = white )
    | $less('#skE_1','#skF_13')
    | ~ $less('#skE_1','#skF_12')
    | ( '#skF_9' != '#skF_9' ) ),
    inference(superposition,[status(thm),theory(equality)],[c_5233,c_7029]) ).

tff(c_7090,plain,
    ( ( white = blue )
    | $less('#skE_1','#skF_13')
    | ~ $less('#skE_1','#skF_12') ),
    inference(demodulation,[status(thm),theory(equality)],[c_236,c_7053]) ).

tff(c_7092,plain,
    ~ $less('#skE_1','#skF_12'),
    inference(negUnitSimplification,[status(thm)],[c_2791,c_220,c_7090]) ).

tff(c_2793,plain,
    ! [A_977: array_color,I_978a: $int,J_979a: $int,C_980: color] :
      ( $less('#skF_8'(A_977,I_978a,J_979a,C_980),J_979a)
      | monochrome(A_977,I_978a,J_979a,C_980) ),
    inference(cnfTransformation,[status(thm)],[f_403]) ).

tff(c_2807,plain,
    $less('#skF_8'(tb2t1(mk_array(color1,'#skF_9',t2tb3('#skF_14'))),'#skF_13',$sum(1,'#skF_12'),white),$sum(1,'#skF_12')),
    inference(resolution,[status(thm)],[c_2793,c_463]) ).

tff(c_3042,plain,
    '#skF_8'(tb2t1(mk_array(color1,'#skF_9',t2tb3('#skF_14'))),'#skF_13',$sum(1,'#skF_12'),white) = '#skE_1',
    inference(define,[status(thm),theory(equality)],[c_2807]) ).

tff(c_3041,plain,
    $less('#skF_8'(tb2t1(mk_array(color1,'#skF_9',t2tb3('#skF_14'))),'#skF_13',$sum(1,'#skF_12'),white),$sum(1,'#skF_12')),
    inference(resolution,[status(thm)],[c_2793,c_463]) ).

tff(c_3049,plain,
    $less('#skE_1',$sum(1,'#skF_12')),
    inference(demodulation,[status(thm),theory(equality)],[c_3042,c_3041]) ).

tff(c_13443,plain,
    $false,
    inference(close,[status(thm),theory('LIA')],[c_13442,c_7092,c_3049]) ).

tff(c_13444,plain,
    t2tb2(white) = t2tb2(blue),
    inference(splitRight,[status(thm)],[c_13411]) ).

tff(c_13658,plain,
    tb2t2(t2tb2(blue)) = white,
    inference(superposition,[status(thm),theory(equality)],[c_13444,c_236]) ).

tff(c_13710,plain,
    white = blue,
    inference(demodulation,[status(thm),theory(equality)],[c_236,c_13658]) ).

tff(c_13712,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_220,c_13710]) ).

tff(c_13802,plain,
    tb2t2(get1(color1,mk_array(color1,'#skF_9',t2tb3('#skF_14')),'#skE_1')) = red,
    inference(splitRight,[status(thm)],[c_4802]) ).

tff(c_13820,plain,
    get1(color1,mk_array(color1,'#skF_9',t2tb3('#skF_14')),'#skE_1') = t2tb2(red),
    inference(superposition,[status(thm),theory(equality)],[c_13802,c_672]) ).

tff(c_17770,plain,
    ( ( t2tb2(white) = t2tb2(red) )
    | ( '#skF_12' != '#skE_1' ) ),
    inference(superposition,[status(thm),theory(equality)],[c_17675,c_13820]) ).

tff(c_17801,plain,
    '#skF_12' != '#skE_1',
    inference(splitLeft,[status(thm)],[c_17770]) ).

tff(c_15250,plain,
    ! [J_4390a: $int,I_4392a: $int,A_4391: array_color,C_4394: color,K_4393a: $int] :
      ( ( tb2t2(get1(color1,t2tb1(A_4391),K_4393a)) = C_4394 )
      | ~ monochrome(A_4391,I_4392a,J_4390a,C_4394)
      | $less(K_4393a,I_4392a)
      | ~ $less(K_4393a,J_4390a) ),
    inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_239]) ).

tff(c_15265,plain,
    ! [K_4393a: $int] :
      ( ( tb2t2(get1(color1,t2tb1(tb2t1(mk_array(color1,'#skF_9',t2tb3('#skF_14')))),K_4393a)) = white )
      | $less(K_4393a,'#skF_13')
      | ~ $less(K_4393a,'#skF_12') ),
    inference(resolution,[status(thm)],[c_319,c_15250]) ).

tff(c_15479,plain,
    ! [K_4408a: $int] :
      ( ( tb2t2(get1(color1,mk_array(color1,'#skF_9',t2tb3('#skF_14')),K_4408a)) = white )
      | $less(K_4408a,'#skF_13')
      | ~ $less(K_4408a,'#skF_12') ),
    inference(demodulation,[status(thm),theory(equality)],[c_232,c_15265]) ).

tff(c_15491,plain,
    ( ( tb2t2(t2tb2(red)) = white )
    | $less('#skE_1','#skF_13')
    | ~ $less('#skE_1','#skF_12')
    | ( '#skF_9' != '#skF_9' ) ),
    inference(superposition,[status(thm),theory(equality)],[c_13820,c_15479]) ).

tff(c_15508,plain,
    ( ( white = red )
    | $less('#skE_1','#skF_13')
    | ~ $less('#skE_1','#skF_12') ),
    inference(demodulation,[status(thm),theory(equality)],[c_236,c_15491]) ).

tff(c_15510,plain,
    ~ $less('#skE_1','#skF_12'),
    inference(negUnitSimplification,[status(thm)],[c_2791,c_224,c_15508]) ).

tff(c_17802,plain,
    $false,
    inference(close,[status(thm),theory('LIA')],[c_17801,c_15510,c_3049]) ).

tff(c_17803,plain,
    t2tb2(white) = t2tb2(red),
    inference(splitRight,[status(thm)],[c_17770]) ).

tff(c_17966,plain,
    tb2t2(t2tb2(red)) = white,
    inference(superposition,[status(thm),theory(equality)],[c_17803,c_236]) ).

tff(c_17984,plain,
    white = red,
    inference(demodulation,[status(thm),theory(equality)],[c_236,c_17966]) ).

tff(c_17986,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_224,c_17984]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SWW597_2 : TPTP v8.1.2. Released v6.1.0.
% 0.00/0.13  % 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
% 0.12/0.34  % Computer : n004.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 300
% 0.12/0.34  % DateTime : Thu Aug  3 19:28:41 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 18.01/5.45  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 18.01/5.47  
% 18.01/5.47  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 18.01/5.50  
% 18.01/5.50  Inference rules
% 18.01/5.50  ----------------------
% 18.01/5.50  #Ref     : 0
% 18.01/5.50  #Sup     : 3236
% 18.01/5.50  #Fact    : 56
% 18.01/5.50  #Define  : 4
% 18.01/5.50  #Split   : 6
% 18.01/5.50  #Chain   : 0
% 18.01/5.50  #Close   : 3
% 18.01/5.50  
% 18.01/5.50  Ordering : LPO
% 18.01/5.50  
% 18.01/5.50  Simplification rules
% 18.01/5.50  ----------------------
% 18.01/5.50  #Subsume      : 374
% 18.01/5.50  #Demod        : 2748
% 18.01/5.50  #Tautology    : 2141
% 18.01/5.50  #SimpNegUnit  : 284
% 18.01/5.50  #BackRed      : 50
% 18.01/5.50  
% 18.01/5.50  #Partial instantiations: 6727
% 18.01/5.50  #Strategies tried      : 1
% 18.01/5.50  
% 18.01/5.50  Timing (in seconds)
% 18.01/5.50  ----------------------
% 18.01/5.50  Preprocessing        : 0.97
% 18.01/5.51  Parsing              : 0.49
% 18.01/5.51  CNF conversion       : 0.07
% 18.01/5.51  Main loop            : 3.46
% 18.01/5.51  Inferencing          : 1.00
% 18.01/5.51  Reduction            : 1.29
% 18.01/5.51  Demodulation         : 1.03
% 18.01/5.51  BG Simplification    : 0.26
% 18.01/5.51  Subsumption          : 0.61
% 18.01/5.51  Abstraction          : 0.12
% 18.01/5.51  MUC search           : 0.06
% 18.01/5.51  Cooper               : 0.16
% 18.01/5.51  Total                : 4.50
% 18.01/5.51  Index Insertion      : 0.00
% 18.01/5.51  Index Deletion       : 0.00
% 18.01/5.51  Index Matching       : 0.00
% 18.01/5.51  BG Taut test         : 0.00
%------------------------------------------------------------------------------