TSTP Solution File: SWW597_2 by Beagle---0.9.51
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%------------------------------------------------------------------------------
% 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
%------------------------------------------------------------------------------