TSTP Solution File: SWW631_2 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SWW631_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 : n020.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 11:07:51 EDT 2023
% Result : Theorem 45.14s 18.59s
% Output : CNFRefutation 45.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 103
% Syntax : Number of formulae : 333 ( 167 unt; 94 typ; 0 def)
% Number of atoms : 407 ( 143 equ)
% Maximal formula atoms : 44 ( 1 avg)
% Number of connectives : 288 ( 120 ~; 113 |; 32 &)
% ( 0 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 30 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number arithmetic : 511 ( 208 atm; 59 fun; 184 num; 60 var)
% Number of types : 7 ( 5 usr; 1 ari)
% Number of type conns : 61 ( 28 >; 33 *; 0 +; 0 <<)
% Number of predicates : 7 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 92 ( 86 usr; 64 con; 0-5 aty)
% Number of variables : 81 (; 78 !; 3 ?; 81 :)
% Comments :
%------------------------------------------------------------------------------
%$ sort > path > distance > set > set1 > match_bool > get > mk_array > make > get1 > const > mk_ref > map > length > elts > contents > #nlpp > witness > tb2t1 > tb2t > t2tb1 > t2tb > ref > f > array > tuple02 > tuple01 > true > real > qtmark > int > false > bool1 > #skF_2 > #skF_8 > #skF_5 > #skF_1 > #skF_7 > #skF_4 > #skF_3
%Foreground sorts:
tff(map_int_int,type,
map_int_int: $tType ).
tff(bool,type,
bool: $tType ).
tff(tuple0,type,
tuple0: $tType ).
tff(ty,type,
ty: $tType ).
tff(uni,type,
uni: $tType ).
%Background operators:
tff(n,type,
n: $int ).
tff('#skE_7',type,
'#skE_7': $int ).
tff('#skE_21',type,
'#skE_21': $int ).
tff('#skE_30',type,
'#skE_30': $int ).
tff('#skE_11',type,
'#skE_11': $int ).
tff('#skE_25',type,
'#skE_25': $int ).
tff('#skE_28',type,
'#skE_28': $int ).
tff('#skE_23',type,
'#skE_23': $int ).
tff('#skE_12',type,
'#skE_12': $int ).
tff('#skE_41',type,
'#skE_41': $int ).
tff('#skE_37',type,
'#skE_37': $int ).
tff('#skF_13',type,
'#skF_13': $int ).
tff('#skF_14',type,
'#skF_14': $int ).
tff('#skE_42',type,
'#skE_42': $int ).
tff('#skF_6',type,
'#skF_6': $int ).
tff('#skE_2',type,
'#skE_2': $int ).
tff('#skE_1',type,
'#skE_1': $int ).
tff('#skE_33',type,
'#skE_33': $int ).
tff('#skF_11',type,
'#skF_11': $int ).
tff('#skE_20',type,
'#skE_20': $int ).
tff('#skE_6',type,
'#skE_6': $int ).
tff('#skE_13',type,
'#skE_13': $int ).
tff('#skE_26',type,
'#skE_26': $int ).
tff('#skE_32',type,
'#skE_32': $int ).
tff('#skE_10',type,
'#skE_10': $int ).
tff('#skE_24',type,
'#skE_24': $int ).
tff('#skE_5',type,
'#skE_5': $int ).
tff('#skE_38',type,
'#skE_38': $int ).
tff('#skE_31',type,
'#skE_31': $int ).
tff('#skE_15',type,
'#skE_15': $int ).
tff('#skE_8',type,
'#skE_8': $int ).
tff('#skE_36',type,
'#skE_36': $int ).
tff('#skE_4',type,
'#skE_4': $int ).
tff('#skF_10',type,
'#skF_10': $int ).
tff('#skF_12',type,
'#skF_12': $int ).
tff('#skE_22',type,
'#skE_22': $int ).
tff('#skE_16',type,
'#skE_16': $int ).
tff('#skE_17',type,
'#skE_17': $int ).
tff('#skE_3',type,
'#skE_3': $int ).
tff('#skE_40',type,
'#skE_40': $int ).
tff('#skE_9',type,
'#skE_9': $int ).
tff('#skE_29',type,
'#skE_29': $int ).
tff('#skE_34',type,
'#skE_34': $int ).
tff('#skE_27',type,
'#skE_27': $int ).
tff('#skF_9',type,
'#skF_9': $int ).
tff('#skE_18',type,
'#skE_18': $int ).
tff('#skE_35',type,
'#skE_35': $int ).
tff('#skE_39',type,
'#skE_39': $int ).
tff('#skE_19',type,
'#skE_19': $int ).
tff('#skE_14',type,
'#skE_14': $int ).
%Foreground operators:
tff(tb2t1,type,
tb2t1: uni > map_int_int ).
tff(tuple02,type,
tuple02: tuple0 ).
tff(const,type,
const: ( ty * ty * uni ) > uni ).
tff(get1,type,
get1: ( ty * uni * $int ) > uni ).
tff('#skF_2',type,
'#skF_2': ( $int * $int ) > $int ).
tff('#skF_8',type,
'#skF_8': map_int_int ).
tff(distance,type,
distance: ( $int * $int ) > $o ).
tff(elts,type,
elts: ( ty * uni ) > uni ).
tff(tuple01,type,
tuple01: ty ).
tff(int,type,
int: ty ).
tff(tb2t,type,
tb2t: uni > $int ).
tff(contents,type,
contents: ( ty * uni ) > uni ).
tff(f,type,
f: $int > $int ).
tff(t2tb,type,
t2tb: $int > uni ).
tff(real,type,
real: ty ).
tff(match_bool,type,
match_bool: ( ty * bool * uni * uni ) > uni ).
tff(false,type,
false: bool ).
tff('#skF_5',type,
'#skF_5': map_int_int ).
tff('#skF_1',type,
'#skF_1': ( $int * $int ) > $int ).
tff(set,type,
set: ( ty * ty * uni * uni * uni ) > uni ).
tff(array,type,
array: ty > ty ).
tff(make,type,
make: ( ty * $int * uni ) > uni ).
tff(length,type,
length: ( ty * uni ) > $int ).
tff(qtmark,type,
qtmark: ty ).
tff(set1,type,
set1: ( ty * uni * $int * uni ) > uni ).
tff(t2tb1,type,
t2tb1: map_int_int > uni ).
tff(get,type,
get: ( ty * ty * uni * uni ) > uni ).
tff(mk_array,type,
mk_array: ( ty * $int * uni ) > uni ).
tff(bool1,type,
bool1: ty ).
tff(path,type,
path: ( $int * $int ) > $o ).
tff(map,type,
map: ( ty * ty ) > ty ).
tff('#skF_7',type,
'#skF_7': map_int_int ).
tff(sort,type,
sort: ( ty * uni ) > $o ).
tff(true,type,
true: bool ).
tff(ref,type,
ref: ty > ty ).
tff('#skF_4',type,
'#skF_4': ( $int * $int ) > $int ).
tff(witness,type,
witness: ty > uni ).
tff('#skF_3',type,
'#skF_3': ( $int * $int ) > $int ).
tff(mk_ref,type,
mk_ref: ( ty * uni ) > uni ).
tff(f_280,negated_conjecture,
~ ( $lesseq(0,n)
=> ( $lesseq(0,n)
=> ( ( $lesseq(0,0)
& $less(0,n) )
=> ! [G: map_int_int] :
( ( $lesseq(0,n)
& ( G = tb2t1(set(int,int,const(int,int,t2tb(0)),t2tb(0),t2tb($uminus(1)))) ) )
=> ( $lesseq(0,n)
=> ( $lesseq(0,n)
=> ( $lesseq(1,$difference(n,1))
=> ! [Counta: $int,D: map_int_int,G1: map_int_int,Ia: $int] :
( ( $lesseq(1,Ia)
& $lesseq(Ia,$difference(n,1)) )
=> ( ( ( tb2t(get(int,int,t2tb1(D),t2tb(0))) = 0 )
& ( tb2t(get(int,int,t2tb1(G1),t2tb(0))) = $uminus(1) )
& $lesseq($sum(Counta,tb2t(get(int,int,t2tb1(D),t2tb($difference(Ia,1))))),$difference(Ia,1))
& ! [Ka: $int] :
( ( $less(0,Ka)
& $less(Ka,Ia) )
=> ( $less(tb2t(get(int,int,t2tb1(G1),get(int,int,t2tb1(G1),t2tb(Ka)))),f(Ka))
& $lesseq(f(Ka),tb2t(get(int,int,t2tb1(G1),t2tb(Ka))))
& $less(tb2t(get(int,int,t2tb1(G1),t2tb(Ka))),Ka)
& $less(0,tb2t(get(int,int,t2tb1(D),t2tb(Ka))))
& ( tb2t(get(int,int,t2tb1(D),t2tb(Ka))) = $sum(tb2t(get(int,int,t2tb1(D),get(int,int,t2tb1(G1),t2tb(Ka)))),1) )
& ! [Kqta: $int] :
( ( $less(tb2t(get(int,int,t2tb1(G1),t2tb(Ka))),Kqta)
& $less(Kqta,Ka) )
=> $less(tb2t(get(int,int,t2tb1(D),get(int,int,t2tb1(G1),t2tb(Ka)))),tb2t(get(int,int,t2tb1(D),t2tb(Kqta)))) ) ) )
& ! [Ka: $int] :
( ( $lesseq(0,Ka)
& $less(Ka,Ia) )
=> path(tb2t(get(int,int,t2tb1(D),t2tb(Ka))),Ka) ) )
=> ! [Ja: $int,Count1a: $int] :
( ( $lesseq(f(Ia),Ja)
& $less(Ja,Ia)
& $lesseq($sum(Count1a,tb2t(get(int,int,t2tb1(D),t2tb(Ja)))),$difference(Ia,1))
& ! [Ka: $int] :
( ( $less(Ja,Ka)
& $less(Ka,Ia) )
=> $less(tb2t(get(int,int,t2tb1(D),t2tb(Ja))),tb2t(get(int,int,t2tb1(D),t2tb(Ka)))) ) )
=> ( ( $lesseq(0,n)
& $lesseq(0,Ja)
& $less(Ja,n) )
=> ( $lesseq(f(Ia),tb2t(get(int,int,t2tb1(G1),t2tb(Ja))))
=> ! [Count2a: $int] :
( ( Count2a = $sum(Count1a,1) )
=> ( ( $lesseq(0,Ja)
& $less(Ja,n) )
=> ! [J1a: $int] :
( ( J1a = tb2t(get(int,int,t2tb1(G1),t2tb(Ja))) )
=> ! [Ka: $int] :
( ( $less(J1a,Ka)
& $less(Ka,Ia) )
=> $less(tb2t(get(int,int,t2tb1(D),t2tb(J1a))),tb2t(get(int,int,t2tb1(D),t2tb(Ka)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',wP_parameter_distance) ).
tff(f_131,axiom,
! [Ka: $int] :
( ( $less(0,Ka)
& $less(Ka,n) )
=> ( $lesseq(0,f(Ka))
& $less(f(Ka),Ka) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f_prop) ).
tff(f_182,axiom,
! [J: uni] : ( t2tb1(tb2t1(J)) = J ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',bridgeR1) ).
tff(f_178,axiom,
! [X: map_int_int] : sort(map(int,int),t2tb1(X)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2tb_sort1) ).
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_110,axiom,
! [Ia: $int] : ( tb2t(t2tb(Ia)) = Ia ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',bridgeL) ).
tff(f_167,axiom,
! [Za: $int,Z1a: $int] :
( path(Za,Z1a)
=> ( ( ( Za = 0 )
& ( Z1a = 0 ) )
| ? [Ia: $int] :
( $lesseq(0,Ia)
& $less(Ia,n)
& ? [Da: $int,Ja: $int] :
( path(Da,Ja)
& $lesseq(f(Ia),Ja)
& $less(Ja,Ia)
& ( Za = $sum(Da,1) )
& ( Z1a = Ia ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',path_inversion) ).
tff(f_112,axiom,
! [J: uni] : ( t2tb(tb2t(J)) = J ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',bridgeR) ).
tff(c_248,plain,
$less('#skF_14','#skF_9'),
inference(cnfTransformation,[status(thm)],[f_280]) ).
tff(c_252,plain,
~ $less(tb2t(get(int,int,t2tb1('#skF_7'),t2tb('#skF_13'))),tb2t(get(int,int,t2tb1('#skF_7'),t2tb('#skF_14')))),
inference(cnfTransformation,[status(thm)],[f_280]) ).
tff(c_1328,plain,
tb2t(get(int,int,t2tb1('#skF_7'),t2tb('#skF_14'))) = '#skE_3',
inference(define,[status(thm),theory(equality)],[c_252]) ).
tff(c_200,plain,
! [K_183a: $int] :
( $less(0,tb2t(get(int,int,t2tb1('#skF_7'),t2tb(K_183a))))
| ~ $less(0,K_183a)
| ~ $less(K_183a,'#skF_9') ),
inference(cnfTransformation,[status(thm)],[f_280]) ).
tff(c_1334,plain,
( $less(0,'#skE_3')
| ~ $less(0,'#skF_14')
| ~ $less('#skF_14','#skF_9') ),
inference(superposition,[status(thm),theory(equality)],[c_1328,c_200]) ).
tff(c_1351,plain,
( $less(0,'#skE_3')
| ~ $less(0,'#skF_14') ),
inference(demodulation,[status(thm),theory(equality)],[c_248,c_1334]) ).
tff(c_1363,plain,
~ $less(0,'#skF_14'),
inference(splitLeft,[status(thm)],[c_1351]) ).
tff(c_133,plain,
$lesseq(f('#skF_9'),'#skF_10'),
inference(cnfTransformation,[status(thm)],[f_280]) ).
tff(c_223,plain,
~ $less('#skF_10',f('#skF_9')),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_133]) ).
tff(c_472,plain,
f('#skF_9') = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_223]) ).
tff(c_67,plain,
! [K_90a: $int] :
( $lesseq(0,f(K_90a))
| ~ $less(0,K_90a)
| ~ $less(K_90a,n) ),
inference(cnfTransformation,[status(thm)],[f_131]) ).
tff(c_1084,plain,
! [K_555a: $int] :
( ~ $less(f(K_555a),0)
| ~ $less(0,K_555a)
| ~ $less(K_555a,n) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_67]) ).
tff(c_1089,plain,
( ~ $less('#skE_1',0)
| ~ $less(0,'#skF_9')
| ~ $less('#skF_9',n) ),
inference(superposition,[status(thm),theory(equality)],[c_472,c_1084]) ).
tff(c_1091,plain,
~ $less('#skF_9',n),
inference(splitLeft,[status(thm)],[c_1089]) ).
tff(c_145,plain,
$lesseq('#skF_9',$difference(n,1)),
inference(cnfTransformation,[status(thm)],[f_280]) ).
tff(c_212,plain,
~ $less(n,$sum(1,'#skF_9')),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_145]) ).
tff(c_1092,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_1091,c_212]) ).
tff(c_1095,plain,
( ~ $less(0,'#skF_9')
| ~ $less('#skE_1',0) ),
inference(splitRight,[status(thm)],[c_1089]) ).
tff(c_1106,plain,
~ $less('#skE_1',0),
inference(splitLeft,[status(thm)],[c_1095]) ).
tff(c_475,plain,
f('#skF_9') = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_223]) ).
tff(c_323,plain,
tb2t(get(int,int,t2tb1('#skF_8'),t2tb('#skF_10'))) = '#skF_13',
inference(cnfTransformation,[status(thm)],[f_280]) ).
tff(c_120,plain,
$lesseq(f('#skF_9'),tb2t(get(int,int,t2tb1('#skF_8'),t2tb('#skF_10')))),
inference(cnfTransformation,[status(thm)],[f_280]) ).
tff(c_239,plain,
~ $less(tb2t(get(int,int,t2tb1('#skF_8'),t2tb('#skF_10'))),f('#skF_9')),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_120]) ).
tff(c_328,plain,
~ $less('#skF_13',f('#skF_9')),
inference(demodulation,[status(thm),theory(equality)],[c_323,c_239]) ).
tff(c_492,plain,
~ $less('#skF_13','#skE_1'),
inference(demodulation,[status(thm),theory(equality)],[c_475,c_328]) ).
tff(c_247,plain,
$less('#skF_13','#skF_14'),
inference(cnfTransformation,[status(thm)],[f_280]) ).
tff(c_1383,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_1363,c_1106,c_492,c_247]) ).
tff(c_1386,plain,
$less(0,'#skE_3'),
inference(splitRight,[status(thm)],[c_1351]) ).
tff(c_107,plain,
! [J_112: uni] : ( t2tb1(tb2t1(J_112)) = J_112 ),
inference(cnfTransformation,[status(thm)],[f_182]) ).
tff(c_424,plain,
! [X_341: map_int_int] : sort(map(int,int),t2tb1(X_341)),
inference(cnfTransformation,[status(thm)],[f_178]) ).
tff(c_426,plain,
! [J_112: uni] : sort(map(int,int),J_112),
inference(superposition,[status(thm),theory(equality)],[c_107,c_424]) ).
tff(c_7206,plain,
! [A_2420: ty,U_2421a: $int,U1_2422: uni] :
( ( elts(A_2420,mk_array(A_2420,U_2421a,U1_2422)) = U1_2422 )
| ~ sort(map(int,A_2420),U1_2422) ),
inference(cnfTransformation,[status(thm)],[f_102]) ).
tff(c_7255,plain,
! [U_2421a: $int,J_112: uni] : ( elts(int,mk_array(int,U_2421a,J_112)) = J_112 ),
inference(resolution,[status(thm)],[c_426,c_7206]) ).
tff(c_7370,plain,
! [A_2446: ty,A1_2447: uni,I_2448a: $int] : ( get(A_2446,int,elts(A_2446,A1_2447),t2tb(I_2448a)) = get1(A_2446,A1_2447,I_2448a) ),
inference(cnfTransformation,[status(thm)],[f_114]) ).
tff(c_10823,plain,
! [J_3391: uni,I_3392a: $int,U_3393a: $int] : ( get(int,int,J_3391,t2tb(I_3392a)) = get1(int,mk_array(int,U_3393a,J_3391),I_3392a) ),
inference(superposition,[status(thm),theory(equality)],[c_7255,c_7370]) ).
tff(c_123,plain,
$lesseq(0,'#skF_10'),
inference(cnfTransformation,[status(thm)],[f_280]) ).
tff(c_234,plain,
~ $less('#skF_10',0),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_123]) ).
tff(c_224,plain,
$less('#skF_10','#skF_9'),
inference(cnfTransformation,[status(thm)],[f_280]) ).
tff(c_141,plain,
tb2t(get(int,int,t2tb1('#skF_8'),t2tb(0))) = $uminus(1),
inference(cnfTransformation,[status(thm)],[f_280]) ).
tff(c_214,plain,
tb2t(get(int,int,t2tb1('#skF_8'),t2tb(0))) = $uminus(1),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_141]) ).
tff(c_246,plain,
tb2t(get(int,int,t2tb1('#skF_8'),t2tb('#skF_10'))) = '#skF_13',
inference(cnfTransformation,[status(thm)],[f_280]) ).
tff(c_943,plain,
( ( '#skF_13' = $uminus(1) )
| ( '#skF_10' != 0 ) ),
inference(superposition,[status(thm),theory(equality)],[c_214,c_246]) ).
tff(c_980,plain,
'#skF_10' != 0,
inference(splitLeft,[status(thm)],[c_943]) ).
tff(c_845,plain,
! [K_475a: $int] :
( $less(tb2t(get(int,int,t2tb1('#skF_8'),t2tb(K_475a))),K_475a)
| ~ $less(0,K_475a)
| ~ $less(K_475a,'#skF_9') ),
inference(cnfTransformation,[status(thm)],[f_280]) ).
tff(c_848,plain,
( $less('#skF_13','#skF_10')
| ~ $less(0,'#skF_10')
| ~ $less('#skF_10','#skF_9') ),
inference(superposition,[status(thm),theory(equality)],[c_246,c_845]) ).
tff(c_852,plain,
( $less('#skF_13','#skF_10')
| ~ $less(0,'#skF_10') ),
inference(demodulation,[status(thm),theory(equality)],[c_224,c_848]) ).
tff(c_854,plain,
~ $less(0,'#skF_10'),
inference(splitLeft,[status(thm)],[c_852]) ).
tff(c_981,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_980,c_854,c_234]) ).
tff(c_984,plain,
'#skF_13' = $uminus(1),
inference(splitRight,[status(thm)],[c_943]) ).
tff(c_1015,plain,
~ $less($uminus(1),'#skE_1'),
inference(demodulation,[status(thm),theory(equality)],[c_984,c_492]) ).
tff(c_885,plain,
! [K_480a: $int] :
( ~ $less(f(K_480a),0)
| ~ $less(0,K_480a)
| ~ $less(K_480a,n) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_67]) ).
tff(c_890,plain,
( ~ $less('#skE_1',0)
| ~ $less(0,'#skF_9')
| ~ $less('#skF_9',n) ),
inference(superposition,[status(thm),theory(equality)],[c_472,c_885]) ).
tff(c_892,plain,
~ $less('#skF_9',n),
inference(splitLeft,[status(thm)],[c_890]) ).
tff(c_893,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_892,c_212]) ).
tff(c_896,plain,
( ~ $less(0,'#skF_9')
| ~ $less('#skE_1',0) ),
inference(splitRight,[status(thm)],[c_890]) ).
tff(c_912,plain,
~ $less('#skE_1',0),
inference(splitLeft,[status(thm)],[c_896]) ).
tff(c_1018,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_1015,c_912]) ).
tff(c_1021,plain,
~ $less(0,'#skF_9'),
inference(splitRight,[status(thm)],[c_896]) ).
tff(c_147,plain,
$lesseq(1,'#skF_9'),
inference(cnfTransformation,[status(thm)],[f_280]) ).
tff(c_211,plain,
~ $less('#skF_9',1),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_147]) ).
tff(c_1023,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_1021,c_211]) ).
tff(c_1027,plain,
$less(0,'#skF_10'),
inference(splitRight,[status(thm)],[c_852]) ).
tff(c_291,plain,
! [I_71a: $int] : ( tb2t(t2tb(I_71a)) = I_71a ),
inference(cnfTransformation,[status(thm)],[f_110]) ).
tff(c_1392,plain,
tb2t(get(int,int,t2tb1('#skF_7'),t2tb('#skF_13'))) = '#skE_2',
inference(define,[status(thm),theory(equality)],[c_252]) ).
tff(c_1421,plain,
( $less(0,'#skE_2')
| ~ $less(0,'#skF_13')
| ~ $less('#skF_13','#skF_9') ),
inference(superposition,[status(thm),theory(equality)],[c_1392,c_200]) ).
tff(c_1463,plain,
~ $less('#skF_13','#skF_9'),
inference(splitLeft,[status(thm)],[c_1421]) ).
tff(c_1464,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_1463,c_247,c_248]) ).
tff(c_1468,plain,
$less('#skF_13','#skF_9'),
inference(splitRight,[status(thm)],[c_1421]) ).
tff(c_1061,plain,
tb2t(get(int,int,t2tb1('#skF_7'),t2tb('#skF_13'))) = '#skE_2',
inference(define,[status(thm),theory(equality)],[c_252]) ).
tff(c_135,plain,
! [K_186a: $int] :
( path(tb2t(get(int,int,t2tb1('#skF_7'),t2tb(K_186a))),K_186a)
| ~ $lesseq(0,K_186a)
| ~ $less(K_186a,'#skF_9') ),
inference(cnfTransformation,[status(thm)],[f_280]) ).
tff(c_1983,plain,
! [K_779a: $int] :
( path(tb2t(get(int,int,t2tb1('#skF_7'),t2tb(K_779a))),K_779a)
| $less(K_779a,0)
| ~ $less(K_779a,'#skF_9') ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_135]) ).
tff(c_1991,plain,
( path('#skE_2','#skF_13')
| $less('#skF_13',0)
| ~ $less('#skF_13','#skF_9') ),
inference(superposition,[status(thm),theory(equality)],[c_1061,c_1983]) ).
tff(c_2013,plain,
( path('#skE_2','#skF_13')
| $less('#skF_13',0) ),
inference(demodulation,[status(thm),theory(equality)],[c_1468,c_1991]) ).
tff(c_2079,plain,
$less('#skF_13',0),
inference(splitLeft,[status(thm)],[c_2013]) ).
tff(c_2080,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_2079,c_1106,c_492]) ).
tff(c_2108,plain,
path('#skE_2','#skF_13'),
inference(splitRight,[status(thm)],[c_2013]) ).
tff(c_275,plain,
! [Z_96a: $int,Z1_97a: $int] :
( ( '#skF_1'(Z_96a,Z1_97a) = Z1_97a )
| ~ path(Z_96a,Z1_97a)
| ( Z_96a = 0 ) ),
inference(cnfTransformation,[status(thm)],[f_167]) ).
tff(c_2153,plain,
( ( '#skF_1'('#skE_2','#skF_13') = '#skF_13' )
| ( '#skE_2' = 0 ) ),
inference(resolution,[status(thm)],[c_2108,c_275]) ).
tff(c_2699,plain,
'#skF_1'('#skE_2','#skF_13') = '#skE_8',
inference(define,[status(thm),theory(equality)],[c_2153]) ).
tff(c_2698,plain,
( ( '#skF_1'('#skE_2','#skF_13') = '#skF_13' )
| ( '#skE_2' = 0 ) ),
inference(resolution,[status(thm)],[c_2108,c_275]) ).
tff(c_2706,plain,
( ( '#skF_13' = '#skE_8' )
| ( '#skE_2' = 0 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_2699,c_2698]) ).
tff(c_2743,plain,
'#skE_2' = 0,
inference(splitLeft,[status(thm)],[c_2706]) ).
tff(c_1467,plain,
( ~ $less(0,'#skF_13')
| $less(0,'#skE_2') ),
inference(splitRight,[status(thm)],[c_1421]) ).
tff(c_1481,plain,
~ $less(0,'#skF_13'),
inference(splitLeft,[status(thm)],[c_1467]) ).
tff(c_213,plain,
tb2t(get(int,int,t2tb1('#skF_7'),t2tb(0))) = 0,
inference(cnfTransformation,[status(thm)],[f_280]) ).
tff(c_290,plain,
! [J_72: uni] : ( t2tb(tb2t(J_72)) = J_72 ),
inference(cnfTransformation,[status(thm)],[f_112]) ).
tff(c_418,plain,
get(int,int,t2tb1('#skF_7'),t2tb(0)) = t2tb(0),
inference(superposition,[status(thm),theory(equality)],[c_213,c_290]) ).
tff(c_1414,plain,
( ( tb2t(t2tb(0)) = '#skE_2' )
| ( '#skF_13' != 0 ) ),
inference(superposition,[status(thm),theory(equality)],[c_418,c_1392]) ).
tff(c_1431,plain,
( ( '#skE_2' = 0 )
| ( '#skF_13' != 0 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_291,c_1414]) ).
tff(c_1461,plain,
'#skF_13' != 0,
inference(splitLeft,[status(thm)],[c_1431]) ).
tff(c_1482,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_1481,c_1461,c_1106,c_492]) ).
tff(c_1485,plain,
$less(0,'#skE_2'),
inference(splitRight,[status(thm)],[c_1467]) ).
tff(c_2759,plain,
$less(0,0),
inference(demodulation,[status(thm),theory(equality)],[c_2743,c_1485]) ).
tff(c_2778,plain,
$false,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_2759]) ).
tff(c_2781,plain,
'#skF_13' = '#skE_8',
inference(splitRight,[status(thm)],[c_2706]) ).
tff(c_1424,plain,
get(int,int,t2tb1('#skF_7'),t2tb('#skF_13')) = t2tb('#skE_2'),
inference(superposition,[status(thm),theory(equality)],[c_1392,c_290]) ).
tff(c_4972,plain,
get(int,int,t2tb1('#skF_7'),t2tb('#skE_8')) = t2tb('#skE_2'),
inference(demodulation,[status(thm),theory(equality)],[c_2781,c_1424]) ).
tff(c_232,plain,
! [K_195a: $int] :
( $less(tb2t(get(int,int,t2tb1('#skF_7'),t2tb('#skF_10'))),tb2t(get(int,int,t2tb1('#skF_7'),t2tb(K_195a))))
| ~ $less('#skF_10',K_195a)
| ~ $less(K_195a,'#skF_9') ),
inference(cnfTransformation,[status(thm)],[f_280]) ).
tff(c_1489,plain,
tb2t(get(int,int,t2tb1('#skF_7'),t2tb('#skF_10'))) = '#skE_4',
inference(define,[status(thm),theory(equality)],[c_232]) ).
tff(c_3959,plain,
get(int,int,t2tb1('#skF_7'),t2tb('#skF_10')) = t2tb('#skE_4'),
inference(superposition,[status(thm),theory(equality)],[c_1489,c_290]) ).
tff(c_443,plain,
tb2t(get(int,int,t2tb1('#skF_8'),t2tb('#skF_10'))) = '#skF_13',
inference(cnfTransformation,[status(thm)],[f_280]) ).
tff(c_459,plain,
get(int,int,t2tb1('#skF_8'),t2tb('#skF_10')) = t2tb('#skF_13'),
inference(superposition,[status(thm),theory(equality)],[c_443,c_290]) ).
tff(c_5693,plain,
get(int,int,t2tb1('#skF_8'),t2tb('#skF_10')) = t2tb('#skE_8'),
inference(demodulation,[status(thm),theory(equality)],[c_2781,c_459]) ).
tff(c_167,plain,
! [K_183a: $int] :
( ( $sum(tb2t(get(int,int,t2tb1('#skF_7'),get(int,int,t2tb1('#skF_8'),t2tb(K_183a)))),1) = tb2t(get(int,int,t2tb1('#skF_7'),t2tb(K_183a))) )
| ~ $less(0,K_183a)
| ~ $less(K_183a,'#skF_9') ),
inference(cnfTransformation,[status(thm)],[f_280]) ).
tff(c_201,plain,
! [K_183a: $int] :
( ( tb2t(get(int,int,t2tb1('#skF_7'),get(int,int,t2tb1('#skF_8'),t2tb(K_183a)))) = $sum($uminus(1),tb2t(get(int,int,t2tb1('#skF_7'),t2tb(K_183a)))) )
| ~ $less(0,K_183a)
| ~ $less(K_183a,'#skF_9') ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_167]) ).
tff(c_5708,plain,
( ( $sum($uminus(1),tb2t(get(int,int,t2tb1('#skF_7'),t2tb('#skF_10')))) = tb2t(get(int,int,t2tb1('#skF_7'),t2tb('#skE_8'))) )
| ~ $less(0,'#skF_10')
| ~ $less('#skF_10','#skF_9') ),
inference(superposition,[status(thm),theory(equality)],[c_5693,c_201]) ).
tff(c_5753,plain,
$sum($uminus(1),'#skE_4') = '#skE_2',
inference(demodulation,[status(thm),theory(equality)],[c_224,c_1027,c_291,c_4972,c_291,c_3959,c_5708]) ).
tff(c_5755,plain,
'#skE_4' = $sum(1,'#skE_2'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_5753]) ).
tff(c_1054,plain,
tb2t(get(int,int,t2tb1('#skF_7'),t2tb('#skF_14'))) = '#skE_3',
inference(define,[status(thm),theory(equality)],[c_252]) ).
tff(c_1053,plain,
tb2t(get(int,int,t2tb1('#skF_7'),t2tb('#skF_13'))) = '#skE_2',
inference(define,[status(thm),theory(equality)],[c_252]) ).
tff(c_332,plain,
~ $less(tb2t(get(int,int,t2tb1('#skF_7'),t2tb('#skF_13'))),tb2t(get(int,int,t2tb1('#skF_7'),t2tb('#skF_14')))),
inference(cnfTransformation,[status(thm)],[f_280]) ).
tff(c_1065,plain,
~ $less('#skE_2','#skE_3'),
inference(demodulation,[status(thm),theory(equality)],[c_1054,c_1053,c_332]) ).
tff(c_1064,plain,
tb2t(get(int,int,t2tb1('#skF_7'),t2tb('#skF_14'))) = '#skE_3',
inference(define,[status(thm),theory(equality)],[c_252]) ).
tff(c_1995,plain,
( path('#skE_3','#skF_14')
| $less('#skF_14',0)
| ~ $less('#skF_14','#skF_9') ),
inference(superposition,[status(thm),theory(equality)],[c_1064,c_1983]) ).
tff(c_2020,plain,
( path('#skE_3','#skF_14')
| $less('#skF_14',0) ),
inference(demodulation,[status(thm),theory(equality)],[c_248,c_1995]) ).
tff(c_2167,plain,
$less('#skF_14',0),
inference(splitLeft,[status(thm)],[c_2020]) ).
tff(c_2192,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_2167,c_1106,c_492,c_247]) ).
tff(c_2201,plain,
path('#skE_3','#skF_14'),
inference(splitRight,[status(thm)],[c_2020]) ).
tff(c_2246,plain,
( ( '#skF_1'('#skE_3','#skF_14') = '#skF_14' )
| ( '#skE_3' = 0 ) ),
inference(resolution,[status(thm)],[c_2201,c_275]) ).
tff(c_2313,plain,
'#skF_1'('#skE_3','#skF_14') = '#skE_6',
inference(define,[status(thm),theory(equality)],[c_2246]) ).
tff(c_2312,plain,
( ( '#skF_1'('#skE_3','#skF_14') = '#skF_14' )
| ( '#skE_3' = 0 ) ),
inference(resolution,[status(thm)],[c_2201,c_275]) ).
tff(c_2320,plain,
( ( '#skF_14' = '#skE_6' )
| ( '#skE_3' = 0 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_2313,c_2312]) ).
tff(c_2322,plain,
'#skE_3' = 0,
inference(splitLeft,[status(thm)],[c_2320]) ).
tff(c_2357,plain,
$less(0,0),
inference(demodulation,[status(thm),theory(equality)],[c_2322,c_1386]) ).
tff(c_2373,plain,
$false,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_2357]) ).
tff(c_2376,plain,
'#skF_14' = '#skE_6',
inference(splitRight,[status(thm)],[c_2320]) ).
tff(c_2421,plain,
$less('#skF_13','#skE_6'),
inference(demodulation,[status(thm),theory(equality)],[c_2376,c_247]) ).
tff(c_2835,plain,
$less('#skE_8','#skE_6'),
inference(demodulation,[status(thm),theory(equality)],[c_2781,c_2421]) ).
tff(c_4397,plain,
get(int,int,t2tb1('#skF_8'),t2tb('#skF_10')) = t2tb('#skE_8'),
inference(demodulation,[status(thm),theory(equality)],[c_2781,c_459]) ).
tff(c_4093,plain,
get(int,int,t2tb1('#skF_7'),t2tb('#skE_8')) = t2tb('#skE_2'),
inference(demodulation,[status(thm),theory(equality)],[c_2781,c_1424]) ).
tff(c_4398,plain,
get(int,int,t2tb1('#skF_8'),t2tb('#skF_10')) = t2tb('#skE_8'),
inference(demodulation,[status(thm),theory(equality)],[c_2781,c_459]) ).
tff(c_1434,plain,
! [K_657a: $int,Kqt_658a: $int] :
( $less(tb2t(get(int,int,t2tb1('#skF_7'),get(int,int,t2tb1('#skF_8'),t2tb(K_657a)))),tb2t(get(int,int,t2tb1('#skF_7'),t2tb(Kqt_658a))))
| ~ $less(tb2t(get(int,int,t2tb1('#skF_8'),t2tb(K_657a))),Kqt_658a)
| ~ $less(0,K_657a)
| ~ $less(K_657a,'#skF_9')
| ~ $less(Kqt_658a,K_657a) ),
inference(cnfTransformation,[status(thm)],[f_280]) ).
tff(c_1454,plain,
! [K_657a: $int] :
( $less(tb2t(get(int,int,t2tb1('#skF_7'),get(int,int,t2tb1('#skF_8'),t2tb(K_657a)))),'#skE_3')
| ~ $less(tb2t(get(int,int,t2tb1('#skF_8'),t2tb(K_657a))),'#skF_14')
| ~ $less(0,K_657a)
| ~ $less(K_657a,'#skF_9')
| ~ $less('#skF_14',K_657a) ),
inference(superposition,[status(thm),theory(equality)],[c_1064,c_1434]) ).
tff(c_2928,plain,
! [K_657a: $int] :
( $less(tb2t(get(int,int,t2tb1('#skF_7'),get(int,int,t2tb1('#skF_8'),t2tb(K_657a)))),'#skE_3')
| ~ $less(tb2t(get(int,int,t2tb1('#skF_8'),t2tb(K_657a))),'#skE_6')
| ~ $less(0,K_657a)
| ~ $less(K_657a,'#skF_9')
| ~ $less('#skE_6',K_657a) ),
inference(demodulation,[status(thm),theory(equality)],[c_2376,c_2376,c_1454]) ).
tff(c_4410,plain,
( $less(tb2t(get(int,int,t2tb1('#skF_7'),t2tb('#skE_8'))),'#skE_3')
| ~ $less(tb2t(get(int,int,t2tb1('#skF_8'),t2tb('#skF_10'))),'#skE_6')
| ~ $less(0,'#skF_10')
| ~ $less('#skF_10','#skF_9')
| ~ $less('#skE_6','#skF_10') ),
inference(superposition,[status(thm),theory(equality)],[c_4398,c_2928]) ).
tff(c_4453,plain,
( $less('#skE_2','#skE_3')
| ~ $less('#skE_6','#skF_10') ),
inference(demodulation,[status(thm),theory(equality)],[c_224,c_1027,c_2835,c_291,c_4397,c_291,c_4093,c_4410]) ).
tff(c_4455,plain,
~ $less('#skE_6','#skF_10'),
inference(negUnitSimplification,[status(thm)],[c_1065,c_4453]) ).
tff(c_2422,plain,
$less('#skE_6','#skF_9'),
inference(demodulation,[status(thm),theory(equality)],[c_2376,c_248]) ).
tff(c_3173,plain,
tb2t(get(int,int,t2tb1('#skF_7'),t2tb('#skE_6'))) = '#skE_3',
inference(demodulation,[status(thm),theory(equality)],[c_2376,c_1064]) ).
tff(c_1182,plain,
tb2t(get(int,int,t2tb1('#skF_7'),t2tb('#skF_10'))) = '#skE_4',
inference(define,[status(thm),theory(equality)],[c_232]) ).
tff(c_318,plain,
! [K_195a: $int] :
( $less(tb2t(get(int,int,t2tb1('#skF_7'),t2tb('#skF_10'))),tb2t(get(int,int,t2tb1('#skF_7'),t2tb(K_195a))))
| ~ $less('#skF_10',K_195a)
| ~ $less(K_195a,'#skF_9') ),
inference(cnfTransformation,[status(thm)],[f_280]) ).
tff(c_1192,plain,
! [K_195a: $int] :
( $less('#skE_4',tb2t(get(int,int,t2tb1('#skF_7'),t2tb(K_195a))))
| ~ $less('#skF_10',K_195a)
| ~ $less(K_195a,'#skF_9') ),
inference(demodulation,[status(thm),theory(equality)],[c_1182,c_318]) ).
tff(c_3179,plain,
( $less('#skE_4','#skE_3')
| ~ $less('#skF_10','#skE_6')
| ~ $less('#skE_6','#skF_9') ),
inference(superposition,[status(thm),theory(equality)],[c_3173,c_1192]) ).
tff(c_3213,plain,
( $less('#skE_4','#skE_3')
| ~ $less('#skF_10','#skE_6') ),
inference(demodulation,[status(thm),theory(equality)],[c_2422,c_3179]) ).
tff(c_3237,plain,
~ $less('#skF_10','#skE_6'),
inference(splitLeft,[status(thm)],[c_3213]) ).
tff(c_1531,plain,
( ( '#skE_4' = '#skE_3' )
| ( '#skF_14' != '#skF_10' ) ),
inference(superposition,[status(thm),theory(equality)],[c_1489,c_1064]) ).
tff(c_1550,plain,
'#skF_14' != '#skF_10',
inference(splitLeft,[status(thm)],[c_1531]) ).
tff(c_2414,plain,
'#skF_10' != '#skE_6',
inference(demodulation,[status(thm),theory(equality)],[c_2376,c_1550]) ).
tff(c_4488,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_4455,c_3237,c_2414]) ).
tff(c_4491,plain,
$less('#skE_4','#skE_3'),
inference(splitRight,[status(thm)],[c_3213]) ).
tff(c_5824,plain,
$less($sum(1,'#skE_2'),'#skE_3'),
inference(demodulation,[status(thm),theory(equality)],[c_5755,c_4491]) ).
tff(c_5842,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_5824,c_1065]) ).
tff(c_5846,plain,
'#skF_14' = '#skF_10',
inference(splitRight,[status(thm)],[c_1531]) ).
tff(c_5876,plain,
tb2t(get(int,int,t2tb1('#skF_7'),t2tb('#skF_10'))) = '#skE_3',
inference(demodulation,[status(thm),theory(equality)],[c_5846,c_1064]) ).
tff(c_6348,plain,
! [K_2040a: $int] :
( path(tb2t(get(int,int,t2tb1('#skF_7'),t2tb(K_2040a))),K_2040a)
| $less(K_2040a,0)
| ~ $less(K_2040a,'#skF_9') ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_135]) ).
tff(c_6352,plain,
( path('#skE_3','#skF_10')
| $less('#skF_10',0)
| ~ $less('#skF_10','#skF_9') ),
inference(superposition,[status(thm),theory(equality)],[c_5876,c_6348]) ).
tff(c_6363,plain,
( path('#skE_3','#skF_10')
| $less('#skF_10',0) ),
inference(demodulation,[status(thm),theory(equality)],[c_224,c_6352]) ).
tff(c_6380,plain,
path('#skE_3','#skF_10'),
inference(negUnitSimplification,[status(thm)],[c_234,c_6363]) ).
tff(c_6413,plain,
( ( '#skF_1'('#skE_3','#skF_10') = '#skF_10' )
| ( '#skE_3' = 0 ) ),
inference(resolution,[status(thm)],[c_6380,c_275]) ).
tff(c_6678,plain,
'#skF_1'('#skE_3','#skF_10') = '#skE_14',
inference(define,[status(thm),theory(equality)],[c_6413]) ).
tff(c_6677,plain,
( ( '#skF_1'('#skE_3','#skF_10') = '#skF_10' )
| ( '#skE_3' = 0 ) ),
inference(resolution,[status(thm)],[c_6380,c_275]) ).
tff(c_6685,plain,
( ( '#skF_10' = '#skE_14' )
| ( '#skE_3' = 0 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_6678,c_6677]) ).
tff(c_6687,plain,
'#skE_3' = 0,
inference(splitLeft,[status(thm)],[c_6685]) ).
tff(c_6737,plain,
$less(0,0),
inference(demodulation,[status(thm),theory(equality)],[c_6687,c_1386]) ).
tff(c_6756,plain,
$false,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_6737]) ).
tff(c_6759,plain,
'#skF_10' = '#skE_14',
inference(splitRight,[status(thm)],[c_6685]) ).
tff(c_6836,plain,
'#skF_14' = '#skE_14',
inference(demodulation,[status(thm),theory(equality)],[c_6759,c_5846]) ).
tff(c_1354,plain,
get(int,int,t2tb1('#skF_7'),t2tb('#skF_14')) = t2tb('#skE_3'),
inference(superposition,[status(thm),theory(equality)],[c_1328,c_290]) ).
tff(c_8270,plain,
get(int,int,t2tb1('#skF_7'),t2tb('#skE_14')) = t2tb('#skE_3'),
inference(demodulation,[status(thm),theory(equality)],[c_6836,c_1354]) ).
tff(c_129,plain,
$lesseq($sum('#skF_11',tb2t(get(int,int,t2tb1('#skF_7'),t2tb('#skF_10')))),$difference('#skF_9',1)),
inference(cnfTransformation,[status(thm)],[f_280]) ).
tff(c_228,plain,
~ $less('#skF_9',$sum(1,$sum('#skF_11',tb2t(get(int,int,t2tb1('#skF_7'),t2tb('#skF_10')))))),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_129]) ).
tff(c_6883,plain,
~ $less('#skF_9',$sum(1,$sum('#skF_11',tb2t(get(int,int,t2tb1('#skF_7'),t2tb('#skE_14')))))),
inference(demodulation,[status(thm),theory(equality)],[c_6759,c_228]) ).
tff(c_6891,plain,
tb2t(get(int,int,t2tb1('#skF_7'),t2tb('#skE_14'))) = '#skE_15',
inference(define,[status(thm),theory(equality)],[c_6883]) ).
tff(c_8400,plain,
'#skE_3' = '#skE_15',
inference(demodulation,[status(thm),theory(equality)],[c_291,c_8270,c_6891]) ).
tff(c_6227,plain,
tb2t(get(int,int,t2tb1('#skF_7'),t2tb('#skF_10'))) = '#skE_3',
inference(demodulation,[status(thm),theory(equality)],[c_5846,c_1064]) ).
tff(c_6267,plain,
get(int,int,t2tb1('#skF_7'),t2tb('#skF_10')) = t2tb('#skE_3'),
inference(superposition,[status(thm),theory(equality)],[c_6227,c_290]) ).
tff(c_10655,plain,
get(int,int,t2tb1('#skF_7'),t2tb('#skE_14')) = t2tb('#skE_15'),
inference(demodulation,[status(thm),theory(equality)],[c_6759,c_8400,c_6267]) ).
tff(c_92897,plain,
! [U_3393a: $int] : ( get1(int,mk_array(int,U_3393a,t2tb1('#skF_7')),'#skE_14') = t2tb('#skE_15') ),
inference(superposition,[status(thm),theory(equality)],[c_10823,c_10655]) ).
tff(c_8459,plain,
$less(0,'#skE_15'),
inference(demodulation,[status(thm),theory(equality)],[c_8400,c_1386]) ).
tff(c_6356,plain,
( path('#skE_2','#skF_13')
| $less('#skF_13',0)
| ~ $less('#skF_13','#skF_9') ),
inference(superposition,[status(thm),theory(equality)],[c_1061,c_6348]) ).
tff(c_6374,plain,
( path('#skE_2','#skF_13')
| $less('#skF_13',0) ),
inference(demodulation,[status(thm),theory(equality)],[c_1468,c_6356]) ).
tff(c_6427,plain,
$less('#skF_13',0),
inference(splitLeft,[status(thm)],[c_6374]) ).
tff(c_6428,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_6427,c_1106,c_492]) ).
tff(c_6455,plain,
path('#skE_2','#skF_13'),
inference(splitRight,[status(thm)],[c_6374]) ).
tff(c_6456,plain,
path('#skE_2','#skF_13'),
inference(splitRight,[status(thm)],[c_6374]) ).
tff(c_276,plain,
! [Z_96a: $int,Z1_97a: $int] :
( ( '#skF_1'(Z_96a,Z1_97a) = Z1_97a )
| ~ path(Z_96a,Z1_97a)
| ( Z1_97a = 0 ) ),
inference(cnfTransformation,[status(thm)],[f_167]) ).
tff(c_6492,plain,
( ( '#skF_1'('#skE_2','#skF_13') = '#skF_13' )
| ( '#skF_13' = 0 ) ),
inference(resolution,[status(thm)],[c_6456,c_276]) ).
tff(c_6511,plain,
'#skF_1'('#skE_2','#skF_13') = '#skF_13',
inference(negUnitSimplification,[status(thm)],[c_1461,c_6492]) ).
tff(c_6433,plain,
path('#skE_2','#skF_13'),
inference(splitRight,[status(thm)],[c_6374]) ).
tff(c_6894,plain,
! [Z_2242a: $int,Z1_2243a: $int] :
( $less('#skF_3'(Z_2242a,Z1_2243a),'#skF_1'(Z_2242a,Z1_2243a))
| ~ path(Z_2242a,Z1_2243a)
| ( Z1_2243a = 0 ) ),
inference(cnfTransformation,[status(thm)],[f_167]) ).
tff(c_6897,plain,
( $less('#skF_3'('#skE_2','#skF_13'),'#skF_1'('#skE_2','#skF_13'))
| ( '#skF_13' = 0 ) ),
inference(resolution,[status(thm)],[c_6433,c_6894]) ).
tff(c_6906,plain,
( $less('#skF_3'('#skE_2','#skF_13'),'#skF_13')
| ( '#skF_13' = 0 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_6511,c_6897]) ).
tff(c_6910,plain,
$less('#skF_3'('#skE_2','#skF_13'),'#skF_13'),
inference(negUnitSimplification,[status(thm)],[c_1461,c_6906]) ).
tff(c_7183,plain,
'#skF_3'('#skE_2','#skF_13') = '#skE_16',
inference(define,[status(thm),theory(equality)],[c_6910]) ).
tff(c_7471,plain,
! [Z_2471a: $int,Z1_2472a: $int] :
( path('#skF_2'(Z_2471a,Z1_2472a),'#skF_3'(Z_2471a,Z1_2472a))
| ~ path(Z_2471a,Z1_2472a)
| ( Z1_2472a = 0 ) ),
inference(cnfTransformation,[status(thm)],[f_167]) ).
tff(c_7475,plain,
( path('#skF_2'('#skE_2','#skF_13'),'#skE_16')
| ~ path('#skE_2','#skF_13')
| ( '#skF_13' = 0 ) ),
inference(superposition,[status(thm),theory(equality)],[c_7183,c_7471]) ).
tff(c_7479,plain,
( path('#skF_2'('#skE_2','#skF_13'),'#skE_16')
| ( '#skF_13' = 0 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_6455,c_7475]) ).
tff(c_7483,plain,
path('#skF_2'('#skE_2','#skF_13'),'#skE_16'),
inference(negUnitSimplification,[status(thm)],[c_1461,c_7479]) ).
tff(c_8131,plain,
'#skF_2'('#skE_2','#skF_13') = '#skE_18',
inference(define,[status(thm),theory(equality)],[c_7483]) ).
tff(c_77,plain,
! [Z_96a: $int,Z1_97a: $int] :
( ( $sum('#skF_2'(Z_96a,Z1_97a),1) = Z_96a )
| ~ path(Z_96a,Z1_97a)
| ( Z_96a = 0 ) ),
inference(cnfTransformation,[status(thm)],[f_167]) ).
tff(c_6617,plain,
! [Z_2118a: $int,Z1_2119a: $int] :
( ( '#skF_2'(Z_2118a,Z1_2119a) = $sum($uminus(1),Z_2118a) )
| ~ path(Z_2118a,Z1_2119a)
| ( Z_2118a = 0 ) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_77]) ).
tff(c_6632,plain,
( ( '#skF_2'('#skE_2','#skF_13') = $sum($uminus(1),'#skE_2') )
| ( '#skE_2' = 0 ) ),
inference(resolution,[status(thm)],[c_6433,c_6617]) ).
tff(c_10179,plain,
( ( $sum($uminus(1),'#skE_2') = '#skE_18' )
| ( '#skE_2' = 0 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_8131,c_6632]) ).
tff(c_10181,plain,
( ( '#skE_2' = $sum(1,'#skE_18') )
| ( '#skE_2' = 0 ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_10179]) ).
tff(c_10183,plain,
'#skE_2' = 0,
inference(splitLeft,[status(thm)],[c_10181]) ).
tff(c_8460,plain,
~ $less('#skE_2','#skE_15'),
inference(demodulation,[status(thm),theory(equality)],[c_8400,c_1065]) ).
tff(c_10229,plain,
~ $less(0,'#skE_15'),
inference(demodulation,[status(thm),theory(equality)],[c_10183,c_8460]) ).
tff(c_10269,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_8459,c_10229]) ).
tff(c_10272,plain,
'#skE_2' = $sum(1,'#skE_18'),
inference(splitRight,[status(thm)],[c_10181]) ).
tff(c_7395,plain,
! [J_112: uni,I_2448a: $int,U_2421a: $int] : ( get(int,int,J_112,t2tb(I_2448a)) = get1(int,mk_array(int,U_2421a,J_112),I_2448a) ),
inference(superposition,[status(thm),theory(equality)],[c_7255,c_7370]) ).
tff(c_6844,plain,
$less('#skE_14','#skF_9'),
inference(demodulation,[status(thm),theory(equality)],[c_6759,c_224]) ).
tff(c_6839,plain,
$less(0,'#skE_14'),
inference(demodulation,[status(thm),theory(equality)],[c_6759,c_1027]) ).
tff(c_8603,plain,
get(int,int,t2tb1('#skF_7'),t2tb('#skF_13')) = t2tb('#skE_2'),
inference(superposition,[status(thm),theory(equality)],[c_1392,c_290]) ).
tff(c_9107,plain,
get(int,int,t2tb1('#skF_8'),t2tb('#skE_14')) = t2tb('#skF_13'),
inference(demodulation,[status(thm),theory(equality)],[c_6759,c_459]) ).
tff(c_9119,plain,
( ( tb2t(get(int,int,t2tb1('#skF_7'),t2tb('#skF_13'))) = $sum($uminus(1),tb2t(get(int,int,t2tb1('#skF_7'),t2tb('#skE_14')))) )
| ~ $less(0,'#skE_14')
| ~ $less('#skE_14','#skF_9') ),
inference(superposition,[status(thm),theory(equality)],[c_9107,c_201]) ).
tff(c_9158,plain,
$sum($uminus(1),tb2t(get(int,int,t2tb1('#skF_7'),t2tb('#skE_14')))) = '#skE_2',
inference(demodulation,[status(thm),theory(equality)],[c_6844,c_6839,c_291,c_8603,c_9119]) ).
tff(c_9161,plain,
tb2t(get(int,int,t2tb1('#skF_7'),t2tb('#skE_14'))) = $sum(1,'#skE_2'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_9158]) ).
tff(c_84339,plain,
! [U_2421a: $int] : ( tb2t(get1(int,mk_array(int,U_2421a,t2tb1('#skF_7')),'#skE_14')) = $sum(1,$sum(1,'#skE_18')) ),
inference(demodulation,[status(thm),theory(equality)],[c_10272,c_7395,c_9161]) ).
tff(c_84342,plain,
! [U_2421a: $int] : ( tb2t(get1(int,mk_array(int,U_2421a,t2tb1('#skF_7')),'#skE_14')) = $sum(2,'#skE_18') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_84339]) ).
tff(c_93075,plain,
tb2t(t2tb('#skE_15')) = $sum(2,'#skE_18'),
inference(demodulation,[status(thm),theory(equality)],[c_92897,c_84342]) ).
tff(c_93095,plain,
$sum(2,'#skE_18') = '#skE_15',
inference(superposition,[status(thm),theory(equality)],[c_93075,c_291]) ).
tff(c_93097,plain,
'#skE_18' = $sum($uminus(2),'#skE_15'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_93095]) ).
tff(c_10328,plain,
~ $less($sum(1,'#skE_18'),'#skE_15'),
inference(demodulation,[status(thm),theory(equality)],[c_10272,c_8460]) ).
tff(c_93222,plain,
~ $less($sum(1,$sum($uminus(2),'#skE_15')),'#skE_15'),
inference(demodulation,[status(thm),theory(equality)],[c_93097,c_10328]) ).
tff(c_93281,plain,
$false,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_93222]) ).
tff(c_93284,plain,
'#skE_2' = 0,
inference(splitRight,[status(thm)],[c_1431]) ).
tff(c_93292,plain,
~ $less(0,'#skE_3'),
inference(demodulation,[status(thm),theory(equality)],[c_93284,c_1065]) ).
tff(c_93304,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_1386,c_93292]) ).
tff(c_93307,plain,
~ $less(0,'#skF_9'),
inference(splitRight,[status(thm)],[c_1095]) ).
tff(c_93326,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_93307,c_211]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : SWW631_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
% 0.15/0.37 % Computer : n020.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Thu Aug 3 19:17:22 EDT 2023
% 0.15/0.37 % CPUTime :
% 45.14/18.59 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 45.22/18.63
% 45.22/18.63 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 45.56/18.68
% 45.56/18.68 Inference rules
% 45.56/18.68 ----------------------
% 45.56/18.68 #Ref : 18
% 45.56/18.68 #Sup : 15768
% 45.56/18.68 #Fact : 1
% 45.56/18.68 #Define : 72
% 45.56/18.68 #Split : 88
% 45.56/18.68 #Chain : 0
% 45.56/18.68 #Close : 21
% 45.56/18.68
% 45.56/18.68 Ordering : LPO
% 45.56/18.68
% 45.56/18.68 Simplification rules
% 45.56/18.68 ----------------------
% 45.56/18.68 #Subsume : 1555
% 45.56/18.68 #Demod : 9315
% 45.56/18.68 #Tautology : 6971
% 45.56/18.68 #SimpNegUnit : 270
% 45.56/18.68 #BackRed : 378
% 45.56/18.68
% 45.56/18.68 #Partial instantiations: 882
% 45.56/18.68 #Strategies tried : 1
% 45.56/18.68
% 45.56/18.68 Timing (in seconds)
% 45.56/18.68 ----------------------
% 45.56/18.68 Preprocessing : 0.81
% 45.56/18.68 Parsing : 0.41
% 45.56/18.68 CNF conversion : 0.06
% 45.56/18.68 Main loop : 16.75
% 45.56/18.68 Inferencing : 2.05
% 45.56/18.68 Reduction : 7.46
% 45.56/18.68 Demodulation : 6.23
% 45.56/18.68 BG Simplification : 0.62
% 45.56/18.68 Subsumption : 4.24
% 45.56/18.68 Abstraction : 0.34
% 45.56/18.68 MUC search : 0.57
% 45.56/18.68 Cooper : 0.95
% 45.56/18.68 Total : 17.67
% 45.56/18.68 Index Insertion : 0.00
% 45.56/18.68 Index Deletion : 0.00
% 45.56/18.68 Index Matching : 0.00
% 45.56/18.68 BG Taut test : 0.00
%------------------------------------------------------------------------------