TSTP Solution File: SWW584_2 by Beagle---0.9.51
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%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SWW584_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 : n003.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 11:07:44 EDT 2023
% Result : Theorem 15.95s 5.05s
% Output : CNFRefutation 16.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 59
% Syntax : Number of formulae : 243 ( 111 unt; 49 typ; 0 def)
% Number of atoms : 389 ( 127 equ)
% Maximal formula atoms : 34 ( 2 avg)
% Number of connectives : 348 ( 153 ~; 159 |; 20 &)
% ( 0 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 3 avg)
% Maximal term depth : 8 ( 2 avg)
% Number arithmetic : 570 ( 235 atm; 129 fun; 127 num; 79 var)
% Number of types : 8 ( 6 usr; 1 ari)
% Number of type conns : 52 ( 25 >; 27 *; 0 +; 0 <<)
% Number of predicates : 6 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 46 ( 41 usr; 20 con; 0-5 aty)
% Number of variables : 123 (; 123 !; 0 ?; 123 :)
% Comments :
%------------------------------------------------------------------------------
%$ sort1 > decrease11 > set > set2 > match_bool1 > get > mk_array1 > make1 > get2 > const > mk_ref > map > length1 > elts > contents > #nlpp > witness1 > tb2t2 > tb2t1 > tb2t > t2tb2 > t2tb1 > t2tb > ref > array > tuple03 > tuple0 > true1 > real > qtmark > int > false1 > bool > #skF_1 > #skF_3
%Foreground sorts:
tff(map_int_int,type,
map_int_int: $tType ).
tff(tuple02,type,
tuple02: $tType ).
tff(bool1,type,
bool1: $tType ).
tff(array_int,type,
array_int: $tType ).
tff(ty,type,
ty: $tType ).
tff(uni,type,
uni: $tType ).
%Background operators:
tff('#skF_6',type,
'#skF_6': $int ).
tff('#skE_2',type,
'#skE_2': $int ).
tff('#skE_1',type,
'#skE_1': $int ).
tff('#skE_4',type,
'#skE_4': $int ).
tff('#skF_5',type,
'#skF_5': $int ).
tff('#skF_4',type,
'#skF_4': $int ).
tff('#skF_2',type,
'#skF_2': $int ).
tff('#skE_3',type,
'#skE_3': $int ).
tff('#skF_7',type,
'#skF_7': $int ).
%Foreground operators:
tff(length1,type,
length1: ( ty * uni ) > $int ).
tff(get2,type,
get2: ( ty * uni * $int ) > uni ).
tff(true1,type,
true1: bool1 ).
tff(const,type,
const: ( ty * ty * uni ) > uni ).
tff('#skF_1',type,
'#skF_1': array_int > $int ).
tff(elts,type,
elts: ( ty * uni ) > uni ).
tff(int,type,
int: ty ).
tff(false1,type,
false1: bool1 ).
tff(tb2t,type,
tb2t: uni > $int ).
tff(sort1,type,
sort1: ( ty * uni ) > $o ).
tff(contents,type,
contents: ( ty * uni ) > uni ).
tff(t2tb,type,
t2tb: $int > uni ).
tff(witness1,type,
witness1: ty > uni ).
tff(real,type,
real: ty ).
tff(set,type,
set: ( ty * ty * uni * uni * uni ) > uni ).
tff(match_bool1,type,
match_bool1: ( ty * bool1 * uni * uni ) > uni ).
tff(array,type,
array: ty > ty ).
tff(decrease11,type,
decrease11: array_int > $o ).
tff(make1,type,
make1: ( ty * $int * uni ) > uni ).
tff(tb2t2,type,
tb2t2: uni > map_int_int ).
tff(tuple0,type,
tuple0: ty ).
tff(qtmark,type,
qtmark: ty ).
tff(tb2t1,type,
tb2t1: uni > array_int ).
tff(t2tb2,type,
t2tb2: map_int_int > uni ).
tff(bool,type,
bool: ty ).
tff(get,type,
get: ( ty * ty * uni * uni ) > uni ).
tff(t2tb1,type,
t2tb1: array_int > uni ).
tff(tuple03,type,
tuple03: tuple02 ).
tff(map,type,
map: ( ty * ty ) > ty ).
tff(set2,type,
set2: ( ty * uni * $int * uni ) > uni ).
tff(ref,type,
ref: ty > ty ).
tff('#skF_3',type,
'#skF_3': map_int_int ).
tff(mk_array1,type,
mk_array1: ( ty * $int * uni ) > uni ).
tff(mk_ref,type,
mk_ref: ( ty * uni ) > uni ).
tff(f_233,negated_conjecture,
~ ! [Aa: $int,A1: map_int_int,Ia: $int] :
( ( $lesseq(0,Aa)
& decrease11(tb2t1(mk_array1(int,Aa,t2tb2(A1))))
& $lesseq(0,Ia) )
=> ( $less(Ia,Aa)
=> ( ( $lesseq(0,Ia)
& $less(Ia,Aa) )
=> ( ( tb2t(get(int,int,t2tb2(A1),t2tb(Ia))) != 0 )
=> ( ( $lesseq(0,Ia)
& $less(Ia,Aa) )
=> ( $less(0,tb2t(get(int,int,t2tb2(A1),t2tb(Ia))))
=> ( ( $lesseq(0,Ia)
& $less(Ia,Aa) )
=> ( ( decrease11(tb2t1(mk_array1(int,Aa,t2tb2(A1))))
& $lesseq(0,$sum(Ia,tb2t(get(int,int,t2tb2(A1),t2tb(Ia))))) )
=> ! [Resulta: $int] :
( ( ( ( Resulta = $uminus(1) )
& ! [Ja: $int] :
( ( $lesseq($sum(Ia,tb2t(get(int,int,t2tb2(A1),t2tb(Ia)))),Ja)
& $less(Ja,Aa) )
=> ( tb2t(get(int,int,t2tb2(A1),t2tb(Ja))) != 0 ) ) )
| ( $lesseq($sum(Ia,tb2t(get(int,int,t2tb2(A1),t2tb(Ia)))),Resulta)
& $less(Resulta,Aa)
& ( tb2t(get(int,int,t2tb2(A1),t2tb(Resulta))) = 0 )
& ! [Ja: $int] :
( ( $lesseq($sum(Ia,tb2t(get(int,int,t2tb2(A1),t2tb(Ia)))),Ja)
& $less(Ja,Resulta) )
=> ( tb2t(get(int,int,t2tb2(A1),t2tb(Ja))) != 0 ) ) ) )
=> ( ( ( Resulta = $uminus(1) )
& ! [Ja: $int] :
( ( $lesseq(Ia,Ja)
& $less(Ja,Aa) )
=> ( tb2t(get(int,int,t2tb2(A1),t2tb(Ja))) != 0 ) ) )
| ( $lesseq(Ia,Resulta)
& $less(Resulta,Aa)
& ( tb2t(get(int,int,t2tb2(A1),t2tb(Resulta))) = 0 )
& ! [Ja: $int] :
( ( $lesseq(Ia,Ja)
& $less(Ja,Resulta) )
=> ( tb2t(get(int,int,t2tb2(A1),t2tb(Ja))) != 0 ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',wP_parameter_search_rec) ).
tff(f_110,axiom,
! [Ia: $int] : ( tb2t(t2tb(Ia)) = Ia ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',bridgeL) ).
tff(f_154,axiom,
! [J: uni] : ( t2tb2(tb2t2(J)) = J ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',bridgeR2) ).
tff(f_150,axiom,
! [X: map_int_int] : sort1(map(int,int),t2tb2(X)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2tb_sort2) ).
tff(f_102,axiom,
! [A: ty,Ua: $int,U1: uni] :
( sort1(map(int,A),U1)
=> ( elts(A,mk_array1(A,Ua,U1)) = U1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',elts_def1) ).
tff(f_114,axiom,
! [A: ty,A1: uni,Ia: $int] : ( get2(A,A1,Ia) = get(A,int,elts(A,A1),t2tb(Ia)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',get_def) ).
tff(f_112,axiom,
! [J: uni] : ( t2tb(tb2t(J)) = J ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',bridgeR) ).
tff(f_96,axiom,
! [A: ty,Ua: $int,U1: uni] : ( length1(A,mk_array1(A,Ua,U1)) = Ua ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',length_def1) ).
tff(f_128,axiom,
! [J: uni] : ( t2tb1(tb2t1(J)) = J ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',bridgeR1) ).
tff(f_148,axiom,
! [A: array_int] :
( decrease11(A)
=> ! [Ia: $int,Ja: $int] :
( ( $lesseq(0,Ia)
& $lesseq(Ia,Ja)
& $less(Ja,length1(int,t2tb1(A))) )
=> $lesseq($difference($sum(tb2t(get2(int,t2tb1(A),Ia)),Ia),Ja),tb2t(get2(int,t2tb1(A),Ja))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',decrease1_induction) ).
tff(c_125,plain,
( ( '#skF_5' != $uminus(1) )
| $lesseq('#skF_4','#skF_6') ),
inference(cnfTransformation,[status(thm)],[f_233]) ).
tff(c_195,plain,
( ( '#skF_5' != $uminus(1) )
| ~ $less('#skF_6','#skF_4') ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_125]) ).
tff(c_429,plain,
~ $less('#skF_6','#skF_4'),
inference(splitLeft,[status(thm)],[c_195]) ).
tff(c_137,plain,
( $less('#skF_5','#skF_2')
| ( '#skF_5' = $uminus(1) ) ),
inference(cnfTransformation,[status(thm)],[f_233]) ).
tff(c_174,plain,
( $less('#skF_5','#skF_2')
| ( '#skF_5' = $uminus(1) ) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_137]) ).
tff(c_437,plain,
'#skF_5' = $uminus(1),
inference(splitLeft,[status(thm)],[c_174]) ).
tff(c_123,plain,
( ( '#skF_5' != $uminus(1) )
| $less('#skF_6','#skF_2') ),
inference(cnfTransformation,[status(thm)],[f_233]) ).
tff(c_196,plain,
( ( '#skF_5' != $uminus(1) )
| $less('#skF_6','#skF_2') ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_123]) ).
tff(c_448,plain,
$less('#skF_6','#skF_2'),
inference(demodulation,[status(thm),theory(equality)],[c_437,c_196]) ).
tff(c_256,plain,
! [I_71a: $int] : ( tb2t(t2tb(I_71a)) = I_71a ),
inference(cnfTransformation,[status(thm)],[f_110]) ).
tff(c_89,plain,
! [J_104: uni] : ( t2tb2(tb2t2(J_104)) = J_104 ),
inference(cnfTransformation,[status(thm)],[f_154]) ).
tff(c_431,plain,
! [X_354: map_int_int] : sort1(map(int,int),t2tb2(X_354)),
inference(cnfTransformation,[status(thm)],[f_150]) ).
tff(c_433,plain,
! [J_104: uni] : sort1(map(int,int),J_104),
inference(superposition,[status(thm),theory(equality)],[c_89,c_431]) ).
tff(c_1342,plain,
! [A_454: ty,U_455a: $int,U1_456: uni] :
( ( elts(A_454,mk_array1(A_454,U_455a,U1_456)) = U1_456 )
| ~ sort1(map(int,A_454),U1_456) ),
inference(cnfTransformation,[status(thm)],[f_102]) ).
tff(c_1389,plain,
! [U_455a: $int,J_104: uni] : ( elts(int,mk_array1(int,U_455a,J_104)) = J_104 ),
inference(resolution,[status(thm)],[c_433,c_1342]) ).
tff(c_1582,plain,
! [A_478: ty,A1_479: uni,I_480a: $int] : ( get(A_478,int,elts(A_478,A1_479),t2tb(I_480a)) = get2(A_478,A1_479,I_480a) ),
inference(cnfTransformation,[status(thm)],[f_114]) ).
tff(c_8705,plain,
! [J_1343: uni,I_1344a: $int,U_1345a: $int] : ( get(int,int,J_1343,t2tb(I_1344a)) = get2(int,mk_array1(int,U_1345a,J_1343),I_1344a) ),
inference(superposition,[status(thm),theory(equality)],[c_1389,c_1582]) ).
tff(c_121,plain,
( ( tb2t(get(int,int,t2tb2('#skF_3'),t2tb('#skF_6'))) = 0 )
| ( '#skF_5' != $uminus(1) ) ),
inference(cnfTransformation,[status(thm)],[f_233]) ).
tff(c_200,plain,
( ( tb2t(get(int,int,t2tb2('#skF_3'),t2tb('#skF_6'))) = 0 )
| ( '#skF_5' != $uminus(1) ) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_121]) ).
tff(c_922,plain,
tb2t(get(int,int,t2tb2('#skF_3'),t2tb('#skF_6'))) = 0,
inference(demodulation,[status(thm),theory(equality)],[c_437,c_200]) ).
tff(c_255,plain,
! [J_72: uni] : ( t2tb(tb2t(J_72)) = J_72 ),
inference(cnfTransformation,[status(thm)],[f_112]) ).
tff(c_947,plain,
get(int,int,t2tb2('#skF_3'),t2tb('#skF_6')) = t2tb(0),
inference(superposition,[status(thm),theory(equality)],[c_922,c_255]) ).
tff(c_8809,plain,
! [U_1345a: $int] : ( get2(int,mk_array1(int,U_1345a,t2tb2('#skF_3')),'#skF_6') = t2tb(0) ),
inference(superposition,[status(thm),theory(equality)],[c_8705,c_947]) ).
tff(c_109,plain,
$lesseq(0,'#skF_4'),
inference(cnfTransformation,[status(thm)],[f_233]) ).
tff(c_218,plain,
~ $less('#skF_4',0),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_109]) ).
tff(c_225,plain,
tb2t(get(int,int,t2tb2('#skF_3'),t2tb('#skF_4'))) != 0,
inference(cnfTransformation,[status(thm)],[f_233]) ).
tff(c_468,plain,
tb2t(get(int,int,t2tb2('#skF_3'),t2tb('#skF_4'))) = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_225]) ).
tff(c_484,plain,
get(int,int,t2tb2('#skF_3'),t2tb('#skF_4')) = t2tb('#skE_1'),
inference(superposition,[status(thm),theory(equality)],[c_468,c_255]) ).
tff(c_9233,plain,
! [U_1405a: $int] : ( get2(int,mk_array1(int,U_1405a,t2tb2('#skF_3')),'#skF_4') = t2tb('#skE_1') ),
inference(superposition,[status(thm),theory(equality)],[c_484,c_8705]) ).
tff(c_261,plain,
! [A_57: ty,U_58a: $int,U1_59: uni] : ( length1(A_57,mk_array1(A_57,U_58a,U1_59)) = U_58a ),
inference(cnfTransformation,[status(thm)],[f_96]) ).
tff(c_70,plain,
! [J_92: uni] : ( t2tb1(tb2t1(J_92)) = J_92 ),
inference(cnfTransformation,[status(thm)],[f_128]) ).
tff(c_217,plain,
decrease11(tb2t1(mk_array1(int,'#skF_2',t2tb2('#skF_3')))),
inference(cnfTransformation,[status(thm)],[f_233]) ).
tff(c_82,plain,
! [I_100a: $int,A_97: array_int,J_101a: $int] :
( $lesseq($difference($sum(I_100a,tb2t(get2(int,t2tb1(A_97),I_100a))),J_101a),tb2t(get2(int,t2tb1(A_97),J_101a)))
| ~ $less(J_101a,length1(int,t2tb1(A_97)))
| ~ decrease11(A_97)
| ~ $lesseq(0,I_100a)
| ~ $lesseq(I_100a,J_101a) ),
inference(cnfTransformation,[status(thm)],[f_148]) ).
tff(c_5888,plain,
! [J_1004a: $int,A_1005: array_int,I_1006a: $int] :
( ~ $less($sum(J_1004a,tb2t(get2(int,t2tb1(A_1005),J_1004a))),$sum(I_1006a,tb2t(get2(int,t2tb1(A_1005),I_1006a))))
| ~ $less(J_1004a,length1(int,t2tb1(A_1005)))
| ~ decrease11(A_1005)
| $less(I_1006a,0)
| $less(J_1004a,I_1006a) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_82]) ).
tff(c_5900,plain,
! [J_1004a: $int,I_1006a: $int] :
( ~ $less($sum(J_1004a,tb2t(get2(int,t2tb1(tb2t1(mk_array1(int,'#skF_2',t2tb2('#skF_3')))),J_1004a))),$sum(I_1006a,tb2t(get2(int,t2tb1(tb2t1(mk_array1(int,'#skF_2',t2tb2('#skF_3')))),I_1006a))))
| ~ $less(J_1004a,length1(int,t2tb1(tb2t1(mk_array1(int,'#skF_2',t2tb2('#skF_3'))))))
| $less(I_1006a,0)
| $less(J_1004a,I_1006a) ),
inference(resolution,[status(thm)],[c_217,c_5888]) ).
tff(c_5912,plain,
! [J_1004a: $int,I_1006a: $int] :
( ~ $less($sum(J_1004a,tb2t(get2(int,mk_array1(int,'#skF_2',t2tb2('#skF_3')),J_1004a))),$sum(I_1006a,tb2t(get2(int,mk_array1(int,'#skF_2',t2tb2('#skF_3')),I_1006a))))
| ~ $less(J_1004a,'#skF_2')
| $less(I_1006a,0)
| $less(J_1004a,I_1006a) ),
inference(demodulation,[status(thm),theory(equality)],[c_261,c_70,c_70,c_70,c_5900]) ).
tff(c_9255,plain,
! [J_1004a: $int] :
( ~ $less($sum(J_1004a,tb2t(get2(int,mk_array1(int,'#skF_2',t2tb2('#skF_3')),J_1004a))),$sum('#skF_4',tb2t(t2tb('#skE_1'))))
| ~ $less(J_1004a,'#skF_2')
| $less('#skF_4',0)
| $less(J_1004a,'#skF_4') ),
inference(superposition,[status(thm),theory(equality)],[c_9233,c_5912]) ).
tff(c_9312,plain,
! [J_1004a: $int] :
( ~ $less($sum(J_1004a,tb2t(get2(int,mk_array1(int,'#skF_2',t2tb2('#skF_3')),J_1004a))),$sum('#skF_4','#skE_1'))
| ~ $less(J_1004a,'#skF_2')
| $less('#skF_4',0)
| $less(J_1004a,'#skF_4') ),
inference(demodulation,[status(thm),theory(equality)],[c_256,c_9255]) ).
tff(c_9677,plain,
! [J_1448a: $int] :
( ~ $less($sum(J_1448a,tb2t(get2(int,mk_array1(int,'#skF_2',t2tb2('#skF_3')),J_1448a))),$sum('#skF_4','#skE_1'))
| ~ $less(J_1448a,'#skF_2')
| $less(J_1448a,'#skF_4') ),
inference(negUnitSimplification,[status(thm)],[c_218,c_9312]) ).
tff(c_9683,plain,
( ~ $less($sum('#skF_6',tb2t(t2tb(0))),$sum('#skF_4','#skE_1'))
| ~ $less('#skF_6','#skF_2')
| $less('#skF_6','#skF_4') ),
inference(superposition,[status(thm),theory(equality)],[c_8809,c_9677]) ).
tff(c_9694,plain,
( ~ $less($sum('#skF_6',0),$sum('#skF_4','#skE_1'))
| $less('#skF_6','#skF_4') ),
inference(demodulation,[status(thm),theory(equality)],[c_448,c_256,c_9683]) ).
tff(c_9695,plain,
~ $less($sum('#skF_6',0),$sum('#skF_4','#skE_1')),
inference(negUnitSimplification,[status(thm)],[c_429,c_9694]) ).
tff(c_9697,plain,
~ $less('#skF_6',$sum('#skF_4','#skE_1')),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_9695]) ).
tff(c_1607,plain,
! [J_104: uni,I_480a: $int,U_455a: $int] : ( get(int,int,J_104,t2tb(I_480a)) = get2(int,mk_array1(int,U_455a,J_104),I_480a) ),
inference(superposition,[status(thm),theory(equality)],[c_1389,c_1582]) ).
tff(c_2213,plain,
get(int,int,t2tb2('#skF_3'),t2tb('#skF_4')) = t2tb('#skE_1'),
inference(superposition,[status(thm),theory(equality)],[c_468,c_255]) ).
tff(c_139,plain,
! [J_118a: $int] :
( ( tb2t(get(int,int,t2tb2('#skF_3'),t2tb(J_118a))) != 0 )
| ~ $lesseq($sum('#skF_4',tb2t(get(int,int,t2tb2('#skF_3'),t2tb('#skF_4')))),J_118a)
| $lesseq($sum('#skF_4',tb2t(get(int,int,t2tb2('#skF_3'),t2tb('#skF_4')))),'#skF_5')
| ~ $less(J_118a,'#skF_2') ),
inference(cnfTransformation,[status(thm)],[f_233]) ).
tff(c_173,plain,
! [J_118a: $int] :
( ( tb2t(get(int,int,t2tb2('#skF_3'),t2tb(J_118a))) != 0 )
| $less(J_118a,$sum('#skF_4',tb2t(get(int,int,t2tb2('#skF_3'),t2tb('#skF_4')))))
| ~ $less('#skF_5',$sum('#skF_4',tb2t(get(int,int,t2tb2('#skF_3'),t2tb('#skF_4')))))
| ~ $less(J_118a,'#skF_2') ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_139]) ).
tff(c_6178,plain,
! [J_118a: $int] :
( ( tb2t(get(int,int,t2tb2('#skF_3'),t2tb(J_118a))) != 0 )
| $less(J_118a,$sum('#skF_4','#skE_1'))
| ~ $less($uminus(1),$sum('#skF_4','#skE_1'))
| ~ $less(J_118a,'#skF_2') ),
inference(demodulation,[status(thm),theory(equality)],[c_256,c_2213,c_437,c_256,c_2213,c_173]) ).
tff(c_6180,plain,
~ $less($uminus(1),$sum('#skF_4','#skE_1')),
inference(splitLeft,[status(thm)],[c_6178]) ).
tff(c_231,plain,
$less(0,tb2t(get(int,int,t2tb2('#skF_3'),t2tb('#skF_4')))),
inference(cnfTransformation,[status(thm)],[f_233]) ).
tff(c_438,plain,
tb2t(get(int,int,t2tb2('#skF_3'),t2tb('#skF_4'))) = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_231]) ).
tff(c_305,plain,
$less(0,tb2t(get(int,int,t2tb2('#skF_3'),t2tb('#skF_4')))),
inference(cnfTransformation,[status(thm)],[f_233]) ).
tff(c_445,plain,
$less(0,'#skE_1'),
inference(demodulation,[status(thm),theory(equality)],[c_438,c_305]) ).
tff(c_6181,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_6180,c_445,c_218]) ).
tff(c_6184,plain,
! [J_118a: $int] :
( ( tb2t(get(int,int,t2tb2('#skF_3'),t2tb(J_118a))) != 0 )
| $less(J_118a,$sum('#skF_4','#skE_1'))
| ~ $less(J_118a,'#skF_2') ),
inference(splitRight,[status(thm)],[c_6178]) ).
tff(c_10513,plain,
! [U_1518a: $int,J_1519a: $int] :
( ( tb2t(get2(int,mk_array1(int,U_1518a,t2tb2('#skF_3')),J_1519a)) != 0 )
| $less(J_1519a,$sum('#skF_4','#skE_1'))
| ~ $less(J_1519a,'#skF_2') ),
inference(demodulation,[status(thm),theory(equality)],[c_1607,c_6184]) ).
tff(c_10522,plain,
( ( tb2t(t2tb(0)) != 0 )
| $less('#skF_6',$sum('#skF_4','#skE_1'))
| ~ $less('#skF_6','#skF_2') ),
inference(superposition,[status(thm),theory(equality)],[c_8809,c_10513]) ).
tff(c_10536,plain,
$less('#skF_6',$sum('#skF_4','#skE_1')),
inference(demodulation,[status(thm),theory(equality)],[c_448,c_256,c_10522]) ).
tff(c_10538,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_9697,c_10536]) ).
tff(c_10542,plain,
'#skF_5' != $uminus(1),
inference(splitRight,[status(thm)],[c_174]) ).
tff(c_467,plain,
tb2t(get(int,int,t2tb2('#skF_3'),t2tb('#skF_4'))) = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_225]) ).
tff(c_141,plain,
( $lesseq($sum('#skF_4',tb2t(get(int,int,t2tb2('#skF_3'),t2tb('#skF_4')))),'#skF_5')
| ( '#skF_5' = $uminus(1) ) ),
inference(cnfTransformation,[status(thm)],[f_233]) ).
tff(c_169,plain,
( ~ $less('#skF_5',$sum('#skF_4',tb2t(get(int,int,t2tb2('#skF_3'),t2tb('#skF_4')))))
| ( '#skF_5' = $uminus(1) ) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_141]) ).
tff(c_15568,plain,
( ~ $less('#skF_5',$sum('#skF_4','#skE_1'))
| ( '#skF_5' = $uminus(1) ) ),
inference(demodulation,[status(thm),theory(equality)],[c_467,c_169]) ).
tff(c_15570,plain,
~ $less('#skF_5',$sum('#skF_4','#skE_1')),
inference(negUnitSimplification,[status(thm)],[c_10542,c_15568]) ).
tff(c_15099,plain,
( ~ $less('#skF_5',$sum('#skF_4','#skE_1'))
| ( '#skF_5' = $uminus(1) ) ),
inference(demodulation,[status(thm),theory(equality)],[c_467,c_169]) ).
tff(c_15101,plain,
~ $less('#skF_5',$sum('#skF_4','#skE_1')),
inference(negUnitSimplification,[status(thm)],[c_10542,c_15099]) ).
tff(c_10541,plain,
$less('#skF_5','#skF_2'),
inference(splitRight,[status(thm)],[c_174]) ).
tff(c_133,plain,
( ( tb2t(get(int,int,t2tb2('#skF_3'),t2tb('#skF_5'))) = 0 )
| ( '#skF_5' = $uminus(1) ) ),
inference(cnfTransformation,[status(thm)],[f_233]) ).
tff(c_182,plain,
( ( tb2t(get(int,int,t2tb2('#skF_3'),t2tb('#skF_5'))) = 0 )
| ( '#skF_5' = $uminus(1) ) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_133]) ).
tff(c_11298,plain,
tb2t(get(int,int,t2tb2('#skF_3'),t2tb('#skF_5'))) = 0,
inference(negUnitSimplification,[status(thm)],[c_10542,c_182]) ).
tff(c_11424,plain,
get(int,int,t2tb2('#skF_3'),t2tb('#skF_5')) = t2tb(0),
inference(superposition,[status(thm),theory(equality)],[c_11298,c_255]) ).
tff(c_117,plain,
( ( tb2t(get(int,int,t2tb2('#skF_3'),t2tb('#skF_5'))) != 0 )
| ~ $lesseq('#skF_4','#skF_5')
| ~ $less('#skF_5','#skF_2')
| $less('#skF_7','#skF_5') ),
inference(cnfTransformation,[status(thm)],[f_233]) ).
tff(c_208,plain,
( ( tb2t(get(int,int,t2tb2('#skF_3'),t2tb('#skF_5'))) != 0 )
| $less('#skF_5','#skF_4')
| ~ $less('#skF_5','#skF_2')
| $less('#skF_7','#skF_5') ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_117]) ).
tff(c_12097,plain,
( $less('#skF_5','#skF_4')
| $less('#skF_7','#skF_5') ),
inference(demodulation,[status(thm),theory(equality)],[c_10541,c_256,c_11424,c_208]) ).
tff(c_12099,plain,
$less('#skF_7','#skF_5'),
inference(splitLeft,[status(thm)],[c_12097]) ).
tff(c_115,plain,
( ( tb2t(get(int,int,t2tb2('#skF_3'),t2tb('#skF_7'))) = 0 )
| ( tb2t(get(int,int,t2tb2('#skF_3'),t2tb('#skF_5'))) != 0 )
| ~ $lesseq('#skF_4','#skF_5')
| ~ $less('#skF_5','#skF_2') ),
inference(cnfTransformation,[status(thm)],[f_233]) ).
tff(c_212,plain,
( ( tb2t(get(int,int,t2tb2('#skF_3'),t2tb('#skF_7'))) = 0 )
| ( tb2t(get(int,int,t2tb2('#skF_3'),t2tb('#skF_5'))) != 0 )
| $less('#skF_5','#skF_4')
| ~ $less('#skF_5','#skF_2') ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_115]) ).
tff(c_12788,plain,
( ( tb2t(get(int,int,t2tb2('#skF_3'),t2tb('#skF_7'))) = 0 )
| $less('#skF_5','#skF_4') ),
inference(demodulation,[status(thm),theory(equality)],[c_10541,c_256,c_11424,c_212]) ).
tff(c_12790,plain,
tb2t(get(int,int,t2tb2('#skF_3'),t2tb('#skF_7'))) = '#skE_3',
inference(define,[status(thm),theory(equality)],[c_12788]) ).
tff(c_12789,plain,
( ( tb2t(get(int,int,t2tb2('#skF_3'),t2tb('#skF_7'))) = 0 )
| $less('#skF_5','#skF_4') ),
inference(demodulation,[status(thm),theory(equality)],[c_10541,c_256,c_11424,c_212]) ).
tff(c_12797,plain,
( ( '#skE_3' = 0 )
| $less('#skF_5','#skF_4') ),
inference(demodulation,[status(thm),theory(equality)],[c_12790,c_12789]) ).
tff(c_12799,plain,
$less('#skF_5','#skF_4'),
inference(splitLeft,[status(thm)],[c_12797]) ).
tff(c_12563,plain,
( ~ $less('#skF_5',$sum('#skF_4','#skE_1'))
| ( '#skF_5' = $uminus(1) ) ),
inference(demodulation,[status(thm),theory(equality)],[c_467,c_169]) ).
tff(c_12565,plain,
~ $less('#skF_5',$sum('#skF_4','#skE_1')),
inference(negUnitSimplification,[status(thm)],[c_10542,c_12563]) ).
tff(c_10559,plain,
tb2t(get(int,int,t2tb2('#skF_3'),t2tb('#skF_4'))) = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_231]) ).
tff(c_10566,plain,
$less(0,'#skE_1'),
inference(demodulation,[status(thm),theory(equality)],[c_10559,c_305]) ).
tff(c_12800,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_12799,c_12565,c_10566]) ).
tff(c_12803,plain,
'#skE_3' = 0,
inference(splitRight,[status(thm)],[c_12797]) ).
tff(c_12796,plain,
tb2t(get(int,int,t2tb2('#skF_3'),t2tb('#skF_7'))) = '#skE_3',
inference(define,[status(thm),theory(equality)],[c_12788]) ).
tff(c_12812,plain,
tb2t(get(int,int,t2tb2('#skF_3'),t2tb('#skF_7'))) = 0,
inference(demodulation,[status(thm),theory(equality)],[c_12803,c_12796]) ).
tff(c_12833,plain,
get(int,int,t2tb2('#skF_3'),t2tb('#skF_7')) = t2tb(0),
inference(superposition,[status(thm),theory(equality)],[c_12812,c_255]) ).
tff(c_10741,plain,
tb2t(get(int,int,t2tb2('#skF_3'),t2tb('#skF_4'))) = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_225]) ).
tff(c_12567,plain,
get(int,int,t2tb2('#skF_3'),t2tb('#skF_4')) = t2tb('#skE_1'),
inference(superposition,[status(thm),theory(equality)],[c_10741,c_255]) ).
tff(c_129,plain,
! [J_119a: $int] :
( ( tb2t(get(int,int,t2tb2('#skF_3'),t2tb(J_119a))) != 0 )
| ~ $lesseq($sum('#skF_4',tb2t(get(int,int,t2tb2('#skF_3'),t2tb('#skF_4')))),J_119a)
| ~ $less(J_119a,'#skF_5')
| ( '#skF_5' = $uminus(1) ) ),
inference(cnfTransformation,[status(thm)],[f_233]) ).
tff(c_190,plain,
! [J_119a: $int] :
( ( tb2t(get(int,int,t2tb2('#skF_3'),t2tb(J_119a))) != 0 )
| $less(J_119a,$sum('#skF_4',tb2t(get(int,int,t2tb2('#skF_3'),t2tb('#skF_4')))))
| ~ $less(J_119a,'#skF_5')
| ( '#skF_5' = $uminus(1) ) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_129]) ).
tff(c_12893,plain,
! [J_119a: $int] :
( ( tb2t(get(int,int,t2tb2('#skF_3'),t2tb(J_119a))) != 0 )
| $less(J_119a,$sum('#skF_4','#skE_1'))
| ~ $less(J_119a,'#skF_5')
| ( '#skF_5' = $uminus(1) ) ),
inference(demodulation,[status(thm),theory(equality)],[c_256,c_12567,c_190]) ).
tff(c_12896,plain,
! [J_1741a: $int] :
( ( tb2t(get(int,int,t2tb2('#skF_3'),t2tb(J_1741a))) != 0 )
| $less(J_1741a,$sum('#skF_4','#skE_1'))
| ~ $less(J_1741a,'#skF_5') ),
inference(negUnitSimplification,[status(thm)],[c_10542,c_12893]) ).
tff(c_12899,plain,
( ( tb2t(t2tb(0)) != 0 )
| $less('#skF_7',$sum('#skF_4','#skE_1'))
| ~ $less('#skF_7','#skF_5') ),
inference(superposition,[status(thm),theory(equality)],[c_12833,c_12896]) ).
tff(c_12909,plain,
$less('#skF_7',$sum('#skF_4','#skE_1')),
inference(demodulation,[status(thm),theory(equality)],[c_12099,c_256,c_12899]) ).
tff(c_119,plain,
( ( tb2t(get(int,int,t2tb2('#skF_3'),t2tb('#skF_5'))) != 0 )
| ~ $lesseq('#skF_4','#skF_5')
| ~ $less('#skF_5','#skF_2')
| $lesseq('#skF_4','#skF_7') ),
inference(cnfTransformation,[status(thm)],[f_233]) ).
tff(c_204,plain,
( ( tb2t(get(int,int,t2tb2('#skF_3'),t2tb('#skF_5'))) != 0 )
| $less('#skF_5','#skF_4')
| ~ $less('#skF_5','#skF_2')
| ~ $less('#skF_7','#skF_4') ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_119]) ).
tff(c_12351,plain,
( $less('#skF_5','#skF_4')
| ~ $less('#skF_7','#skF_4') ),
inference(demodulation,[status(thm),theory(equality)],[c_10541,c_256,c_11424,c_204]) ).
tff(c_12353,plain,
~ $less('#skF_7','#skF_4'),
inference(splitLeft,[status(thm)],[c_12351]) ).
tff(c_11452,plain,
! [A_1620: ty,U_1621a: $int,U1_1622: uni] :
( ( elts(A_1620,mk_array1(A_1620,U_1621a,U1_1622)) = U1_1622 )
| ~ sort1(map(int,A_1620),U1_1622) ),
inference(cnfTransformation,[status(thm)],[f_102]) ).
tff(c_11506,plain,
! [U_1623a: $int,J_1624: uni] : ( elts(int,mk_array1(int,U_1623a,J_1624)) = J_1624 ),
inference(resolution,[status(thm)],[c_433,c_11452]) ).
tff(c_254,plain,
! [A_73: ty,A1_74: uni,I_75a: $int] : ( get(A_73,int,elts(A_73,A1_74),t2tb(I_75a)) = get2(A_73,A1_74,I_75a) ),
inference(cnfTransformation,[status(thm)],[f_114]) ).
tff(c_13563,plain,
! [J_1810: uni,I_1811a: $int,U_1812a: $int] : ( get(int,int,J_1810,t2tb(I_1811a)) = get2(int,mk_array1(int,U_1812a,J_1810),I_1811a) ),
inference(superposition,[status(thm),theory(equality)],[c_11506,c_254]) ).
tff(c_13665,plain,
! [U_1812a: $int] : ( get2(int,mk_array1(int,U_1812a,t2tb2('#skF_3')),'#skF_7') = t2tb(0) ),
inference(superposition,[status(thm),theory(equality)],[c_12833,c_13563]) ).
tff(c_10757,plain,
get(int,int,t2tb2('#skF_3'),t2tb('#skF_4')) = t2tb('#skE_1'),
inference(superposition,[status(thm),theory(equality)],[c_10741,c_255]) ).
tff(c_14408,plain,
! [U_1890a: $int] : ( get2(int,mk_array1(int,U_1890a,t2tb2('#skF_3')),'#skF_4') = t2tb('#skE_1') ),
inference(superposition,[status(thm),theory(equality)],[c_13563,c_10757]) ).
tff(c_13054,plain,
! [J_1751a: $int,A_1752: array_int,I_1753a: $int] :
( ~ $less($sum(J_1751a,tb2t(get2(int,t2tb1(A_1752),J_1751a))),$sum(I_1753a,tb2t(get2(int,t2tb1(A_1752),I_1753a))))
| ~ $less(J_1751a,length1(int,t2tb1(A_1752)))
| ~ decrease11(A_1752)
| $less(I_1753a,0)
| $less(J_1751a,I_1753a) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_82]) ).
tff(c_13066,plain,
! [J_1751a: $int,I_1753a: $int] :
( ~ $less($sum(J_1751a,tb2t(get2(int,t2tb1(tb2t1(mk_array1(int,'#skF_2',t2tb2('#skF_3')))),J_1751a))),$sum(I_1753a,tb2t(get2(int,t2tb1(tb2t1(mk_array1(int,'#skF_2',t2tb2('#skF_3')))),I_1753a))))
| ~ $less(J_1751a,length1(int,t2tb1(tb2t1(mk_array1(int,'#skF_2',t2tb2('#skF_3'))))))
| $less(I_1753a,0)
| $less(J_1751a,I_1753a) ),
inference(resolution,[status(thm)],[c_217,c_13054]) ).
tff(c_13078,plain,
! [J_1751a: $int,I_1753a: $int] :
( ~ $less($sum(J_1751a,tb2t(get2(int,mk_array1(int,'#skF_2',t2tb2('#skF_3')),J_1751a))),$sum(I_1753a,tb2t(get2(int,mk_array1(int,'#skF_2',t2tb2('#skF_3')),I_1753a))))
| ~ $less(J_1751a,'#skF_2')
| $less(I_1753a,0)
| $less(J_1751a,I_1753a) ),
inference(demodulation,[status(thm),theory(equality)],[c_261,c_70,c_70,c_70,c_13066]) ).
tff(c_14429,plain,
! [J_1751a: $int] :
( ~ $less($sum(J_1751a,tb2t(get2(int,mk_array1(int,'#skF_2',t2tb2('#skF_3')),J_1751a))),$sum('#skF_4',tb2t(t2tb('#skE_1'))))
| ~ $less(J_1751a,'#skF_2')
| $less('#skF_4',0)
| $less(J_1751a,'#skF_4') ),
inference(superposition,[status(thm),theory(equality)],[c_14408,c_13078]) ).
tff(c_14486,plain,
! [J_1751a: $int] :
( ~ $less($sum(J_1751a,tb2t(get2(int,mk_array1(int,'#skF_2',t2tb2('#skF_3')),J_1751a))),$sum('#skF_4','#skE_1'))
| ~ $less(J_1751a,'#skF_2')
| $less('#skF_4',0)
| $less(J_1751a,'#skF_4') ),
inference(demodulation,[status(thm),theory(equality)],[c_256,c_14429]) ).
tff(c_14944,plain,
! [J_1938a: $int] :
( ~ $less($sum(J_1938a,tb2t(get2(int,mk_array1(int,'#skF_2',t2tb2('#skF_3')),J_1938a))),$sum('#skF_4','#skE_1'))
| ~ $less(J_1938a,'#skF_2')
| $less(J_1938a,'#skF_4') ),
inference(negUnitSimplification,[status(thm)],[c_218,c_14486]) ).
tff(c_14950,plain,
( ~ $less($sum('#skF_7',tb2t(t2tb(0))),$sum('#skF_4','#skE_1'))
| ~ $less('#skF_7','#skF_2')
| $less('#skF_7','#skF_4') ),
inference(superposition,[status(thm),theory(equality)],[c_13665,c_14944]) ).
tff(c_14960,plain,
( ~ $less($sum('#skF_7',0),$sum('#skF_4','#skE_1'))
| ~ $less('#skF_7','#skF_2')
| $less('#skF_7','#skF_4') ),
inference(demodulation,[status(thm),theory(equality)],[c_256,c_14950]) ).
tff(c_14961,plain,
( ~ $less($sum('#skF_7',0),$sum('#skF_4','#skE_1'))
| ~ $less('#skF_7','#skF_2') ),
inference(negUnitSimplification,[status(thm)],[c_12353,c_14960]) ).
tff(c_14963,plain,
( ~ $less('#skF_7',$sum('#skF_4','#skE_1'))
| ~ $less('#skF_7','#skF_2') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_14961]) ).
tff(c_14972,plain,
~ $less('#skF_7','#skF_2'),
inference(demodulation,[status(thm),theory(equality)],[c_12909,c_14963]) ).
tff(c_14973,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_14972,c_12099,c_10541]) ).
tff(c_14976,plain,
$less('#skF_5','#skF_4'),
inference(splitRight,[status(thm)],[c_12351]) ).
tff(c_15102,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_15101,c_14976,c_10566]) ).
tff(c_15105,plain,
$less('#skF_5','#skF_4'),
inference(splitRight,[status(thm)],[c_12097]) ).
tff(c_15571,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_15570,c_15105,c_10566]) ).
tff(c_15574,plain,
'#skF_5' != $uminus(1),
inference(splitRight,[status(thm)],[c_195]) ).
tff(c_15676,plain,
tb2t(get(int,int,t2tb2('#skF_3'),t2tb('#skF_4'))) = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_225]) ).
tff(c_17285,plain,
get(int,int,t2tb2('#skF_3'),t2tb('#skF_4')) = t2tb('#skE_1'),
inference(superposition,[status(thm),theory(equality)],[c_15676,c_255]) ).
tff(c_20794,plain,
( ~ $less('#skF_5',$sum('#skF_4','#skE_1'))
| ( '#skF_5' = $uminus(1) ) ),
inference(demodulation,[status(thm),theory(equality)],[c_256,c_17285,c_169]) ).
tff(c_20796,plain,
~ $less('#skF_5',$sum('#skF_4','#skE_1')),
inference(negUnitSimplification,[status(thm)],[c_15574,c_20794]) ).
tff(c_20312,plain,
( ~ $less('#skF_5',$sum('#skF_4','#skE_1'))
| ( '#skF_5' = $uminus(1) ) ),
inference(demodulation,[status(thm),theory(equality)],[c_256,c_17285,c_169]) ).
tff(c_20314,plain,
~ $less('#skF_5',$sum('#skF_4','#skE_1')),
inference(negUnitSimplification,[status(thm)],[c_15574,c_20312]) ).
tff(c_15583,plain,
$less('#skF_5','#skF_2'),
inference(negUnitSimplification,[status(thm)],[c_15574,c_174]) ).
tff(c_16470,plain,
tb2t(get(int,int,t2tb2('#skF_3'),t2tb('#skF_5'))) = 0,
inference(negUnitSimplification,[status(thm)],[c_15574,c_182]) ).
tff(c_16596,plain,
get(int,int,t2tb2('#skF_3'),t2tb('#skF_5')) = t2tb(0),
inference(superposition,[status(thm),theory(equality)],[c_16470,c_255]) ).
tff(c_17016,plain,
( $less('#skF_5','#skF_4')
| $less('#skF_7','#skF_5') ),
inference(demodulation,[status(thm),theory(equality)],[c_15583,c_256,c_16596,c_208]) ).
tff(c_17018,plain,
$less('#skF_7','#skF_5'),
inference(splitLeft,[status(thm)],[c_17016]) ).
tff(c_17660,plain,
( ( tb2t(get(int,int,t2tb2('#skF_3'),t2tb('#skF_7'))) = 0 )
| $less('#skF_5','#skF_4') ),
inference(demodulation,[status(thm),theory(equality)],[c_15583,c_256,c_16596,c_212]) ).
tff(c_17662,plain,
tb2t(get(int,int,t2tb2('#skF_3'),t2tb('#skF_7'))) = '#skE_3',
inference(define,[status(thm),theory(equality)],[c_17660]) ).
tff(c_17661,plain,
( ( tb2t(get(int,int,t2tb2('#skF_3'),t2tb('#skF_7'))) = 0 )
| $less('#skF_5','#skF_4') ),
inference(demodulation,[status(thm),theory(equality)],[c_15583,c_256,c_16596,c_212]) ).
tff(c_17669,plain,
( ( '#skE_3' = 0 )
| $less('#skF_5','#skF_4') ),
inference(demodulation,[status(thm),theory(equality)],[c_17662,c_17661]) ).
tff(c_17671,plain,
$less('#skF_5','#skF_4'),
inference(splitLeft,[status(thm)],[c_17669]) ).
tff(c_17497,plain,
( ~ $less('#skF_5',$sum('#skF_4','#skE_1'))
| ( '#skF_5' = $uminus(1) ) ),
inference(demodulation,[status(thm),theory(equality)],[c_256,c_17285,c_169]) ).
tff(c_17499,plain,
~ $less('#skF_5',$sum('#skF_4','#skE_1')),
inference(negUnitSimplification,[status(thm)],[c_15574,c_17497]) ).
tff(c_15586,plain,
tb2t(get(int,int,t2tb2('#skF_3'),t2tb('#skF_4'))) = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_231]) ).
tff(c_15593,plain,
$less(0,'#skE_1'),
inference(demodulation,[status(thm),theory(equality)],[c_15586,c_305]) ).
tff(c_17672,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_17671,c_17499,c_15593]) ).
tff(c_17675,plain,
'#skE_3' = 0,
inference(splitRight,[status(thm)],[c_17669]) ).
tff(c_17668,plain,
tb2t(get(int,int,t2tb2('#skF_3'),t2tb('#skF_7'))) = '#skE_3',
inference(define,[status(thm),theory(equality)],[c_17660]) ).
tff(c_17684,plain,
tb2t(get(int,int,t2tb2('#skF_3'),t2tb('#skF_7'))) = 0,
inference(demodulation,[status(thm),theory(equality)],[c_17675,c_17668]) ).
tff(c_17705,plain,
get(int,int,t2tb2('#skF_3'),t2tb('#skF_7')) = t2tb(0),
inference(superposition,[status(thm),theory(equality)],[c_17684,c_255]) ).
tff(c_17818,plain,
! [J_119a: $int] :
( ( tb2t(get(int,int,t2tb2('#skF_3'),t2tb(J_119a))) != 0 )
| $less(J_119a,$sum('#skF_4','#skE_1'))
| ~ $less(J_119a,'#skF_5')
| ( '#skF_5' = $uminus(1) ) ),
inference(demodulation,[status(thm),theory(equality)],[c_256,c_17285,c_190]) ).
tff(c_17821,plain,
! [J_2193a: $int] :
( ( tb2t(get(int,int,t2tb2('#skF_3'),t2tb(J_2193a))) != 0 )
| $less(J_2193a,$sum('#skF_4','#skE_1'))
| ~ $less(J_2193a,'#skF_5') ),
inference(negUnitSimplification,[status(thm)],[c_15574,c_17818]) ).
tff(c_17824,plain,
( ( tb2t(t2tb(0)) != 0 )
| $less('#skF_7',$sum('#skF_4','#skE_1'))
| ~ $less('#skF_7','#skF_5') ),
inference(superposition,[status(thm),theory(equality)],[c_17705,c_17821]) ).
tff(c_17834,plain,
$less('#skF_7',$sum('#skF_4','#skE_1')),
inference(demodulation,[status(thm),theory(equality)],[c_17018,c_256,c_17824]) ).
tff(c_17280,plain,
( $less('#skF_5','#skF_4')
| ~ $less('#skF_7','#skF_4') ),
inference(demodulation,[status(thm),theory(equality)],[c_15583,c_256,c_16596,c_204]) ).
tff(c_17282,plain,
~ $less('#skF_7','#skF_4'),
inference(splitLeft,[status(thm)],[c_17280]) ).
tff(c_15577,plain,
! [X_1982: map_int_int] : sort1(map(int,int),t2tb2(X_1982)),
inference(cnfTransformation,[status(thm)],[f_150]) ).
tff(c_15579,plain,
! [J_104: uni] : sort1(map(int,int),J_104),
inference(superposition,[status(thm),theory(equality)],[c_89,c_15577]) ).
tff(c_16411,plain,
! [A_2077: ty,U_2078a: $int,U1_2079: uni] :
( ( elts(A_2077,mk_array1(A_2077,U_2078a,U1_2079)) = U1_2079 )
| ~ sort1(map(int,A_2077),U1_2079) ),
inference(cnfTransformation,[status(thm)],[f_102]) ).
tff(c_16458,plain,
! [U_2078a: $int,J_104: uni] : ( elts(int,mk_array1(int,U_2078a,J_104)) = J_104 ),
inference(resolution,[status(thm)],[c_15579,c_16411]) ).
tff(c_16719,plain,
! [A_2105: ty,A1_2106: uni,I_2107a: $int] : ( get(A_2105,int,elts(A_2105,A1_2106),t2tb(I_2107a)) = get2(A_2105,A1_2106,I_2107a) ),
inference(cnfTransformation,[status(thm)],[f_114]) ).
tff(c_18599,plain,
! [J_2270: uni,I_2271a: $int,U_2272a: $int] : ( get(int,int,J_2270,t2tb(I_2271a)) = get2(int,mk_array1(int,U_2272a,J_2270),I_2271a) ),
inference(superposition,[status(thm),theory(equality)],[c_16458,c_16719]) ).
tff(c_18684,plain,
! [U_2272a: $int] : ( get2(int,mk_array1(int,U_2272a,t2tb2('#skF_3')),'#skF_7') = t2tb(0) ),
inference(superposition,[status(thm),theory(equality)],[c_18599,c_17705]) ).
tff(c_15692,plain,
get(int,int,t2tb2('#skF_3'),t2tb('#skF_4')) = t2tb('#skE_1'),
inference(superposition,[status(thm),theory(equality)],[c_15676,c_255]) ).
tff(c_20007,plain,
! [U_2388a: $int] : ( get2(int,mk_array1(int,U_2388a,t2tb2('#skF_3')),'#skF_4') = t2tb('#skE_1') ),
inference(superposition,[status(thm),theory(equality)],[c_15692,c_18599]) ).
tff(c_17968,plain,
! [J_2203a: $int,A_2204: array_int,I_2205a: $int] :
( ~ $less($sum(J_2203a,tb2t(get2(int,t2tb1(A_2204),J_2203a))),$sum(I_2205a,tb2t(get2(int,t2tb1(A_2204),I_2205a))))
| ~ $less(J_2203a,length1(int,t2tb1(A_2204)))
| ~ decrease11(A_2204)
| $less(I_2205a,0)
| $less(J_2203a,I_2205a) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_82]) ).
tff(c_17980,plain,
! [J_2203a: $int,I_2205a: $int] :
( ~ $less($sum(J_2203a,tb2t(get2(int,t2tb1(tb2t1(mk_array1(int,'#skF_2',t2tb2('#skF_3')))),J_2203a))),$sum(I_2205a,tb2t(get2(int,t2tb1(tb2t1(mk_array1(int,'#skF_2',t2tb2('#skF_3')))),I_2205a))))
| ~ $less(J_2203a,length1(int,t2tb1(tb2t1(mk_array1(int,'#skF_2',t2tb2('#skF_3'))))))
| $less(I_2205a,0)
| $less(J_2203a,I_2205a) ),
inference(resolution,[status(thm)],[c_217,c_17968]) ).
tff(c_17992,plain,
! [J_2203a: $int,I_2205a: $int] :
( ~ $less($sum(J_2203a,tb2t(get2(int,mk_array1(int,'#skF_2',t2tb2('#skF_3')),J_2203a))),$sum(I_2205a,tb2t(get2(int,mk_array1(int,'#skF_2',t2tb2('#skF_3')),I_2205a))))
| ~ $less(J_2203a,'#skF_2')
| $less(I_2205a,0)
| $less(J_2203a,I_2205a) ),
inference(demodulation,[status(thm),theory(equality)],[c_261,c_70,c_70,c_70,c_17980]) ).
tff(c_20028,plain,
! [J_2203a: $int] :
( ~ $less($sum(J_2203a,tb2t(get2(int,mk_array1(int,'#skF_2',t2tb2('#skF_3')),J_2203a))),$sum('#skF_4',tb2t(t2tb('#skE_1'))))
| ~ $less(J_2203a,'#skF_2')
| $less('#skF_4',0)
| $less(J_2203a,'#skF_4') ),
inference(superposition,[status(thm),theory(equality)],[c_20007,c_17992]) ).
tff(c_20085,plain,
! [J_2203a: $int] :
( ~ $less($sum(J_2203a,tb2t(get2(int,mk_array1(int,'#skF_2',t2tb2('#skF_3')),J_2203a))),$sum('#skF_4','#skE_1'))
| ~ $less(J_2203a,'#skF_2')
| $less('#skF_4',0)
| $less(J_2203a,'#skF_4') ),
inference(demodulation,[status(thm),theory(equality)],[c_256,c_20028]) ).
tff(c_20205,plain,
! [J_2419a: $int] :
( ~ $less($sum(J_2419a,tb2t(get2(int,mk_array1(int,'#skF_2',t2tb2('#skF_3')),J_2419a))),$sum('#skF_4','#skE_1'))
| ~ $less(J_2419a,'#skF_2')
| $less(J_2419a,'#skF_4') ),
inference(negUnitSimplification,[status(thm)],[c_218,c_20085]) ).
tff(c_20214,plain,
( ~ $less($sum('#skF_7',tb2t(t2tb(0))),$sum('#skF_4','#skE_1'))
| ~ $less('#skF_7','#skF_2')
| $less('#skF_7','#skF_4') ),
inference(superposition,[status(thm),theory(equality)],[c_18684,c_20205]) ).
tff(c_20227,plain,
( ~ $less($sum('#skF_7',0),$sum('#skF_4','#skE_1'))
| ~ $less('#skF_7','#skF_2')
| $less('#skF_7','#skF_4') ),
inference(demodulation,[status(thm),theory(equality)],[c_256,c_20214]) ).
tff(c_20228,plain,
( ~ $less($sum('#skF_7',0),$sum('#skF_4','#skE_1'))
| ~ $less('#skF_7','#skF_2') ),
inference(negUnitSimplification,[status(thm)],[c_17282,c_20227]) ).
tff(c_20230,plain,
( ~ $less('#skF_7',$sum('#skF_4','#skE_1'))
| ~ $less('#skF_7','#skF_2') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_20228]) ).
tff(c_20233,plain,
~ $less('#skF_7','#skF_2'),
inference(demodulation,[status(thm),theory(equality)],[c_17834,c_20230]) ).
tff(c_20234,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_20233,c_17018,c_15583]) ).
tff(c_20237,plain,
$less('#skF_5','#skF_4'),
inference(splitRight,[status(thm)],[c_17280]) ).
tff(c_20315,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_20314,c_20237,c_15593]) ).
tff(c_20318,plain,
$less('#skF_5','#skF_4'),
inference(splitRight,[status(thm)],[c_17016]) ).
tff(c_20797,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_20796,c_20318,c_15593]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13 % Problem : SWW584_2 : TPTP v8.1.2. Released v6.1.0.
% 0.13/0.14 % 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
% 0.14/0.36 % Computer : n003.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Thu Aug 3 19:17:38 EDT 2023
% 0.14/0.36 % CPUTime :
% 15.95/5.05 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 15.95/5.08
% 15.95/5.08 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 16.44/5.12
% 16.44/5.12 Inference rules
% 16.44/5.12 ----------------------
% 16.44/5.12 #Ref : 0
% 16.44/5.12 #Sup : 4191
% 16.44/5.12 #Fact : 1
% 16.44/5.12 #Define : 10
% 16.44/5.12 #Split : 39
% 16.44/5.12 #Chain : 0
% 16.44/5.12 #Close : 13
% 16.44/5.12
% 16.44/5.12 Ordering : LPO
% 16.44/5.12
% 16.44/5.12 Simplification rules
% 16.44/5.12 ----------------------
% 16.44/5.12 #Subsume : 288
% 16.44/5.12 #Demod : 3347
% 16.44/5.12 #Tautology : 2941
% 16.44/5.12 #SimpNegUnit : 44
% 16.44/5.12 #BackRed : 17
% 16.44/5.12
% 16.44/5.12 #Partial instantiations: 508
% 16.44/5.12 #Strategies tried : 1
% 16.44/5.12
% 16.44/5.12 Timing (in seconds)
% 16.44/5.12 ----------------------
% 16.44/5.13 Preprocessing : 0.80
% 16.44/5.13 Parsing : 0.41
% 16.44/5.13 CNF conversion : 0.06
% 16.44/5.13 Main loop : 3.13
% 16.44/5.13 Inferencing : 0.89
% 16.44/5.13 Reduction : 1.05
% 16.44/5.13 Demodulation : 0.85
% 16.44/5.13 BG Simplification : 0.24
% 16.44/5.13 Subsumption : 0.49
% 16.44/5.13 Abstraction : 0.12
% 16.44/5.13 MUC search : 0.14
% 16.44/5.13 Cooper : 0.28
% 16.44/5.13 Total : 4.01
% 16.44/5.13 Index Insertion : 0.00
% 16.44/5.13 Index Deletion : 0.00
% 16.44/5.13 Index Matching : 0.00
% 16.44/5.13 BG Taut test : 0.00
%------------------------------------------------------------------------------