TSTP Solution File: SWW598_2 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SWW598_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 : n011.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 107.92s 72.07s
% Output : CNFRefutation 108.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 75
% Syntax : Number of formulae : 828 ( 394 unt; 66 typ; 0 def)
% Number of atoms : 1740 ( 610 equ)
% Maximal formula atoms : 46 ( 2 avg)
% Number of connectives : 1645 ( 667 ~; 927 |; 27 &)
% ( 1 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 32 ( 3 avg)
% Maximal term depth : 8 ( 1 avg)
% Number arithmetic : 1458 ( 609 atm; 401 fun; 248 num; 200 var)
% Number of types : 7 ( 5 usr; 1 ari)
% Number of type conns : 24 ( 12 >; 12 *; 0 +; 0 <<)
% Number of predicates : 6 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 64 ( 59 usr; 52 con; 0-4 aty)
% Number of variables : 260 (; 260 !; 0 ?; 260 :)
% Comments :
%------------------------------------------------------------------------------
%$ sort > mem > match_tree > match_bool > node > min > max > #nlpp > witness > size > node_proj_3 > node_proj_2 > node_proj_1 > tuple02 > tuple01 > true > tree1 > real > qtmark > int > false > empty > bool1 > #skF_18 > #skF_8 > #skF_4 > #skF_6 > #skF_13 > #skF_2 > #skF_1 > #skF_16 > #skF_11
%Foreground sorts:
tff(tree,type,
tree: $tType ).
tff(bool,type,
bool: $tType ).
tff(tuple0,type,
tuple0: $tType ).
tff(ty,type,
ty: $tType ).
tff(uni,type,
uni: $tType ).
%Background operators:
tff('#skE_7',type,
'#skE_7': $int ).
tff('#skE_11',type,
'#skE_11': $int ).
tff('#skE_12',type,
'#skE_12': $int ).
tff('#skF_14',type,
'#skF_14': $int ).
tff('#skE_2',type,
'#skE_2': $int ).
tff('#skE_1',type,
'#skE_1': $int ).
tff('#skF_20',type,
'#skF_20': $int ).
tff('#skE_6',type,
'#skE_6': $int ).
tff('#skF_15',type,
'#skF_15': $int ).
tff('#skE_13',type,
'#skE_13': $int ).
tff('#skF_17',type,
'#skF_17': $int ).
tff('#skE_10',type,
'#skE_10': $int ).
tff('#skE_5',type,
'#skE_5': $int ).
tff('#skF_21',type,
'#skF_21': $int ).
tff('#skE_15',type,
'#skE_15': $int ).
tff('#skE_8',type,
'#skE_8': $int ).
tff('#skE_4',type,
'#skE_4': $int ).
tff('#skF_5',type,
'#skF_5': $int ).
tff('#skF_10',type,
'#skF_10': $int ).
tff('#skF_3',type,
'#skF_3': $int ).
tff('#skF_12',type,
'#skF_12': $int ).
tff('#skE_16',type,
'#skE_16': $int ).
tff('#skE_17',type,
'#skE_17': $int ).
tff('#skE_3',type,
'#skE_3': $int ).
tff('#skF_7',type,
'#skF_7': $int ).
tff('#skE_9',type,
'#skE_9': $int ).
tff('#skF_19',type,
'#skF_19': $int ).
tff('#skF_9',type,
'#skF_9': $int ).
tff('#skE_18',type,
'#skE_18': $int ).
tff('#skE_14',type,
'#skE_14': $int ).
%Foreground operators:
tff(node_proj_1,type,
node_proj_1: tree > tree ).
tff('#skF_18',type,
'#skF_18': tree ).
tff('#skF_8',type,
'#skF_8': tree ).
tff(tuple02,type,
tuple02: tuple0 ).
tff('#skF_4',type,
'#skF_4': tree ).
tff(tuple01,type,
tuple01: ty ).
tff(int,type,
int: ty ).
tff(node_proj_2,type,
node_proj_2: tree > $int ).
tff(tree1,type,
tree1: ty ).
tff('#skF_6',type,
'#skF_6': tree ).
tff(empty,type,
empty: tree ).
tff('#skF_13',type,
'#skF_13': tree ).
tff('#skF_2',type,
'#skF_2': tree ).
tff(real,type,
real: ty ).
tff(match_bool,type,
match_bool: ( ty * bool * uni * uni ) > uni ).
tff(false,type,
false: bool ).
tff(match_tree,type,
match_tree: ( ty * tree * uni * uni ) > uni ).
tff('#skF_1',type,
'#skF_1': tree ).
tff(max,type,
max: ( $int * $int ) > $int ).
tff('#skF_16',type,
'#skF_16': tree ).
tff(qtmark,type,
qtmark: ty ).
tff(bool1,type,
bool1: ty ).
tff(node,type,
node: ( tree * $int * tree ) > tree ).
tff('#skF_11',type,
'#skF_11': tree ).
tff(mem,type,
mem: ( $int * tree ) > $o ).
tff(sort,type,
sort: ( ty * uni ) > $o ).
tff(true,type,
true: bool ).
tff(size,type,
size: tree > $int ).
tff(witness,type,
witness: ty > uni ).
tff(node_proj_3,type,
node_proj_3: tree > tree ).
tff(min,type,
min: ( $int * $int ) > $int ).
tff(f_249,negated_conjecture,
~ ! [T: tree] :
( ( T != empty )
=> ( ( ( T = empty )
=> $false )
& ! [X: tree,X1a: $int,X2: tree] :
( ( T = node(X,X1a,X2) )
=> ( ( ( X2 = empty )
=> ( ( ( X = empty )
=> ( mem(X1a,T)
& ! [X3a: $int] :
( mem(X3a,T)
=> $lesseq(X3a,X1a) ) ) )
& ! [W: tree,W1a: $int,W2: tree] :
( ( X = node(W,W1a,W2) )
=> ( $lesseq(0,size(T))
& $less(size(X),size(T))
& ( X != empty )
& ! [Oa: $int] :
( ( mem(Oa,X)
& ! [X3a: $int] :
( mem(X3a,X)
=> $lesseq(X3a,Oa) ) )
=> ( mem(max(Oa,X1a),T)
& ! [X3a: $int] :
( mem(X3a,T)
=> $lesseq(X3a,max(Oa,X1a)) ) ) ) ) ) ) )
& ! [W: tree,W1a: $int,W2: tree] :
( ( X2 = node(W,W1a,W2) )
=> ( ( ( X = empty )
=> ( $lesseq(0,size(T))
& $less(size(X2),size(T))
& ( X2 != empty )
& ! [Oa: $int] :
( ( mem(Oa,X2)
& ! [X3a: $int] :
( mem(X3a,X2)
=> $lesseq(X3a,Oa) ) )
=> ( mem(max(Oa,X1a),T)
& ! [X3a: $int] :
( mem(X3a,T)
=> $lesseq(X3a,max(Oa,X1a)) ) ) ) ) )
& ! [W3: tree,W4a: $int,W5: tree] :
( ( X = node(W3,W4a,W5) )
=> ( $lesseq(0,size(T))
& $less(size(X2),size(T))
& ( X2 != empty )
& ! [Oa: $int] :
( ( mem(Oa,X2)
& ! [X3a: $int] :
( mem(X3a,X2)
=> $lesseq(X3a,Oa) ) )
=> ( $lesseq(0,size(T))
& $less(size(X),size(T))
& ( X != empty )
& ! [O1a: $int] :
( ( mem(O1a,X)
& ! [X3a: $int] :
( mem(X3a,X)
=> $lesseq(X3a,O1a) ) )
=> ( mem(max(O1a,max(X1a,Oa)),T)
& ! [X3a: $int] :
( mem(X3a,T)
=> $lesseq(X3a,max(O1a,max(X1a,Oa))) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',wP_parameter_maximum) ).
tff(f_107,axiom,
! [V: tree,V1a: $int,V2: tree] : ( empty != node(V,V1a,V2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_Node) ).
tff(f_135,axiom,
! [Xa: $int] :
( ~ mem(Xa,empty)
& ! [X1: tree,X2a: $int,X3: tree] :
( mem(Xa,node(X1,X2a,X3))
<=> ( mem(Xa,X1)
| ( Xa = X2a )
| mem(Xa,X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mem_def) ).
tff(f_121,axiom,
( ( size(empty) = 0 )
& ! [X: tree,X1a: $int,X2: tree] : ( size(node(X,X1a,X2)) = $sum($sum(1,size(X)),size(X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',size_def) ).
tff(f_123,axiom,
! [T: tree] : $lesseq(0,size(T)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',size_nonneg) ).
tff(f_62,axiom,
! [Xa: $int,Ya: $int] :
( ( max(Xa,Ya) = Xa )
| ( max(Xa,Ya) = Ya ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',max_is_some) ).
tff(f_78,axiom,
! [Xa: $int,Ya: $int] :
( $lesseq(Xa,Ya)
=> ( max(Xa,Ya) = Ya ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',max_y) ).
tff(f_58,axiom,
! [Xa: $int,Ya: $int] :
( $lesseq(Xa,max(Xa,Ya))
& $lesseq(Ya,max(Xa,Ya)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',max_is_ge) ).
tff(f_74,axiom,
! [Xa: $int,Ya: $int] :
( $lesseq(Ya,Xa)
=> ( max(Xa,Ya) = Xa ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',max_x) ).
tff(c_79,plain,
empty != '#skF_1',
inference(cnfTransformation,[status(thm)],[f_249]) ).
tff(c_1503,plain,
( ( empty = '#skF_4' )
| ( node('#skF_11','#skF_12','#skF_13') = '#skF_4' )
| ( empty = '#skF_1' ) ),
inference(cnfTransformation,[status(thm)],[f_249]) ).
tff(c_4913,plain,
( ( empty = '#skF_4' )
| ( node('#skF_11','#skF_12','#skF_13') = '#skF_4' ) ),
inference(negUnitSimplification,[status(thm)],[c_79,c_1503]) ).
tff(c_5549,plain,
empty = '#skF_4',
inference(splitLeft,[status(thm)],[c_4913]) ).
tff(c_3737,plain,
! [V_50: tree,V1_51a: $int,V2_52: tree] : ( node(V_50,V1_51a,V2_52) != empty ),
inference(cnfTransformation,[status(thm)],[f_107]) ).
tff(c_5557,plain,
! [V_50: tree,V1_51a: $int,V2_52: tree] : ( node(V_50,V1_51a,V2_52) != '#skF_4' ),
inference(demodulation,[status(thm),theory(equality)],[c_5549,c_3737]) ).
tff(c_1451,plain,
( ( empty = '#skF_2' )
| ( node('#skF_6','#skF_7','#skF_8') = '#skF_2' )
| ( node('#skF_11','#skF_12','#skF_13') = '#skF_4' )
| ( empty = '#skF_1' ) ),
inference(cnfTransformation,[status(thm)],[f_249]) ).
tff(c_4909,plain,
( ( empty = '#skF_2' )
| ( node('#skF_6','#skF_7','#skF_8') = '#skF_2' )
| ( node('#skF_11','#skF_12','#skF_13') = '#skF_4' ) ),
inference(negUnitSimplification,[status(thm)],[c_79,c_1451]) ).
tff(c_5923,plain,
( ( '#skF_4' = '#skF_2' )
| ( node('#skF_6','#skF_7','#skF_8') = '#skF_2' )
| ( node('#skF_11','#skF_12','#skF_13') = '#skF_4' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_5549,c_4909]) ).
tff(c_5927,plain,
( ( '#skF_4' = '#skF_2' )
| ( node('#skF_6','#skF_7','#skF_8') = '#skF_2' ) ),
inference(negUnitSimplification,[status(thm)],[c_5557,c_5923]) ).
tff(c_5929,plain,
'#skF_4' = '#skF_2',
inference(splitLeft,[status(thm)],[c_5927]) ).
tff(c_5944,plain,
! [V_50: tree,V1_51a: $int,V2_52: tree] : ( node(V_50,V1_51a,V2_52) != '#skF_2' ),
inference(demodulation,[status(thm),theory(equality)],[c_5929,c_5557]) ).
tff(c_3723,plain,
( ( node('#skF_2','#skF_3','#skF_4') = '#skF_1' )
| ( empty = '#skF_1' ) ),
inference(cnfTransformation,[status(thm)],[f_249]) ).
tff(c_4905,plain,
node('#skF_2','#skF_3','#skF_4') = '#skF_1',
inference(negUnitSimplification,[status(thm)],[c_79,c_3723]) ).
tff(c_5542,plain,
! [X2_8253a: $int,X1_8254: tree,X3_8255: tree] : mem(X2_8253a,node(X1_8254,X2_8253a,X3_8255)),
inference(cnfTransformation,[status(thm)],[f_135]) ).
tff(c_5598,plain,
mem('#skF_3','#skF_1'),
inference(superposition,[status(thm),theory(equality)],[c_4905,c_5542]) ).
tff(c_1443,plain,
( mem('#skF_5','#skF_1')
| ~ mem('#skF_3','#skF_1')
| ( node('#skF_6','#skF_7','#skF_8') = '#skF_2' )
| ( node('#skF_11','#skF_12','#skF_13') = '#skF_4' )
| ( empty = '#skF_1' ) ),
inference(cnfTransformation,[status(thm)],[f_249]) ).
tff(c_4967,plain,
( mem('#skF_5','#skF_1')
| ~ mem('#skF_3','#skF_1')
| ( node('#skF_6','#skF_7','#skF_8') = '#skF_2' )
| ( node('#skF_11','#skF_12','#skF_13') = '#skF_4' ) ),
inference(negUnitSimplification,[status(thm)],[c_79,c_1443]) ).
tff(c_6579,plain,
( mem('#skF_5','#skF_1')
| ( node('#skF_6','#skF_7','#skF_8') = '#skF_2' )
| ( node('#skF_11','#skF_12','#skF_13') = '#skF_2' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_5929,c_5598,c_4967]) ).
tff(c_6583,plain,
mem('#skF_5','#skF_1'),
inference(negUnitSimplification,[status(thm)],[c_5944,c_5944,c_6579]) ).
tff(c_3728,plain,
! [X_67a: $int] : ~ mem(X_67a,empty),
inference(cnfTransformation,[status(thm)],[f_135]) ).
tff(c_5559,plain,
! [X_67a: $int] : ~ mem(X_67a,'#skF_4'),
inference(demodulation,[status(thm),theory(equality)],[c_5549,c_3728]) ).
tff(c_5945,plain,
! [X_67a: $int] : ~ mem(X_67a,'#skF_2'),
inference(demodulation,[status(thm),theory(equality)],[c_5929,c_5559]) ).
tff(c_5949,plain,
node('#skF_2','#skF_3','#skF_2') = '#skF_1',
inference(demodulation,[status(thm),theory(equality)],[c_5929,c_4905]) ).
tff(c_7059,plain,
! [X_8374a: $int,X3_8375: tree,X1_8376: tree,X2_8377a: $int] :
( mem(X_8374a,X3_8375)
| mem(X_8374a,X1_8376)
| ~ mem(X_8374a,node(X1_8376,X2_8377a,X3_8375))
| ( X_8374a = X2_8377a ) ),
inference(cnfTransformation,[status(thm)],[f_135]) ).
tff(c_7068,plain,
! [X_8374a: $int] :
( mem(X_8374a,'#skF_2')
| ~ mem(X_8374a,'#skF_1')
| ( X_8374a = '#skF_3' ) ),
inference(superposition,[status(thm),theory(equality)],[c_5949,c_7059]) ).
tff(c_7083,plain,
! [X_8378a: $int] :
( ~ mem(X_8378a,'#skF_1')
| ( X_8378a = '#skF_3' ) ),
inference(negUnitSimplification,[status(thm)],[c_5945,c_5945,c_7068]) ).
tff(c_7091,plain,
'#skF_5' = '#skF_3',
inference(resolution,[status(thm)],[c_6583,c_7083]) ).
tff(c_1413,plain,
( ~ mem('#skF_3','#skF_1')
| ( node('#skF_6','#skF_7','#skF_8') = '#skF_2' )
| ( node('#skF_11','#skF_12','#skF_13') = '#skF_4' )
| ( empty = '#skF_1' )
| ~ $lesseq('#skF_5','#skF_3') ),
inference(cnfTransformation,[status(thm)],[f_249]) ).
tff(c_1447,plain,
( ~ mem('#skF_3','#skF_1')
| ( node('#skF_6','#skF_7','#skF_8') = '#skF_2' )
| ( node('#skF_11','#skF_12','#skF_13') = '#skF_4' )
| ( empty = '#skF_1' )
| $less('#skF_3','#skF_5') ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_1413]) ).
tff(c_4959,plain,
( ~ mem('#skF_3','#skF_1')
| ( node('#skF_6','#skF_7','#skF_8') = '#skF_2' )
| ( node('#skF_11','#skF_12','#skF_13') = '#skF_4' )
| $less('#skF_3','#skF_5') ),
inference(negUnitSimplification,[status(thm)],[c_79,c_1447]) ).
tff(c_6391,plain,
( ( node('#skF_6','#skF_7','#skF_8') = '#skF_2' )
| ( node('#skF_11','#skF_12','#skF_13') = '#skF_2' )
| $less('#skF_3','#skF_5') ),
inference(demodulation,[status(thm),theory(equality)],[c_5929,c_5598,c_4959]) ).
tff(c_6394,plain,
$less('#skF_3','#skF_5'),
inference(negUnitSimplification,[status(thm)],[c_5944,c_5944,c_6391]) ).
tff(c_7100,plain,
$less('#skF_3','#skF_3'),
inference(demodulation,[status(thm),theory(equality)],[c_7091,c_6394]) ).
tff(c_7105,plain,
$false,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_7100]) ).
tff(c_7107,plain,
'#skF_4' != '#skF_2',
inference(splitRight,[status(thm)],[c_5927]) ).
tff(c_3730,plain,
size(empty) = 0,
inference(cnfTransformation,[status(thm)],[f_121]) ).
tff(c_5558,plain,
size('#skF_4') = 0,
inference(demodulation,[status(thm),theory(equality)],[c_5549,c_3730]) ).
tff(c_62,plain,
! [X_63: tree,X1_64a: $int,X2_65: tree] : ( size(node(X_63,X1_64a,X2_65)) = $sum($sum(1,size(X_63)),size(X2_65)) ),
inference(cnfTransformation,[status(thm)],[f_121]) ).
tff(c_63,plain,
! [X_63: tree,X1_64a: $int,X2_65: tree] : ( size(node(X_63,X1_64a,X2_65)) = $sum(1,$sum(size(X_63),size(X2_65))) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_62]) ).
tff(c_8114,plain,
! [X_8458: tree,X1_8459a: $int,X2_8460: tree] : ( size(node(X_8458,X1_8459a,X2_8460)) = $sum(1,$sum(size(X2_8460),size(X_8458))) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_63]) ).
tff(c_8128,plain,
$sum(1,$sum(size('#skF_4'),size('#skF_2'))) = size('#skF_1'),
inference(superposition,[status(thm),theory(equality)],[c_4905,c_8114]) ).
tff(c_8139,plain,
$sum(1,$sum(0,size('#skF_2'))) = size('#skF_1'),
inference(demodulation,[status(thm),theory(equality)],[c_5558,c_8128]) ).
tff(c_8141,plain,
size('#skF_2') = $sum($uminus(1),size('#skF_1')),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_8139]) ).
tff(c_8146,plain,
size('#skF_2') = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_8141]) ).
tff(c_8143,plain,
size('#skF_1') = '#skE_2',
inference(define,[status(thm),theory(equality)],[c_8141]) ).
tff(c_8142,plain,
size('#skF_2') = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_8141]) ).
tff(c_8145,plain,
$sum($uminus(1),'#skE_2') = '#skE_1',
inference(demodulation,[status(thm),theory(equality)],[c_8143,c_8142,c_8141]) ).
tff(c_8149,plain,
'#skE_2' = $sum(1,'#skE_1'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_8145]) ).
tff(c_8147,plain,
size('#skF_1') = '#skE_2',
inference(define,[status(thm),theory(equality)],[c_8141]) ).
tff(c_8175,plain,
size('#skF_1') = $sum(1,'#skE_1'),
inference(demodulation,[status(thm),theory(equality)],[c_8149,c_8147]) ).
tff(c_67,plain,
! [T_66: tree] : $lesseq(0,size(T_66)),
inference(cnfTransformation,[status(thm)],[f_123]) ).
tff(c_3729,plain,
! [T_66: tree] : ~ $less(size(T_66),0),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_67]) ).
tff(c_1390,plain,
( mem('#skF_10','#skF_1')
| ~ mem(max('#skF_9','#skF_3'),'#skF_1')
| ( empty = '#skF_2' )
| ~ $less(size('#skF_2'),size('#skF_1'))
| ~ $lesseq(0,size('#skF_1'))
| ( node('#skF_11','#skF_12','#skF_13') = '#skF_4' )
| ( empty = '#skF_1' ) ),
inference(cnfTransformation,[status(thm)],[f_249]) ).
tff(c_1487,plain,
( mem('#skF_10','#skF_1')
| ~ mem(max('#skF_9','#skF_3'),'#skF_1')
| ( empty = '#skF_2' )
| ~ $less(size('#skF_2'),size('#skF_1'))
| $less(size('#skF_1'),0)
| ( node('#skF_11','#skF_12','#skF_13') = '#skF_4' )
| ( empty = '#skF_1' ) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_1390]) ).
tff(c_5081,plain,
( mem('#skF_10','#skF_1')
| ~ mem(max('#skF_9','#skF_3'),'#skF_1')
| ( empty = '#skF_2' )
| ~ $less(size('#skF_2'),size('#skF_1'))
| $less(size('#skF_1'),0)
| ( node('#skF_11','#skF_12','#skF_13') = '#skF_4' ) ),
inference(negUnitSimplification,[status(thm)],[c_79,c_1487]) ).
tff(c_5331,plain,
( mem('#skF_10','#skF_1')
| ~ mem(max('#skF_9','#skF_3'),'#skF_1')
| ( empty = '#skF_2' )
| ~ $less(size('#skF_2'),size('#skF_1'))
| ( node('#skF_11','#skF_12','#skF_13') = '#skF_4' ) ),
inference(negUnitSimplification,[status(thm)],[c_3729,c_5081]) ).
tff(c_9405,plain,
( mem('#skF_10','#skF_1')
| ~ mem(max('#skF_9','#skF_3'),'#skF_1')
| ( '#skF_4' = '#skF_2' )
| ~ $less('#skE_1',$sum(1,'#skE_1'))
| ( node('#skF_11','#skF_12','#skF_13') = '#skF_4' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_8175,c_8146,c_5549,c_5331]) ).
tff(c_9407,plain,
( mem('#skF_10','#skF_1')
| ~ mem(max('#skF_9','#skF_3'),'#skF_1')
| ~ $less('#skE_1',$sum(1,'#skE_1')) ),
inference(negUnitSimplification,[status(thm)],[c_5557,c_7107,c_9405]) ).
tff(c_9410,plain,
( mem('#skF_10','#skF_1')
| ~ mem(max('#skF_9','#skF_3'),'#skF_1') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_9407]) ).
tff(c_9424,plain,
max('#skF_9','#skF_3') = '#skE_5',
inference(define,[status(thm),theory(equality)],[c_9410]) ).
tff(c_9425,plain,
max('#skF_9','#skF_3') = '#skE_5',
inference(define,[status(thm),theory(equality)],[c_9410]) ).
tff(c_3748,plain,
! [X_19a: $int,Y_20a: $int] :
( ( max(X_19a,Y_20a) = Y_20a )
| ( max(X_19a,Y_20a) = X_19a ) ),
inference(cnfTransformation,[status(thm)],[f_62]) ).
tff(c_9447,plain,
( ( '#skF_3' = '#skE_5' )
| ( max('#skF_9','#skF_3') = '#skF_9' ) ),
inference(superposition,[status(thm),theory(equality)],[c_9425,c_3748]) ).
tff(c_9510,plain,
( ( '#skF_3' = '#skE_5' )
| ( '#skF_9' = '#skE_5' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_9424,c_9447]) ).
tff(c_9550,plain,
'#skF_9' = '#skE_5',
inference(splitLeft,[status(thm)],[c_9510]) ).
tff(c_1404,plain,
( mem('#skF_9','#skF_2')
| ( empty = '#skF_2' )
| ~ $less(size('#skF_2'),size('#skF_1'))
| ~ $lesseq(0,size('#skF_1'))
| ( node('#skF_11','#skF_12','#skF_13') = '#skF_4' )
| ( empty = '#skF_1' ) ),
inference(cnfTransformation,[status(thm)],[f_249]) ).
tff(c_1463,plain,
( mem('#skF_9','#skF_2')
| ( empty = '#skF_2' )
| ~ $less(size('#skF_2'),size('#skF_1'))
| $less(size('#skF_1'),0)
| ( node('#skF_11','#skF_12','#skF_13') = '#skF_4' )
| ( empty = '#skF_1' ) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_1404]) ).
tff(c_4963,plain,
( mem('#skF_9','#skF_2')
| ( empty = '#skF_2' )
| ~ $less(size('#skF_2'),size('#skF_1'))
| $less(size('#skF_1'),0)
| ( node('#skF_11','#skF_12','#skF_13') = '#skF_4' ) ),
inference(negUnitSimplification,[status(thm)],[c_79,c_1463]) ).
tff(c_5225,plain,
( mem('#skF_9','#skF_2')
| ( empty = '#skF_2' )
| ~ $less(size('#skF_2'),size('#skF_1'))
| ( node('#skF_11','#skF_12','#skF_13') = '#skF_4' ) ),
inference(negUnitSimplification,[status(thm)],[c_3729,c_4963]) ).
tff(c_8640,plain,
( mem('#skF_9','#skF_2')
| ( '#skF_4' = '#skF_2' )
| ~ $less('#skE_1',$sum(1,'#skE_1'))
| ( node('#skF_11','#skF_12','#skF_13') = '#skF_4' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_8175,c_8146,c_5549,c_5225]) ).
tff(c_8642,plain,
( mem('#skF_9','#skF_2')
| ~ $less('#skE_1',$sum(1,'#skE_1')) ),
inference(negUnitSimplification,[status(thm)],[c_5557,c_7107,c_8640]) ).
tff(c_8647,plain,
mem('#skF_9','#skF_2'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_8642]) ).
tff(c_7708,plain,
! [X_8425a: $int,X1_8426: tree,X2_8427a: $int,X3_8428: tree] :
( ~ mem(X_8425a,X1_8426)
| mem(X_8425a,node(X1_8426,X2_8427a,X3_8428)) ),
inference(cnfTransformation,[status(thm)],[f_135]) ).
tff(c_7718,plain,
! [X_8425a: $int] :
( ~ mem(X_8425a,'#skF_2')
| mem(X_8425a,'#skF_1') ),
inference(superposition,[status(thm),theory(equality)],[c_4905,c_7708]) ).
tff(c_8653,plain,
mem('#skF_9','#skF_1'),
inference(resolution,[status(thm)],[c_8647,c_7718]) ).
tff(c_9643,plain,
mem('#skE_5','#skF_1'),
inference(demodulation,[status(thm),theory(equality)],[c_9550,c_8653]) ).
tff(c_35,plain,
! [X_27a: $int,Y_28a: $int] :
( ( max(X_27a,Y_28a) = Y_28a )
| ~ $lesseq(X_27a,Y_28a) ),
inference(cnfTransformation,[status(thm)],[f_78]) ).
tff(c_3743,plain,
! [X_27a: $int,Y_28a: $int] :
( ( max(X_27a,Y_28a) = Y_28a )
| $less(Y_28a,X_27a) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_35]) ).
tff(c_9515,plain,
( ( '#skF_3' = '#skE_5' )
| $less('#skF_3','#skF_9') ),
inference(superposition,[status(thm),theory(equality)],[c_9425,c_3743]) ).
tff(c_9613,plain,
( ( '#skF_3' = '#skE_5' )
| $less('#skF_3','#skE_5') ),
inference(demodulation,[status(thm),theory(equality)],[c_9550,c_9515]) ).
tff(c_9615,plain,
$less('#skF_3','#skE_5'),
inference(splitLeft,[status(thm)],[c_9613]) ).
tff(c_1382,plain,
( ~ $lesseq('#skF_10',max('#skF_9','#skF_3'))
| ~ mem(max('#skF_9','#skF_3'),'#skF_1')
| ( empty = '#skF_2' )
| ~ $less(size('#skF_2'),size('#skF_1'))
| ~ $lesseq(0,size('#skF_1'))
| ( node('#skF_11','#skF_12','#skF_13') = '#skF_4' )
| ( empty = '#skF_1' ) ),
inference(cnfTransformation,[status(thm)],[f_249]) ).
tff(c_1499,plain,
( $less(max('#skF_9','#skF_3'),'#skF_10')
| ~ mem(max('#skF_9','#skF_3'),'#skF_1')
| ( empty = '#skF_2' )
| ~ $less(size('#skF_2'),size('#skF_1'))
| $less(size('#skF_1'),0)
| ( node('#skF_11','#skF_12','#skF_13') = '#skF_4' )
| ( empty = '#skF_1' ) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_1382]) ).
tff(c_5003,plain,
( $less(max('#skF_9','#skF_3'),'#skF_10')
| ~ mem(max('#skF_9','#skF_3'),'#skF_1')
| ( empty = '#skF_2' )
| ~ $less(size('#skF_2'),size('#skF_1'))
| $less(size('#skF_1'),0)
| ( node('#skF_11','#skF_12','#skF_13') = '#skF_4' ) ),
inference(negUnitSimplification,[status(thm)],[c_79,c_1499]) ).
tff(c_5355,plain,
( $less(max('#skF_9','#skF_3'),'#skF_10')
| ~ mem(max('#skF_9','#skF_3'),'#skF_1')
| ( empty = '#skF_2' )
| ~ $less(size('#skF_2'),size('#skF_1'))
| ( node('#skF_11','#skF_12','#skF_13') = '#skF_4' ) ),
inference(negUnitSimplification,[status(thm)],[c_3729,c_5003]) ).
tff(c_9646,plain,
( $less(max('#skE_5','#skF_3'),'#skF_10')
| ~ mem(max('#skE_5','#skF_3'),'#skF_1')
| ( '#skF_4' = '#skF_2' )
| ~ $less('#skE_1',$sum(1,'#skE_1'))
| ( node('#skF_11','#skF_12','#skF_13') = '#skF_4' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_8175,c_8146,c_5549,c_9550,c_9550,c_5355]) ).
tff(c_9648,plain,
( $less(max('#skE_5','#skF_3'),'#skF_10')
| ~ mem(max('#skE_5','#skF_3'),'#skF_1')
| ~ $less('#skE_1',$sum(1,'#skE_1')) ),
inference(negUnitSimplification,[status(thm)],[c_5557,c_7107,c_9646]) ).
tff(c_9651,plain,
( $less(max('#skE_5','#skF_3'),'#skF_10')
| ~ mem(max('#skE_5','#skF_3'),'#skF_1') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_9648]) ).
tff(c_9691,plain,
max('#skE_5','#skF_3') = '#skE_6',
inference(define,[status(thm),theory(equality)],[c_9651]) ).
tff(c_7348,plain,
! [X_8405a: $int,Y_8406a: $int] :
( ( max(X_8405a,Y_8406a) = Y_8406a )
| ( max(X_8405a,Y_8406a) = X_8405a ) ),
inference(cnfTransformation,[status(thm)],[f_62]) ).
tff(c_18,plain,
! [X_17a: $int,Y_18a: $int] : $lesseq(X_17a,max(X_17a,Y_18a)),
inference(cnfTransformation,[status(thm)],[f_58]) ).
tff(c_3750,plain,
! [X_17a: $int,Y_18a: $int] : ~ $less(max(X_17a,Y_18a),X_17a),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_18]) ).
tff(c_7413,plain,
! [Y_8406a: $int,X_8405a: $int] :
( ~ $less(Y_8406a,X_8405a)
| ( max(X_8405a,Y_8406a) = X_8405a ) ),
inference(superposition,[status(thm),theory(equality)],[c_7348,c_3750]) ).
tff(c_9706,plain,
( ~ $less('#skF_3','#skE_5')
| ( '#skE_6' = '#skE_5' ) ),
inference(superposition,[status(thm),theory(equality)],[c_9691,c_7413]) ).
tff(c_9775,plain,
'#skE_6' = '#skE_5',
inference(demodulation,[status(thm),theory(equality)],[c_9615,c_9706]) ).
tff(c_9653,plain,
max('#skE_5','#skF_3') = '#skE_6',
inference(define,[status(thm),theory(equality)],[c_9651]) ).
tff(c_9652,plain,
( $less(max('#skE_5','#skF_3'),'#skF_10')
| ~ mem(max('#skE_5','#skF_3'),'#skF_1') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_9648]) ).
tff(c_9663,plain,
( $less('#skE_6','#skF_10')
| ~ mem('#skE_6','#skF_1') ),
inference(demodulation,[status(thm),theory(equality)],[c_9653,c_9653,c_9652]) ).
tff(c_10045,plain,
$less('#skE_5','#skF_10'),
inference(demodulation,[status(thm),theory(equality)],[c_9643,c_9775,c_9775,c_9663]) ).
tff(c_9412,plain,
max('#skF_9','#skF_3') = '#skE_5',
inference(define,[status(thm),theory(equality)],[c_9410]) ).
tff(c_9411,plain,
( mem('#skF_10','#skF_1')
| ~ mem(max('#skF_9','#skF_3'),'#skF_1') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_9407]) ).
tff(c_9422,plain,
( mem('#skF_10','#skF_1')
| ~ mem('#skE_5','#skF_1') ),
inference(demodulation,[status(thm),theory(equality)],[c_9412,c_9411]) ).
tff(c_10057,plain,
mem('#skF_10','#skF_1'),
inference(demodulation,[status(thm),theory(equality)],[c_9643,c_9422]) ).
tff(c_8402,plain,
! [X_8522a: $int,X3_8523: tree,X1_8524: tree,X2_8525a: $int] :
( mem(X_8522a,X3_8523)
| mem(X_8522a,X1_8524)
| ~ mem(X_8522a,node(X1_8524,X2_8525a,X3_8523))
| ( X_8522a = X2_8525a ) ),
inference(cnfTransformation,[status(thm)],[f_135]) ).
tff(c_8417,plain,
! [X_8522a: $int] :
( mem(X_8522a,'#skF_4')
| mem(X_8522a,'#skF_2')
| ~ mem(X_8522a,'#skF_1')
| ( X_8522a = '#skF_3' ) ),
inference(superposition,[status(thm),theory(equality)],[c_4905,c_8402]) ).
tff(c_8430,plain,
! [X_8522a: $int] :
( mem(X_8522a,'#skF_2')
| ~ mem(X_8522a,'#skF_1')
| ( X_8522a = '#skF_3' ) ),
inference(negUnitSimplification,[status(thm)],[c_5559,c_8417]) ).
tff(c_1397,plain,
! [X3_339a: $int] :
( ( empty = '#skF_2' )
| ~ mem(X3_339a,'#skF_2')
| ( empty = '#skF_2' )
| ~ $less(size('#skF_2'),size('#skF_1'))
| ~ $lesseq(0,size('#skF_1'))
| ( node('#skF_11','#skF_12','#skF_13') = '#skF_4' )
| ( empty = '#skF_1' )
| $lesseq(X3_339a,'#skF_9') ),
inference(cnfTransformation,[status(thm)],[f_249]) ).
tff(c_1475,plain,
! [X3_339a: $int] :
( ~ mem(X3_339a,'#skF_2')
| ( empty = '#skF_2' )
| ~ $less(size('#skF_2'),size('#skF_1'))
| $less(size('#skF_1'),0)
| ( node('#skF_11','#skF_12','#skF_13') = '#skF_4' )
| ( empty = '#skF_1' )
| ~ $less('#skF_9',X3_339a) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_1397]) ).
tff(c_4971,plain,
! [X3_339a: $int] :
( ~ mem(X3_339a,'#skF_2')
| ( empty = '#skF_2' )
| ~ $less(size('#skF_2'),size('#skF_1'))
| $less(size('#skF_1'),0)
| ( node('#skF_11','#skF_12','#skF_13') = '#skF_4' )
| ~ $less('#skF_9',X3_339a) ),
inference(negUnitSimplification,[status(thm)],[c_79,c_1475]) ).
tff(c_5297,plain,
! [X3_339a: $int] :
( ~ mem(X3_339a,'#skF_2')
| ( empty = '#skF_2' )
| ~ $less(size('#skF_2'),size('#skF_1'))
| ( node('#skF_11','#skF_12','#skF_13') = '#skF_4' )
| ~ $less('#skF_9',X3_339a) ),
inference(negUnitSimplification,[status(thm)],[c_3729,c_4971]) ).
tff(c_8799,plain,
! [X3_339a: $int] :
( ~ mem(X3_339a,'#skF_2')
| ( '#skF_4' = '#skF_2' )
| ~ $less('#skE_1',$sum(1,'#skE_1'))
| ( node('#skF_11','#skF_12','#skF_13') = '#skF_4' )
| ~ $less('#skF_9',X3_339a) ),
inference(demodulation,[status(thm),theory(equality)],[c_8175,c_8146,c_5549,c_5297]) ).
tff(c_8801,plain,
! [X3_339a: $int] :
( ~ mem(X3_339a,'#skF_2')
| ~ $less('#skE_1',$sum(1,'#skE_1'))
| ~ $less('#skF_9',X3_339a) ),
inference(negUnitSimplification,[status(thm)],[c_5557,c_7107,c_8799]) ).
tff(c_8804,plain,
! [X3_8609a: $int] :
( ~ mem(X3_8609a,'#skF_2')
| ~ $less('#skF_9',X3_8609a) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_8801]) ).
tff(c_8821,plain,
! [X_8522a: $int] :
( ~ $less('#skF_9',X_8522a)
| ~ mem(X_8522a,'#skF_1')
| ( X_8522a = '#skF_3' ) ),
inference(resolution,[status(thm)],[c_8430,c_8804]) ).
tff(c_9580,plain,
! [X_8522a: $int] :
( ~ $less('#skE_5',X_8522a)
| ~ mem(X_8522a,'#skF_1')
| ( X_8522a = '#skF_3' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_9550,c_8821]) ).
tff(c_10060,plain,
( ~ $less('#skE_5','#skF_10')
| ( '#skF_3' = '#skF_10' ) ),
inference(resolution,[status(thm)],[c_10057,c_9580]) ).
tff(c_10064,plain,
'#skF_3' = '#skF_10',
inference(demodulation,[status(thm),theory(equality)],[c_10045,c_10060]) ).
tff(c_21,plain,
! [Y_18a: $int,X_17a: $int] : $lesseq(Y_18a,max(X_17a,Y_18a)),
inference(cnfTransformation,[status(thm)],[f_58]) ).
tff(c_3749,plain,
! [X_17a: $int,Y_18a: $int] : ~ $less(max(X_17a,Y_18a),Y_18a),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_21]) ).
tff(c_9521,plain,
~ $less('#skE_5','#skF_3'),
inference(superposition,[status(thm),theory(equality)],[c_9425,c_3749]) ).
tff(c_10076,plain,
~ $less('#skE_5','#skF_10'),
inference(demodulation,[status(thm),theory(equality)],[c_10064,c_9521]) ).
tff(c_10100,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_10045,c_10076]) ).
tff(c_10103,plain,
'#skF_3' = '#skE_5',
inference(splitRight,[status(thm)],[c_9613]) ).
tff(c_5548,plain,
mem('#skF_3','#skF_1'),
inference(superposition,[status(thm),theory(equality)],[c_4905,c_5542]) ).
tff(c_10227,plain,
mem('#skE_5','#skF_1'),
inference(demodulation,[status(thm),theory(equality)],[c_10103,c_5548]) ).
tff(c_7345,plain,
! [X_19a: $int] : ( max(X_19a,X_19a) = X_19a ),
inference(factorization,[status(thm),theory(equality)],[c_3748]) ).
tff(c_10316,plain,
( $less('#skE_5','#skF_10')
| ( '#skF_4' = '#skF_2' )
| ~ $less('#skE_1',$sum(1,'#skE_1'))
| ( node('#skF_11','#skF_12','#skF_13') = '#skF_4' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_8146,c_8175,c_5549,c_10227,c_7345,c_10103,c_9550,c_7345,c_10103,c_9550,c_5355]) ).
tff(c_10318,plain,
( $less('#skE_5','#skF_10')
| ~ $less('#skE_1',$sum(1,'#skE_1')) ),
inference(negUnitSimplification,[status(thm)],[c_5557,c_7107,c_10316]) ).
tff(c_10320,plain,
$less('#skE_5','#skF_10'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_10318]) ).
tff(c_10329,plain,
mem('#skF_10','#skF_1'),
inference(demodulation,[status(thm),theory(equality)],[c_10227,c_9422]) ).
tff(c_10281,plain,
! [X_8957a: $int] :
( mem(X_8957a,'#skF_2')
| ~ mem(X_8957a,'#skF_1')
| ( X_8957a = '#skE_5' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_10103,c_8430]) ).
tff(c_8803,plain,
! [X3_339a: $int] :
( ~ mem(X3_339a,'#skF_2')
| ~ $less('#skF_9',X3_339a) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_8801]) ).
tff(c_9583,plain,
! [X3_339a: $int] :
( ~ mem(X3_339a,'#skF_2')
| ~ $less('#skE_5',X3_339a) ),
inference(demodulation,[status(thm),theory(equality)],[c_9550,c_8803]) ).
tff(c_10289,plain,
! [X_8957a: $int] :
( ~ $less('#skE_5',X_8957a)
| ~ mem(X_8957a,'#skF_1')
| ( X_8957a = '#skE_5' ) ),
inference(resolution,[status(thm)],[c_10281,c_9583]) ).
tff(c_10332,plain,
( ~ $less('#skE_5','#skF_10')
| ( '#skF_10' = '#skE_5' ) ),
inference(resolution,[status(thm)],[c_10329,c_10289]) ).
tff(c_10336,plain,
'#skF_10' = '#skE_5',
inference(demodulation,[status(thm),theory(equality)],[c_10320,c_10332]) ).
tff(c_10343,plain,
$less('#skE_5','#skE_5'),
inference(demodulation,[status(thm),theory(equality)],[c_10336,c_10320]) ).
tff(c_10348,plain,
$false,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_10343]) ).
tff(c_10351,plain,
'#skF_3' = '#skE_5',
inference(splitRight,[status(thm)],[c_9510]) ).
tff(c_10506,plain,
mem('#skE_5','#skF_1'),
inference(demodulation,[status(thm),theory(equality)],[c_10351,c_5548]) ).
tff(c_9419,plain,
max('#skF_9','#skF_3') = '#skE_5',
inference(define,[status(thm),theory(equality)],[c_9410]) ).
tff(c_10521,plain,
max('#skF_9','#skE_5') = '#skE_5',
inference(demodulation,[status(thm),theory(equality)],[c_10351,c_9419]) ).
tff(c_10896,plain,
( $less('#skE_5','#skF_10')
| ( '#skF_4' = '#skF_2' )
| ~ $less('#skE_1',$sum(1,'#skE_1'))
| ( node('#skF_11','#skF_12','#skF_13') = '#skF_4' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_8146,c_8175,c_5549,c_10506,c_10521,c_10351,c_10521,c_10351,c_5355]) ).
tff(c_10898,plain,
( $less('#skE_5','#skF_10')
| ~ $less('#skE_1',$sum(1,'#skE_1')) ),
inference(negUnitSimplification,[status(thm)],[c_5557,c_7107,c_10896]) ).
tff(c_10900,plain,
$less('#skE_5','#skF_10'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_10898]) ).
tff(c_10722,plain,
mem('#skF_10','#skF_1'),
inference(demodulation,[status(thm),theory(equality)],[c_10506,c_9422]) ).
tff(c_10382,plain,
! [X_8522a: $int] :
( ~ $less('#skF_9',X_8522a)
| ~ mem(X_8522a,'#skF_1')
| ( X_8522a = '#skE_5' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_10351,c_8821]) ).
tff(c_10727,plain,
( ~ $less('#skF_9','#skF_10')
| ( '#skF_10' = '#skE_5' ) ),
inference(resolution,[status(thm)],[c_10722,c_10382]) ).
tff(c_10729,plain,
~ $less('#skF_9','#skF_10'),
inference(splitLeft,[status(thm)],[c_10727]) ).
tff(c_9519,plain,
~ $less('#skE_5','#skF_9'),
inference(superposition,[status(thm),theory(equality)],[c_9425,c_3750]) ).
tff(c_10902,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_10900,c_10729,c_9519]) ).
tff(c_10905,plain,
'#skF_10' = '#skE_5',
inference(splitRight,[status(thm)],[c_10727]) ).
tff(c_11154,plain,
( $less('#skE_5','#skE_5')
| ( '#skF_4' = '#skF_2' )
| ~ $less('#skE_1',$sum(1,'#skE_1'))
| ( node('#skF_11','#skF_12','#skF_13') = '#skF_4' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_8146,c_8175,c_5549,c_10506,c_10521,c_10351,c_10521,c_10905,c_10351,c_5355]) ).
tff(c_11156,plain,
( $less('#skE_5','#skE_5')
| ~ $less('#skE_1',$sum(1,'#skE_1')) ),
inference(negUnitSimplification,[status(thm)],[c_5557,c_7107,c_11154]) ).
tff(c_11158,plain,
$false,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_11156]) ).
tff(c_11160,plain,
empty != '#skF_4',
inference(splitRight,[status(thm)],[c_4913]) ).
tff(c_1567,plain,
( ( empty = '#skF_4' )
| ( empty = '#skF_2' )
| ( node('#skF_16','#skF_17','#skF_18') = '#skF_2' )
| ( empty = '#skF_1' ) ),
inference(cnfTransformation,[status(thm)],[f_249]) ).
tff(c_4925,plain,
( ( empty = '#skF_4' )
| ( empty = '#skF_2' )
| ( node('#skF_16','#skF_17','#skF_18') = '#skF_2' ) ),
inference(negUnitSimplification,[status(thm)],[c_79,c_1567]) ).
tff(c_11182,plain,
( ( empty = '#skF_2' )
| ( node('#skF_16','#skF_17','#skF_18') = '#skF_2' ) ),
inference(negUnitSimplification,[status(thm)],[c_11160,c_4925]) ).
tff(c_11184,plain,
empty = '#skF_2',
inference(splitLeft,[status(thm)],[c_11182]) ).
tff(c_11193,plain,
! [V_50: tree,V1_51a: $int,V2_52: tree] : ( node(V_50,V1_51a,V2_52) != '#skF_2' ),
inference(demodulation,[status(thm),theory(equality)],[c_11184,c_3737]) ).
tff(c_11185,plain,
'#skF_4' != '#skF_2',
inference(demodulation,[status(thm),theory(equality)],[c_11184,c_11160]) ).
tff(c_1105,plain,
( mem('#skF_14','#skF_4')
| mem('#skF_19','#skF_4')
| ( empty = '#skF_4' )
| ~ $less(size('#skF_4'),size('#skF_1'))
| ~ $lesseq(0,size('#skF_1'))
| ( empty = '#skF_1' ) ),
inference(cnfTransformation,[status(thm)],[f_249]) ).
tff(c_1951,plain,
( mem('#skF_14','#skF_4')
| mem('#skF_19','#skF_4')
| ( empty = '#skF_4' )
| ~ $less(size('#skF_4'),size('#skF_1'))
| $less(size('#skF_1'),0)
| ( empty = '#skF_1' ) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_1105]) ).
tff(c_4921,plain,
( mem('#skF_14','#skF_4')
| mem('#skF_19','#skF_4')
| ( empty = '#skF_4' )
| ~ $less(size('#skF_4'),size('#skF_1'))
| $less(size('#skF_1'),0) ),
inference(negUnitSimplification,[status(thm)],[c_79,c_1951]) ).
tff(c_5217,plain,
( mem('#skF_14','#skF_4')
| mem('#skF_19','#skF_4')
| ( empty = '#skF_4' )
| ~ $less(size('#skF_4'),size('#skF_1')) ),
inference(negUnitSimplification,[status(thm)],[c_3729,c_4921]) ).
tff(c_12473,plain,
( mem('#skF_14','#skF_4')
| mem('#skF_19','#skF_4')
| ( '#skF_4' = '#skF_2' )
| ~ $less(size('#skF_4'),size('#skF_1')) ),
inference(demodulation,[status(thm),theory(equality)],[c_11184,c_5217]) ).
tff(c_12477,plain,
( mem('#skF_14','#skF_4')
| mem('#skF_19','#skF_4')
| ~ $less(size('#skF_4'),size('#skF_1')) ),
inference(negUnitSimplification,[status(thm)],[c_11185,c_12473]) ).
tff(c_12485,plain,
size('#skF_1') = '#skE_2',
inference(define,[status(thm),theory(equality)],[c_12477]) ).
tff(c_12484,plain,
size('#skF_4') = '#skE_7',
inference(define,[status(thm),theory(equality)],[c_12477]) ).
tff(c_11194,plain,
size('#skF_2') = 0,
inference(demodulation,[status(thm),theory(equality)],[c_11184,c_3730]) ).
tff(c_12507,plain,
! [X_9186: tree,X1_9187a: $int,X2_9188: tree] : ( size(node(X_9186,X1_9187a,X2_9188)) = $sum(1,$sum(size(X2_9188),size(X_9186))) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_63]) ).
tff(c_12521,plain,
$sum(1,$sum(size('#skF_4'),size('#skF_2'))) = size('#skF_1'),
inference(superposition,[status(thm),theory(equality)],[c_4905,c_12507]) ).
tff(c_12534,plain,
$sum(1,$sum('#skE_7',0)) = '#skE_2',
inference(demodulation,[status(thm),theory(equality)],[c_12485,c_12484,c_11194,c_12521]) ).
tff(c_12536,plain,
'#skE_7' = $sum($uminus(1),'#skE_2'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_12534]) ).
tff(c_12612,plain,
size('#skF_4') = $sum($uminus(1),'#skE_2'),
inference(demodulation,[status(thm),theory(equality)],[c_12536,c_12484]) ).
tff(c_862,plain,
! [X3_396a: $int] :
( ( empty = '#skF_4' )
| mem('#skF_15','#skF_1')
| ~ mem(max('#skF_14','#skF_3'),'#skF_1')
| ( empty = '#skF_4' )
| ~ $less(size('#skF_4'),size('#skF_1'))
| ~ $lesseq(0,size('#skF_1'))
| ~ mem(X3_396a,'#skF_4')
| ( empty = '#skF_4' )
| ~ $less(size('#skF_4'),size('#skF_1'))
| ~ $lesseq(0,size('#skF_1'))
| ( empty = '#skF_1' )
| $lesseq(X3_396a,'#skF_19') ),
inference(cnfTransformation,[status(thm)],[f_249]) ).
tff(c_2387,plain,
! [X3_396a: $int] :
( mem('#skF_15','#skF_1')
| ~ mem(max('#skF_14','#skF_3'),'#skF_1')
| ~ mem(X3_396a,'#skF_4')
| ( empty = '#skF_4' )
| ~ $less(size('#skF_4'),size('#skF_1'))
| $less(size('#skF_1'),0)
| ( empty = '#skF_1' )
| ~ $less('#skF_19',X3_396a) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_862]) ).
tff(c_5037,plain,
! [X3_396a: $int] :
( mem('#skF_15','#skF_1')
| ~ mem(max('#skF_14','#skF_3'),'#skF_1')
| ~ mem(X3_396a,'#skF_4')
| ( empty = '#skF_4' )
| ~ $less(size('#skF_4'),size('#skF_1'))
| $less(size('#skF_1'),0)
| ~ $less('#skF_19',X3_396a) ),
inference(negUnitSimplification,[status(thm)],[c_79,c_2387]) ).
tff(c_5285,plain,
! [X3_396a: $int] :
( mem('#skF_15','#skF_1')
| ~ mem(max('#skF_14','#skF_3'),'#skF_1')
| ~ mem(X3_396a,'#skF_4')
| ( empty = '#skF_4' )
| ~ $less(size('#skF_4'),size('#skF_1'))
| ~ $less('#skF_19',X3_396a) ),
inference(negUnitSimplification,[status(thm)],[c_3729,c_5037]) ).
tff(c_41264,plain,
! [X3_396a: $int] :
( mem('#skF_15','#skF_1')
| ~ mem(max('#skF_14','#skF_3'),'#skF_1')
| ~ mem(X3_396a,'#skF_4')
| ( '#skF_4' = '#skF_2' )
| ~ $less($sum($uminus(1),'#skE_2'),'#skE_2')
| ~ $less('#skF_19',X3_396a) ),
inference(demodulation,[status(thm),theory(equality)],[c_12485,c_12612,c_11184,c_5285]) ).
tff(c_41266,plain,
! [X3_396a: $int] :
( mem('#skF_15','#skF_1')
| ~ mem(max('#skF_14','#skF_3'),'#skF_1')
| ~ mem(X3_396a,'#skF_4')
| ~ $less($sum($uminus(1),'#skE_2'),'#skE_2')
| ~ $less('#skF_19',X3_396a) ),
inference(negUnitSimplification,[status(thm)],[c_11185,c_41264]) ).
tff(c_41269,plain,
! [X3_396a: $int] :
( mem('#skF_15','#skF_1')
| ~ mem(max('#skF_14','#skF_3'),'#skF_1')
| ~ mem(X3_396a,'#skF_4')
| ~ $less('#skF_19',X3_396a) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_41266]) ).
tff(c_41283,plain,
max('#skF_14','#skF_3') = '#skE_10',
inference(define,[status(thm),theory(equality)],[c_41269]) ).
tff(c_41284,plain,
max('#skF_14','#skF_3') = '#skE_10',
inference(define,[status(thm),theory(equality)],[c_41269]) ).
tff(c_41306,plain,
( ( '#skF_3' = '#skE_10' )
| ( max('#skF_14','#skF_3') = '#skF_14' ) ),
inference(superposition,[status(thm),theory(equality)],[c_41284,c_3748]) ).
tff(c_41369,plain,
( ( '#skF_3' = '#skE_10' )
| ( '#skF_14' = '#skE_10' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_41283,c_41306]) ).
tff(c_41412,plain,
'#skF_14' = '#skE_10',
inference(splitLeft,[status(thm)],[c_41369]) ).
tff(c_26357,plain,
! [X3_396a: $int] :
( mem('#skF_15','#skF_1')
| ~ mem(max('#skF_14','#skF_3'),'#skF_1')
| ~ mem(X3_396a,'#skF_4')
| ( '#skF_4' = '#skF_2' )
| ~ $less($sum($uminus(1),'#skE_2'),'#skE_2')
| ~ $less('#skF_19',X3_396a) ),
inference(demodulation,[status(thm),theory(equality)],[c_12485,c_12612,c_11184,c_5285]) ).
tff(c_26359,plain,
! [X3_396a: $int] :
( mem('#skF_15','#skF_1')
| ~ mem(max('#skF_14','#skF_3'),'#skF_1')
| ~ mem(X3_396a,'#skF_4')
| ~ $less($sum($uminus(1),'#skE_2'),'#skE_2')
| ~ $less('#skF_19',X3_396a) ),
inference(negUnitSimplification,[status(thm)],[c_11185,c_26357]) ).
tff(c_26362,plain,
! [X3_396a: $int] :
( mem('#skF_15','#skF_1')
| ~ mem(max('#skF_14','#skF_3'),'#skF_1')
| ~ mem(X3_396a,'#skF_4')
| ~ $less('#skF_19',X3_396a) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_26359]) ).
tff(c_26376,plain,
max('#skF_14','#skF_3') = '#skE_10',
inference(define,[status(thm),theory(equality)],[c_26362]) ).
tff(c_26377,plain,
max('#skF_14','#skF_3') = '#skE_10',
inference(define,[status(thm),theory(equality)],[c_26362]) ).
tff(c_26402,plain,
( ( max('#skF_14','#skF_3') = '#skF_3' )
| ( '#skF_14' = '#skE_10' ) ),
inference(superposition,[status(thm),theory(equality)],[c_26377,c_3748]) ).
tff(c_26465,plain,
( ( '#skF_3' = '#skE_10' )
| ( '#skF_14' = '#skE_10' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_26376,c_26402]) ).
tff(c_26509,plain,
'#skF_14' = '#skE_10',
inference(splitLeft,[status(thm)],[c_26465]) ).
tff(c_1228,plain,
( mem('#skF_15','#skF_1')
| ~ mem(max('#skF_14','#skF_3'),'#skF_1')
| ( empty = '#skF_4' )
| ~ $less(size('#skF_4'),size('#skF_1'))
| ~ $lesseq(0,size('#skF_1'))
| ( node('#skF_16','#skF_17','#skF_18') = '#skF_2' )
| ( empty = '#skF_1' ) ),
inference(cnfTransformation,[status(thm)],[f_249]) ).
tff(c_1759,plain,
( mem('#skF_15','#skF_1')
| ~ mem(max('#skF_14','#skF_3'),'#skF_1')
| ( empty = '#skF_4' )
| ~ $less(size('#skF_4'),size('#skF_1'))
| $less(size('#skF_1'),0)
| ( node('#skF_16','#skF_17','#skF_18') = '#skF_2' )
| ( empty = '#skF_1' ) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_1228]) ).
tff(c_5023,plain,
( mem('#skF_15','#skF_1')
| ~ mem(max('#skF_14','#skF_3'),'#skF_1')
| ( empty = '#skF_4' )
| ~ $less(size('#skF_4'),size('#skF_1'))
| $less(size('#skF_1'),0)
| ( node('#skF_16','#skF_17','#skF_18') = '#skF_2' ) ),
inference(negUnitSimplification,[status(thm)],[c_79,c_1759]) ).
tff(c_5271,plain,
( mem('#skF_15','#skF_1')
| ~ mem(max('#skF_14','#skF_3'),'#skF_1')
| ( empty = '#skF_4' )
| ~ $less(size('#skF_4'),size('#skF_1'))
| ( node('#skF_16','#skF_17','#skF_18') = '#skF_2' ) ),
inference(negUnitSimplification,[status(thm)],[c_3729,c_5023]) ).
tff(c_17090,plain,
( mem('#skF_15','#skF_1')
| ~ mem(max('#skF_14','#skF_3'),'#skF_1')
| ( '#skF_4' = '#skF_2' )
| ~ $less($sum($uminus(1),'#skE_2'),'#skE_2')
| ( node('#skF_16','#skF_17','#skF_18') = '#skF_2' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_12485,c_12612,c_11184,c_5271]) ).
tff(c_17092,plain,
( mem('#skF_15','#skF_1')
| ~ mem(max('#skF_14','#skF_3'),'#skF_1')
| ~ $less($sum($uminus(1),'#skE_2'),'#skE_2') ),
inference(negUnitSimplification,[status(thm)],[c_11193,c_11185,c_17090]) ).
tff(c_17095,plain,
( mem('#skF_15','#skF_1')
| ~ mem(max('#skF_14','#skF_3'),'#skF_1') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_17092]) ).
tff(c_17110,plain,
max('#skF_14','#skF_3') = '#skE_10',
inference(define,[status(thm),theory(equality)],[c_17095]) ).
tff(c_33,plain,
! [X_25a: $int,Y_26a: $int] :
( ( max(X_25a,Y_26a) = X_25a )
| ~ $lesseq(Y_26a,X_25a) ),
inference(cnfTransformation,[status(thm)],[f_74]) ).
tff(c_3744,plain,
! [X_25a: $int,Y_26a: $int] :
( ( max(X_25a,Y_26a) = X_25a )
| $less(X_25a,Y_26a) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_33]) ).
tff(c_17200,plain,
( ( '#skF_14' = '#skE_10' )
| $less('#skF_14','#skF_3') ),
inference(superposition,[status(thm),theory(equality)],[c_17110,c_3744]) ).
tff(c_17243,plain,
$less('#skF_14','#skF_3'),
inference(splitLeft,[status(thm)],[c_17200]) ).
tff(c_17231,plain,
( ( '#skF_3' = '#skE_10' )
| $less('#skF_3','#skF_14') ),
inference(superposition,[status(thm),theory(equality)],[c_3743,c_17110]) ).
tff(c_17237,plain,
$less('#skF_3','#skF_14'),
inference(splitLeft,[status(thm)],[c_17231]) ).
tff(c_17244,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_17243,c_17237]) ).
tff(c_17247,plain,
'#skF_14' = '#skE_10',
inference(splitRight,[status(thm)],[c_17200]) ).
tff(c_1301,plain,
( mem('#skF_14','#skF_4')
| ( empty = '#skF_4' )
| ~ $less(size('#skF_4'),size('#skF_1'))
| ~ $lesseq(0,size('#skF_1'))
| ( node('#skF_16','#skF_17','#skF_18') = '#skF_2' )
| ( empty = '#skF_1' ) ),
inference(cnfTransformation,[status(thm)],[f_249]) ).
tff(c_1631,plain,
( mem('#skF_14','#skF_4')
| ( empty = '#skF_4' )
| ~ $less(size('#skF_4'),size('#skF_1'))
| $less(size('#skF_1'),0)
| ( node('#skF_16','#skF_17','#skF_18') = '#skF_2' )
| ( empty = '#skF_1' ) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_1301]) ).
tff(c_4955,plain,
( mem('#skF_14','#skF_4')
| ( empty = '#skF_4' )
| ~ $less(size('#skF_4'),size('#skF_1'))
| $less(size('#skF_1'),0)
| ( node('#skF_16','#skF_17','#skF_18') = '#skF_2' ) ),
inference(negUnitSimplification,[status(thm)],[c_79,c_1631]) ).
tff(c_5221,plain,
( mem('#skF_14','#skF_4')
| ( empty = '#skF_4' )
| ~ $less(size('#skF_4'),size('#skF_1'))
| ( node('#skF_16','#skF_17','#skF_18') = '#skF_2' ) ),
inference(negUnitSimplification,[status(thm)],[c_3729,c_4955]) ).
tff(c_12879,plain,
( mem('#skF_14','#skF_4')
| ( '#skF_4' = '#skF_2' )
| ~ $less($sum($uminus(1),'#skE_2'),'#skE_2')
| ( node('#skF_16','#skF_17','#skF_18') = '#skF_2' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_12612,c_12485,c_11184,c_5221]) ).
tff(c_12881,plain,
( mem('#skF_14','#skF_4')
| ~ $less($sum($uminus(1),'#skE_2'),'#skE_2') ),
inference(negUnitSimplification,[status(thm)],[c_11193,c_11185,c_12879]) ).
tff(c_12884,plain,
mem('#skF_14','#skF_4'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_12881]) ).
tff(c_17346,plain,
mem('#skE_10','#skF_4'),
inference(demodulation,[status(thm),theory(equality)],[c_17247,c_12884]) ).
tff(c_12027,plain,
! [X_9108a: $int,X3_9109: tree,X1_9110: tree,X2_9111a: $int] :
( ~ mem(X_9108a,X3_9109)
| mem(X_9108a,node(X1_9110,X2_9111a,X3_9109)) ),
inference(cnfTransformation,[status(thm)],[f_135]) ).
tff(c_12037,plain,
! [X_9108a: $int] :
( ~ mem(X_9108a,'#skF_4')
| mem(X_9108a,'#skF_1') ),
inference(superposition,[status(thm),theory(equality)],[c_4905,c_12027]) ).
tff(c_17376,plain,
mem('#skE_10','#skF_1'),
inference(resolution,[status(thm)],[c_17346,c_12037]) ).
tff(c_17097,plain,
max('#skF_14','#skF_3') = '#skE_10',
inference(define,[status(thm),theory(equality)],[c_17095]) ).
tff(c_17096,plain,
( mem('#skF_15','#skF_1')
| ~ mem(max('#skF_14','#skF_3'),'#skF_1') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_17092]) ).
tff(c_17107,plain,
( mem('#skF_15','#skF_1')
| ~ mem('#skE_10','#skF_1') ),
inference(demodulation,[status(thm),theory(equality)],[c_17097,c_17096]) ).
tff(c_17643,plain,
mem('#skF_15','#skF_1'),
inference(demodulation,[status(thm),theory(equality)],[c_17376,c_17107]) ).
tff(c_11195,plain,
! [X_67a: $int] : ~ mem(X_67a,'#skF_2'),
inference(demodulation,[status(thm),theory(equality)],[c_11184,c_3728]) ).
tff(c_12752,plain,
! [X_9218a: $int,X3_9219: tree,X1_9220: tree,X2_9221a: $int] :
( mem(X_9218a,X3_9219)
| mem(X_9218a,X1_9220)
| ~ mem(X_9218a,node(X1_9220,X2_9221a,X3_9219))
| ( X_9218a = X2_9221a ) ),
inference(cnfTransformation,[status(thm)],[f_135]) ).
tff(c_12767,plain,
! [X_9218a: $int] :
( mem(X_9218a,'#skF_4')
| mem(X_9218a,'#skF_2')
| ~ mem(X_9218a,'#skF_1')
| ( X_9218a = '#skF_3' ) ),
inference(superposition,[status(thm),theory(equality)],[c_4905,c_12752]) ).
tff(c_12780,plain,
! [X_9218a: $int] :
( mem(X_9218a,'#skF_4')
| ~ mem(X_9218a,'#skF_1')
| ( X_9218a = '#skF_3' ) ),
inference(negUnitSimplification,[status(thm)],[c_11195,c_12767]) ).
tff(c_1268,plain,
! [X3_376a: $int] :
( ( empty = '#skF_4' )
| ~ mem(X3_376a,'#skF_4')
| ( empty = '#skF_4' )
| ~ $less(size('#skF_4'),size('#skF_1'))
| ~ $lesseq(0,size('#skF_1'))
| ( node('#skF_16','#skF_17','#skF_18') = '#skF_2' )
| ( empty = '#skF_1' )
| $lesseq(X3_376a,'#skF_14') ),
inference(cnfTransformation,[status(thm)],[f_249]) ).
tff(c_1695,plain,
! [X3_376a: $int] :
( ~ mem(X3_376a,'#skF_4')
| ( empty = '#skF_4' )
| ~ $less(size('#skF_4'),size('#skF_1'))
| $less(size('#skF_1'),0)
| ( node('#skF_16','#skF_17','#skF_18') = '#skF_2' )
| ( empty = '#skF_1' )
| ~ $less('#skF_14',X3_376a) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_1268]) ).
tff(c_5015,plain,
! [X3_376a: $int] :
( ~ mem(X3_376a,'#skF_4')
| ( empty = '#skF_4' )
| ~ $less(size('#skF_4'),size('#skF_1'))
| $less(size('#skF_1'),0)
| ( node('#skF_16','#skF_17','#skF_18') = '#skF_2' )
| ~ $less('#skF_14',X3_376a) ),
inference(negUnitSimplification,[status(thm)],[c_79,c_1695]) ).
tff(c_5263,plain,
! [X3_376a: $int] :
( ~ mem(X3_376a,'#skF_4')
| ( empty = '#skF_4' )
| ~ $less(size('#skF_4'),size('#skF_1'))
| ( node('#skF_16','#skF_17','#skF_18') = '#skF_2' )
| ~ $less('#skF_14',X3_376a) ),
inference(negUnitSimplification,[status(thm)],[c_3729,c_5015]) ).
tff(c_13222,plain,
! [X3_376a: $int] :
( ~ mem(X3_376a,'#skF_4')
| ( '#skF_4' = '#skF_2' )
| ~ $less($sum($uminus(1),'#skE_2'),'#skE_2')
| ( node('#skF_16','#skF_17','#skF_18') = '#skF_2' )
| ~ $less('#skF_14',X3_376a) ),
inference(demodulation,[status(thm),theory(equality)],[c_12612,c_12485,c_11184,c_5263]) ).
tff(c_13224,plain,
! [X3_376a: $int] :
( ~ mem(X3_376a,'#skF_4')
| ~ $less($sum($uminus(1),'#skE_2'),'#skE_2')
| ~ $less('#skF_14',X3_376a) ),
inference(negUnitSimplification,[status(thm)],[c_11193,c_11185,c_13222]) ).
tff(c_13226,plain,
! [X3_376a: $int] :
( ~ mem(X3_376a,'#skF_4')
| ~ $less('#skF_14',X3_376a) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_13224]) ).
tff(c_17401,plain,
! [X3_9925a: $int] :
( ~ mem(X3_9925a,'#skF_4')
| ~ $less('#skE_10',X3_9925a) ),
inference(demodulation,[status(thm),theory(equality)],[c_17247,c_13226]) ).
tff(c_17424,plain,
! [X_9218a: $int] :
( ~ $less('#skE_10',X_9218a)
| ~ mem(X_9218a,'#skF_1')
| ( X_9218a = '#skF_3' ) ),
inference(resolution,[status(thm)],[c_12780,c_17401]) ).
tff(c_17651,plain,
( ~ $less('#skE_10','#skF_15')
| ( '#skF_3' = '#skF_15' ) ),
inference(resolution,[status(thm)],[c_17643,c_17424]) ).
tff(c_17661,plain,
~ $less('#skE_10','#skF_15'),
inference(splitLeft,[status(thm)],[c_17651]) ).
tff(c_17104,plain,
max('#skF_14','#skF_3') = '#skE_10',
inference(define,[status(thm),theory(equality)],[c_17095]) ).
tff(c_17487,plain,
max('#skE_10','#skF_3') = '#skE_10',
inference(demodulation,[status(thm),theory(equality)],[c_17247,c_17104]) ).
tff(c_1187,plain,
( ~ $lesseq('#skF_15',max('#skF_14','#skF_3'))
| ~ mem(max('#skF_14','#skF_3'),'#skF_1')
| ( empty = '#skF_4' )
| ~ $less(size('#skF_4'),size('#skF_1'))
| ~ $lesseq(0,size('#skF_1'))
| ( node('#skF_16','#skF_17','#skF_18') = '#skF_2' )
| ( empty = '#skF_1' ) ),
inference(cnfTransformation,[status(thm)],[f_249]) ).
tff(c_1823,plain,
( $less(max('#skF_14','#skF_3'),'#skF_15')
| ~ mem(max('#skF_14','#skF_3'),'#skF_1')
| ( empty = '#skF_4' )
| ~ $less(size('#skF_4'),size('#skF_1'))
| $less(size('#skF_1'),0)
| ( node('#skF_16','#skF_17','#skF_18') = '#skF_2' )
| ( empty = '#skF_1' ) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_1187]) ).
tff(c_5019,plain,
( $less(max('#skF_14','#skF_3'),'#skF_15')
| ~ mem(max('#skF_14','#skF_3'),'#skF_1')
| ( empty = '#skF_4' )
| ~ $less(size('#skF_4'),size('#skF_1'))
| $less(size('#skF_1'),0)
| ( node('#skF_16','#skF_17','#skF_18') = '#skF_2' ) ),
inference(negUnitSimplification,[status(thm)],[c_79,c_1823]) ).
tff(c_5267,plain,
( $less(max('#skF_14','#skF_3'),'#skF_15')
| ~ mem(max('#skF_14','#skF_3'),'#skF_1')
| ( empty = '#skF_4' )
| ~ $less(size('#skF_4'),size('#skF_1'))
| ( node('#skF_16','#skF_17','#skF_18') = '#skF_2' ) ),
inference(negUnitSimplification,[status(thm)],[c_3729,c_5019]) ).
tff(c_17831,plain,
( $less('#skE_10','#skF_15')
| ( '#skF_4' = '#skF_2' )
| ~ $less($sum($uminus(1),'#skE_2'),'#skE_2')
| ( node('#skF_16','#skF_17','#skF_18') = '#skF_2' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_12485,c_12612,c_11184,c_17376,c_17487,c_17247,c_17487,c_17247,c_5267]) ).
tff(c_17833,plain,
~ $less($sum($uminus(1),'#skE_2'),'#skE_2'),
inference(negUnitSimplification,[status(thm)],[c_11193,c_11185,c_17661,c_17831]) ).
tff(c_17835,plain,
$false,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_17833]) ).
tff(c_17839,plain,
$less('#skE_10','#skF_15'),
inference(splitRight,[status(thm)],[c_17651]) ).
tff(c_12782,plain,
! [X_9223a: $int] :
( mem(X_9223a,'#skF_4')
| ~ mem(X_9223a,'#skF_1')
| ( X_9223a = '#skF_3' ) ),
inference(negUnitSimplification,[status(thm)],[c_11195,c_12767]) ).
tff(c_926,plain,
! [X3_396a: $int] :
( ( empty = '#skF_4' )
| mem('#skF_14','#skF_4')
| ( empty = '#skF_4' )
| ~ $less(size('#skF_4'),size('#skF_1'))
| ~ $lesseq(0,size('#skF_1'))
| ~ mem(X3_396a,'#skF_4')
| ( empty = '#skF_4' )
| ~ $less(size('#skF_4'),size('#skF_1'))
| ~ $lesseq(0,size('#skF_1'))
| ( empty = '#skF_1' )
| $lesseq(X3_396a,'#skF_19') ),
inference(cnfTransformation,[status(thm)],[f_249]) ).
tff(c_2265,plain,
! [X3_396a: $int] :
( mem('#skF_14','#skF_4')
| ~ mem(X3_396a,'#skF_4')
| ( empty = '#skF_4' )
| ~ $less(size('#skF_4'),size('#skF_1'))
| $less(size('#skF_1'),0)
| ( empty = '#skF_1' )
| ~ $less('#skF_19',X3_396a) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_926]) ).
tff(c_4931,plain,
! [X3_396a: $int] :
( mem('#skF_14','#skF_4')
| ~ mem(X3_396a,'#skF_4')
| ( empty = '#skF_4' )
| ~ $less(size('#skF_4'),size('#skF_1'))
| $less(size('#skF_1'),0)
| ~ $less('#skF_19',X3_396a) ),
inference(negUnitSimplification,[status(thm)],[c_79,c_2265]) ).
tff(c_5201,plain,
! [X3_396a: $int] :
( mem('#skF_14','#skF_4')
| ~ mem(X3_396a,'#skF_4')
| ( empty = '#skF_4' )
| ~ $less(size('#skF_4'),size('#skF_1'))
| ~ $less('#skF_19',X3_396a) ),
inference(negUnitSimplification,[status(thm)],[c_3729,c_4931]) ).
tff(c_12708,plain,
! [X3_396a: $int] :
( mem('#skF_14','#skF_4')
| ~ mem(X3_396a,'#skF_4')
| ( '#skF_4' = '#skF_2' )
| ~ $less($sum($uminus(1),'#skE_2'),'#skE_2')
| ~ $less('#skF_19',X3_396a) ),
inference(demodulation,[status(thm),theory(equality)],[c_12612,c_12485,c_11184,c_5201]) ).
tff(c_12710,plain,
! [X3_396a: $int] :
( mem('#skF_14','#skF_4')
| ~ mem(X3_396a,'#skF_4')
| ~ $less($sum($uminus(1),'#skE_2'),'#skE_2')
| ~ $less('#skF_19',X3_396a) ),
inference(negUnitSimplification,[status(thm)],[c_11185,c_12708]) ).
tff(c_12713,plain,
! [X3_396a: $int] :
( mem('#skF_14','#skF_4')
| ~ mem(X3_396a,'#skF_4')
| ~ $less('#skF_19',X3_396a) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_12710]) ).
tff(c_12716,plain,
! [X3_396a: $int] :
( ~ mem(X3_396a,'#skF_4')
| ~ $less('#skF_19',X3_396a) ),
inference(splitLeft,[status(thm)],[c_12713]) ).
tff(c_12790,plain,
! [X_9223a: $int] :
( ~ $less('#skF_19',X_9223a)
| ~ mem(X_9223a,'#skF_1')
| ( X_9223a = '#skF_3' ) ),
inference(resolution,[status(thm)],[c_12782,c_12716]) ).
tff(c_17653,plain,
( ~ $less('#skF_19','#skF_15')
| ( '#skF_3' = '#skF_15' ) ),
inference(resolution,[status(thm)],[c_17643,c_12790]) ).
tff(c_17655,plain,
~ $less('#skF_19','#skF_15'),
inference(splitLeft,[status(thm)],[c_17653]) ).
tff(c_12480,plain,
size('#skF_1') = '#skE_2',
inference(define,[status(thm),theory(equality)],[c_12477]) ).
tff(c_12479,plain,
size('#skF_4') = '#skE_7',
inference(define,[status(thm),theory(equality)],[c_12477]) ).
tff(c_12478,plain,
( mem('#skF_14','#skF_4')
| mem('#skF_19','#skF_4')
| ~ $less(size('#skF_4'),size('#skF_1')) ),
inference(negUnitSimplification,[status(thm)],[c_11185,c_12473]) ).
tff(c_12488,plain,
( mem('#skF_14','#skF_4')
| mem('#skF_19','#skF_4')
| ~ $less('#skE_7','#skE_2') ),
inference(demodulation,[status(thm),theory(equality)],[c_12480,c_12479,c_12478]) ).
tff(c_12698,plain,
( mem('#skF_14','#skF_4')
| mem('#skF_19','#skF_4')
| ~ $less($sum($uminus(1),'#skE_2'),'#skE_2') ),
inference(demodulation,[status(thm),theory(equality)],[c_12536,c_12488]) ).
tff(c_12701,plain,
( mem('#skF_14','#skF_4')
| mem('#skF_19','#skF_4') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_12698]) ).
tff(c_12706,plain,
mem('#skF_19','#skF_4'),
inference(splitLeft,[status(thm)],[c_12701]) ).
tff(c_13227,plain,
! [X3_9314a: $int] :
( ~ mem(X3_9314a,'#skF_4')
| ~ $less('#skF_14',X3_9314a) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_13224]) ).
tff(c_13252,plain,
~ $less('#skF_14','#skF_19'),
inference(resolution,[status(thm)],[c_12706,c_13227]) ).
tff(c_17304,plain,
~ $less('#skE_10','#skF_19'),
inference(demodulation,[status(thm),theory(equality)],[c_17247,c_13252]) ).
tff(c_17965,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_17839,c_17655,c_17304]) ).
tff(c_17968,plain,
'#skF_3' = '#skF_15',
inference(splitRight,[status(thm)],[c_17653]) ).
tff(c_17292,plain,
$less('#skF_3','#skE_10'),
inference(demodulation,[status(thm),theory(equality)],[c_17247,c_17237]) ).
tff(c_18003,plain,
$less('#skF_15','#skE_10'),
inference(demodulation,[status(thm),theory(equality)],[c_17968,c_17292]) ).
tff(c_17969,plain,
$less('#skF_19','#skF_15'),
inference(splitRight,[status(thm)],[c_17653]) ).
tff(c_12886,plain,
mem('#skF_14','#skF_4'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_12881]) ).
tff(c_12900,plain,
~ $less('#skF_19','#skF_14'),
inference(resolution,[status(thm)],[c_12886,c_12716]) ).
tff(c_17310,plain,
~ $less('#skF_19','#skE_10'),
inference(demodulation,[status(thm),theory(equality)],[c_17247,c_12900]) ).
tff(c_18034,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_18003,c_17969,c_17310]) ).
tff(c_18037,plain,
'#skF_3' = '#skE_10',
inference(splitRight,[status(thm)],[c_17231]) ).
tff(c_18183,plain,
mem('#skE_10','#skF_1'),
inference(demodulation,[status(thm),theory(equality)],[c_18037,c_5548]) ).
tff(c_18292,plain,
max('#skF_14','#skE_10') = '#skE_10',
inference(demodulation,[status(thm),theory(equality)],[c_18037,c_17104]) ).
tff(c_18636,plain,
( $less('#skE_10','#skF_15')
| ( '#skF_4' = '#skF_2' )
| ~ $less($sum($uminus(1),'#skE_2'),'#skE_2')
| ( node('#skF_16','#skF_17','#skF_18') = '#skF_2' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_12485,c_12612,c_11184,c_18183,c_18292,c_18037,c_18292,c_18037,c_5267]) ).
tff(c_18638,plain,
( $less('#skE_10','#skF_15')
| ~ $less($sum($uminus(1),'#skE_2'),'#skE_2') ),
inference(negUnitSimplification,[status(thm)],[c_11193,c_11185,c_18636]) ).
tff(c_18640,plain,
$less('#skE_10','#skF_15'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_18638]) ).
tff(c_18450,plain,
mem('#skF_15','#skF_1'),
inference(demodulation,[status(thm),theory(equality)],[c_18183,c_17107]) ).
tff(c_13250,plain,
! [X_9218a: $int] :
( ~ $less('#skF_14',X_9218a)
| ~ mem(X_9218a,'#skF_1')
| ( X_9218a = '#skF_3' ) ),
inference(resolution,[status(thm)],[c_12780,c_13227]) ).
tff(c_18071,plain,
! [X_9218a: $int] :
( ~ $less('#skF_14',X_9218a)
| ~ mem(X_9218a,'#skF_1')
| ( X_9218a = '#skE_10' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_18037,c_13250]) ).
tff(c_18458,plain,
( ~ $less('#skF_14','#skF_15')
| ( '#skF_15' = '#skE_10' ) ),
inference(resolution,[status(thm)],[c_18450,c_18071]) ).
tff(c_18462,plain,
~ $less('#skF_14','#skF_15'),
inference(splitLeft,[status(thm)],[c_18458]) ).
tff(c_17204,plain,
~ $less('#skE_10','#skF_14'),
inference(superposition,[status(thm),theory(equality)],[c_17110,c_3750]) ).
tff(c_18642,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_18640,c_18462,c_17204]) ).
tff(c_18645,plain,
'#skF_15' = '#skE_10',
inference(splitRight,[status(thm)],[c_18458]) ).
tff(c_19031,plain,
( $less('#skE_10','#skE_10')
| ( '#skF_4' = '#skF_2' )
| ~ $less($sum($uminus(1),'#skE_2'),'#skE_2')
| ( node('#skF_16','#skF_17','#skF_18') = '#skF_2' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_12485,c_12612,c_11184,c_18183,c_18292,c_18037,c_18292,c_18645,c_18037,c_5267]) ).
tff(c_19033,plain,
( $less('#skE_10','#skE_10')
| ~ $less($sum($uminus(1),'#skE_2'),'#skE_2') ),
inference(negUnitSimplification,[status(thm)],[c_11193,c_11185,c_19031]) ).
tff(c_19035,plain,
$false,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_19033]) ).
tff(c_19039,plain,
mem('#skF_14','#skF_4'),
inference(splitRight,[status(thm)],[c_12713]) ).
tff(c_26759,plain,
mem('#skE_10','#skF_4'),
inference(demodulation,[status(thm),theory(equality)],[c_26509,c_19039]) ).
tff(c_26806,plain,
mem('#skE_10','#skF_1'),
inference(resolution,[status(thm)],[c_26759,c_12037]) ).
tff(c_11370,plain,
! [X_19a: $int] : ( max(X_19a,X_19a) = X_19a ),
inference(factorization,[status(thm),theory(equality)],[c_3748]) ).
tff(c_26488,plain,
( ( '#skF_3' = '#skE_10' )
| ( '#skF_3' != '#skF_14' ) ),
inference(superposition,[status(thm),theory(equality)],[c_11370,c_26377]) ).
tff(c_26505,plain,
'#skF_3' != '#skF_14',
inference(splitLeft,[status(thm)],[c_26488]) ).
tff(c_26549,plain,
'#skF_3' != '#skE_10',
inference(demodulation,[status(thm),theory(equality)],[c_26509,c_26505]) ).
tff(c_26469,plain,
( ( '#skF_3' = '#skE_10' )
| $less('#skF_3','#skF_14') ),
inference(superposition,[status(thm),theory(equality)],[c_26377,c_3743]) ).
tff(c_26592,plain,
( ( '#skF_3' = '#skE_10' )
| $less('#skF_3','#skE_10') ),
inference(demodulation,[status(thm),theory(equality)],[c_26509,c_26469]) ).
tff(c_26594,plain,
$less('#skF_3','#skE_10'),
inference(negUnitSimplification,[status(thm)],[c_26549,c_26592]) ).
tff(c_26574,plain,
( mem('#skF_15','#skF_1')
| ~ mem(max('#skE_10','#skF_3'),'#skF_1')
| ( '#skF_4' = '#skF_2' )
| ~ $less($sum($uminus(1),'#skE_2'),'#skE_2')
| ( node('#skF_16','#skF_17','#skF_18') = '#skF_2' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_12485,c_12612,c_11184,c_26509,c_5271]) ).
tff(c_26576,plain,
( mem('#skF_15','#skF_1')
| ~ mem(max('#skE_10','#skF_3'),'#skF_1')
| ~ $less($sum($uminus(1),'#skE_2'),'#skE_2') ),
inference(negUnitSimplification,[status(thm)],[c_11193,c_11185,c_26574]) ).
tff(c_26579,plain,
( mem('#skF_15','#skF_1')
| ~ mem(max('#skE_10','#skF_3'),'#skF_1') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_26576]) ).
tff(c_26605,plain,
max('#skE_10','#skF_3') = '#skE_13',
inference(define,[status(thm),theory(equality)],[c_26579]) ).
tff(c_11373,plain,
! [X_9079a: $int,Y_9080a: $int] :
( ( max(X_9079a,Y_9080a) = Y_9080a )
| ( max(X_9079a,Y_9080a) = X_9079a ) ),
inference(cnfTransformation,[status(thm)],[f_62]) ).
tff(c_11438,plain,
! [Y_9080a: $int,X_9079a: $int] :
( ~ $less(Y_9080a,X_9079a)
| ( max(X_9079a,Y_9080a) = X_9079a ) ),
inference(superposition,[status(thm),theory(equality)],[c_11373,c_3750]) ).
tff(c_26617,plain,
( ~ $less('#skF_3','#skE_10')
| ( '#skE_13' = '#skE_10' ) ),
inference(superposition,[status(thm),theory(equality)],[c_26605,c_11438]) ).
tff(c_26687,plain,
'#skE_13' = '#skE_10',
inference(demodulation,[status(thm),theory(equality)],[c_26594,c_26617]) ).
tff(c_26879,plain,
( $less(max('#skE_10','#skF_3'),'#skF_15')
| ~ mem(max('#skE_10','#skF_3'),'#skF_1')
| ( '#skF_4' = '#skF_2' )
| ~ $less($sum($uminus(1),'#skE_2'),'#skE_2')
| ( node('#skF_16','#skF_17','#skF_18') = '#skF_2' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_12485,c_12612,c_11184,c_26509,c_26509,c_5267]) ).
tff(c_26881,plain,
( $less(max('#skE_10','#skF_3'),'#skF_15')
| ~ mem(max('#skE_10','#skF_3'),'#skF_1')
| ~ $less($sum($uminus(1),'#skE_2'),'#skE_2') ),
inference(negUnitSimplification,[status(thm)],[c_11193,c_11185,c_26879]) ).
tff(c_26884,plain,
( $less(max('#skE_10','#skF_3'),'#skF_15')
| ~ mem(max('#skE_10','#skF_3'),'#skF_1') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_26881]) ).
tff(c_26886,plain,
max('#skE_10','#skF_3') = '#skE_13',
inference(define,[status(thm),theory(equality)],[c_26884]) ).
tff(c_26885,plain,
( $less(max('#skE_10','#skF_3'),'#skF_15')
| ~ mem(max('#skE_10','#skF_3'),'#skF_1') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_26881]) ).
tff(c_26889,plain,
( $less('#skE_13','#skF_15')
| ~ mem('#skE_13','#skF_1') ),
inference(demodulation,[status(thm),theory(equality)],[c_26886,c_26886,c_26885]) ).
tff(c_26900,plain,
$less('#skE_10','#skF_15'),
inference(demodulation,[status(thm),theory(equality)],[c_26806,c_26687,c_26687,c_26889]) ).
tff(c_26581,plain,
max('#skE_10','#skF_3') = '#skE_13',
inference(define,[status(thm),theory(equality)],[c_26579]) ).
tff(c_26580,plain,
( mem('#skF_15','#skF_1')
| ~ mem(max('#skE_10','#skF_3'),'#skF_1') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_26576]) ).
tff(c_26591,plain,
( mem('#skF_15','#skF_1')
| ~ mem('#skE_13','#skF_1') ),
inference(demodulation,[status(thm),theory(equality)],[c_26581,c_26580]) ).
tff(c_27131,plain,
mem('#skF_15','#skF_1'),
inference(demodulation,[status(thm),theory(equality)],[c_26806,c_26687,c_26591]) ).
tff(c_19089,plain,
! [X_10129a: $int,X3_10130: tree,X1_10131: tree,X2_10132a: $int] :
( mem(X_10129a,X3_10130)
| mem(X_10129a,X1_10131)
| ~ mem(X_10129a,node(X1_10131,X2_10132a,X3_10130))
| ( X_10129a = X2_10132a ) ),
inference(cnfTransformation,[status(thm)],[f_135]) ).
tff(c_19104,plain,
! [X_10129a: $int] :
( mem(X_10129a,'#skF_4')
| mem(X_10129a,'#skF_2')
| ~ mem(X_10129a,'#skF_1')
| ( X_10129a = '#skF_3' ) ),
inference(superposition,[status(thm),theory(equality)],[c_4905,c_19089]) ).
tff(c_19117,plain,
! [X_10129a: $int] :
( mem(X_10129a,'#skF_4')
| ~ mem(X_10129a,'#skF_1')
| ( X_10129a = '#skF_3' ) ),
inference(negUnitSimplification,[status(thm)],[c_11195,c_19104]) ).
tff(c_19477,plain,
! [X3_376a: $int] :
( ~ mem(X3_376a,'#skF_4')
| ( '#skF_4' = '#skF_2' )
| ~ $less($sum($uminus(1),'#skE_2'),'#skE_2')
| ( node('#skF_16','#skF_17','#skF_18') = '#skF_2' )
| ~ $less('#skF_14',X3_376a) ),
inference(demodulation,[status(thm),theory(equality)],[c_12485,c_12612,c_11184,c_5263]) ).
tff(c_19479,plain,
! [X3_376a: $int] :
( ~ mem(X3_376a,'#skF_4')
| ~ $less($sum($uminus(1),'#skE_2'),'#skE_2')
| ~ $less('#skF_14',X3_376a) ),
inference(negUnitSimplification,[status(thm)],[c_11193,c_11185,c_19477]) ).
tff(c_19481,plain,
! [X3_376a: $int] :
( ~ mem(X3_376a,'#skF_4')
| ~ $less('#skF_14',X3_376a) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_19479]) ).
tff(c_26846,plain,
! [X3_11643a: $int] :
( ~ mem(X3_11643a,'#skF_4')
| ~ $less('#skE_10',X3_11643a) ),
inference(demodulation,[status(thm),theory(equality)],[c_26509,c_19481]) ).
tff(c_26869,plain,
! [X_10129a: $int] :
( ~ $less('#skE_10',X_10129a)
| ~ mem(X_10129a,'#skF_1')
| ( X_10129a = '#skF_3' ) ),
inference(resolution,[status(thm)],[c_19117,c_26846]) ).
tff(c_27134,plain,
( ~ $less('#skE_10','#skF_15')
| ( '#skF_3' = '#skF_15' ) ),
inference(resolution,[status(thm)],[c_27131,c_26869]) ).
tff(c_27138,plain,
'#skF_3' = '#skF_15',
inference(demodulation,[status(thm),theory(equality)],[c_26900,c_27134]) ).
tff(c_26473,plain,
~ $less('#skE_10','#skF_3'),
inference(superposition,[status(thm),theory(equality)],[c_26377,c_3749]) ).
tff(c_27156,plain,
~ $less('#skE_10','#skF_15'),
inference(demodulation,[status(thm),theory(equality)],[c_27138,c_26473]) ).
tff(c_27179,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_26900,c_27156]) ).
tff(c_27182,plain,
'#skF_3' = '#skE_10',
inference(splitRight,[status(thm)],[c_26465]) ).
tff(c_27341,plain,
mem('#skE_10','#skF_1'),
inference(demodulation,[status(thm),theory(equality)],[c_27182,c_5548]) ).
tff(c_27183,plain,
'#skF_14' != '#skE_10',
inference(splitRight,[status(thm)],[c_26465]) ).
tff(c_26467,plain,
( ( '#skF_14' = '#skE_10' )
| $less('#skF_14','#skF_3') ),
inference(superposition,[status(thm),theory(equality)],[c_26377,c_3744]) ).
tff(c_27335,plain,
( ( '#skF_14' = '#skE_10' )
| $less('#skF_14','#skE_10') ),
inference(demodulation,[status(thm),theory(equality)],[c_27182,c_26467]) ).
tff(c_27337,plain,
$less('#skF_14','#skE_10'),
inference(negUnitSimplification,[status(thm)],[c_27183,c_27335]) ).
tff(c_27307,plain,
( mem('#skF_15','#skF_1')
| ~ mem(max('#skF_14','#skE_10'),'#skF_1')
| ( '#skF_4' = '#skF_2' )
| ~ $less($sum($uminus(1),'#skE_2'),'#skE_2')
| ( node('#skF_16','#skF_17','#skF_18') = '#skF_2' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_12485,c_12612,c_11184,c_27182,c_5271]) ).
tff(c_27309,plain,
( mem('#skF_15','#skF_1')
| ~ mem(max('#skF_14','#skE_10'),'#skF_1')
| ~ $less($sum($uminus(1),'#skE_2'),'#skE_2') ),
inference(negUnitSimplification,[status(thm)],[c_11193,c_11185,c_27307]) ).
tff(c_27312,plain,
( mem('#skF_15','#skF_1')
| ~ mem(max('#skF_14','#skE_10'),'#skF_1') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_27309]) ).
tff(c_27349,plain,
max('#skF_14','#skE_10') = '#skE_14',
inference(define,[status(thm),theory(equality)],[c_27312]) ).
tff(c_11447,plain,
! [X_9079a: $int,Y_9080a: $int] :
( ~ $less(X_9079a,Y_9080a)
| ( max(X_9079a,Y_9080a) = Y_9080a ) ),
inference(superposition,[status(thm),theory(equality)],[c_11373,c_3749]) ).
tff(c_27364,plain,
( ~ $less('#skF_14','#skE_10')
| ( '#skE_14' = '#skE_10' ) ),
inference(superposition,[status(thm),theory(equality)],[c_27349,c_11447]) ).
tff(c_27433,plain,
'#skE_14' = '#skE_10',
inference(demodulation,[status(thm),theory(equality)],[c_27337,c_27364]) ).
tff(c_27314,plain,
max('#skF_14','#skE_10') = '#skE_14',
inference(define,[status(thm),theory(equality)],[c_27312]) ).
tff(c_27313,plain,
( mem('#skF_15','#skF_1')
| ~ mem(max('#skF_14','#skE_10'),'#skF_1') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_27309]) ).
tff(c_27324,plain,
( mem('#skF_15','#skF_1')
| ~ mem('#skE_14','#skF_1') ),
inference(demodulation,[status(thm),theory(equality)],[c_27314,c_27313]) ).
tff(c_27862,plain,
mem('#skF_15','#skF_1'),
inference(demodulation,[status(thm),theory(equality)],[c_27341,c_27433,c_27324]) ).
tff(c_19482,plain,
! [X3_10188a: $int] :
( ~ mem(X3_10188a,'#skF_4')
| ~ $less('#skF_14',X3_10188a) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_19479]) ).
tff(c_19502,plain,
! [X_10129a: $int] :
( ~ $less('#skF_14',X_10129a)
| ~ mem(X_10129a,'#skF_1')
| ( X_10129a = '#skF_3' ) ),
inference(resolution,[status(thm)],[c_19117,c_19482]) ).
tff(c_27214,plain,
! [X_10129a: $int] :
( ~ $less('#skF_14',X_10129a)
| ~ mem(X_10129a,'#skF_1')
| ( X_10129a = '#skE_10' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_27182,c_19502]) ).
tff(c_27872,plain,
( ~ $less('#skF_14','#skF_15')
| ( '#skF_15' = '#skE_10' ) ),
inference(resolution,[status(thm)],[c_27862,c_27214]) ).
tff(c_27874,plain,
~ $less('#skF_14','#skF_15'),
inference(splitLeft,[status(thm)],[c_27872]) ).
tff(c_26371,plain,
max('#skF_14','#skF_3') = '#skE_10',
inference(define,[status(thm),theory(equality)],[c_26362]) ).
tff(c_27611,plain,
max('#skF_14','#skE_10') = '#skE_10',
inference(demodulation,[status(thm),theory(equality)],[c_27182,c_26371]) ).
tff(c_27849,plain,
( $less('#skE_10','#skF_15')
| ( '#skF_4' = '#skF_2' )
| ~ $less($sum($uminus(1),'#skE_2'),'#skE_2')
| ( node('#skF_16','#skF_17','#skF_18') = '#skF_2' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_12485,c_12612,c_11184,c_27341,c_27611,c_27182,c_27611,c_27182,c_5267]) ).
tff(c_27851,plain,
( $less('#skE_10','#skF_15')
| ~ $less($sum($uminus(1),'#skE_2'),'#skE_2') ),
inference(negUnitSimplification,[status(thm)],[c_11193,c_11185,c_27849]) ).
tff(c_27853,plain,
$less('#skE_10','#skF_15'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_27851]) ).
tff(c_26471,plain,
~ $less('#skE_10','#skF_14'),
inference(superposition,[status(thm),theory(equality)],[c_26377,c_3750]) ).
tff(c_27876,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_27874,c_27853,c_26471]) ).
tff(c_27879,plain,
'#skF_15' = '#skE_10',
inference(splitRight,[status(thm)],[c_27872]) ).
tff(c_27890,plain,
$less('#skE_10','#skE_10'),
inference(demodulation,[status(thm),theory(equality)],[c_27879,c_27853]) ).
tff(c_27895,plain,
$false,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_27890]) ).
tff(c_27898,plain,
'#skF_3' = '#skE_10',
inference(splitRight,[status(thm)],[c_26488]) ).
tff(c_27899,plain,
'#skF_3' = '#skF_14',
inference(splitRight,[status(thm)],[c_26488]) ).
tff(c_27936,plain,
'#skF_14' = '#skE_10',
inference(demodulation,[status(thm),theory(equality)],[c_27898,c_27899]) ).
tff(c_19049,plain,
mem('#skF_14','#skF_4'),
inference(splitRight,[status(thm)],[c_12713]) ).
tff(c_19055,plain,
mem('#skF_14','#skF_1'),
inference(resolution,[status(thm)],[c_19049,c_12037]) ).
tff(c_28163,plain,
mem('#skE_10','#skF_1'),
inference(demodulation,[status(thm),theory(equality)],[c_27936,c_19055]) ).
tff(c_28003,plain,
( mem('#skF_15','#skF_1')
| ~ mem('#skE_10','#skF_1')
| ( '#skF_4' = '#skF_2' )
| ~ $less($sum($uminus(1),'#skE_2'),'#skE_2')
| ( node('#skF_16','#skF_17','#skF_18') = '#skF_2' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_12485,c_12612,c_11184,c_11370,c_27936,c_27898,c_5271]) ).
tff(c_28005,plain,
( mem('#skF_15','#skF_1')
| ~ mem('#skE_10','#skF_1')
| ~ $less($sum($uminus(1),'#skE_2'),'#skE_2') ),
inference(negUnitSimplification,[status(thm)],[c_11193,c_11185,c_28003]) ).
tff(c_28008,plain,
( mem('#skF_15','#skF_1')
| ~ mem('#skE_10','#skF_1') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_28005]) ).
tff(c_28013,plain,
~ mem('#skE_10','#skF_1'),
inference(splitLeft,[status(thm)],[c_28008]) ).
tff(c_28166,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_28163,c_28013]) ).
tff(c_28170,plain,
mem('#skF_15','#skF_1'),
inference(splitRight,[status(thm)],[c_28008]) ).
tff(c_27926,plain,
! [X_10129a: $int] :
( ~ $less('#skF_14',X_10129a)
| ~ mem(X_10129a,'#skF_1')
| ( X_10129a = '#skF_14' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_27899,c_19502]) ).
tff(c_28384,plain,
! [X_11872a: $int] :
( ~ $less('#skE_10',X_11872a)
| ~ mem(X_11872a,'#skF_1')
| ( X_11872a = '#skE_10' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_27936,c_27936,c_27926]) ).
tff(c_28404,plain,
( ~ $less('#skE_10','#skF_15')
| ( '#skF_15' = '#skE_10' ) ),
inference(resolution,[status(thm)],[c_28170,c_28384]) ).
tff(c_28411,plain,
~ $less('#skE_10','#skF_15'),
inference(splitLeft,[status(thm)],[c_28404]) ).
tff(c_28517,plain,
( $less('#skE_10','#skF_15')
| ( '#skF_4' = '#skF_2' )
| ~ $less($sum($uminus(1),'#skE_2'),'#skE_2')
| ( node('#skF_16','#skF_17','#skF_18') = '#skF_2' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_12485,c_12612,c_11184,c_28163,c_11370,c_27898,c_27936,c_11370,c_27898,c_27936,c_5267]) ).
tff(c_28519,plain,
~ $less($sum($uminus(1),'#skE_2'),'#skE_2'),
inference(negUnitSimplification,[status(thm)],[c_11193,c_11185,c_28411,c_28517]) ).
tff(c_28521,plain,
$false,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_28519]) ).
tff(c_28524,plain,
'#skF_15' = '#skE_10',
inference(splitRight,[status(thm)],[c_28404]) ).
tff(c_28525,plain,
$less('#skE_10','#skF_15'),
inference(splitRight,[status(thm)],[c_28404]) ).
tff(c_28533,plain,
$less('#skE_10','#skE_10'),
inference(demodulation,[status(thm),theory(equality)],[c_28524,c_28525]) ).
tff(c_28535,plain,
$false,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_28533]) ).
tff(c_28539,plain,
mem('#skF_14','#skF_4'),
inference(splitRight,[status(thm)],[c_12701]) ).
tff(c_42275,plain,
mem('#skE_10','#skF_4'),
inference(demodulation,[status(thm),theory(equality)],[c_41412,c_28539]) ).
tff(c_42495,plain,
mem('#skE_10','#skF_1'),
inference(resolution,[status(thm)],[c_42275,c_12037]) ).
tff(c_41395,plain,
( ( '#skF_3' = '#skE_10' )
| ( '#skF_3' != '#skF_14' ) ),
inference(superposition,[status(thm),theory(equality)],[c_11370,c_41284]) ).
tff(c_41410,plain,
'#skF_3' != '#skF_14',
inference(splitLeft,[status(thm)],[c_41395]) ).
tff(c_41457,plain,
'#skF_3' != '#skE_10',
inference(demodulation,[status(thm),theory(equality)],[c_41412,c_41410]) ).
tff(c_41376,plain,
( ( '#skF_3' = '#skE_10' )
| $less('#skF_3','#skF_14') ),
inference(superposition,[status(thm),theory(equality)],[c_41284,c_3743]) ).
tff(c_42268,plain,
( ( '#skF_3' = '#skE_10' )
| $less('#skF_3','#skE_10') ),
inference(demodulation,[status(thm),theory(equality)],[c_41412,c_41376]) ).
tff(c_42270,plain,
$less('#skF_3','#skE_10'),
inference(negUnitSimplification,[status(thm)],[c_41457,c_42268]) ).
tff(c_42248,plain,
( mem('#skF_15','#skF_1')
| ~ mem(max('#skE_10','#skF_3'),'#skF_1')
| ( '#skF_4' = '#skF_2' )
| ~ $less($sum($uminus(1),'#skE_2'),'#skE_2')
| ( node('#skF_16','#skF_17','#skF_18') = '#skF_2' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_12485,c_12612,c_11184,c_41412,c_5271]) ).
tff(c_42250,plain,
( mem('#skF_15','#skF_1')
| ~ mem(max('#skE_10','#skF_3'),'#skF_1')
| ~ $less($sum($uminus(1),'#skE_2'),'#skE_2') ),
inference(negUnitSimplification,[status(thm)],[c_11193,c_11185,c_42248]) ).
tff(c_42253,plain,
( mem('#skF_15','#skF_1')
| ~ mem(max('#skE_10','#skF_3'),'#skF_1') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_42250]) ).
tff(c_42290,plain,
max('#skE_10','#skF_3') = '#skE_13',
inference(define,[status(thm),theory(equality)],[c_42253]) ).
tff(c_42302,plain,
( ~ $less('#skF_3','#skE_10')
| ( '#skE_13' = '#skE_10' ) ),
inference(superposition,[status(thm),theory(equality)],[c_42290,c_11438]) ).
tff(c_42372,plain,
'#skE_13' = '#skE_10',
inference(demodulation,[status(thm),theory(equality)],[c_42270,c_42302]) ).
tff(c_42654,plain,
( $less(max('#skE_10','#skF_3'),'#skF_15')
| ~ mem(max('#skE_10','#skF_3'),'#skF_1')
| ( '#skF_4' = '#skF_2' )
| ~ $less($sum($uminus(1),'#skE_2'),'#skE_2')
| ( node('#skF_16','#skF_17','#skF_18') = '#skF_2' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_12485,c_12612,c_11184,c_41412,c_41412,c_5267]) ).
tff(c_42656,plain,
( $less(max('#skE_10','#skF_3'),'#skF_15')
| ~ mem(max('#skE_10','#skF_3'),'#skF_1')
| ~ $less($sum($uminus(1),'#skE_2'),'#skE_2') ),
inference(negUnitSimplification,[status(thm)],[c_11193,c_11185,c_42654]) ).
tff(c_42659,plain,
( $less(max('#skE_10','#skF_3'),'#skF_15')
| ~ mem(max('#skE_10','#skF_3'),'#skF_1') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_42656]) ).
tff(c_42661,plain,
max('#skE_10','#skF_3') = '#skE_13',
inference(define,[status(thm),theory(equality)],[c_42659]) ).
tff(c_42660,plain,
( $less(max('#skE_10','#skF_3'),'#skF_15')
| ~ mem(max('#skE_10','#skF_3'),'#skF_1') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_42656]) ).
tff(c_42664,plain,
( $less('#skE_13','#skF_15')
| ~ mem('#skE_13','#skF_1') ),
inference(demodulation,[status(thm),theory(equality)],[c_42661,c_42661,c_42660]) ).
tff(c_42675,plain,
$less('#skE_10','#skF_15'),
inference(demodulation,[status(thm),theory(equality)],[c_42495,c_42372,c_42372,c_42664]) ).
tff(c_42255,plain,
max('#skE_10','#skF_3') = '#skE_13',
inference(define,[status(thm),theory(equality)],[c_42253]) ).
tff(c_42254,plain,
( mem('#skF_15','#skF_1')
| ~ mem(max('#skE_10','#skF_3'),'#skF_1') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_42250]) ).
tff(c_42265,plain,
( mem('#skF_15','#skF_1')
| ~ mem('#skE_13','#skF_1') ),
inference(demodulation,[status(thm),theory(equality)],[c_42255,c_42254]) ).
tff(c_42838,plain,
mem('#skF_15','#skF_1'),
inference(demodulation,[status(thm),theory(equality)],[c_42495,c_42372,c_42265]) ).
tff(c_28540,plain,
! [X_11885a: $int,X3_11886: tree,X1_11887: tree,X2_11888a: $int] :
( mem(X_11885a,X3_11886)
| mem(X_11885a,X1_11887)
| ~ mem(X_11885a,node(X1_11887,X2_11888a,X3_11886))
| ( X_11885a = X2_11888a ) ),
inference(cnfTransformation,[status(thm)],[f_135]) ).
tff(c_28555,plain,
! [X_11885a: $int] :
( mem(X_11885a,'#skF_4')
| mem(X_11885a,'#skF_2')
| ~ mem(X_11885a,'#skF_1')
| ( X_11885a = '#skF_3' ) ),
inference(superposition,[status(thm),theory(equality)],[c_4905,c_28540]) ).
tff(c_28568,plain,
! [X_11885a: $int] :
( mem(X_11885a,'#skF_4')
| ~ mem(X_11885a,'#skF_1')
| ( X_11885a = '#skF_3' ) ),
inference(negUnitSimplification,[status(thm)],[c_11195,c_28555]) ).
tff(c_35354,plain,
! [X3_376a: $int] :
( ~ mem(X3_376a,'#skF_4')
| ( '#skF_4' = '#skF_2' )
| ~ $less($sum($uminus(1),'#skE_2'),'#skE_2')
| ( node('#skF_16','#skF_17','#skF_18') = '#skF_2' )
| ~ $less('#skF_14',X3_376a) ),
inference(demodulation,[status(thm),theory(equality)],[c_12485,c_12612,c_11184,c_5263]) ).
tff(c_35356,plain,
! [X3_376a: $int] :
( ~ mem(X3_376a,'#skF_4')
| ~ $less($sum($uminus(1),'#skE_2'),'#skE_2')
| ~ $less('#skF_14',X3_376a) ),
inference(negUnitSimplification,[status(thm)],[c_11193,c_11185,c_35354]) ).
tff(c_35359,plain,
! [X3_13087a: $int] :
( ~ mem(X3_13087a,'#skF_4')
| ~ $less('#skF_14',X3_13087a) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_35356]) ).
tff(c_35381,plain,
! [X_11885a: $int] :
( ~ $less('#skF_14',X_11885a)
| ~ mem(X_11885a,'#skF_1')
| ( X_11885a = '#skF_3' ) ),
inference(resolution,[status(thm)],[c_28568,c_35359]) ).
tff(c_41465,plain,
! [X_11885a: $int] :
( ~ $less('#skE_10',X_11885a)
| ~ mem(X_11885a,'#skF_1')
| ( X_11885a = '#skF_3' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_41412,c_35381]) ).
tff(c_42841,plain,
( ~ $less('#skE_10','#skF_15')
| ( '#skF_3' = '#skF_15' ) ),
inference(resolution,[status(thm)],[c_42838,c_41465]) ).
tff(c_42848,plain,
'#skF_3' = '#skF_15',
inference(demodulation,[status(thm),theory(equality)],[c_42675,c_42841]) ).
tff(c_41380,plain,
~ $less('#skE_10','#skF_3'),
inference(superposition,[status(thm),theory(equality)],[c_41284,c_3749]) ).
tff(c_42866,plain,
~ $less('#skE_10','#skF_15'),
inference(demodulation,[status(thm),theory(equality)],[c_42848,c_41380]) ).
tff(c_42890,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_42675,c_42866]) ).
tff(c_42893,plain,
'#skF_3' = '#skE_10',
inference(splitRight,[status(thm)],[c_41369]) ).
tff(c_43056,plain,
mem('#skE_10','#skF_1'),
inference(demodulation,[status(thm),theory(equality)],[c_42893,c_5548]) ).
tff(c_41278,plain,
max('#skF_14','#skF_3') = '#skE_10',
inference(define,[status(thm),theory(equality)],[c_41269]) ).
tff(c_43302,plain,
max('#skF_14','#skE_10') = '#skE_10',
inference(demodulation,[status(thm),theory(equality)],[c_42893,c_41278]) ).
tff(c_43832,plain,
( $less('#skE_10','#skF_15')
| ( '#skF_4' = '#skF_2' )
| ~ $less($sum($uminus(1),'#skE_2'),'#skE_2')
| ( node('#skF_16','#skF_17','#skF_18') = '#skF_2' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_12485,c_12612,c_11184,c_43056,c_43302,c_42893,c_43302,c_42893,c_5267]) ).
tff(c_43834,plain,
( $less('#skE_10','#skF_15')
| ~ $less($sum($uminus(1),'#skE_2'),'#skE_2') ),
inference(negUnitSimplification,[status(thm)],[c_11193,c_11185,c_43832]) ).
tff(c_43836,plain,
$less('#skE_10','#skF_15'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_43834]) ).
tff(c_42894,plain,
'#skF_14' != '#skE_10',
inference(splitRight,[status(thm)],[c_41369]) ).
tff(c_41374,plain,
( ( '#skF_14' = '#skE_10' )
| $less('#skF_14','#skF_3') ),
inference(superposition,[status(thm),theory(equality)],[c_41284,c_3744]) ).
tff(c_42977,plain,
( ( '#skF_14' = '#skE_10' )
| $less('#skF_14','#skE_10') ),
inference(demodulation,[status(thm),theory(equality)],[c_42893,c_41374]) ).
tff(c_42979,plain,
$less('#skF_14','#skE_10'),
inference(negUnitSimplification,[status(thm)],[c_42894,c_42977]) ).
tff(c_42959,plain,
( mem('#skF_15','#skF_1')
| ~ mem(max('#skF_14','#skE_10'),'#skF_1')
| ( '#skF_4' = '#skF_2' )
| ~ $less($sum($uminus(1),'#skE_2'),'#skE_2')
| ( node('#skF_16','#skF_17','#skF_18') = '#skF_2' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_12485,c_12612,c_11184,c_42893,c_5271]) ).
tff(c_42961,plain,
( mem('#skF_15','#skF_1')
| ~ mem(max('#skF_14','#skE_10'),'#skF_1')
| ~ $less($sum($uminus(1),'#skE_2'),'#skE_2') ),
inference(negUnitSimplification,[status(thm)],[c_11193,c_11185,c_42959]) ).
tff(c_42964,plain,
( mem('#skF_15','#skF_1')
| ~ mem(max('#skF_14','#skE_10'),'#skF_1') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_42961]) ).
tff(c_43062,plain,
max('#skF_14','#skE_10') = '#skE_14',
inference(define,[status(thm),theory(equality)],[c_42964]) ).
tff(c_43077,plain,
( ~ $less('#skF_14','#skE_10')
| ( '#skE_14' = '#skE_10' ) ),
inference(superposition,[status(thm),theory(equality)],[c_43062,c_11447]) ).
tff(c_43146,plain,
'#skE_14' = '#skE_10',
inference(demodulation,[status(thm),theory(equality)],[c_42979,c_43077]) ).
tff(c_42966,plain,
max('#skF_14','#skE_10') = '#skE_14',
inference(define,[status(thm),theory(equality)],[c_42964]) ).
tff(c_42965,plain,
( mem('#skF_15','#skF_1')
| ~ mem(max('#skF_14','#skE_10'),'#skF_1') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_42961]) ).
tff(c_42976,plain,
( mem('#skF_15','#skF_1')
| ~ mem('#skE_14','#skF_1') ),
inference(demodulation,[status(thm),theory(equality)],[c_42966,c_42965]) ).
tff(c_43544,plain,
mem('#skF_15','#skF_1'),
inference(demodulation,[status(thm),theory(equality)],[c_43056,c_43146,c_42976]) ).
tff(c_43244,plain,
! [X_14429a: $int] :
( mem(X_14429a,'#skF_4')
| ~ mem(X_14429a,'#skF_1')
| ( X_14429a = '#skE_10' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_42893,c_28568]) ).
tff(c_35358,plain,
! [X3_376a: $int] :
( ~ mem(X3_376a,'#skF_4')
| ~ $less('#skF_14',X3_376a) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_35356]) ).
tff(c_43255,plain,
! [X_14429a: $int] :
( ~ $less('#skF_14',X_14429a)
| ~ mem(X_14429a,'#skF_1')
| ( X_14429a = '#skE_10' ) ),
inference(resolution,[status(thm)],[c_43244,c_35358]) ).
tff(c_43554,plain,
( ~ $less('#skF_14','#skF_15')
| ( '#skF_15' = '#skE_10' ) ),
inference(resolution,[status(thm)],[c_43544,c_43255]) ).
tff(c_43556,plain,
~ $less('#skF_14','#skF_15'),
inference(splitLeft,[status(thm)],[c_43554]) ).
tff(c_41378,plain,
~ $less('#skE_10','#skF_14'),
inference(superposition,[status(thm),theory(equality)],[c_41284,c_3750]) ).
tff(c_43838,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_43836,c_43556,c_41378]) ).
tff(c_43841,plain,
'#skF_15' = '#skE_10',
inference(splitRight,[status(thm)],[c_43554]) ).
tff(c_44225,plain,
( $less('#skE_10','#skE_10')
| ( '#skF_4' = '#skF_2' )
| ~ $less($sum($uminus(1),'#skE_2'),'#skE_2')
| ( node('#skF_16','#skF_17','#skF_18') = '#skF_2' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_12485,c_12612,c_11184,c_43056,c_43302,c_42893,c_43302,c_43841,c_42893,c_5267]) ).
tff(c_44227,plain,
( $less('#skE_10','#skE_10')
| ~ $less($sum($uminus(1),'#skE_2'),'#skE_2') ),
inference(negUnitSimplification,[status(thm)],[c_11193,c_11185,c_44225]) ).
tff(c_44229,plain,
$false,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_44227]) ).
tff(c_44232,plain,
'#skF_3' = '#skE_10',
inference(splitRight,[status(thm)],[c_41395]) ).
tff(c_44233,plain,
'#skF_3' = '#skF_14',
inference(splitRight,[status(thm)],[c_41395]) ).
tff(c_44270,plain,
'#skF_14' = '#skE_10',
inference(demodulation,[status(thm),theory(equality)],[c_44232,c_44233]) ).
tff(c_28571,plain,
mem('#skF_14','#skF_4'),
inference(splitRight,[status(thm)],[c_12701]) ).
tff(c_28577,plain,
mem('#skF_14','#skF_1'),
inference(resolution,[status(thm)],[c_28571,c_12037]) ).
tff(c_44544,plain,
mem('#skE_10','#skF_1'),
inference(demodulation,[status(thm),theory(equality)],[c_44270,c_28577]) ).
tff(c_44426,plain,
( mem('#skF_15','#skF_1')
| ~ mem('#skE_10','#skF_1')
| ( '#skF_4' = '#skF_2' )
| ~ $less($sum($uminus(1),'#skE_2'),'#skE_2')
| ( node('#skF_16','#skF_17','#skF_18') = '#skF_2' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_12485,c_12612,c_11184,c_11370,c_44270,c_44232,c_5271]) ).
tff(c_44428,plain,
( mem('#skF_15','#skF_1')
| ~ mem('#skE_10','#skF_1')
| ~ $less($sum($uminus(1),'#skE_2'),'#skE_2') ),
inference(negUnitSimplification,[status(thm)],[c_11193,c_11185,c_44426]) ).
tff(c_44431,plain,
( mem('#skF_15','#skF_1')
| ~ mem('#skE_10','#skF_1') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_44428]) ).
tff(c_44436,plain,
~ mem('#skE_10','#skF_1'),
inference(splitLeft,[status(thm)],[c_44431]) ).
tff(c_44549,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_44544,c_44436]) ).
tff(c_44553,plain,
mem('#skF_15','#skF_1'),
inference(splitRight,[status(thm)],[c_44431]) ).
tff(c_44260,plain,
! [X_11885a: $int] :
( ~ $less('#skF_14',X_11885a)
| ~ mem(X_11885a,'#skF_1')
| ( X_11885a = '#skF_14' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_44233,c_35381]) ).
tff(c_44748,plain,
! [X_14647a: $int] :
( ~ $less('#skE_10',X_14647a)
| ~ mem(X_14647a,'#skF_1')
| ( X_14647a = '#skE_10' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_44270,c_44270,c_44260]) ).
tff(c_44768,plain,
( ~ $less('#skE_10','#skF_15')
| ( '#skF_15' = '#skE_10' ) ),
inference(resolution,[status(thm)],[c_44553,c_44748]) ).
tff(c_44781,plain,
~ $less('#skE_10','#skF_15'),
inference(splitLeft,[status(thm)],[c_44768]) ).
tff(c_45146,plain,
( $less('#skE_10','#skF_15')
| ( '#skF_4' = '#skF_2' )
| ~ $less($sum($uminus(1),'#skE_2'),'#skE_2')
| ( node('#skF_16','#skF_17','#skF_18') = '#skF_2' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_12485,c_12612,c_11184,c_44544,c_11370,c_44232,c_44270,c_11370,c_44232,c_44270,c_5267]) ).
tff(c_45148,plain,
~ $less($sum($uminus(1),'#skE_2'),'#skE_2'),
inference(negUnitSimplification,[status(thm)],[c_11193,c_11185,c_44781,c_45146]) ).
tff(c_45150,plain,
$false,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_45148]) ).
tff(c_45153,plain,
'#skF_15' = '#skE_10',
inference(splitRight,[status(thm)],[c_44768]) ).
tff(c_45154,plain,
$less('#skE_10','#skF_15'),
inference(splitRight,[status(thm)],[c_44768]) ).
tff(c_45162,plain,
$less('#skE_10','#skE_10'),
inference(demodulation,[status(thm),theory(equality)],[c_45153,c_45154]) ).
tff(c_45164,plain,
$false,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_45162]) ).
tff(c_45166,plain,
empty != '#skF_2',
inference(splitRight,[status(thm)],[c_11182]) ).
tff(c_1146,plain,
( ( empty = '#skF_2' )
| mem('#skF_19','#skF_4')
| ( empty = '#skF_4' )
| ~ $less(size('#skF_4'),size('#skF_1'))
| ~ $lesseq(0,size('#skF_1'))
| ( empty = '#skF_1' ) ),
inference(cnfTransformation,[status(thm)],[f_249]) ).
tff(c_1887,plain,
( ( empty = '#skF_2' )
| mem('#skF_19','#skF_4')
| ( empty = '#skF_4' )
| ~ $less(size('#skF_4'),size('#skF_1'))
| $less(size('#skF_1'),0)
| ( empty = '#skF_1' ) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_1146]) ).
tff(c_4935,plain,
( ( empty = '#skF_2' )
| mem('#skF_19','#skF_4')
| ( empty = '#skF_4' )
| ~ $less(size('#skF_4'),size('#skF_1'))
| $less(size('#skF_1'),0) ),
inference(negUnitSimplification,[status(thm)],[c_79,c_1887]) ).
tff(c_5205,plain,
( ( empty = '#skF_2' )
| mem('#skF_19','#skF_4')
| ( empty = '#skF_4' )
| ~ $less(size('#skF_4'),size('#skF_1')) ),
inference(negUnitSimplification,[status(thm)],[c_3729,c_4935]) ).
tff(c_46022,plain,
( mem('#skF_19','#skF_4')
| ~ $less(size('#skF_4'),size('#skF_1')) ),
inference(negUnitSimplification,[status(thm)],[c_11160,c_45166,c_5205]) ).
tff(c_46030,plain,
size('#skF_1') = '#skE_2',
inference(define,[status(thm),theory(equality)],[c_46022]) ).
tff(c_46029,plain,
size('#skF_4') = '#skE_7',
inference(define,[status(thm),theory(equality)],[c_46022]) ).
tff(c_47330,plain,
! [X_14936: tree,X1_14937a: $int,X2_14938: tree] : ( size(node(X_14936,X1_14937a,X2_14938)) = $sum(1,$sum(size(X2_14938),size(X_14936))) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_63]) ).
tff(c_47347,plain,
$sum(1,$sum(size('#skF_4'),size('#skF_2'))) = size('#skF_1'),
inference(superposition,[status(thm),theory(equality)],[c_4905,c_47330]) ).
tff(c_47365,plain,
$sum(1,$sum('#skE_7',size('#skF_2'))) = '#skE_2',
inference(demodulation,[status(thm),theory(equality)],[c_46029,c_46030,c_47347]) ).
tff(c_47367,plain,
size('#skF_2') = $sum($uminus(1),$sum($uminus('#skE_7'),'#skE_2')),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_47365]) ).
tff(c_45169,plain,
node('#skF_16','#skF_17','#skF_18') = '#skF_2',
inference(splitRight,[status(thm)],[c_11182]) ).
tff(c_47359,plain,
$sum(1,$sum(size('#skF_18'),size('#skF_16'))) = size('#skF_2'),
inference(superposition,[status(thm),theory(equality)],[c_45169,c_47330]) ).
tff(c_47361,plain,
size('#skF_18') = $sum($uminus(1),$sum($uminus(size('#skF_16')),size('#skF_2'))),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_47359]) ).
tff(c_47658,plain,
size('#skF_18') = $sum($uminus(1),$sum($uminus(size('#skF_16')),$sum($uminus(1),$sum($uminus('#skE_7'),'#skE_2')))),
inference(demodulation,[status(thm),theory(equality)],[c_47367,c_47361]) ).
tff(c_47661,plain,
size('#skF_18') = $sum($uminus(2),$sum($uminus('#skE_7'),$sum('#skE_2',$uminus(size('#skF_16'))))),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_47658]) ).
tff(c_47664,plain,
size('#skF_16') = '#skE_4',
inference(define,[status(thm),theory(equality)],[c_47661]) ).
tff(c_47663,plain,
size('#skF_18') = '#skE_16',
inference(define,[status(thm),theory(equality)],[c_47661]) ).
tff(c_47662,plain,
size('#skF_18') = $sum($uminus(2),$sum($uminus('#skE_7'),$sum('#skE_2',$uminus(size('#skF_16'))))),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_47658]) ).
tff(c_47666,plain,
$sum($uminus(2),$sum($uminus('#skE_7'),$sum('#skE_2',$uminus('#skE_4')))) = '#skE_16',
inference(demodulation,[status(thm),theory(equality)],[c_47664,c_47663,c_47662]) ).
tff(c_47670,plain,
'#skE_7' = $sum($uminus(2),$sum('#skE_2',$sum($uminus('#skE_4'),$uminus('#skE_16')))),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_47666]) ).
tff(c_147688,plain,
size('#skF_2') = $sum($uminus(1),$sum($uminus($sum($uminus(2),$sum('#skE_2',$sum($uminus('#skE_4'),$uminus('#skE_16'))))),'#skE_2')),
inference(demodulation,[status(thm),theory(equality)],[c_47670,c_47367]) ).
tff(c_147760,plain,
size('#skF_2') = $sum(1,$sum('#skE_4','#skE_16')),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_147688]) ).
tff(c_46582,plain,
! [X_14853: tree,X1_14854a: $int,X2_14855: tree] : ( size(node(X_14853,X1_14854a,X2_14855)) = $sum(1,$sum(size(X2_14855),size(X_14853))) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_63]) ).
tff(c_46599,plain,
$sum(1,$sum(size('#skF_4'),size('#skF_2'))) = size('#skF_1'),
inference(superposition,[status(thm),theory(equality)],[c_4905,c_46582]) ).
tff(c_46617,plain,
$sum(1,$sum('#skE_7',size('#skF_2'))) = '#skE_2',
inference(demodulation,[status(thm),theory(equality)],[c_46030,c_46029,c_46599]) ).
tff(c_46619,plain,
size('#skF_2') = $sum($uminus(1),$sum($uminus('#skE_7'),'#skE_2')),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_46617]) ).
tff(c_46740,plain,
~ $less($sum($uminus(1),$sum($uminus('#skE_7'),'#skE_2')),0),
inference(superposition,[status(thm),theory(equality)],[c_46619,c_3729]) ).
tff(c_46753,plain,
~ $less('#skE_2',$sum(1,'#skE_7')),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_46740]) ).
tff(c_46025,plain,
size('#skF_1') = '#skE_2',
inference(define,[status(thm),theory(equality)],[c_46022]) ).
tff(c_46024,plain,
size('#skF_4') = '#skE_7',
inference(define,[status(thm),theory(equality)],[c_46022]) ).
tff(c_46023,plain,
( mem('#skF_19','#skF_4')
| ~ $less(size('#skF_4'),size('#skF_1')) ),
inference(negUnitSimplification,[status(thm)],[c_11160,c_45166,c_5205]) ).
tff(c_46033,plain,
( mem('#skF_19','#skF_4')
| ~ $less('#skE_7','#skE_2') ),
inference(demodulation,[status(thm),theory(equality)],[c_46025,c_46024,c_46023]) ).
tff(c_46058,plain,
~ $less('#skE_7','#skE_2'),
inference(splitLeft,[status(thm)],[c_46033]) ).
tff(c_46756,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_46753,c_46058]) ).
tff(c_46762,plain,
$less('#skE_7','#skE_2'),
inference(splitRight,[status(thm)],[c_46033]) ).
tff(c_434,plain,
( mem('#skF_21','#skF_1')
| ~ mem(max('#skF_20',max('#skF_3','#skF_19')),'#skF_1')
| ( empty = '#skF_2' )
| ~ $less(size('#skF_2'),size('#skF_1'))
| ( empty = '#skF_4' )
| ~ $less(size('#skF_4'),size('#skF_1'))
| ~ $lesseq(0,size('#skF_1'))
| ( empty = '#skF_1' ) ),
inference(cnfTransformation,[status(thm)],[f_249]) ).
tff(c_3143,plain,
( mem('#skF_21','#skF_1')
| ~ mem(max('#skF_20',max('#skF_3','#skF_19')),'#skF_1')
| ( empty = '#skF_2' )
| ~ $less(size('#skF_2'),size('#skF_1'))
| ( empty = '#skF_4' )
| ~ $less(size('#skF_4'),size('#skF_1'))
| $less(size('#skF_1'),0)
| ( empty = '#skF_1' ) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_434]) ).
tff(c_4999,plain,
( mem('#skF_21','#skF_1')
| ~ mem(max('#skF_20',max('#skF_3','#skF_19')),'#skF_1')
| ( empty = '#skF_2' )
| ~ $less(size('#skF_2'),size('#skF_1'))
| ( empty = '#skF_4' )
| ~ $less(size('#skF_4'),size('#skF_1'))
| $less(size('#skF_1'),0) ),
inference(negUnitSimplification,[status(thm)],[c_79,c_3143]) ).
tff(c_5255,plain,
( mem('#skF_21','#skF_1')
| ~ mem(max('#skF_20',max('#skF_3','#skF_19')),'#skF_1')
| ( empty = '#skF_2' )
| ~ $less(size('#skF_2'),size('#skF_1'))
| ( empty = '#skF_4' )
| ~ $less(size('#skF_4'),size('#skF_1')) ),
inference(negUnitSimplification,[status(thm)],[c_3729,c_4999]) ).
tff(c_48637,plain,
( mem('#skF_21','#skF_1')
| ~ mem(max('#skF_20',max('#skF_3','#skF_19')),'#skF_1')
| ( empty = '#skF_2' )
| ~ $less($sum($uminus(1),$sum($uminus('#skE_7'),'#skE_2')),'#skE_2')
| ( empty = '#skF_4' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_46762,c_46029,c_46030,c_46030,c_47367,c_5255]) ).
tff(c_48639,plain,
( mem('#skF_21','#skF_1')
| ~ mem(max('#skF_20',max('#skF_3','#skF_19')),'#skF_1')
| ~ $less($sum($uminus(1),$sum($uminus('#skE_7'),'#skE_2')),'#skE_2') ),
inference(negUnitSimplification,[status(thm)],[c_11160,c_45166,c_48637]) ).
tff(c_48642,plain,
( mem('#skF_21','#skF_1')
| ~ mem(max('#skF_20',max('#skF_3','#skF_19')),'#skF_1')
| ~ $less($uminus(1),'#skE_7') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_48639]) ).
tff(c_48661,plain,
max('#skF_3','#skF_19') = '#skE_17',
inference(define,[status(thm),theory(equality)],[c_48642]) ).
tff(c_48757,plain,
~ $less('#skE_17','#skF_19'),
inference(superposition,[status(thm),theory(equality)],[c_48661,c_3749]) ).
tff(c_48660,plain,
max('#skF_3','#skF_19') = '#skE_17',
inference(define,[status(thm),theory(equality)],[c_48642]) ).
tff(c_48686,plain,
( ( max('#skF_3','#skF_19') = '#skF_19' )
| ( '#skF_3' = '#skE_17' ) ),
inference(superposition,[status(thm),theory(equality)],[c_48661,c_3748]) ).
tff(c_48749,plain,
( ( '#skF_19' = '#skE_17' )
| ( '#skF_3' = '#skE_17' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_48660,c_48686]) ).
tff(c_48798,plain,
'#skF_3' = '#skE_17',
inference(splitLeft,[status(thm)],[c_48749]) ).
tff(c_48782,plain,
( ( '#skF_3' = '#skE_17' )
| $less('#skF_3','#skF_19') ),
inference(superposition,[status(thm),theory(equality)],[c_3744,c_48661]) ).
tff(c_48796,plain,
$less('#skF_3','#skF_19'),
inference(splitLeft,[status(thm)],[c_48782]) ).
tff(c_48800,plain,
$less('#skE_17','#skF_19'),
inference(demodulation,[status(thm),theory(equality)],[c_48798,c_48796]) ).
tff(c_48830,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_48757,c_48800]) ).
tff(c_48833,plain,
'#skF_19' = '#skE_17',
inference(splitRight,[status(thm)],[c_48749]) ).
tff(c_48651,plain,
max('#skF_3','#skF_19') = '#skE_17',
inference(define,[status(thm),theory(equality)],[c_48642]) ).
tff(c_49391,plain,
max('#skF_3','#skE_17') = '#skE_17',
inference(demodulation,[status(thm),theory(equality)],[c_48833,c_48651]) ).
tff(c_238,plain,
( ~ $lesseq('#skF_21',max('#skF_20',max('#skF_3','#skF_19')))
| ~ mem(max('#skF_20',max('#skF_3','#skF_19')),'#skF_1')
| ( empty = '#skF_2' )
| ~ $less(size('#skF_2'),size('#skF_1'))
| ( empty = '#skF_4' )
| ~ $less(size('#skF_4'),size('#skF_1'))
| ~ $lesseq(0,size('#skF_1'))
| ( empty = '#skF_1' ) ),
inference(cnfTransformation,[status(thm)],[f_249]) ).
tff(c_3463,plain,
( $less(max('#skF_20',max('#skF_3','#skF_19')),'#skF_21')
| ~ mem(max('#skF_20',max('#skF_3','#skF_19')),'#skF_1')
| ( empty = '#skF_2' )
| ~ $less(size('#skF_2'),size('#skF_1'))
| ( empty = '#skF_4' )
| ~ $less(size('#skF_4'),size('#skF_1'))
| $less(size('#skF_1'),0)
| ( empty = '#skF_1' ) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_238]) ).
tff(c_5099,plain,
( $less(max('#skF_20',max('#skF_3','#skF_19')),'#skF_21')
| ~ mem(max('#skF_20',max('#skF_3','#skF_19')),'#skF_1')
| ( empty = '#skF_2' )
| ~ $less(size('#skF_2'),size('#skF_1'))
| ( empty = '#skF_4' )
| ~ $less(size('#skF_4'),size('#skF_1'))
| $less(size('#skF_1'),0) ),
inference(negUnitSimplification,[status(thm)],[c_79,c_3463]) ).
tff(c_5349,plain,
( $less(max('#skF_20',max('#skF_3','#skF_19')),'#skF_21')
| ~ mem(max('#skF_20',max('#skF_3','#skF_19')),'#skF_1')
| ( empty = '#skF_2' )
| ~ $less(size('#skF_2'),size('#skF_1'))
| ( empty = '#skF_4' )
| ~ $less(size('#skF_4'),size('#skF_1')) ),
inference(negUnitSimplification,[status(thm)],[c_3729,c_5099]) ).
tff(c_49569,plain,
( $less(max('#skF_20','#skE_17'),'#skF_21')
| ~ mem(max('#skF_20','#skE_17'),'#skF_1')
| ( empty = '#skF_2' )
| ~ $less($sum($uminus(1),$sum($uminus('#skE_7'),'#skE_2')),'#skE_2')
| ( empty = '#skF_4' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_46762,c_46029,c_46030,c_46030,c_47367,c_49391,c_48833,c_49391,c_48833,c_5349]) ).
tff(c_49571,plain,
( $less(max('#skF_20','#skE_17'),'#skF_21')
| ~ mem(max('#skF_20','#skE_17'),'#skF_1')
| ~ $less($sum($uminus(1),$sum($uminus('#skE_7'),'#skE_2')),'#skE_2') ),
inference(negUnitSimplification,[status(thm)],[c_11160,c_45166,c_49569]) ).
tff(c_49574,plain,
( $less(max('#skF_20','#skE_17'),'#skF_21')
| ~ mem(max('#skF_20','#skE_17'),'#skF_1')
| ~ $less($uminus(1),'#skE_7') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_49571]) ).
tff(c_49589,plain,
max('#skF_20','#skE_17') = '#skE_18',
inference(define,[status(thm),theory(equality)],[c_49574]) ).
tff(c_49702,plain,
~ $less('#skE_18','#skE_17'),
inference(superposition,[status(thm),theory(equality)],[c_49589,c_3749]) ).
tff(c_46761,plain,
mem('#skF_19','#skF_4'),
inference(splitRight,[status(thm)],[c_46033]) ).
tff(c_49123,plain,
mem('#skE_17','#skF_4'),
inference(demodulation,[status(thm),theory(equality)],[c_48833,c_46761]) ).
tff(c_46831,plain,
! [X_14888a: $int,X3_14889: tree,X1_14890: tree,X2_14891a: $int] :
( ~ mem(X_14888a,X3_14889)
| mem(X_14888a,node(X1_14890,X2_14891a,X3_14889)) ),
inference(cnfTransformation,[status(thm)],[f_135]) ).
tff(c_46846,plain,
! [X_14888a: $int] :
( ~ mem(X_14888a,'#skF_4')
| mem(X_14888a,'#skF_1') ),
inference(superposition,[status(thm),theory(equality)],[c_4905,c_46831]) ).
tff(c_49191,plain,
mem('#skE_17','#skF_1'),
inference(resolution,[status(thm)],[c_49123,c_46846]) ).
tff(c_49588,plain,
max('#skF_20','#skE_17') = '#skE_18',
inference(define,[status(thm),theory(equality)],[c_49574]) ).
tff(c_49662,plain,
( ( '#skF_20' = '#skE_18' )
| ( max('#skF_20','#skE_17') = '#skE_17' ) ),
inference(superposition,[status(thm),theory(equality)],[c_3748,c_49589]) ).
tff(c_49728,plain,
( ( '#skF_20' = '#skE_18' )
| ( '#skE_18' = '#skE_17' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_49588,c_49662]) ).
tff(c_49749,plain,
'#skE_18' = '#skE_17',
inference(splitLeft,[status(thm)],[c_49728]) ).
tff(c_49576,plain,
max('#skF_20','#skE_17') = '#skE_18',
inference(define,[status(thm),theory(equality)],[c_49574]) ).
tff(c_49575,plain,
( $less(max('#skF_20','#skE_17'),'#skF_21')
| ~ mem(max('#skF_20','#skE_17'),'#skF_1')
| ~ $less($uminus(1),'#skE_7') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_49571]) ).
tff(c_49586,plain,
( $less('#skE_18','#skF_21')
| ~ mem('#skE_18','#skF_1')
| ~ $less($uminus(1),'#skE_7') ),
inference(demodulation,[status(thm),theory(equality)],[c_49576,c_49576,c_49575]) ).
tff(c_51961,plain,
( $less('#skE_17','#skF_21')
| ~ $less($uminus(1),$sum($uminus(2),$sum('#skE_2',$sum($uminus('#skE_4'),$uminus('#skE_16'))))) ),
inference(demodulation,[status(thm),theory(equality)],[c_47670,c_49191,c_49749,c_49749,c_49586]) ).
tff(c_51963,plain,
( $less('#skE_17','#skF_21')
| ~ $less($sum(1,$sum('#skE_4','#skE_16')),'#skE_2') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_51961]) ).
tff(c_51965,plain,
~ $less($sum(1,$sum('#skE_4','#skE_16')),'#skE_2'),
inference(splitLeft,[status(thm)],[c_51963]) ).
tff(c_46040,plain,
~ $less('#skE_7',0),
inference(superposition,[status(thm),theory(equality)],[c_46029,c_3729]) ).
tff(c_50899,plain,
~ $less($sum($uminus(2),$sum('#skE_2',$sum($uminus('#skE_4'),$uminus('#skE_16')))),0),
inference(demodulation,[status(thm),theory(equality)],[c_47670,c_46040]) ).
tff(c_50901,plain,
~ $less('#skE_2',$sum(2,$sum('#skE_16','#skE_4'))),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_50899]) ).
tff(c_50967,plain,
~ $less('#skE_2',$sum(2,$sum('#skE_4','#skE_16'))),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_50901]) ).
tff(c_51966,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_51965,c_50967]) ).
tff(c_51969,plain,
$less('#skE_17','#skF_21'),
inference(splitRight,[status(thm)],[c_51963]) ).
tff(c_51970,plain,
$less($sum(1,$sum('#skE_4','#skE_16')),'#skE_2'),
inference(splitRight,[status(thm)],[c_51963]) ).
tff(c_49583,plain,
max('#skF_20','#skE_17') = '#skE_18',
inference(define,[status(thm),theory(equality)],[c_49574]) ).
tff(c_49814,plain,
max('#skF_20','#skE_17') = '#skE_17',
inference(demodulation,[status(thm),theory(equality)],[c_49749,c_49583]) ).
tff(c_48644,plain,
max('#skF_3','#skF_19') = '#skE_17',
inference(define,[status(thm),theory(equality)],[c_48642]) ).
tff(c_48643,plain,
( mem('#skF_21','#skF_1')
| ~ mem(max('#skF_20',max('#skF_3','#skF_19')),'#skF_1')
| ~ $less($uminus(1),'#skE_7') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_48639]) ).
tff(c_48654,plain,
( mem('#skF_21','#skF_1')
| ~ mem(max('#skF_20','#skE_17'),'#skF_1')
| ~ $less($uminus(1),'#skE_7') ),
inference(demodulation,[status(thm),theory(equality)],[c_48644,c_48643]) ).
tff(c_52262,plain,
( mem('#skF_21','#skF_1')
| ~ $less($uminus(1),$sum($uminus(2),$sum('#skE_2',$sum($uminus('#skE_4'),$uminus('#skE_16'))))) ),
inference(demodulation,[status(thm),theory(equality)],[c_47670,c_49191,c_49814,c_48654]) ).
tff(c_52265,plain,
( mem('#skF_21','#skF_1')
| ~ $less($sum(1,$sum('#skE_4','#skE_16')),'#skE_2') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_52262]) ).
tff(c_52267,plain,
~ $less($sum(1,$sum('#skE_4','#skE_16')),'#skE_2'),
inference(splitLeft,[status(thm)],[c_52265]) ).
tff(c_52270,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_51970,c_52267]) ).
tff(c_52279,plain,
mem('#skF_21','#skF_1'),
inference(splitRight,[status(thm)],[c_52265]) ).
tff(c_47582,plain,
! [X_14969a: $int,X3_14970: tree,X1_14971: tree,X2_14972a: $int] :
( mem(X_14969a,X3_14970)
| mem(X_14969a,X1_14971)
| ~ mem(X_14969a,node(X1_14971,X2_14972a,X3_14970))
| ( X_14969a = X2_14972a ) ),
inference(cnfTransformation,[status(thm)],[f_135]) ).
tff(c_47613,plain,
! [X_14969a: $int] :
( mem(X_14969a,'#skF_4')
| mem(X_14969a,'#skF_2')
| ~ mem(X_14969a,'#skF_1')
| ( X_14969a = '#skF_3' ) ),
inference(superposition,[status(thm),theory(equality)],[c_4905,c_47582]) ).
tff(c_958,plain,
! [X3_396a: $int] :
( ( empty = '#skF_4' )
| ( empty = '#skF_2' )
| ~ mem(X3_396a,'#skF_4')
| ( empty = '#skF_4' )
| ~ $less(size('#skF_4'),size('#skF_1'))
| ~ $lesseq(0,size('#skF_1'))
| ( empty = '#skF_1' )
| $lesseq(X3_396a,'#skF_19') ),
inference(cnfTransformation,[status(thm)],[f_249]) ).
tff(c_2201,plain,
! [X3_396a: $int] :
( ( empty = '#skF_4' )
| ( empty = '#skF_2' )
| ~ mem(X3_396a,'#skF_4')
| ( empty = '#skF_4' )
| ~ $less(size('#skF_4'),size('#skF_1'))
| $less(size('#skF_1'),0)
| ( empty = '#skF_1' )
| ~ $less('#skF_19',X3_396a) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_958]) ).
tff(c_4927,plain,
! [X3_396a: $int] :
( ( empty = '#skF_4' )
| ( empty = '#skF_2' )
| ~ mem(X3_396a,'#skF_4')
| ( empty = '#skF_4' )
| ~ $less(size('#skF_4'),size('#skF_1'))
| $less(size('#skF_1'),0)
| ~ $less('#skF_19',X3_396a) ),
inference(negUnitSimplification,[status(thm)],[c_79,c_2201]) ).
tff(c_5197,plain,
! [X3_396a: $int] :
( ( empty = '#skF_4' )
| ( empty = '#skF_2' )
| ~ mem(X3_396a,'#skF_4')
| ( empty = '#skF_4' )
| ~ $less(size('#skF_4'),size('#skF_1'))
| ~ $less('#skF_19',X3_396a) ),
inference(negUnitSimplification,[status(thm)],[c_3729,c_4927]) ).
tff(c_46763,plain,
! [X3_396a: $int] :
( ( empty = '#skF_4' )
| ( empty = '#skF_2' )
| ~ mem(X3_396a,'#skF_4')
| ( empty = '#skF_4' )
| ~ $less('#skE_7','#skE_2')
| ~ $less('#skF_19',X3_396a) ),
inference(demodulation,[status(thm),theory(equality)],[c_46029,c_46030,c_5197]) ).
tff(c_46765,plain,
! [X3_396a: $int] :
( ~ mem(X3_396a,'#skF_4')
| ~ $less('#skE_7','#skE_2')
| ~ $less('#skF_19',X3_396a) ),
inference(negUnitSimplification,[status(thm)],[c_11160,c_45166,c_11160,c_46763]) ).
tff(c_46767,plain,
~ $less('#skE_7','#skE_2'),
inference(splitLeft,[status(thm)],[c_46765]) ).
tff(c_46769,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_46762,c_46767]) ).
tff(c_46772,plain,
! [X3_396a: $int] :
( ~ mem(X3_396a,'#skF_4')
| ~ $less('#skF_19',X3_396a) ),
inference(splitRight,[status(thm)],[c_46765]) ).
tff(c_49201,plain,
! [X3_15294a: $int] :
( ~ mem(X3_15294a,'#skF_4')
| ~ $less('#skE_17',X3_15294a) ),
inference(demodulation,[status(thm),theory(equality)],[c_48833,c_46772]) ).
tff(c_49766,plain,
! [X_15392a: $int] :
( ~ $less('#skE_17',X_15392a)
| mem(X_15392a,'#skF_2')
| ~ mem(X_15392a,'#skF_1')
| ( X_15392a = '#skF_3' ) ),
inference(resolution,[status(thm)],[c_47613,c_49201]) ).
tff(c_602,plain,
! [X3_399a: $int] :
( ( empty = '#skF_4' )
| ( empty = '#skF_2' )
| ~ mem(X3_399a,'#skF_2')
| ( empty = '#skF_2' )
| ~ $less(size('#skF_2'),size('#skF_1'))
| ~ $lesseq(0,size('#skF_1'))
| ( empty = '#skF_4' )
| ~ $less(size('#skF_4'),size('#skF_1'))
| ~ $lesseq(0,size('#skF_1'))
| ( empty = '#skF_1' )
| $lesseq(X3_399a,'#skF_20') ),
inference(cnfTransformation,[status(thm)],[f_249]) ).
tff(c_2829,plain,
! [X3_399a: $int] :
( ( empty = '#skF_4' )
| ( empty = '#skF_2' )
| ~ mem(X3_399a,'#skF_2')
| ( empty = '#skF_2' )
| ~ $less(size('#skF_2'),size('#skF_1'))
| $less(size('#skF_1'),0)
| ( empty = '#skF_4' )
| ~ $less(size('#skF_4'),size('#skF_1'))
| $less(size('#skF_1'),0)
| ( empty = '#skF_1' )
| ~ $less('#skF_20',X3_399a) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_602]) ).
tff(c_5077,plain,
! [X3_399a: $int] :
( ( empty = '#skF_4' )
| ( empty = '#skF_2' )
| ~ mem(X3_399a,'#skF_2')
| ( empty = '#skF_2' )
| ~ $less(size('#skF_2'),size('#skF_1'))
| $less(size('#skF_1'),0)
| ( empty = '#skF_4' )
| ~ $less(size('#skF_4'),size('#skF_1'))
| $less(size('#skF_1'),0)
| ~ $less('#skF_20',X3_399a) ),
inference(negUnitSimplification,[status(thm)],[c_79,c_2829]) ).
tff(c_5243,plain,
! [X3_399a: $int] :
( ( empty = '#skF_4' )
| ( empty = '#skF_2' )
| ~ mem(X3_399a,'#skF_2')
| ( empty = '#skF_2' )
| ~ $less(size('#skF_2'),size('#skF_1'))
| ( empty = '#skF_4' )
| ~ $less(size('#skF_4'),size('#skF_1'))
| ~ $less('#skF_20',X3_399a) ),
inference(negUnitSimplification,[status(thm)],[c_3729,c_3729,c_5077]) ).
tff(c_47990,plain,
! [X3_399a: $int] :
( ~ mem(X3_399a,'#skF_2')
| ( empty = '#skF_2' )
| ~ $less($sum($uminus(1),$sum($uminus('#skE_7'),'#skE_2')),'#skE_2')
| ( empty = '#skF_4' )
| ~ $less('#skF_20',X3_399a) ),
inference(demodulation,[status(thm),theory(equality)],[c_46762,c_46029,c_46030,c_46030,c_47367,c_5243]) ).
tff(c_47991,plain,
! [X3_399a: $int] :
( ~ mem(X3_399a,'#skF_2')
| ~ $less($sum($uminus(1),$sum($uminus('#skE_7'),'#skE_2')),'#skE_2')
| ~ $less('#skF_20',X3_399a) ),
inference(negUnitSimplification,[status(thm)],[c_11160,c_45166,c_47990]) ).
tff(c_47993,plain,
! [X3_399a: $int] :
( ~ mem(X3_399a,'#skF_2')
| ~ $less($uminus(1),'#skE_7')
| ~ $less('#skF_20',X3_399a) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_47991]) ).
tff(c_47995,plain,
~ $less($uminus(1),'#skE_7'),
inference(splitLeft,[status(thm)],[c_47993]) ).
tff(c_47996,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_47995,c_46040]) ).
tff(c_47999,plain,
! [X3_399a: $int] :
( ~ mem(X3_399a,'#skF_2')
| ~ $less('#skF_20',X3_399a) ),
inference(splitRight,[status(thm)],[c_47993]) ).
tff(c_49774,plain,
! [X_15392a: $int] :
( ~ $less('#skF_20',X_15392a)
| ~ $less('#skE_17',X_15392a)
| ~ mem(X_15392a,'#skF_1')
| ( X_15392a = '#skF_3' ) ),
inference(resolution,[status(thm)],[c_49766,c_47999]) ).
tff(c_52282,plain,
( ~ $less('#skF_20','#skF_21')
| ~ $less('#skE_17','#skF_21')
| ( '#skF_3' = '#skF_21' ) ),
inference(resolution,[status(thm)],[c_52279,c_49774]) ).
tff(c_52289,plain,
( ~ $less('#skF_20','#skF_21')
| ( '#skF_3' = '#skF_21' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_51969,c_52282]) ).
tff(c_52293,plain,
~ $less('#skF_20','#skF_21'),
inference(splitLeft,[status(thm)],[c_52289]) ).
tff(c_49698,plain,
( ( '#skF_20' = '#skE_18' )
| $less('#skF_20','#skE_17') ),
inference(superposition,[status(thm),theory(equality)],[c_49589,c_3744]) ).
tff(c_49747,plain,
$less('#skF_20','#skE_17'),
inference(splitLeft,[status(thm)],[c_49698]) ).
tff(c_52294,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_52293,c_51969,c_49747]) ).
tff(c_52297,plain,
'#skF_3' = '#skF_21',
inference(splitRight,[status(thm)],[c_52289]) ).
tff(c_48755,plain,
~ $less('#skE_17','#skF_3'),
inference(superposition,[status(thm),theory(equality)],[c_48661,c_3750]) ).
tff(c_52340,plain,
~ $less('#skE_17','#skF_21'),
inference(demodulation,[status(thm),theory(equality)],[c_52297,c_48755]) ).
tff(c_52379,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_51969,c_52340]) ).
tff(c_52382,plain,
'#skF_20' = '#skE_18',
inference(splitRight,[status(thm)],[c_49728]) ).
tff(c_52385,plain,
$less('#skE_18','#skE_17'),
inference(demodulation,[status(thm),theory(equality)],[c_52382,c_49747]) ).
tff(c_52413,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_49702,c_52385]) ).
tff(c_52416,plain,
'#skF_20' = '#skE_18',
inference(splitRight,[status(thm)],[c_49698]) ).
tff(c_790,plain,
( mem('#skF_20','#skF_2')
| ( empty = '#skF_2' )
| ~ $less(size('#skF_2'),size('#skF_1'))
| ( empty = '#skF_4' )
| ~ $less(size('#skF_4'),size('#skF_1'))
| ~ $lesseq(0,size('#skF_1'))
| ( empty = '#skF_1' ) ),
inference(cnfTransformation,[status(thm)],[f_249]) ).
tff(c_2515,plain,
( mem('#skF_20','#skF_2')
| ( empty = '#skF_2' )
| ~ $less(size('#skF_2'),size('#skF_1'))
| ( empty = '#skF_4' )
| ~ $less(size('#skF_4'),size('#skF_1'))
| $less(size('#skF_1'),0)
| ( empty = '#skF_1' ) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_790]) ).
tff(c_5049,plain,
( mem('#skF_20','#skF_2')
| ( empty = '#skF_2' )
| ~ $less(size('#skF_2'),size('#skF_1'))
| ( empty = '#skF_4' )
| ~ $less(size('#skF_4'),size('#skF_1'))
| $less(size('#skF_1'),0) ),
inference(negUnitSimplification,[status(thm)],[c_79,c_2515]) ).
tff(c_5229,plain,
( mem('#skF_20','#skF_2')
| ( empty = '#skF_2' )
| ~ $less(size('#skF_2'),size('#skF_1'))
| ( empty = '#skF_4' )
| ~ $less(size('#skF_4'),size('#skF_1')) ),
inference(negUnitSimplification,[status(thm)],[c_3729,c_5049]) ).
tff(c_47747,plain,
( mem('#skF_20','#skF_2')
| ( empty = '#skF_2' )
| ~ $less($sum($uminus(1),$sum($uminus('#skE_7'),'#skE_2')),'#skE_2')
| ( empty = '#skF_4' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_46762,c_46029,c_46030,c_47367,c_46030,c_5229]) ).
tff(c_47749,plain,
( mem('#skF_20','#skF_2')
| ~ $less($sum($uminus(1),$sum($uminus('#skE_7'),'#skE_2')),'#skE_2') ),
inference(negUnitSimplification,[status(thm)],[c_11160,c_45166,c_47747]) ).
tff(c_47752,plain,
( mem('#skF_20','#skF_2')
| ~ $less($uminus(1),'#skE_7') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_47749]) ).
tff(c_47755,plain,
~ $less($uminus(1),'#skE_7'),
inference(splitLeft,[status(thm)],[c_47752]) ).
tff(c_47756,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_47755,c_46040]) ).
tff(c_47764,plain,
mem('#skF_20','#skF_2'),
inference(splitRight,[status(thm)],[c_47752]) ).
tff(c_45989,plain,
! [X_14787a: $int,X1_14788: tree,X2_14789a: $int,X3_14790: tree] :
( ~ mem(X_14787a,X1_14788)
| mem(X_14787a,node(X1_14788,X2_14789a,X3_14790)) ),
inference(cnfTransformation,[status(thm)],[f_135]) ).
tff(c_46004,plain,
! [X_14787a: $int] :
( ~ mem(X_14787a,'#skF_2')
| mem(X_14787a,'#skF_1') ),
inference(superposition,[status(thm),theory(equality)],[c_4905,c_45989]) ).
tff(c_47770,plain,
mem('#skF_20','#skF_1'),
inference(resolution,[status(thm)],[c_47764,c_46004]) ).
tff(c_52474,plain,
mem('#skE_18','#skF_1'),
inference(demodulation,[status(thm),theory(equality)],[c_52416,c_47770]) ).
tff(c_55007,plain,
( $less('#skE_18','#skF_21')
| ~ $less($uminus(1),$sum($uminus(2),$sum('#skE_2',$sum($uminus('#skE_4'),$uminus('#skE_16'))))) ),
inference(demodulation,[status(thm),theory(equality)],[c_47670,c_52474,c_49586]) ).
tff(c_55009,plain,
( $less('#skE_18','#skF_21')
| ~ $less($sum(1,$sum('#skE_4','#skE_16')),'#skE_2') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_55007]) ).
tff(c_55011,plain,
~ $less($sum(1,$sum('#skE_4','#skE_16')),'#skE_2'),
inference(splitLeft,[status(thm)],[c_55009]) ).
tff(c_53380,plain,
~ $less($sum($uminus(2),$sum('#skE_2',$sum($uminus('#skE_4'),$uminus('#skE_16')))),0),
inference(demodulation,[status(thm),theory(equality)],[c_47670,c_46040]) ).
tff(c_53382,plain,
~ $less('#skE_2',$sum(2,$sum('#skE_16','#skE_4'))),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_53380]) ).
tff(c_53448,plain,
~ $less('#skE_2',$sum(2,$sum('#skE_4','#skE_16'))),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_53382]) ).
tff(c_55012,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_55011,c_53448]) ).
tff(c_55015,plain,
$less('#skE_18','#skF_21'),
inference(splitRight,[status(thm)],[c_55009]) ).
tff(c_55016,plain,
$less($sum(1,$sum('#skE_4','#skE_16')),'#skE_2'),
inference(splitRight,[status(thm)],[c_55009]) ).
tff(c_52755,plain,
max('#skE_18','#skE_17') = '#skE_18',
inference(demodulation,[status(thm),theory(equality)],[c_52416,c_49583]) ).
tff(c_57238,plain,
( mem('#skF_21','#skF_1')
| ~ $less($uminus(1),$sum($uminus(2),$sum('#skE_2',$sum($uminus('#skE_4'),$uminus('#skE_16'))))) ),
inference(demodulation,[status(thm),theory(equality)],[c_47670,c_52474,c_52755,c_52416,c_48654]) ).
tff(c_57241,plain,
( mem('#skF_21','#skF_1')
| ~ $less($sum(1,$sum('#skE_4','#skE_16')),'#skE_2') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_57238]) ).
tff(c_57243,plain,
~ $less($sum(1,$sum('#skE_4','#skE_16')),'#skE_2'),
inference(splitLeft,[status(thm)],[c_57241]) ).
tff(c_57246,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_55016,c_57243]) ).
tff(c_57255,plain,
mem('#skF_21','#skF_1'),
inference(splitRight,[status(thm)],[c_57241]) ).
tff(c_49221,plain,
! [X_14969a: $int] :
( ~ $less('#skE_17',X_14969a)
| mem(X_14969a,'#skF_2')
| ~ mem(X_14969a,'#skF_1')
| ( X_14969a = '#skF_3' ) ),
inference(resolution,[status(thm)],[c_47613,c_49201]) ).
tff(c_52488,plain,
! [X3_15726a: $int] :
( ~ mem(X3_15726a,'#skF_2')
| ~ $less('#skE_18',X3_15726a) ),
inference(demodulation,[status(thm),theory(equality)],[c_52416,c_47999]) ).
tff(c_52508,plain,
! [X_14969a: $int] :
( ~ $less('#skE_18',X_14969a)
| ~ $less('#skE_17',X_14969a)
| ~ mem(X_14969a,'#skF_1')
| ( X_14969a = '#skF_3' ) ),
inference(resolution,[status(thm)],[c_49221,c_52488]) ).
tff(c_57258,plain,
( ~ $less('#skE_18','#skF_21')
| ~ $less('#skE_17','#skF_21')
| ( '#skF_3' = '#skF_21' ) ),
inference(resolution,[status(thm)],[c_57255,c_52508]) ).
tff(c_57265,plain,
( ~ $less('#skE_17','#skF_21')
| ( '#skF_3' = '#skF_21' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_55015,c_57258]) ).
tff(c_57273,plain,
~ $less('#skE_17','#skF_21'),
inference(splitLeft,[status(thm)],[c_57265]) ).
tff(c_57274,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_57273,c_55015,c_49702]) ).
tff(c_57277,plain,
'#skF_3' = '#skF_21',
inference(splitRight,[status(thm)],[c_57265]) ).
tff(c_48869,plain,
$less('#skF_3','#skE_17'),
inference(demodulation,[status(thm),theory(equality)],[c_48833,c_48796]) ).
tff(c_57356,plain,
$less('#skF_21','#skE_17'),
inference(demodulation,[status(thm),theory(equality)],[c_57277,c_48869]) ).
tff(c_57450,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_57356,c_55015,c_49702]) ).
tff(c_57453,plain,
'#skF_3' = '#skE_17',
inference(splitRight,[status(thm)],[c_48782]) ).
tff(c_57633,plain,
max('#skE_17','#skF_19') = '#skE_17',
inference(demodulation,[status(thm),theory(equality)],[c_57453,c_48651]) ).
tff(c_147847,plain,
( $less(max('#skF_20','#skE_17'),'#skF_21')
| ~ mem(max('#skF_20','#skE_17'),'#skF_1')
| ( empty = '#skF_2' )
| ~ $less($sum(1,$sum('#skE_4','#skE_16')),'#skE_2')
| ( empty = '#skF_4' )
| ~ $less(size('#skF_4'),'#skE_2') ),
inference(demodulation,[status(thm),theory(equality)],[c_46030,c_147760,c_46030,c_57633,c_57453,c_57633,c_57453,c_5349]) ).
tff(c_147851,plain,
( $less(max('#skF_20','#skE_17'),'#skF_21')
| ~ mem(max('#skF_20','#skE_17'),'#skF_1')
| ~ $less($sum(1,$sum('#skE_4','#skE_16')),'#skE_2')
| ~ $less(size('#skF_4'),'#skE_2') ),
inference(negUnitSimplification,[status(thm)],[c_11160,c_45166,c_147847]) ).
tff(c_147874,plain,
max('#skF_20','#skE_17') = '#skE_18',
inference(define,[status(thm),theory(equality)],[c_147851]) ).
tff(c_147987,plain,
~ $less('#skE_18','#skE_17'),
inference(superposition,[status(thm),theory(equality)],[c_147874,c_3749]) ).
tff(c_57582,plain,
mem('#skE_17','#skF_1'),
inference(demodulation,[status(thm),theory(equality)],[c_57453,c_5548]) ).
tff(c_147873,plain,
max('#skF_20','#skE_17') = '#skE_18',
inference(define,[status(thm),theory(equality)],[c_147851]) ).
tff(c_147902,plain,
( ( '#skE_18' = '#skE_17' )
| ( max('#skF_20','#skE_17') = '#skF_20' ) ),
inference(superposition,[status(thm),theory(equality)],[c_147874,c_3748]) ).
tff(c_147976,plain,
( ( '#skE_18' = '#skE_17' )
| ( '#skF_20' = '#skE_18' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_147873,c_147902]) ).
tff(c_148037,plain,
'#skF_20' = '#skE_18',
inference(splitLeft,[status(thm)],[c_147976]) ).
tff(c_147983,plain,
( ( '#skF_20' = '#skE_18' )
| $less('#skF_20','#skE_17') ),
inference(superposition,[status(thm),theory(equality)],[c_147874,c_3744]) ).
tff(c_148033,plain,
$less('#skF_20','#skE_17'),
inference(splitLeft,[status(thm)],[c_147983]) ).
tff(c_148039,plain,
$less('#skE_18','#skE_17'),
inference(demodulation,[status(thm),theory(equality)],[c_148037,c_148033]) ).
tff(c_148067,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_147987,c_148039]) ).
tff(c_148070,plain,
'#skE_18' = '#skE_17',
inference(splitRight,[status(thm)],[c_147976]) ).
tff(c_147861,plain,
max('#skF_20','#skE_17') = '#skE_18',
inference(define,[status(thm),theory(equality)],[c_147851]) ).
tff(c_148110,plain,
max('#skF_20','#skE_17') = '#skE_17',
inference(demodulation,[status(thm),theory(equality)],[c_148070,c_147861]) ).
tff(c_149343,plain,
( mem('#skF_21','#skF_1')
| ~ $less($uminus(1),$sum($uminus(2),$sum('#skE_2',$sum($uminus('#skE_4'),$uminus('#skE_16'))))) ),
inference(demodulation,[status(thm),theory(equality)],[c_47670,c_57582,c_148110,c_48654]) ).
tff(c_149346,plain,
( mem('#skF_21','#skF_1')
| ~ $less($sum(1,$sum('#skE_4','#skE_16')),'#skE_2') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_149343]) ).
tff(c_149349,plain,
~ $less($sum(1,$sum('#skE_4','#skE_16')),'#skE_2'),
inference(splitLeft,[status(thm)],[c_149346]) ).
tff(c_147694,plain,
~ $less($sum($uminus(2),$sum('#skE_2',$sum($uminus('#skE_4'),$uminus('#skE_16')))),0),
inference(demodulation,[status(thm),theory(equality)],[c_47670,c_46040]) ).
tff(c_147696,plain,
~ $less('#skE_2',$sum(2,$sum('#skE_16','#skE_4'))),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_147694]) ).
tff(c_147762,plain,
~ $less('#skE_2',$sum(2,$sum('#skE_4','#skE_16'))),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_147696]) ).
tff(c_149350,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_149349,c_147762]) ).
tff(c_149356,plain,
$less($sum(1,$sum('#skE_4','#skE_16')),'#skE_2'),
inference(splitRight,[status(thm)],[c_149346]) ).
tff(c_147854,plain,
size('#skF_4') = '#skE_7',
inference(define,[status(thm),theory(equality)],[c_147851]) ).
tff(c_147853,plain,
max('#skF_20','#skE_17') = '#skE_18',
inference(define,[status(thm),theory(equality)],[c_147851]) ).
tff(c_147852,plain,
( $less(max('#skF_20','#skE_17'),'#skF_21')
| ~ mem(max('#skF_20','#skE_17'),'#skF_1')
| ~ $less($sum(1,$sum('#skE_4','#skE_16')),'#skE_2')
| ~ $less(size('#skF_4'),'#skE_2') ),
inference(negUnitSimplification,[status(thm)],[c_11160,c_45166,c_147847]) ).
tff(c_147857,plain,
( $less('#skE_18','#skF_21')
| ~ mem('#skE_18','#skF_1')
| ~ $less($sum(1,$sum('#skE_4','#skE_16')),'#skE_2')
| ~ $less('#skE_7','#skE_2') ),
inference(demodulation,[status(thm),theory(equality)],[c_147854,c_147853,c_147853,c_147852]) ).
tff(c_147868,plain,
( $less('#skE_18','#skF_21')
| ~ mem('#skE_18','#skF_1')
| ~ $less($sum(1,$sum('#skE_4','#skE_16')),'#skE_2')
| ~ $less($sum($uminus(2),$sum('#skE_2',$sum($uminus('#skE_4'),$uminus('#skE_16')))),'#skE_2') ),
inference(demodulation,[status(thm),theory(equality)],[c_47670,c_147857]) ).
tff(c_147871,plain,
( $less('#skE_18','#skF_21')
| ~ mem('#skE_18','#skF_1')
| ~ $less($sum(1,$sum('#skE_4','#skE_16')),'#skE_2')
| ~ $less($uminus(2),$sum('#skE_16','#skE_4')) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_147868]) ).
tff(c_173537,plain,
( $less('#skE_17','#skF_21')
| ~ $less($uminus(2),$sum('#skE_16','#skE_4')) ),
inference(demodulation,[status(thm),theory(equality)],[c_149356,c_57582,c_148070,c_148070,c_147871]) ).
tff(c_173539,plain,
~ $less($uminus(2),$sum('#skE_16','#skE_4')),
inference(splitLeft,[status(thm)],[c_173537]) ).
tff(c_47667,plain,
size('#skF_18') = '#skE_16',
inference(define,[status(thm),theory(equality)],[c_47661]) ).
tff(c_47742,plain,
~ $less('#skE_16',0),
inference(superposition,[status(thm),theory(equality)],[c_47667,c_3729]) ).
tff(c_47668,plain,
size('#skF_16') = '#skE_4',
inference(define,[status(thm),theory(equality)],[c_47661]) ).
tff(c_47705,plain,
~ $less('#skE_4',0),
inference(superposition,[status(thm),theory(equality)],[c_47668,c_3729]) ).
tff(c_173540,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_173539,c_47742,c_47705]) ).
tff(c_173543,plain,
$less('#skE_17','#skF_21'),
inference(splitRight,[status(thm)],[c_173537]) ).
tff(c_156816,plain,
( $less('#skE_17','#skF_21')
| ~ $less($uminus(2),$sum('#skE_16','#skE_4')) ),
inference(demodulation,[status(thm),theory(equality)],[c_149356,c_57582,c_148070,c_148070,c_147871]) ).
tff(c_156818,plain,
~ $less($uminus(2),$sum('#skE_16','#skE_4')),
inference(splitLeft,[status(thm)],[c_156816]) ).
tff(c_156819,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_156818,c_47742,c_47705]) ).
tff(c_156822,plain,
$less('#skE_17','#skF_21'),
inference(splitRight,[status(thm)],[c_156816]) ).
tff(c_149359,plain,
mem('#skF_21','#skF_1'),
inference(splitRight,[status(thm)],[c_149346]) ).
tff(c_47644,plain,
! [X_14978a: $int] :
( mem(X_14978a,'#skF_4')
| mem(X_14978a,'#skF_2')
| ~ mem(X_14978a,'#skF_1')
| ( X_14978a = '#skF_3' ) ),
inference(superposition,[status(thm),theory(equality)],[c_4905,c_47582]) ).
tff(c_48060,plain,
! [X_15045a: $int] :
( ~ $less('#skF_19',X_15045a)
| mem(X_15045a,'#skF_2')
| ~ mem(X_15045a,'#skF_1')
| ( X_15045a = '#skF_3' ) ),
inference(resolution,[status(thm)],[c_47644,c_46772]) ).
tff(c_48068,plain,
! [X_15045a: $int] :
( ~ $less('#skF_20',X_15045a)
| ~ $less('#skF_19',X_15045a)
| ~ mem(X_15045a,'#skF_1')
| ( X_15045a = '#skF_3' ) ),
inference(resolution,[status(thm)],[c_48060,c_47999]) ).
tff(c_57493,plain,
! [X_15045a: $int] :
( ~ $less('#skF_20',X_15045a)
| ~ $less('#skF_19',X_15045a)
| ~ mem(X_15045a,'#skF_1')
| ( X_15045a = '#skE_17' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_57453,c_48068]) ).
tff(c_149364,plain,
( ~ $less('#skF_20','#skF_21')
| ~ $less('#skF_19','#skF_21')
| ( '#skF_21' = '#skE_17' ) ),
inference(resolution,[status(thm)],[c_149359,c_57493]) ).
tff(c_149442,plain,
~ $less('#skF_19','#skF_21'),
inference(splitLeft,[status(thm)],[c_149364]) ).
tff(c_156823,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_156822,c_149442,c_48757]) ).
tff(c_156826,plain,
( ~ $less('#skF_20','#skF_21')
| ( '#skF_21' = '#skE_17' ) ),
inference(splitRight,[status(thm)],[c_149364]) ).
tff(c_156829,plain,
~ $less('#skF_20','#skF_21'),
inference(splitLeft,[status(thm)],[c_156826]) ).
tff(c_173544,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_173543,c_156829,c_148033]) ).
tff(c_173547,plain,
'#skF_21' = '#skE_17',
inference(splitRight,[status(thm)],[c_156826]) ).
tff(c_194410,plain,
( $less('#skE_17','#skE_17')
| ~ $less($uminus(2),$sum('#skE_16','#skE_4')) ),
inference(demodulation,[status(thm),theory(equality)],[c_149356,c_57582,c_148070,c_173547,c_148070,c_147871]) ).
tff(c_194412,plain,
~ $less($uminus(2),$sum('#skE_16','#skE_4')),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_194410]) ).
tff(c_194413,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_194412,c_47742,c_47705]) ).
tff(c_194416,plain,
'#skF_20' = '#skE_18',
inference(splitRight,[status(thm)],[c_147983]) ).
tff(c_194470,plain,
mem('#skE_18','#skF_1'),
inference(demodulation,[status(thm),theory(equality)],[c_194416,c_47770]) ).
tff(c_194520,plain,
max('#skE_18','#skE_17') = '#skE_18',
inference(demodulation,[status(thm),theory(equality)],[c_194416,c_147861]) ).
tff(c_195647,plain,
( mem('#skF_21','#skF_1')
| ~ $less($uminus(1),$sum($uminus(2),$sum('#skE_2',$sum($uminus('#skE_4'),$uminus('#skE_16'))))) ),
inference(demodulation,[status(thm),theory(equality)],[c_47670,c_194470,c_194520,c_194416,c_48654]) ).
tff(c_195650,plain,
( mem('#skF_21','#skF_1')
| ~ $less($sum(1,$sum('#skE_4','#skE_16')),'#skE_2') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_195647]) ).
tff(c_195653,plain,
~ $less($sum(1,$sum('#skE_4','#skE_16')),'#skE_2'),
inference(splitLeft,[status(thm)],[c_195650]) ).
tff(c_195654,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_195653,c_147762]) ).
tff(c_195660,plain,
$less($sum(1,$sum('#skE_4','#skE_16')),'#skE_2'),
inference(splitRight,[status(thm)],[c_195650]) ).
tff(c_210566,plain,
( $less('#skE_18','#skF_21')
| ~ $less($uminus(2),$sum('#skE_16','#skE_4')) ),
inference(demodulation,[status(thm),theory(equality)],[c_195660,c_194470,c_147871]) ).
tff(c_210568,plain,
~ $less($uminus(2),$sum('#skE_16','#skE_4')),
inference(splitLeft,[status(thm)],[c_210566]) ).
tff(c_210569,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_210568,c_47742,c_47705]) ).
tff(c_210572,plain,
$less('#skE_18','#skF_21'),
inference(splitRight,[status(thm)],[c_210566]) ).
tff(c_195704,plain,
mem('#skF_21','#skF_1'),
inference(splitRight,[status(thm)],[c_195650]) ).
tff(c_194730,plain,
! [X_15045a: $int] :
( ~ $less('#skE_18',X_15045a)
| ~ $less('#skF_19',X_15045a)
| ~ mem(X_15045a,'#skF_1')
| ( X_15045a = '#skE_17' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_194416,c_57493]) ).
tff(c_195709,plain,
( ~ $less('#skE_18','#skF_21')
| ~ $less('#skF_19','#skF_21')
| ( '#skF_21' = '#skE_17' ) ),
inference(resolution,[status(thm)],[c_195704,c_194730]) ).
tff(c_195711,plain,
~ $less('#skF_19','#skF_21'),
inference(splitLeft,[status(thm)],[c_195709]) ).
tff(c_210573,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_210572,c_195711,c_147987,c_48757]) ).
tff(c_210576,plain,
( ~ $less('#skE_18','#skF_21')
| ( '#skF_21' = '#skE_17' ) ),
inference(splitRight,[status(thm)],[c_195709]) ).
tff(c_210579,plain,
~ $less('#skE_18','#skF_21'),
inference(splitLeft,[status(thm)],[c_210576]) ).
tff(c_227543,plain,
( $less('#skE_18','#skF_21')
| ~ $less($uminus(2),$sum('#skE_16','#skE_4')) ),
inference(demodulation,[status(thm),theory(equality)],[c_195660,c_194470,c_147871]) ).
tff(c_227545,plain,
~ $less($uminus(2),$sum('#skE_16','#skE_4')),
inference(negUnitSimplification,[status(thm)],[c_210579,c_227543]) ).
tff(c_227546,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_227545,c_47742,c_47705]) ).
tff(c_227549,plain,
'#skF_21' = '#skE_17',
inference(splitRight,[status(thm)],[c_210576]) ).
tff(c_227550,plain,
$less('#skE_18','#skF_21'),
inference(splitRight,[status(thm)],[c_210576]) ).
tff(c_227561,plain,
$less('#skE_18','#skE_17'),
inference(demodulation,[status(thm),theory(equality)],[c_227549,c_227550]) ).
tff(c_227562,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_147987,c_227561]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : SWW598_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
% 0.16/0.37 % Computer : n011.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Thu Aug 3 19:10:21 EDT 2023
% 0.16/0.37 % CPUTime :
% 107.92/72.07 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 108.00/72.13
% 108.00/72.13 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 108.46/72.22
% 108.46/72.22 Inference rules
% 108.46/72.22 ----------------------
% 108.46/72.22 #Ref : 0
% 108.46/72.22 #Sup : 35879
% 108.46/72.22 #Fact : 15
% 108.46/72.22 #Define : 80
% 108.46/72.22 #Split : 195
% 108.46/72.22 #Chain : 0
% 108.46/72.22 #Close : 65
% 108.46/72.22
% 108.46/72.22 Ordering : LPO
% 108.46/72.22
% 108.46/72.22 Simplification rules
% 108.46/72.22 ----------------------
% 108.46/72.22 #Subsume : 7945
% 108.46/72.22 #Demod : 15795
% 108.46/72.22 #Tautology : 6703
% 108.46/72.22 #SimpNegUnit : 1982
% 108.46/72.22 #BackRed : 1340
% 108.46/72.22
% 108.46/72.22 #Partial instantiations: 3491
% 108.46/72.22 #Strategies tried : 1
% 108.46/72.22
% 108.46/72.22 Timing (in seconds)
% 108.46/72.22 ----------------------
% 108.46/72.22 Preprocessing : 1.69
% 108.46/72.22 Parsing : 0.38
% 108.46/72.22 CNF conversion : 0.11
% 108.46/72.22 Main loop : 69.25
% 108.46/72.22 Inferencing : 3.38
% 108.46/72.22 Reduction : 14.54
% 108.46/72.22 Demodulation : 9.64
% 108.46/72.22 BG Simplification : 1.27
% 108.46/72.22 Subsumption : 14.96
% 108.46/72.22 Abstraction : 0.84
% 108.46/72.22 MUC search : 19.66
% 108.46/72.22 Cooper : 31.53
% 108.46/72.22 Total : 71.11
% 108.46/72.22 Index Insertion : 0.00
% 108.46/72.22 Index Deletion : 0.00
% 108.46/72.22 Index Matching : 0.00
% 108.46/72.22 BG Taut test : 0.00
%------------------------------------------------------------------------------