TSTP Solution File: NUM861_1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : NUM861_1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Aug 22 10:52:58 EDT 2023
% Result : Theorem 10.04s 3.56s
% Output : CNFRefutation 11.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 34
% Syntax : Number of formulae : 636 ( 386 unt; 26 typ; 0 def)
% Number of atoms : 986 ( 101 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 675 ( 299 ~; 364 |; 4 &)
% ( 6 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number arithmetic : 1206 ( 539 atm; 306 fun; 48 num; 313 var)
% Number of types : 2 ( 0 usr; 1 ari)
% Number of type conns : 27 ( 10 >; 17 *; 0 +; 0 <<)
% Number of predicates : 9 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 23 ( 21 usr; 17 con; 0-3 aty)
% Number of variables : 313 (; 312 !; 1 ?; 313 :)
% Comments :
%------------------------------------------------------------------------------
%$ ub > model_ub > model_max > minsol_model_ub > minsol_model_max > max > #nlpp > summation > #skF_3 > #skF_1 > #skF_2
%Foreground sorts:
%Background operators:
tff('#skE_7',type,
'#skE_7': $int ).
tff(c,type,
c: $int ).
tff('#skF_6',type,
'#skF_6': $int ).
tff('#skE_2',type,
'#skE_2': $int ).
tff('#skE_1',type,
'#skE_1': $int ).
tff('#skE_6',type,
'#skE_6': $int ).
tff('#skE_5',type,
'#skE_5': $int ).
tff('#skE_8',type,
'#skE_8': $int ).
tff('#skF_8',type,
'#skF_8': $int ).
tff('#skE_4',type,
'#skE_4': $int ).
tff('#skF_5',type,
'#skF_5': $int ).
tff('#skF_4',type,
'#skF_4': $int ).
tff('#skE_3',type,
'#skE_3': $int ).
tff('#skF_7',type,
'#skF_7': $int ).
tff('#skE_9',type,
'#skE_9': $int ).
tff('#skF_9',type,
'#skF_9': $int ).
%Foreground operators:
tff(minsol_model_ub,type,
minsol_model_ub: ( $int * $int * $int ) > $o ).
tff('#skF_3',type,
'#skF_3': ( $int * $int * $int ) > $int ).
tff(model_max,type,
model_max: ( $int * $int * $int ) > $o ).
tff(minsol_model_max,type,
minsol_model_max: ( $int * $int * $int ) > $o ).
tff(summation,type,
summation: $int > $int ).
tff(max,type,
max: ( $int * $int ) > $int ).
tff('#skF_1',type,
'#skF_1': ( $int * $int * $int ) > $int ).
tff(model_ub,type,
model_ub: ( $int * $int * $int ) > $o ).
tff(ub,type,
ub: ( $int * $int * $int ) > $o ).
tff('#skF_2',type,
'#skF_2': ( $int * $int * $int ) > $int ).
tff(f_56,axiom,
! [Xa: $int,Ya: $int,Za: $int] :
( ub(Xa,Ya,Za)
<=> ( $lesseq(Xa,Za)
& $lesseq(Ya,Za) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ub) ).
tff(f_69,axiom,
! [Xa: $int,Ya: $int,Na: $int] :
( model_ub(Xa,Ya,Na)
<=> ? [Za: $int] :
( ub(Xa,Ya,Za)
& $lesseq($sum(c,Za),Na) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',model_ub_4) ).
tff(f_89,axiom,
! [Xa: $int,Ya: $int,Na: $int] :
( minsol_model_ub(Xa,Ya,Na)
<=> ( model_ub(Xa,Ya,Na)
& ! [Za: $int] :
( model_ub(Xa,Ya,Za)
=> $lesseq(Na,Za) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',minsol_model_ub) ).
tff(f_49,axiom,
! [Xa: $int,Ya: $int] :
( ( max(Xa,Ya) = Ya )
| ~ $lesseq(Xa,Ya) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',max_2) ).
tff(f_61,axiom,
! [Xa: $int,Ya: $int,Na: $int] :
( model_max(Xa,Ya,Na)
<=> $lesseq($sum(c,max(Xa,Ya)),Na) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',model_max_4) ).
tff(f_79,axiom,
! [Xa: $int,Ya: $int,Na: $int] :
( minsol_model_max(Xa,Ya,Na)
<=> ( model_max(Xa,Ya,Na)
& ! [Za: $int] :
( model_max(Xa,Ya,Za)
=> $lesseq(Na,Za) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',minsol_model_max) ).
tff(f_95,negated_conjecture,
~ ! [Xa: $int,Ya: $int,Za: $int] :
( minsol_model_ub(Xa,Ya,Za)
<=> minsol_model_max(Xa,Ya,Za) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',max_is_ub_1) ).
tff(f_44,axiom,
! [Xa: $int,Ya: $int] :
( ( max(Xa,Ya) = Xa )
| ~ $lesseq(Ya,Xa) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',max_1) ).
tff(c_13,plain,
! [X_7a: $int,Y_8a: $int,Z_9a: $int] :
( ub(X_7a,Y_8a,Z_9a)
| ~ $lesseq(X_7a,Z_9a)
| ~ $lesseq(Y_8a,Z_9a) ),
inference(cnfTransformation,[status(thm)],[f_56]) ).
tff(c_93,plain,
! [X_7a: $int,Y_8a: $int,Z_9a: $int] :
( ub(X_7a,Y_8a,Z_9a)
| $less(Z_9a,X_7a)
| $less(Z_9a,Y_8a) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_13]) ).
tff(c_21,plain,
! [X_13a: $int,Y_14a: $int,N_15a: $int,Z_18a: $int] :
( model_ub(X_13a,Y_14a,N_15a)
| ~ ub(X_13a,Y_14a,Z_18a)
| ~ $lesseq($sum(c,Z_18a),N_15a) ),
inference(cnfTransformation,[status(thm)],[f_69]) ).
tff(c_22,plain,
! [X_13a: $int,Y_14a: $int,N_15a: $int,Z_18a: $int] :
( model_ub(X_13a,Y_14a,N_15a)
| ~ ub(X_13a,Y_14a,Z_18a)
| $less(N_15a,$sum(Z_18a,c)) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_21]) ).
tff(c_3975,plain,
! [X_1825a: $int,Y_1826a: $int,N_1827a: $int,Z_1828a: $int] :
( model_ub(X_1825a,Y_1826a,N_1827a)
| ~ ub(X_1825a,Y_1826a,Z_1828a)
| $less(N_1827a,$sum(c,Z_1828a)) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_22]) ).
tff(c_3980,plain,
! [X_7a: $int,Y_8a: $int,N_1827a: $int,Z_9a: $int] :
( model_ub(X_7a,Y_8a,N_1827a)
| $less(N_1827a,$sum(c,Z_9a))
| $less(Z_9a,X_7a)
| $less(Z_9a,Y_8a) ),
inference(resolution,[status(thm)],[c_93,c_3975]) ).
tff(c_7173,plain,
! [X_3250a: $int,Y_3251a: $int,N_3252a: $int,Z_3253a: $int] :
( model_ub(X_3250a,Y_3251a,N_3252a)
| $less(N_3252a,$sum(c,Z_3253a))
| $less(Z_3253a,X_3250a)
| $less(Z_3253a,Y_3251a) ),
inference(resolution,[status(thm)],[c_93,c_3975]) ).
tff(c_42,plain,
! [N_27a: $int,X_25a: $int,Y_26a: $int] :
( ~ $lesseq(N_27a,'#skF_3'(X_25a,Y_26a,N_27a))
| minsol_model_ub(X_25a,Y_26a,N_27a)
| ~ model_ub(X_25a,Y_26a,N_27a) ),
inference(cnfTransformation,[status(thm)],[f_89]) ).
tff(c_71,plain,
! [X_25a: $int,Y_26a: $int,N_27a: $int] :
( $less('#skF_3'(X_25a,Y_26a,N_27a),N_27a)
| minsol_model_ub(X_25a,Y_26a,N_27a)
| ~ model_ub(X_25a,Y_26a,N_27a) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_42]) ).
tff(c_7793,plain,
! [X_3522a: $int,Y_3523a: $int,N_3524a: $int,Z_3525a: $int] :
( $less('#skF_3'(X_3522a,Y_3523a,N_3524a),N_3524a)
| minsol_model_ub(X_3522a,Y_3523a,N_3524a)
| $less(N_3524a,$sum(c,Z_3525a))
| $less(Z_3525a,X_3522a)
| $less(Z_3525a,Y_3523a) ),
inference(resolution,[status(thm)],[c_7173,c_71]) ).
tff(c_7433,plain,
! [X_3358a: $int,Y_3359a: $int,N_3360a: $int,Z_3361a: $int] :
( $less('#skF_3'(X_3358a,Y_3359a,N_3360a),N_3360a)
| minsol_model_ub(X_3358a,Y_3359a,N_3360a)
| $less(N_3360a,$sum(c,Z_3361a))
| $less(Z_3361a,X_3358a)
| $less(Z_3361a,Y_3359a) ),
inference(resolution,[status(thm)],[c_7173,c_71]) ).
tff(c_4040,plain,
! [X_1871a: $int,Y_1872a: $int,N_1873a: $int,Z_1874a: $int] :
( model_ub(X_1871a,Y_1872a,N_1873a)
| $less(N_1873a,$sum(c,Z_1874a))
| $less(Z_1874a,X_1871a)
| $less(Z_1874a,Y_1872a) ),
inference(resolution,[status(thm)],[c_93,c_3975]) ).
tff(c_6555,plain,
! [X_2971a: $int,Y_2972a: $int,N_2973a: $int,Z_2974a: $int] :
( $less('#skF_3'(X_2971a,Y_2972a,N_2973a),N_2973a)
| minsol_model_ub(X_2971a,Y_2972a,N_2973a)
| $less(N_2973a,$sum(c,Z_2974a))
| $less(Z_2974a,X_2971a)
| $less(Z_2974a,Y_2972a) ),
inference(resolution,[status(thm)],[c_4040,c_71]) ).
tff(c_5748,plain,
! [X_2634a: $int,Y_2635a: $int,N_2636a: $int,Z_2637a: $int] :
( $less('#skF_3'(X_2634a,Y_2635a,N_2636a),N_2636a)
| minsol_model_ub(X_2634a,Y_2635a,N_2636a)
| $less(N_2636a,$sum(c,Z_2637a))
| $less(Z_2637a,X_2634a)
| $less(Z_2637a,Y_2635a) ),
inference(resolution,[status(thm)],[c_4040,c_71]) ).
tff(c_7,plain,
! [X_5a: $int,Y_6a: $int] :
( ( max(X_5a,Y_6a) = Y_6a )
| ~ $lesseq(X_5a,Y_6a) ),
inference(cnfTransformation,[status(thm)],[f_49]) ).
tff(c_96,plain,
! [X_5a: $int,Y_6a: $int] :
( ( max(X_5a,Y_6a) = Y_6a )
| $less(Y_6a,X_5a) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_7]) ).
tff(c_19,plain,
! [X_10a: $int,Y_11a: $int,N_12a: $int] :
( model_max(X_10a,Y_11a,N_12a)
| ~ $lesseq($sum(c,max(X_10a,Y_11a)),N_12a) ),
inference(cnfTransformation,[status(thm)],[f_61]) ).
tff(c_88,plain,
! [X_10a: $int,Y_11a: $int,N_12a: $int] :
( model_max(X_10a,Y_11a,N_12a)
| $less(N_12a,$sum(c,max(X_10a,Y_11a))) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_19]) ).
tff(c_33,plain,
! [N_21a: $int,X_19a: $int,Y_20a: $int] :
( ~ $lesseq(N_21a,'#skF_2'(X_19a,Y_20a,N_21a))
| minsol_model_max(X_19a,Y_20a,N_21a)
| ~ model_max(X_19a,Y_20a,N_21a) ),
inference(cnfTransformation,[status(thm)],[f_79]) ).
tff(c_4016,plain,
! [X_1852a: $int,Y_1853a: $int,N_1854a: $int] :
( $less('#skF_2'(X_1852a,Y_1853a,N_1854a),N_1854a)
| minsol_model_max(X_1852a,Y_1853a,N_1854a)
| ~ model_max(X_1852a,Y_1853a,N_1854a) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_33]) ).
tff(c_4105,plain,
! [X_1902a: $int,Y_1903a: $int,N_1904a: $int] :
( $less('#skF_2'(X_1902a,Y_1903a,N_1904a),N_1904a)
| minsol_model_max(X_1902a,Y_1903a,N_1904a)
| $less(N_1904a,$sum(c,max(X_1902a,Y_1903a))) ),
inference(resolution,[status(thm)],[c_88,c_4016]) ).
tff(c_65,plain,
( minsol_model_max('#skF_4','#skF_5','#skF_6')
| ~ minsol_model_max('#skF_7','#skF_8','#skF_9') ),
inference(cnfTransformation,[status(thm)],[f_95]) ).
tff(c_4012,plain,
~ minsol_model_max('#skF_7','#skF_8','#skF_9'),
inference(splitLeft,[status(thm)],[c_65]) ).
tff(c_4122,plain,
( $less('#skF_2'('#skF_7','#skF_8','#skF_9'),'#skF_9')
| $less('#skF_9',$sum(c,max('#skF_7','#skF_8'))) ),
inference(resolution,[status(thm)],[c_4105,c_4012]) ).
tff(c_4177,plain,
max('#skF_7','#skF_8') = '#skE_3',
inference(define,[status(thm),theory(equality)],[c_4122]) ).
tff(c_4209,plain,
( ( '#skF_8' = '#skE_3' )
| $less('#skF_8','#skF_7') ),
inference(superposition,[status(thm),theory(equality)],[c_96,c_4177]) ).
tff(c_4215,plain,
$less('#skF_8','#skF_7'),
inference(splitLeft,[status(thm)],[c_4209]) ).
tff(c_5,plain,
! [X_3a: $int,Y_4a: $int] :
( ( max(X_3a,Y_4a) = X_3a )
| ~ $lesseq(Y_4a,X_3a) ),
inference(cnfTransformation,[status(thm)],[f_44]) ).
tff(c_97,plain,
! [X_3a: $int,Y_4a: $int] :
( ( max(X_3a,Y_4a) = X_3a )
| $less(X_3a,Y_4a) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_5]) ).
tff(c_4200,plain,
( ( '#skF_7' = '#skE_3' )
| $less('#skF_7','#skF_8') ),
inference(superposition,[status(thm),theory(equality)],[c_4177,c_97]) ).
tff(c_4211,plain,
$less('#skF_7','#skF_8'),
inference(splitLeft,[status(thm)],[c_4200]) ).
tff(c_4238,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_4215,c_4211]) ).
tff(c_4241,plain,
'#skF_8' = '#skE_3',
inference(splitRight,[status(thm)],[c_4209]) ).
tff(c_4173,plain,
max('#skF_7','#skF_8') = '#skE_3',
inference(define,[status(thm),theory(equality)],[c_4122]) ).
tff(c_4303,plain,
max('#skF_7','#skE_3') = '#skE_3',
inference(demodulation,[status(thm),theory(equality)],[c_4241,c_4173]) ).
tff(c_57,plain,
( minsol_model_max('#skF_4','#skF_5','#skF_6')
| minsol_model_ub('#skF_7','#skF_8','#skF_9') ),
inference(cnfTransformation,[status(thm)],[f_95]) ).
tff(c_4064,plain,
minsol_model_ub('#skF_7','#skF_8','#skF_9'),
inference(splitLeft,[status(thm)],[c_57]) ).
tff(c_4370,plain,
minsol_model_ub('#skF_7','#skE_3','#skF_9'),
inference(demodulation,[status(thm),theory(equality)],[c_4241,c_4064]) ).
tff(c_72,plain,
! [X_25a: $int,Y_26a: $int,N_27a: $int] :
( model_ub(X_25a,Y_26a,N_27a)
| ~ minsol_model_ub(X_25a,Y_26a,N_27a) ),
inference(cnfTransformation,[status(thm)],[f_89]) ).
tff(c_4067,plain,
minsol_model_ub('#skF_7','#skF_8','#skF_9'),
inference(splitLeft,[status(thm)],[c_57]) ).
tff(c_24,plain,
! [X_13a: $int,Y_14a: $int,N_15a: $int] :
( $lesseq($sum(c,'#skF_1'(X_13a,Y_14a,N_15a)),N_15a)
| ~ model_ub(X_13a,Y_14a,N_15a) ),
inference(cnfTransformation,[status(thm)],[f_69]) ).
tff(c_4028,plain,
! [N_1856a: $int,X_1858a: $int,Y_1859a: $int] :
( ~ $less(N_1856a,$sum(c,'#skF_1'(X_1858a,Y_1859a,N_1856a)))
| ~ model_ub(X_1858a,Y_1859a,N_1856a) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_24]) ).
tff(c_4034,plain,
! [N_27a: $int,X_25a: $int,Y_26a: $int] :
( ~ $less(N_27a,$sum(c,'#skF_1'(X_25a,Y_26a,N_27a)))
| ~ minsol_model_ub(X_25a,Y_26a,N_27a) ),
inference(resolution,[status(thm)],[c_72,c_4028]) ).
tff(c_4083,plain,
~ $less('#skF_9',$sum(c,'#skF_1'('#skF_7','#skF_8','#skF_9'))),
inference(resolution,[status(thm)],[c_4067,c_4034]) ).
tff(c_4140,plain,
'#skF_1'('#skF_7','#skF_8','#skF_9') = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_4083]) ).
tff(c_78,plain,
! [X_13a: $int,Y_14a: $int,N_15a: $int] :
( ub(X_13a,Y_14a,'#skF_1'(X_13a,Y_14a,N_15a))
| ~ model_ub(X_13a,Y_14a,N_15a) ),
inference(cnfTransformation,[status(thm)],[f_69]) ).
tff(c_4156,plain,
( ub('#skF_7','#skF_8','#skE_1')
| ~ model_ub('#skF_7','#skF_8','#skF_9') ),
inference(superposition,[status(thm),theory(equality)],[c_4140,c_78]) ).
tff(c_4436,plain,
( ub('#skF_7','#skE_3','#skE_1')
| ~ model_ub('#skF_7','#skE_3','#skF_9') ),
inference(demodulation,[status(thm),theory(equality)],[c_4241,c_4241,c_4156]) ).
tff(c_4444,plain,
~ model_ub('#skF_7','#skE_3','#skF_9'),
inference(splitLeft,[status(thm)],[c_4436]) ).
tff(c_4450,plain,
~ minsol_model_ub('#skF_7','#skE_3','#skF_9'),
inference(resolution,[status(thm)],[c_72,c_4444]) ).
tff(c_4456,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_4370,c_4450]) ).
tff(c_4463,plain,
ub('#skF_7','#skE_3','#skE_1'),
inference(splitRight,[status(thm)],[c_4436]) ).
tff(c_9,plain,
! [X_7a: $int,Y_8a: $int,Z_9a: $int] :
( ~ ub(X_7a,Y_8a,Z_9a)
| $lesseq(Y_8a,Z_9a) ),
inference(cnfTransformation,[status(thm)],[f_56]) ).
tff(c_95,plain,
! [X_7a: $int,Y_8a: $int,Z_9a: $int] :
( ~ ub(X_7a,Y_8a,Z_9a)
| ~ $less(Z_9a,Y_8a) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_9]) ).
tff(c_4477,plain,
~ $less('#skE_1','#skE_3'),
inference(resolution,[status(thm)],[c_4463,c_95]) ).
tff(c_4163,plain,
max('#skF_7','#skF_8') = '#skE_3',
inference(define,[status(thm),theory(equality)],[c_4122]) ).
tff(c_4162,plain,
'#skF_2'('#skF_7','#skF_8','#skF_9') = '#skE_2',
inference(define,[status(thm),theory(equality)],[c_4122]) ).
tff(c_4161,plain,
( $less('#skF_2'('#skF_7','#skF_8','#skF_9'),'#skF_9')
| $less('#skF_9',$sum(c,max('#skF_7','#skF_8'))) ),
inference(resolution,[status(thm)],[c_4105,c_4012]) ).
tff(c_4174,plain,
( $less('#skE_2','#skF_9')
| $less('#skF_9',$sum(c,'#skE_3')) ),
inference(demodulation,[status(thm),theory(equality)],[c_4163,c_4162,c_4161]) ).
tff(c_4342,plain,
$less('#skF_9',$sum(c,'#skE_3')),
inference(splitLeft,[status(thm)],[c_4174]) ).
tff(c_4130,plain,
'#skF_1'('#skF_7','#skF_8','#skF_9') = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_4083]) ).
tff(c_4129,plain,
~ $less('#skF_9',$sum(c,'#skF_1'('#skF_7','#skF_8','#skF_9'))),
inference(resolution,[status(thm)],[c_4067,c_4034]) ).
tff(c_4137,plain,
~ $less('#skF_9',$sum(c,'#skE_1')),
inference(demodulation,[status(thm),theory(equality)],[c_4130,c_4129]) ).
tff(c_4480,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_4477,c_4342,c_4137]) ).
tff(c_4484,plain,
~ $less('#skF_9',$sum(c,'#skE_3')),
inference(splitRight,[status(thm)],[c_4174]) ).
tff(c_4170,plain,
'#skF_2'('#skF_7','#skF_8','#skF_9') = '#skE_2',
inference(define,[status(thm),theory(equality)],[c_4122]) ).
tff(c_4513,plain,
'#skF_2'('#skF_7','#skE_3','#skF_9') = '#skE_2',
inference(demodulation,[status(thm),theory(equality)],[c_4241,c_4170]) ).
tff(c_74,plain,
! [X_19a: $int,Y_20a: $int,N_21a: $int] :
( model_max(X_19a,Y_20a,'#skF_2'(X_19a,Y_20a,N_21a))
| minsol_model_max(X_19a,Y_20a,N_21a)
| ~ model_max(X_19a,Y_20a,N_21a) ),
inference(cnfTransformation,[status(thm)],[f_79]) ).
tff(c_4529,plain,
( model_max('#skF_7','#skE_3','#skE_2')
| minsol_model_max('#skF_7','#skE_3','#skF_9')
| ~ model_max('#skF_7','#skE_3','#skF_9') ),
inference(superposition,[status(thm),theory(equality)],[c_4513,c_74]) ).
tff(c_4982,plain,
~ model_max('#skF_7','#skE_3','#skF_9'),
inference(splitLeft,[status(thm)],[c_4529]) ).
tff(c_4985,plain,
$less('#skF_9',$sum(c,max('#skF_7','#skE_3'))),
inference(resolution,[status(thm)],[c_88,c_4982]) ).
tff(c_4990,plain,
$less('#skF_9',$sum(c,'#skE_3')),
inference(demodulation,[status(thm),theory(equality)],[c_4303,c_4985]) ).
tff(c_4992,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_4484,c_4990]) ).
tff(c_4996,plain,
( minsol_model_max('#skF_7','#skE_3','#skF_9')
| model_max('#skF_7','#skE_3','#skE_2') ),
inference(splitRight,[status(thm)],[c_4529]) ).
tff(c_5005,plain,
model_max('#skF_7','#skE_3','#skE_2'),
inference(splitLeft,[status(thm)],[c_4996]) ).
tff(c_16,plain,
! [X_10a: $int,Y_11a: $int,N_12a: $int] :
( $lesseq($sum(c,max(X_10a,Y_11a)),N_12a)
| ~ model_max(X_10a,Y_11a,N_12a) ),
inference(cnfTransformation,[status(thm)],[f_61]) ).
tff(c_92,plain,
! [N_12a: $int,X_10a: $int,Y_11a: $int] :
( ~ $less(N_12a,$sum(c,max(X_10a,Y_11a)))
| ~ model_max(X_10a,Y_11a,N_12a) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_16]) ).
tff(c_5011,plain,
~ $less('#skE_2',$sum(c,max('#skF_7','#skE_3'))),
inference(resolution,[status(thm)],[c_5005,c_92]) ).
tff(c_5020,plain,
~ $less('#skE_2',$sum(c,'#skE_3')),
inference(demodulation,[status(thm),theory(equality)],[c_4303,c_5011]) ).
tff(c_4485,plain,
minsol_model_ub('#skF_7','#skE_3','#skF_9'),
inference(demodulation,[status(thm),theory(equality)],[c_4241,c_4064]) ).
tff(c_37,plain,
! [X_25a: $int,Y_26a: $int,Z_30a: $int,N_27a: $int] :
( ~ model_ub(X_25a,Y_26a,Z_30a)
| ~ minsol_model_ub(X_25a,Y_26a,N_27a)
| $lesseq(N_27a,Z_30a) ),
inference(cnfTransformation,[status(thm)],[f_89]) ).
tff(c_73,plain,
! [X_25a: $int,Y_26a: $int,Z_30a: $int,N_27a: $int] :
( ~ model_ub(X_25a,Y_26a,Z_30a)
| ~ minsol_model_ub(X_25a,Y_26a,N_27a)
| ~ $less(Z_30a,N_27a) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_37]) ).
tff(c_4056,plain,
! [Y_1872a: $int,X_1871a: $int,N_1873a: $int,Z_1874a: $int,N_27a: $int] :
( ~ minsol_model_ub(X_1871a,Y_1872a,N_27a)
| ~ $less(N_1873a,N_27a)
| $less(N_1873a,$sum(c,Z_1874a))
| $less(Z_1874a,X_1871a)
| $less(Z_1874a,Y_1872a) ),
inference(resolution,[status(thm)],[c_4040,c_73]) ).
tff(c_4498,plain,
! [N_1873a: $int,Z_1874a: $int] :
( ~ $less(N_1873a,'#skF_9')
| $less(N_1873a,$sum(c,Z_1874a))
| $less(Z_1874a,'#skF_7')
| $less(Z_1874a,'#skE_3') ),
inference(resolution,[status(thm)],[c_4485,c_4056]) ).
tff(c_4631,plain,
( $lesseq('#skF_9',$sum(c,'#skF_7'))
| $lesseq('#skF_9',$sum(c,'#skE_3')) ),
inference(quantifierElimination,[status(thm),theory('LIA')],[c_4498]) ).
tff(c_4633,plain,
( ~ $less($sum('#skF_7',c),'#skF_9')
| ~ $less($sum('#skE_3',c),'#skF_9') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_4631]) ).
tff(c_4483,plain,
$less('#skE_2','#skF_9'),
inference(splitRight,[status(thm)],[c_4174]) ).
tff(c_4242,plain,
~ $less('#skF_8','#skF_7'),
inference(splitRight,[status(thm)],[c_4209]) ).
tff(c_4290,plain,
~ $less('#skE_3','#skF_7'),
inference(demodulation,[status(thm),theory(equality)],[c_4241,c_4242]) ).
tff(c_5026,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_5020,c_4633,c_4483,c_4290]) ).
tff(c_5032,plain,
minsol_model_max('#skF_7','#skE_3','#skF_9'),
inference(splitRight,[status(thm)],[c_4996]) ).
tff(c_4288,plain,
~ minsol_model_max('#skF_7','#skE_3','#skF_9'),
inference(demodulation,[status(thm),theory(equality)],[c_4241,c_4012]) ).
tff(c_5035,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_5032,c_4288]) ).
tff(c_5038,plain,
'#skF_7' = '#skE_3',
inference(splitRight,[status(thm)],[c_4200]) ).
tff(c_5136,plain,
max('#skE_3','#skF_8') = '#skE_3',
inference(demodulation,[status(thm),theory(equality)],[c_5038,c_4173]) ).
tff(c_5177,plain,
minsol_model_ub('#skE_3','#skF_8','#skF_9'),
inference(demodulation,[status(thm),theory(equality)],[c_5038,c_4064]) ).
tff(c_5244,plain,
( ub('#skE_3','#skF_8','#skE_1')
| ~ model_ub('#skE_3','#skF_8','#skF_9') ),
inference(demodulation,[status(thm),theory(equality)],[c_5038,c_5038,c_4156]) ).
tff(c_5252,plain,
~ model_ub('#skE_3','#skF_8','#skF_9'),
inference(splitLeft,[status(thm)],[c_5244]) ).
tff(c_5258,plain,
~ minsol_model_ub('#skE_3','#skF_8','#skF_9'),
inference(resolution,[status(thm)],[c_72,c_5252]) ).
tff(c_5264,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_5177,c_5258]) ).
tff(c_5271,plain,
ub('#skE_3','#skF_8','#skE_1'),
inference(splitRight,[status(thm)],[c_5244]) ).
tff(c_11,plain,
! [X_7a: $int,Y_8a: $int,Z_9a: $int] :
( ~ ub(X_7a,Y_8a,Z_9a)
| $lesseq(X_7a,Z_9a) ),
inference(cnfTransformation,[status(thm)],[f_56]) ).
tff(c_94,plain,
! [X_7a: $int,Y_8a: $int,Z_9a: $int] :
( ~ ub(X_7a,Y_8a,Z_9a)
| ~ $less(Z_9a,X_7a) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_11]) ).
tff(c_5287,plain,
~ $less('#skE_1','#skE_3'),
inference(resolution,[status(thm)],[c_5271,c_94]) ).
tff(c_5175,plain,
$less('#skF_9',$sum(c,'#skE_3')),
inference(splitLeft,[status(thm)],[c_4174]) ).
tff(c_5288,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_5287,c_5175,c_4137]) ).
tff(c_5292,plain,
~ $less('#skF_9',$sum(c,'#skE_3')),
inference(splitRight,[status(thm)],[c_4174]) ).
tff(c_5094,plain,
'#skF_2'('#skE_3','#skF_8','#skF_9') = '#skE_2',
inference(demodulation,[status(thm),theory(equality)],[c_5038,c_4170]) ).
tff(c_5110,plain,
( model_max('#skE_3','#skF_8','#skE_2')
| minsol_model_max('#skE_3','#skF_8','#skF_9')
| ~ model_max('#skE_3','#skF_8','#skF_9') ),
inference(superposition,[status(thm),theory(equality)],[c_5094,c_74]) ).
tff(c_5451,plain,
~ model_max('#skE_3','#skF_8','#skF_9'),
inference(splitLeft,[status(thm)],[c_5110]) ).
tff(c_5454,plain,
$less('#skF_9',$sum(c,max('#skE_3','#skF_8'))),
inference(resolution,[status(thm)],[c_88,c_5451]) ).
tff(c_5459,plain,
$less('#skF_9',$sum(c,'#skE_3')),
inference(demodulation,[status(thm),theory(equality)],[c_5136,c_5454]) ).
tff(c_5461,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_5292,c_5459]) ).
tff(c_5465,plain,
( minsol_model_max('#skE_3','#skF_8','#skF_9')
| model_max('#skE_3','#skF_8','#skE_2') ),
inference(splitRight,[status(thm)],[c_5110]) ).
tff(c_5474,plain,
model_max('#skE_3','#skF_8','#skE_2'),
inference(splitLeft,[status(thm)],[c_5465]) ).
tff(c_5480,plain,
~ $less('#skE_2',$sum(c,max('#skE_3','#skF_8'))),
inference(resolution,[status(thm)],[c_5474,c_92]) ).
tff(c_5489,plain,
~ $less('#skE_2',$sum(c,'#skE_3')),
inference(demodulation,[status(thm),theory(equality)],[c_5136,c_5480]) ).
tff(c_4080,plain,
! [N_1873a: $int,Z_1874a: $int] :
( ~ $less(N_1873a,'#skF_9')
| $less(N_1873a,$sum(c,Z_1874a))
| $less(Z_1874a,'#skF_7')
| $less(Z_1874a,'#skF_8') ),
inference(resolution,[status(thm)],[c_4067,c_4056]) ).
tff(c_5075,plain,
! [N_1873a: $int,Z_1874a: $int] :
( ~ $less(N_1873a,'#skF_9')
| $less(N_1873a,$sum(c,Z_1874a))
| $less(Z_1874a,'#skE_3')
| $less(Z_1874a,'#skF_8') ),
inference(demodulation,[status(thm),theory(equality)],[c_5038,c_4080]) ).
tff(c_5232,plain,
( $lesseq('#skF_9',$sum(c,'#skE_3'))
| $lesseq('#skF_9',$sum(c,'#skF_8')) ),
inference(quantifierElimination,[status(thm),theory('LIA')],[c_5075]) ).
tff(c_5234,plain,
( ~ $less($sum('#skE_3',c),'#skF_9')
| ~ $less($sum('#skF_8',c),'#skF_9') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_5232]) ).
tff(c_5291,plain,
$less('#skE_2','#skF_9'),
inference(splitRight,[status(thm)],[c_4174]) ).
tff(c_5039,plain,
~ $less('#skF_7','#skF_8'),
inference(splitRight,[status(thm)],[c_4200]) ).
tff(c_5087,plain,
~ $less('#skE_3','#skF_8'),
inference(demodulation,[status(thm),theory(equality)],[c_5038,c_5039]) ).
tff(c_5493,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_5489,c_5234,c_5291,c_5087]) ).
tff(c_5499,plain,
minsol_model_max('#skE_3','#skF_8','#skF_9'),
inference(splitRight,[status(thm)],[c_5465]) ).
tff(c_5085,plain,
~ minsol_model_max('#skE_3','#skF_8','#skF_9'),
inference(demodulation,[status(thm),theory(equality)],[c_5038,c_4012]) ).
tff(c_5502,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_5499,c_5085]) ).
tff(c_5509,plain,
minsol_model_max('#skF_4','#skF_5','#skF_6'),
inference(splitRight,[status(thm)],[c_57]) ).
tff(c_76,plain,
! [X_19a: $int,Y_20a: $int,N_21a: $int] :
( model_max(X_19a,Y_20a,N_21a)
| ~ minsol_model_max(X_19a,Y_20a,N_21a) ),
inference(cnfTransformation,[status(thm)],[f_79]) ).
tff(c_3981,plain,
! [N_1829a: $int,X_1831a: $int,Y_1832a: $int] :
( ~ $less(N_1829a,$sum(c,max(X_1831a,Y_1832a)))
| ~ model_max(X_1831a,Y_1832a,N_1829a) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_16]) ).
tff(c_3987,plain,
! [N_21a: $int,X_19a: $int,Y_20a: $int] :
( ~ $less(N_21a,$sum(c,max(X_19a,Y_20a)))
| ~ minsol_model_max(X_19a,Y_20a,N_21a) ),
inference(resolution,[status(thm)],[c_76,c_3981]) ).
tff(c_5528,plain,
~ $less('#skF_6',$sum(c,max('#skF_4','#skF_5'))),
inference(resolution,[status(thm)],[c_5509,c_3987]) ).
tff(c_5555,plain,
max('#skF_4','#skF_5') = '#skE_5',
inference(define,[status(thm),theory(equality)],[c_5528]) ).
tff(c_5587,plain,
( ( '#skF_5' = '#skE_5' )
| $less('#skF_5','#skF_4') ),
inference(superposition,[status(thm),theory(equality)],[c_96,c_5555]) ).
tff(c_5591,plain,
$less('#skF_5','#skF_4'),
inference(splitLeft,[status(thm)],[c_5587]) ).
tff(c_5578,plain,
( ( '#skF_4' = '#skE_5' )
| $less('#skF_4','#skF_5') ),
inference(superposition,[status(thm),theory(equality)],[c_5555,c_97]) ).
tff(c_5589,plain,
$less('#skF_4','#skF_5'),
inference(splitLeft,[status(thm)],[c_5578]) ).
tff(c_5592,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_5591,c_5589]) ).
tff(c_5595,plain,
'#skF_5' = '#skE_5',
inference(splitRight,[status(thm)],[c_5587]) ).
tff(c_230,plain,
! [X_159a: $int,Y_160a: $int,N_161a: $int] :
( $less('#skF_2'(X_159a,Y_160a,N_161a),N_161a)
| minsol_model_max(X_159a,Y_160a,N_161a)
| ~ model_max(X_159a,Y_160a,N_161a) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_33]) ).
tff(c_3045,plain,
! [X_1371a: $int,Y_1372a: $int,N_1373a: $int] :
( $less('#skF_2'(X_1371a,Y_1372a,N_1373a),N_1373a)
| minsol_model_max(X_1371a,Y_1372a,N_1373a)
| $less(N_1373a,$sum(c,max(X_1371a,Y_1372a))) ),
inference(resolution,[status(thm)],[c_88,c_230]) ).
tff(c_69,plain,
( ~ minsol_model_ub('#skF_4','#skF_5','#skF_6')
| ~ minsol_model_max('#skF_7','#skF_8','#skF_9') ),
inference(cnfTransformation,[status(thm)],[f_95]) ).
tff(c_159,plain,
~ minsol_model_max('#skF_7','#skF_8','#skF_9'),
inference(splitLeft,[status(thm)],[c_69]) ).
tff(c_3067,plain,
( $less('#skF_2'('#skF_7','#skF_8','#skF_9'),'#skF_9')
| $less('#skF_9',$sum(c,max('#skF_7','#skF_8'))) ),
inference(resolution,[status(thm)],[c_3045,c_159]) ).
tff(c_3150,plain,
max('#skF_7','#skF_8') = '#skE_3',
inference(define,[status(thm),theory(equality)],[c_3067]) ).
tff(c_3182,plain,
( ( '#skF_8' = '#skE_3' )
| $less('#skF_8','#skF_7') ),
inference(superposition,[status(thm),theory(equality)],[c_96,c_3150]) ).
tff(c_3186,plain,
$less('#skF_8','#skF_7'),
inference(splitLeft,[status(thm)],[c_3182]) ).
tff(c_3173,plain,
( ( '#skF_7' = '#skE_3' )
| $less('#skF_7','#skF_8') ),
inference(superposition,[status(thm),theory(equality)],[c_3150,c_97]) ).
tff(c_3184,plain,
$less('#skF_7','#skF_8'),
inference(splitLeft,[status(thm)],[c_3173]) ).
tff(c_3187,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_3186,c_3184]) ).
tff(c_3190,plain,
'#skF_8' = '#skE_3',
inference(splitRight,[status(thm)],[c_3182]) ).
tff(c_3146,plain,
max('#skF_7','#skF_8') = '#skE_3',
inference(define,[status(thm),theory(equality)],[c_3067]) ).
tff(c_3313,plain,
max('#skF_7','#skE_3') = '#skE_3',
inference(demodulation,[status(thm),theory(equality)],[c_3190,c_3146]) ).
tff(c_3136,plain,
max('#skF_7','#skF_8') = '#skE_3',
inference(define,[status(thm),theory(equality)],[c_3067]) ).
tff(c_3135,plain,
'#skF_2'('#skF_7','#skF_8','#skF_9') = '#skE_2',
inference(define,[status(thm),theory(equality)],[c_3067]) ).
tff(c_3134,plain,
( $less('#skF_2'('#skF_7','#skF_8','#skF_9'),'#skF_9')
| $less('#skF_9',$sum(c,max('#skF_7','#skF_8'))) ),
inference(resolution,[status(thm)],[c_3045,c_159]) ).
tff(c_3147,plain,
( $less('#skE_2','#skF_9')
| $less('#skF_9',$sum(c,'#skE_3')) ),
inference(demodulation,[status(thm),theory(equality)],[c_3136,c_3135,c_3134]) ).
tff(c_3352,plain,
$less('#skF_9',$sum(c,'#skE_3')),
inference(splitLeft,[status(thm)],[c_3147]) ).
tff(c_189,plain,
! [X_133a: $int,Y_134a: $int,N_135a: $int,Z_136a: $int] :
( model_ub(X_133a,Y_134a,N_135a)
| ~ ub(X_133a,Y_134a,Z_136a)
| $less(N_135a,$sum(c,Z_136a)) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_22]) ).
tff(c_194,plain,
! [X_7a: $int,Y_8a: $int,N_135a: $int,Z_9a: $int] :
( model_ub(X_7a,Y_8a,N_135a)
| $less(N_135a,$sum(c,Z_9a))
| $less(Z_9a,X_7a)
| $less(Z_9a,Y_8a) ),
inference(resolution,[status(thm)],[c_93,c_189]) ).
tff(c_254,plain,
! [X_179a: $int,Y_180a: $int,N_181a: $int,Z_182a: $int] :
( model_ub(X_179a,Y_180a,N_181a)
| $less(N_181a,$sum(c,Z_182a))
| $less(Z_182a,X_179a)
| $less(Z_182a,Y_180a) ),
inference(resolution,[status(thm)],[c_93,c_189]) ).
tff(c_2634,plain,
! [X_1181a: $int,Y_1182a: $int,N_1183a: $int,Z_1184a: $int] :
( $less('#skF_3'(X_1181a,Y_1182a,N_1183a),N_1183a)
| minsol_model_ub(X_1181a,Y_1182a,N_1183a)
| $less(N_1183a,$sum(c,Z_1184a))
| $less(Z_1184a,X_1181a)
| $less(Z_1184a,Y_1182a) ),
inference(resolution,[status(thm)],[c_254,c_71]) ).
tff(c_1965,plain,
! [X_915a: $int,Y_916a: $int,N_917a: $int,Z_918a: $int] :
( $less('#skF_3'(X_915a,Y_916a,N_917a),N_917a)
| minsol_model_ub(X_915a,Y_916a,N_917a)
| $less(N_917a,$sum(c,Z_918a))
| $less(Z_918a,X_915a)
| $less(Z_918a,Y_916a) ),
inference(resolution,[status(thm)],[c_254,c_71]) ).
tff(c_277,plain,
! [X_194a: $int,Y_195a: $int,N_196a: $int] :
( $less('#skF_2'(X_194a,Y_195a,N_196a),N_196a)
| minsol_model_max(X_194a,Y_195a,N_196a)
| $less(N_196a,$sum(c,max(X_194a,Y_195a))) ),
inference(resolution,[status(thm)],[c_88,c_230]) ).
tff(c_299,plain,
( $less('#skF_2'('#skF_7','#skF_8','#skF_9'),'#skF_9')
| $less('#skF_9',$sum(c,max('#skF_7','#skF_8'))) ),
inference(resolution,[status(thm)],[c_277,c_159]) ).
tff(c_435,plain,
max('#skF_7','#skF_8') = '#skE_3',
inference(define,[status(thm),theory(equality)],[c_299]) ).
tff(c_467,plain,
( ( '#skF_8' = '#skE_3' )
| $less('#skF_8','#skF_7') ),
inference(superposition,[status(thm),theory(equality)],[c_96,c_435]) ).
tff(c_473,plain,
$less('#skF_8','#skF_7'),
inference(splitLeft,[status(thm)],[c_467]) ).
tff(c_458,plain,
( ( '#skF_7' = '#skE_3' )
| $less('#skF_7','#skF_8') ),
inference(superposition,[status(thm),theory(equality)],[c_435,c_97]) ).
tff(c_469,plain,
$less('#skF_7','#skF_8'),
inference(splitLeft,[status(thm)],[c_458]) ).
tff(c_496,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_473,c_469]) ).
tff(c_499,plain,
'#skF_8' = '#skE_3',
inference(splitRight,[status(thm)],[c_467]) ).
tff(c_431,plain,
max('#skF_7','#skF_8') = '#skE_3',
inference(define,[status(thm),theory(equality)],[c_299]) ).
tff(c_587,plain,
max('#skF_7','#skE_3') = '#skE_3',
inference(demodulation,[status(thm),theory(equality)],[c_499,c_431]) ).
tff(c_421,plain,
max('#skF_7','#skF_8') = '#skE_3',
inference(define,[status(thm),theory(equality)],[c_299]) ).
tff(c_420,plain,
'#skF_2'('#skF_7','#skF_8','#skF_9') = '#skE_2',
inference(define,[status(thm),theory(equality)],[c_299]) ).
tff(c_419,plain,
( $less('#skF_2'('#skF_7','#skF_8','#skF_9'),'#skF_9')
| $less('#skF_9',$sum(c,max('#skF_7','#skF_8'))) ),
inference(resolution,[status(thm)],[c_277,c_159]) ).
tff(c_432,plain,
( $less('#skE_2','#skF_9')
| $less('#skF_9',$sum(c,'#skE_3')) ),
inference(demodulation,[status(thm),theory(equality)],[c_421,c_420,c_419]) ).
tff(c_652,plain,
$less('#skF_9',$sum(c,'#skE_3')),
inference(splitLeft,[status(thm)],[c_432]) ).
tff(c_305,plain,
minsol_model_ub('#skF_7','#skF_8','#skF_9'),
inference(splitLeft,[status(thm)],[c_57]) ).
tff(c_306,plain,
minsol_model_ub('#skF_7','#skF_8','#skF_9'),
inference(splitLeft,[status(thm)],[c_57]) ).
tff(c_223,plain,
! [N_154a: $int,X_156a: $int,Y_157a: $int] :
( ~ $less(N_154a,$sum(c,'#skF_1'(X_156a,Y_157a,N_154a)))
| ~ model_ub(X_156a,Y_157a,N_154a) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_24]) ).
tff(c_229,plain,
! [N_27a: $int,X_25a: $int,Y_26a: $int] :
( ~ $less(N_27a,$sum(c,'#skF_1'(X_25a,Y_26a,N_27a)))
| ~ minsol_model_ub(X_25a,Y_26a,N_27a) ),
inference(resolution,[status(thm)],[c_72,c_223]) ).
tff(c_324,plain,
~ $less('#skF_9',$sum(c,'#skF_1'('#skF_7','#skF_8','#skF_9'))),
inference(resolution,[status(thm)],[c_306,c_229]) ).
tff(c_354,plain,
'#skF_1'('#skF_7','#skF_8','#skF_9') = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_324]) ).
tff(c_370,plain,
( ub('#skF_7','#skF_8','#skE_1')
| ~ model_ub('#skF_7','#skF_8','#skF_9') ),
inference(superposition,[status(thm),theory(equality)],[c_354,c_78]) ).
tff(c_382,plain,
~ model_ub('#skF_7','#skF_8','#skF_9'),
inference(splitLeft,[status(thm)],[c_370]) ).
tff(c_388,plain,
~ minsol_model_ub('#skF_7','#skF_8','#skF_9'),
inference(resolution,[status(thm)],[c_72,c_382]) ).
tff(c_394,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_305,c_388]) ).
tff(c_401,plain,
ub('#skF_7','#skF_8','#skE_1'),
inference(splitRight,[status(thm)],[c_370]) ).
tff(c_415,plain,
~ $less('#skE_1','#skF_8'),
inference(resolution,[status(thm)],[c_401,c_95]) ).
tff(c_541,plain,
~ $less('#skE_1','#skE_3'),
inference(demodulation,[status(thm),theory(equality)],[c_499,c_415]) ).
tff(c_344,plain,
'#skF_1'('#skF_7','#skF_8','#skF_9') = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_324]) ).
tff(c_343,plain,
~ $less('#skF_9',$sum(c,'#skF_1'('#skF_7','#skF_8','#skF_9'))),
inference(resolution,[status(thm)],[c_306,c_229]) ).
tff(c_351,plain,
~ $less('#skF_9',$sum(c,'#skE_1')),
inference(demodulation,[status(thm),theory(equality)],[c_344,c_343]) ).
tff(c_654,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_652,c_541,c_351]) ).
tff(c_658,plain,
~ $less('#skF_9',$sum(c,'#skE_3')),
inference(splitRight,[status(thm)],[c_432]) ).
tff(c_428,plain,
'#skF_2'('#skF_7','#skF_8','#skF_9') = '#skE_2',
inference(define,[status(thm),theory(equality)],[c_299]) ).
tff(c_631,plain,
'#skF_2'('#skF_7','#skE_3','#skF_9') = '#skE_2',
inference(demodulation,[status(thm),theory(equality)],[c_499,c_428]) ).
tff(c_647,plain,
( model_max('#skF_7','#skE_3','#skE_2')
| minsol_model_max('#skF_7','#skE_3','#skF_9')
| ~ model_max('#skF_7','#skE_3','#skF_9') ),
inference(superposition,[status(thm),theory(equality)],[c_631,c_74]) ).
tff(c_1087,plain,
~ model_max('#skF_7','#skE_3','#skF_9'),
inference(splitLeft,[status(thm)],[c_647]) ).
tff(c_1090,plain,
$less('#skF_9',$sum(c,max('#skF_7','#skE_3'))),
inference(resolution,[status(thm)],[c_88,c_1087]) ).
tff(c_1095,plain,
$less('#skF_9',$sum(c,'#skE_3')),
inference(demodulation,[status(thm),theory(equality)],[c_587,c_1090]) ).
tff(c_1097,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_658,c_1095]) ).
tff(c_1101,plain,
( minsol_model_max('#skF_7','#skE_3','#skF_9')
| model_max('#skF_7','#skE_3','#skE_2') ),
inference(splitRight,[status(thm)],[c_647]) ).
tff(c_1110,plain,
model_max('#skF_7','#skE_3','#skE_2'),
inference(splitLeft,[status(thm)],[c_1101]) ).
tff(c_1116,plain,
~ $less('#skE_2',$sum(c,max('#skF_7','#skE_3'))),
inference(resolution,[status(thm)],[c_1110,c_92]) ).
tff(c_1125,plain,
~ $less('#skE_2',$sum(c,'#skE_3')),
inference(demodulation,[status(thm),theory(equality)],[c_587,c_1116]) ).
tff(c_270,plain,
! [Y_180a: $int,X_179a: $int,Z_182a: $int,N_181a: $int,N_27a: $int] :
( ~ minsol_model_ub(X_179a,Y_180a,N_27a)
| ~ $less(N_181a,N_27a)
| $less(N_181a,$sum(c,Z_182a))
| $less(Z_182a,X_179a)
| $less(Z_182a,Y_180a) ),
inference(resolution,[status(thm)],[c_254,c_73]) ).
tff(c_319,plain,
! [N_181a: $int,Z_182a: $int] :
( ~ $less(N_181a,'#skF_9')
| $less(N_181a,$sum(c,Z_182a))
| $less(Z_182a,'#skF_7')
| $less(Z_182a,'#skF_8') ),
inference(resolution,[status(thm)],[c_306,c_270]) ).
tff(c_548,plain,
! [N_181a: $int,Z_182a: $int] :
( ~ $less(N_181a,'#skF_9')
| $less(N_181a,$sum(c,Z_182a))
| $less(Z_182a,'#skF_7')
| $less(Z_182a,'#skE_3') ),
inference(demodulation,[status(thm),theory(equality)],[c_499,c_319]) ).
tff(c_749,plain,
( $lesseq('#skF_9',$sum(c,'#skF_7'))
| $lesseq('#skF_9',$sum(c,'#skE_3')) ),
inference(quantifierElimination,[status(thm),theory('LIA')],[c_548]) ).
tff(c_751,plain,
( ~ $less($sum('#skF_7',c),'#skF_9')
| ~ $less($sum('#skE_3',c),'#skF_9') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_749]) ).
tff(c_657,plain,
$less('#skE_2','#skF_9'),
inference(splitRight,[status(thm)],[c_432]) ).
tff(c_500,plain,
~ $less('#skF_8','#skF_7'),
inference(splitRight,[status(thm)],[c_467]) ).
tff(c_559,plain,
~ $less('#skE_3','#skF_7'),
inference(demodulation,[status(thm),theory(equality)],[c_499,c_500]) ).
tff(c_1129,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_1125,c_751,c_657,c_559]) ).
tff(c_1135,plain,
minsol_model_max('#skF_7','#skE_3','#skF_9'),
inference(splitRight,[status(thm)],[c_1101]) ).
tff(c_557,plain,
~ minsol_model_max('#skF_7','#skE_3','#skF_9'),
inference(demodulation,[status(thm),theory(equality)],[c_499,c_159]) ).
tff(c_1138,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_1135,c_557]) ).
tff(c_1141,plain,
'#skF_7' = '#skE_3',
inference(splitRight,[status(thm)],[c_458]) ).
tff(c_1248,plain,
max('#skE_3','#skF_8') = '#skE_3',
inference(demodulation,[status(thm),theory(equality)],[c_1141,c_431]) ).
tff(c_1287,plain,
$less('#skF_9',$sum(c,'#skE_3')),
inference(splitLeft,[status(thm)],[c_432]) ).
tff(c_417,plain,
~ $less('#skE_1','#skF_7'),
inference(resolution,[status(thm)],[c_401,c_94]) ).
tff(c_1210,plain,
~ $less('#skE_1','#skE_3'),
inference(demodulation,[status(thm),theory(equality)],[c_1141,c_417]) ).
tff(c_1288,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_1287,c_1210,c_351]) ).
tff(c_1292,plain,
~ $less('#skF_9',$sum(c,'#skE_3')),
inference(splitRight,[status(thm)],[c_432]) ).
tff(c_1143,plain,
'#skF_2'('#skF_7','#skF_8','#skF_9') = '#skE_2',
inference(define,[status(thm),theory(equality)],[c_299]) ).
tff(c_1159,plain,
( model_max('#skF_7','#skF_8','#skE_2')
| minsol_model_max('#skF_7','#skF_8','#skF_9')
| ~ model_max('#skF_7','#skF_8','#skF_9') ),
inference(superposition,[status(thm),theory(equality)],[c_1143,c_74]) ).
tff(c_1439,plain,
( model_max('#skE_3','#skF_8','#skE_2')
| minsol_model_max('#skE_3','#skF_8','#skF_9')
| ~ model_max('#skE_3','#skF_8','#skF_9') ),
inference(demodulation,[status(thm),theory(equality)],[c_1141,c_1141,c_1141,c_1159]) ).
tff(c_1447,plain,
~ model_max('#skE_3','#skF_8','#skF_9'),
inference(splitLeft,[status(thm)],[c_1439]) ).
tff(c_1450,plain,
$less('#skF_9',$sum(c,max('#skE_3','#skF_8'))),
inference(resolution,[status(thm)],[c_88,c_1447]) ).
tff(c_1455,plain,
$less('#skF_9',$sum(c,'#skE_3')),
inference(demodulation,[status(thm),theory(equality)],[c_1248,c_1450]) ).
tff(c_1457,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_1292,c_1455]) ).
tff(c_1461,plain,
( minsol_model_max('#skE_3','#skF_8','#skF_9')
| model_max('#skE_3','#skF_8','#skE_2') ),
inference(splitRight,[status(thm)],[c_1439]) ).
tff(c_1484,plain,
model_max('#skE_3','#skF_8','#skE_2'),
inference(splitLeft,[status(thm)],[c_1461]) ).
tff(c_1490,plain,
~ $less('#skE_2',$sum(c,max('#skE_3','#skF_8'))),
inference(resolution,[status(thm)],[c_1484,c_92]) ).
tff(c_1499,plain,
~ $less('#skE_2',$sum(c,'#skE_3')),
inference(demodulation,[status(thm),theory(equality)],[c_1248,c_1490]) ).
tff(c_1217,plain,
! [N_181a: $int,Z_182a: $int] :
( ~ $less(N_181a,'#skF_9')
| $less(N_181a,$sum(c,Z_182a))
| $less(Z_182a,'#skE_3')
| $less(Z_182a,'#skF_8') ),
inference(demodulation,[status(thm),theory(equality)],[c_1141,c_319]) ).
tff(c_1392,plain,
( $lesseq('#skF_9',$sum(c,'#skE_3'))
| $lesseq('#skF_9',$sum(c,'#skF_8')) ),
inference(quantifierElimination,[status(thm),theory('LIA')],[c_1217]) ).
tff(c_1394,plain,
( ~ $less($sum('#skE_3',c),'#skF_9')
| ~ $less($sum('#skF_8',c),'#skF_9') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_1392]) ).
tff(c_1291,plain,
$less('#skE_2','#skF_9'),
inference(splitRight,[status(thm)],[c_432]) ).
tff(c_1142,plain,
~ $less('#skF_7','#skF_8'),
inference(splitRight,[status(thm)],[c_458]) ).
tff(c_1229,plain,
~ $less('#skE_3','#skF_8'),
inference(demodulation,[status(thm),theory(equality)],[c_1141,c_1142]) ).
tff(c_1503,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_1499,c_1394,c_1291,c_1229]) ).
tff(c_1509,plain,
minsol_model_max('#skE_3','#skF_8','#skF_9'),
inference(splitRight,[status(thm)],[c_1461]) ).
tff(c_1227,plain,
~ minsol_model_max('#skE_3','#skF_8','#skF_9'),
inference(demodulation,[status(thm),theory(equality)],[c_1141,c_159]) ).
tff(c_1512,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_1509,c_1227]) ).
tff(c_1519,plain,
minsol_model_max('#skF_4','#skF_5','#skF_6'),
inference(splitRight,[status(thm)],[c_57]) ).
tff(c_195,plain,
! [N_137a: $int,X_139a: $int,Y_140a: $int] :
( ~ $less(N_137a,$sum(c,max(X_139a,Y_140a)))
| ~ model_max(X_139a,Y_140a,N_137a) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_16]) ).
tff(c_201,plain,
! [N_21a: $int,X_19a: $int,Y_20a: $int] :
( ~ $less(N_21a,$sum(c,max(X_19a,Y_20a)))
| ~ minsol_model_max(X_19a,Y_20a,N_21a) ),
inference(resolution,[status(thm)],[c_76,c_195]) ).
tff(c_1536,plain,
~ $less('#skF_6',$sum(c,max('#skF_4','#skF_5'))),
inference(resolution,[status(thm)],[c_1519,c_201]) ).
tff(c_1581,plain,
max('#skF_4','#skF_5') = '#skE_5',
inference(define,[status(thm),theory(equality)],[c_1536]) ).
tff(c_1606,plain,
( ( '#skF_5' = '#skE_5' )
| $less('#skF_5','#skF_4') ),
inference(superposition,[status(thm),theory(equality)],[c_1581,c_96]) ).
tff(c_1621,plain,
$less('#skF_5','#skF_4'),
inference(splitLeft,[status(thm)],[c_1606]) ).
tff(c_1604,plain,
( ( '#skF_4' = '#skE_5' )
| $less('#skF_4','#skF_5') ),
inference(superposition,[status(thm),theory(equality)],[c_1581,c_97]) ).
tff(c_1615,plain,
$less('#skF_4','#skF_5'),
inference(splitLeft,[status(thm)],[c_1604]) ).
tff(c_1622,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_1621,c_1615]) ).
tff(c_1625,plain,
'#skF_5' = '#skE_5',
inference(splitRight,[status(thm)],[c_1606]) ).
tff(c_61,plain,
( ~ minsol_model_ub('#skF_4','#skF_5','#skF_6')
| minsol_model_ub('#skF_7','#skF_8','#skF_9') ),
inference(cnfTransformation,[status(thm)],[f_95]) ).
tff(c_250,plain,
~ minsol_model_ub('#skF_4','#skF_5','#skF_6'),
inference(splitLeft,[status(thm)],[c_61]) ).
tff(c_1661,plain,
~ minsol_model_ub('#skF_4','#skE_5','#skF_6'),
inference(demodulation,[status(thm),theory(equality)],[c_1625,c_250]) ).
tff(c_1979,plain,
! [Z_918a: $int] :
( $less('#skF_3'('#skF_4','#skE_5','#skF_6'),'#skF_6')
| $less('#skF_6',$sum(c,Z_918a))
| $less(Z_918a,'#skF_4')
| $less(Z_918a,'#skE_5') ),
inference(resolution,[status(thm)],[c_1965,c_1661]) ).
tff(c_2111,plain,
'#skF_3'('#skF_4','#skE_5','#skF_6') = '#skE_6',
inference(define,[status(thm),theory(equality)],[c_1979]) ).
tff(c_70,plain,
! [X_25a: $int,Y_26a: $int,N_27a: $int] :
( model_ub(X_25a,Y_26a,'#skF_3'(X_25a,Y_26a,N_27a))
| minsol_model_ub(X_25a,Y_26a,N_27a)
| ~ model_ub(X_25a,Y_26a,N_27a) ),
inference(cnfTransformation,[status(thm)],[f_89]) ).
tff(c_2127,plain,
( model_ub('#skF_4','#skE_5','#skE_6')
| minsol_model_ub('#skF_4','#skE_5','#skF_6')
| ~ model_ub('#skF_4','#skE_5','#skF_6') ),
inference(superposition,[status(thm),theory(equality)],[c_2111,c_70]) ).
tff(c_2149,plain,
~ model_ub('#skF_4','#skE_5','#skF_6'),
inference(splitLeft,[status(thm)],[c_2127]) ).
tff(c_2157,plain,
! [Z_9a: $int] :
( $less('#skF_6',$sum(c,Z_9a))
| $less(Z_9a,'#skF_4')
| $less(Z_9a,'#skE_5') ),
inference(resolution,[status(thm)],[c_194,c_2149]) ).
tff(c_2159,plain,
( $lesseq($sum(1,'#skF_6'),$sum(c,'#skF_4'))
| $lesseq($sum(1,'#skF_6'),$sum(c,'#skE_5')) ),
inference(quantifierElimination,[status(thm),theory('LIA')],[c_2157]) ).
tff(c_2161,plain,
( ~ $less($sum('#skF_4',c),$sum(1,'#skF_6'))
| ~ $less($sum('#skE_5',c),$sum(1,'#skF_6')) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_2159]) ).
tff(c_1626,plain,
~ $less('#skF_5','#skF_4'),
inference(splitRight,[status(thm)],[c_1606]) ).
tff(c_1688,plain,
~ $less('#skE_5','#skF_4'),
inference(demodulation,[status(thm),theory(equality)],[c_1625,c_1626]) ).
tff(c_1561,plain,
max('#skF_4','#skF_5') = '#skE_5',
inference(define,[status(thm),theory(equality)],[c_1536]) ).
tff(c_1560,plain,
~ $less('#skF_6',$sum(c,max('#skF_4','#skF_5'))),
inference(resolution,[status(thm)],[c_1519,c_201]) ).
tff(c_1568,plain,
~ $less('#skF_6',$sum(c,'#skE_5')),
inference(demodulation,[status(thm),theory(equality)],[c_1561,c_1560]) ).
tff(c_2162,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_2161,c_1688,c_1568]) ).
tff(c_2166,plain,
( minsol_model_ub('#skF_4','#skE_5','#skF_6')
| model_ub('#skF_4','#skE_5','#skE_6') ),
inference(splitRight,[status(thm)],[c_2127]) ).
tff(c_2177,plain,
model_ub('#skF_4','#skE_5','#skE_6'),
inference(splitLeft,[status(thm)],[c_2166]) ).
tff(c_2178,plain,
model_ub('#skF_4','#skE_5','#skE_6'),
inference(splitLeft,[status(thm)],[c_2166]) ).
tff(c_82,plain,
! [N_15a: $int,X_13a: $int,Y_14a: $int] :
( ~ $less(N_15a,$sum(c,'#skF_1'(X_13a,Y_14a,N_15a)))
| ~ model_ub(X_13a,Y_14a,N_15a) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_24]) ).
tff(c_2190,plain,
~ $less('#skE_6',$sum(c,'#skF_1'('#skF_4','#skE_5','#skE_6'))),
inference(resolution,[status(thm)],[c_2178,c_82]) ).
tff(c_2218,plain,
'#skF_1'('#skF_4','#skE_5','#skE_6') = '#skE_7',
inference(define,[status(thm),theory(equality)],[c_2190]) ).
tff(c_2228,plain,
( ub('#skF_4','#skE_5','#skE_7')
| ~ model_ub('#skF_4','#skE_5','#skE_6') ),
inference(superposition,[status(thm),theory(equality)],[c_2218,c_78]) ).
tff(c_2249,plain,
ub('#skF_4','#skE_5','#skE_7'),
inference(demodulation,[status(thm),theory(equality)],[c_2177,c_2228]) ).
tff(c_2263,plain,
~ $less('#skE_7','#skE_5'),
inference(resolution,[status(thm)],[c_2249,c_95]) ).
tff(c_2208,plain,
'#skF_1'('#skF_4','#skE_5','#skE_6') = '#skE_7',
inference(define,[status(thm),theory(equality)],[c_2190]) ).
tff(c_2207,plain,
~ $less('#skE_6',$sum(c,'#skF_1'('#skF_4','#skE_5','#skE_6'))),
inference(resolution,[status(thm)],[c_2178,c_82]) ).
tff(c_2215,plain,
~ $less('#skE_6',$sum(c,'#skE_7')),
inference(demodulation,[status(thm),theory(equality)],[c_2208,c_2207]) ).
tff(c_2101,plain,
'#skF_3'('#skF_4','#skE_5','#skF_6') = '#skE_6',
inference(define,[status(thm),theory(equality)],[c_1979]) ).
tff(c_2100,plain,
! [Z_918a: $int] :
( $less('#skF_3'('#skF_4','#skE_5','#skF_6'),'#skF_6')
| $less('#skF_6',$sum(c,Z_918a))
| $less(Z_918a,'#skF_4')
| $less(Z_918a,'#skE_5') ),
inference(resolution,[status(thm)],[c_1965,c_1661]) ).
tff(c_2108,plain,
! [Z_918a: $int] :
( $less('#skE_6','#skF_6')
| $less('#skF_6',$sum(c,Z_918a))
| $less(Z_918a,'#skF_4')
| $less(Z_918a,'#skE_5') ),
inference(demodulation,[status(thm),theory(equality)],[c_2101,c_2100]) ).
tff(c_2132,plain,
$less('#skE_6','#skF_6'),
inference(splitLeft,[status(thm)],[c_2108]) ).
tff(c_202,plain,
! [X_142a: $int,Y_143a: $int,N_144a: $int] :
( model_max(X_142a,Y_143a,N_144a)
| $less(N_144a,$sum(c,max(X_142a,Y_143a))) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_19]) ).
tff(c_28,plain,
! [X_19a: $int,Y_20a: $int,Z_24a: $int,N_21a: $int] :
( ~ model_max(X_19a,Y_20a,Z_24a)
| ~ minsol_model_max(X_19a,Y_20a,N_21a)
| $lesseq(N_21a,Z_24a) ),
inference(cnfTransformation,[status(thm)],[f_79]) ).
tff(c_77,plain,
! [X_19a: $int,Y_20a: $int,Z_24a: $int,N_21a: $int] :
( ~ model_max(X_19a,Y_20a,Z_24a)
| ~ minsol_model_max(X_19a,Y_20a,N_21a)
| ~ $less(Z_24a,N_21a) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_28]) ).
tff(c_213,plain,
! [X_142a: $int,Y_143a: $int,N_21a: $int,N_144a: $int] :
( ~ minsol_model_max(X_142a,Y_143a,N_21a)
| ~ $less(N_144a,N_21a)
| $less(N_144a,$sum(c,max(X_142a,Y_143a))) ),
inference(resolution,[status(thm)],[c_202,c_77]) ).
tff(c_1533,plain,
! [N_144a: $int] :
( ~ $less(N_144a,'#skF_6')
| $less(N_144a,$sum(c,max('#skF_4','#skF_5'))) ),
inference(resolution,[status(thm)],[c_1519,c_213]) ).
tff(c_1571,plain,
max('#skF_4','#skF_5') = '#skE_5',
inference(define,[status(thm),theory(equality)],[c_1533]) ).
tff(c_1570,plain,
! [N_144a: $int] :
( ~ $less(N_144a,'#skF_6')
| $less(N_144a,$sum(c,max('#skF_4','#skF_5'))) ),
inference(resolution,[status(thm)],[c_1519,c_213]) ).
tff(c_1578,plain,
! [N_144a: $int] :
( ~ $less(N_144a,'#skF_6')
| $less(N_144a,$sum(c,'#skE_5')) ),
inference(demodulation,[status(thm),theory(equality)],[c_1571,c_1570]) ).
tff(c_1733,plain,
$lesseq('#skF_6',$sum('#skE_5',c)),
inference(quantifierElimination,[status(thm),theory('LIA')],[c_1578]) ).
tff(c_1735,plain,
~ $less($sum(c,'#skE_5'),'#skF_6'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_1733]) ).
tff(c_2266,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_2263,c_2215,c_2132,c_1735]) ).
tff(c_2272,plain,
minsol_model_ub('#skF_4','#skE_5','#skF_6'),
inference(splitRight,[status(thm)],[c_2166]) ).
tff(c_2275,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_2272,c_1661]) ).
tff(c_2278,plain,
! [Z_918a: $int] :
( $less('#skF_6',$sum(c,Z_918a))
| $less(Z_918a,'#skF_4')
| $less(Z_918a,'#skE_5') ),
inference(splitRight,[status(thm)],[c_2108]) ).
tff(c_2282,plain,
( $lesseq($sum(1,'#skF_6'),$sum(c,'#skF_4'))
| $lesseq($sum(1,'#skF_6'),$sum(c,'#skE_5')) ),
inference(quantifierElimination,[status(thm),theory('LIA')],[c_2278]) ).
tff(c_2284,plain,
( ~ $less($sum('#skF_4',c),$sum(1,'#skF_6'))
| ~ $less($sum('#skE_5',c),$sum(1,'#skF_6')) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_2282]) ).
tff(c_2285,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_2284,c_1688,c_1568]) ).
tff(c_2288,plain,
'#skF_4' = '#skE_5',
inference(splitRight,[status(thm)],[c_1604]) ).
tff(c_2324,plain,
~ minsol_model_ub('#skE_5','#skF_5','#skF_6'),
inference(demodulation,[status(thm),theory(equality)],[c_2288,c_250]) ).
tff(c_2648,plain,
! [Z_1184a: $int] :
( $less('#skF_3'('#skE_5','#skF_5','#skF_6'),'#skF_6')
| $less('#skF_6',$sum(c,Z_1184a))
| $less(Z_1184a,'#skE_5')
| $less(Z_1184a,'#skF_5') ),
inference(resolution,[status(thm)],[c_2634,c_2324]) ).
tff(c_2788,plain,
'#skF_3'('#skE_5','#skF_5','#skF_6') = '#skE_8',
inference(define,[status(thm),theory(equality)],[c_2648]) ).
tff(c_2804,plain,
( model_ub('#skE_5','#skF_5','#skE_8')
| minsol_model_ub('#skE_5','#skF_5','#skF_6')
| ~ model_ub('#skE_5','#skF_5','#skF_6') ),
inference(superposition,[status(thm),theory(equality)],[c_2788,c_70]) ).
tff(c_2819,plain,
~ model_ub('#skE_5','#skF_5','#skF_6'),
inference(splitLeft,[status(thm)],[c_2804]) ).
tff(c_2827,plain,
! [Z_9a: $int] :
( $less('#skF_6',$sum(c,Z_9a))
| $less(Z_9a,'#skE_5')
| $less(Z_9a,'#skF_5') ),
inference(resolution,[status(thm)],[c_194,c_2819]) ).
tff(c_2829,plain,
( $lesseq($sum(1,'#skF_6'),$sum(c,'#skE_5'))
| $lesseq($sum(1,'#skF_6'),$sum(c,'#skF_5')) ),
inference(quantifierElimination,[status(thm),theory('LIA')],[c_2827]) ).
tff(c_2831,plain,
( ~ $less($sum('#skE_5',c),$sum(1,'#skF_6'))
| ~ $less($sum('#skF_5',c),$sum(1,'#skF_6')) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_2829]) ).
tff(c_2289,plain,
~ $less('#skF_4','#skF_5'),
inference(splitRight,[status(thm)],[c_1604]) ).
tff(c_2326,plain,
~ $less('#skE_5','#skF_5'),
inference(demodulation,[status(thm),theory(equality)],[c_2288,c_2289]) ).
tff(c_2832,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_2831,c_2326,c_1568]) ).
tff(c_2836,plain,
( minsol_model_ub('#skE_5','#skF_5','#skF_6')
| model_ub('#skE_5','#skF_5','#skE_8') ),
inference(splitRight,[status(thm)],[c_2804]) ).
tff(c_2846,plain,
model_ub('#skE_5','#skF_5','#skE_8'),
inference(splitLeft,[status(thm)],[c_2836]) ).
tff(c_2847,plain,
model_ub('#skE_5','#skF_5','#skE_8'),
inference(splitLeft,[status(thm)],[c_2836]) ).
tff(c_2859,plain,
~ $less('#skE_8',$sum(c,'#skF_1'('#skE_5','#skF_5','#skE_8'))),
inference(resolution,[status(thm)],[c_2847,c_82]) ).
tff(c_2887,plain,
'#skF_1'('#skE_5','#skF_5','#skE_8') = '#skE_9',
inference(define,[status(thm),theory(equality)],[c_2859]) ).
tff(c_2897,plain,
( ub('#skE_5','#skF_5','#skE_9')
| ~ model_ub('#skE_5','#skF_5','#skE_8') ),
inference(superposition,[status(thm),theory(equality)],[c_2887,c_78]) ).
tff(c_2918,plain,
ub('#skE_5','#skF_5','#skE_9'),
inference(demodulation,[status(thm),theory(equality)],[c_2846,c_2897]) ).
tff(c_2934,plain,
~ $less('#skE_9','#skE_5'),
inference(resolution,[status(thm)],[c_2918,c_94]) ).
tff(c_2877,plain,
'#skF_1'('#skE_5','#skF_5','#skE_8') = '#skE_9',
inference(define,[status(thm),theory(equality)],[c_2859]) ).
tff(c_2876,plain,
~ $less('#skE_8',$sum(c,'#skF_1'('#skE_5','#skF_5','#skE_8'))),
inference(resolution,[status(thm)],[c_2847,c_82]) ).
tff(c_2884,plain,
~ $less('#skE_8',$sum(c,'#skE_9')),
inference(demodulation,[status(thm),theory(equality)],[c_2877,c_2876]) ).
tff(c_2778,plain,
'#skF_3'('#skE_5','#skF_5','#skF_6') = '#skE_8',
inference(define,[status(thm),theory(equality)],[c_2648]) ).
tff(c_2777,plain,
! [Z_1184a: $int] :
( $less('#skF_3'('#skE_5','#skF_5','#skF_6'),'#skF_6')
| $less('#skF_6',$sum(c,Z_1184a))
| $less(Z_1184a,'#skE_5')
| $less(Z_1184a,'#skF_5') ),
inference(resolution,[status(thm)],[c_2634,c_2324]) ).
tff(c_2785,plain,
! [Z_1184a: $int] :
( $less('#skE_8','#skF_6')
| $less('#skF_6',$sum(c,Z_1184a))
| $less(Z_1184a,'#skE_5')
| $less(Z_1184a,'#skF_5') ),
inference(demodulation,[status(thm),theory(equality)],[c_2778,c_2777]) ).
tff(c_2809,plain,
$less('#skE_8','#skF_6'),
inference(splitLeft,[status(thm)],[c_2785]) ).
tff(c_2935,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_2934,c_2884,c_2809,c_1735]) ).
tff(c_2941,plain,
minsol_model_ub('#skE_5','#skF_5','#skF_6'),
inference(splitRight,[status(thm)],[c_2836]) ).
tff(c_2944,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_2941,c_2324]) ).
tff(c_2947,plain,
! [Z_1184a: $int] :
( $less('#skF_6',$sum(c,Z_1184a))
| $less(Z_1184a,'#skE_5')
| $less(Z_1184a,'#skF_5') ),
inference(splitRight,[status(thm)],[c_2785]) ).
tff(c_2951,plain,
( $lesseq($sum(1,'#skF_6'),$sum(c,'#skE_5'))
| $lesseq($sum(1,'#skF_6'),$sum(c,'#skF_5')) ),
inference(quantifierElimination,[status(thm),theory('LIA')],[c_2947]) ).
tff(c_2953,plain,
( ~ $less($sum('#skE_5',c),$sum(1,'#skF_6'))
| ~ $less($sum('#skF_5',c),$sum(1,'#skF_6')) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_2951]) ).
tff(c_2954,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_2953,c_2326,c_1568]) ).
tff(c_2960,plain,
minsol_model_ub('#skF_7','#skF_8','#skF_9'),
inference(splitRight,[status(thm)],[c_61]) ).
tff(c_2961,plain,
minsol_model_ub('#skF_7','#skF_8','#skF_9'),
inference(splitRight,[status(thm)],[c_61]) ).
tff(c_2969,plain,
~ $less('#skF_9',$sum(c,'#skF_1'('#skF_7','#skF_8','#skF_9'))),
inference(resolution,[status(thm)],[c_2961,c_229]) ).
tff(c_3025,plain,
'#skF_1'('#skF_7','#skF_8','#skF_9') = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_2969]) ).
tff(c_3041,plain,
( ub('#skF_7','#skF_8','#skE_1')
| ~ model_ub('#skF_7','#skF_8','#skF_9') ),
inference(superposition,[status(thm),theory(equality)],[c_3025,c_78]) ).
tff(c_3076,plain,
~ model_ub('#skF_7','#skF_8','#skF_9'),
inference(splitLeft,[status(thm)],[c_3041]) ).
tff(c_3082,plain,
~ minsol_model_ub('#skF_7','#skF_8','#skF_9'),
inference(resolution,[status(thm)],[c_72,c_3076]) ).
tff(c_3088,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_2960,c_3082]) ).
tff(c_3095,plain,
ub('#skF_7','#skF_8','#skE_1'),
inference(splitRight,[status(thm)],[c_3041]) ).
tff(c_3109,plain,
~ $less('#skE_1','#skF_8'),
inference(resolution,[status(thm)],[c_3095,c_95]) ).
tff(c_3270,plain,
~ $less('#skE_1','#skE_3'),
inference(demodulation,[status(thm),theory(equality)],[c_3190,c_3109]) ).
tff(c_3015,plain,
'#skF_1'('#skF_7','#skF_8','#skF_9') = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_2969]) ).
tff(c_3014,plain,
~ $less('#skF_9',$sum(c,'#skF_1'('#skF_7','#skF_8','#skF_9'))),
inference(resolution,[status(thm)],[c_2961,c_229]) ).
tff(c_3022,plain,
~ $less('#skF_9',$sum(c,'#skE_1')),
inference(demodulation,[status(thm),theory(equality)],[c_3015,c_3014]) ).
tff(c_3372,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_3352,c_3270,c_3022]) ).
tff(c_3376,plain,
~ $less('#skF_9',$sum(c,'#skE_3')),
inference(splitRight,[status(thm)],[c_3147]) ).
tff(c_3194,plain,
'#skF_2'('#skF_7','#skF_8','#skF_9') = '#skE_2',
inference(define,[status(thm),theory(equality)],[c_3067]) ).
tff(c_3210,plain,
( model_max('#skF_7','#skF_8','#skE_2')
| minsol_model_max('#skF_7','#skF_8','#skF_9')
| ~ model_max('#skF_7','#skF_8','#skF_9') ),
inference(superposition,[status(thm),theory(equality)],[c_3194,c_74]) ).
tff(c_3510,plain,
( model_max('#skF_7','#skE_3','#skE_2')
| minsol_model_max('#skF_7','#skE_3','#skF_9')
| ~ model_max('#skF_7','#skE_3','#skF_9') ),
inference(demodulation,[status(thm),theory(equality)],[c_3190,c_3190,c_3190,c_3210]) ).
tff(c_3518,plain,
~ model_max('#skF_7','#skE_3','#skF_9'),
inference(splitLeft,[status(thm)],[c_3510]) ).
tff(c_3521,plain,
$less('#skF_9',$sum(c,max('#skF_7','#skE_3'))),
inference(resolution,[status(thm)],[c_88,c_3518]) ).
tff(c_3526,plain,
$less('#skF_9',$sum(c,'#skE_3')),
inference(demodulation,[status(thm),theory(equality)],[c_3313,c_3521]) ).
tff(c_3528,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_3376,c_3526]) ).
tff(c_3532,plain,
( minsol_model_max('#skF_7','#skE_3','#skF_9')
| model_max('#skF_7','#skE_3','#skE_2') ),
inference(splitRight,[status(thm)],[c_3510]) ).
tff(c_3563,plain,
model_max('#skF_7','#skE_3','#skE_2'),
inference(splitLeft,[status(thm)],[c_3532]) ).
tff(c_3569,plain,
~ $less('#skE_2',$sum(c,max('#skF_7','#skE_3'))),
inference(resolution,[status(thm)],[c_3563,c_92]) ).
tff(c_3578,plain,
~ $less('#skE_2',$sum(c,'#skE_3')),
inference(demodulation,[status(thm),theory(equality)],[c_3313,c_3569]) ).
tff(c_2958,plain,
minsol_model_ub('#skF_7','#skF_8','#skF_9'),
inference(splitRight,[status(thm)],[c_61]) ).
tff(c_2982,plain,
! [X_1337a: $int,Y_1338a: $int,N_1339a: $int,Z_1340a: $int] :
( model_ub(X_1337a,Y_1338a,N_1339a)
| $less(N_1339a,$sum(c,Z_1340a))
| $less(Z_1340a,X_1337a)
| $less(Z_1340a,Y_1338a) ),
inference(resolution,[status(thm)],[c_93,c_189]) ).
tff(c_3004,plain,
! [X_1353a: $int,N_1351a: $int,N_1352a: $int,Y_1354a: $int,Z_1350a: $int] :
( ~ minsol_model_ub(X_1353a,Y_1354a,N_1351a)
| ~ $less(N_1352a,N_1351a)
| $less(N_1352a,$sum(c,Z_1350a))
| $less(Z_1350a,X_1353a)
| $less(Z_1350a,Y_1354a) ),
inference(resolution,[status(thm)],[c_2982,c_73]) ).
tff(c_3009,plain,
! [N_1352a: $int,Z_1350a: $int] :
( ~ $less(N_1352a,'#skF_9')
| $less(N_1352a,$sum(c,Z_1350a))
| $less(Z_1350a,'#skF_7')
| $less(Z_1350a,'#skF_8') ),
inference(resolution,[status(thm)],[c_2958,c_3004]) ).
tff(c_3277,plain,
! [N_1352a: $int,Z_1350a: $int] :
( ~ $less(N_1352a,'#skF_9')
| $less(N_1352a,$sum(c,Z_1350a))
| $less(Z_1350a,'#skF_7')
| $less(Z_1350a,'#skE_3') ),
inference(demodulation,[status(thm),theory(equality)],[c_3190,c_3009]) ).
tff(c_3462,plain,
( $lesseq('#skF_9',$sum(c,'#skF_7'))
| $lesseq('#skF_9',$sum(c,'#skE_3')) ),
inference(quantifierElimination,[status(thm),theory('LIA')],[c_3277]) ).
tff(c_3464,plain,
( ~ $less($sum('#skF_7',c),'#skF_9')
| ~ $less($sum('#skE_3',c),'#skF_9') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_3462]) ).
tff(c_3375,plain,
$less('#skE_2','#skF_9'),
inference(splitRight,[status(thm)],[c_3147]) ).
tff(c_3191,plain,
~ $less('#skF_8','#skF_7'),
inference(splitRight,[status(thm)],[c_3182]) ).
tff(c_3288,plain,
~ $less('#skE_3','#skF_7'),
inference(demodulation,[status(thm),theory(equality)],[c_3190,c_3191]) ).
tff(c_3582,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_3578,c_3464,c_3375,c_3288]) ).
tff(c_3588,plain,
minsol_model_max('#skF_7','#skE_3','#skF_9'),
inference(splitRight,[status(thm)],[c_3532]) ).
tff(c_3286,plain,
~ minsol_model_max('#skF_7','#skE_3','#skF_9'),
inference(demodulation,[status(thm),theory(equality)],[c_3190,c_159]) ).
tff(c_3591,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_3588,c_3286]) ).
tff(c_3594,plain,
'#skF_7' = '#skE_3',
inference(splitRight,[status(thm)],[c_3173]) ).
tff(c_3688,plain,
max('#skE_3','#skF_8') = '#skE_3',
inference(demodulation,[status(thm),theory(equality)],[c_3594,c_3146]) ).
tff(c_3753,plain,
$less('#skF_9',$sum(c,'#skE_3')),
inference(splitLeft,[status(thm)],[c_3147]) ).
tff(c_3111,plain,
~ $less('#skE_1','#skF_7'),
inference(resolution,[status(thm)],[c_3095,c_94]) ).
tff(c_3641,plain,
~ $less('#skE_1','#skE_3'),
inference(demodulation,[status(thm),theory(equality)],[c_3594,c_3111]) ).
tff(c_3755,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_3753,c_3641,c_3022]) ).
tff(c_3759,plain,
~ $less('#skF_9',$sum(c,'#skE_3')),
inference(splitRight,[status(thm)],[c_3147]) ).
tff(c_3143,plain,
'#skF_2'('#skF_7','#skF_8','#skF_9') = '#skE_2',
inference(define,[status(thm),theory(equality)],[c_3067]) ).
tff(c_3732,plain,
'#skF_2'('#skE_3','#skF_8','#skF_9') = '#skE_2',
inference(demodulation,[status(thm),theory(equality)],[c_3594,c_3143]) ).
tff(c_3748,plain,
( model_max('#skE_3','#skF_8','#skE_2')
| minsol_model_max('#skE_3','#skF_8','#skF_9')
| ~ model_max('#skE_3','#skF_8','#skF_9') ),
inference(superposition,[status(thm),theory(equality)],[c_3732,c_74]) ).
tff(c_3890,plain,
~ model_max('#skE_3','#skF_8','#skF_9'),
inference(splitLeft,[status(thm)],[c_3748]) ).
tff(c_3893,plain,
$less('#skF_9',$sum(c,max('#skE_3','#skF_8'))),
inference(resolution,[status(thm)],[c_88,c_3890]) ).
tff(c_3898,plain,
$less('#skF_9',$sum(c,'#skE_3')),
inference(demodulation,[status(thm),theory(equality)],[c_3688,c_3893]) ).
tff(c_3900,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_3759,c_3898]) ).
tff(c_3904,plain,
( minsol_model_max('#skE_3','#skF_8','#skF_9')
| model_max('#skE_3','#skF_8','#skE_2') ),
inference(splitRight,[status(thm)],[c_3748]) ).
tff(c_3913,plain,
model_max('#skE_3','#skF_8','#skE_2'),
inference(splitLeft,[status(thm)],[c_3904]) ).
tff(c_3919,plain,
~ $less('#skE_2',$sum(c,max('#skE_3','#skF_8'))),
inference(resolution,[status(thm)],[c_3913,c_92]) ).
tff(c_3928,plain,
~ $less('#skE_2',$sum(c,'#skE_3')),
inference(demodulation,[status(thm),theory(equality)],[c_3688,c_3919]) ).
tff(c_3662,plain,
minsol_model_ub('#skE_3','#skF_8','#skF_9'),
inference(demodulation,[status(thm),theory(equality)],[c_3594,c_2958]) ).
tff(c_2998,plain,
! [Z_1340a: $int,Y_1338a: $int,X_1337a: $int,N_27a: $int,N_1339a: $int] :
( ~ minsol_model_ub(X_1337a,Y_1338a,N_27a)
| ~ $less(N_1339a,N_27a)
| $less(N_1339a,$sum(c,Z_1340a))
| $less(Z_1340a,X_1337a)
| $less(Z_1340a,Y_1338a) ),
inference(resolution,[status(thm)],[c_2982,c_73]) ).
tff(c_3672,plain,
! [N_1339a: $int,Z_1340a: $int] :
( ~ $less(N_1339a,'#skF_9')
| $less(N_1339a,$sum(c,Z_1340a))
| $less(Z_1340a,'#skE_3')
| $less(Z_1340a,'#skF_8') ),
inference(resolution,[status(thm)],[c_3662,c_2998]) ).
tff(c_3844,plain,
( $lesseq('#skF_9',$sum(c,'#skE_3'))
| $lesseq('#skF_9',$sum(c,'#skF_8')) ),
inference(quantifierElimination,[status(thm),theory('LIA')],[c_3672]) ).
tff(c_3846,plain,
( ~ $less($sum('#skE_3',c),'#skF_9')
| ~ $less($sum('#skF_8',c),'#skF_9') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_3844]) ).
tff(c_3758,plain,
$less('#skE_2','#skF_9'),
inference(splitRight,[status(thm)],[c_3147]) ).
tff(c_3595,plain,
~ $less('#skF_7','#skF_8'),
inference(splitRight,[status(thm)],[c_3173]) ).
tff(c_3659,plain,
~ $less('#skE_3','#skF_8'),
inference(demodulation,[status(thm),theory(equality)],[c_3594,c_3595]) ).
tff(c_3932,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_3928,c_3846,c_3758,c_3659]) ).
tff(c_3938,plain,
minsol_model_max('#skE_3','#skF_8','#skF_9'),
inference(splitRight,[status(thm)],[c_3904]) ).
tff(c_3657,plain,
~ minsol_model_max('#skE_3','#skF_8','#skF_9'),
inference(demodulation,[status(thm),theory(equality)],[c_3594,c_159]) ).
tff(c_3941,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_3938,c_3657]) ).
tff(c_3945,plain,
~ minsol_model_ub('#skF_4','#skF_5','#skF_6'),
inference(splitRight,[status(thm)],[c_69]) ).
tff(c_5631,plain,
~ minsol_model_ub('#skF_4','#skE_5','#skF_6'),
inference(demodulation,[status(thm),theory(equality)],[c_5595,c_3945]) ).
tff(c_5762,plain,
! [Z_2637a: $int] :
( $less('#skF_3'('#skF_4','#skE_5','#skF_6'),'#skF_6')
| $less('#skF_6',$sum(c,Z_2637a))
| $less(Z_2637a,'#skF_4')
| $less(Z_2637a,'#skE_5') ),
inference(resolution,[status(thm)],[c_5748,c_5631]) ).
tff(c_6045,plain,
'#skF_3'('#skF_4','#skE_5','#skF_6') = '#skE_6',
inference(define,[status(thm),theory(equality)],[c_5762]) ).
tff(c_6061,plain,
( model_ub('#skF_4','#skE_5','#skE_6')
| minsol_model_ub('#skF_4','#skE_5','#skF_6')
| ~ model_ub('#skF_4','#skE_5','#skF_6') ),
inference(superposition,[status(thm),theory(equality)],[c_6045,c_70]) ).
tff(c_6263,plain,
~ model_ub('#skF_4','#skE_5','#skF_6'),
inference(splitLeft,[status(thm)],[c_6061]) ).
tff(c_6271,plain,
! [Z_9a: $int] :
( $less('#skF_6',$sum(c,Z_9a))
| $less(Z_9a,'#skF_4')
| $less(Z_9a,'#skE_5') ),
inference(resolution,[status(thm)],[c_3980,c_6263]) ).
tff(c_6273,plain,
( $lesseq($sum(1,'#skF_6'),$sum(c,'#skF_4'))
| $lesseq($sum(1,'#skF_6'),$sum(c,'#skE_5')) ),
inference(quantifierElimination,[status(thm),theory('LIA')],[c_6271]) ).
tff(c_6275,plain,
( ~ $less($sum('#skF_4',c),$sum(1,'#skF_6'))
| ~ $less($sum('#skE_5',c),$sum(1,'#skF_6')) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_6273]) ).
tff(c_5596,plain,
~ $less('#skF_5','#skF_4'),
inference(splitRight,[status(thm)],[c_5587]) ).
tff(c_5633,plain,
~ $less('#skE_5','#skF_4'),
inference(demodulation,[status(thm),theory(equality)],[c_5595,c_5596]) ).
tff(c_5545,plain,
max('#skF_4','#skF_5') = '#skE_5',
inference(define,[status(thm),theory(equality)],[c_5528]) ).
tff(c_5544,plain,
~ $less('#skF_6',$sum(c,max('#skF_4','#skF_5'))),
inference(resolution,[status(thm)],[c_5509,c_3987]) ).
tff(c_5552,plain,
~ $less('#skF_6',$sum(c,'#skE_5')),
inference(demodulation,[status(thm),theory(equality)],[c_5545,c_5544]) ).
tff(c_6276,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_6275,c_5633,c_5552]) ).
tff(c_6280,plain,
( minsol_model_ub('#skF_4','#skE_5','#skF_6')
| model_ub('#skF_4','#skE_5','#skE_6') ),
inference(splitRight,[status(thm)],[c_6061]) ).
tff(c_6289,plain,
model_ub('#skF_4','#skE_5','#skE_6'),
inference(splitLeft,[status(thm)],[c_6280]) ).
tff(c_6290,plain,
model_ub('#skF_4','#skE_5','#skE_6'),
inference(splitLeft,[status(thm)],[c_6280]) ).
tff(c_6302,plain,
~ $less('#skE_6',$sum(c,'#skF_1'('#skF_4','#skE_5','#skE_6'))),
inference(resolution,[status(thm)],[c_6290,c_82]) ).
tff(c_6330,plain,
'#skF_1'('#skF_4','#skE_5','#skE_6') = '#skE_7',
inference(define,[status(thm),theory(equality)],[c_6302]) ).
tff(c_6340,plain,
( ub('#skF_4','#skE_5','#skE_7')
| ~ model_ub('#skF_4','#skE_5','#skE_6') ),
inference(superposition,[status(thm),theory(equality)],[c_6330,c_78]) ).
tff(c_6361,plain,
ub('#skF_4','#skE_5','#skE_7'),
inference(demodulation,[status(thm),theory(equality)],[c_6289,c_6340]) ).
tff(c_6375,plain,
~ $less('#skE_7','#skE_5'),
inference(resolution,[status(thm)],[c_6361,c_95]) ).
tff(c_6320,plain,
'#skF_1'('#skF_4','#skE_5','#skE_6') = '#skE_7',
inference(define,[status(thm),theory(equality)],[c_6302]) ).
tff(c_6319,plain,
~ $less('#skE_6',$sum(c,'#skF_1'('#skF_4','#skE_5','#skE_6'))),
inference(resolution,[status(thm)],[c_6290,c_82]) ).
tff(c_6327,plain,
~ $less('#skE_6',$sum(c,'#skE_7')),
inference(demodulation,[status(thm),theory(equality)],[c_6320,c_6319]) ).
tff(c_5867,plain,
'#skF_3'('#skF_4','#skE_5','#skF_6') = '#skE_6',
inference(define,[status(thm),theory(equality)],[c_5762]) ).
tff(c_5866,plain,
! [Z_2637a: $int] :
( $less('#skF_3'('#skF_4','#skE_5','#skF_6'),'#skF_6')
| $less('#skF_6',$sum(c,Z_2637a))
| $less(Z_2637a,'#skF_4')
| $less(Z_2637a,'#skE_5') ),
inference(resolution,[status(thm)],[c_5748,c_5631]) ).
tff(c_5874,plain,
! [Z_2637a: $int] :
( $less('#skE_6','#skF_6')
| $less('#skF_6',$sum(c,Z_2637a))
| $less(Z_2637a,'#skF_4')
| $less(Z_2637a,'#skE_5') ),
inference(demodulation,[status(thm),theory(equality)],[c_5867,c_5866]) ).
tff(c_6172,plain,
$less('#skE_6','#skF_6'),
inference(splitLeft,[status(thm)],[c_5874]) ).
tff(c_5551,plain,
max('#skF_4','#skF_5') = '#skE_5',
inference(define,[status(thm),theory(equality)],[c_5528]) ).
tff(c_5642,plain,
max('#skF_4','#skE_5') = '#skE_5',
inference(demodulation,[status(thm),theory(equality)],[c_5595,c_5551]) ).
tff(c_5506,plain,
minsol_model_max('#skF_4','#skF_5','#skF_6'),
inference(splitRight,[status(thm)],[c_57]) ).
tff(c_5682,plain,
minsol_model_max('#skF_4','#skE_5','#skF_6'),
inference(demodulation,[status(thm),theory(equality)],[c_5595,c_5506]) ).
tff(c_3988,plain,
! [X_1834a: $int,Y_1835a: $int,N_1836a: $int] :
( model_max(X_1834a,Y_1835a,N_1836a)
| $less(N_1836a,$sum(c,max(X_1834a,Y_1835a))) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_19]) ).
tff(c_3999,plain,
! [X_1834a: $int,Y_1835a: $int,N_21a: $int,N_1836a: $int] :
( ~ minsol_model_max(X_1834a,Y_1835a,N_21a)
| ~ $less(N_1836a,N_21a)
| $less(N_1836a,$sum(c,max(X_1834a,Y_1835a))) ),
inference(resolution,[status(thm)],[c_3988,c_77]) ).
tff(c_5685,plain,
! [N_1836a: $int] :
( ~ $less(N_1836a,'#skF_6')
| $less(N_1836a,$sum(c,max('#skF_4','#skE_5'))) ),
inference(resolution,[status(thm)],[c_5682,c_3999]) ).
tff(c_5696,plain,
! [N_1836a: $int] :
( ~ $less(N_1836a,'#skF_6')
| $less(N_1836a,$sum(c,'#skE_5')) ),
inference(demodulation,[status(thm),theory(equality)],[c_5642,c_5685]) ).
tff(c_5727,plain,
$lesseq('#skF_6',$sum('#skE_5',c)),
inference(quantifierElimination,[status(thm),theory('LIA')],[c_5696]) ).
tff(c_5729,plain,
~ $less($sum(c,'#skE_5'),'#skF_6'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_5727]) ).
tff(c_6378,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_6375,c_6327,c_6172,c_5729]) ).
tff(c_6384,plain,
minsol_model_ub('#skF_4','#skE_5','#skF_6'),
inference(splitRight,[status(thm)],[c_6280]) ).
tff(c_6387,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_6384,c_5631]) ).
tff(c_6390,plain,
! [Z_2637a: $int] :
( $less('#skF_6',$sum(c,Z_2637a))
| $less(Z_2637a,'#skF_4')
| $less(Z_2637a,'#skE_5') ),
inference(splitRight,[status(thm)],[c_5874]) ).
tff(c_6393,plain,
( $lesseq($sum(1,'#skF_6'),$sum(c,'#skF_4'))
| $lesseq($sum(1,'#skF_6'),$sum(c,'#skE_5')) ),
inference(quantifierElimination,[status(thm),theory('LIA')],[c_6390]) ).
tff(c_6395,plain,
( ~ $less($sum('#skF_4',c),$sum(1,'#skF_6'))
| ~ $less($sum('#skE_5',c),$sum(1,'#skF_6')) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_6393]) ).
tff(c_6396,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_6395,c_5633,c_5552]) ).
tff(c_6399,plain,
'#skF_4' = '#skE_5',
inference(splitRight,[status(thm)],[c_5578]) ).
tff(c_6435,plain,
~ minsol_model_ub('#skE_5','#skF_5','#skF_6'),
inference(demodulation,[status(thm),theory(equality)],[c_6399,c_3945]) ).
tff(c_6569,plain,
! [Z_2974a: $int] :
( $less('#skF_3'('#skE_5','#skF_5','#skF_6'),'#skF_6')
| $less('#skF_6',$sum(c,Z_2974a))
| $less(Z_2974a,'#skE_5')
| $less(Z_2974a,'#skF_5') ),
inference(resolution,[status(thm)],[c_6555,c_6435]) ).
tff(c_6781,plain,
'#skF_3'('#skE_5','#skF_5','#skF_6') = '#skE_8',
inference(define,[status(thm),theory(equality)],[c_6569]) ).
tff(c_6797,plain,
( model_ub('#skE_5','#skF_5','#skE_8')
| minsol_model_ub('#skE_5','#skF_5','#skF_6')
| ~ model_ub('#skE_5','#skF_5','#skF_6') ),
inference(superposition,[status(thm),theory(equality)],[c_6781,c_70]) ).
tff(c_6983,plain,
~ model_ub('#skE_5','#skF_5','#skF_6'),
inference(splitLeft,[status(thm)],[c_6797]) ).
tff(c_6991,plain,
! [Z_9a: $int] :
( $less('#skF_6',$sum(c,Z_9a))
| $less(Z_9a,'#skE_5')
| $less(Z_9a,'#skF_5') ),
inference(resolution,[status(thm)],[c_3980,c_6983]) ).
tff(c_6993,plain,
( $lesseq($sum(1,'#skF_6'),$sum(c,'#skE_5'))
| $lesseq($sum(1,'#skF_6'),$sum(c,'#skF_5')) ),
inference(quantifierElimination,[status(thm),theory('LIA')],[c_6991]) ).
tff(c_6995,plain,
( ~ $less($sum('#skE_5',c),$sum(1,'#skF_6'))
| ~ $less($sum('#skF_5',c),$sum(1,'#skF_6')) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_6993]) ).
tff(c_6400,plain,
~ $less('#skF_4','#skF_5'),
inference(splitRight,[status(thm)],[c_5578]) ).
tff(c_6437,plain,
~ $less('#skE_5','#skF_5'),
inference(demodulation,[status(thm),theory(equality)],[c_6399,c_6400]) ).
tff(c_6996,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_6995,c_6437,c_5552]) ).
tff(c_7000,plain,
( minsol_model_ub('#skE_5','#skF_5','#skF_6')
| model_ub('#skE_5','#skF_5','#skE_8') ),
inference(splitRight,[status(thm)],[c_6797]) ).
tff(c_7009,plain,
model_ub('#skE_5','#skF_5','#skE_8'),
inference(splitLeft,[status(thm)],[c_7000]) ).
tff(c_7010,plain,
model_ub('#skE_5','#skF_5','#skE_8'),
inference(splitLeft,[status(thm)],[c_7000]) ).
tff(c_7022,plain,
~ $less('#skE_8',$sum(c,'#skF_1'('#skE_5','#skF_5','#skE_8'))),
inference(resolution,[status(thm)],[c_7010,c_82]) ).
tff(c_7050,plain,
'#skF_1'('#skE_5','#skF_5','#skE_8') = '#skE_9',
inference(define,[status(thm),theory(equality)],[c_7022]) ).
tff(c_7060,plain,
( ub('#skE_5','#skF_5','#skE_9')
| ~ model_ub('#skE_5','#skF_5','#skE_8') ),
inference(superposition,[status(thm),theory(equality)],[c_7050,c_78]) ).
tff(c_7081,plain,
ub('#skE_5','#skF_5','#skE_9'),
inference(demodulation,[status(thm),theory(equality)],[c_7009,c_7060]) ).
tff(c_7097,plain,
~ $less('#skE_9','#skE_5'),
inference(resolution,[status(thm)],[c_7081,c_94]) ).
tff(c_7040,plain,
'#skF_1'('#skE_5','#skF_5','#skE_8') = '#skE_9',
inference(define,[status(thm),theory(equality)],[c_7022]) ).
tff(c_7039,plain,
~ $less('#skE_8',$sum(c,'#skF_1'('#skE_5','#skF_5','#skE_8'))),
inference(resolution,[status(thm)],[c_7010,c_82]) ).
tff(c_7047,plain,
~ $less('#skE_8',$sum(c,'#skE_9')),
inference(demodulation,[status(thm),theory(equality)],[c_7040,c_7039]) ).
tff(c_6771,plain,
'#skF_3'('#skE_5','#skF_5','#skF_6') = '#skE_8',
inference(define,[status(thm),theory(equality)],[c_6569]) ).
tff(c_6770,plain,
! [Z_2974a: $int] :
( $less('#skF_3'('#skE_5','#skF_5','#skF_6'),'#skF_6')
| $less('#skF_6',$sum(c,Z_2974a))
| $less(Z_2974a,'#skE_5')
| $less(Z_2974a,'#skF_5') ),
inference(resolution,[status(thm)],[c_6555,c_6435]) ).
tff(c_6778,plain,
! [Z_2974a: $int] :
( $less('#skE_8','#skF_6')
| $less('#skF_6',$sum(c,Z_2974a))
| $less(Z_2974a,'#skE_5')
| $less(Z_2974a,'#skF_5') ),
inference(demodulation,[status(thm),theory(equality)],[c_6771,c_6770]) ).
tff(c_6824,plain,
$less('#skE_8','#skF_6'),
inference(splitLeft,[status(thm)],[c_6778]) ).
tff(c_6447,plain,
max('#skE_5','#skF_5') = '#skE_5',
inference(demodulation,[status(thm),theory(equality)],[c_6399,c_5551]) ).
tff(c_6487,plain,
minsol_model_max('#skE_5','#skF_5','#skF_6'),
inference(demodulation,[status(thm),theory(equality)],[c_6399,c_5506]) ).
tff(c_6490,plain,
! [N_1836a: $int] :
( ~ $less(N_1836a,'#skF_6')
| $less(N_1836a,$sum(c,max('#skE_5','#skF_5'))) ),
inference(resolution,[status(thm)],[c_6487,c_3999]) ).
tff(c_6501,plain,
! [N_1836a: $int] :
( ~ $less(N_1836a,'#skF_6')
| $less(N_1836a,$sum(c,'#skE_5')) ),
inference(demodulation,[status(thm),theory(equality)],[c_6447,c_6490]) ).
tff(c_6509,plain,
$lesseq('#skF_6',$sum('#skE_5',c)),
inference(quantifierElimination,[status(thm),theory('LIA')],[c_6501]) ).
tff(c_6511,plain,
~ $less($sum(c,'#skE_5'),'#skF_6'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_6509]) ).
tff(c_7098,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_7097,c_7047,c_6824,c_6511]) ).
tff(c_7104,plain,
minsol_model_ub('#skE_5','#skF_5','#skF_6'),
inference(splitRight,[status(thm)],[c_7000]) ).
tff(c_7107,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_7104,c_6435]) ).
tff(c_7110,plain,
! [Z_2974a: $int] :
( $less('#skF_6',$sum(c,Z_2974a))
| $less(Z_2974a,'#skE_5')
| $less(Z_2974a,'#skF_5') ),
inference(splitRight,[status(thm)],[c_6778]) ).
tff(c_7114,plain,
( $lesseq($sum(1,'#skF_6'),$sum(c,'#skE_5'))
| $lesseq($sum(1,'#skF_6'),$sum(c,'#skF_5')) ),
inference(quantifierElimination,[status(thm),theory('LIA')],[c_7110]) ).
tff(c_7116,plain,
( ~ $less($sum('#skE_5',c),$sum(1,'#skF_6'))
| ~ $less($sum('#skF_5',c),$sum(1,'#skF_6')) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_7114]) ).
tff(c_7117,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_7116,c_6437,c_5552]) ).
tff(c_7124,plain,
minsol_model_max('#skF_4','#skF_5','#skF_6'),
inference(splitRight,[status(thm)],[c_65]) ).
tff(c_7132,plain,
~ $less('#skF_6',$sum(c,max('#skF_4','#skF_5'))),
inference(resolution,[status(thm)],[c_7124,c_3987]) ).
tff(c_7202,plain,
max('#skF_4','#skF_5') = '#skE_5',
inference(define,[status(thm),theory(equality)],[c_7132]) ).
tff(c_7227,plain,
( ( '#skF_5' = '#skE_5' )
| $less('#skF_5','#skF_4') ),
inference(superposition,[status(thm),theory(equality)],[c_7202,c_96]) ).
tff(c_7240,plain,
$less('#skF_5','#skF_4'),
inference(splitLeft,[status(thm)],[c_7227]) ).
tff(c_7225,plain,
( ( '#skF_4' = '#skE_5' )
| $less('#skF_4','#skF_5') ),
inference(superposition,[status(thm),theory(equality)],[c_7202,c_97]) ).
tff(c_7236,plain,
$less('#skF_4','#skF_5'),
inference(splitLeft,[status(thm)],[c_7225]) ).
tff(c_7241,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_7240,c_7236]) ).
tff(c_7244,plain,
'#skF_5' = '#skE_5',
inference(splitRight,[status(thm)],[c_7227]) ).
tff(c_7324,plain,
~ minsol_model_ub('#skF_4','#skE_5','#skF_6'),
inference(demodulation,[status(thm),theory(equality)],[c_7244,c_3945]) ).
tff(c_7449,plain,
! [Z_3361a: $int] :
( $less('#skF_3'('#skF_4','#skE_5','#skF_6'),'#skF_6')
| $less('#skF_6',$sum(c,Z_3361a))
| $less(Z_3361a,'#skF_4')
| $less(Z_3361a,'#skE_5') ),
inference(resolution,[status(thm)],[c_7433,c_7324]) ).
tff(c_7465,plain,
'#skF_3'('#skF_4','#skE_5','#skF_6') = '#skE_6',
inference(define,[status(thm),theory(equality)],[c_7449]) ).
tff(c_7481,plain,
( model_ub('#skF_4','#skE_5','#skE_6')
| minsol_model_ub('#skF_4','#skE_5','#skF_6')
| ~ model_ub('#skF_4','#skE_5','#skF_6') ),
inference(superposition,[status(thm),theory(equality)],[c_7465,c_70]) ).
tff(c_7516,plain,
~ model_ub('#skF_4','#skE_5','#skF_6'),
inference(splitLeft,[status(thm)],[c_7481]) ).
tff(c_7524,plain,
! [Z_9a: $int] :
( $less('#skF_6',$sum(c,Z_9a))
| $less(Z_9a,'#skF_4')
| $less(Z_9a,'#skE_5') ),
inference(resolution,[status(thm)],[c_3980,c_7516]) ).
tff(c_7526,plain,
( $lesseq($sum(1,'#skF_6'),$sum(c,'#skF_4'))
| $lesseq($sum(1,'#skF_6'),$sum(c,'#skE_5')) ),
inference(quantifierElimination,[status(thm),theory('LIA')],[c_7524]) ).
tff(c_7528,plain,
( ~ $less($sum('#skF_4',c),$sum(1,'#skF_6'))
| ~ $less($sum('#skE_5',c),$sum(1,'#skF_6')) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_7526]) ).
tff(c_7270,plain,
$less('#skF_4','#skE_5'),
inference(demodulation,[status(thm),theory(equality)],[c_7244,c_7236]) ).
tff(c_7234,plain,
( ( '#skF_5' = '#skE_5' )
| $less('#skF_5','#skF_4') ),
inference(superposition,[status(thm),theory(equality)],[c_96,c_7202]) ).
tff(c_7247,plain,
$less('#skF_5','#skF_4'),
inference(splitLeft,[status(thm)],[c_7234]) ).
tff(c_7284,plain,
$less('#skE_5','#skF_4'),
inference(demodulation,[status(thm),theory(equality)],[c_7244,c_7247]) ).
tff(c_7285,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_7270,c_7284]) ).
tff(c_7289,plain,
~ $less('#skF_5','#skF_4'),
inference(splitRight,[status(thm)],[c_7234]) ).
tff(c_7327,plain,
~ $less('#skE_5','#skF_4'),
inference(demodulation,[status(thm),theory(equality)],[c_7244,c_7289]) ).
tff(c_7192,plain,
max('#skF_4','#skF_5') = '#skE_5',
inference(define,[status(thm),theory(equality)],[c_7132]) ).
tff(c_7191,plain,
~ $less('#skF_6',$sum(c,max('#skF_4','#skF_5'))),
inference(resolution,[status(thm)],[c_7124,c_3987]) ).
tff(c_7199,plain,
~ $less('#skF_6',$sum(c,'#skE_5')),
inference(demodulation,[status(thm),theory(equality)],[c_7192,c_7191]) ).
tff(c_7529,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_7528,c_7327,c_7199]) ).
tff(c_7533,plain,
( minsol_model_ub('#skF_4','#skE_5','#skF_6')
| model_ub('#skF_4','#skE_5','#skE_6') ),
inference(splitRight,[status(thm)],[c_7481]) ).
tff(c_7541,plain,
model_ub('#skF_4','#skE_5','#skE_6'),
inference(splitLeft,[status(thm)],[c_7533]) ).
tff(c_7542,plain,
model_ub('#skF_4','#skE_5','#skE_6'),
inference(splitLeft,[status(thm)],[c_7533]) ).
tff(c_7554,plain,
~ $less('#skE_6',$sum(c,'#skF_1'('#skF_4','#skE_5','#skE_6'))),
inference(resolution,[status(thm)],[c_7542,c_82]) ).
tff(c_7582,plain,
'#skF_1'('#skF_4','#skE_5','#skE_6') = '#skE_7',
inference(define,[status(thm),theory(equality)],[c_7554]) ).
tff(c_7592,plain,
( ub('#skF_4','#skE_5','#skE_7')
| ~ model_ub('#skF_4','#skE_5','#skE_6') ),
inference(superposition,[status(thm),theory(equality)],[c_7582,c_78]) ).
tff(c_7613,plain,
ub('#skF_4','#skE_5','#skE_7'),
inference(demodulation,[status(thm),theory(equality)],[c_7541,c_7592]) ).
tff(c_7627,plain,
~ $less('#skE_7','#skE_5'),
inference(resolution,[status(thm)],[c_7613,c_95]) ).
tff(c_7572,plain,
'#skF_1'('#skF_4','#skE_5','#skE_6') = '#skE_7',
inference(define,[status(thm),theory(equality)],[c_7554]) ).
tff(c_7571,plain,
~ $less('#skE_6',$sum(c,'#skF_1'('#skF_4','#skE_5','#skE_6'))),
inference(resolution,[status(thm)],[c_7542,c_82]) ).
tff(c_7579,plain,
~ $less('#skE_6',$sum(c,'#skE_7')),
inference(demodulation,[status(thm),theory(equality)],[c_7572,c_7571]) ).
tff(c_7455,plain,
'#skF_3'('#skF_4','#skE_5','#skF_6') = '#skE_6',
inference(define,[status(thm),theory(equality)],[c_7449]) ).
tff(c_7454,plain,
! [Z_3361a: $int] :
( $less('#skF_3'('#skF_4','#skE_5','#skF_6'),'#skF_6')
| $less('#skF_6',$sum(c,Z_3361a))
| $less(Z_3361a,'#skF_4')
| $less(Z_3361a,'#skE_5') ),
inference(resolution,[status(thm)],[c_7433,c_7324]) ).
tff(c_7462,plain,
! [Z_3361a: $int] :
( $less('#skE_6','#skF_6')
| $less('#skF_6',$sum(c,Z_3361a))
| $less(Z_3361a,'#skF_4')
| $less(Z_3361a,'#skE_5') ),
inference(demodulation,[status(thm),theory(equality)],[c_7455,c_7454]) ).
tff(c_7486,plain,
$less('#skE_6','#skF_6'),
inference(splitLeft,[status(thm)],[c_7462]) ).
tff(c_7198,plain,
max('#skF_4','#skF_5') = '#skE_5',
inference(define,[status(thm),theory(equality)],[c_7132]) ).
tff(c_7330,plain,
max('#skF_4','#skE_5') = '#skE_5',
inference(demodulation,[status(thm),theory(equality)],[c_7244,c_7198]) ).
tff(c_7121,plain,
minsol_model_max('#skF_4','#skF_5','#skF_6'),
inference(splitRight,[status(thm)],[c_65]) ).
tff(c_7321,plain,
minsol_model_max('#skF_4','#skE_5','#skF_6'),
inference(demodulation,[status(thm),theory(equality)],[c_7244,c_7121]) ).
tff(c_7394,plain,
! [X_3334a: $int,Y_3337a: $int,N_3335a: $int,N_3336a: $int] :
( ~ minsol_model_max(X_3334a,Y_3337a,N_3335a)
| ~ $less(N_3336a,N_3335a)
| $less(N_3336a,$sum(c,max(X_3334a,Y_3337a))) ),
inference(resolution,[status(thm)],[c_3988,c_77]) ).
tff(c_7397,plain,
! [N_3336a: $int] :
( ~ $less(N_3336a,'#skF_6')
| $less(N_3336a,$sum(c,max('#skF_4','#skE_5'))) ),
inference(resolution,[status(thm)],[c_7321,c_7394]) ).
tff(c_7400,plain,
! [N_3336a: $int] :
( ~ $less(N_3336a,'#skF_6')
| $less(N_3336a,$sum(c,'#skE_5')) ),
inference(demodulation,[status(thm),theory(equality)],[c_7330,c_7397]) ).
tff(c_7401,plain,
$lesseq('#skF_6',$sum('#skE_5',c)),
inference(quantifierElimination,[status(thm),theory('LIA')],[c_7400]) ).
tff(c_7403,plain,
~ $less($sum(c,'#skE_5'),'#skF_6'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_7401]) ).
tff(c_7630,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_7627,c_7579,c_7486,c_7403]) ).
tff(c_7636,plain,
minsol_model_ub('#skF_4','#skE_5','#skF_6'),
inference(splitRight,[status(thm)],[c_7533]) ).
tff(c_7639,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_7636,c_7324]) ).
tff(c_7642,plain,
! [Z_3361a: $int] :
( $less('#skF_6',$sum(c,Z_3361a))
| $less(Z_3361a,'#skF_4')
| $less(Z_3361a,'#skE_5') ),
inference(splitRight,[status(thm)],[c_7462]) ).
tff(c_7644,plain,
( $lesseq($sum(1,'#skF_6'),$sum(c,'#skF_4'))
| $lesseq($sum(1,'#skF_6'),$sum(c,'#skE_5')) ),
inference(quantifierElimination,[status(thm),theory('LIA')],[c_7642]) ).
tff(c_7646,plain,
( ~ $less($sum('#skF_4',c),$sum(1,'#skF_6'))
| ~ $less($sum('#skE_5',c),$sum(1,'#skF_6')) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_7644]) ).
tff(c_7647,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_7646,c_7327,c_7199]) ).
tff(c_7650,plain,
'#skF_4' = '#skE_5',
inference(splitRight,[status(thm)],[c_7225]) ).
tff(c_7685,plain,
~ minsol_model_ub('#skE_5','#skF_5','#skF_6'),
inference(demodulation,[status(thm),theory(equality)],[c_7650,c_3945]) ).
tff(c_7809,plain,
! [Z_3525a: $int] :
( $less('#skF_3'('#skE_5','#skF_5','#skF_6'),'#skF_6')
| $less('#skF_6',$sum(c,Z_3525a))
| $less(Z_3525a,'#skE_5')
| $less(Z_3525a,'#skF_5') ),
inference(resolution,[status(thm)],[c_7793,c_7685]) ).
tff(c_7855,plain,
'#skF_3'('#skE_5','#skF_5','#skF_6') = '#skE_8',
inference(define,[status(thm),theory(equality)],[c_7809]) ).
tff(c_7871,plain,
( model_ub('#skE_5','#skF_5','#skE_8')
| minsol_model_ub('#skE_5','#skF_5','#skF_6')
| ~ model_ub('#skE_5','#skF_5','#skF_6') ),
inference(superposition,[status(thm),theory(equality)],[c_7855,c_70]) ).
tff(c_7951,plain,
~ model_ub('#skE_5','#skF_5','#skF_6'),
inference(splitLeft,[status(thm)],[c_7871]) ).
tff(c_7959,plain,
! [Z_9a: $int] :
( $less('#skF_6',$sum(c,Z_9a))
| $less(Z_9a,'#skE_5')
| $less(Z_9a,'#skF_5') ),
inference(resolution,[status(thm)],[c_3980,c_7951]) ).
tff(c_7961,plain,
( $lesseq($sum(1,'#skF_6'),$sum(c,'#skE_5'))
| $lesseq($sum(1,'#skF_6'),$sum(c,'#skF_5')) ),
inference(quantifierElimination,[status(thm),theory('LIA')],[c_7959]) ).
tff(c_7963,plain,
( ~ $less($sum('#skE_5',c),$sum(1,'#skF_6'))
| ~ $less($sum('#skF_5',c),$sum(1,'#skF_6')) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_7961]) ).
tff(c_7651,plain,
~ $less('#skF_4','#skF_5'),
inference(splitRight,[status(thm)],[c_7225]) ).
tff(c_7687,plain,
~ $less('#skE_5','#skF_5'),
inference(demodulation,[status(thm),theory(equality)],[c_7650,c_7651]) ).
tff(c_7964,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_7963,c_7687,c_7199]) ).
tff(c_7968,plain,
( minsol_model_ub('#skE_5','#skF_5','#skF_6')
| model_ub('#skE_5','#skF_5','#skE_8') ),
inference(splitRight,[status(thm)],[c_7871]) ).
tff(c_7977,plain,
model_ub('#skE_5','#skF_5','#skE_8'),
inference(splitLeft,[status(thm)],[c_7968]) ).
tff(c_7978,plain,
model_ub('#skE_5','#skF_5','#skE_8'),
inference(splitLeft,[status(thm)],[c_7968]) ).
tff(c_7990,plain,
~ $less('#skE_8',$sum(c,'#skF_1'('#skE_5','#skF_5','#skE_8'))),
inference(resolution,[status(thm)],[c_7978,c_82]) ).
tff(c_8018,plain,
'#skF_1'('#skE_5','#skF_5','#skE_8') = '#skE_9',
inference(define,[status(thm),theory(equality)],[c_7990]) ).
tff(c_8028,plain,
( ub('#skE_5','#skF_5','#skE_9')
| ~ model_ub('#skE_5','#skF_5','#skE_8') ),
inference(superposition,[status(thm),theory(equality)],[c_8018,c_78]) ).
tff(c_8049,plain,
ub('#skE_5','#skF_5','#skE_9'),
inference(demodulation,[status(thm),theory(equality)],[c_7977,c_8028]) ).
tff(c_8065,plain,
~ $less('#skE_9','#skE_5'),
inference(resolution,[status(thm)],[c_8049,c_94]) ).
tff(c_8008,plain,
'#skF_1'('#skE_5','#skF_5','#skE_8') = '#skE_9',
inference(define,[status(thm),theory(equality)],[c_7990]) ).
tff(c_8007,plain,
~ $less('#skE_8',$sum(c,'#skF_1'('#skE_5','#skF_5','#skE_8'))),
inference(resolution,[status(thm)],[c_7978,c_82]) ).
tff(c_8015,plain,
~ $less('#skE_8',$sum(c,'#skE_9')),
inference(demodulation,[status(thm),theory(equality)],[c_8008,c_8007]) ).
tff(c_7845,plain,
'#skF_3'('#skE_5','#skF_5','#skF_6') = '#skE_8',
inference(define,[status(thm),theory(equality)],[c_7809]) ).
tff(c_7844,plain,
! [Z_3525a: $int] :
( $less('#skF_3'('#skE_5','#skF_5','#skF_6'),'#skF_6')
| $less('#skF_6',$sum(c,Z_3525a))
| $less(Z_3525a,'#skE_5')
| $less(Z_3525a,'#skF_5') ),
inference(resolution,[status(thm)],[c_7793,c_7685]) ).
tff(c_7852,plain,
! [Z_3525a: $int] :
( $less('#skE_8','#skF_6')
| $less('#skF_6',$sum(c,Z_3525a))
| $less(Z_3525a,'#skE_5')
| $less(Z_3525a,'#skF_5') ),
inference(demodulation,[status(thm),theory(equality)],[c_7845,c_7844]) ).
tff(c_7876,plain,
$less('#skE_8','#skF_6'),
inference(splitLeft,[status(thm)],[c_7852]) ).
tff(c_7695,plain,
max('#skE_5','#skF_5') = '#skE_5',
inference(demodulation,[status(thm),theory(equality)],[c_7650,c_7198]) ).
tff(c_7682,plain,
minsol_model_max('#skE_5','#skF_5','#skF_6'),
inference(demodulation,[status(thm),theory(equality)],[c_7650,c_7121]) ).
tff(c_7759,plain,
! [X_3503a: $int,Y_3506a: $int,N_3504a: $int,N_3505a: $int] :
( ~ minsol_model_max(X_3503a,Y_3506a,N_3504a)
| ~ $less(N_3505a,N_3504a)
| $less(N_3505a,$sum(c,max(X_3503a,Y_3506a))) ),
inference(resolution,[status(thm)],[c_3988,c_77]) ).
tff(c_7762,plain,
! [N_3505a: $int] :
( ~ $less(N_3505a,'#skF_6')
| $less(N_3505a,$sum(c,max('#skE_5','#skF_5'))) ),
inference(resolution,[status(thm)],[c_7682,c_7759]) ).
tff(c_7765,plain,
! [N_3505a: $int] :
( ~ $less(N_3505a,'#skF_6')
| $less(N_3505a,$sum(c,'#skE_5')) ),
inference(demodulation,[status(thm),theory(equality)],[c_7695,c_7762]) ).
tff(c_7766,plain,
$lesseq('#skF_6',$sum('#skE_5',c)),
inference(quantifierElimination,[status(thm),theory('LIA')],[c_7765]) ).
tff(c_7768,plain,
~ $less($sum(c,'#skE_5'),'#skF_6'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_7766]) ).
tff(c_8066,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_8065,c_8015,c_7876,c_7768]) ).
tff(c_8072,plain,
minsol_model_ub('#skE_5','#skF_5','#skF_6'),
inference(splitRight,[status(thm)],[c_7968]) ).
tff(c_8075,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_8072,c_7685]) ).
tff(c_8078,plain,
! [Z_3525a: $int] :
( $less('#skF_6',$sum(c,Z_3525a))
| $less(Z_3525a,'#skE_5')
| $less(Z_3525a,'#skF_5') ),
inference(splitRight,[status(thm)],[c_7852]) ).
tff(c_8080,plain,
( $lesseq($sum(1,'#skF_6'),$sum(c,'#skE_5'))
| $lesseq($sum(1,'#skF_6'),$sum(c,'#skF_5')) ),
inference(quantifierElimination,[status(thm),theory('LIA')],[c_8078]) ).
tff(c_8082,plain,
( ~ $less($sum('#skE_5',c),$sum(1,'#skF_6'))
| ~ $less($sum('#skF_5',c),$sum(1,'#skF_6')) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_8080]) ).
tff(c_8083,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_8082,c_7687,c_7199]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM861_1 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.14 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.14/0.36 % Computer : n003.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Thu Aug 3 14:42:23 EDT 2023
% 0.20/0.36 % CPUTime :
% 10.04/3.56 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 10.66/3.70
% 10.66/3.70 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 11.29/3.80
% 11.29/3.80 Inference rules
% 11.29/3.80 ----------------------
% 11.29/3.80 #Ref : 0
% 11.29/3.80 #Sup : 833
% 11.29/3.80 #Fact : 14
% 11.29/3.80 #Define : 35
% 11.29/3.80 #Split : 88
% 11.29/3.80 #Chain : 0
% 11.29/3.80 #Close : 41
% 11.29/3.80
% 11.29/3.80 Ordering : LPO
% 11.29/3.80
% 11.29/3.80 Simplification rules
% 11.29/3.80 ----------------------
% 11.29/3.80 #Subsume : 157
% 11.29/3.80 #Demod : 464
% 11.29/3.80 #Tautology : 338
% 11.29/3.80 #SimpNegUnit : 30
% 11.29/3.80 #BackRed : 113
% 11.29/3.80
% 11.29/3.80 #Partial instantiations: 0
% 11.29/3.80 #Strategies tried : 1
% 11.29/3.80
% 11.29/3.80 Timing (in seconds)
% 11.29/3.80 ----------------------
% 11.29/3.80 Preprocessing : 0.59
% 11.29/3.80 Parsing : 0.31
% 11.29/3.80 CNF conversion : 0.04
% 11.29/3.80 Main loop : 1.87
% 11.29/3.80 Inferencing : 0.43
% 11.29/3.80 Reduction : 0.41
% 11.29/3.80 Demodulation : 0.30
% 11.29/3.80 BG Simplification : 0.12
% 11.29/3.80 Subsumption : 0.30
% 11.29/3.80 Abstraction : 0.07
% 11.29/3.81 MUC search : 0.19
% 11.29/3.81 Cooper : 0.40
% 11.29/3.81 Total : 2.71
% 11.29/3.81 Index Insertion : 0.00
% 11.29/3.81 Index Deletion : 0.00
% 11.29/3.81 Index Matching : 0.00
% 11.29/3.81 BG Taut test : 0.00
%------------------------------------------------------------------------------