TSTP Solution File: NUM858_1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : NUM858_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/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n031.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 10:52:56 EDT 2023
% Result : Theorem 11.68s 3.95s
% Output : CNFRefutation 12.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 34
% Syntax : Number of formulae : 563 ( 324 unt; 26 typ; 0 def)
% Number of atoms : 851 ( 147 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 557 ( 243 ~; 303 |; 3 &)
% ( 6 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number arithmetic : 640 ( 360 atm; 0 fun; 0 num; 280 var)
% Number of types : 2 ( 0 usr; 1 ari)
% Number of type conns : 24 ( 9 >; 15 *; 0 +; 0 <<)
% Number of predicates : 9 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 21 ( 21 usr; 17 con; 0-3 aty)
% Number of variables : 280 (; 280 !; 0 ?; 280 :)
% Comments :
%------------------------------------------------------------------------------
%$ ub > model_ub > model_max > minsol_model_ub > minsol_model_max > max > #nlpp > summation > #skF_1 > #skF_2
%Foreground sorts:
%Background operators:
tff('#skE_7',type,
'#skE_7': $int ).
tff('#skE_11',type,
'#skE_11': $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_10',type,
'#skE_10': $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('#skF_3',type,
'#skF_3': $int ).
tff('#skE_3',type,
'#skE_3': $int ).
tff('#skF_7',type,
'#skF_7': $int ).
tff('#skE_9',type,
'#skE_9': $int ).
%Foreground operators:
tff(minsol_model_ub,type,
minsol_model_ub: ( $int * $int * $int ) > $o ).
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_49,axiom,
! [Xa: $int,Ya: $int] :
( ( max(Xa,Ya) = Ya )
| ~ $lesseq(Xa,Ya) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',max_2) ).
tff(f_92,negated_conjecture,
~ ! [Xa: $int,Ya: $int,Za: $int] :
( minsol_model_ub(Xa,Ya,Za)
<=> minsol_model_max(Xa,Ya,Za) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',max_is_ub_1) ).
tff(f_86,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/sandbox2/benchmark/theBenchmark.p',minsol_model_ub) ).
tff(f_66,axiom,
! [Xa: $int,Ya: $int,Na: $int] :
( model_ub(Xa,Ya,Na)
<=> ub(Xa,Ya,Na) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',model_ub_1) ).
tff(f_56,axiom,
! [Xa: $int,Ya: $int,Za: $int] :
( ub(Xa,Ya,Za)
<=> ( $lesseq(Xa,Za)
& $lesseq(Ya,Za) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ub) ).
tff(f_44,axiom,
! [Xa: $int,Ya: $int] :
( ( max(Xa,Ya) = Xa )
| ~ $lesseq(Ya,Xa) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',max_1) ).
tff(f_61,axiom,
! [Xa: $int,Ya: $int,Na: $int] :
( model_max(Xa,Ya,Na)
<=> ( Na = max(Xa,Ya) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',model_max_1) ).
tff(f_76,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/sandbox2/benchmark/theBenchmark.p',minsol_model_max) ).
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_80,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_52,plain,
( minsol_model_max('#skF_3','#skF_4','#skF_5')
| minsol_model_ub('#skF_6','#skF_7','#skF_8') ),
inference(cnfTransformation,[status(thm)],[f_92]) ).
tff(c_349,plain,
minsol_model_ub('#skF_6','#skF_7','#skF_8'),
inference(splitLeft,[status(thm)],[c_52]) ).
tff(c_67,plain,
! [X_22a: $int,Y_23a: $int,N_24a: $int] :
( model_ub(X_22a,Y_23a,N_24a)
| ~ minsol_model_ub(X_22a,Y_23a,N_24a) ),
inference(cnfTransformation,[status(thm)],[f_86]) ).
tff(c_163,plain,
! [X_111a: $int,Y_112a: $int,N_113a: $int] :
( ub(X_111a,Y_112a,N_113a)
| ~ model_ub(X_111a,Y_112a,N_113a) ),
inference(cnfTransformation,[status(thm)],[f_66]) ).
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_79,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_195,plain,
! [N_117a: $int,Y_118a: $int,X_119a: $int] :
( ~ $less(N_117a,Y_118a)
| ~ model_ub(X_119a,Y_118a,N_117a) ),
inference(resolution,[status(thm)],[c_163,c_79]) ).
tff(c_200,plain,
! [N_24a: $int,Y_23a: $int,X_22a: $int] :
( ~ $less(N_24a,Y_23a)
| ~ minsol_model_ub(X_22a,Y_23a,N_24a) ),
inference(resolution,[status(thm)],[c_67,c_195]) ).
tff(c_374,plain,
~ $less('#skF_8','#skF_7'),
inference(resolution,[status(thm)],[c_349,c_200]) ).
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_110,plain,
! [X_86a: $int,Y_87a: $int] :
( ( max(X_86a,Y_87a) = X_86a )
| $less(X_86a,Y_87a) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_5]) ).
tff(c_75,plain,
! [X_10a: $int,Y_11a: $int] : model_max(X_10a,Y_11a,max(X_10a,Y_11a)),
inference(cnfTransformation,[status(thm)],[f_61]) ).
tff(c_129,plain,
! [X_86a: $int,Y_87a: $int] :
( model_max(X_86a,Y_87a,X_86a)
| $less(X_86a,Y_87a) ),
inference(superposition,[status(thm),theory(equality)],[c_110,c_75]) ).
tff(c_28,plain,
! [N_18a: $int,X_16a: $int,Y_17a: $int] :
( ~ $lesseq(N_18a,'#skF_1'(X_16a,Y_17a,N_18a))
| minsol_model_max(X_16a,Y_17a,N_18a)
| ~ model_max(X_16a,Y_17a,N_18a) ),
inference(cnfTransformation,[status(thm)],[f_76]) ).
tff(c_264,plain,
! [X_170a: $int,Y_171a: $int,N_172a: $int] :
( $less('#skF_1'(X_170a,Y_171a,N_172a),N_172a)
| minsol_model_max(X_170a,Y_171a,N_172a)
| ~ model_max(X_170a,Y_171a,N_172a) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_28]) ).
tff(c_280,plain,
! [X_173a: $int,Y_174a: $int] :
( $less('#skF_1'(X_173a,Y_174a,X_173a),X_173a)
| minsol_model_max(X_173a,Y_174a,X_173a)
| $less(X_173a,Y_174a) ),
inference(resolution,[status(thm)],[c_129,c_264]) ).
tff(c_60,plain,
( minsol_model_max('#skF_3','#skF_4','#skF_5')
| ~ minsol_model_max('#skF_6','#skF_7','#skF_8') ),
inference(cnfTransformation,[status(thm)],[f_92]) ).
tff(c_140,plain,
~ minsol_model_max('#skF_6','#skF_7','#skF_8'),
inference(splitLeft,[status(thm)],[c_60]) ).
tff(c_304,plain,
( ( '#skF_8' != '#skF_6' )
| $less('#skF_1'('#skF_8','#skF_7','#skF_8'),'#skF_8')
| $less('#skF_8','#skF_7') ),
inference(resolution,[status(thm)],[c_280,c_140]) ).
tff(c_521,plain,
( ( '#skF_8' != '#skF_6' )
| $less('#skF_1'('#skF_8','#skF_7','#skF_8'),'#skF_8') ),
inference(negUnitSimplification,[status(thm)],[c_374,c_304]) ).
tff(c_523,plain,
'#skF_1'('#skF_8','#skF_7','#skF_8') = '#skE_2',
inference(define,[status(thm),theory(equality)],[c_521]) ).
tff(c_522,plain,
( ( '#skF_8' != '#skF_6' )
| $less('#skF_1'('#skF_8','#skF_7','#skF_8'),'#skF_8') ),
inference(negUnitSimplification,[status(thm)],[c_374,c_304]) ).
tff(c_530,plain,
( ( '#skF_8' != '#skF_6' )
| $less('#skE_2','#skF_8') ),
inference(demodulation,[status(thm),theory(equality)],[c_523,c_522]) ).
tff(c_532,plain,
'#skF_8' != '#skF_6',
inference(splitLeft,[status(thm)],[c_530]) ).
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_78,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_201,plain,
! [N_120a: $int,X_121a: $int,Y_122a: $int] :
( ~ $less(N_120a,X_121a)
| ~ model_ub(X_121a,Y_122a,N_120a) ),
inference(resolution,[status(thm)],[c_163,c_78]) ).
tff(c_206,plain,
! [N_24a: $int,X_22a: $int,Y_23a: $int] :
( ~ $less(N_24a,X_22a)
| ~ minsol_model_ub(X_22a,Y_23a,N_24a) ),
inference(resolution,[status(thm)],[c_67,c_201]) ).
tff(c_372,plain,
~ $less('#skF_8','#skF_6'),
inference(resolution,[status(thm)],[c_349,c_206]) ).
tff(c_95,plain,
! [X_84a: $int,Y_85a: $int] :
( ( max(X_84a,Y_85a) = Y_85a )
| $less(Y_85a,X_84a) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_7]) ).
tff(c_107,plain,
! [X_84a: $int,Y_85a: $int] :
( model_max(X_84a,Y_85a,Y_85a)
| $less(Y_85a,X_84a) ),
inference(superposition,[status(thm),theory(equality)],[c_95,c_75]) ).
tff(c_306,plain,
! [X_179a: $int,Y_180a: $int] :
( $less('#skF_1'(X_179a,Y_180a,Y_180a),Y_180a)
| minsol_model_max(X_179a,Y_180a,Y_180a)
| $less(Y_180a,X_179a) ),
inference(resolution,[status(thm)],[c_107,c_264]) ).
tff(c_330,plain,
( ( '#skF_8' != '#skF_7' )
| $less('#skF_1'('#skF_6','#skF_8','#skF_8'),'#skF_8')
| $less('#skF_8','#skF_6') ),
inference(resolution,[status(thm)],[c_306,c_140]) ).
tff(c_395,plain,
( ( '#skF_8' != '#skF_7' )
| $less('#skF_1'('#skF_6','#skF_8','#skF_8'),'#skF_8') ),
inference(negUnitSimplification,[status(thm)],[c_372,c_330]) ).
tff(c_397,plain,
'#skF_1'('#skF_6','#skF_8','#skF_8') = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_395]) ).
tff(c_396,plain,
( ( '#skF_8' != '#skF_7' )
| $less('#skF_1'('#skF_6','#skF_8','#skF_8'),'#skF_8') ),
inference(negUnitSimplification,[status(thm)],[c_372,c_330]) ).
tff(c_404,plain,
( ( '#skF_8' != '#skF_7' )
| $less('#skE_1','#skF_8') ),
inference(demodulation,[status(thm),theory(equality)],[c_397,c_396]) ).
tff(c_406,plain,
'#skF_8' != '#skF_7',
inference(splitLeft,[status(thm)],[c_404]) ).
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_179,plain,
! [X_114a: $int,Y_115a: $int,Z_116a: $int] :
( ub(X_114a,Y_115a,Z_116a)
| $less(Z_116a,X_114a)
| $less(Z_116a,Y_115a) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_13]) ).
tff(c_73,plain,
! [X_13a: $int,Y_14a: $int,N_15a: $int] :
( model_ub(X_13a,Y_14a,N_15a)
| ~ ub(X_13a,Y_14a,N_15a) ),
inference(cnfTransformation,[status(thm)],[f_66]) ).
tff(c_190,plain,
! [X_114a: $int,Y_115a: $int,Z_116a: $int] :
( model_ub(X_114a,Y_115a,Z_116a)
| $less(Z_116a,X_114a)
| $less(Z_116a,Y_115a) ),
inference(resolution,[status(thm)],[c_179,c_73]) ).
tff(c_32,plain,
! [X_22a: $int,Y_23a: $int,Z_27a: $int,N_24a: $int] :
( ~ model_ub(X_22a,Y_23a,Z_27a)
| ~ minsol_model_ub(X_22a,Y_23a,N_24a)
| $lesseq(N_24a,Z_27a) ),
inference(cnfTransformation,[status(thm)],[f_86]) ).
tff(c_232,plain,
! [X_144a: $int,Y_145a: $int,Z_146a: $int,N_147a: $int] :
( ~ model_ub(X_144a,Y_145a,Z_146a)
| ~ minsol_model_ub(X_144a,Y_145a,N_147a)
| ~ $less(Z_146a,N_147a) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_32]) ).
tff(c_240,plain,
! [X_114a: $int,Y_115a: $int,N_147a: $int,Z_116a: $int] :
( ~ minsol_model_ub(X_114a,Y_115a,N_147a)
| ~ $less(Z_116a,N_147a)
| $less(Z_116a,X_114a)
| $less(Z_116a,Y_115a) ),
inference(resolution,[status(thm)],[c_190,c_232]) ).
tff(c_365,plain,
! [Z_116a: $int] :
( ~ $less(Z_116a,'#skF_8')
| $less(Z_116a,'#skF_6')
| $less(Z_116a,'#skF_7') ),
inference(resolution,[status(thm)],[c_349,c_240]) ).
tff(c_378,plain,
( $lesseq('#skF_8','#skF_6')
| $lesseq('#skF_8','#skF_7') ),
inference(quantifierElimination,[status(thm),theory('LIA')],[c_365]) ).
tff(c_380,plain,
( ~ $less('#skF_6','#skF_8')
| ~ $less('#skF_7','#skF_8') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_378]) ).
tff(c_533,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_532,c_406,c_380,c_374,c_372]) ).
tff(c_537,plain,
'#skF_8' = '#skF_6',
inference(splitRight,[status(thm)],[c_530]) ).
tff(c_574,plain,
~ $less('#skF_6','#skF_7'),
inference(demodulation,[status(thm),theory(equality)],[c_537,c_374]) ).
tff(c_529,plain,
'#skF_1'('#skF_8','#skF_7','#skF_8') = '#skE_2',
inference(define,[status(thm),theory(equality)],[c_521]) ).
tff(c_588,plain,
'#skF_1'('#skF_6','#skF_7','#skF_6') = '#skE_2',
inference(demodulation,[status(thm),theory(equality)],[c_537,c_537,c_529]) ).
tff(c_69,plain,
! [X_16a: $int,Y_17a: $int,N_18a: $int] :
( model_max(X_16a,Y_17a,'#skF_1'(X_16a,Y_17a,N_18a))
| minsol_model_max(X_16a,Y_17a,N_18a)
| ~ model_max(X_16a,Y_17a,N_18a) ),
inference(cnfTransformation,[status(thm)],[f_76]) ).
tff(c_604,plain,
( model_max('#skF_6','#skF_7','#skE_2')
| minsol_model_max('#skF_6','#skF_7','#skF_6')
| ~ model_max('#skF_6','#skF_7','#skF_6') ),
inference(superposition,[status(thm),theory(equality)],[c_588,c_69]) ).
tff(c_1671,plain,
~ model_max('#skF_6','#skF_7','#skF_6'),
inference(splitLeft,[status(thm)],[c_604]) ).
tff(c_1688,plain,
$less('#skF_6','#skF_7'),
inference(resolution,[status(thm)],[c_129,c_1671]) ).
tff(c_1690,plain,
$less('#skF_6','#skF_7'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_1688]) ).
tff(c_1699,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_574,c_1690]) ).
tff(c_1703,plain,
( minsol_model_max('#skF_6','#skF_7','#skF_6')
| model_max('#skF_6','#skF_7','#skE_2') ),
inference(splitRight,[status(thm)],[c_604]) ).
tff(c_1712,plain,
model_max('#skF_6','#skF_7','#skE_2'),
inference(splitLeft,[status(thm)],[c_1703]) ).
tff(c_76,plain,
! [X_10a: $int,Y_11a: $int,N_12a: $int] :
( ( max(X_10a,Y_11a) = N_12a )
| ~ model_max(X_10a,Y_11a,N_12a) ),
inference(cnfTransformation,[status(thm)],[f_61]) ).
tff(c_1733,plain,
max('#skF_6','#skF_7') = '#skE_2',
inference(resolution,[status(thm)],[c_1712,c_76]) ).
tff(c_81,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_1769,plain,
( ( '#skF_6' = '#skE_2' )
| $less('#skF_6','#skF_7') ),
inference(superposition,[status(thm),theory(equality)],[c_1733,c_81]) ).
tff(c_1790,plain,
'#skF_6' = '#skE_2',
inference(negUnitSimplification,[status(thm)],[c_574,c_1769]) ).
tff(c_536,plain,
$less('#skE_2','#skF_8'),
inference(splitRight,[status(thm)],[c_530]) ).
tff(c_609,plain,
$less('#skE_2','#skF_6'),
inference(demodulation,[status(thm),theory(equality)],[c_537,c_536]) ).
tff(c_1851,plain,
$less('#skE_2','#skE_2'),
inference(demodulation,[status(thm),theory(equality)],[c_1790,c_609]) ).
tff(c_1903,plain,
$false,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_1851]) ).
tff(c_1914,plain,
minsol_model_max('#skF_6','#skF_7','#skF_6'),
inference(splitRight,[status(thm)],[c_1703]) ).
tff(c_580,plain,
~ minsol_model_max('#skF_6','#skF_7','#skF_6'),
inference(demodulation,[status(thm),theory(equality)],[c_537,c_140]) ).
tff(c_1917,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_1914,c_580]) ).
tff(c_1921,plain,
'#skF_8' = '#skF_7',
inference(splitRight,[status(thm)],[c_404]) ).
tff(c_1947,plain,
~ $less('#skF_7','#skF_6'),
inference(demodulation,[status(thm),theory(equality)],[c_1921,c_372]) ).
tff(c_403,plain,
'#skF_1'('#skF_6','#skF_8','#skF_8') = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_395]) ).
tff(c_1991,plain,
'#skF_1'('#skF_6','#skF_7','#skF_7') = '#skE_1',
inference(demodulation,[status(thm),theory(equality)],[c_1921,c_1921,c_403]) ).
tff(c_2007,plain,
( model_max('#skF_6','#skF_7','#skE_1')
| minsol_model_max('#skF_6','#skF_7','#skF_7')
| ~ model_max('#skF_6','#skF_7','#skF_7') ),
inference(superposition,[status(thm),theory(equality)],[c_1991,c_69]) ).
tff(c_3208,plain,
~ model_max('#skF_6','#skF_7','#skF_7'),
inference(splitLeft,[status(thm)],[c_2007]) ).
tff(c_3228,plain,
$less('#skF_7','#skF_6'),
inference(resolution,[status(thm)],[c_107,c_3208]) ).
tff(c_3230,plain,
$less('#skF_7','#skF_6'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_3228]) ).
tff(c_3231,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_1947,c_3230]) ).
tff(c_3235,plain,
( minsol_model_max('#skF_6','#skF_7','#skF_7')
| model_max('#skF_6','#skF_7','#skE_1') ),
inference(splitRight,[status(thm)],[c_2007]) ).
tff(c_3244,plain,
model_max('#skF_6','#skF_7','#skE_1'),
inference(splitLeft,[status(thm)],[c_3235]) ).
tff(c_3265,plain,
max('#skF_6','#skF_7') = '#skE_1',
inference(resolution,[status(thm)],[c_3244,c_76]) ).
tff(c_3315,plain,
( ( '#skF_7' = '#skE_1' )
| $less('#skF_7','#skF_6') ),
inference(superposition,[status(thm),theory(equality)],[c_80,c_3265]) ).
tff(c_3356,plain,
'#skF_7' = '#skE_1',
inference(negUnitSimplification,[status(thm)],[c_1947,c_3315]) ).
tff(c_1920,plain,
$less('#skE_1','#skF_8'),
inference(splitRight,[status(thm)],[c_404]) ).
tff(c_1955,plain,
$less('#skE_1','#skF_7'),
inference(demodulation,[status(thm),theory(equality)],[c_1921,c_1920]) ).
tff(c_3433,plain,
$less('#skE_1','#skE_1'),
inference(demodulation,[status(thm),theory(equality)],[c_3356,c_1955]) ).
tff(c_3483,plain,
$false,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_3433]) ).
tff(c_3489,plain,
minsol_model_max('#skF_6','#skF_7','#skF_7'),
inference(splitRight,[status(thm)],[c_3235]) ).
tff(c_1953,plain,
~ minsol_model_max('#skF_6','#skF_7','#skF_7'),
inference(demodulation,[status(thm),theory(equality)],[c_1921,c_140]) ).
tff(c_3492,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_3489,c_1953]) ).
tff(c_3499,plain,
minsol_model_max('#skF_3','#skF_4','#skF_5'),
inference(splitRight,[status(thm)],[c_52]) ).
tff(c_71,plain,
! [X_16a: $int,Y_17a: $int,N_18a: $int] :
( model_max(X_16a,Y_17a,N_18a)
| ~ minsol_model_max(X_16a,Y_17a,N_18a) ),
inference(cnfTransformation,[status(thm)],[f_76]) ).
tff(c_142,plain,
! [X_103a: $int,Y_104a: $int,N_105a: $int] :
( ( max(X_103a,Y_104a) = N_105a )
| ~ model_max(X_103a,Y_104a,N_105a) ),
inference(cnfTransformation,[status(thm)],[f_61]) ).
tff(c_153,plain,
! [X_16a: $int,Y_17a: $int,N_18a: $int] :
( ( max(X_16a,Y_17a) = N_18a )
| ~ minsol_model_max(X_16a,Y_17a,N_18a) ),
inference(resolution,[status(thm)],[c_71,c_142]) ).
tff(c_4619,plain,
max('#skF_3','#skF_4') = '#skF_5',
inference(resolution,[status(thm)],[c_3499,c_153]) ).
tff(c_4649,plain,
( ( '#skF_5' = '#skF_4' )
| $less('#skF_4','#skF_3') ),
inference(superposition,[status(thm),theory(equality)],[c_4619,c_80]) ).
tff(c_4662,plain,
$less('#skF_4','#skF_3'),
inference(splitLeft,[status(thm)],[c_4649]) ).
tff(c_4110,plain,
max('#skF_3','#skF_4') = '#skF_5',
inference(resolution,[status(thm)],[c_3499,c_153]) ).
tff(c_4137,plain,
( ( '#skF_5' = '#skF_3' )
| $less('#skF_3','#skF_4') ),
inference(superposition,[status(thm),theory(equality)],[c_4110,c_81]) ).
tff(c_4151,plain,
$less('#skF_3','#skF_4'),
inference(splitLeft,[status(thm)],[c_4137]) ).
tff(c_37,plain,
! [N_24a: $int,X_22a: $int,Y_23a: $int] :
( ~ $lesseq(N_24a,'#skF_2'(X_22a,Y_23a,N_24a))
| minsol_model_ub(X_22a,Y_23a,N_24a)
| ~ model_ub(X_22a,Y_23a,N_24a) ),
inference(cnfTransformation,[status(thm)],[f_86]) ).
tff(c_332,plain,
! [X_185a: $int,Y_186a: $int,N_187a: $int] :
( $less('#skF_2'(X_185a,Y_186a,N_187a),N_187a)
| minsol_model_ub(X_185a,Y_186a,N_187a)
| ~ model_ub(X_185a,Y_186a,N_187a) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_37]) ).
tff(c_3863,plain,
! [X_1681a: $int,Y_1682a: $int,Z_1683a: $int] :
( $less('#skF_2'(X_1681a,Y_1682a,Z_1683a),Z_1683a)
| minsol_model_ub(X_1681a,Y_1682a,Z_1683a)
| $less(Z_1683a,X_1681a)
| $less(Z_1683a,Y_1682a) ),
inference(resolution,[status(thm)],[c_190,c_332]) ).
tff(c_3535,plain,
max('#skF_3','#skF_4') = '#skF_5',
inference(resolution,[status(thm)],[c_3499,c_153]) ).
tff(c_3562,plain,
( ( '#skF_5' = '#skF_3' )
| $less('#skF_3','#skF_4') ),
inference(superposition,[status(thm),theory(equality)],[c_3535,c_81]) ).
tff(c_3576,plain,
$less('#skF_3','#skF_4'),
inference(splitLeft,[status(thm)],[c_3562]) ).
tff(c_3574,plain,
( ( '#skF_5' = '#skF_4' )
| $less('#skF_4','#skF_3') ),
inference(superposition,[status(thm),theory(equality)],[c_80,c_3535]) ).
tff(c_3579,plain,
$less('#skF_4','#skF_3'),
inference(splitLeft,[status(thm)],[c_3574]) ).
tff(c_3580,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_3579,c_3576]) ).
tff(c_3583,plain,
'#skF_5' = '#skF_4',
inference(splitRight,[status(thm)],[c_3574]) ).
tff(c_23,plain,
! [X_16a: $int,Y_17a: $int,Z_21a: $int,N_18a: $int] :
( ~ model_max(X_16a,Y_17a,Z_21a)
| ~ minsol_model_max(X_16a,Y_17a,N_18a)
| $lesseq(N_18a,Z_21a) ),
inference(cnfTransformation,[status(thm)],[f_76]) ).
tff(c_243,plain,
! [X_148a: $int,Y_149a: $int,Z_150a: $int,N_151a: $int] :
( ~ model_max(X_148a,Y_149a,Z_150a)
| ~ minsol_model_max(X_148a,Y_149a,N_151a)
| ~ $less(Z_150a,N_151a) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_23]) ).
tff(c_256,plain,
! [X_86a: $int,Y_87a: $int,N_151a: $int] :
( ~ minsol_model_max(X_86a,Y_87a,N_151a)
| ~ $less(X_86a,N_151a)
| $less(X_86a,Y_87a) ),
inference(resolution,[status(thm)],[c_129,c_243]) ).
tff(c_3520,plain,
( ~ $less('#skF_3','#skF_5')
| $less('#skF_3','#skF_4') ),
inference(resolution,[status(thm)],[c_3499,c_256]) ).
tff(c_3530,plain,
~ $less('#skF_3','#skF_5'),
inference(splitLeft,[status(thm)],[c_3520]) ).
tff(c_3594,plain,
~ $less('#skF_3','#skF_4'),
inference(demodulation,[status(thm),theory(equality)],[c_3583,c_3530]) ).
tff(c_3610,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_3576,c_3594]) ).
tff(c_3613,plain,
'#skF_5' = '#skF_3',
inference(splitRight,[status(thm)],[c_3562]) ).
tff(c_258,plain,
! [X_84a: $int,Y_85a: $int,N_151a: $int] :
( ~ minsol_model_max(X_84a,Y_85a,N_151a)
| ~ $less(Y_85a,N_151a)
| $less(Y_85a,X_84a) ),
inference(resolution,[status(thm)],[c_107,c_243]) ).
tff(c_3518,plain,
( ~ $less('#skF_4','#skF_5')
| $less('#skF_4','#skF_3') ),
inference(resolution,[status(thm)],[c_3499,c_258]) ).
tff(c_3532,plain,
~ $less('#skF_4','#skF_5'),
inference(splitLeft,[status(thm)],[c_3518]) ).
tff(c_3667,plain,
~ $less('#skF_4','#skF_3'),
inference(demodulation,[status(thm),theory(equality)],[c_3613,c_3532]) ).
tff(c_3564,plain,
( ( '#skF_5' = '#skF_4' )
| $less('#skF_4','#skF_3') ),
inference(superposition,[status(thm),theory(equality)],[c_3535,c_80]) ).
tff(c_3674,plain,
( ( '#skF_4' = '#skF_3' )
| $less('#skF_4','#skF_3') ),
inference(demodulation,[status(thm),theory(equality)],[c_3613,c_3564]) ).
tff(c_3676,plain,
'#skF_4' = '#skF_3',
inference(negUnitSimplification,[status(thm)],[c_3667,c_3674]) ).
tff(c_56,plain,
( ~ minsol_model_ub('#skF_3','#skF_4','#skF_5')
| minsol_model_ub('#skF_6','#skF_7','#skF_8') ),
inference(cnfTransformation,[status(thm)],[f_92]) ).
tff(c_211,plain,
~ minsol_model_ub('#skF_3','#skF_4','#skF_5'),
inference(splitLeft,[status(thm)],[c_56]) ).
tff(c_3673,plain,
~ minsol_model_ub('#skF_3','#skF_4','#skF_3'),
inference(demodulation,[status(thm),theory(equality)],[c_3613,c_211]) ).
tff(c_3808,plain,
~ minsol_model_ub('#skF_3','#skF_3','#skF_3'),
inference(demodulation,[status(thm),theory(equality)],[c_3676,c_3673]) ).
tff(c_3878,plain,
( $less('#skF_2'('#skF_3','#skF_3','#skF_3'),'#skF_3')
| $less('#skF_3','#skF_3') ),
inference(resolution,[status(thm)],[c_3863,c_3808]) ).
tff(c_3881,plain,
$less('#skF_2'('#skF_3','#skF_3','#skF_3'),'#skF_3'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_3878]) ).
tff(c_3893,plain,
'#skF_2'('#skF_3','#skF_3','#skF_3') = '#skE_6',
inference(define,[status(thm),theory(equality)],[c_3881]) ).
tff(c_3892,plain,
$less('#skF_2'('#skF_3','#skF_3','#skF_3'),'#skF_3'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_3878]) ).
tff(c_3900,plain,
$less('#skE_6','#skF_3'),
inference(demodulation,[status(thm),theory(equality)],[c_3893,c_3892]) ).
tff(c_3914,plain,
'#skF_2'('#skF_3','#skF_3','#skF_3') = '#skE_6',
inference(define,[status(thm),theory(equality)],[c_3881]) ).
tff(c_65,plain,
! [X_22a: $int,Y_23a: $int,N_24a: $int] :
( model_ub(X_22a,Y_23a,'#skF_2'(X_22a,Y_23a,N_24a))
| minsol_model_ub(X_22a,Y_23a,N_24a)
| ~ model_ub(X_22a,Y_23a,N_24a) ),
inference(cnfTransformation,[status(thm)],[f_86]) ).
tff(c_3930,plain,
( model_ub('#skF_3','#skF_3','#skE_6')
| minsol_model_ub('#skF_3','#skF_3','#skF_3')
| ~ model_ub('#skF_3','#skF_3','#skF_3') ),
inference(superposition,[status(thm),theory(equality)],[c_3914,c_65]) ).
tff(c_3982,plain,
~ model_ub('#skF_3','#skF_3','#skF_3'),
inference(splitLeft,[status(thm)],[c_3930]) ).
tff(c_3989,plain,
$less('#skF_3','#skF_3'),
inference(resolution,[status(thm)],[c_190,c_3982]) ).
tff(c_3992,plain,
$false,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_3989]) ).
tff(c_3996,plain,
( minsol_model_ub('#skF_3','#skF_3','#skF_3')
| model_ub('#skF_3','#skF_3','#skE_6') ),
inference(splitRight,[status(thm)],[c_3930]) ).
tff(c_4074,plain,
model_ub('#skF_3','#skF_3','#skE_6'),
inference(splitLeft,[status(thm)],[c_3996]) ).
tff(c_178,plain,
! [N_113a: $int,X_111a: $int,Y_112a: $int] :
( ~ $less(N_113a,X_111a)
| ~ model_ub(X_111a,Y_112a,N_113a) ),
inference(resolution,[status(thm)],[c_163,c_78]) ).
tff(c_4083,plain,
~ $less('#skE_6','#skF_3'),
inference(resolution,[status(thm)],[c_4074,c_178]) ).
tff(c_4096,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_3900,c_4083]) ).
tff(c_4102,plain,
minsol_model_ub('#skF_3','#skF_3','#skF_3'),
inference(splitRight,[status(thm)],[c_3996]) ).
tff(c_4105,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_4102,c_3808]) ).
tff(c_4108,plain,
$less('#skF_4','#skF_3'),
inference(splitRight,[status(thm)],[c_3518]) ).
tff(c_4152,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_4151,c_4108]) ).
tff(c_4156,plain,
~ $less('#skF_3','#skF_4'),
inference(splitRight,[status(thm)],[c_4137]) ).
tff(c_4389,plain,
! [X_1886a: $int,Y_1887a: $int,Z_1888a: $int] :
( $less('#skF_2'(X_1886a,Y_1887a,Z_1888a),Z_1888a)
| minsol_model_ub(X_1886a,Y_1887a,Z_1888a)
| $less(Z_1888a,X_1886a)
| $less(Z_1888a,Y_1887a) ),
inference(resolution,[status(thm)],[c_190,c_332]) ).
tff(c_4155,plain,
'#skF_5' = '#skF_3',
inference(splitRight,[status(thm)],[c_4137]) ).
tff(c_4186,plain,
~ minsol_model_ub('#skF_3','#skF_4','#skF_3'),
inference(demodulation,[status(thm),theory(equality)],[c_4155,c_211]) ).
tff(c_4404,plain,
( $less('#skF_2'('#skF_3','#skF_4','#skF_3'),'#skF_3')
| $less('#skF_3','#skF_3')
| $less('#skF_3','#skF_4') ),
inference(resolution,[status(thm)],[c_4389,c_4186]) ).
tff(c_4407,plain,
( $less('#skF_2'('#skF_3','#skF_4','#skF_3'),'#skF_3')
| $less('#skF_3','#skF_4') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_4404]) ).
tff(c_4511,plain,
$less('#skF_2'('#skF_3','#skF_4','#skF_3'),'#skF_3'),
inference(negUnitSimplification,[status(thm)],[c_4156,c_4407]) ).
tff(c_4513,plain,
'#skF_2'('#skF_3','#skF_4','#skF_3') = '#skE_7',
inference(define,[status(thm),theory(equality)],[c_4511]) ).
tff(c_4512,plain,
$less('#skF_2'('#skF_3','#skF_4','#skF_3'),'#skF_3'),
inference(negUnitSimplification,[status(thm)],[c_4156,c_4407]) ).
tff(c_4520,plain,
$less('#skE_7','#skF_3'),
inference(demodulation,[status(thm),theory(equality)],[c_4513,c_4512]) ).
tff(c_4523,plain,
'#skF_2'('#skF_3','#skF_4','#skF_3') = '#skE_7',
inference(define,[status(thm),theory(equality)],[c_4511]) ).
tff(c_4539,plain,
( model_ub('#skF_3','#skF_4','#skE_7')
| minsol_model_ub('#skF_3','#skF_4','#skF_3')
| ~ model_ub('#skF_3','#skF_4','#skF_3') ),
inference(superposition,[status(thm),theory(equality)],[c_4523,c_65]) ).
tff(c_4551,plain,
~ model_ub('#skF_3','#skF_4','#skF_3'),
inference(splitLeft,[status(thm)],[c_4539]) ).
tff(c_4558,plain,
( $less('#skF_3','#skF_3')
| $less('#skF_3','#skF_4') ),
inference(resolution,[status(thm)],[c_190,c_4551]) ).
tff(c_4560,plain,
$less('#skF_3','#skF_4'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_4558]) ).
tff(c_4562,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_4156,c_4560]) ).
tff(c_4566,plain,
( minsol_model_ub('#skF_3','#skF_4','#skF_3')
| model_ub('#skF_3','#skF_4','#skE_7') ),
inference(splitRight,[status(thm)],[c_4539]) ).
tff(c_4581,plain,
model_ub('#skF_3','#skF_4','#skE_7'),
inference(splitLeft,[status(thm)],[c_4566]) ).
tff(c_4590,plain,
~ $less('#skE_7','#skF_3'),
inference(resolution,[status(thm)],[c_4581,c_178]) ).
tff(c_4603,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_4520,c_4590]) ).
tff(c_4609,plain,
minsol_model_ub('#skF_3','#skF_4','#skF_3'),
inference(splitRight,[status(thm)],[c_4566]) ).
tff(c_4612,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_4609,c_4186]) ).
tff(c_4615,plain,
$less('#skF_3','#skF_4'),
inference(splitRight,[status(thm)],[c_3520]) ).
tff(c_4663,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_4662,c_4615]) ).
tff(c_4667,plain,
~ $less('#skF_4','#skF_3'),
inference(splitRight,[status(thm)],[c_4649]) ).
tff(c_4838,plain,
! [X_2052a: $int,Y_2053a: $int,Z_2054a: $int] :
( $less('#skF_2'(X_2052a,Y_2053a,Z_2054a),Z_2054a)
| minsol_model_ub(X_2052a,Y_2053a,Z_2054a)
| $less(Z_2054a,X_2052a)
| $less(Z_2054a,Y_2053a) ),
inference(resolution,[status(thm)],[c_190,c_332]) ).
tff(c_4666,plain,
'#skF_5' = '#skF_4',
inference(splitRight,[status(thm)],[c_4649]) ).
tff(c_4697,plain,
~ minsol_model_ub('#skF_3','#skF_4','#skF_4'),
inference(demodulation,[status(thm),theory(equality)],[c_4666,c_211]) ).
tff(c_4853,plain,
( $less('#skF_2'('#skF_3','#skF_4','#skF_4'),'#skF_4')
| $less('#skF_4','#skF_3')
| $less('#skF_4','#skF_4') ),
inference(resolution,[status(thm)],[c_4838,c_4697]) ).
tff(c_4856,plain,
( $less('#skF_2'('#skF_3','#skF_4','#skF_4'),'#skF_4')
| $less('#skF_4','#skF_3') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_4853]) ).
tff(c_4958,plain,
$less('#skF_2'('#skF_3','#skF_4','#skF_4'),'#skF_4'),
inference(negUnitSimplification,[status(thm)],[c_4667,c_4856]) ).
tff(c_4960,plain,
'#skF_2'('#skF_3','#skF_4','#skF_4') = '#skE_8',
inference(define,[status(thm),theory(equality)],[c_4958]) ).
tff(c_4959,plain,
$less('#skF_2'('#skF_3','#skF_4','#skF_4'),'#skF_4'),
inference(negUnitSimplification,[status(thm)],[c_4667,c_4856]) ).
tff(c_4967,plain,
$less('#skE_8','#skF_4'),
inference(demodulation,[status(thm),theory(equality)],[c_4960,c_4959]) ).
tff(c_4970,plain,
'#skF_2'('#skF_3','#skF_4','#skF_4') = '#skE_8',
inference(define,[status(thm),theory(equality)],[c_4958]) ).
tff(c_4986,plain,
( model_ub('#skF_3','#skF_4','#skE_8')
| minsol_model_ub('#skF_3','#skF_4','#skF_4')
| ~ model_ub('#skF_3','#skF_4','#skF_4') ),
inference(superposition,[status(thm),theory(equality)],[c_4970,c_65]) ).
tff(c_5128,plain,
~ model_ub('#skF_3','#skF_4','#skF_4'),
inference(splitLeft,[status(thm)],[c_4986]) ).
tff(c_5135,plain,
( $less('#skF_4','#skF_3')
| $less('#skF_4','#skF_4') ),
inference(resolution,[status(thm)],[c_190,c_5128]) ).
tff(c_5137,plain,
$less('#skF_4','#skF_3'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_5135]) ).
tff(c_5139,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_4667,c_5137]) ).
tff(c_5143,plain,
( minsol_model_ub('#skF_3','#skF_4','#skF_4')
| model_ub('#skF_3','#skF_4','#skE_8') ),
inference(splitRight,[status(thm)],[c_4986]) ).
tff(c_5197,plain,
model_ub('#skF_3','#skF_4','#skE_8'),
inference(splitLeft,[status(thm)],[c_5143]) ).
tff(c_176,plain,
! [N_113a: $int,Y_112a: $int,X_111a: $int] :
( ~ $less(N_113a,Y_112a)
| ~ model_ub(X_111a,Y_112a,N_113a) ),
inference(resolution,[status(thm)],[c_163,c_79]) ).
tff(c_5209,plain,
~ $less('#skE_8','#skF_4'),
inference(resolution,[status(thm)],[c_5197,c_176]) ).
tff(c_5221,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_4967,c_5209]) ).
tff(c_5227,plain,
minsol_model_ub('#skF_3','#skF_4','#skF_4'),
inference(splitRight,[status(thm)],[c_5143]) ).
tff(c_5230,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_5227,c_4697]) ).
tff(c_5245,plain,
minsol_model_ub('#skF_6','#skF_7','#skF_8'),
inference(splitRight,[status(thm)],[c_56]) ).
tff(c_5253,plain,
~ $less('#skF_8','#skF_6'),
inference(resolution,[status(thm)],[c_5245,c_206]) ).
tff(c_5302,plain,
! [X_2253a: $int,Y_2254a: $int,N_2255a: $int] :
( $less('#skF_1'(X_2253a,Y_2254a,N_2255a),N_2255a)
| minsol_model_max(X_2253a,Y_2254a,N_2255a)
| ~ model_max(X_2253a,Y_2254a,N_2255a) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_28]) ).
tff(c_5390,plain,
! [X_2284a: $int,Y_2285a: $int] :
( $less('#skF_1'(X_2284a,Y_2285a,Y_2285a),Y_2285a)
| minsol_model_max(X_2284a,Y_2285a,Y_2285a)
| $less(Y_2285a,X_2284a) ),
inference(resolution,[status(thm)],[c_107,c_5302]) ).
tff(c_5414,plain,
( ( '#skF_8' != '#skF_7' )
| $less('#skF_1'('#skF_6','#skF_8','#skF_8'),'#skF_8')
| $less('#skF_8','#skF_6') ),
inference(resolution,[status(thm)],[c_5390,c_140]) ).
tff(c_5449,plain,
( ( '#skF_8' != '#skF_7' )
| $less('#skF_1'('#skF_6','#skF_8','#skF_8'),'#skF_8') ),
inference(negUnitSimplification,[status(thm)],[c_5253,c_5414]) ).
tff(c_5451,plain,
'#skF_1'('#skF_6','#skF_8','#skF_8') = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_5449]) ).
tff(c_5450,plain,
( ( '#skF_8' != '#skF_7' )
| $less('#skF_1'('#skF_6','#skF_8','#skF_8'),'#skF_8') ),
inference(negUnitSimplification,[status(thm)],[c_5253,c_5414]) ).
tff(c_5458,plain,
( ( '#skF_8' != '#skF_7' )
| $less('#skE_1','#skF_8') ),
inference(demodulation,[status(thm),theory(equality)],[c_5451,c_5450]) ).
tff(c_5460,plain,
'#skF_8' != '#skF_7',
inference(splitLeft,[status(thm)],[c_5458]) ).
tff(c_5234,plain,
minsol_model_ub('#skF_6','#skF_7','#skF_8'),
inference(splitRight,[status(thm)],[c_56]) ).
tff(c_5290,plain,
! [X_2245a: $int,Y_2246a: $int,Z_2247a: $int,N_2248a: $int] :
( ~ model_ub(X_2245a,Y_2246a,Z_2247a)
| ~ minsol_model_ub(X_2245a,Y_2246a,N_2248a)
| ~ $less(Z_2247a,N_2248a) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_32]) ).
tff(c_5416,plain,
! [X_2290a: $int,Y_2291a: $int,N_2292a: $int,Z_2293a: $int] :
( ~ minsol_model_ub(X_2290a,Y_2291a,N_2292a)
| ~ $less(Z_2293a,N_2292a)
| $less(Z_2293a,X_2290a)
| $less(Z_2293a,Y_2291a) ),
inference(resolution,[status(thm)],[c_190,c_5290]) ).
tff(c_5421,plain,
! [Z_2293a: $int] :
( ~ $less(Z_2293a,'#skF_8')
| $less(Z_2293a,'#skF_6')
| $less(Z_2293a,'#skF_7') ),
inference(resolution,[status(thm)],[c_5234,c_5416]) ).
tff(c_5433,plain,
( $lesseq('#skF_8','#skF_6')
| $lesseq('#skF_8','#skF_7') ),
inference(quantifierElimination,[status(thm),theory('LIA')],[c_5421]) ).
tff(c_5435,plain,
( ~ $less('#skF_6','#skF_8')
| ~ $less('#skF_7','#skF_8') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_5433]) ).
tff(c_5255,plain,
~ $less('#skF_8','#skF_7'),
inference(resolution,[status(thm)],[c_5245,c_200]) ).
tff(c_5333,plain,
! [X_2265a: $int,Y_2266a: $int] :
( $less('#skF_1'(X_2265a,Y_2266a,X_2265a),X_2265a)
| minsol_model_max(X_2265a,Y_2266a,X_2265a)
| $less(X_2265a,Y_2266a) ),
inference(resolution,[status(thm)],[c_129,c_5302]) ).
tff(c_5357,plain,
( ( '#skF_8' != '#skF_6' )
| $less('#skF_1'('#skF_8','#skF_7','#skF_8'),'#skF_8')
| $less('#skF_8','#skF_7') ),
inference(resolution,[status(thm)],[c_5333,c_140]) ).
tff(c_5363,plain,
( ( '#skF_8' != '#skF_6' )
| $less('#skF_1'('#skF_8','#skF_7','#skF_8'),'#skF_8') ),
inference(negUnitSimplification,[status(thm)],[c_5255,c_5357]) ).
tff(c_5365,plain,
'#skF_1'('#skF_8','#skF_7','#skF_8') = '#skE_2',
inference(define,[status(thm),theory(equality)],[c_5363]) ).
tff(c_5364,plain,
( ( '#skF_8' != '#skF_6' )
| $less('#skF_1'('#skF_8','#skF_7','#skF_8'),'#skF_8') ),
inference(negUnitSimplification,[status(thm)],[c_5255,c_5357]) ).
tff(c_5372,plain,
( ( '#skF_8' != '#skF_6' )
| $less('#skE_2','#skF_8') ),
inference(demodulation,[status(thm),theory(equality)],[c_5365,c_5364]) ).
tff(c_5374,plain,
'#skF_8' != '#skF_6',
inference(splitLeft,[status(thm)],[c_5372]) ).
tff(c_5461,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_5460,c_5435,c_5374,c_5255,c_5253]) ).
tff(c_5465,plain,
'#skF_8' = '#skF_7',
inference(splitRight,[status(thm)],[c_5458]) ).
tff(c_5502,plain,
~ $less('#skF_7','#skF_6'),
inference(demodulation,[status(thm),theory(equality)],[c_5465,c_5253]) ).
tff(c_5457,plain,
'#skF_1'('#skF_6','#skF_8','#skF_8') = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_5449]) ).
tff(c_5518,plain,
'#skF_1'('#skF_6','#skF_7','#skF_7') = '#skE_1',
inference(demodulation,[status(thm),theory(equality)],[c_5465,c_5465,c_5457]) ).
tff(c_5534,plain,
( model_max('#skF_6','#skF_7','#skE_1')
| minsol_model_max('#skF_6','#skF_7','#skF_7')
| ~ model_max('#skF_6','#skF_7','#skF_7') ),
inference(superposition,[status(thm),theory(equality)],[c_5518,c_69]) ).
tff(c_6604,plain,
~ model_max('#skF_6','#skF_7','#skF_7'),
inference(splitLeft,[status(thm)],[c_5534]) ).
tff(c_6624,plain,
$less('#skF_7','#skF_6'),
inference(resolution,[status(thm)],[c_107,c_6604]) ).
tff(c_6626,plain,
$less('#skF_7','#skF_6'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_6624]) ).
tff(c_6627,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_5502,c_6626]) ).
tff(c_6631,plain,
( minsol_model_max('#skF_6','#skF_7','#skF_7')
| model_max('#skF_6','#skF_7','#skE_1') ),
inference(splitRight,[status(thm)],[c_5534]) ).
tff(c_6640,plain,
model_max('#skF_6','#skF_7','#skE_1'),
inference(splitLeft,[status(thm)],[c_6631]) ).
tff(c_6661,plain,
max('#skF_6','#skF_7') = '#skE_1',
inference(resolution,[status(thm)],[c_6640,c_76]) ).
tff(c_6699,plain,
( ( '#skF_7' = '#skE_1' )
| $less('#skF_7','#skF_6') ),
inference(superposition,[status(thm),theory(equality)],[c_6661,c_80]) ).
tff(c_6720,plain,
'#skF_7' = '#skE_1',
inference(negUnitSimplification,[status(thm)],[c_5502,c_6699]) ).
tff(c_5464,plain,
$less('#skE_1','#skF_8'),
inference(splitRight,[status(thm)],[c_5458]) ).
tff(c_5510,plain,
$less('#skE_1','#skF_7'),
inference(demodulation,[status(thm),theory(equality)],[c_5465,c_5464]) ).
tff(c_6790,plain,
$less('#skE_1','#skE_1'),
inference(demodulation,[status(thm),theory(equality)],[c_6720,c_5510]) ).
tff(c_6838,plain,
$false,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_6790]) ).
tff(c_6844,plain,
minsol_model_max('#skF_6','#skF_7','#skF_7'),
inference(splitRight,[status(thm)],[c_6631]) ).
tff(c_5508,plain,
~ minsol_model_max('#skF_6','#skF_7','#skF_7'),
inference(demodulation,[status(thm),theory(equality)],[c_5465,c_140]) ).
tff(c_6847,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_6844,c_5508]) ).
tff(c_6851,plain,
'#skF_8' = '#skF_6',
inference(splitRight,[status(thm)],[c_5372]) ).
tff(c_6896,plain,
~ $less('#skF_6','#skF_7'),
inference(demodulation,[status(thm),theory(equality)],[c_6851,c_5255]) ).
tff(c_5371,plain,
'#skF_1'('#skF_8','#skF_7','#skF_8') = '#skE_2',
inference(define,[status(thm),theory(equality)],[c_5363]) ).
tff(c_6892,plain,
'#skF_1'('#skF_6','#skF_7','#skF_6') = '#skE_2',
inference(demodulation,[status(thm),theory(equality)],[c_6851,c_6851,c_5371]) ).
tff(c_7043,plain,
! [X_3026a: $int,Y_3027a: $int,N_3028a: $int] :
( model_max(X_3026a,Y_3027a,'#skF_1'(X_3026a,Y_3027a,N_3028a))
| minsol_model_max(X_3026a,Y_3027a,N_3028a)
| ~ model_max(X_3026a,Y_3027a,N_3028a) ),
inference(cnfTransformation,[status(thm)],[f_76]) ).
tff(c_7057,plain,
( model_max('#skF_6','#skF_7','#skE_2')
| minsol_model_max('#skF_6','#skF_7','#skF_6')
| ~ model_max('#skF_6','#skF_7','#skF_6') ),
inference(superposition,[status(thm),theory(equality)],[c_6892,c_7043]) ).
tff(c_8578,plain,
~ model_max('#skF_6','#skF_7','#skF_6'),
inference(splitLeft,[status(thm)],[c_7057]) ).
tff(c_8595,plain,
$less('#skF_6','#skF_7'),
inference(resolution,[status(thm)],[c_129,c_8578]) ).
tff(c_8597,plain,
$less('#skF_6','#skF_7'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_8595]) ).
tff(c_8601,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_6896,c_8597]) ).
tff(c_8605,plain,
( minsol_model_max('#skF_6','#skF_7','#skF_6')
| model_max('#skF_6','#skF_7','#skE_2') ),
inference(splitRight,[status(thm)],[c_7057]) ).
tff(c_8614,plain,
model_max('#skF_6','#skF_7','#skE_2'),
inference(splitLeft,[status(thm)],[c_8605]) ).
tff(c_8635,plain,
max('#skF_6','#skF_7') = '#skE_2',
inference(resolution,[status(thm)],[c_8614,c_76]) ).
tff(c_8671,plain,
( ( '#skF_6' = '#skE_2' )
| $less('#skF_6','#skF_7') ),
inference(superposition,[status(thm),theory(equality)],[c_8635,c_81]) ).
tff(c_8687,plain,
'#skF_6' = '#skE_2',
inference(negUnitSimplification,[status(thm)],[c_6896,c_8671]) ).
tff(c_6850,plain,
$less('#skE_2','#skF_8'),
inference(splitRight,[status(thm)],[c_5372]) ).
tff(c_6904,plain,
$less('#skE_2','#skF_6'),
inference(demodulation,[status(thm),theory(equality)],[c_6851,c_6850]) ).
tff(c_8757,plain,
$less('#skE_2','#skE_2'),
inference(demodulation,[status(thm),theory(equality)],[c_8687,c_6904]) ).
tff(c_8803,plain,
$false,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_8757]) ).
tff(c_8809,plain,
minsol_model_max('#skF_6','#skF_7','#skF_6'),
inference(splitRight,[status(thm)],[c_8605]) ).
tff(c_6902,plain,
~ minsol_model_max('#skF_6','#skF_7','#skF_6'),
inference(demodulation,[status(thm),theory(equality)],[c_6851,c_140]) ).
tff(c_8812,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_8809,c_6902]) ).
tff(c_8816,plain,
minsol_model_max('#skF_3','#skF_4','#skF_5'),
inference(splitRight,[status(thm)],[c_60]) ).
tff(c_8818,plain,
! [X_3812a: $int,Y_3813a: $int,N_3814a: $int] :
( ( max(X_3812a,Y_3813a) = N_3814a )
| ~ model_max(X_3812a,Y_3813a,N_3814a) ),
inference(cnfTransformation,[status(thm)],[f_61]) ).
tff(c_9994,plain,
! [X_4286a: $int,Y_4287a: $int,N_4288a: $int] :
( ( max(X_4286a,Y_4287a) = N_4288a )
| ~ minsol_model_max(X_4286a,Y_4287a,N_4288a) ),
inference(resolution,[status(thm)],[c_71,c_8818]) ).
tff(c_10007,plain,
max('#skF_3','#skF_4') = '#skF_5',
inference(resolution,[status(thm)],[c_8816,c_9994]) ).
tff(c_10046,plain,
( ( '#skF_5' = '#skF_4' )
| $less('#skF_4','#skF_3') ),
inference(superposition,[status(thm),theory(equality)],[c_80,c_10007]) ).
tff(c_10050,plain,
$less('#skF_4','#skF_3'),
inference(splitLeft,[status(thm)],[c_10046]) ).
tff(c_10034,plain,
( ( '#skF_5' = '#skF_3' )
| $less('#skF_3','#skF_4') ),
inference(superposition,[status(thm),theory(equality)],[c_10007,c_81]) ).
tff(c_10048,plain,
$less('#skF_3','#skF_4'),
inference(splitLeft,[status(thm)],[c_10034]) ).
tff(c_10064,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_10050,c_10048]) ).
tff(c_10068,plain,
~ $less('#skF_4','#skF_3'),
inference(splitRight,[status(thm)],[c_10046]) ).
tff(c_9977,plain,
! [X_4280a: $int,Y_4281a: $int,Z_4282a: $int] :
( ub(X_4280a,Y_4281a,Z_4282a)
| $less(Z_4282a,X_4280a)
| $less(Z_4282a,Y_4281a) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_13]) ).
tff(c_9988,plain,
! [X_4280a: $int,Y_4281a: $int,Z_4282a: $int] :
( model_ub(X_4280a,Y_4281a,Z_4282a)
| $less(Z_4282a,X_4280a)
| $less(Z_4282a,Y_4281a) ),
inference(resolution,[status(thm)],[c_9977,c_73]) ).
tff(c_14633,plain,
! [X_6123a: $int,Y_6124a: $int,N_6125a: $int] :
( $less('#skF_2'(X_6123a,Y_6124a,N_6125a),N_6125a)
| minsol_model_ub(X_6123a,Y_6124a,N_6125a)
| ~ model_ub(X_6123a,Y_6124a,N_6125a) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_37]) ).
tff(c_14646,plain,
! [X_6132a: $int,Y_6133a: $int,Z_6134a: $int] :
( $less('#skF_2'(X_6132a,Y_6133a,Z_6134a),Z_6134a)
| minsol_model_ub(X_6132a,Y_6133a,Z_6134a)
| $less(Z_6134a,X_6132a)
| $less(Z_6134a,Y_6133a) ),
inference(resolution,[status(thm)],[c_9988,c_14633]) ).
tff(c_10067,plain,
'#skF_5' = '#skF_4',
inference(splitRight,[status(thm)],[c_10046]) ).
tff(c_8876,plain,
! [X_3841a: $int,Y_3842a: $int,N_3843a: $int] :
( ( max(X_3841a,Y_3842a) = N_3843a )
| ~ minsol_model_max(X_3841a,Y_3842a,N_3843a) ),
inference(resolution,[status(thm)],[c_71,c_8818]) ).
tff(c_8885,plain,
max('#skF_3','#skF_4') = '#skF_5',
inference(resolution,[status(thm)],[c_8816,c_8876]) ).
tff(c_8924,plain,
( ( '#skF_5' = '#skF_4' )
| $less('#skF_4','#skF_3') ),
inference(superposition,[status(thm),theory(equality)],[c_80,c_8885]) ).
tff(c_8944,plain,
$less('#skF_4','#skF_3'),
inference(splitLeft,[status(thm)],[c_8924]) ).
tff(c_8912,plain,
( ( '#skF_5' = '#skF_3' )
| $less('#skF_3','#skF_4') ),
inference(superposition,[status(thm),theory(equality)],[c_8885,c_81]) ).
tff(c_8942,plain,
$less('#skF_3','#skF_4'),
inference(splitLeft,[status(thm)],[c_8912]) ).
tff(c_8949,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_8944,c_8942]) ).
tff(c_8953,plain,
~ $less('#skF_4','#skF_3'),
inference(splitRight,[status(thm)],[c_8924]) ).
tff(c_8925,plain,
! [X_3852a: $int,Y_3853a: $int,Z_3854a: $int] :
( ub(X_3852a,Y_3853a,Z_3854a)
| $less(Z_3854a,X_3852a)
| $less(Z_3854a,Y_3853a) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_13]) ).
tff(c_8936,plain,
! [X_3852a: $int,Y_3853a: $int,Z_3854a: $int] :
( model_ub(X_3852a,Y_3853a,Z_3854a)
| $less(Z_3854a,X_3852a)
| $less(Z_3854a,Y_3853a) ),
inference(resolution,[status(thm)],[c_8925,c_73]) ).
tff(c_9164,plain,
! [X_3958a: $int,Y_3959a: $int,N_3960a: $int] :
( $less('#skF_2'(X_3958a,Y_3959a,N_3960a),N_3960a)
| minsol_model_ub(X_3958a,Y_3959a,N_3960a)
| ~ model_ub(X_3958a,Y_3959a,N_3960a) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_37]) ).
tff(c_9295,plain,
! [X_3996a: $int,Y_3997a: $int,Z_3998a: $int] :
( $less('#skF_2'(X_3996a,Y_3997a,Z_3998a),Z_3998a)
| minsol_model_ub(X_3996a,Y_3997a,Z_3998a)
| $less(Z_3998a,X_3996a)
| $less(Z_3998a,Y_3997a) ),
inference(resolution,[status(thm)],[c_8936,c_9164]) ).
tff(c_8952,plain,
'#skF_5' = '#skF_4',
inference(splitRight,[status(thm)],[c_8924]) ).
tff(c_8874,plain,
~ minsol_model_ub('#skF_3','#skF_4','#skF_5'),
inference(splitLeft,[status(thm)],[c_56]) ).
tff(c_8979,plain,
~ minsol_model_ub('#skF_3','#skF_4','#skF_4'),
inference(demodulation,[status(thm),theory(equality)],[c_8952,c_8874]) ).
tff(c_9320,plain,
( $less('#skF_2'('#skF_3','#skF_4','#skF_4'),'#skF_4')
| $less('#skF_4','#skF_3')
| $less('#skF_4','#skF_4') ),
inference(resolution,[status(thm)],[c_9295,c_8979]) ).
tff(c_9323,plain,
( $less('#skF_2'('#skF_3','#skF_4','#skF_4'),'#skF_4')
| $less('#skF_4','#skF_3') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_9320]) ).
tff(c_9368,plain,
$less('#skF_2'('#skF_3','#skF_4','#skF_4'),'#skF_4'),
inference(negUnitSimplification,[status(thm)],[c_8953,c_9323]) ).
tff(c_9370,plain,
'#skF_2'('#skF_3','#skF_4','#skF_4') = '#skE_8',
inference(define,[status(thm),theory(equality)],[c_9368]) ).
tff(c_9369,plain,
$less('#skF_2'('#skF_3','#skF_4','#skF_4'),'#skF_4'),
inference(negUnitSimplification,[status(thm)],[c_8953,c_9323]) ).
tff(c_9377,plain,
$less('#skE_8','#skF_4'),
inference(demodulation,[status(thm),theory(equality)],[c_9370,c_9369]) ).
tff(c_9381,plain,
'#skF_2'('#skF_3','#skF_4','#skF_4') = '#skE_8',
inference(define,[status(thm),theory(equality)],[c_9368]) ).
tff(c_9397,plain,
( model_ub('#skF_3','#skF_4','#skE_8')
| minsol_model_ub('#skF_3','#skF_4','#skF_4')
| ~ model_ub('#skF_3','#skF_4','#skF_4') ),
inference(superposition,[status(thm),theory(equality)],[c_9381,c_65]) ).
tff(c_9438,plain,
~ model_ub('#skF_3','#skF_4','#skF_4'),
inference(splitLeft,[status(thm)],[c_9397]) ).
tff(c_9445,plain,
( $less('#skF_4','#skF_3')
| $less('#skF_4','#skF_4') ),
inference(resolution,[status(thm)],[c_8936,c_9438]) ).
tff(c_9447,plain,
$less('#skF_4','#skF_3'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_9445]) ).
tff(c_9449,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_8953,c_9447]) ).
tff(c_9453,plain,
( minsol_model_ub('#skF_3','#skF_4','#skF_4')
| model_ub('#skF_3','#skF_4','#skE_8') ),
inference(splitRight,[status(thm)],[c_9397]) ).
tff(c_9462,plain,
model_ub('#skF_3','#skF_4','#skE_8'),
inference(splitLeft,[status(thm)],[c_9453]) ).
tff(c_8839,plain,
! [X_3820a: $int,Y_3821a: $int,N_3822a: $int] :
( ub(X_3820a,Y_3821a,N_3822a)
| ~ model_ub(X_3820a,Y_3821a,N_3822a) ),
inference(cnfTransformation,[status(thm)],[f_66]) ).
tff(c_8852,plain,
! [N_3822a: $int,Y_3821a: $int,X_3820a: $int] :
( ~ $less(N_3822a,Y_3821a)
| ~ model_ub(X_3820a,Y_3821a,N_3822a) ),
inference(resolution,[status(thm)],[c_8839,c_79]) ).
tff(c_9474,plain,
~ $less('#skE_8','#skF_4'),
inference(resolution,[status(thm)],[c_9462,c_8852]) ).
tff(c_9486,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_9377,c_9474]) ).
tff(c_9492,plain,
minsol_model_ub('#skF_3','#skF_4','#skF_4'),
inference(splitRight,[status(thm)],[c_9453]) ).
tff(c_9495,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_9492,c_8979]) ).
tff(c_9499,plain,
~ $less('#skF_3','#skF_4'),
inference(splitRight,[status(thm)],[c_8912]) ).
tff(c_9691,plain,
! [X_4171a: $int,Y_4172a: $int,N_4173a: $int] :
( $less('#skF_2'(X_4171a,Y_4172a,N_4173a),N_4173a)
| minsol_model_ub(X_4171a,Y_4172a,N_4173a)
| ~ model_ub(X_4171a,Y_4172a,N_4173a) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_37]) ).
tff(c_9795,plain,
! [X_4199a: $int,Y_4200a: $int,Z_4201a: $int] :
( $less('#skF_2'(X_4199a,Y_4200a,Z_4201a),Z_4201a)
| minsol_model_ub(X_4199a,Y_4200a,Z_4201a)
| $less(Z_4201a,X_4199a)
| $less(Z_4201a,Y_4200a) ),
inference(resolution,[status(thm)],[c_8936,c_9691]) ).
tff(c_9498,plain,
'#skF_5' = '#skF_3',
inference(splitRight,[status(thm)],[c_8912]) ).
tff(c_9526,plain,
~ minsol_model_ub('#skF_3','#skF_4','#skF_3'),
inference(demodulation,[status(thm),theory(equality)],[c_9498,c_8874]) ).
tff(c_9814,plain,
( $less('#skF_2'('#skF_3','#skF_4','#skF_3'),'#skF_3')
| $less('#skF_3','#skF_3')
| $less('#skF_3','#skF_4') ),
inference(resolution,[status(thm)],[c_9795,c_9526]) ).
tff(c_9817,plain,
( $less('#skF_2'('#skF_3','#skF_4','#skF_3'),'#skF_3')
| $less('#skF_3','#skF_4') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_9814]) ).
tff(c_9862,plain,
$less('#skF_2'('#skF_3','#skF_4','#skF_3'),'#skF_3'),
inference(negUnitSimplification,[status(thm)],[c_9499,c_9817]) ).
tff(c_9864,plain,
'#skF_2'('#skF_3','#skF_4','#skF_3') = '#skE_7',
inference(define,[status(thm),theory(equality)],[c_9862]) ).
tff(c_9863,plain,
$less('#skF_2'('#skF_3','#skF_4','#skF_3'),'#skF_3'),
inference(negUnitSimplification,[status(thm)],[c_9499,c_9817]) ).
tff(c_9871,plain,
$less('#skE_7','#skF_3'),
inference(demodulation,[status(thm),theory(equality)],[c_9864,c_9863]) ).
tff(c_9874,plain,
'#skF_2'('#skF_3','#skF_4','#skF_3') = '#skE_7',
inference(define,[status(thm),theory(equality)],[c_9862]) ).
tff(c_9890,plain,
( model_ub('#skF_3','#skF_4','#skE_7')
| minsol_model_ub('#skF_3','#skF_4','#skF_3')
| ~ model_ub('#skF_3','#skF_4','#skF_3') ),
inference(superposition,[status(thm),theory(equality)],[c_9874,c_65]) ).
tff(c_9917,plain,
~ model_ub('#skF_3','#skF_4','#skF_3'),
inference(splitLeft,[status(thm)],[c_9890]) ).
tff(c_9924,plain,
( $less('#skF_3','#skF_3')
| $less('#skF_3','#skF_4') ),
inference(resolution,[status(thm)],[c_8936,c_9917]) ).
tff(c_9926,plain,
$less('#skF_3','#skF_4'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_9924]) ).
tff(c_9928,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_9499,c_9926]) ).
tff(c_9932,plain,
( minsol_model_ub('#skF_3','#skF_4','#skF_3')
| model_ub('#skF_3','#skF_4','#skE_7') ),
inference(splitRight,[status(thm)],[c_9890]) ).
tff(c_9941,plain,
model_ub('#skF_3','#skF_4','#skE_7'),
inference(splitLeft,[status(thm)],[c_9932]) ).
tff(c_8854,plain,
! [N_3822a: $int,X_3820a: $int,Y_3821a: $int] :
( ~ $less(N_3822a,X_3820a)
| ~ model_ub(X_3820a,Y_3821a,N_3822a) ),
inference(resolution,[status(thm)],[c_8839,c_78]) ).
tff(c_9950,plain,
~ $less('#skE_7','#skF_3'),
inference(resolution,[status(thm)],[c_9941,c_8854]) ).
tff(c_9963,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_9871,c_9950]) ).
tff(c_9969,plain,
minsol_model_ub('#skF_3','#skF_4','#skF_3'),
inference(splitRight,[status(thm)],[c_9932]) ).
tff(c_9972,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_9969,c_9526]) ).
tff(c_10139,plain,
minsol_model_ub('#skF_6','#skF_7','#skF_8'),
inference(splitRight,[status(thm)],[c_56]) ).
tff(c_8864,plain,
! [N_3829a: $int,X_3830a: $int,Y_3831a: $int] :
( ~ $less(N_3829a,X_3830a)
| ~ model_ub(X_3830a,Y_3831a,N_3829a) ),
inference(resolution,[status(thm)],[c_8839,c_78]) ).
tff(c_8869,plain,
! [N_24a: $int,X_22a: $int,Y_23a: $int] :
( ~ $less(N_24a,X_22a)
| ~ minsol_model_ub(X_22a,Y_23a,N_24a) ),
inference(resolution,[status(thm)],[c_67,c_8864]) ).
tff(c_10147,plain,
~ $less('#skF_8','#skF_6'),
inference(resolution,[status(thm)],[c_10139,c_8869]) ).
tff(c_10301,plain,
! [X_4392a: $int,Y_4393a: $int,N_4394a: $int] :
( $less('#skF_1'(X_4392a,Y_4393a,N_4394a),N_4394a)
| minsol_model_max(X_4392a,Y_4393a,N_4394a)
| ~ model_max(X_4392a,Y_4393a,N_4394a) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_28]) ).
tff(c_10397,plain,
! [X_4426a: $int,Y_4427a: $int] :
( $less('#skF_1'(X_4426a,Y_4427a,Y_4427a),Y_4427a)
| minsol_model_max(X_4426a,Y_4427a,Y_4427a)
| $less(Y_4427a,X_4426a) ),
inference(resolution,[status(thm)],[c_107,c_10301]) ).
tff(c_64,plain,
( ~ minsol_model_ub('#skF_3','#skF_4','#skF_5')
| ~ minsol_model_max('#skF_6','#skF_7','#skF_8') ),
inference(cnfTransformation,[status(thm)],[f_92]) ).
tff(c_10072,plain,
~ minsol_model_max('#skF_6','#skF_7','#skF_8'),
inference(splitLeft,[status(thm)],[c_64]) ).
tff(c_10433,plain,
( ( '#skF_8' != '#skF_7' )
| $less('#skF_1'('#skF_6','#skF_8','#skF_8'),'#skF_8')
| $less('#skF_8','#skF_6') ),
inference(resolution,[status(thm)],[c_10397,c_10072]) ).
tff(c_10510,plain,
( ( '#skF_8' != '#skF_7' )
| $less('#skF_1'('#skF_6','#skF_8','#skF_8'),'#skF_8') ),
inference(negUnitSimplification,[status(thm)],[c_10147,c_10433]) ).
tff(c_10512,plain,
'#skF_1'('#skF_6','#skF_8','#skF_8') = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_10510]) ).
tff(c_10511,plain,
( ( '#skF_8' != '#skF_7' )
| $less('#skF_1'('#skF_6','#skF_8','#skF_8'),'#skF_8') ),
inference(negUnitSimplification,[status(thm)],[c_10147,c_10433]) ).
tff(c_10519,plain,
( ( '#skF_8' != '#skF_7' )
| $less('#skE_1','#skF_8') ),
inference(demodulation,[status(thm),theory(equality)],[c_10512,c_10511]) ).
tff(c_10521,plain,
'#skF_8' != '#skF_7',
inference(splitLeft,[status(thm)],[c_10519]) ).
tff(c_8858,plain,
! [N_3826a: $int,Y_3827a: $int,X_3828a: $int] :
( ~ $less(N_3826a,Y_3827a)
| ~ model_ub(X_3828a,Y_3827a,N_3826a) ),
inference(resolution,[status(thm)],[c_8839,c_79]) ).
tff(c_8863,plain,
! [N_24a: $int,Y_23a: $int,X_22a: $int] :
( ~ $less(N_24a,Y_23a)
| ~ minsol_model_ub(X_22a,Y_23a,N_24a) ),
inference(resolution,[status(thm)],[c_67,c_8858]) ).
tff(c_10149,plain,
~ $less('#skF_8','#skF_7'),
inference(resolution,[status(thm)],[c_10139,c_8863]) ).
tff(c_10325,plain,
! [X_4399a: $int,Y_4400a: $int] :
( $less('#skF_1'(X_4399a,Y_4400a,X_4399a),X_4399a)
| minsol_model_max(X_4399a,Y_4400a,X_4399a)
| $less(X_4399a,Y_4400a) ),
inference(resolution,[status(thm)],[c_129,c_10301]) ).
tff(c_10364,plain,
( ( '#skF_8' != '#skF_6' )
| $less('#skF_1'('#skF_8','#skF_7','#skF_8'),'#skF_8')
| $less('#skF_8','#skF_7') ),
inference(resolution,[status(thm)],[c_10325,c_10072]) ).
tff(c_10370,plain,
( ( '#skF_8' != '#skF_6' )
| $less('#skF_1'('#skF_8','#skF_7','#skF_8'),'#skF_8') ),
inference(negUnitSimplification,[status(thm)],[c_10149,c_10364]) ).
tff(c_10372,plain,
'#skF_1'('#skF_8','#skF_7','#skF_8') = '#skE_2',
inference(define,[status(thm),theory(equality)],[c_10370]) ).
tff(c_10371,plain,
( ( '#skF_8' != '#skF_6' )
| $less('#skF_1'('#skF_8','#skF_7','#skF_8'),'#skF_8') ),
inference(negUnitSimplification,[status(thm)],[c_10149,c_10364]) ).
tff(c_10379,plain,
( ( '#skF_8' != '#skF_6' )
| $less('#skE_2','#skF_8') ),
inference(demodulation,[status(thm),theory(equality)],[c_10372,c_10371]) ).
tff(c_10381,plain,
'#skF_8' != '#skF_6',
inference(splitLeft,[status(thm)],[c_10379]) ).
tff(c_9976,plain,
minsol_model_ub('#skF_6','#skF_7','#skF_8'),
inference(splitRight,[status(thm)],[c_56]) ).
tff(c_10195,plain,
! [X_4348a: $int,Y_4349a: $int,Z_4350a: $int,N_4351a: $int] :
( ~ model_ub(X_4348a,Y_4349a,Z_4350a)
| ~ minsol_model_ub(X_4348a,Y_4349a,N_4351a)
| ~ $less(Z_4350a,N_4351a) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_32]) ).
tff(c_10281,plain,
! [X_4385a: $int,Y_4386a: $int,N_4387a: $int,Z_4388a: $int] :
( ~ minsol_model_ub(X_4385a,Y_4386a,N_4387a)
| ~ $less(Z_4388a,N_4387a)
| $less(Z_4388a,X_4385a)
| $less(Z_4388a,Y_4386a) ),
inference(resolution,[status(thm)],[c_9988,c_10195]) ).
tff(c_10286,plain,
! [Z_4388a: $int] :
( ~ $less(Z_4388a,'#skF_8')
| $less(Z_4388a,'#skF_6')
| $less(Z_4388a,'#skF_7') ),
inference(resolution,[status(thm)],[c_9976,c_10281]) ).
tff(c_10298,plain,
( $lesseq('#skF_8','#skF_6')
| $lesseq('#skF_8','#skF_7') ),
inference(quantifierElimination,[status(thm),theory('LIA')],[c_10286]) ).
tff(c_10300,plain,
( ~ $less('#skF_6','#skF_8')
| ~ $less('#skF_7','#skF_8') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_10298]) ).
tff(c_10522,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_10521,c_10381,c_10300,c_10149,c_10147]) ).
tff(c_10526,plain,
'#skF_8' = '#skF_7',
inference(splitRight,[status(thm)],[c_10519]) ).
tff(c_10566,plain,
~ $less('#skF_7','#skF_6'),
inference(demodulation,[status(thm),theory(equality)],[c_10526,c_10147]) ).
tff(c_10518,plain,
'#skF_1'('#skF_6','#skF_8','#skF_8') = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_10510]) ).
tff(c_10577,plain,
'#skF_1'('#skF_6','#skF_7','#skF_7') = '#skE_1',
inference(demodulation,[status(thm),theory(equality)],[c_10526,c_10526,c_10518]) ).
tff(c_10593,plain,
( model_max('#skF_6','#skF_7','#skE_1')
| minsol_model_max('#skF_6','#skF_7','#skF_7')
| ~ model_max('#skF_6','#skF_7','#skF_7') ),
inference(superposition,[status(thm),theory(equality)],[c_10577,c_69]) ).
tff(c_12206,plain,
~ model_max('#skF_6','#skF_7','#skF_7'),
inference(splitLeft,[status(thm)],[c_10593]) ).
tff(c_12231,plain,
$less('#skF_7','#skF_6'),
inference(resolution,[status(thm)],[c_107,c_12206]) ).
tff(c_12233,plain,
$less('#skF_7','#skF_6'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_12231]) ).
tff(c_12234,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_10566,c_12233]) ).
tff(c_12238,plain,
( minsol_model_max('#skF_6','#skF_7','#skF_7')
| model_max('#skF_6','#skF_7','#skE_1') ),
inference(splitRight,[status(thm)],[c_10593]) ).
tff(c_12247,plain,
model_max('#skF_6','#skF_7','#skE_1'),
inference(splitLeft,[status(thm)],[c_12238]) ).
tff(c_12268,plain,
max('#skF_6','#skF_7') = '#skE_1',
inference(resolution,[status(thm)],[c_12247,c_76]) ).
tff(c_12328,plain,
( ( '#skF_7' = '#skE_1' )
| $less('#skF_7','#skF_6') ),
inference(superposition,[status(thm),theory(equality)],[c_80,c_12268]) ).
tff(c_12332,plain,
'#skF_7' = '#skE_1',
inference(negUnitSimplification,[status(thm)],[c_10566,c_12328]) ).
tff(c_10525,plain,
$less('#skE_1','#skF_8'),
inference(splitRight,[status(thm)],[c_10519]) ).
tff(c_10598,plain,
$less('#skE_1','#skF_7'),
inference(demodulation,[status(thm),theory(equality)],[c_10526,c_10525]) ).
tff(c_12397,plain,
$less('#skE_1','#skE_1'),
inference(demodulation,[status(thm),theory(equality)],[c_12332,c_10598]) ).
tff(c_12449,plain,
$false,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_12397]) ).
tff(c_12455,plain,
minsol_model_max('#skF_6','#skF_7','#skF_7'),
inference(splitRight,[status(thm)],[c_12238]) ).
tff(c_10565,plain,
~ minsol_model_max('#skF_6','#skF_7','#skF_7'),
inference(demodulation,[status(thm),theory(equality)],[c_10526,c_10072]) ).
tff(c_12458,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_12455,c_10565]) ).
tff(c_12462,plain,
'#skF_8' = '#skF_6',
inference(splitRight,[status(thm)],[c_10379]) ).
tff(c_12491,plain,
~ $less('#skF_6','#skF_7'),
inference(demodulation,[status(thm),theory(equality)],[c_12462,c_10149]) ).
tff(c_10378,plain,
'#skF_1'('#skF_8','#skF_7','#skF_8') = '#skE_2',
inference(define,[status(thm),theory(equality)],[c_10370]) ).
tff(c_12540,plain,
'#skF_1'('#skF_6','#skF_7','#skF_6') = '#skE_2',
inference(demodulation,[status(thm),theory(equality)],[c_12462,c_12462,c_10378]) ).
tff(c_12565,plain,
! [X_5334a: $int,Y_5335a: $int,N_5336a: $int] :
( model_max(X_5334a,Y_5335a,'#skF_1'(X_5334a,Y_5335a,N_5336a))
| minsol_model_max(X_5334a,Y_5335a,N_5336a)
| ~ model_max(X_5334a,Y_5335a,N_5336a) ),
inference(cnfTransformation,[status(thm)],[f_76]) ).
tff(c_12572,plain,
( model_max('#skF_6','#skF_7','#skE_2')
| minsol_model_max('#skF_6','#skF_7','#skF_6')
| ~ model_max('#skF_6','#skF_7','#skF_6') ),
inference(superposition,[status(thm),theory(equality)],[c_12540,c_12565]) ).
tff(c_14064,plain,
~ model_max('#skF_6','#skF_7','#skF_6'),
inference(splitLeft,[status(thm)],[c_12572]) ).
tff(c_14086,plain,
$less('#skF_6','#skF_7'),
inference(resolution,[status(thm)],[c_129,c_14064]) ).
tff(c_14088,plain,
$less('#skF_6','#skF_7'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_14086]) ).
tff(c_14092,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_12491,c_14088]) ).
tff(c_14096,plain,
( minsol_model_max('#skF_6','#skF_7','#skF_6')
| model_max('#skF_6','#skF_7','#skE_2') ),
inference(splitRight,[status(thm)],[c_12572]) ).
tff(c_14105,plain,
model_max('#skF_6','#skF_7','#skE_2'),
inference(splitLeft,[status(thm)],[c_14096]) ).
tff(c_14126,plain,
max('#skF_6','#skF_7') = '#skE_2',
inference(resolution,[status(thm)],[c_14105,c_76]) ).
tff(c_14170,plain,
( ( '#skF_6' = '#skE_2' )
| $less('#skF_6','#skF_7') ),
inference(superposition,[status(thm),theory(equality)],[c_14126,c_81]) ).
tff(c_14188,plain,
'#skF_6' = '#skE_2',
inference(negUnitSimplification,[status(thm)],[c_12491,c_14170]) ).
tff(c_12461,plain,
$less('#skE_2','#skF_8'),
inference(splitRight,[status(thm)],[c_10379]) ).
tff(c_12496,plain,
$less('#skE_2','#skF_6'),
inference(demodulation,[status(thm),theory(equality)],[c_12462,c_12461]) ).
tff(c_14258,plain,
$less('#skE_2','#skE_2'),
inference(demodulation,[status(thm),theory(equality)],[c_14188,c_12496]) ).
tff(c_14306,plain,
$false,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_14258]) ).
tff(c_14312,plain,
minsol_model_max('#skF_6','#skF_7','#skF_6'),
inference(splitRight,[status(thm)],[c_14096]) ).
tff(c_12490,plain,
~ minsol_model_max('#skF_6','#skF_7','#skF_6'),
inference(demodulation,[status(thm),theory(equality)],[c_12462,c_10072]) ).
tff(c_14315,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_14312,c_12490]) ).
tff(c_14319,plain,
~ minsol_model_ub('#skF_3','#skF_4','#skF_5'),
inference(splitRight,[status(thm)],[c_64]) ).
tff(c_14343,plain,
~ minsol_model_ub('#skF_3','#skF_4','#skF_4'),
inference(demodulation,[status(thm),theory(equality)],[c_10067,c_14319]) ).
tff(c_14671,plain,
( $less('#skF_2'('#skF_3','#skF_4','#skF_4'),'#skF_4')
| $less('#skF_4','#skF_3')
| $less('#skF_4','#skF_4') ),
inference(resolution,[status(thm)],[c_14646,c_14343]) ).
tff(c_14674,plain,
( $less('#skF_2'('#skF_3','#skF_4','#skF_4'),'#skF_4')
| $less('#skF_4','#skF_3') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_14671]) ).
tff(c_14719,plain,
$less('#skF_2'('#skF_3','#skF_4','#skF_4'),'#skF_4'),
inference(negUnitSimplification,[status(thm)],[c_10068,c_14674]) ).
tff(c_14721,plain,
'#skF_2'('#skF_3','#skF_4','#skF_4') = '#skE_8',
inference(define,[status(thm),theory(equality)],[c_14719]) ).
tff(c_14720,plain,
$less('#skF_2'('#skF_3','#skF_4','#skF_4'),'#skF_4'),
inference(negUnitSimplification,[status(thm)],[c_10068,c_14674]) ).
tff(c_14728,plain,
$less('#skE_8','#skF_4'),
inference(demodulation,[status(thm),theory(equality)],[c_14721,c_14720]) ).
tff(c_14732,plain,
'#skF_2'('#skF_3','#skF_4','#skF_4') = '#skE_8',
inference(define,[status(thm),theory(equality)],[c_14719]) ).
tff(c_14748,plain,
( model_ub('#skF_3','#skF_4','#skE_8')
| minsol_model_ub('#skF_3','#skF_4','#skF_4')
| ~ model_ub('#skF_3','#skF_4','#skF_4') ),
inference(superposition,[status(thm),theory(equality)],[c_14732,c_65]) ).
tff(c_14789,plain,
~ model_ub('#skF_3','#skF_4','#skF_4'),
inference(splitLeft,[status(thm)],[c_14748]) ).
tff(c_14796,plain,
( $less('#skF_4','#skF_3')
| $less('#skF_4','#skF_4') ),
inference(resolution,[status(thm)],[c_9988,c_14789]) ).
tff(c_14798,plain,
$less('#skF_4','#skF_3'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_14796]) ).
tff(c_14800,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_10068,c_14798]) ).
tff(c_14804,plain,
( minsol_model_ub('#skF_3','#skF_4','#skF_4')
| model_ub('#skF_3','#skF_4','#skE_8') ),
inference(splitRight,[status(thm)],[c_14748]) ).
tff(c_14813,plain,
model_ub('#skF_3','#skF_4','#skE_8'),
inference(splitLeft,[status(thm)],[c_14804]) ).
tff(c_14825,plain,
~ $less('#skE_8','#skF_4'),
inference(resolution,[status(thm)],[c_14813,c_8852]) ).
tff(c_14837,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_14728,c_14825]) ).
tff(c_14843,plain,
minsol_model_ub('#skF_3','#skF_4','#skF_4'),
inference(splitRight,[status(thm)],[c_14804]) ).
tff(c_14846,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_14843,c_14343]) ).
tff(c_14850,plain,
~ $less('#skF_3','#skF_4'),
inference(splitRight,[status(thm)],[c_10034]) ).
tff(c_18874,plain,
! [X_7920a: $int,Y_7921a: $int,N_7922a: $int] :
( $less('#skF_2'(X_7920a,Y_7921a,N_7922a),N_7922a)
| minsol_model_ub(X_7920a,Y_7921a,N_7922a)
| ~ model_ub(X_7920a,Y_7921a,N_7922a) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_37]) ).
tff(c_18978,plain,
! [X_7948a: $int,Y_7949a: $int,Z_7950a: $int] :
( $less('#skF_2'(X_7948a,Y_7949a,Z_7950a),Z_7950a)
| minsol_model_ub(X_7948a,Y_7949a,Z_7950a)
| $less(Z_7950a,X_7948a)
| $less(Z_7950a,Y_7949a) ),
inference(resolution,[status(thm)],[c_9988,c_18874]) ).
tff(c_14873,plain,
minsol_model_ub('#skF_6','#skF_7','#skF_8'),
inference(splitRight,[status(thm)],[c_56]) ).
tff(c_14881,plain,
~ $less('#skF_8','#skF_6'),
inference(resolution,[status(thm)],[c_14873,c_8869]) ).
tff(c_15045,plain,
! [X_6302a: $int,Y_6303a: $int,N_6304a: $int] :
( $less('#skF_1'(X_6302a,Y_6303a,N_6304a),N_6304a)
| minsol_model_max(X_6302a,Y_6303a,N_6304a)
| ~ model_max(X_6302a,Y_6303a,N_6304a) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_28]) ).
tff(c_15097,plain,
! [X_6321a: $int,Y_6322a: $int] :
( $less('#skF_1'(X_6321a,Y_6322a,Y_6322a),Y_6322a)
| minsol_model_max(X_6321a,Y_6322a,Y_6322a)
| $less(Y_6322a,X_6321a) ),
inference(resolution,[status(thm)],[c_107,c_15045]) ).
tff(c_14849,plain,
'#skF_5' = '#skF_3',
inference(splitRight,[status(thm)],[c_10034]) ).
tff(c_14888,plain,
( ~ minsol_model_ub('#skF_3','#skF_4','#skF_3')
| ~ minsol_model_max('#skF_6','#skF_7','#skF_8') ),
inference(demodulation,[status(thm),theory(equality)],[c_14849,c_64]) ).
tff(c_14893,plain,
~ minsol_model_max('#skF_6','#skF_7','#skF_8'),
inference(splitLeft,[status(thm)],[c_14888]) ).
tff(c_15131,plain,
( ( '#skF_8' != '#skF_7' )
| $less('#skF_1'('#skF_6','#skF_8','#skF_8'),'#skF_8')
| $less('#skF_8','#skF_6') ),
inference(resolution,[status(thm)],[c_15097,c_14893]) ).
tff(c_15317,plain,
( ( '#skF_8' != '#skF_7' )
| $less('#skF_1'('#skF_6','#skF_8','#skF_8'),'#skF_8') ),
inference(negUnitSimplification,[status(thm)],[c_14881,c_15131]) ).
tff(c_15319,plain,
'#skF_1'('#skF_6','#skF_8','#skF_8') = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_15317]) ).
tff(c_15318,plain,
( ( '#skF_8' != '#skF_7' )
| $less('#skF_1'('#skF_6','#skF_8','#skF_8'),'#skF_8') ),
inference(negUnitSimplification,[status(thm)],[c_14881,c_15131]) ).
tff(c_15326,plain,
( ( '#skF_8' != '#skF_7' )
| $less('#skE_1','#skF_8') ),
inference(demodulation,[status(thm),theory(equality)],[c_15319,c_15318]) ).
tff(c_15328,plain,
'#skF_8' != '#skF_7',
inference(splitLeft,[status(thm)],[c_15326]) ).
tff(c_14883,plain,
~ $less('#skF_8','#skF_7'),
inference(resolution,[status(thm)],[c_14873,c_8863]) ).
tff(c_15138,plain,
! [X_6335a: $int,Y_6336a: $int] :
( $less('#skF_1'(X_6335a,Y_6336a,X_6335a),X_6335a)
| minsol_model_max(X_6335a,Y_6336a,X_6335a)
| $less(X_6335a,Y_6336a) ),
inference(resolution,[status(thm)],[c_129,c_15045]) ).
tff(c_15169,plain,
( ( '#skF_8' != '#skF_6' )
| $less('#skF_1'('#skF_8','#skF_7','#skF_8'),'#skF_8')
| $less('#skF_8','#skF_7') ),
inference(resolution,[status(thm)],[c_15138,c_14893]) ).
tff(c_15279,plain,
( ( '#skF_8' != '#skF_6' )
| $less('#skF_1'('#skF_8','#skF_7','#skF_8'),'#skF_8') ),
inference(negUnitSimplification,[status(thm)],[c_14883,c_15169]) ).
tff(c_15281,plain,
'#skF_1'('#skF_8','#skF_7','#skF_8') = '#skE_2',
inference(define,[status(thm),theory(equality)],[c_15279]) ).
tff(c_15280,plain,
( ( '#skF_8' != '#skF_6' )
| $less('#skF_1'('#skF_8','#skF_7','#skF_8'),'#skF_8') ),
inference(negUnitSimplification,[status(thm)],[c_14883,c_15169]) ).
tff(c_15288,plain,
( ( '#skF_8' != '#skF_6' )
| $less('#skE_2','#skF_8') ),
inference(demodulation,[status(thm),theory(equality)],[c_15281,c_15280]) ).
tff(c_15290,plain,
'#skF_8' != '#skF_6',
inference(splitLeft,[status(thm)],[c_15288]) ).
tff(c_15022,plain,
! [X_6286a: $int,Y_6287a: $int,Z_6288a: $int,N_6289a: $int] :
( ~ model_ub(X_6286a,Y_6287a,Z_6288a)
| ~ minsol_model_ub(X_6286a,Y_6287a,N_6289a)
| ~ $less(Z_6288a,N_6289a) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_32]) ).
tff(c_15176,plain,
! [X_6341a: $int,Y_6342a: $int,N_6343a: $int,Z_6344a: $int] :
( ~ minsol_model_ub(X_6341a,Y_6342a,N_6343a)
| ~ $less(Z_6344a,N_6343a)
| $less(Z_6344a,X_6341a)
| $less(Z_6344a,Y_6342a) ),
inference(resolution,[status(thm)],[c_9988,c_15022]) ).
tff(c_15181,plain,
! [Z_6344a: $int] :
( ~ $less(Z_6344a,'#skF_8')
| $less(Z_6344a,'#skF_6')
| $less(Z_6344a,'#skF_7') ),
inference(resolution,[status(thm)],[c_9976,c_15176]) ).
tff(c_15182,plain,
( $lesseq('#skF_8','#skF_6')
| $lesseq('#skF_8','#skF_7') ),
inference(quantifierElimination,[status(thm),theory('LIA')],[c_15181]) ).
tff(c_15184,plain,
( ~ $less('#skF_6','#skF_8')
| ~ $less('#skF_7','#skF_8') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_15182]) ).
tff(c_15329,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_15328,c_15290,c_15184,c_14883,c_14881]) ).
tff(c_15333,plain,
'#skF_8' = '#skF_7',
inference(splitRight,[status(thm)],[c_15326]) ).
tff(c_15423,plain,
~ $less('#skF_7','#skF_6'),
inference(demodulation,[status(thm),theory(equality)],[c_15333,c_14881]) ).
tff(c_15336,plain,
'#skF_1'('#skF_6','#skF_8','#skF_8') = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_15317]) ).
tff(c_15361,plain,
( model_max('#skF_6','#skF_8','#skE_1')
| minsol_model_max('#skF_6','#skF_8','#skF_8')
| ~ model_max('#skF_6','#skF_8','#skF_8') ),
inference(superposition,[status(thm),theory(equality)],[c_15336,c_69]) ).
tff(c_16464,plain,
( model_max('#skF_6','#skF_7','#skE_1')
| minsol_model_max('#skF_6','#skF_7','#skF_7')
| ~ model_max('#skF_6','#skF_7','#skF_7') ),
inference(demodulation,[status(thm),theory(equality)],[c_15333,c_15333,c_15333,c_15333,c_15333,c_15361]) ).
tff(c_16532,plain,
~ model_max('#skF_6','#skF_7','#skF_7'),
inference(splitLeft,[status(thm)],[c_16464]) ).
tff(c_16551,plain,
$less('#skF_7','#skF_6'),
inference(resolution,[status(thm)],[c_107,c_16532]) ).
tff(c_16553,plain,
$less('#skF_7','#skF_6'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_16551]) ).
tff(c_16554,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_15423,c_16553]) ).
tff(c_16558,plain,
( minsol_model_max('#skF_6','#skF_7','#skF_7')
| model_max('#skF_6','#skF_7','#skE_1') ),
inference(splitRight,[status(thm)],[c_16464]) ).
tff(c_16708,plain,
model_max('#skF_6','#skF_7','#skE_1'),
inference(splitLeft,[status(thm)],[c_16558]) ).
tff(c_16729,plain,
max('#skF_6','#skF_7') = '#skE_1',
inference(resolution,[status(thm)],[c_16708,c_76]) ).
tff(c_16789,plain,
( ( '#skF_7' = '#skE_1' )
| $less('#skF_7','#skF_6') ),
inference(superposition,[status(thm),theory(equality)],[c_80,c_16729]) ).
tff(c_16793,plain,
'#skF_7' = '#skE_1',
inference(negUnitSimplification,[status(thm)],[c_15423,c_16789]) ).
tff(c_15332,plain,
$less('#skE_1','#skF_8'),
inference(splitRight,[status(thm)],[c_15326]) ).
tff(c_15428,plain,
$less('#skE_1','#skF_7'),
inference(demodulation,[status(thm),theory(equality)],[c_15333,c_15332]) ).
tff(c_16863,plain,
$less('#skE_1','#skE_1'),
inference(demodulation,[status(thm),theory(equality)],[c_16793,c_15428]) ).
tff(c_16913,plain,
$false,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_16863]) ).
tff(c_16919,plain,
minsol_model_max('#skF_6','#skF_7','#skF_7'),
inference(splitRight,[status(thm)],[c_16558]) ).
tff(c_15422,plain,
~ minsol_model_max('#skF_6','#skF_7','#skF_7'),
inference(demodulation,[status(thm),theory(equality)],[c_15333,c_14893]) ).
tff(c_16922,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_16919,c_15422]) ).
tff(c_16926,plain,
'#skF_8' = '#skF_6',
inference(splitRight,[status(thm)],[c_15288]) ).
tff(c_16991,plain,
~ $less('#skF_6','#skF_7'),
inference(demodulation,[status(thm),theory(equality)],[c_16926,c_14883]) ).
tff(c_16927,plain,
'#skF_1'('#skF_8','#skF_7','#skF_8') = '#skE_2',
inference(define,[status(thm),theory(equality)],[c_15279]) ).
tff(c_16943,plain,
( model_max('#skF_8','#skF_7','#skE_2')
| minsol_model_max('#skF_8','#skF_7','#skF_8')
| ~ model_max('#skF_8','#skF_7','#skF_8') ),
inference(superposition,[status(thm),theory(equality)],[c_16927,c_69]) ).
tff(c_17090,plain,
( model_max('#skF_6','#skF_7','#skE_2')
| minsol_model_max('#skF_6','#skF_7','#skF_6')
| ~ model_max('#skF_6','#skF_7','#skF_6') ),
inference(demodulation,[status(thm),theory(equality)],[c_16926,c_16926,c_16926,c_16926,c_16926,c_16943]) ).
tff(c_17098,plain,
~ model_max('#skF_6','#skF_7','#skF_6'),
inference(splitLeft,[status(thm)],[c_17090]) ).
tff(c_17114,plain,
$less('#skF_6','#skF_7'),
inference(resolution,[status(thm)],[c_129,c_17098]) ).
tff(c_17116,plain,
$less('#skF_6','#skF_7'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_17114]) ).
tff(c_17120,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_16991,c_17116]) ).
tff(c_17124,plain,
( minsol_model_max('#skF_6','#skF_7','#skF_6')
| model_max('#skF_6','#skF_7','#skE_2') ),
inference(splitRight,[status(thm)],[c_17090]) ).
tff(c_18476,plain,
model_max('#skF_6','#skF_7','#skE_2'),
inference(splitLeft,[status(thm)],[c_17124]) ).
tff(c_18497,plain,
max('#skF_6','#skF_7') = '#skE_2',
inference(resolution,[status(thm)],[c_18476,c_76]) ).
tff(c_18541,plain,
( ( '#skF_6' = '#skE_2' )
| $less('#skF_6','#skF_7') ),
inference(superposition,[status(thm),theory(equality)],[c_18497,c_81]) ).
tff(c_18559,plain,
'#skF_6' = '#skE_2',
inference(negUnitSimplification,[status(thm)],[c_16991,c_18541]) ).
tff(c_16925,plain,
$less('#skE_2','#skF_8'),
inference(splitRight,[status(thm)],[c_15288]) ).
tff(c_16996,plain,
$less('#skE_2','#skF_6'),
inference(demodulation,[status(thm),theory(equality)],[c_16926,c_16925]) ).
tff(c_18629,plain,
$less('#skE_2','#skE_2'),
inference(demodulation,[status(thm),theory(equality)],[c_18559,c_16996]) ).
tff(c_18677,plain,
$false,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_18629]) ).
tff(c_18683,plain,
minsol_model_max('#skF_6','#skF_7','#skF_6'),
inference(splitRight,[status(thm)],[c_17124]) ).
tff(c_16990,plain,
~ minsol_model_max('#skF_6','#skF_7','#skF_6'),
inference(demodulation,[status(thm),theory(equality)],[c_16926,c_14893]) ).
tff(c_18686,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_18683,c_16990]) ).
tff(c_18690,plain,
~ minsol_model_ub('#skF_3','#skF_4','#skF_3'),
inference(splitRight,[status(thm)],[c_14888]) ).
tff(c_19003,plain,
( $less('#skF_2'('#skF_3','#skF_4','#skF_3'),'#skF_3')
| $less('#skF_3','#skF_3')
| $less('#skF_3','#skF_4') ),
inference(resolution,[status(thm)],[c_18978,c_18690]) ).
tff(c_19006,plain,
( $less('#skF_2'('#skF_3','#skF_4','#skF_3'),'#skF_3')
| $less('#skF_3','#skF_4') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_19003]) ).
tff(c_19051,plain,
$less('#skF_2'('#skF_3','#skF_4','#skF_3'),'#skF_3'),
inference(negUnitSimplification,[status(thm)],[c_14850,c_19006]) ).
tff(c_19053,plain,
'#skF_2'('#skF_3','#skF_4','#skF_3') = '#skE_7',
inference(define,[status(thm),theory(equality)],[c_19051]) ).
tff(c_19052,plain,
$less('#skF_2'('#skF_3','#skF_4','#skF_3'),'#skF_3'),
inference(negUnitSimplification,[status(thm)],[c_14850,c_19006]) ).
tff(c_19060,plain,
$less('#skE_7','#skF_3'),
inference(demodulation,[status(thm),theory(equality)],[c_19053,c_19052]) ).
tff(c_19063,plain,
'#skF_2'('#skF_3','#skF_4','#skF_3') = '#skE_7',
inference(define,[status(thm),theory(equality)],[c_19051]) ).
tff(c_19079,plain,
( model_ub('#skF_3','#skF_4','#skE_7')
| minsol_model_ub('#skF_3','#skF_4','#skF_3')
| ~ model_ub('#skF_3','#skF_4','#skF_3') ),
inference(superposition,[status(thm),theory(equality)],[c_19063,c_65]) ).
tff(c_19112,plain,
~ model_ub('#skF_3','#skF_4','#skF_3'),
inference(splitLeft,[status(thm)],[c_19079]) ).
tff(c_19119,plain,
( $less('#skF_3','#skF_3')
| $less('#skF_3','#skF_4') ),
inference(resolution,[status(thm)],[c_9988,c_19112]) ).
tff(c_19121,plain,
$less('#skF_3','#skF_4'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_19119]) ).
tff(c_19123,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_14850,c_19121]) ).
tff(c_19127,plain,
( minsol_model_ub('#skF_3','#skF_4','#skF_3')
| model_ub('#skF_3','#skF_4','#skE_7') ),
inference(splitRight,[status(thm)],[c_19079]) ).
tff(c_19136,plain,
model_ub('#skF_3','#skF_4','#skE_7'),
inference(splitLeft,[status(thm)],[c_19127]) ).
tff(c_19145,plain,
~ $less('#skE_7','#skF_3'),
inference(resolution,[status(thm)],[c_19136,c_8854]) ).
tff(c_19158,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_19060,c_19145]) ).
tff(c_19164,plain,
minsol_model_ub('#skF_3','#skF_4','#skF_3'),
inference(splitRight,[status(thm)],[c_19127]) ).
tff(c_19167,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_19164,c_18690]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : NUM858_1 : TPTP v8.1.2. Released v4.1.0.
% 0.08/0.15 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.15/0.36 % Computer : n031.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Thu Aug 3 15:44:29 EDT 2023
% 0.15/0.37 % CPUTime :
% 11.68/3.95 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 11.68/4.03
% 11.68/4.03 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 12.63/4.12
% 12.63/4.12 Inference rules
% 12.63/4.12 ----------------------
% 12.63/4.12 #Ref : 0
% 12.63/4.12 #Sup : 2095
% 12.63/4.12 #Fact : 0
% 12.63/4.12 #Define : 35
% 12.63/4.12 #Split : 139
% 12.63/4.12 #Chain : 0
% 12.63/4.12 #Close : 10
% 12.63/4.12
% 12.63/4.12 Ordering : LPO
% 12.63/4.12
% 12.63/4.12 Simplification rules
% 12.63/4.12 ----------------------
% 12.63/4.12 #Subsume : 392
% 12.63/4.12 #Demod : 1783
% 12.63/4.12 #Tautology : 1179
% 12.63/4.12 #SimpNegUnit : 93
% 12.63/4.12 #BackRed : 510
% 12.63/4.12
% 12.63/4.12 #Partial instantiations: 0
% 12.63/4.12 #Strategies tried : 1
% 12.63/4.12
% 12.63/4.12 Timing (in seconds)
% 12.63/4.12 ----------------------
% 12.63/4.12 Preprocessing : 0.57
% 12.63/4.12 Parsing : 0.30
% 12.63/4.12 CNF conversion : 0.04
% 12.63/4.12 Main loop : 2.22
% 12.63/4.12 Inferencing : 0.57
% 12.63/4.12 Reduction : 0.56
% 12.63/4.12 Demodulation : 0.40
% 12.63/4.12 BG Simplification : 0.23
% 12.63/4.12 Subsumption : 0.47
% 12.63/4.12 Abstraction : 0.09
% 12.63/4.12 MUC search : 0.03
% 12.63/4.12 Cooper : 0.14
% 12.63/4.12 Total : 2.98
% 12.63/4.12 Index Insertion : 0.00
% 12.63/4.12 Index Deletion : 0.00
% 12.63/4.12 Index Matching : 0.00
% 12.63/4.12 BG Taut test : 0.00
%------------------------------------------------------------------------------