TSTP Solution File: NUM860_1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : NUM860_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 : n016.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 10:52:57 EDT 2023
% Result : Theorem 14.79s 4.63s
% Output : CNFRefutation 16.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 42
% Syntax : Number of formulae : 997 ( 618 unt; 33 typ; 0 def)
% Number of atoms : 1523 ( 229 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 1023 ( 464 ~; 546 |; 4 &)
% ( 7 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number arithmetic : 1304 ( 860 atm; 0 fun; 0 num; 444 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 : 28 ( 28 usr; 23 con; 0-3 aty)
% Number of variables : 444 (; 443 !; 1 ?; 444 :)
% 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('#skE_11',type,
'#skE_11': $int ).
tff('#skE_12',type,
'#skE_12': $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_13',type,
'#skE_13': $int ).
tff('#skE_10',type,
'#skE_10': $int ).
tff('#skE_5',type,
'#skE_5': $int ).
tff('#skE_15',type,
'#skE_15': $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_16',type,
'#skE_16': $int ).
tff('#skE_17',type,
'#skE_17': $int ).
tff('#skE_3',type,
'#skE_3': $int ).
tff('#skF_7',type,
'#skF_7': $int ).
tff('#skE_9',type,
'#skE_9': $int ).
tff('#skF_9',type,
'#skF_9': $int ).
tff('#skE_14',type,
'#skE_14': $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_49,axiom,
! [Xa: $int,Ya: $int] :
( ( max(Xa,Ya) = Ya )
| ~ $lesseq(Xa,Ya) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',max_2) ).
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(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_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_69,axiom,
! [Xa: $int,Ya: $int,Na: $int] :
( model_ub(Xa,Ya,Na)
<=> ? [Za: $int] :
( ub(Xa,Ya,Za)
& $lesseq(summation(Za),Na) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',model_ub_3) ).
tff(f_61,axiom,
! [Xa: $int,Ya: $int,Na: $int] :
( model_max(Xa,Ya,Na)
<=> $lesseq(summation(max(Xa,Ya)),Na) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',model_max_3) ).
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_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_38,axiom,
! [Xa: $int,Ya: $int] :
( $lesseq(Xa,Ya)
<=> $lesseq(summation(Xa),summation(Ya)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',summation_monotone) ).
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_87,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_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_88,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_58,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_276,plain,
minsol_model_ub('#skF_7','#skF_8','#skF_9'),
inference(splitLeft,[status(thm)],[c_58]) ).
tff(c_73,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_25,plain,
! [X_13a: $int,Y_14a: $int,N_15a: $int] :
( $lesseq(summation('#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_173,plain,
! [N_120a: $int,X_121a: $int,Y_122a: $int] :
( ~ $less(N_120a,summation('#skF_1'(X_121a,Y_122a,N_120a)))
| ~ model_ub(X_121a,Y_122a,N_120a) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_25]) ).
tff(c_178,plain,
! [N_27a: $int,X_25a: $int,Y_26a: $int] :
( ~ $less(N_27a,summation('#skF_1'(X_25a,Y_26a,N_27a)))
| ~ minsol_model_ub(X_25a,Y_26a,N_27a) ),
inference(resolution,[status(thm)],[c_73,c_173]) ).
tff(c_290,plain,
~ $less('#skF_9',summation('#skF_1'('#skF_7','#skF_8','#skF_9'))),
inference(resolution,[status(thm)],[c_276,c_178]) ).
tff(c_306,plain,
'#skF_1'('#skF_7','#skF_8','#skF_9') = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_290]) ).
tff(c_305,plain,
~ $less('#skF_9',summation('#skF_1'('#skF_7','#skF_8','#skF_9'))),
inference(resolution,[status(thm)],[c_276,c_178]) ).
tff(c_316,plain,
~ $less('#skF_9',summation('#skE_1')),
inference(demodulation,[status(thm),theory(equality)],[c_306,c_305]) ).
tff(c_328,plain,
summation('#skE_1') = '#skE_2',
inference(define,[status(thm),theory(equality)],[c_316]) ).
tff(c_19,plain,
! [X_10a: $int,Y_11a: $int,N_12a: $int] :
( model_max(X_10a,Y_11a,N_12a)
| ~ $lesseq(summation(max(X_10a,Y_11a)),N_12a) ),
inference(cnfTransformation,[status(thm)],[f_61]) ).
tff(c_82,plain,
! [X_10a: $int,Y_11a: $int,N_12a: $int] :
( model_max(X_10a,Y_11a,N_12a)
| $less(N_12a,summation(max(X_10a,Y_11a))) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_19]) ).
tff(c_34,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_213,plain,
! [X_156a: $int,Y_157a: $int,N_158a: $int] :
( $less('#skF_2'(X_156a,Y_157a,N_158a),N_158a)
| minsol_model_max(X_156a,Y_157a,N_158a)
| ~ model_max(X_156a,Y_157a,N_158a) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_34]) ).
tff(c_248,plain,
! [X_172a: $int,Y_173a: $int,N_174a: $int] :
( $less('#skF_2'(X_172a,Y_173a,N_174a),N_174a)
| minsol_model_max(X_172a,Y_173a,N_174a)
| $less(N_174a,summation(max(X_172a,Y_173a))) ),
inference(resolution,[status(thm)],[c_82,c_213]) ).
tff(c_66,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_193,plain,
~ minsol_model_max('#skF_7','#skF_8','#skF_9'),
inference(splitLeft,[status(thm)],[c_66]) ).
tff(c_266,plain,
( $less('#skF_2'('#skF_7','#skF_8','#skF_9'),'#skF_9')
| $less('#skF_9',summation(max('#skF_7','#skF_8'))) ),
inference(resolution,[status(thm)],[c_248,c_193]) ).
tff(c_467,plain,
max('#skF_7','#skF_8') = '#skE_4',
inference(define,[status(thm),theory(equality)],[c_266]) ).
tff(c_499,plain,
( ( '#skF_8' = '#skE_4' )
| $less('#skF_8','#skF_7') ),
inference(superposition,[status(thm),theory(equality)],[c_87,c_467]) ).
tff(c_505,plain,
$less('#skF_8','#skF_7'),
inference(splitLeft,[status(thm)],[c_499]) ).
tff(c_490,plain,
( ( '#skF_7' = '#skE_4' )
| $less('#skF_7','#skF_8') ),
inference(superposition,[status(thm),theory(equality)],[c_467,c_88]) ).
tff(c_501,plain,
$less('#skF_7','#skF_8'),
inference(splitLeft,[status(thm)],[c_490]) ).
tff(c_528,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_505,c_501]) ).
tff(c_531,plain,
'#skF_8' = '#skE_4',
inference(splitRight,[status(thm)],[c_499]) ).
tff(c_532,plain,
~ $less('#skF_8','#skF_7'),
inference(splitRight,[status(thm)],[c_499]) ).
tff(c_577,plain,
~ $less('#skE_4','#skF_7'),
inference(demodulation,[status(thm),theory(equality)],[c_531,c_532]) ).
tff(c_450,plain,
max('#skF_7','#skF_8') = '#skE_4',
inference(define,[status(thm),theory(equality)],[c_266]) ).
tff(c_449,plain,
'#skF_2'('#skF_7','#skF_8','#skF_9') = '#skE_3',
inference(define,[status(thm),theory(equality)],[c_266]) ).
tff(c_448,plain,
( $less('#skF_2'('#skF_7','#skF_8','#skF_9'),'#skF_9')
| $less('#skF_9',summation(max('#skF_7','#skF_8'))) ),
inference(resolution,[status(thm)],[c_248,c_193]) ).
tff(c_464,plain,
( $less('#skE_3','#skF_9')
| $less('#skF_9',summation('#skE_4')) ),
inference(demodulation,[status(thm),theory(equality)],[c_450,c_449,c_448]) ).
tff(c_724,plain,
summation('#skE_4') = '#skE_5',
inference(define,[status(thm),theory(equality)],[c_464]) ).
tff(c_273,plain,
minsol_model_ub('#skF_7','#skF_8','#skF_9'),
inference(splitLeft,[status(thm)],[c_58]) ).
tff(c_572,plain,
minsol_model_ub('#skF_7','#skE_4','#skF_9'),
inference(demodulation,[status(thm),theory(equality)],[c_531,c_273]) ).
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_84,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_22,plain,
! [X_13a: $int,Y_14a: $int,N_15a: $int,Z_18a: $int] :
( model_ub(X_13a,Y_14a,N_15a)
| ~ $lesseq(summation(Z_18a),N_15a)
| ~ ub(X_13a,Y_14a,Z_18a) ),
inference(cnfTransformation,[status(thm)],[f_69]) ).
tff(c_206,plain,
! [X_148a: $int,Y_149a: $int,N_150a: $int,Z_151a: $int] :
( model_ub(X_148a,Y_149a,N_150a)
| $less(N_150a,summation(Z_151a))
| ~ ub(X_148a,Y_149a,Z_151a) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_22]) ).
tff(c_230,plain,
! [X_162a: $int,Y_163a: $int,N_164a: $int,Z_165a: $int] :
( model_ub(X_162a,Y_163a,N_164a)
| $less(N_164a,summation(Z_165a))
| $less(Z_165a,X_162a)
| $less(Z_165a,Y_163a) ),
inference(resolution,[status(thm)],[c_84,c_206]) ).
tff(c_38,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_74,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_38]) ).
tff(c_1225,plain,
! [X_485a: $int,N_482a: $int,N_484a: $int,Z_481a: $int,Y_483a: $int] :
( ~ minsol_model_ub(X_485a,Y_483a,N_482a)
| ~ $less(N_484a,N_482a)
| $less(N_484a,summation(Z_481a))
| $less(Z_481a,X_485a)
| $less(Z_481a,Y_483a) ),
inference(resolution,[status(thm)],[c_230,c_74]) ).
tff(c_1231,plain,
! [N_486a: $int,Z_487a: $int] :
( ~ $less(N_486a,'#skF_9')
| $less(N_486a,summation(Z_487a))
| $less(Z_487a,'#skF_7')
| $less(Z_487a,'#skE_4') ),
inference(resolution,[status(thm)],[c_572,c_1225]) ).
tff(c_1248,plain,
! [N_486a: $int] :
( ~ $less(N_486a,'#skF_9')
| $less(N_486a,'#skE_5')
| $less('#skE_4','#skF_7')
| $less('#skE_4','#skE_4') ),
inference(superposition,[status(thm),theory(equality)],[c_724,c_1231]) ).
tff(c_1250,plain,
! [N_486a: $int] :
( ~ $less(N_486a,'#skF_9')
| $less(N_486a,'#skE_5')
| $less('#skE_4','#skF_7') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_1248]) ).
tff(c_1253,plain,
! [N_486a: $int] :
( ~ $less(N_486a,'#skF_9')
| $less(N_486a,'#skE_5') ),
inference(negUnitSimplification,[status(thm)],[c_577,c_1250]) ).
tff(c_1254,plain,
$lesseq('#skF_9','#skE_5'),
inference(quantifierElimination,[status(thm),theory('LIA')],[c_1253]) ).
tff(c_1256,plain,
~ $less('#skE_5','#skF_9'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_1254]) ).
tff(c_728,plain,
summation('#skE_4') = '#skE_5',
inference(define,[status(thm),theory(equality)],[c_464]) ).
tff(c_329,plain,
summation('#skE_1') = '#skE_2',
inference(define,[status(thm),theory(equality)],[c_316]) ).
tff(c_1,plain,
! [X_1a: $int,Y_2a: $int] :
( $lesseq(summation(X_1a),summation(Y_2a))
| ~ $lesseq(X_1a,Y_2a) ),
inference(cnfTransformation,[status(thm)],[f_38]) ).
tff(c_90,plain,
! [Y_2a: $int,X_1a: $int] :
( ~ $less(summation(Y_2a),summation(X_1a))
| $less(Y_2a,X_1a) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_1]) ).
tff(c_363,plain,
! [X_1a: $int] :
( ~ $less('#skE_2',summation(X_1a))
| $less('#skE_1',X_1a) ),
inference(superposition,[status(thm),theory(equality)],[c_329,c_90]) ).
tff(c_777,plain,
( ~ $less('#skE_2','#skE_5')
| $less('#skE_1','#skE_4') ),
inference(superposition,[status(thm),theory(equality)],[c_728,c_363]) ).
tff(c_825,plain,
~ $less('#skE_2','#skE_5'),
inference(splitLeft,[status(thm)],[c_777]) ).
tff(c_3,plain,
! [X_1a: $int,Y_2a: $int] :
( ~ $lesseq(summation(X_1a),summation(Y_2a))
| $lesseq(X_1a,Y_2a) ),
inference(cnfTransformation,[status(thm)],[f_38]) ).
tff(c_89,plain,
! [Y_2a: $int,X_1a: $int] :
( $less(summation(Y_2a),summation(X_1a))
| ~ $less(Y_2a,X_1a) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_3]) ).
tff(c_357,plain,
! [X_1a: $int] :
( $less('#skE_2',summation(X_1a))
| ~ $less('#skE_1',X_1a) ),
inference(superposition,[status(thm),theory(equality)],[c_329,c_89]) ).
tff(c_779,plain,
( $less('#skE_2','#skE_5')
| ~ $less('#skE_1','#skE_4') ),
inference(superposition,[status(thm),theory(equality)],[c_728,c_357]) ).
tff(c_830,plain,
~ $less('#skE_1','#skE_4'),
inference(negUnitSimplification,[status(thm)],[c_825,c_779]) ).
tff(c_366,plain,
! [Y_2a: $int] :
( ~ $less(summation(Y_2a),'#skE_2')
| $less(Y_2a,'#skE_1') ),
inference(superposition,[status(thm),theory(equality)],[c_329,c_90]) ).
tff(c_773,plain,
( ~ $less('#skE_5','#skE_2')
| $less('#skE_4','#skE_1') ),
inference(superposition,[status(thm),theory(equality)],[c_728,c_366]) ).
tff(c_802,plain,
~ $less('#skE_5','#skE_2'),
inference(splitLeft,[status(thm)],[c_773]) ).
tff(c_360,plain,
! [Y_2a: $int] :
( $less(summation(Y_2a),'#skE_2')
| ~ $less(Y_2a,'#skE_1') ),
inference(superposition,[status(thm),theory(equality)],[c_329,c_89]) ).
tff(c_775,plain,
( $less('#skE_5','#skE_2')
| ~ $less('#skE_4','#skE_1') ),
inference(superposition,[status(thm),theory(equality)],[c_728,c_360]) ).
tff(c_823,plain,
~ $less('#skE_4','#skE_1'),
inference(negUnitSimplification,[status(thm)],[c_802,c_775]) ).
tff(c_325,plain,
summation('#skE_1') = '#skE_2',
inference(define,[status(thm),theory(equality)],[c_316]) ).
tff(c_781,plain,
( ( '#skE_5' = '#skE_2' )
| ( '#skE_4' != '#skE_1' ) ),
inference(superposition,[status(thm),theory(equality)],[c_728,c_325]) ).
tff(c_800,plain,
'#skE_4' != '#skE_1',
inference(splitLeft,[status(thm)],[c_781]) ).
tff(c_831,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_830,c_823,c_800]) ).
tff(c_834,plain,
$less('#skE_1','#skE_4'),
inference(splitRight,[status(thm)],[c_777]) ).
tff(c_579,plain,
minsol_model_ub('#skF_7','#skE_4','#skF_9'),
inference(demodulation,[status(thm),theory(equality)],[c_531,c_273]) ).
tff(c_381,plain,
'#skF_1'('#skF_7','#skF_8','#skF_9') = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_290]) ).
tff(c_79,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_404,plain,
( ub('#skF_7','#skF_8','#skE_1')
| ~ model_ub('#skF_7','#skF_8','#skF_9') ),
inference(superposition,[status(thm),theory(equality)],[c_381,c_79]) ).
tff(c_921,plain,
( ub('#skF_7','#skE_4','#skE_1')
| ~ model_ub('#skF_7','#skE_4','#skF_9') ),
inference(demodulation,[status(thm),theory(equality)],[c_531,c_531,c_404]) ).
tff(c_929,plain,
~ model_ub('#skF_7','#skE_4','#skF_9'),
inference(splitLeft,[status(thm)],[c_921]) ).
tff(c_935,plain,
~ minsol_model_ub('#skF_7','#skE_4','#skF_9'),
inference(resolution,[status(thm)],[c_73,c_929]) ).
tff(c_942,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_579,c_935]) ).
tff(c_949,plain,
ub('#skF_7','#skE_4','#skE_1'),
inference(splitRight,[status(thm)],[c_921]) ).
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_86,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_955,plain,
~ $less('#skE_1','#skE_4'),
inference(resolution,[status(thm)],[c_949,c_86]) ).
tff(c_968,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_834,c_955]) ).
tff(c_972,plain,
$less('#skE_5','#skE_2'),
inference(splitRight,[status(thm)],[c_773]) ).
tff(c_319,plain,
summation('#skE_1') = '#skE_2',
inference(define,[status(thm),theory(equality)],[c_316]) ).
tff(c_318,plain,
~ $less('#skF_9',summation('#skE_1')),
inference(demodulation,[status(thm),theory(equality)],[c_306,c_305]) ).
tff(c_326,plain,
~ $less('#skF_9','#skE_2'),
inference(demodulation,[status(thm),theory(equality)],[c_319,c_318]) ).
tff(c_1257,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_1256,c_972,c_326]) ).
tff(c_1261,plain,
'#skE_4' = '#skE_1',
inference(splitRight,[status(thm)],[c_781]) ).
tff(c_461,plain,
max('#skF_7','#skF_8') = '#skE_4',
inference(define,[status(thm),theory(equality)],[c_266]) ).
tff(c_563,plain,
max('#skF_7','#skE_4') = '#skE_4',
inference(demodulation,[status(thm),theory(equality)],[c_531,c_461]) ).
tff(c_1363,plain,
max('#skF_7','#skE_1') = '#skE_1',
inference(demodulation,[status(thm),theory(equality)],[c_1261,c_1261,c_563]) ).
tff(c_458,plain,
'#skF_2'('#skF_7','#skF_8','#skF_9') = '#skE_3',
inference(define,[status(thm),theory(equality)],[c_266]) ).
tff(c_656,plain,
'#skF_2'('#skF_7','#skE_4','#skF_9') = '#skE_3',
inference(demodulation,[status(thm),theory(equality)],[c_531,c_458]) ).
tff(c_75,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_672,plain,
( model_max('#skF_7','#skE_4','#skE_3')
| minsol_model_max('#skF_7','#skE_4','#skF_9')
| ~ model_max('#skF_7','#skE_4','#skF_9') ),
inference(superposition,[status(thm),theory(equality)],[c_656,c_75]) ).
tff(c_1850,plain,
( model_max('#skF_7','#skE_1','#skE_3')
| minsol_model_max('#skF_7','#skE_1','#skF_9')
| ~ model_max('#skF_7','#skE_1','#skF_9') ),
inference(demodulation,[status(thm),theory(equality)],[c_1261,c_1261,c_1261,c_672]) ).
tff(c_1858,plain,
~ model_max('#skF_7','#skE_1','#skF_9'),
inference(splitLeft,[status(thm)],[c_1850]) ).
tff(c_1861,plain,
$less('#skF_9',summation(max('#skF_7','#skE_1'))),
inference(resolution,[status(thm)],[c_82,c_1858]) ).
tff(c_1866,plain,
$less('#skF_9','#skE_2'),
inference(demodulation,[status(thm),theory(equality)],[c_328,c_1363,c_1861]) ).
tff(c_1868,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_326,c_1866]) ).
tff(c_1872,plain,
( minsol_model_max('#skF_7','#skE_1','#skF_9')
| model_max('#skF_7','#skE_1','#skE_3') ),
inference(splitRight,[status(thm)],[c_1850]) ).
tff(c_1881,plain,
model_max('#skF_7','#skE_1','#skE_3'),
inference(splitLeft,[status(thm)],[c_1872]) ).
tff(c_16,plain,
! [X_10a: $int,Y_11a: $int,N_12a: $int] :
( $lesseq(summation(max(X_10a,Y_11a)),N_12a)
| ~ model_max(X_10a,Y_11a,N_12a) ),
inference(cnfTransformation,[status(thm)],[f_61]) ).
tff(c_83,plain,
! [N_12a: $int,X_10a: $int,Y_11a: $int] :
( ~ $less(N_12a,summation(max(X_10a,Y_11a)))
| ~ model_max(X_10a,Y_11a,N_12a) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_16]) ).
tff(c_1890,plain,
~ $less('#skE_3',summation(max('#skF_7','#skE_1'))),
inference(resolution,[status(thm)],[c_1881,c_83]) ).
tff(c_1899,plain,
~ $less('#skE_3','#skE_2'),
inference(demodulation,[status(thm),theory(equality)],[c_328,c_1363,c_1890]) ).
tff(c_1324,plain,
minsol_model_ub('#skF_7','#skE_1','#skF_9'),
inference(demodulation,[status(thm),theory(equality)],[c_1261,c_572]) ).
tff(c_1330,plain,
minsol_model_ub('#skF_7','#skE_1','#skF_9'),
inference(demodulation,[status(thm),theory(equality)],[c_1261,c_572]) ).
tff(c_1326,plain,
'#skF_8' = '#skE_1',
inference(demodulation,[status(thm),theory(equality)],[c_1261,c_531]) ).
tff(c_1480,plain,
( ub('#skF_7','#skE_1','#skE_1')
| ~ model_ub('#skF_7','#skE_1','#skF_9') ),
inference(demodulation,[status(thm),theory(equality)],[c_1326,c_1326,c_404]) ).
tff(c_1488,plain,
~ model_ub('#skF_7','#skE_1','#skF_9'),
inference(splitLeft,[status(thm)],[c_1480]) ).
tff(c_1494,plain,
~ minsol_model_ub('#skF_7','#skE_1','#skF_9'),
inference(resolution,[status(thm)],[c_73,c_1488]) ).
tff(c_1501,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_1330,c_1494]) ).
tff(c_1508,plain,
ub('#skF_7','#skE_1','#skE_1'),
inference(splitRight,[status(thm)],[c_1480]) ).
tff(c_81,plain,
! [X_13a: $int,Y_14a: $int,N_15a: $int,Z_18a: $int] :
( model_ub(X_13a,Y_14a,N_15a)
| $less(N_15a,summation(Z_18a))
| ~ ub(X_13a,Y_14a,Z_18a) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_22]) ).
tff(c_1511,plain,
! [N_15a: $int] :
( model_ub('#skF_7','#skE_1',N_15a)
| $less(N_15a,summation('#skE_1')) ),
inference(resolution,[status(thm)],[c_1508,c_81]) ).
tff(c_1541,plain,
! [N_624a: $int] :
( model_ub('#skF_7','#skE_1',N_624a)
| $less(N_624a,'#skE_2') ),
inference(demodulation,[status(thm),theory(equality)],[c_328,c_1511]) ).
tff(c_1578,plain,
! [N_639a: $int,N_640a: $int] :
( ~ minsol_model_ub('#skF_7','#skE_1',N_639a)
| ~ $less(N_640a,N_639a)
| $less(N_640a,'#skE_2') ),
inference(resolution,[status(thm)],[c_1541,c_74]) ).
tff(c_1582,plain,
! [N_640a: $int] :
( ~ $less(N_640a,'#skF_9')
| $less(N_640a,'#skE_2') ),
inference(resolution,[status(thm)],[c_1324,c_1578]) ).
tff(c_1584,plain,
! [N_640a: $int] :
( ~ $less(N_640a,'#skF_9')
| $less(N_640a,'#skE_2') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_1582]) ).
tff(c_1585,plain,
$lesseq('#skF_9','#skE_2'),
inference(quantifierElimination,[status(thm),theory('LIA')],[c_1584]) ).
tff(c_1587,plain,
~ $less('#skE_2','#skF_9'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_1585]) ).
tff(c_1260,plain,
'#skE_5' = '#skE_2',
inference(splitRight,[status(thm)],[c_781]) ).
tff(c_718,plain,
summation('#skE_4') = '#skE_5',
inference(define,[status(thm),theory(equality)],[c_464]) ).
tff(c_717,plain,
( $less('#skE_3','#skF_9')
| $less('#skF_9',summation('#skE_4')) ),
inference(demodulation,[status(thm),theory(equality)],[c_450,c_449,c_448]) ).
tff(c_725,plain,
( $less('#skE_3','#skF_9')
| $less('#skF_9','#skE_5') ),
inference(demodulation,[status(thm),theory(equality)],[c_718,c_717]) ).
tff(c_1401,plain,
( $less('#skE_3','#skF_9')
| $less('#skF_9','#skE_2') ),
inference(demodulation,[status(thm),theory(equality)],[c_1260,c_725]) ).
tff(c_1403,plain,
$less('#skE_3','#skF_9'),
inference(negUnitSimplification,[status(thm)],[c_326,c_1401]) ).
tff(c_1901,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_1899,c_1587,c_1403]) ).
tff(c_1907,plain,
minsol_model_max('#skF_7','#skE_1','#skF_9'),
inference(splitRight,[status(thm)],[c_1872]) ).
tff(c_575,plain,
~ minsol_model_max('#skF_7','#skE_4','#skF_9'),
inference(demodulation,[status(thm),theory(equality)],[c_531,c_193]) ).
tff(c_1317,plain,
~ minsol_model_max('#skF_7','#skE_1','#skF_9'),
inference(demodulation,[status(thm),theory(equality)],[c_1261,c_575]) ).
tff(c_1910,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_1907,c_1317]) ).
tff(c_1913,plain,
'#skF_7' = '#skE_4',
inference(splitRight,[status(thm)],[c_490]) ).
tff(c_1914,plain,
~ $less('#skF_7','#skF_8'),
inference(splitRight,[status(thm)],[c_490]) ).
tff(c_1959,plain,
~ $less('#skE_4','#skF_8'),
inference(demodulation,[status(thm),theory(equality)],[c_1913,c_1914]) ).
tff(c_2183,plain,
summation('#skE_4') = '#skE_5',
inference(define,[status(thm),theory(equality)],[c_464]) ).
tff(c_1954,plain,
minsol_model_ub('#skE_4','#skF_8','#skF_9'),
inference(demodulation,[status(thm),theory(equality)],[c_1913,c_273]) ).
tff(c_2398,plain,
! [N_951a: $int,N_949a: $int,X_952a: $int,Z_948a: $int,Y_950a: $int] :
( ~ minsol_model_ub(X_952a,Y_950a,N_949a)
| ~ $less(N_951a,N_949a)
| $less(N_951a,summation(Z_948a))
| $less(Z_948a,X_952a)
| $less(Z_948a,Y_950a) ),
inference(resolution,[status(thm)],[c_230,c_74]) ).
tff(c_2407,plain,
! [N_953a: $int,Z_954a: $int] :
( ~ $less(N_953a,'#skF_9')
| $less(N_953a,summation(Z_954a))
| $less(Z_954a,'#skE_4')
| $less(Z_954a,'#skF_8') ),
inference(resolution,[status(thm)],[c_1954,c_2398]) ).
tff(c_2424,plain,
! [N_953a: $int] :
( ~ $less(N_953a,'#skF_9')
| $less(N_953a,'#skE_5')
| $less('#skE_4','#skE_4')
| $less('#skE_4','#skF_8') ),
inference(superposition,[status(thm),theory(equality)],[c_2183,c_2407]) ).
tff(c_2426,plain,
! [N_953a: $int] :
( ~ $less(N_953a,'#skF_9')
| $less(N_953a,'#skE_5')
| $less('#skE_4','#skF_8') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_2424]) ).
tff(c_2429,plain,
! [N_953a: $int] :
( ~ $less(N_953a,'#skF_9')
| $less(N_953a,'#skE_5') ),
inference(negUnitSimplification,[status(thm)],[c_1959,c_2426]) ).
tff(c_2430,plain,
$lesseq('#skF_9','#skE_5'),
inference(quantifierElimination,[status(thm),theory('LIA')],[c_2429]) ).
tff(c_2432,plain,
~ $less('#skE_5','#skF_9'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_2430]) ).
tff(c_2187,plain,
summation('#skE_4') = '#skE_5',
inference(define,[status(thm),theory(equality)],[c_464]) ).
tff(c_2234,plain,
( $less('#skE_5','#skE_2')
| ~ $less('#skE_4','#skE_1') ),
inference(superposition,[status(thm),theory(equality)],[c_2187,c_360]) ).
tff(c_2261,plain,
~ $less('#skE_4','#skE_1'),
inference(splitLeft,[status(thm)],[c_2234]) ).
tff(c_2240,plain,
( ( '#skE_5' = '#skE_2' )
| ( '#skE_4' != '#skE_1' ) ),
inference(superposition,[status(thm),theory(equality)],[c_2187,c_325]) ).
tff(c_2259,plain,
'#skE_4' != '#skE_1',
inference(splitLeft,[status(thm)],[c_2240]) ).
tff(c_2047,plain,
minsol_model_ub('#skE_4','#skF_8','#skF_9'),
inference(demodulation,[status(thm),theory(equality)],[c_1913,c_273]) ).
tff(c_2098,plain,
( ub('#skE_4','#skF_8','#skE_1')
| ~ model_ub('#skE_4','#skF_8','#skF_9') ),
inference(demodulation,[status(thm),theory(equality)],[c_1913,c_1913,c_404]) ).
tff(c_2106,plain,
~ model_ub('#skE_4','#skF_8','#skF_9'),
inference(splitLeft,[status(thm)],[c_2098]) ).
tff(c_2112,plain,
~ minsol_model_ub('#skE_4','#skF_8','#skF_9'),
inference(resolution,[status(thm)],[c_73,c_2106]) ).
tff(c_2119,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_2047,c_2112]) ).
tff(c_2126,plain,
ub('#skE_4','#skF_8','#skE_1'),
inference(splitRight,[status(thm)],[c_2098]) ).
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_85,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_2145,plain,
~ $less('#skE_1','#skE_4'),
inference(resolution,[status(thm)],[c_2126,c_85]) ).
tff(c_2264,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_2261,c_2259,c_2145]) ).
tff(c_2267,plain,
$less('#skE_5','#skE_2'),
inference(splitRight,[status(thm)],[c_2234]) ).
tff(c_2433,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_2432,c_2267,c_326]) ).
tff(c_2437,plain,
'#skE_4' = '#skE_1',
inference(splitRight,[status(thm)],[c_2240]) ).
tff(c_1944,plain,
max('#skE_4','#skF_8') = '#skE_4',
inference(demodulation,[status(thm),theory(equality)],[c_1913,c_461]) ).
tff(c_2564,plain,
max('#skE_1','#skF_8') = '#skE_1',
inference(demodulation,[status(thm),theory(equality)],[c_2437,c_2437,c_1944]) ).
tff(c_1966,plain,
'#skF_2'('#skE_4','#skF_8','#skF_9') = '#skE_3',
inference(demodulation,[status(thm),theory(equality)],[c_1913,c_458]) ).
tff(c_1982,plain,
( model_max('#skE_4','#skF_8','#skE_3')
| minsol_model_max('#skE_4','#skF_8','#skF_9')
| ~ model_max('#skE_4','#skF_8','#skF_9') ),
inference(superposition,[status(thm),theory(equality)],[c_1966,c_75]) ).
tff(c_2903,plain,
( model_max('#skE_1','#skF_8','#skE_3')
| minsol_model_max('#skE_1','#skF_8','#skF_9')
| ~ model_max('#skE_1','#skF_8','#skF_9') ),
inference(demodulation,[status(thm),theory(equality)],[c_2437,c_2437,c_2437,c_1982]) ).
tff(c_2911,plain,
~ model_max('#skE_1','#skF_8','#skF_9'),
inference(splitLeft,[status(thm)],[c_2903]) ).
tff(c_2914,plain,
$less('#skF_9',summation(max('#skE_1','#skF_8'))),
inference(resolution,[status(thm)],[c_82,c_2911]) ).
tff(c_2919,plain,
$less('#skF_9','#skE_2'),
inference(demodulation,[status(thm),theory(equality)],[c_328,c_2564,c_2914]) ).
tff(c_2921,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_326,c_2919]) ).
tff(c_2925,plain,
( minsol_model_max('#skE_1','#skF_8','#skF_9')
| model_max('#skE_1','#skF_8','#skE_3') ),
inference(splitRight,[status(thm)],[c_2903]) ).
tff(c_2948,plain,
model_max('#skE_1','#skF_8','#skE_3'),
inference(splitLeft,[status(thm)],[c_2925]) ).
tff(c_2957,plain,
~ $less('#skE_3',summation(max('#skE_1','#skF_8'))),
inference(resolution,[status(thm)],[c_2948,c_83]) ).
tff(c_2966,plain,
~ $less('#skE_3','#skE_2'),
inference(demodulation,[status(thm),theory(equality)],[c_328,c_2564,c_2957]) ).
tff(c_2512,plain,
minsol_model_ub('#skE_1','#skF_8','#skF_9'),
inference(demodulation,[status(thm),theory(equality)],[c_2437,c_1954]) ).
tff(c_2129,plain,
! [N_15a: $int] :
( model_ub('#skE_4','#skF_8',N_15a)
| $less(N_15a,summation('#skE_1')) ),
inference(resolution,[status(thm)],[c_2126,c_81]) ).
tff(c_2158,plain,
! [N_912a: $int] :
( model_ub('#skE_4','#skF_8',N_912a)
| $less(N_912a,'#skE_2') ),
inference(demodulation,[status(thm),theory(equality)],[c_328,c_2129]) ).
tff(c_2173,plain,
! [N_27a: $int,N_912a: $int] :
( ~ minsol_model_ub('#skE_4','#skF_8',N_27a)
| ~ $less(N_912a,N_27a)
| $less(N_912a,'#skE_2') ),
inference(resolution,[status(thm)],[c_2158,c_74]) ).
tff(c_2758,plain,
! [N_1104a: $int,N_1105a: $int] :
( ~ minsol_model_ub('#skE_1','#skF_8',N_1104a)
| ~ $less(N_1105a,N_1104a)
| $less(N_1105a,'#skE_2') ),
inference(demodulation,[status(thm),theory(equality)],[c_2437,c_2173]) ).
tff(c_2762,plain,
! [N_1105a: $int] :
( ~ $less(N_1105a,'#skF_9')
| $less(N_1105a,'#skE_2') ),
inference(resolution,[status(thm)],[c_2512,c_2758]) ).
tff(c_2764,plain,
! [N_1105a: $int] :
( ~ $less(N_1105a,'#skF_9')
| $less(N_1105a,'#skE_2') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_2762]) ).
tff(c_2766,plain,
$lesseq('#skF_9','#skE_2'),
inference(quantifierElimination,[status(thm),theory('LIA')],[c_2764]) ).
tff(c_2768,plain,
~ $less('#skE_2','#skF_9'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_2766]) ).
tff(c_2436,plain,
'#skE_5' = '#skE_2',
inference(splitRight,[status(thm)],[c_2240]) ).
tff(c_2177,plain,
summation('#skE_4') = '#skE_5',
inference(define,[status(thm),theory(equality)],[c_464]) ).
tff(c_2184,plain,
( $less('#skE_3','#skF_9')
| $less('#skF_9','#skE_5') ),
inference(demodulation,[status(thm),theory(equality)],[c_2177,c_717]) ).
tff(c_2560,plain,
( $less('#skE_3','#skF_9')
| $less('#skF_9','#skE_2') ),
inference(demodulation,[status(thm),theory(equality)],[c_2436,c_2184]) ).
tff(c_2562,plain,
$less('#skE_3','#skF_9'),
inference(negUnitSimplification,[status(thm)],[c_326,c_2560]) ).
tff(c_2967,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_2966,c_2768,c_2562]) ).
tff(c_2973,plain,
minsol_model_max('#skE_1','#skF_8','#skF_9'),
inference(splitRight,[status(thm)],[c_2925]) ).
tff(c_1957,plain,
~ minsol_model_max('#skE_4','#skF_8','#skF_9'),
inference(demodulation,[status(thm),theory(equality)],[c_1913,c_193]) ).
tff(c_2518,plain,
~ minsol_model_max('#skE_1','#skF_8','#skF_9'),
inference(demodulation,[status(thm),theory(equality)],[c_2437,c_1957]) ).
tff(c_2976,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_2973,c_2518]) ).
tff(c_2983,plain,
minsol_model_max('#skF_4','#skF_5','#skF_6'),
inference(splitRight,[status(thm)],[c_58]) ).
tff(c_77,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_145,plain,
! [N_102a: $int,X_103a: $int,Y_104a: $int] :
( ~ $less(N_102a,summation(max(X_103a,Y_104a)))
| ~ model_max(X_103a,Y_104a,N_102a) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_16]) ).
tff(c_150,plain,
! [N_21a: $int,X_19a: $int,Y_20a: $int] :
( ~ $less(N_21a,summation(max(X_19a,Y_20a)))
| ~ minsol_model_max(X_19a,Y_20a,N_21a) ),
inference(resolution,[status(thm)],[c_77,c_145]) ).
tff(c_3005,plain,
~ $less('#skF_6',summation(max('#skF_4','#skF_5'))),
inference(resolution,[status(thm)],[c_2983,c_150]) ).
tff(c_3038,plain,
max('#skF_4','#skF_5') = '#skE_7',
inference(define,[status(thm),theory(equality)],[c_3005]) ).
tff(c_3068,plain,
( ( '#skF_4' = '#skE_7' )
| $less('#skF_4','#skF_5') ),
inference(superposition,[status(thm),theory(equality)],[c_88,c_3038]) ).
tff(c_3132,plain,
$less('#skF_4','#skF_5'),
inference(splitLeft,[status(thm)],[c_3068]) ).
tff(c_3070,plain,
( ( '#skF_5' = '#skE_7' )
| $less('#skF_5','#skF_4') ),
inference(superposition,[status(thm),theory(equality)],[c_87,c_3038]) ).
tff(c_3130,plain,
$less('#skF_5','#skF_4'),
inference(splitLeft,[status(thm)],[c_3070]) ).
tff(c_3133,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_3132,c_3130]) ).
tff(c_3136,plain,
'#skF_4' = '#skE_7',
inference(splitRight,[status(thm)],[c_3068]) ).
tff(c_3137,plain,
~ $less('#skF_4','#skF_5'),
inference(splitRight,[status(thm)],[c_3068]) ).
tff(c_3177,plain,
~ $less('#skE_7','#skF_5'),
inference(demodulation,[status(thm),theory(equality)],[c_3136,c_3137]) ).
tff(c_3037,plain,
max('#skF_4','#skF_5') = '#skE_7',
inference(define,[status(thm),theory(equality)],[c_3005]) ).
tff(c_29,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_179,plain,
! [X_123a: $int,Y_124a: $int,Z_125a: $int,N_126a: $int] :
( ~ model_max(X_123a,Y_124a,Z_125a)
| ~ minsol_model_max(X_123a,Y_124a,N_126a)
| ~ $less(Z_125a,N_126a) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_29]) ).
tff(c_187,plain,
! [X_10a: $int,Y_11a: $int,N_126a: $int,N_12a: $int] :
( ~ minsol_model_max(X_10a,Y_11a,N_126a)
| ~ $less(N_12a,N_126a)
| $less(N_12a,summation(max(X_10a,Y_11a))) ),
inference(resolution,[status(thm)],[c_82,c_179]) ).
tff(c_2997,plain,
! [N_12a: $int] :
( ~ $less(N_12a,'#skF_6')
| $less(N_12a,summation(max('#skF_4','#skF_5'))) ),
inference(resolution,[status(thm)],[c_2983,c_187]) ).
tff(c_3076,plain,
! [N_12a: $int] :
( ~ $less(N_12a,'#skF_6')
| $less(N_12a,summation('#skE_7')) ),
inference(demodulation,[status(thm),theory(equality)],[c_3037,c_2997]) ).
tff(c_3087,plain,
summation('#skE_7') = '#skE_8',
inference(define,[status(thm),theory(equality)],[c_3076]) ).
tff(c_3025,plain,
max('#skF_4','#skF_5') = '#skE_7',
inference(define,[status(thm),theory(equality)],[c_3005]) ).
tff(c_3024,plain,
~ $less('#skF_6',summation(max('#skF_4','#skF_5'))),
inference(resolution,[status(thm)],[c_2983,c_150]) ).
tff(c_3035,plain,
~ $less('#skF_6',summation('#skE_7')),
inference(demodulation,[status(thm),theory(equality)],[c_3025,c_3024]) ).
tff(c_3260,plain,
~ $less('#skF_6','#skE_8'),
inference(demodulation,[status(thm),theory(equality)],[c_3087,c_3035]) ).
tff(c_3084,plain,
summation('#skE_7') = '#skE_8',
inference(define,[status(thm),theory(equality)],[c_3076]) ).
tff(c_211,plain,
! [X_7a: $int,Y_8a: $int,N_150a: $int,Z_9a: $int] :
( model_ub(X_7a,Y_8a,N_150a)
| $less(N_150a,summation(Z_9a))
| $less(Z_9a,X_7a)
| $less(Z_9a,Y_8a) ),
inference(resolution,[status(thm)],[c_84,c_206]) ).
tff(c_43,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_72,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_43]) ).
tff(c_3342,plain,
! [X_1324a: $int,Y_1325a: $int,N_1326a: $int,Z_1327a: $int] :
( $less('#skF_3'(X_1324a,Y_1325a,N_1326a),N_1326a)
| minsol_model_ub(X_1324a,Y_1325a,N_1326a)
| $less(N_1326a,summation(Z_1327a))
| $less(Z_1327a,X_1324a)
| $less(Z_1327a,Y_1325a) ),
inference(resolution,[status(thm)],[c_230,c_72]) ).
tff(c_62,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_144,plain,
~ minsol_model_ub('#skF_4','#skF_5','#skF_6'),
inference(splitLeft,[status(thm)],[c_62]) ).
tff(c_3175,plain,
~ minsol_model_ub('#skE_7','#skF_5','#skF_6'),
inference(demodulation,[status(thm),theory(equality)],[c_3136,c_144]) ).
tff(c_3358,plain,
! [Z_1327a: $int] :
( $less('#skF_3'('#skE_7','#skF_5','#skF_6'),'#skF_6')
| $less('#skF_6',summation(Z_1327a))
| $less(Z_1327a,'#skE_7')
| $less(Z_1327a,'#skF_5') ),
inference(resolution,[status(thm)],[c_3342,c_3175]) ).
tff(c_3801,plain,
'#skF_3'('#skE_7','#skF_5','#skF_6') = '#skE_9',
inference(define,[status(thm),theory(equality)],[c_3358]) ).
tff(c_71,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_3817,plain,
( model_ub('#skE_7','#skF_5','#skE_9')
| minsol_model_ub('#skE_7','#skF_5','#skF_6')
| ~ model_ub('#skE_7','#skF_5','#skF_6') ),
inference(superposition,[status(thm),theory(equality)],[c_3801,c_71]) ).
tff(c_3908,plain,
~ model_ub('#skE_7','#skF_5','#skF_6'),
inference(splitLeft,[status(thm)],[c_3817]) ).
tff(c_3921,plain,
! [Z_1485a: $int] :
( $less('#skF_6',summation(Z_1485a))
| $less(Z_1485a,'#skE_7')
| $less(Z_1485a,'#skF_5') ),
inference(resolution,[status(thm)],[c_211,c_3908]) ).
tff(c_3940,plain,
( $less('#skF_6','#skE_8')
| $less('#skE_7','#skE_7')
| $less('#skE_7','#skF_5') ),
inference(superposition,[status(thm),theory(equality)],[c_3084,c_3921]) ).
tff(c_3942,plain,
( $less('#skF_6','#skE_8')
| $less('#skE_7','#skF_5') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_3940]) ).
tff(c_3943,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_3177,c_3260,c_3942]) ).
tff(c_3947,plain,
( minsol_model_ub('#skE_7','#skF_5','#skF_6')
| model_ub('#skE_7','#skF_5','#skE_9') ),
inference(splitRight,[status(thm)],[c_3817]) ).
tff(c_3998,plain,
model_ub('#skE_7','#skF_5','#skE_9'),
inference(splitLeft,[status(thm)],[c_3947]) ).
tff(c_80,plain,
! [N_15a: $int,X_13a: $int,Y_14a: $int] :
( ~ $less(N_15a,summation('#skF_1'(X_13a,Y_14a,N_15a)))
| ~ model_ub(X_13a,Y_14a,N_15a) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_25]) ).
tff(c_4016,plain,
~ $less('#skE_9',summation('#skF_1'('#skE_7','#skF_5','#skE_9'))),
inference(resolution,[status(thm)],[c_3998,c_80]) ).
tff(c_4028,plain,
'#skF_1'('#skE_7','#skF_5','#skE_9') = '#skE_10',
inference(define,[status(thm),theory(equality)],[c_4016]) ).
tff(c_4027,plain,
~ $less('#skE_9',summation('#skF_1'('#skE_7','#skF_5','#skE_9'))),
inference(resolution,[status(thm)],[c_3998,c_80]) ).
tff(c_4038,plain,
~ $less('#skE_9',summation('#skE_10')),
inference(demodulation,[status(thm),theory(equality)],[c_4028,c_4027]) ).
tff(c_4052,plain,
summation('#skE_10') = '#skE_11',
inference(define,[status(thm),theory(equality)],[c_4038]) ).
tff(c_3088,plain,
summation('#skE_7') = '#skE_8',
inference(define,[status(thm),theory(equality)],[c_3076]) ).
tff(c_3125,plain,
! [Y_2a: $int] :
( ~ $less(summation(Y_2a),'#skE_8')
| $less(Y_2a,'#skE_7') ),
inference(superposition,[status(thm),theory(equality)],[c_3088,c_90]) ).
tff(c_4125,plain,
( ~ $less('#skE_11','#skE_8')
| $less('#skE_10','#skE_7') ),
inference(superposition,[status(thm),theory(equality)],[c_4052,c_3125]) ).
tff(c_4193,plain,
~ $less('#skE_11','#skE_8'),
inference(splitLeft,[status(thm)],[c_4125]) ).
tff(c_4042,plain,
summation('#skE_10') = '#skE_11',
inference(define,[status(thm),theory(equality)],[c_4038]) ).
tff(c_4041,plain,
~ $less('#skE_9',summation('#skE_10')),
inference(demodulation,[status(thm),theory(equality)],[c_4028,c_4027]) ).
tff(c_4049,plain,
~ $less('#skE_9','#skE_11'),
inference(demodulation,[status(thm),theory(equality)],[c_4042,c_4041]) ).
tff(c_3788,plain,
'#skF_3'('#skE_7','#skF_5','#skF_6') = '#skE_9',
inference(define,[status(thm),theory(equality)],[c_3358]) ).
tff(c_3787,plain,
! [Z_1327a: $int] :
( $less('#skF_3'('#skE_7','#skF_5','#skF_6'),'#skF_6')
| $less('#skF_6',summation(Z_1327a))
| $less(Z_1327a,'#skE_7')
| $less(Z_1327a,'#skF_5') ),
inference(resolution,[status(thm)],[c_3342,c_3175]) ).
tff(c_3798,plain,
! [Z_1327a: $int] :
( $less('#skE_9','#skF_6')
| $less('#skF_6',summation(Z_1327a))
| $less(Z_1327a,'#skE_7')
| $less(Z_1327a,'#skF_5') ),
inference(demodulation,[status(thm),theory(equality)],[c_3788,c_3787]) ).
tff(c_3824,plain,
$less('#skE_9','#skF_6'),
inference(splitLeft,[status(thm)],[c_3798]) ).
tff(c_3078,plain,
summation('#skE_7') = '#skE_8',
inference(define,[status(thm),theory(equality)],[c_3076]) ).
tff(c_3077,plain,
! [N_12a: $int] :
( ~ $less(N_12a,'#skF_6')
| $less(N_12a,summation('#skE_7')) ),
inference(demodulation,[status(thm),theory(equality)],[c_3037,c_2997]) ).
tff(c_3085,plain,
! [N_12a: $int] :
( ~ $less(N_12a,'#skF_6')
| $less(N_12a,'#skE_8') ),
inference(demodulation,[status(thm),theory(equality)],[c_3078,c_3077]) ).
tff(c_3207,plain,
$lesseq('#skF_6','#skE_8'),
inference(quantifierElimination,[status(thm),theory('LIA')],[c_3085]) ).
tff(c_3209,plain,
~ $less('#skE_8','#skF_6'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_3207]) ).
tff(c_4194,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_4193,c_4049,c_3824,c_3209]) ).
tff(c_4197,plain,
$less('#skE_10','#skE_7'),
inference(splitRight,[status(thm)],[c_4125]) ).
tff(c_3997,plain,
model_ub('#skE_7','#skF_5','#skE_9'),
inference(splitLeft,[status(thm)],[c_3947]) ).
tff(c_4157,plain,
'#skF_1'('#skE_7','#skF_5','#skE_9') = '#skE_10',
inference(define,[status(thm),theory(equality)],[c_4016]) ).
tff(c_4168,plain,
( ub('#skE_7','#skF_5','#skE_10')
| ~ model_ub('#skE_7','#skF_5','#skE_9') ),
inference(superposition,[status(thm),theory(equality)],[c_4157,c_79]) ).
tff(c_4366,plain,
ub('#skE_7','#skF_5','#skE_10'),
inference(demodulation,[status(thm),theory(equality)],[c_3997,c_4168]) ).
tff(c_4375,plain,
~ $less('#skE_10','#skE_7'),
inference(resolution,[status(thm)],[c_4366,c_85]) ).
tff(c_4387,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_4197,c_4375]) ).
tff(c_4393,plain,
minsol_model_ub('#skE_7','#skF_5','#skF_6'),
inference(splitRight,[status(thm)],[c_3947]) ).
tff(c_4396,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_4393,c_3175]) ).
tff(c_4405,plain,
! [Z_1601a: $int] :
( $less('#skF_6',summation(Z_1601a))
| $less(Z_1601a,'#skE_7')
| $less(Z_1601a,'#skF_5') ),
inference(splitRight,[status(thm)],[c_3798]) ).
tff(c_4424,plain,
( $less('#skF_6','#skE_8')
| $less('#skE_7','#skE_7')
| $less('#skE_7','#skF_5') ),
inference(superposition,[status(thm),theory(equality)],[c_3084,c_4405]) ).
tff(c_4426,plain,
( $less('#skF_6','#skE_8')
| $less('#skE_7','#skF_5') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_4424]) ).
tff(c_4437,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_3177,c_3260,c_4426]) ).
tff(c_4440,plain,
'#skF_5' = '#skE_7',
inference(splitRight,[status(thm)],[c_3070]) ).
tff(c_4441,plain,
~ $less('#skF_5','#skF_4'),
inference(splitRight,[status(thm)],[c_3070]) ).
tff(c_4475,plain,
~ $less('#skE_7','#skF_4'),
inference(demodulation,[status(thm),theory(equality)],[c_4440,c_4441]) ).
tff(c_4527,plain,
~ $less('#skF_6','#skE_8'),
inference(demodulation,[status(thm),theory(equality)],[c_3087,c_3035]) ).
tff(c_5069,plain,
! [X_1815a: $int,Y_1816a: $int,N_1817a: $int,Z_1818a: $int] :
( $less('#skF_3'(X_1815a,Y_1816a,N_1817a),N_1817a)
| minsol_model_ub(X_1815a,Y_1816a,N_1817a)
| $less(N_1817a,summation(Z_1818a))
| $less(Z_1818a,X_1815a)
| $less(Z_1818a,Y_1816a) ),
inference(resolution,[status(thm)],[c_230,c_72]) ).
tff(c_4473,plain,
~ minsol_model_ub('#skF_4','#skE_7','#skF_6'),
inference(demodulation,[status(thm),theory(equality)],[c_4440,c_144]) ).
tff(c_5085,plain,
! [Z_1818a: $int] :
( $less('#skF_3'('#skF_4','#skE_7','#skF_6'),'#skF_6')
| $less('#skF_6',summation(Z_1818a))
| $less(Z_1818a,'#skF_4')
| $less(Z_1818a,'#skE_7') ),
inference(resolution,[status(thm)],[c_5069,c_4473]) ).
tff(c_5198,plain,
'#skF_3'('#skF_4','#skE_7','#skF_6') = '#skE_12',
inference(define,[status(thm),theory(equality)],[c_5085]) ).
tff(c_5214,plain,
( model_ub('#skF_4','#skE_7','#skE_12')
| minsol_model_ub('#skF_4','#skE_7','#skF_6')
| ~ model_ub('#skF_4','#skE_7','#skF_6') ),
inference(superposition,[status(thm),theory(equality)],[c_5198,c_71]) ).
tff(c_5258,plain,
~ model_ub('#skF_4','#skE_7','#skF_6'),
inference(splitLeft,[status(thm)],[c_5214]) ).
tff(c_5271,plain,
! [Z_1897a: $int] :
( $less('#skF_6',summation(Z_1897a))
| $less(Z_1897a,'#skF_4')
| $less(Z_1897a,'#skE_7') ),
inference(resolution,[status(thm)],[c_211,c_5258]) ).
tff(c_5290,plain,
( $less('#skF_6','#skE_8')
| $less('#skE_7','#skF_4')
| $less('#skE_7','#skE_7') ),
inference(superposition,[status(thm),theory(equality)],[c_3084,c_5271]) ).
tff(c_5292,plain,
( $less('#skF_6','#skE_8')
| $less('#skE_7','#skF_4') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_5290]) ).
tff(c_5293,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_4475,c_4527,c_5292]) ).
tff(c_5297,plain,
( minsol_model_ub('#skF_4','#skE_7','#skF_6')
| model_ub('#skF_4','#skE_7','#skE_12') ),
inference(splitRight,[status(thm)],[c_5214]) ).
tff(c_5306,plain,
model_ub('#skF_4','#skE_7','#skE_12'),
inference(splitLeft,[status(thm)],[c_5297]) ).
tff(c_5324,plain,
~ $less('#skE_12',summation('#skF_1'('#skF_4','#skE_7','#skE_12'))),
inference(resolution,[status(thm)],[c_5306,c_80]) ).
tff(c_5336,plain,
'#skF_1'('#skF_4','#skE_7','#skE_12') = '#skE_13',
inference(define,[status(thm),theory(equality)],[c_5324]) ).
tff(c_5335,plain,
~ $less('#skE_12',summation('#skF_1'('#skF_4','#skE_7','#skE_12'))),
inference(resolution,[status(thm)],[c_5306,c_80]) ).
tff(c_5346,plain,
~ $less('#skE_12',summation('#skE_13')),
inference(demodulation,[status(thm),theory(equality)],[c_5336,c_5335]) ).
tff(c_5359,plain,
summation('#skE_13') = '#skE_14',
inference(define,[status(thm),theory(equality)],[c_5346]) ).
tff(c_5436,plain,
( ~ $less('#skE_14','#skE_8')
| $less('#skE_13','#skE_7') ),
inference(superposition,[status(thm),theory(equality)],[c_5359,c_3125]) ).
tff(c_5514,plain,
~ $less('#skE_14','#skE_8'),
inference(splitLeft,[status(thm)],[c_5436]) ).
tff(c_5349,plain,
summation('#skE_13') = '#skE_14',
inference(define,[status(thm),theory(equality)],[c_5346]) ).
tff(c_5348,plain,
~ $less('#skE_12',summation('#skE_13')),
inference(demodulation,[status(thm),theory(equality)],[c_5336,c_5335]) ).
tff(c_5356,plain,
~ $less('#skE_12','#skE_14'),
inference(demodulation,[status(thm),theory(equality)],[c_5349,c_5348]) ).
tff(c_5185,plain,
'#skF_3'('#skF_4','#skE_7','#skF_6') = '#skE_12',
inference(define,[status(thm),theory(equality)],[c_5085]) ).
tff(c_5184,plain,
! [Z_1818a: $int] :
( $less('#skF_3'('#skF_4','#skE_7','#skF_6'),'#skF_6')
| $less('#skF_6',summation(Z_1818a))
| $less(Z_1818a,'#skF_4')
| $less(Z_1818a,'#skE_7') ),
inference(resolution,[status(thm)],[c_5069,c_4473]) ).
tff(c_5195,plain,
! [Z_1818a: $int] :
( $less('#skE_12','#skF_6')
| $less('#skF_6',summation(Z_1818a))
| $less(Z_1818a,'#skF_4')
| $less(Z_1818a,'#skE_7') ),
inference(demodulation,[status(thm),theory(equality)],[c_5185,c_5184]) ).
tff(c_5221,plain,
$less('#skE_12','#skF_6'),
inference(splitLeft,[status(thm)],[c_5195]) ).
tff(c_5515,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_5514,c_5356,c_5221,c_3209]) ).
tff(c_5518,plain,
$less('#skE_13','#skE_7'),
inference(splitRight,[status(thm)],[c_5436]) ).
tff(c_5305,plain,
model_ub('#skF_4','#skE_7','#skE_12'),
inference(splitLeft,[status(thm)],[c_5297]) ).
tff(c_5520,plain,
'#skF_1'('#skF_4','#skE_7','#skE_12') = '#skE_13',
inference(define,[status(thm),theory(equality)],[c_5324]) ).
tff(c_5531,plain,
( ub('#skF_4','#skE_7','#skE_13')
| ~ model_ub('#skF_4','#skE_7','#skE_12') ),
inference(superposition,[status(thm),theory(equality)],[c_5520,c_79]) ).
tff(c_5703,plain,
ub('#skF_4','#skE_7','#skE_13'),
inference(demodulation,[status(thm),theory(equality)],[c_5305,c_5531]) ).
tff(c_5709,plain,
~ $less('#skE_13','#skE_7'),
inference(resolution,[status(thm)],[c_5703,c_86]) ).
tff(c_5722,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_5518,c_5709]) ).
tff(c_5728,plain,
minsol_model_ub('#skF_4','#skE_7','#skF_6'),
inference(splitRight,[status(thm)],[c_5297]) ).
tff(c_5731,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_5728,c_4473]) ).
tff(c_5740,plain,
! [Z_1993a: $int] :
( $less('#skF_6',summation(Z_1993a))
| $less(Z_1993a,'#skF_4')
| $less(Z_1993a,'#skE_7') ),
inference(splitRight,[status(thm)],[c_5195]) ).
tff(c_5759,plain,
( $less('#skF_6','#skE_8')
| $less('#skE_7','#skF_4')
| $less('#skE_7','#skE_7') ),
inference(superposition,[status(thm),theory(equality)],[c_3084,c_5740]) ).
tff(c_5761,plain,
( $less('#skF_6','#skE_8')
| $less('#skE_7','#skF_4') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_5759]) ).
tff(c_5766,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_4475,c_4527,c_5761]) ).
tff(c_5773,plain,
minsol_model_max('#skF_4','#skF_5','#skF_6'),
inference(splitRight,[status(thm)],[c_66]) ).
tff(c_5779,plain,
~ $less('#skF_6',summation(max('#skF_4','#skF_5'))),
inference(resolution,[status(thm)],[c_5773,c_150]) ).
tff(c_5834,plain,
max('#skF_4','#skF_5') = '#skE_7',
inference(define,[status(thm),theory(equality)],[c_5779]) ).
tff(c_5859,plain,
( ( '#skF_5' = '#skE_7' )
| $less('#skF_5','#skF_4') ),
inference(superposition,[status(thm),theory(equality)],[c_5834,c_87]) ).
tff(c_5870,plain,
$less('#skF_5','#skF_4'),
inference(splitLeft,[status(thm)],[c_5859]) ).
tff(c_5857,plain,
( ( '#skF_4' = '#skE_7' )
| $less('#skF_4','#skF_5') ),
inference(superposition,[status(thm),theory(equality)],[c_5834,c_88]) ).
tff(c_5868,plain,
$less('#skF_4','#skF_5'),
inference(splitLeft,[status(thm)],[c_5857]) ).
tff(c_5871,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_5870,c_5868]) ).
tff(c_5874,plain,
'#skF_5' = '#skE_7',
inference(splitRight,[status(thm)],[c_5859]) ).
tff(c_5875,plain,
~ $less('#skF_5','#skF_4'),
inference(splitRight,[status(thm)],[c_5859]) ).
tff(c_5912,plain,
~ $less('#skE_7','#skF_4'),
inference(demodulation,[status(thm),theory(equality)],[c_5874,c_5875]) ).
tff(c_5821,plain,
max('#skF_4','#skF_5') = '#skE_7',
inference(define,[status(thm),theory(equality)],[c_5779]) ).
tff(c_5820,plain,
~ $less('#skF_6',summation(max('#skF_4','#skF_5'))),
inference(resolution,[status(thm)],[c_5773,c_150]) ).
tff(c_5831,plain,
~ $less('#skF_6',summation('#skE_7')),
inference(demodulation,[status(thm),theory(equality)],[c_5821,c_5820]) ).
tff(c_5983,plain,
summation('#skE_7') = '#skE_8',
inference(define,[status(thm),theory(equality)],[c_5831]) ).
tff(c_5982,plain,
~ $less('#skF_6',summation('#skE_7')),
inference(demodulation,[status(thm),theory(equality)],[c_5821,c_5820]) ).
tff(c_5990,plain,
~ $less('#skF_6','#skE_8'),
inference(demodulation,[status(thm),theory(equality)],[c_5983,c_5982]) ).
tff(c_5989,plain,
summation('#skE_7') = '#skE_8',
inference(define,[status(thm),theory(equality)],[c_5831]) ).
tff(c_5807,plain,
! [X_2029a: $int,Y_2030a: $int,N_2031a: $int,Z_2032a: $int] :
( model_ub(X_2029a,Y_2030a,N_2031a)
| $less(N_2031a,summation(Z_2032a))
| ~ ub(X_2029a,Y_2030a,Z_2032a) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_22]) ).
tff(c_5812,plain,
! [X_7a: $int,Y_8a: $int,N_2031a: $int,Z_9a: $int] :
( model_ub(X_7a,Y_8a,N_2031a)
| $less(N_2031a,summation(Z_9a))
| $less(Z_9a,X_7a)
| $less(Z_9a,Y_8a) ),
inference(resolution,[status(thm)],[c_84,c_5807]) ).
tff(c_6109,plain,
! [X_2124a: $int,Y_2125a: $int,N_2126a: $int,Z_2127a: $int] :
( model_ub(X_2124a,Y_2125a,N_2126a)
| $less(N_2126a,summation(Z_2127a))
| $less(Z_2127a,X_2124a)
| $less(Z_2127a,Y_2125a) ),
inference(resolution,[status(thm)],[c_84,c_5807]) ).
tff(c_6166,plain,
! [X_2153a: $int,Y_2154a: $int,N_2155a: $int,Z_2156a: $int] :
( $less('#skF_3'(X_2153a,Y_2154a,N_2155a),N_2155a)
| minsol_model_ub(X_2153a,Y_2154a,N_2155a)
| $less(N_2155a,summation(Z_2156a))
| $less(Z_2156a,X_2153a)
| $less(Z_2156a,Y_2154a) ),
inference(resolution,[status(thm)],[c_6109,c_72]) ).
tff(c_5910,plain,
~ minsol_model_ub('#skF_4','#skE_7','#skF_6'),
inference(demodulation,[status(thm),theory(equality)],[c_5874,c_144]) ).
tff(c_6182,plain,
! [Z_2156a: $int] :
( $less('#skF_3'('#skF_4','#skE_7','#skF_6'),'#skF_6')
| $less('#skF_6',summation(Z_2156a))
| $less(Z_2156a,'#skF_4')
| $less(Z_2156a,'#skE_7') ),
inference(resolution,[status(thm)],[c_6166,c_5910]) ).
tff(c_6313,plain,
'#skF_3'('#skF_4','#skE_7','#skF_6') = '#skE_12',
inference(define,[status(thm),theory(equality)],[c_6182]) ).
tff(c_6329,plain,
( model_ub('#skF_4','#skE_7','#skE_12')
| minsol_model_ub('#skF_4','#skE_7','#skF_6')
| ~ model_ub('#skF_4','#skE_7','#skF_6') ),
inference(superposition,[status(thm),theory(equality)],[c_6313,c_71]) ).
tff(c_6368,plain,
~ model_ub('#skF_4','#skE_7','#skF_6'),
inference(splitLeft,[status(thm)],[c_6329]) ).
tff(c_6381,plain,
! [Z_2244a: $int] :
( $less('#skF_6',summation(Z_2244a))
| $less(Z_2244a,'#skF_4')
| $less(Z_2244a,'#skE_7') ),
inference(resolution,[status(thm)],[c_5812,c_6368]) ).
tff(c_6390,plain,
( $less('#skF_6','#skE_8')
| $less('#skE_7','#skF_4')
| $less('#skE_7','#skE_7') ),
inference(superposition,[status(thm),theory(equality)],[c_5989,c_6381]) ).
tff(c_6392,plain,
( $less('#skF_6','#skE_8')
| $less('#skE_7','#skF_4') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_6390]) ).
tff(c_6393,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_5912,c_5990,c_6392]) ).
tff(c_6397,plain,
( minsol_model_ub('#skF_4','#skE_7','#skF_6')
| model_ub('#skF_4','#skE_7','#skE_12') ),
inference(splitRight,[status(thm)],[c_6329]) ).
tff(c_6406,plain,
model_ub('#skF_4','#skE_7','#skE_12'),
inference(splitLeft,[status(thm)],[c_6397]) ).
tff(c_6424,plain,
~ $less('#skE_12',summation('#skF_1'('#skF_4','#skE_7','#skE_12'))),
inference(resolution,[status(thm)],[c_6406,c_80]) ).
tff(c_6436,plain,
'#skF_1'('#skF_4','#skE_7','#skE_12') = '#skE_13',
inference(define,[status(thm),theory(equality)],[c_6424]) ).
tff(c_6435,plain,
~ $less('#skE_12',summation('#skF_1'('#skF_4','#skE_7','#skE_12'))),
inference(resolution,[status(thm)],[c_6406,c_80]) ).
tff(c_6446,plain,
~ $less('#skE_12',summation('#skE_13')),
inference(demodulation,[status(thm),theory(equality)],[c_6436,c_6435]) ).
tff(c_6459,plain,
summation('#skE_13') = '#skE_14',
inference(define,[status(thm),theory(equality)],[c_6446]) ).
tff(c_5993,plain,
summation('#skE_7') = '#skE_8',
inference(define,[status(thm),theory(equality)],[c_5831]) ).
tff(c_6021,plain,
! [X_1a: $int] :
( $less('#skE_8',summation(X_1a))
| ~ $less('#skE_7',X_1a) ),
inference(superposition,[status(thm),theory(equality)],[c_5993,c_89]) ).
tff(c_6510,plain,
( $less('#skE_8','#skE_14')
| ~ $less('#skE_7','#skE_13') ),
inference(superposition,[status(thm),theory(equality)],[c_6459,c_6021]) ).
tff(c_6535,plain,
~ $less('#skE_7','#skE_13'),
inference(splitLeft,[status(thm)],[c_6510]) ).
tff(c_6024,plain,
! [Y_2a: $int] :
( $less(summation(Y_2a),'#skE_8')
| ~ $less(Y_2a,'#skE_7') ),
inference(superposition,[status(thm),theory(equality)],[c_5993,c_89]) ).
tff(c_6504,plain,
( $less('#skE_14','#skE_8')
| ~ $less('#skE_13','#skE_7') ),
inference(superposition,[status(thm),theory(equality)],[c_6459,c_6024]) ).
tff(c_6533,plain,
~ $less('#skE_13','#skE_7'),
inference(splitLeft,[status(thm)],[c_6504]) ).
tff(c_6512,plain,
( ( '#skE_8' = '#skE_14' )
| ( '#skE_7' != '#skE_13' ) ),
inference(superposition,[status(thm),theory(equality)],[c_6459,c_5989]) ).
tff(c_6531,plain,
'#skE_7' != '#skE_13',
inference(splitLeft,[status(thm)],[c_6512]) ).
tff(c_6536,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_6535,c_6533,c_6531]) ).
tff(c_6539,plain,
$less('#skE_8','#skE_14'),
inference(splitRight,[status(thm)],[c_6510]) ).
tff(c_6449,plain,
summation('#skE_13') = '#skE_14',
inference(define,[status(thm),theory(equality)],[c_6446]) ).
tff(c_6448,plain,
~ $less('#skE_12',summation('#skE_13')),
inference(demodulation,[status(thm),theory(equality)],[c_6436,c_6435]) ).
tff(c_6456,plain,
~ $less('#skE_12','#skE_14'),
inference(demodulation,[status(thm),theory(equality)],[c_6449,c_6448]) ).
tff(c_6300,plain,
'#skF_3'('#skF_4','#skE_7','#skF_6') = '#skE_12',
inference(define,[status(thm),theory(equality)],[c_6182]) ).
tff(c_6299,plain,
! [Z_2156a: $int] :
( $less('#skF_3'('#skF_4','#skE_7','#skF_6'),'#skF_6')
| $less('#skF_6',summation(Z_2156a))
| $less(Z_2156a,'#skF_4')
| $less(Z_2156a,'#skE_7') ),
inference(resolution,[status(thm)],[c_6166,c_5910]) ).
tff(c_6310,plain,
! [Z_2156a: $int] :
( $less('#skE_12','#skF_6')
| $less('#skF_6',summation(Z_2156a))
| $less(Z_2156a,'#skF_4')
| $less(Z_2156a,'#skE_7') ),
inference(demodulation,[status(thm),theory(equality)],[c_6300,c_6299]) ).
tff(c_6336,plain,
$less('#skE_12','#skF_6'),
inference(splitLeft,[status(thm)],[c_6310]) ).
tff(c_5992,plain,
summation('#skE_7') = '#skE_8',
inference(define,[status(thm),theory(equality)],[c_5831]) ).
tff(c_5828,plain,
max('#skF_4','#skF_5') = '#skE_7',
inference(define,[status(thm),theory(equality)],[c_5779]) ).
tff(c_5943,plain,
max('#skF_4','#skE_7') = '#skE_7',
inference(demodulation,[status(thm),theory(equality)],[c_5874,c_5828]) ).
tff(c_5770,plain,
minsol_model_max('#skF_4','#skF_5','#skF_6'),
inference(splitRight,[status(thm)],[c_66]) ).
tff(c_5907,plain,
minsol_model_max('#skF_4','#skE_7','#skF_6'),
inference(demodulation,[status(thm),theory(equality)],[c_5874,c_5770]) ).
tff(c_6098,plain,
! [X_2117a: $int,Y_2118a: $int,N_2119a: $int,N_2120a: $int] :
( ~ minsol_model_max(X_2117a,Y_2118a,N_2119a)
| ~ $less(N_2120a,N_2119a)
| $less(N_2120a,summation(max(X_2117a,Y_2118a))) ),
inference(resolution,[status(thm)],[c_82,c_179]) ).
tff(c_6101,plain,
! [N_2120a: $int] :
( ~ $less(N_2120a,'#skF_6')
| $less(N_2120a,summation(max('#skF_4','#skE_7'))) ),
inference(resolution,[status(thm)],[c_5907,c_6098]) ).
tff(c_6104,plain,
! [N_2120a: $int] :
( ~ $less(N_2120a,'#skF_6')
| $less(N_2120a,'#skE_8') ),
inference(demodulation,[status(thm),theory(equality)],[c_5992,c_5943,c_6101]) ).
tff(c_6105,plain,
$lesseq('#skF_6','#skE_8'),
inference(quantifierElimination,[status(thm),theory('LIA')],[c_6104]) ).
tff(c_6107,plain,
~ $less('#skE_8','#skF_6'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_6105]) ).
tff(c_6541,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_6539,c_6456,c_6336,c_6107]) ).
tff(c_6545,plain,
$less('#skE_13','#skE_7'),
inference(splitRight,[status(thm)],[c_6504]) ).
tff(c_6405,plain,
model_ub('#skF_4','#skE_7','#skE_12'),
inference(splitLeft,[status(thm)],[c_6397]) ).
tff(c_6548,plain,
'#skF_1'('#skF_4','#skE_7','#skE_12') = '#skE_13',
inference(define,[status(thm),theory(equality)],[c_6424]) ).
tff(c_6559,plain,
( ub('#skF_4','#skE_7','#skE_13')
| ~ model_ub('#skF_4','#skE_7','#skE_12') ),
inference(superposition,[status(thm),theory(equality)],[c_6548,c_79]) ).
tff(c_6681,plain,
ub('#skF_4','#skE_7','#skE_13'),
inference(demodulation,[status(thm),theory(equality)],[c_6405,c_6559]) ).
tff(c_6687,plain,
~ $less('#skE_13','#skE_7'),
inference(resolution,[status(thm)],[c_6681,c_86]) ).
tff(c_6700,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_6545,c_6687]) ).
tff(c_6703,plain,
'#skE_8' = '#skE_14',
inference(splitRight,[status(thm)],[c_6512]) ).
tff(c_6750,plain,
! [N_2120a: $int] :
( ~ $less(N_2120a,'#skF_6')
| $less(N_2120a,'#skE_14') ),
inference(demodulation,[status(thm),theory(equality)],[c_6703,c_6104]) ).
tff(c_6884,plain,
$lesseq('#skF_6','#skE_14'),
inference(quantifierElimination,[status(thm),theory('LIA')],[c_6750]) ).
tff(c_6886,plain,
~ $less('#skE_14','#skF_6'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_6884]) ).
tff(c_6887,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_6886,c_6456,c_6336]) ).
tff(c_6893,plain,
minsol_model_ub('#skF_4','#skE_7','#skF_6'),
inference(splitRight,[status(thm)],[c_6397]) ).
tff(c_6896,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_6893,c_5910]) ).
tff(c_6905,plain,
! [Z_2438a: $int] :
( $less('#skF_6',summation(Z_2438a))
| $less(Z_2438a,'#skF_4')
| $less(Z_2438a,'#skE_7') ),
inference(splitRight,[status(thm)],[c_6310]) ).
tff(c_6914,plain,
( $less('#skF_6','#skE_8')
| $less('#skE_7','#skF_4')
| $less('#skE_7','#skE_7') ),
inference(superposition,[status(thm),theory(equality)],[c_5989,c_6905]) ).
tff(c_6916,plain,
( $less('#skF_6','#skE_8')
| $less('#skE_7','#skF_4') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_6914]) ).
tff(c_6917,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_5912,c_5990,c_6916]) ).
tff(c_6920,plain,
'#skF_4' = '#skE_7',
inference(splitRight,[status(thm)],[c_5857]) ).
tff(c_6921,plain,
~ $less('#skF_4','#skF_5'),
inference(splitRight,[status(thm)],[c_5857]) ).
tff(c_6955,plain,
~ $less('#skE_7','#skF_5'),
inference(demodulation,[status(thm),theory(equality)],[c_6920,c_6921]) ).
tff(c_7014,plain,
summation('#skE_7') = '#skE_8',
inference(define,[status(thm),theory(equality)],[c_5831]) ).
tff(c_7021,plain,
~ $less('#skF_6','#skE_8'),
inference(demodulation,[status(thm),theory(equality)],[c_7014,c_5982]) ).
tff(c_7020,plain,
summation('#skE_7') = '#skE_8',
inference(define,[status(thm),theory(equality)],[c_5831]) ).
tff(c_7156,plain,
! [X_2515a: $int,Y_2516a: $int,N_2517a: $int,Z_2518a: $int] :
( model_ub(X_2515a,Y_2516a,N_2517a)
| $less(N_2517a,summation(Z_2518a))
| $less(Z_2518a,X_2515a)
| $less(Z_2518a,Y_2516a) ),
inference(resolution,[status(thm)],[c_84,c_5807]) ).
tff(c_7214,plain,
! [X_2547a: $int,Y_2548a: $int,N_2549a: $int,Z_2550a: $int] :
( $less('#skF_3'(X_2547a,Y_2548a,N_2549a),N_2549a)
| minsol_model_ub(X_2547a,Y_2548a,N_2549a)
| $less(N_2549a,summation(Z_2550a))
| $less(Z_2550a,X_2547a)
| $less(Z_2550a,Y_2548a) ),
inference(resolution,[status(thm)],[c_7156,c_72]) ).
tff(c_6953,plain,
~ minsol_model_ub('#skE_7','#skF_5','#skF_6'),
inference(demodulation,[status(thm),theory(equality)],[c_6920,c_144]) ).
tff(c_7230,plain,
! [Z_2550a: $int] :
( $less('#skF_3'('#skE_7','#skF_5','#skF_6'),'#skF_6')
| $less('#skF_6',summation(Z_2550a))
| $less(Z_2550a,'#skE_7')
| $less(Z_2550a,'#skF_5') ),
inference(resolution,[status(thm)],[c_7214,c_6953]) ).
tff(c_7384,plain,
'#skF_3'('#skE_7','#skF_5','#skF_6') = '#skE_9',
inference(define,[status(thm),theory(equality)],[c_7230]) ).
tff(c_7400,plain,
( model_ub('#skE_7','#skF_5','#skE_9')
| minsol_model_ub('#skE_7','#skF_5','#skF_6')
| ~ model_ub('#skE_7','#skF_5','#skF_6') ),
inference(superposition,[status(thm),theory(equality)],[c_7384,c_71]) ).
tff(c_7471,plain,
~ model_ub('#skE_7','#skF_5','#skF_6'),
inference(splitLeft,[status(thm)],[c_7400]) ).
tff(c_7484,plain,
! [Z_2650a: $int] :
( $less('#skF_6',summation(Z_2650a))
| $less(Z_2650a,'#skE_7')
| $less(Z_2650a,'#skF_5') ),
inference(resolution,[status(thm)],[c_5812,c_7471]) ).
tff(c_7493,plain,
( $less('#skF_6','#skE_8')
| $less('#skE_7','#skE_7')
| $less('#skE_7','#skF_5') ),
inference(superposition,[status(thm),theory(equality)],[c_7020,c_7484]) ).
tff(c_7495,plain,
( $less('#skF_6','#skE_8')
| $less('#skE_7','#skF_5') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_7493]) ).
tff(c_7496,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_6955,c_7021,c_7495]) ).
tff(c_7500,plain,
( minsol_model_ub('#skE_7','#skF_5','#skF_6')
| model_ub('#skE_7','#skF_5','#skE_9') ),
inference(splitRight,[status(thm)],[c_7400]) ).
tff(c_7512,plain,
model_ub('#skE_7','#skF_5','#skE_9'),
inference(splitLeft,[status(thm)],[c_7500]) ).
tff(c_7530,plain,
~ $less('#skE_9',summation('#skF_1'('#skE_7','#skF_5','#skE_9'))),
inference(resolution,[status(thm)],[c_7512,c_80]) ).
tff(c_7542,plain,
'#skF_1'('#skE_7','#skF_5','#skE_9') = '#skE_10',
inference(define,[status(thm),theory(equality)],[c_7530]) ).
tff(c_7541,plain,
~ $less('#skE_9',summation('#skF_1'('#skE_7','#skF_5','#skE_9'))),
inference(resolution,[status(thm)],[c_7512,c_80]) ).
tff(c_7552,plain,
~ $less('#skE_9',summation('#skE_10')),
inference(demodulation,[status(thm),theory(equality)],[c_7542,c_7541]) ).
tff(c_7565,plain,
summation('#skE_10') = '#skE_11',
inference(define,[status(thm),theory(equality)],[c_7552]) ).
tff(c_7041,plain,
summation('#skE_7') = '#skE_8',
inference(define,[status(thm),theory(equality)],[c_5831]) ).
tff(c_7072,plain,
! [Y_2a: $int] :
( $less(summation(Y_2a),'#skE_8')
| ~ $less(Y_2a,'#skE_7') ),
inference(superposition,[status(thm),theory(equality)],[c_7041,c_89]) ).
tff(c_7632,plain,
( $less('#skE_11','#skE_8')
| ~ $less('#skE_10','#skE_7') ),
inference(superposition,[status(thm),theory(equality)],[c_7565,c_7072]) ).
tff(c_7659,plain,
~ $less('#skE_10','#skE_7'),
inference(splitLeft,[status(thm)],[c_7632]) ).
tff(c_7069,plain,
! [X_1a: $int] :
( $less('#skE_8',summation(X_1a))
| ~ $less('#skE_7',X_1a) ),
inference(superposition,[status(thm),theory(equality)],[c_7041,c_89]) ).
tff(c_7634,plain,
( $less('#skE_8','#skE_11')
| ~ $less('#skE_7','#skE_10') ),
inference(superposition,[status(thm),theory(equality)],[c_7565,c_7069]) ).
tff(c_7657,plain,
~ $less('#skE_7','#skE_10'),
inference(splitLeft,[status(thm)],[c_7634]) ).
tff(c_7636,plain,
( ( '#skE_8' = '#skE_11' )
| ( '#skE_7' != '#skE_10' ) ),
inference(superposition,[status(thm),theory(equality)],[c_7565,c_7020]) ).
tff(c_7655,plain,
'#skE_7' != '#skE_10',
inference(splitLeft,[status(thm)],[c_7636]) ).
tff(c_7660,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_7659,c_7657,c_7655]) ).
tff(c_7664,plain,
$less('#skE_10','#skE_7'),
inference(splitRight,[status(thm)],[c_7632]) ).
tff(c_7511,plain,
model_ub('#skE_7','#skF_5','#skE_9'),
inference(splitLeft,[status(thm)],[c_7500]) ).
tff(c_7667,plain,
'#skF_1'('#skE_7','#skF_5','#skE_9') = '#skE_10',
inference(define,[status(thm),theory(equality)],[c_7530]) ).
tff(c_7678,plain,
( ub('#skE_7','#skF_5','#skE_10')
| ~ model_ub('#skE_7','#skF_5','#skE_9') ),
inference(superposition,[status(thm),theory(equality)],[c_7667,c_79]) ).
tff(c_7846,plain,
ub('#skE_7','#skF_5','#skE_10'),
inference(demodulation,[status(thm),theory(equality)],[c_7511,c_7678]) ).
tff(c_7855,plain,
~ $less('#skE_10','#skE_7'),
inference(resolution,[status(thm)],[c_7846,c_85]) ).
tff(c_7867,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_7664,c_7855]) ).
tff(c_7870,plain,
$less('#skE_8','#skE_11'),
inference(splitRight,[status(thm)],[c_7634]) ).
tff(c_7555,plain,
summation('#skE_10') = '#skE_11',
inference(define,[status(thm),theory(equality)],[c_7552]) ).
tff(c_7554,plain,
~ $less('#skE_9',summation('#skE_10')),
inference(demodulation,[status(thm),theory(equality)],[c_7542,c_7541]) ).
tff(c_7562,plain,
~ $less('#skE_9','#skE_11'),
inference(demodulation,[status(thm),theory(equality)],[c_7555,c_7554]) ).
tff(c_7371,plain,
'#skF_3'('#skE_7','#skF_5','#skF_6') = '#skE_9',
inference(define,[status(thm),theory(equality)],[c_7230]) ).
tff(c_7370,plain,
! [Z_2550a: $int] :
( $less('#skF_3'('#skE_7','#skF_5','#skF_6'),'#skF_6')
| $less('#skF_6',summation(Z_2550a))
| $less(Z_2550a,'#skE_7')
| $less(Z_2550a,'#skF_5') ),
inference(resolution,[status(thm)],[c_7214,c_6953]) ).
tff(c_7381,plain,
! [Z_2550a: $int] :
( $less('#skE_9','#skF_6')
| $less('#skF_6',summation(Z_2550a))
| $less(Z_2550a,'#skE_7')
| $less(Z_2550a,'#skF_5') ),
inference(demodulation,[status(thm),theory(equality)],[c_7371,c_7370]) ).
tff(c_7407,plain,
$less('#skE_9','#skF_6'),
inference(splitLeft,[status(thm)],[c_7381]) ).
tff(c_7040,plain,
summation('#skE_7') = '#skE_8',
inference(define,[status(thm),theory(equality)],[c_5831]) ).
tff(c_6976,plain,
max('#skE_7','#skF_5') = '#skE_7',
inference(demodulation,[status(thm),theory(equality)],[c_6920,c_5828]) ).
tff(c_6950,plain,
minsol_model_max('#skE_7','#skF_5','#skF_6'),
inference(demodulation,[status(thm),theory(equality)],[c_6920,c_5770]) ).
tff(c_7146,plain,
! [X_2511a: $int,Y_2512a: $int,N_2513a: $int,N_2514a: $int] :
( ~ minsol_model_max(X_2511a,Y_2512a,N_2513a)
| ~ $less(N_2514a,N_2513a)
| $less(N_2514a,summation(max(X_2511a,Y_2512a))) ),
inference(resolution,[status(thm)],[c_82,c_179]) ).
tff(c_7149,plain,
! [N_2514a: $int] :
( ~ $less(N_2514a,'#skF_6')
| $less(N_2514a,summation(max('#skE_7','#skF_5'))) ),
inference(resolution,[status(thm)],[c_6950,c_7146]) ).
tff(c_7152,plain,
! [N_2514a: $int] :
( ~ $less(N_2514a,'#skF_6')
| $less(N_2514a,'#skE_8') ),
inference(demodulation,[status(thm),theory(equality)],[c_7040,c_6976,c_7149]) ).
tff(c_7153,plain,
$lesseq('#skF_6','#skE_8'),
inference(quantifierElimination,[status(thm),theory('LIA')],[c_7152]) ).
tff(c_7155,plain,
~ $less('#skE_8','#skF_6'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_7153]) ).
tff(c_7872,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_7870,c_7562,c_7407,c_7155]) ).
tff(c_7875,plain,
'#skE_8' = '#skE_11',
inference(splitRight,[status(thm)],[c_7636]) ).
tff(c_7933,plain,
! [N_2514a: $int] :
( ~ $less(N_2514a,'#skF_6')
| $less(N_2514a,'#skE_11') ),
inference(demodulation,[status(thm),theory(equality)],[c_7875,c_7152]) ).
tff(c_8062,plain,
$lesseq('#skF_6','#skE_11'),
inference(quantifierElimination,[status(thm),theory('LIA')],[c_7933]) ).
tff(c_8064,plain,
~ $less('#skE_11','#skF_6'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_8062]) ).
tff(c_8065,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_8064,c_7562,c_7407]) ).
tff(c_8071,plain,
minsol_model_ub('#skE_7','#skF_5','#skF_6'),
inference(splitRight,[status(thm)],[c_7500]) ).
tff(c_8074,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_8071,c_6953]) ).
tff(c_8119,plain,
! [Z_2879a: $int] :
( $less('#skF_6',summation(Z_2879a))
| $less(Z_2879a,'#skE_7')
| $less(Z_2879a,'#skF_5') ),
inference(splitRight,[status(thm)],[c_7381]) ).
tff(c_8128,plain,
( $less('#skF_6','#skE_8')
| $less('#skE_7','#skE_7')
| $less('#skE_7','#skF_5') ),
inference(superposition,[status(thm),theory(equality)],[c_7020,c_8119]) ).
tff(c_8130,plain,
( $less('#skF_6','#skE_8')
| $less('#skE_7','#skF_5') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_8128]) ).
tff(c_8131,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_6955,c_7021,c_8130]) ).
tff(c_8135,plain,
minsol_model_ub('#skF_7','#skF_8','#skF_9'),
inference(splitRight,[status(thm)],[c_62]) ).
tff(c_11416,plain,
! [N_4076a: $int,X_4077a: $int,Y_4078a: $int] :
( ~ $less(N_4076a,summation('#skF_1'(X_4077a,Y_4078a,N_4076a)))
| ~ model_ub(X_4077a,Y_4078a,N_4076a) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_25]) ).
tff(c_11449,plain,
! [N_4103a: $int,X_4104a: $int,Y_4105a: $int] :
( ~ $less(N_4103a,summation('#skF_1'(X_4104a,Y_4105a,N_4103a)))
| ~ minsol_model_ub(X_4104a,Y_4105a,N_4103a) ),
inference(resolution,[status(thm)],[c_73,c_11416]) ).
tff(c_11455,plain,
~ $less('#skF_9',summation('#skF_1'('#skF_7','#skF_8','#skF_9'))),
inference(resolution,[status(thm)],[c_8135,c_11449]) ).
tff(c_11519,plain,
'#skF_1'('#skF_7','#skF_8','#skF_9') = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_11455]) ).
tff(c_11518,plain,
~ $less('#skF_9',summation('#skF_1'('#skF_7','#skF_8','#skF_9'))),
inference(resolution,[status(thm)],[c_8135,c_11449]) ).
tff(c_11529,plain,
~ $less('#skF_9',summation('#skE_1')),
inference(demodulation,[status(thm),theory(equality)],[c_11519,c_11518]) ).
tff(c_11563,plain,
summation('#skE_1') = '#skE_2',
inference(define,[status(thm),theory(equality)],[c_11529]) ).
tff(c_11478,plain,
! [X_4127a: $int,Y_4128a: $int,N_4129a: $int] :
( $less('#skF_2'(X_4127a,Y_4128a,N_4129a),N_4129a)
| minsol_model_max(X_4127a,Y_4128a,N_4129a)
| ~ model_max(X_4127a,Y_4128a,N_4129a) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_34]) ).
tff(c_11774,plain,
! [X_4225a: $int,Y_4226a: $int,N_4227a: $int] :
( $less('#skF_2'(X_4225a,Y_4226a,N_4227a),N_4227a)
| minsol_model_max(X_4225a,Y_4226a,N_4227a)
| $less(N_4227a,summation(max(X_4225a,Y_4226a))) ),
inference(resolution,[status(thm)],[c_82,c_11478]) ).
tff(c_11438,plain,
~ minsol_model_max('#skF_7','#skF_8','#skF_9'),
inference(splitLeft,[status(thm)],[c_66]) ).
tff(c_11792,plain,
( $less('#skF_2'('#skF_7','#skF_8','#skF_9'),'#skF_9')
| $less('#skF_9',summation(max('#skF_7','#skF_8'))) ),
inference(resolution,[status(thm)],[c_11774,c_11438]) ).
tff(c_11842,plain,
max('#skF_7','#skF_8') = '#skE_4',
inference(define,[status(thm),theory(equality)],[c_11792]) ).
tff(c_11867,plain,
( ( '#skF_8' = '#skE_4' )
| $less('#skF_8','#skF_7') ),
inference(superposition,[status(thm),theory(equality)],[c_11842,c_87]) ).
tff(c_11880,plain,
$less('#skF_8','#skF_7'),
inference(splitLeft,[status(thm)],[c_11867]) ).
tff(c_11865,plain,
( ( '#skF_7' = '#skE_4' )
| $less('#skF_7','#skF_8') ),
inference(superposition,[status(thm),theory(equality)],[c_11842,c_88]) ).
tff(c_11876,plain,
$less('#skF_7','#skF_8'),
inference(splitLeft,[status(thm)],[c_11865]) ).
tff(c_11903,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_11880,c_11876]) ).
tff(c_11906,plain,
'#skF_8' = '#skE_4',
inference(splitRight,[status(thm)],[c_11867]) ).
tff(c_11907,plain,
~ $less('#skF_8','#skF_7'),
inference(splitRight,[status(thm)],[c_11867]) ).
tff(c_11990,plain,
~ $less('#skE_4','#skF_7'),
inference(demodulation,[status(thm),theory(equality)],[c_11906,c_11907]) ).
tff(c_11836,plain,
max('#skF_7','#skF_8') = '#skE_4',
inference(define,[status(thm),theory(equality)],[c_11792]) ).
tff(c_12018,plain,
max('#skF_7','#skE_4') = '#skE_4',
inference(demodulation,[status(thm),theory(equality)],[c_11906,c_11836]) ).
tff(c_11833,plain,
'#skF_2'('#skF_7','#skF_8','#skF_9') = '#skE_3',
inference(define,[status(thm),theory(equality)],[c_11792]) ).
tff(c_12061,plain,
'#skF_2'('#skF_7','#skE_4','#skF_9') = '#skE_3',
inference(demodulation,[status(thm),theory(equality)],[c_11906,c_11833]) ).
tff(c_11486,plain,
! [X_10a: $int,Y_11a: $int,N_12a: $int] :
( $less('#skF_2'(X_10a,Y_11a,N_12a),N_12a)
| minsol_model_max(X_10a,Y_11a,N_12a)
| $less(N_12a,summation(max(X_10a,Y_11a))) ),
inference(resolution,[status(thm)],[c_82,c_11478]) ).
tff(c_12107,plain,
~ minsol_model_max('#skF_7','#skE_4','#skF_9'),
inference(demodulation,[status(thm),theory(equality)],[c_11906,c_11438]) ).
tff(c_12110,plain,
( $less('#skF_2'('#skF_7','#skE_4','#skF_9'),'#skF_9')
| $less('#skF_9',summation(max('#skF_7','#skE_4'))) ),
inference(resolution,[status(thm)],[c_11486,c_12107]) ).
tff(c_12116,plain,
( $less('#skE_3','#skF_9')
| $less('#skF_9',summation('#skE_4')) ),
inference(demodulation,[status(thm),theory(equality)],[c_12018,c_12061,c_12110]) ).
tff(c_12181,plain,
summation('#skE_4') = '#skE_5',
inference(define,[status(thm),theory(equality)],[c_12116]) ).
tff(c_11462,plain,
! [X_4116a: $int,Y_4117a: $int,N_4118a: $int,Z_4119a: $int] :
( model_ub(X_4116a,Y_4117a,N_4118a)
| $less(N_4118a,summation(Z_4119a))
| ~ ub(X_4116a,Y_4117a,Z_4119a) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_22]) ).
tff(c_11499,plain,
! [X_4136a: $int,Y_4137a: $int,N_4138a: $int,Z_4139a: $int] :
( model_ub(X_4136a,Y_4137a,N_4138a)
| $less(N_4138a,summation(Z_4139a))
| $less(Z_4139a,X_4136a)
| $less(Z_4139a,Y_4137a) ),
inference(resolution,[status(thm)],[c_84,c_11462]) ).
tff(c_11806,plain,
! [N_4240a: $int,Z_4239a: $int,N_4241a: $int,Y_4243a: $int,X_4242a: $int] :
( ~ minsol_model_ub(X_4242a,Y_4243a,N_4240a)
| ~ $less(N_4241a,N_4240a)
| $less(N_4241a,summation(Z_4239a))
| $less(Z_4239a,X_4242a)
| $less(Z_4239a,Y_4243a) ),
inference(resolution,[status(thm)],[c_11499,c_74]) ).
tff(c_11811,plain,
! [N_4241a: $int,Z_4239a: $int] :
( ~ $less(N_4241a,'#skF_9')
| $less(N_4241a,summation(Z_4239a))
| $less(Z_4239a,'#skF_7')
| $less(Z_4239a,'#skF_8') ),
inference(resolution,[status(thm)],[c_8135,c_11806]) ).
tff(c_12386,plain,
! [N_4425a: $int,Z_4426a: $int] :
( ~ $less(N_4425a,'#skF_9')
| $less(N_4425a,summation(Z_4426a))
| $less(Z_4426a,'#skF_7')
| $less(Z_4426a,'#skE_4') ),
inference(demodulation,[status(thm),theory(equality)],[c_11906,c_11811]) ).
tff(c_12403,plain,
! [N_4425a: $int] :
( ~ $less(N_4425a,'#skF_9')
| $less(N_4425a,'#skE_5')
| $less('#skE_4','#skF_7')
| $less('#skE_4','#skE_4') ),
inference(superposition,[status(thm),theory(equality)],[c_12181,c_12386]) ).
tff(c_12405,plain,
! [N_4425a: $int] :
( ~ $less(N_4425a,'#skF_9')
| $less(N_4425a,'#skE_5')
| $less('#skE_4','#skF_7') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_12403]) ).
tff(c_12409,plain,
! [N_4425a: $int] :
( ~ $less(N_4425a,'#skF_9')
| $less(N_4425a,'#skE_5') ),
inference(negUnitSimplification,[status(thm)],[c_11990,c_12405]) ).
tff(c_12410,plain,
$lesseq('#skF_9','#skE_5'),
inference(quantifierElimination,[status(thm),theory('LIA')],[c_12409]) ).
tff(c_12412,plain,
~ $less('#skE_5','#skF_9'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_12410]) ).
tff(c_12185,plain,
summation('#skE_4') = '#skE_5',
inference(define,[status(thm),theory(equality)],[c_12116]) ).
tff(c_11564,plain,
summation('#skE_1') = '#skE_2',
inference(define,[status(thm),theory(equality)],[c_11529]) ).
tff(c_11601,plain,
! [Y_2a: $int] :
( ~ $less(summation(Y_2a),'#skE_2')
| $less(Y_2a,'#skE_1') ),
inference(superposition,[status(thm),theory(equality)],[c_11564,c_90]) ).
tff(c_12232,plain,
( ~ $less('#skE_5','#skE_2')
| $less('#skE_4','#skE_1') ),
inference(superposition,[status(thm),theory(equality)],[c_12185,c_11601]) ).
tff(c_12271,plain,
~ $less('#skE_5','#skE_2'),
inference(splitLeft,[status(thm)],[c_12232]) ).
tff(c_11595,plain,
! [Y_2a: $int] :
( $less(summation(Y_2a),'#skE_2')
| ~ $less(Y_2a,'#skE_1') ),
inference(superposition,[status(thm),theory(equality)],[c_11564,c_89]) ).
tff(c_12230,plain,
( $less('#skE_5','#skE_2')
| ~ $less('#skE_4','#skE_1') ),
inference(superposition,[status(thm),theory(equality)],[c_12185,c_11595]) ).
tff(c_12277,plain,
~ $less('#skE_4','#skE_1'),
inference(negUnitSimplification,[status(thm)],[c_12271,c_12230]) ).
tff(c_11560,plain,
summation('#skE_1') = '#skE_2',
inference(define,[status(thm),theory(equality)],[c_11529]) ).
tff(c_12238,plain,
( ( '#skE_5' = '#skE_2' )
| ( '#skE_4' != '#skE_1' ) ),
inference(superposition,[status(thm),theory(equality)],[c_12185,c_11560]) ).
tff(c_12257,plain,
'#skE_4' != '#skE_1',
inference(splitLeft,[status(thm)],[c_12238]) ).
tff(c_8137,plain,
minsol_model_ub('#skF_7','#skF_8','#skF_9'),
inference(splitRight,[status(thm)],[c_62]) ).
tff(c_11532,plain,
'#skF_1'('#skF_7','#skF_8','#skF_9') = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_11455]) ).
tff(c_11548,plain,
( ub('#skF_7','#skF_8','#skE_1')
| ~ model_ub('#skF_7','#skF_8','#skF_9') ),
inference(superposition,[status(thm),theory(equality)],[c_11532,c_79]) ).
tff(c_11661,plain,
~ model_ub('#skF_7','#skF_8','#skF_9'),
inference(splitLeft,[status(thm)],[c_11548]) ).
tff(c_11667,plain,
~ minsol_model_ub('#skF_7','#skF_8','#skF_9'),
inference(resolution,[status(thm)],[c_73,c_11661]) ).
tff(c_11674,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_8137,c_11667]) ).
tff(c_11721,plain,
ub('#skF_7','#skF_8','#skE_1'),
inference(splitRight,[status(thm)],[c_11548]) ).
tff(c_11738,plain,
~ $less('#skE_1','#skF_8'),
inference(resolution,[status(thm)],[c_11721,c_86]) ).
tff(c_11973,plain,
~ $less('#skE_1','#skE_4'),
inference(demodulation,[status(thm),theory(equality)],[c_11906,c_11738]) ).
tff(c_12278,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_12277,c_12257,c_11973]) ).
tff(c_12282,plain,
$less('#skE_5','#skE_2'),
inference(splitRight,[status(thm)],[c_12232]) ).
tff(c_11554,plain,
summation('#skE_1') = '#skE_2',
inference(define,[status(thm),theory(equality)],[c_11529]) ).
tff(c_11553,plain,
~ $less('#skF_9',summation('#skE_1')),
inference(demodulation,[status(thm),theory(equality)],[c_11519,c_11518]) ).
tff(c_11561,plain,
~ $less('#skF_9','#skE_2'),
inference(demodulation,[status(thm),theory(equality)],[c_11554,c_11553]) ).
tff(c_12413,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_12412,c_12282,c_11561]) ).
tff(c_12417,plain,
'#skE_4' = '#skE_1',
inference(splitRight,[status(thm)],[c_12238]) ).
tff(c_11962,plain,
max('#skF_7','#skE_4') = '#skE_4',
inference(demodulation,[status(thm),theory(equality)],[c_11906,c_11836]) ).
tff(c_12542,plain,
max('#skF_7','#skE_1') = '#skE_1',
inference(demodulation,[status(thm),theory(equality)],[c_12417,c_12417,c_11962]) ).
tff(c_12062,plain,
'#skF_2'('#skF_7','#skE_4','#skF_9') = '#skE_3',
inference(demodulation,[status(thm),theory(equality)],[c_11906,c_11833]) ).
tff(c_12078,plain,
( model_max('#skF_7','#skE_4','#skE_3')
| minsol_model_max('#skF_7','#skE_4','#skF_9')
| ~ model_max('#skF_7','#skE_4','#skF_9') ),
inference(superposition,[status(thm),theory(equality)],[c_12062,c_75]) ).
tff(c_12785,plain,
( model_max('#skF_7','#skE_1','#skE_3')
| minsol_model_max('#skF_7','#skE_1','#skF_9')
| ~ model_max('#skF_7','#skE_1','#skF_9') ),
inference(demodulation,[status(thm),theory(equality)],[c_12417,c_12417,c_12417,c_12078]) ).
tff(c_12793,plain,
~ model_max('#skF_7','#skE_1','#skF_9'),
inference(splitLeft,[status(thm)],[c_12785]) ).
tff(c_12796,plain,
$less('#skF_9',summation(max('#skF_7','#skE_1'))),
inference(resolution,[status(thm)],[c_82,c_12793]) ).
tff(c_12801,plain,
$less('#skF_9','#skE_2'),
inference(demodulation,[status(thm),theory(equality)],[c_11563,c_12542,c_12796]) ).
tff(c_12803,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_11561,c_12801]) ).
tff(c_12807,plain,
( minsol_model_max('#skF_7','#skE_1','#skF_9')
| model_max('#skF_7','#skE_1','#skE_3') ),
inference(splitRight,[status(thm)],[c_12785]) ).
tff(c_12848,plain,
model_max('#skF_7','#skE_1','#skE_3'),
inference(splitLeft,[status(thm)],[c_12807]) ).
tff(c_12857,plain,
~ $less('#skE_3',summation(max('#skF_7','#skE_1'))),
inference(resolution,[status(thm)],[c_12848,c_83]) ).
tff(c_12866,plain,
~ $less('#skE_3','#skE_2'),
inference(demodulation,[status(thm),theory(equality)],[c_11563,c_12542,c_12857]) ).
tff(c_12416,plain,
'#skE_5' = '#skE_2',
inference(splitRight,[status(thm)],[c_12238]) ).
tff(c_12175,plain,
summation('#skE_4') = '#skE_5',
inference(define,[status(thm),theory(equality)],[c_12116]) ).
tff(c_12174,plain,
( $less('#skE_3','#skF_9')
| $less('#skF_9',summation('#skE_4')) ),
inference(demodulation,[status(thm),theory(equality)],[c_12018,c_12061,c_12110]) ).
tff(c_12182,plain,
( $less('#skE_3','#skF_9')
| $less('#skF_9','#skE_5') ),
inference(demodulation,[status(thm),theory(equality)],[c_12175,c_12174]) ).
tff(c_12580,plain,
( $less('#skE_3','#skF_9')
| $less('#skF_9','#skE_2') ),
inference(demodulation,[status(thm),theory(equality)],[c_12416,c_12182]) ).
tff(c_12582,plain,
$less('#skE_3','#skF_9'),
inference(negUnitSimplification,[status(thm)],[c_11561,c_12580]) ).
tff(c_11724,plain,
! [N_15a: $int] :
( model_ub('#skF_7','#skF_8',N_15a)
| $less(N_15a,summation('#skE_1')) ),
inference(resolution,[status(thm)],[c_11721,c_81]) ).
tff(c_11743,plain,
! [N_4212a: $int] :
( model_ub('#skF_7','#skF_8',N_4212a)
| $less(N_4212a,'#skE_2') ),
inference(demodulation,[status(thm),theory(equality)],[c_11563,c_11724]) ).
tff(c_11764,plain,
! [N_4223a: $int,N_4224a: $int] :
( ~ minsol_model_ub('#skF_7','#skF_8',N_4223a)
| ~ $less(N_4224a,N_4223a)
| $less(N_4224a,'#skE_2') ),
inference(resolution,[status(thm)],[c_11743,c_74]) ).
tff(c_11768,plain,
! [N_4224a: $int] :
( ~ $less(N_4224a,'#skF_9')
| $less(N_4224a,'#skE_2') ),
inference(resolution,[status(thm)],[c_8135,c_11764]) ).
tff(c_11770,plain,
! [N_4224a: $int] :
( ~ $less(N_4224a,'#skF_9')
| $less(N_4224a,'#skE_2') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_11768]) ).
tff(c_11771,plain,
$lesseq('#skF_9','#skE_2'),
inference(quantifierElimination,[status(thm),theory('LIA')],[c_11770]) ).
tff(c_11773,plain,
~ $less('#skE_2','#skF_9'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_11771]) ).
tff(c_12867,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_12866,c_12582,c_11773]) ).
tff(c_12873,plain,
minsol_model_max('#skF_7','#skE_1','#skF_9'),
inference(splitRight,[status(thm)],[c_12807]) ).
tff(c_11985,plain,
~ minsol_model_max('#skF_7','#skE_4','#skF_9'),
inference(demodulation,[status(thm),theory(equality)],[c_11906,c_11438]) ).
tff(c_12486,plain,
~ minsol_model_max('#skF_7','#skE_1','#skF_9'),
inference(demodulation,[status(thm),theory(equality)],[c_12417,c_11985]) ).
tff(c_12876,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_12873,c_12486]) ).
tff(c_12879,plain,
'#skF_7' = '#skE_4',
inference(splitRight,[status(thm)],[c_11865]) ).
tff(c_12880,plain,
~ $less('#skF_7','#skF_8'),
inference(splitRight,[status(thm)],[c_11865]) ).
tff(c_12963,plain,
~ $less('#skE_4','#skF_8'),
inference(demodulation,[status(thm),theory(equality)],[c_12879,c_12880]) ).
tff(c_11825,plain,
max('#skF_7','#skF_8') = '#skE_4',
inference(define,[status(thm),theory(equality)],[c_11792]) ).
tff(c_11824,plain,
'#skF_2'('#skF_7','#skF_8','#skF_9') = '#skE_3',
inference(define,[status(thm),theory(equality)],[c_11792]) ).
tff(c_11823,plain,
( $less('#skF_2'('#skF_7','#skF_8','#skF_9'),'#skF_9')
| $less('#skF_9',summation(max('#skF_7','#skF_8'))) ),
inference(resolution,[status(thm)],[c_11774,c_11438]) ).
tff(c_11839,plain,
( $less('#skE_3','#skF_9')
| $less('#skF_9',summation('#skE_4')) ),
inference(demodulation,[status(thm),theory(equality)],[c_11825,c_11824,c_11823]) ).
tff(c_13156,plain,
summation('#skE_4') = '#skE_5',
inference(define,[status(thm),theory(equality)],[c_11839]) ).
tff(c_13326,plain,
! [N_4802a: $int,Z_4803a: $int] :
( ~ $less(N_4802a,'#skF_9')
| $less(N_4802a,summation(Z_4803a))
| $less(Z_4803a,'#skE_4')
| $less(Z_4803a,'#skF_8') ),
inference(demodulation,[status(thm),theory(equality)],[c_12879,c_11811]) ).
tff(c_13343,plain,
! [N_4802a: $int] :
( ~ $less(N_4802a,'#skF_9')
| $less(N_4802a,'#skE_5')
| $less('#skE_4','#skE_4')
| $less('#skE_4','#skF_8') ),
inference(superposition,[status(thm),theory(equality)],[c_13156,c_13326]) ).
tff(c_13345,plain,
! [N_4802a: $int] :
( ~ $less(N_4802a,'#skF_9')
| $less(N_4802a,'#skE_5')
| $less('#skE_4','#skF_8') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_13343]) ).
tff(c_13396,plain,
! [N_4802a: $int] :
( ~ $less(N_4802a,'#skF_9')
| $less(N_4802a,'#skE_5') ),
inference(negUnitSimplification,[status(thm)],[c_12963,c_13345]) ).
tff(c_13397,plain,
$lesseq('#skF_9','#skE_5'),
inference(quantifierElimination,[status(thm),theory('LIA')],[c_13396]) ).
tff(c_13399,plain,
~ $less('#skE_5','#skF_9'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_13397]) ).
tff(c_13160,plain,
summation('#skE_4') = '#skE_5',
inference(define,[status(thm),theory(equality)],[c_11839]) ).
tff(c_13207,plain,
( ~ $less('#skE_5','#skE_2')
| $less('#skE_4','#skE_1') ),
inference(superposition,[status(thm),theory(equality)],[c_13160,c_11601]) ).
tff(c_13260,plain,
~ $less('#skE_5','#skE_2'),
inference(splitLeft,[status(thm)],[c_13207]) ).
tff(c_13205,plain,
( $less('#skE_5','#skE_2')
| ~ $less('#skE_4','#skE_1') ),
inference(superposition,[status(thm),theory(equality)],[c_13160,c_11595]) ).
tff(c_13283,plain,
~ $less('#skE_4','#skE_1'),
inference(negUnitSimplification,[status(thm)],[c_13260,c_13205]) ).
tff(c_13213,plain,
( ( '#skE_5' = '#skE_2' )
| ( '#skE_4' != '#skE_1' ) ),
inference(superposition,[status(thm),theory(equality)],[c_13160,c_11560]) ).
tff(c_13236,plain,
'#skE_4' != '#skE_1',
inference(splitLeft,[status(thm)],[c_13213]) ).
tff(c_11740,plain,
~ $less('#skE_1','#skF_7'),
inference(resolution,[status(thm)],[c_11721,c_85]) ).
tff(c_12945,plain,
~ $less('#skE_1','#skE_4'),
inference(demodulation,[status(thm),theory(equality)],[c_12879,c_11740]) ).
tff(c_13284,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_13283,c_13236,c_12945]) ).
tff(c_13288,plain,
$less('#skE_5','#skE_2'),
inference(splitRight,[status(thm)],[c_13207]) ).
tff(c_13400,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_13399,c_13288,c_11561]) ).
tff(c_13404,plain,
'#skE_4' = '#skE_1',
inference(splitRight,[status(thm)],[c_13213]) ).
tff(c_12934,plain,
max('#skE_4','#skF_8') = '#skE_4',
inference(demodulation,[status(thm),theory(equality)],[c_12879,c_11836]) ).
tff(c_13532,plain,
max('#skE_1','#skF_8') = '#skE_1',
inference(demodulation,[status(thm),theory(equality)],[c_13404,c_13404,c_12934]) ).
tff(c_12987,plain,
'#skF_2'('#skE_4','#skF_8','#skF_9') = '#skE_3',
inference(demodulation,[status(thm),theory(equality)],[c_12879,c_11833]) ).
tff(c_13003,plain,
( model_max('#skE_4','#skF_8','#skE_3')
| minsol_model_max('#skE_4','#skF_8','#skF_9')
| ~ model_max('#skE_4','#skF_8','#skF_9') ),
inference(superposition,[status(thm),theory(equality)],[c_12987,c_75]) ).
tff(c_13999,plain,
( model_max('#skE_1','#skF_8','#skE_3')
| minsol_model_max('#skE_1','#skF_8','#skF_9')
| ~ model_max('#skE_1','#skF_8','#skF_9') ),
inference(demodulation,[status(thm),theory(equality)],[c_13404,c_13404,c_13404,c_13003]) ).
tff(c_14007,plain,
~ model_max('#skE_1','#skF_8','#skF_9'),
inference(splitLeft,[status(thm)],[c_13999]) ).
tff(c_14010,plain,
$less('#skF_9',summation(max('#skE_1','#skF_8'))),
inference(resolution,[status(thm)],[c_82,c_14007]) ).
tff(c_14015,plain,
$less('#skF_9','#skE_2'),
inference(demodulation,[status(thm),theory(equality)],[c_11563,c_13532,c_14010]) ).
tff(c_14017,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_11561,c_14015]) ).
tff(c_14021,plain,
( minsol_model_max('#skE_1','#skF_8','#skF_9')
| model_max('#skE_1','#skF_8','#skE_3') ),
inference(splitRight,[status(thm)],[c_13999]) ).
tff(c_14030,plain,
model_max('#skE_1','#skF_8','#skE_3'),
inference(splitLeft,[status(thm)],[c_14021]) ).
tff(c_14039,plain,
~ $less('#skE_3',summation(max('#skE_1','#skF_8'))),
inference(resolution,[status(thm)],[c_14030,c_83]) ).
tff(c_14048,plain,
~ $less('#skE_3','#skE_2'),
inference(demodulation,[status(thm),theory(equality)],[c_11563,c_13532,c_14039]) ).
tff(c_13403,plain,
'#skE_5' = '#skE_2',
inference(splitRight,[status(thm)],[c_13213]) ).
tff(c_13150,plain,
summation('#skE_4') = '#skE_5',
inference(define,[status(thm),theory(equality)],[c_11839]) ).
tff(c_13149,plain,
( $less('#skE_3','#skF_9')
| $less('#skF_9',summation('#skE_4')) ),
inference(demodulation,[status(thm),theory(equality)],[c_11825,c_11824,c_11823]) ).
tff(c_13157,plain,
( $less('#skE_3','#skF_9')
| $less('#skF_9','#skE_5') ),
inference(demodulation,[status(thm),theory(equality)],[c_13150,c_13149]) ).
tff(c_13570,plain,
( $less('#skE_3','#skF_9')
| $less('#skF_9','#skE_2') ),
inference(demodulation,[status(thm),theory(equality)],[c_13403,c_13157]) ).
tff(c_13572,plain,
$less('#skE_3','#skF_9'),
inference(negUnitSimplification,[status(thm)],[c_11561,c_13570]) ).
tff(c_14050,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_14048,c_13572,c_11773]) ).
tff(c_14056,plain,
minsol_model_max('#skE_1','#skF_8','#skF_9'),
inference(splitRight,[status(thm)],[c_14021]) ).
tff(c_12957,plain,
~ minsol_model_max('#skE_4','#skF_8','#skF_9'),
inference(demodulation,[status(thm),theory(equality)],[c_12879,c_11438]) ).
tff(c_13488,plain,
~ minsol_model_max('#skE_1','#skF_8','#skF_9'),
inference(demodulation,[status(thm),theory(equality)],[c_13404,c_12957]) ).
tff(c_14059,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_14056,c_13488]) ).
tff(c_14066,plain,
minsol_model_max('#skF_4','#skF_5','#skF_6'),
inference(splitRight,[status(thm)],[c_66]) ).
tff(c_8151,plain,
! [N_2892a: $int,X_2893a: $int,Y_2894a: $int] :
( ~ $less(N_2892a,summation(max(X_2893a,Y_2894a)))
| ~ model_max(X_2893a,Y_2894a,N_2892a) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_16]) ).
tff(c_8161,plain,
! [N_21a: $int,X_19a: $int,Y_20a: $int] :
( ~ $less(N_21a,summation(max(X_19a,Y_20a)))
| ~ minsol_model_max(X_19a,Y_20a,N_21a) ),
inference(resolution,[status(thm)],[c_77,c_8151]) ).
tff(c_14072,plain,
~ $less('#skF_6',summation(max('#skF_4','#skF_5'))),
inference(resolution,[status(thm)],[c_14066,c_8161]) ).
tff(c_14138,plain,
max('#skF_4','#skF_5') = '#skE_7',
inference(define,[status(thm),theory(equality)],[c_14072]) ).
tff(c_14170,plain,
( ( '#skF_5' = '#skE_7' )
| $less('#skF_5','#skF_4') ),
inference(superposition,[status(thm),theory(equality)],[c_87,c_14138]) ).
tff(c_14185,plain,
$less('#skF_5','#skF_4'),
inference(splitLeft,[status(thm)],[c_14170]) ).
tff(c_14161,plain,
( ( '#skF_4' = '#skE_7' )
| $less('#skF_4','#skF_5') ),
inference(superposition,[status(thm),theory(equality)],[c_14138,c_88]) ).
tff(c_14172,plain,
$less('#skF_4','#skF_5'),
inference(splitLeft,[status(thm)],[c_14161]) ).
tff(c_14186,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_14185,c_14172]) ).
tff(c_14189,plain,
'#skF_5' = '#skE_7',
inference(splitRight,[status(thm)],[c_14170]) ).
tff(c_14190,plain,
~ $less('#skF_5','#skF_4'),
inference(splitRight,[status(thm)],[c_14170]) ).
tff(c_14235,plain,
~ $less('#skE_7','#skF_4'),
inference(demodulation,[status(thm),theory(equality)],[c_14189,c_14190]) ).
tff(c_14125,plain,
max('#skF_4','#skF_5') = '#skE_7',
inference(define,[status(thm),theory(equality)],[c_14072]) ).
tff(c_14124,plain,
~ $less('#skF_6',summation(max('#skF_4','#skF_5'))),
inference(resolution,[status(thm)],[c_14066,c_8161]) ).
tff(c_14135,plain,
~ $less('#skF_6',summation('#skE_7')),
inference(demodulation,[status(thm),theory(equality)],[c_14125,c_14124]) ).
tff(c_14287,plain,
summation('#skE_7') = '#skE_8',
inference(define,[status(thm),theory(equality)],[c_14135]) ).
tff(c_14286,plain,
~ $less('#skF_6',summation('#skE_7')),
inference(demodulation,[status(thm),theory(equality)],[c_14125,c_14124]) ).
tff(c_14294,plain,
~ $less('#skF_6','#skE_8'),
inference(demodulation,[status(thm),theory(equality)],[c_14287,c_14286]) ).
tff(c_14293,plain,
summation('#skE_7') = '#skE_8',
inference(define,[status(thm),theory(equality)],[c_14135]) ).
tff(c_14085,plain,
! [X_5128a: $int,Y_5129a: $int,N_5130a: $int,Z_5131a: $int] :
( model_ub(X_5128a,Y_5129a,N_5130a)
| $less(N_5130a,summation(Z_5131a))
| ~ ub(X_5128a,Y_5129a,Z_5131a) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_22]) ).
tff(c_14090,plain,
! [X_7a: $int,Y_8a: $int,N_5130a: $int,Z_9a: $int] :
( model_ub(X_7a,Y_8a,N_5130a)
| $less(N_5130a,summation(Z_9a))
| $less(Z_9a,X_7a)
| $less(Z_9a,Y_8a) ),
inference(resolution,[status(thm)],[c_84,c_14085]) ).
tff(c_14820,plain,
! [X_5320a: $int,Y_5321a: $int,N_5322a: $int,Z_5323a: $int] :
( model_ub(X_5320a,Y_5321a,N_5322a)
| $less(N_5322a,summation(Z_5323a))
| $less(Z_5323a,X_5320a)
| $less(Z_5323a,Y_5321a) ),
inference(resolution,[status(thm)],[c_84,c_14085]) ).
tff(c_14950,plain,
! [X_5358a: $int,Y_5359a: $int,N_5360a: $int,Z_5361a: $int] :
( $less('#skF_3'(X_5358a,Y_5359a,N_5360a),N_5360a)
| minsol_model_ub(X_5358a,Y_5359a,N_5360a)
| $less(N_5360a,summation(Z_5361a))
| $less(Z_5361a,X_5358a)
| $less(Z_5361a,Y_5359a) ),
inference(resolution,[status(thm)],[c_14820,c_72]) ).
tff(c_8170,plain,
! [N_2904a: $int,X_2905a: $int,Y_2906a: $int] :
( ~ $less(N_2904a,summation('#skF_1'(X_2905a,Y_2906a,N_2904a)))
| ~ model_ub(X_2905a,Y_2906a,N_2904a) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_25]) ).
tff(c_8201,plain,
! [N_2928a: $int,X_2929a: $int,Y_2930a: $int] :
( ~ $less(N_2928a,summation('#skF_1'(X_2929a,Y_2930a,N_2928a)))
| ~ minsol_model_ub(X_2929a,Y_2930a,N_2928a) ),
inference(resolution,[status(thm)],[c_73,c_8170]) ).
tff(c_8207,plain,
~ $less('#skF_9',summation('#skF_1'('#skF_7','#skF_8','#skF_9'))),
inference(resolution,[status(thm)],[c_8135,c_8201]) ).
tff(c_8261,plain,
'#skF_1'('#skF_7','#skF_8','#skF_9') = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_8207]) ).
tff(c_8260,plain,
~ $less('#skF_9',summation('#skF_1'('#skF_7','#skF_8','#skF_9'))),
inference(resolution,[status(thm)],[c_8135,c_8201]) ).
tff(c_8271,plain,
~ $less('#skF_9',summation('#skE_1')),
inference(demodulation,[status(thm),theory(equality)],[c_8261,c_8260]) ).
tff(c_8287,plain,
summation('#skE_1') = '#skE_2',
inference(define,[status(thm),theory(equality)],[c_8271]) ).
tff(c_8224,plain,
! [X_2946a: $int,Y_2947a: $int,N_2948a: $int] :
( $less('#skF_2'(X_2946a,Y_2947a,N_2948a),N_2948a)
| minsol_model_max(X_2946a,Y_2947a,N_2948a)
| ~ model_max(X_2946a,Y_2947a,N_2948a) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_34]) ).
tff(c_8399,plain,
! [X_3004a: $int,Y_3005a: $int,N_3006a: $int] :
( $less('#skF_2'(X_3004a,Y_3005a,N_3006a),N_3006a)
| minsol_model_max(X_3004a,Y_3005a,N_3006a)
| $less(N_3006a,summation(max(X_3004a,Y_3005a))) ),
inference(resolution,[status(thm)],[c_82,c_8224]) ).
tff(c_70,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_8165,plain,
~ minsol_model_max('#skF_7','#skF_8','#skF_9'),
inference(splitLeft,[status(thm)],[c_70]) ).
tff(c_8419,plain,
( $less('#skF_2'('#skF_7','#skF_8','#skF_9'),'#skF_9')
| $less('#skF_9',summation(max('#skF_7','#skF_8'))) ),
inference(resolution,[status(thm)],[c_8399,c_8165]) ).
tff(c_8440,plain,
max('#skF_7','#skF_8') = '#skE_4',
inference(define,[status(thm),theory(equality)],[c_8419]) ).
tff(c_8465,plain,
( ( '#skF_8' = '#skE_4' )
| $less('#skF_8','#skF_7') ),
inference(superposition,[status(thm),theory(equality)],[c_8440,c_87]) ).
tff(c_8478,plain,
$less('#skF_8','#skF_7'),
inference(splitLeft,[status(thm)],[c_8465]) ).
tff(c_8463,plain,
( ( '#skF_7' = '#skE_4' )
| $less('#skF_7','#skF_8') ),
inference(superposition,[status(thm),theory(equality)],[c_8440,c_88]) ).
tff(c_8474,plain,
$less('#skF_7','#skF_8'),
inference(splitLeft,[status(thm)],[c_8463]) ).
tff(c_8501,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_8478,c_8474]) ).
tff(c_8504,plain,
'#skF_8' = '#skE_4',
inference(splitRight,[status(thm)],[c_8465]) ).
tff(c_8505,plain,
~ $less('#skF_8','#skF_7'),
inference(splitRight,[status(thm)],[c_8465]) ).
tff(c_8550,plain,
~ $less('#skE_4','#skF_7'),
inference(demodulation,[status(thm),theory(equality)],[c_8504,c_8505]) ).
tff(c_8423,plain,
max('#skF_7','#skF_8') = '#skE_4',
inference(define,[status(thm),theory(equality)],[c_8419]) ).
tff(c_8422,plain,
'#skF_2'('#skF_7','#skF_8','#skF_9') = '#skE_3',
inference(define,[status(thm),theory(equality)],[c_8419]) ).
tff(c_8421,plain,
( $less('#skF_2'('#skF_7','#skF_8','#skF_9'),'#skF_9')
| $less('#skF_9',summation(max('#skF_7','#skF_8'))) ),
inference(resolution,[status(thm)],[c_8399,c_8165]) ).
tff(c_8437,plain,
( $less('#skE_3','#skF_9')
| $less('#skF_9',summation('#skE_4')) ),
inference(demodulation,[status(thm),theory(equality)],[c_8423,c_8422,c_8421]) ).
tff(c_8685,plain,
summation('#skE_4') = '#skE_5',
inference(define,[status(thm),theory(equality)],[c_8437]) ).
tff(c_8548,plain,
minsol_model_ub('#skF_7','#skE_4','#skF_9'),
inference(demodulation,[status(thm),theory(equality)],[c_8504,c_8135]) ).
tff(c_8217,plain,
! [X_2938a: $int,Y_2939a: $int,N_2940a: $int,Z_2941a: $int] :
( model_ub(X_2938a,Y_2939a,N_2940a)
| $less(N_2940a,summation(Z_2941a))
| ~ ub(X_2938a,Y_2939a,Z_2941a) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_22]) ).
tff(c_8242,plain,
! [X_2955a: $int,Y_2956a: $int,N_2957a: $int,Z_2958a: $int] :
( model_ub(X_2955a,Y_2956a,N_2957a)
| $less(N_2957a,summation(Z_2958a))
| $less(Z_2958a,X_2955a)
| $less(Z_2958a,Y_2956a) ),
inference(resolution,[status(thm)],[c_84,c_8217]) ).
tff(c_9231,plain,
! [Y_3260a: $int,Z_3261a: $int,X_3262a: $int,N_3259a: $int,N_3258a: $int] :
( ~ minsol_model_ub(X_3262a,Y_3260a,N_3258a)
| ~ $less(N_3259a,N_3258a)
| $less(N_3259a,summation(Z_3261a))
| $less(Z_3261a,X_3262a)
| $less(Z_3261a,Y_3260a) ),
inference(resolution,[status(thm)],[c_8242,c_74]) ).
tff(c_9237,plain,
! [N_3263a: $int,Z_3264a: $int] :
( ~ $less(N_3263a,'#skF_9')
| $less(N_3263a,summation(Z_3264a))
| $less(Z_3264a,'#skF_7')
| $less(Z_3264a,'#skE_4') ),
inference(resolution,[status(thm)],[c_8548,c_9231]) ).
tff(c_9254,plain,
! [N_3263a: $int] :
( ~ $less(N_3263a,'#skF_9')
| $less(N_3263a,'#skE_5')
| $less('#skE_4','#skF_7')
| $less('#skE_4','#skE_4') ),
inference(superposition,[status(thm),theory(equality)],[c_8685,c_9237]) ).
tff(c_9256,plain,
! [N_3263a: $int] :
( ~ $less(N_3263a,'#skF_9')
| $less(N_3263a,'#skE_5')
| $less('#skE_4','#skF_7') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_9254]) ).
tff(c_9259,plain,
! [N_3263a: $int] :
( ~ $less(N_3263a,'#skF_9')
| $less(N_3263a,'#skE_5') ),
inference(negUnitSimplification,[status(thm)],[c_8550,c_9256]) ).
tff(c_9260,plain,
$lesseq('#skF_9','#skE_5'),
inference(quantifierElimination,[status(thm),theory('LIA')],[c_9259]) ).
tff(c_9262,plain,
~ $less('#skE_5','#skF_9'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_9260]) ).
tff(c_8691,plain,
summation('#skE_4') = '#skE_5',
inference(define,[status(thm),theory(equality)],[c_8437]) ).
tff(c_8288,plain,
summation('#skE_1') = '#skE_2',
inference(define,[status(thm),theory(equality)],[c_8271]) ).
tff(c_8322,plain,
! [X_1a: $int] :
( ~ $less('#skE_2',summation(X_1a))
| $less('#skE_1',X_1a) ),
inference(superposition,[status(thm),theory(equality)],[c_8288,c_90]) ).
tff(c_8740,plain,
( ~ $less('#skE_2','#skE_5')
| $less('#skE_1','#skE_4') ),
inference(superposition,[status(thm),theory(equality)],[c_8691,c_8322]) ).
tff(c_8788,plain,
~ $less('#skE_2','#skE_5'),
inference(splitLeft,[status(thm)],[c_8740]) ).
tff(c_8284,plain,
summation('#skE_1') = '#skE_2',
inference(define,[status(thm),theory(equality)],[c_8271]) ).
tff(c_8798,plain,
! [Y_3153a: $int] :
( $less(summation(Y_3153a),'#skE_5')
| ~ $less(Y_3153a,'#skE_4') ),
inference(superposition,[status(thm),theory(equality)],[c_8691,c_89]) ).
tff(c_8814,plain,
( $less('#skE_2','#skE_5')
| ~ $less('#skE_1','#skE_4') ),
inference(superposition,[status(thm),theory(equality)],[c_8284,c_8798]) ).
tff(c_8817,plain,
~ $less('#skE_1','#skE_4'),
inference(negUnitSimplification,[status(thm)],[c_8788,c_8814]) ).
tff(c_8319,plain,
! [Y_2a: $int] :
( $less(summation(Y_2a),'#skE_2')
| ~ $less(Y_2a,'#skE_1') ),
inference(superposition,[status(thm),theory(equality)],[c_8288,c_89]) ).
tff(c_8736,plain,
( $less('#skE_5','#skE_2')
| ~ $less('#skE_4','#skE_1') ),
inference(superposition,[status(thm),theory(equality)],[c_8691,c_8319]) ).
tff(c_8765,plain,
~ $less('#skE_4','#skE_1'),
inference(splitLeft,[status(thm)],[c_8736]) ).
tff(c_8744,plain,
( ( '#skE_5' = '#skE_2' )
| ( '#skE_4' != '#skE_1' ) ),
inference(superposition,[status(thm),theory(equality)],[c_8691,c_8284]) ).
tff(c_8763,plain,
'#skE_4' != '#skE_1',
inference(splitLeft,[status(thm)],[c_8744]) ).
tff(c_8818,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_8817,c_8765,c_8763]) ).
tff(c_8821,plain,
$less('#skE_1','#skE_4'),
inference(splitRight,[status(thm)],[c_8740]) ).
tff(c_8552,plain,
minsol_model_ub('#skF_7','#skE_4','#skF_9'),
inference(demodulation,[status(thm),theory(equality)],[c_8504,c_8135]) ).
tff(c_8355,plain,
'#skF_1'('#skF_7','#skF_8','#skF_9') = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_8207]) ).
tff(c_8371,plain,
( ub('#skF_7','#skF_8','#skE_1')
| ~ model_ub('#skF_7','#skF_8','#skF_9') ),
inference(superposition,[status(thm),theory(equality)],[c_8355,c_79]) ).
tff(c_8861,plain,
( ub('#skF_7','#skE_4','#skE_1')
| ~ model_ub('#skF_7','#skE_4','#skF_9') ),
inference(demodulation,[status(thm),theory(equality)],[c_8504,c_8504,c_8371]) ).
tff(c_8913,plain,
~ model_ub('#skF_7','#skE_4','#skF_9'),
inference(splitLeft,[status(thm)],[c_8861]) ).
tff(c_8919,plain,
~ minsol_model_ub('#skF_7','#skE_4','#skF_9'),
inference(resolution,[status(thm)],[c_73,c_8913]) ).
tff(c_8926,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_8552,c_8919]) ).
tff(c_8978,plain,
ub('#skF_7','#skE_4','#skE_1'),
inference(splitRight,[status(thm)],[c_8861]) ).
tff(c_8984,plain,
~ $less('#skE_1','#skE_4'),
inference(resolution,[status(thm)],[c_8978,c_86]) ).
tff(c_8997,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_8821,c_8984]) ).
tff(c_9000,plain,
$less('#skE_5','#skE_2'),
inference(splitRight,[status(thm)],[c_8736]) ).
tff(c_8278,plain,
summation('#skE_1') = '#skE_2',
inference(define,[status(thm),theory(equality)],[c_8271]) ).
tff(c_8277,plain,
~ $less('#skF_9',summation('#skE_1')),
inference(demodulation,[status(thm),theory(equality)],[c_8261,c_8260]) ).
tff(c_8285,plain,
~ $less('#skF_9','#skE_2'),
inference(demodulation,[status(thm),theory(equality)],[c_8278,c_8277]) ).
tff(c_9263,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_9262,c_9000,c_8285]) ).
tff(c_9267,plain,
'#skE_4' = '#skE_1',
inference(splitRight,[status(thm)],[c_8744]) ).
tff(c_8434,plain,
max('#skF_7','#skF_8') = '#skE_4',
inference(define,[status(thm),theory(equality)],[c_8419]) ).
tff(c_8536,plain,
max('#skF_7','#skE_4') = '#skE_4',
inference(demodulation,[status(thm),theory(equality)],[c_8504,c_8434]) ).
tff(c_9449,plain,
max('#skF_7','#skE_1') = '#skE_1',
inference(demodulation,[status(thm),theory(equality)],[c_9267,c_9267,c_8536]) ).
tff(c_8431,plain,
'#skF_2'('#skF_7','#skF_8','#skF_9') = '#skE_3',
inference(define,[status(thm),theory(equality)],[c_8419]) ).
tff(c_8622,plain,
'#skF_2'('#skF_7','#skE_4','#skF_9') = '#skE_3',
inference(demodulation,[status(thm),theory(equality)],[c_8504,c_8431]) ).
tff(c_9519,plain,
'#skF_2'('#skF_7','#skE_1','#skF_9') = '#skE_3',
inference(demodulation,[status(thm),theory(equality)],[c_9267,c_8622]) ).
tff(c_9535,plain,
( model_max('#skF_7','#skE_1','#skE_3')
| minsol_model_max('#skF_7','#skE_1','#skF_9')
| ~ model_max('#skF_7','#skE_1','#skF_9') ),
inference(superposition,[status(thm),theory(equality)],[c_9519,c_75]) ).
tff(c_9799,plain,
~ model_max('#skF_7','#skE_1','#skF_9'),
inference(splitLeft,[status(thm)],[c_9535]) ).
tff(c_9802,plain,
$less('#skF_9',summation(max('#skF_7','#skE_1'))),
inference(resolution,[status(thm)],[c_82,c_9799]) ).
tff(c_9807,plain,
$less('#skF_9','#skE_2'),
inference(demodulation,[status(thm),theory(equality)],[c_8287,c_9449,c_9802]) ).
tff(c_9809,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_8285,c_9807]) ).
tff(c_9813,plain,
( minsol_model_max('#skF_7','#skE_1','#skF_9')
| model_max('#skF_7','#skE_1','#skE_3') ),
inference(splitRight,[status(thm)],[c_9535]) ).
tff(c_9822,plain,
model_max('#skF_7','#skE_1','#skE_3'),
inference(splitLeft,[status(thm)],[c_9813]) ).
tff(c_9831,plain,
~ $less('#skE_3',summation(max('#skF_7','#skE_1'))),
inference(resolution,[status(thm)],[c_9822,c_83]) ).
tff(c_9840,plain,
~ $less('#skE_3','#skE_2'),
inference(demodulation,[status(thm),theory(equality)],[c_8287,c_9449,c_9831]) ).
tff(c_9406,plain,
~ $less('#skE_1','#skF_7'),
inference(demodulation,[status(thm),theory(equality)],[c_9267,c_8550]) ).
tff(c_9405,plain,
minsol_model_ub('#skF_7','#skE_1','#skF_9'),
inference(demodulation,[status(thm),theory(equality)],[c_9267,c_8548]) ).
tff(c_9551,plain,
! [N_3418a: $int,Y_3420a: $int,N_3419a: $int,X_3422a: $int,Z_3421a: $int] :
( ~ minsol_model_ub(X_3422a,Y_3420a,N_3418a)
| ~ $less(N_3419a,N_3418a)
| $less(N_3419a,summation(Z_3421a))
| $less(Z_3421a,X_3422a)
| $less(Z_3421a,Y_3420a) ),
inference(resolution,[status(thm)],[c_8242,c_74]) ).
tff(c_9557,plain,
! [N_3423a: $int,Z_3424a: $int] :
( ~ $less(N_3423a,'#skF_9')
| $less(N_3423a,summation(Z_3424a))
| $less(Z_3424a,'#skF_7')
| $less(Z_3424a,'#skE_1') ),
inference(resolution,[status(thm)],[c_9405,c_9551]) ).
tff(c_9566,plain,
! [N_3423a: $int] :
( ~ $less(N_3423a,'#skF_9')
| $less(N_3423a,'#skE_2')
| $less('#skE_1','#skF_7')
| $less('#skE_1','#skE_1') ),
inference(superposition,[status(thm),theory(equality)],[c_8284,c_9557]) ).
tff(c_9568,plain,
! [N_3423a: $int] :
( ~ $less(N_3423a,'#skF_9')
| $less(N_3423a,'#skE_2')
| $less('#skE_1','#skF_7') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_9566]) ).
tff(c_9570,plain,
! [N_3423a: $int] :
( ~ $less(N_3423a,'#skF_9')
| $less(N_3423a,'#skE_2') ),
inference(negUnitSimplification,[status(thm)],[c_9406,c_9568]) ).
tff(c_9571,plain,
$lesseq('#skF_9','#skE_2'),
inference(quantifierElimination,[status(thm),theory('LIA')],[c_9570]) ).
tff(c_9573,plain,
~ $less('#skE_2','#skF_9'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_9571]) ).
tff(c_9266,plain,
'#skE_5' = '#skE_2',
inference(splitRight,[status(thm)],[c_8744]) ).
tff(c_8679,plain,
summation('#skE_4') = '#skE_5',
inference(define,[status(thm),theory(equality)],[c_8437]) ).
tff(c_8678,plain,
( $less('#skE_3','#skF_9')
| $less('#skF_9',summation('#skE_4')) ),
inference(demodulation,[status(thm),theory(equality)],[c_8423,c_8422,c_8421]) ).
tff(c_8686,plain,
( $less('#skE_3','#skF_9')
| $less('#skF_9','#skE_5') ),
inference(demodulation,[status(thm),theory(equality)],[c_8679,c_8678]) ).
tff(c_9269,plain,
$less('#skF_9','#skE_5'),
inference(splitLeft,[status(thm)],[c_8686]) ).
tff(c_9337,plain,
$less('#skF_9','#skE_2'),
inference(demodulation,[status(thm),theory(equality)],[c_9266,c_9269]) ).
tff(c_9338,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_8285,c_9337]) ).
tff(c_9341,plain,
$less('#skE_3','#skF_9'),
inference(splitRight,[status(thm)],[c_8686]) ).
tff(c_9842,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_9840,c_9573,c_9341]) ).
tff(c_9848,plain,
minsol_model_max('#skF_7','#skE_1','#skF_9'),
inference(splitRight,[status(thm)],[c_9813]) ).
tff(c_8545,plain,
~ minsol_model_max('#skF_7','#skE_4','#skF_9'),
inference(demodulation,[status(thm),theory(equality)],[c_8504,c_8165]) ).
tff(c_9398,plain,
~ minsol_model_max('#skF_7','#skE_1','#skF_9'),
inference(demodulation,[status(thm),theory(equality)],[c_9267,c_8545]) ).
tff(c_9851,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_9848,c_9398]) ).
tff(c_9854,plain,
'#skF_7' = '#skE_4',
inference(splitRight,[status(thm)],[c_8463]) ).
tff(c_9855,plain,
~ $less('#skF_7','#skF_8'),
inference(splitRight,[status(thm)],[c_8463]) ).
tff(c_9897,plain,
~ $less('#skE_4','#skF_8'),
inference(demodulation,[status(thm),theory(equality)],[c_9854,c_9855]) ).
tff(c_10088,plain,
summation('#skE_4') = '#skE_5',
inference(define,[status(thm),theory(equality)],[c_8437]) ).
tff(c_9895,plain,
minsol_model_ub('#skE_4','#skF_8','#skF_9'),
inference(demodulation,[status(thm),theory(equality)],[c_9854,c_8135]) ).
tff(c_10339,plain,
! [X_3711a: $int,Z_3710a: $int,N_3707a: $int,N_3708a: $int,Y_3709a: $int] :
( ~ minsol_model_ub(X_3711a,Y_3709a,N_3707a)
| ~ $less(N_3708a,N_3707a)
| $less(N_3708a,summation(Z_3710a))
| $less(Z_3710a,X_3711a)
| $less(Z_3710a,Y_3709a) ),
inference(resolution,[status(thm)],[c_8242,c_74]) ).
tff(c_10345,plain,
! [N_3712a: $int,Z_3713a: $int] :
( ~ $less(N_3712a,'#skF_9')
| $less(N_3712a,summation(Z_3713a))
| $less(Z_3713a,'#skE_4')
| $less(Z_3713a,'#skF_8') ),
inference(resolution,[status(thm)],[c_9895,c_10339]) ).
tff(c_10362,plain,
! [N_3712a: $int] :
( ~ $less(N_3712a,'#skF_9')
| $less(N_3712a,'#skE_5')
| $less('#skE_4','#skE_4')
| $less('#skE_4','#skF_8') ),
inference(superposition,[status(thm),theory(equality)],[c_10088,c_10345]) ).
tff(c_10364,plain,
! [N_3712a: $int] :
( ~ $less(N_3712a,'#skF_9')
| $less(N_3712a,'#skE_5')
| $less('#skE_4','#skF_8') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_10362]) ).
tff(c_10367,plain,
! [N_3712a: $int] :
( ~ $less(N_3712a,'#skF_9')
| $less(N_3712a,'#skE_5') ),
inference(negUnitSimplification,[status(thm)],[c_9897,c_10364]) ).
tff(c_10368,plain,
$lesseq('#skF_9','#skE_5'),
inference(quantifierElimination,[status(thm),theory('LIA')],[c_10367]) ).
tff(c_10370,plain,
~ $less('#skE_5','#skF_9'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_10368]) ).
tff(c_10092,plain,
summation('#skE_4') = '#skE_5',
inference(define,[status(thm),theory(equality)],[c_8437]) ).
tff(c_8325,plain,
! [Y_2a: $int] :
( ~ $less(summation(Y_2a),'#skE_2')
| $less(Y_2a,'#skE_1') ),
inference(superposition,[status(thm),theory(equality)],[c_8288,c_90]) ).
tff(c_10139,plain,
( ~ $less('#skE_5','#skE_2')
| $less('#skE_4','#skE_1') ),
inference(superposition,[status(thm),theory(equality)],[c_10092,c_8325]) ).
tff(c_10187,plain,
~ $less('#skE_5','#skE_2'),
inference(splitLeft,[status(thm)],[c_10139]) ).
tff(c_10137,plain,
( $less('#skE_5','#skE_2')
| ~ $less('#skE_4','#skE_1') ),
inference(superposition,[status(thm),theory(equality)],[c_10092,c_8319]) ).
tff(c_10191,plain,
~ $less('#skE_4','#skE_1'),
inference(negUnitSimplification,[status(thm)],[c_10187,c_10137]) ).
tff(c_10145,plain,
( ( '#skE_5' = '#skE_2' )
| ( '#skE_4' != '#skE_1' ) ),
inference(superposition,[status(thm),theory(equality)],[c_10092,c_8284]) ).
tff(c_10164,plain,
'#skE_4' != '#skE_1',
inference(splitLeft,[status(thm)],[c_10145]) ).
tff(c_9934,plain,
minsol_model_ub('#skE_4','#skF_8','#skF_9'),
inference(demodulation,[status(thm),theory(equality)],[c_9854,c_8135]) ).
tff(c_10034,plain,
( ub('#skE_4','#skF_8','#skE_1')
| ~ model_ub('#skE_4','#skF_8','#skF_9') ),
inference(demodulation,[status(thm),theory(equality)],[c_9854,c_9854,c_8371]) ).
tff(c_10042,plain,
~ model_ub('#skE_4','#skF_8','#skF_9'),
inference(splitLeft,[status(thm)],[c_10034]) ).
tff(c_10048,plain,
~ minsol_model_ub('#skE_4','#skF_8','#skF_9'),
inference(resolution,[status(thm)],[c_73,c_10042]) ).
tff(c_10055,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_9934,c_10048]) ).
tff(c_10062,plain,
ub('#skE_4','#skF_8','#skE_1'),
inference(splitRight,[status(thm)],[c_10034]) ).
tff(c_10081,plain,
~ $less('#skE_1','#skE_4'),
inference(resolution,[status(thm)],[c_10062,c_85]) ).
tff(c_10192,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_10191,c_10164,c_10081]) ).
tff(c_10196,plain,
$less('#skE_5','#skE_2'),
inference(splitRight,[status(thm)],[c_10139]) ).
tff(c_10371,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_10370,c_10196,c_8285]) ).
tff(c_10375,plain,
'#skE_4' = '#skE_1',
inference(splitRight,[status(thm)],[c_10145]) ).
tff(c_9935,plain,
minsol_model_ub('#skE_4','#skF_8','#skF_9'),
inference(demodulation,[status(thm),theory(equality)],[c_9854,c_8135]) ).
tff(c_8175,plain,
! [N_27a: $int,X_25a: $int,Y_26a: $int] :
( ~ $less(N_27a,summation('#skF_1'(X_25a,Y_26a,N_27a)))
| ~ minsol_model_ub(X_25a,Y_26a,N_27a) ),
inference(resolution,[status(thm)],[c_73,c_8170]) ).
tff(c_9943,plain,
~ $less('#skF_9',summation('#skF_1'('#skE_4','#skF_8','#skF_9'))),
inference(resolution,[status(thm)],[c_9935,c_8175]) ).
tff(c_10548,plain,
~ $less('#skF_9',summation('#skF_1'('#skE_1','#skF_8','#skF_9'))),
inference(demodulation,[status(thm),theory(equality)],[c_10375,c_9943]) ).
tff(c_10550,plain,
'#skF_1'('#skE_1','#skF_8','#skF_9') = '#skE_15',
inference(define,[status(thm),theory(equality)],[c_10548]) ).
tff(c_10549,plain,
~ $less('#skF_9',summation('#skF_1'('#skE_1','#skF_8','#skF_9'))),
inference(demodulation,[status(thm),theory(equality)],[c_10375,c_9943]) ).
tff(c_10560,plain,
~ $less('#skF_9',summation('#skE_15')),
inference(demodulation,[status(thm),theory(equality)],[c_10550,c_10549]) ).
tff(c_10573,plain,
summation('#skE_15') = '#skE_16',
inference(define,[status(thm),theory(equality)],[c_10560]) ).
tff(c_10626,plain,
( ( '#skE_2' = '#skE_16' )
| ( '#skE_15' != '#skE_1' ) ),
inference(superposition,[status(thm),theory(equality)],[c_10573,c_8284]) ).
tff(c_10645,plain,
'#skE_15' != '#skE_1',
inference(splitLeft,[status(thm)],[c_10626]) ).
tff(c_8268,plain,
'#skF_1'('#skF_7','#skF_8','#skF_9') = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_8207]) ).
tff(c_9886,plain,
'#skF_1'('#skE_4','#skF_8','#skF_9') = '#skE_1',
inference(demodulation,[status(thm),theory(equality)],[c_9854,c_8268]) ).
tff(c_10812,plain,
'#skF_1'('#skE_1','#skF_8','#skF_9') = '#skE_1',
inference(demodulation,[status(thm),theory(equality)],[c_10375,c_9886]) ).
tff(c_10557,plain,
'#skF_1'('#skE_1','#skF_8','#skF_9') = '#skE_15',
inference(define,[status(thm),theory(equality)],[c_10548]) ).
tff(c_10818,plain,
( ( '#skE_15' = '#skE_1' )
| ( '#skF_9' != '#skF_9' )
| ( '#skF_8' != '#skF_8' )
| ( '#skE_1' != '#skE_1' ) ),
inference(superposition,[status(thm),theory(equality)],[c_10812,c_10557]) ).
tff(c_10834,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_10645,c_10818]) ).
tff(c_10837,plain,
$false,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_10834]) ).
tff(c_10841,plain,
'#skE_15' = '#skE_1',
inference(splitRight,[status(thm)],[c_10626]) ).
tff(c_10569,plain,
summation('#skE_15') = '#skE_16',
inference(define,[status(thm),theory(equality)],[c_10560]) ).
tff(c_10924,plain,
summation('#skE_1') = '#skE_16',
inference(demodulation,[status(thm),theory(equality)],[c_10841,c_10569]) ).
tff(c_9883,plain,
max('#skE_4','#skF_8') = '#skE_4',
inference(demodulation,[status(thm),theory(equality)],[c_9854,c_8434]) ).
tff(c_10485,plain,
max('#skE_1','#skF_8') = '#skE_1',
inference(demodulation,[status(thm),theory(equality)],[c_10375,c_10375,c_9883]) ).
tff(c_10563,plain,
summation('#skE_15') = '#skE_16',
inference(define,[status(thm),theory(equality)],[c_10560]) ).
tff(c_10562,plain,
~ $less('#skF_9',summation('#skE_15')),
inference(demodulation,[status(thm),theory(equality)],[c_10550,c_10549]) ).
tff(c_10570,plain,
~ $less('#skF_9','#skE_16'),
inference(demodulation,[status(thm),theory(equality)],[c_10563,c_10562]) ).
tff(c_9904,plain,
'#skF_2'('#skE_4','#skF_8','#skF_9') = '#skE_3',
inference(demodulation,[status(thm),theory(equality)],[c_9854,c_8431]) ).
tff(c_11075,plain,
'#skF_2'('#skE_1','#skF_8','#skF_9') = '#skE_3',
inference(demodulation,[status(thm),theory(equality)],[c_10375,c_9904]) ).
tff(c_11091,plain,
( model_max('#skE_1','#skF_8','#skE_3')
| minsol_model_max('#skE_1','#skF_8','#skF_9')
| ~ model_max('#skE_1','#skF_8','#skF_9') ),
inference(superposition,[status(thm),theory(equality)],[c_11075,c_75]) ).
tff(c_11345,plain,
~ model_max('#skE_1','#skF_8','#skF_9'),
inference(splitLeft,[status(thm)],[c_11091]) ).
tff(c_11348,plain,
$less('#skF_9',summation(max('#skE_1','#skF_8'))),
inference(resolution,[status(thm)],[c_82,c_11345]) ).
tff(c_11353,plain,
$less('#skF_9','#skE_16'),
inference(demodulation,[status(thm),theory(equality)],[c_10924,c_10485,c_11348]) ).
tff(c_11355,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_10570,c_11353]) ).
tff(c_11359,plain,
( minsol_model_max('#skE_1','#skF_8','#skF_9')
| model_max('#skE_1','#skF_8','#skE_3') ),
inference(splitRight,[status(thm)],[c_11091]) ).
tff(c_11368,plain,
model_max('#skE_1','#skF_8','#skE_3'),
inference(splitLeft,[status(thm)],[c_11359]) ).
tff(c_11377,plain,
~ $less('#skE_3',summation(max('#skE_1','#skF_8'))),
inference(resolution,[status(thm)],[c_11368,c_83]) ).
tff(c_11386,plain,
~ $less('#skE_3','#skE_16'),
inference(demodulation,[status(thm),theory(equality)],[c_10924,c_10485,c_11377]) ).
tff(c_10445,plain,
minsol_model_ub('#skE_1','#skF_8','#skF_9'),
inference(demodulation,[status(thm),theory(equality)],[c_10375,c_9895]) ).
tff(c_10840,plain,
'#skE_2' = '#skE_16',
inference(splitRight,[status(thm)],[c_10626]) ).
tff(c_10065,plain,
! [N_15a: $int] :
( model_ub('#skE_4','#skF_8',N_15a)
| $less(N_15a,summation('#skE_1')) ),
inference(resolution,[status(thm)],[c_10062,c_81]) ).
tff(c_10077,plain,
! [N_15a: $int] :
( model_ub('#skE_4','#skF_8',N_15a)
| $less(N_15a,'#skE_2') ),
inference(demodulation,[status(thm),theory(equality)],[c_8287,c_10065]) ).
tff(c_11101,plain,
! [N_3945a: $int] :
( model_ub('#skE_1','#skF_8',N_3945a)
| $less(N_3945a,'#skE_16') ),
inference(demodulation,[status(thm),theory(equality)],[c_10840,c_10375,c_10077]) ).
tff(c_11139,plain,
! [N_3960a: $int,N_3961a: $int] :
( ~ minsol_model_ub('#skE_1','#skF_8',N_3960a)
| ~ $less(N_3961a,N_3960a)
| $less(N_3961a,'#skE_16') ),
inference(resolution,[status(thm)],[c_11101,c_74]) ).
tff(c_11143,plain,
! [N_3961a: $int] :
( ~ $less(N_3961a,'#skF_9')
| $less(N_3961a,'#skE_16') ),
inference(resolution,[status(thm)],[c_10445,c_11139]) ).
tff(c_11145,plain,
! [N_3961a: $int] :
( ~ $less(N_3961a,'#skF_9')
| $less(N_3961a,'#skE_16') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_11143]) ).
tff(c_11146,plain,
$lesseq('#skF_9','#skE_16'),
inference(quantifierElimination,[status(thm),theory('LIA')],[c_11145]) ).
tff(c_11148,plain,
~ $less('#skE_16','#skF_9'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_11146]) ).
tff(c_10374,plain,
'#skE_5' = '#skE_2',
inference(splitRight,[status(thm)],[c_10145]) ).
tff(c_10082,plain,
summation('#skE_4') = '#skE_5',
inference(define,[status(thm),theory(equality)],[c_8437]) ).
tff(c_10089,plain,
( $less('#skE_3','#skF_9')
| $less('#skF_9','#skE_5') ),
inference(demodulation,[status(thm),theory(equality)],[c_10082,c_8678]) ).
tff(c_10481,plain,
( $less('#skE_3','#skF_9')
| $less('#skF_9','#skE_2') ),
inference(demodulation,[status(thm),theory(equality)],[c_10374,c_10089]) ).
tff(c_10483,plain,
$less('#skE_3','#skF_9'),
inference(negUnitSimplification,[status(thm)],[c_8285,c_10481]) ).
tff(c_11392,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_11386,c_11148,c_10483]) ).
tff(c_11398,plain,
minsol_model_max('#skE_1','#skF_8','#skF_9'),
inference(splitRight,[status(thm)],[c_11359]) ).
tff(c_9892,plain,
~ minsol_model_max('#skE_4','#skF_8','#skF_9'),
inference(demodulation,[status(thm),theory(equality)],[c_9854,c_8165]) ).
tff(c_10439,plain,
~ minsol_model_max('#skE_1','#skF_8','#skF_9'),
inference(demodulation,[status(thm),theory(equality)],[c_10375,c_9892]) ).
tff(c_11401,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_11398,c_10439]) ).
tff(c_11405,plain,
~ minsol_model_ub('#skF_4','#skF_5','#skF_6'),
inference(splitRight,[status(thm)],[c_70]) ).
tff(c_14225,plain,
~ minsol_model_ub('#skF_4','#skE_7','#skF_6'),
inference(demodulation,[status(thm),theory(equality)],[c_14189,c_11405]) ).
tff(c_14975,plain,
! [Z_5361a: $int] :
( $less('#skF_3'('#skF_4','#skE_7','#skF_6'),'#skF_6')
| $less('#skF_6',summation(Z_5361a))
| $less(Z_5361a,'#skF_4')
| $less(Z_5361a,'#skE_7') ),
inference(resolution,[status(thm)],[c_14950,c_14225]) ).
tff(c_15172,plain,
'#skF_3'('#skF_4','#skE_7','#skF_6') = '#skE_12',
inference(define,[status(thm),theory(equality)],[c_14975]) ).
tff(c_15193,plain,
( model_ub('#skF_4','#skE_7','#skE_12')
| minsol_model_ub('#skF_4','#skE_7','#skF_6')
| ~ model_ub('#skF_4','#skE_7','#skF_6') ),
inference(superposition,[status(thm),theory(equality)],[c_15172,c_71]) ).
tff(c_15228,plain,
~ model_ub('#skF_4','#skE_7','#skF_6'),
inference(splitLeft,[status(thm)],[c_15193]) ).
tff(c_15246,plain,
! [Z_5483a: $int] :
( $less('#skF_6',summation(Z_5483a))
| $less(Z_5483a,'#skF_4')
| $less(Z_5483a,'#skE_7') ),
inference(resolution,[status(thm)],[c_14090,c_15228]) ).
tff(c_15266,plain,
( $less('#skF_6','#skE_8')
| $less('#skE_7','#skF_4')
| $less('#skE_7','#skE_7') ),
inference(superposition,[status(thm),theory(equality)],[c_14293,c_15246]) ).
tff(c_15268,plain,
( $less('#skF_6','#skE_8')
| $less('#skE_7','#skF_4') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_15266]) ).
tff(c_15296,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_14235,c_14294,c_15268]) ).
tff(c_15300,plain,
( minsol_model_ub('#skF_4','#skE_7','#skF_6')
| model_ub('#skF_4','#skE_7','#skE_12') ),
inference(splitRight,[status(thm)],[c_15193]) ).
tff(c_15309,plain,
model_ub('#skF_4','#skE_7','#skE_12'),
inference(splitLeft,[status(thm)],[c_15300]) ).
tff(c_15327,plain,
~ $less('#skE_12',summation('#skF_1'('#skF_4','#skE_7','#skE_12'))),
inference(resolution,[status(thm)],[c_15309,c_80]) ).
tff(c_15350,plain,
'#skF_1'('#skF_4','#skE_7','#skE_12') = '#skE_13',
inference(define,[status(thm),theory(equality)],[c_15327]) ).
tff(c_15349,plain,
~ $less('#skE_12',summation('#skF_1'('#skF_4','#skE_7','#skE_12'))),
inference(resolution,[status(thm)],[c_15309,c_80]) ).
tff(c_15360,plain,
~ $less('#skE_12',summation('#skE_13')),
inference(demodulation,[status(thm),theory(equality)],[c_15350,c_15349]) ).
tff(c_15373,plain,
summation('#skE_13') = '#skE_14',
inference(define,[status(thm),theory(equality)],[c_15360]) ).
tff(c_14314,plain,
summation('#skE_7') = '#skE_8',
inference(define,[status(thm),theory(equality)],[c_14135]) ).
tff(c_14351,plain,
! [Y_2a: $int] :
( ~ $less(summation(Y_2a),'#skE_8')
| $less(Y_2a,'#skE_7') ),
inference(superposition,[status(thm),theory(equality)],[c_14314,c_90]) ).
tff(c_15451,plain,
( ~ $less('#skE_14','#skE_8')
| $less('#skE_13','#skE_7') ),
inference(superposition,[status(thm),theory(equality)],[c_15373,c_14351]) ).
tff(c_15843,plain,
~ $less('#skE_14','#skE_8'),
inference(splitLeft,[status(thm)],[c_15451]) ).
tff(c_15363,plain,
summation('#skE_13') = '#skE_14',
inference(define,[status(thm),theory(equality)],[c_15360]) ).
tff(c_15362,plain,
~ $less('#skE_12',summation('#skE_13')),
inference(demodulation,[status(thm),theory(equality)],[c_15350,c_15349]) ).
tff(c_15370,plain,
~ $less('#skE_12','#skE_14'),
inference(demodulation,[status(thm),theory(equality)],[c_15363,c_15362]) ).
tff(c_15159,plain,
'#skF_3'('#skF_4','#skE_7','#skF_6') = '#skE_12',
inference(define,[status(thm),theory(equality)],[c_14975]) ).
tff(c_15158,plain,
! [Z_5361a: $int] :
( $less('#skF_3'('#skF_4','#skE_7','#skF_6'),'#skF_6')
| $less('#skF_6',summation(Z_5361a))
| $less(Z_5361a,'#skF_4')
| $less(Z_5361a,'#skE_7') ),
inference(resolution,[status(thm)],[c_14950,c_14225]) ).
tff(c_15169,plain,
! [Z_5361a: $int] :
( $less('#skE_12','#skF_6')
| $less('#skF_6',summation(Z_5361a))
| $less(Z_5361a,'#skF_4')
| $less(Z_5361a,'#skE_7') ),
inference(demodulation,[status(thm),theory(equality)],[c_15159,c_15158]) ).
tff(c_15200,plain,
$less('#skE_12','#skF_6'),
inference(splitLeft,[status(thm)],[c_15169]) ).
tff(c_14313,plain,
summation('#skE_7') = '#skE_8',
inference(define,[status(thm),theory(equality)],[c_14135]) ).
tff(c_14132,plain,
max('#skF_4','#skF_5') = '#skE_7',
inference(define,[status(thm),theory(equality)],[c_14072]) ).
tff(c_14247,plain,
max('#skF_4','#skE_7') = '#skE_7',
inference(demodulation,[status(thm),theory(equality)],[c_14189,c_14132]) ).
tff(c_14063,plain,
minsol_model_max('#skF_4','#skF_5','#skF_6'),
inference(splitRight,[status(thm)],[c_66]) ).
tff(c_14222,plain,
minsol_model_max('#skF_4','#skE_7','#skF_6'),
inference(demodulation,[status(thm),theory(equality)],[c_14189,c_14063]) ).
tff(c_11424,plain,
! [X_4085a: $int,Y_4086a: $int,Z_4087a: $int,N_4088a: $int] :
( ~ model_max(X_4085a,Y_4086a,Z_4087a)
| ~ minsol_model_max(X_4085a,Y_4086a,N_4088a)
| ~ $less(Z_4087a,N_4088a) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_29]) ).
tff(c_14813,plain,
! [X_5316a: $int,Y_5317a: $int,N_5318a: $int,N_5319a: $int] :
( ~ minsol_model_max(X_5316a,Y_5317a,N_5318a)
| ~ $less(N_5319a,N_5318a)
| $less(N_5319a,summation(max(X_5316a,Y_5317a))) ),
inference(resolution,[status(thm)],[c_82,c_11424]) ).
tff(c_14816,plain,
! [N_5319a: $int] :
( ~ $less(N_5319a,'#skF_6')
| $less(N_5319a,summation(max('#skF_4','#skE_7'))) ),
inference(resolution,[status(thm)],[c_14222,c_14813]) ).
tff(c_14819,plain,
! [N_5319a: $int] :
( ~ $less(N_5319a,'#skF_6')
| $less(N_5319a,'#skE_8') ),
inference(demodulation,[status(thm),theory(equality)],[c_14313,c_14247,c_14816]) ).
tff(c_14836,plain,
$lesseq('#skF_6','#skE_8'),
inference(quantifierElimination,[status(thm),theory('LIA')],[c_14819]) ).
tff(c_14838,plain,
~ $less('#skE_8','#skF_6'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_14836]) ).
tff(c_15844,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_15843,c_15370,c_15200,c_14838]) ).
tff(c_15847,plain,
$less('#skE_13','#skE_7'),
inference(splitRight,[status(thm)],[c_15451]) ).
tff(c_15308,plain,
model_ub('#skF_4','#skE_7','#skE_12'),
inference(splitLeft,[status(thm)],[c_15300]) ).
tff(c_15516,plain,
'#skF_1'('#skF_4','#skE_7','#skE_12') = '#skE_13',
inference(define,[status(thm),theory(equality)],[c_15327]) ).
tff(c_15534,plain,
( ub('#skF_4','#skE_7','#skE_13')
| ~ model_ub('#skF_4','#skE_7','#skE_12') ),
inference(superposition,[status(thm),theory(equality)],[c_15516,c_79]) ).
tff(c_16076,plain,
ub('#skF_4','#skE_7','#skE_13'),
inference(demodulation,[status(thm),theory(equality)],[c_15308,c_15534]) ).
tff(c_16082,plain,
~ $less('#skE_13','#skE_7'),
inference(resolution,[status(thm)],[c_16076,c_86]) ).
tff(c_16095,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_15847,c_16082]) ).
tff(c_16101,plain,
minsol_model_ub('#skF_4','#skE_7','#skF_6'),
inference(splitRight,[status(thm)],[c_15300]) ).
tff(c_16104,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_16101,c_14225]) ).
tff(c_16113,plain,
! [Z_5658a: $int] :
( $less('#skF_6',summation(Z_5658a))
| $less(Z_5658a,'#skF_4')
| $less(Z_5658a,'#skE_7') ),
inference(splitRight,[status(thm)],[c_15169]) ).
tff(c_16133,plain,
( $less('#skF_6','#skE_8')
| $less('#skE_7','#skF_4')
| $less('#skE_7','#skE_7') ),
inference(superposition,[status(thm),theory(equality)],[c_14293,c_16113]) ).
tff(c_16135,plain,
( $less('#skF_6','#skE_8')
| $less('#skE_7','#skF_4') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_16133]) ).
tff(c_16137,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_14235,c_14294,c_16135]) ).
tff(c_16140,plain,
'#skF_4' = '#skE_7',
inference(splitRight,[status(thm)],[c_14161]) ).
tff(c_16141,plain,
~ $less('#skF_4','#skF_5'),
inference(splitRight,[status(thm)],[c_14161]) ).
tff(c_16178,plain,
~ $less('#skE_7','#skF_5'),
inference(demodulation,[status(thm),theory(equality)],[c_16140,c_16141]) ).
tff(c_16251,plain,
summation('#skE_7') = '#skE_8',
inference(define,[status(thm),theory(equality)],[c_14135]) ).
tff(c_16258,plain,
~ $less('#skF_6','#skE_8'),
inference(demodulation,[status(thm),theory(equality)],[c_16251,c_14286]) ).
tff(c_16257,plain,
summation('#skE_7') = '#skE_8',
inference(define,[status(thm),theory(equality)],[c_14135]) ).
tff(c_16387,plain,
! [X_5737a: $int,Y_5738a: $int,N_5739a: $int,Z_5740a: $int] :
( model_ub(X_5737a,Y_5738a,N_5739a)
| $less(N_5739a,summation(Z_5740a))
| $less(Z_5740a,X_5737a)
| $less(Z_5740a,Y_5738a) ),
inference(resolution,[status(thm)],[c_84,c_14085]) ).
tff(c_16924,plain,
! [X_5856a: $int,Y_5857a: $int,N_5858a: $int,Z_5859a: $int] :
( $less('#skF_3'(X_5856a,Y_5857a,N_5858a),N_5858a)
| minsol_model_ub(X_5856a,Y_5857a,N_5858a)
| $less(N_5858a,summation(Z_5859a))
| $less(Z_5859a,X_5856a)
| $less(Z_5859a,Y_5857a) ),
inference(resolution,[status(thm)],[c_16387,c_72]) ).
tff(c_16176,plain,
~ minsol_model_ub('#skE_7','#skF_5','#skF_6'),
inference(demodulation,[status(thm),theory(equality)],[c_16140,c_11405]) ).
tff(c_16949,plain,
! [Z_5859a: $int] :
( $less('#skF_3'('#skE_7','#skF_5','#skF_6'),'#skF_6')
| $less('#skF_6',summation(Z_5859a))
| $less(Z_5859a,'#skE_7')
| $less(Z_5859a,'#skF_5') ),
inference(resolution,[status(thm)],[c_16924,c_16176]) ).
tff(c_17332,plain,
'#skF_3'('#skE_7','#skF_5','#skF_6') = '#skE_9',
inference(define,[status(thm),theory(equality)],[c_16949]) ).
tff(c_17353,plain,
( model_ub('#skE_7','#skF_5','#skE_9')
| minsol_model_ub('#skE_7','#skF_5','#skF_6')
| ~ model_ub('#skE_7','#skF_5','#skF_6') ),
inference(superposition,[status(thm),theory(equality)],[c_17332,c_71]) ).
tff(c_17396,plain,
~ model_ub('#skE_7','#skF_5','#skF_6'),
inference(splitLeft,[status(thm)],[c_17353]) ).
tff(c_17414,plain,
! [Z_6053a: $int] :
( $less('#skF_6',summation(Z_6053a))
| $less(Z_6053a,'#skE_7')
| $less(Z_6053a,'#skF_5') ),
inference(resolution,[status(thm)],[c_14090,c_17396]) ).
tff(c_17434,plain,
( $less('#skF_6','#skE_8')
| $less('#skE_7','#skE_7')
| $less('#skE_7','#skF_5') ),
inference(superposition,[status(thm),theory(equality)],[c_16257,c_17414]) ).
tff(c_17436,plain,
( $less('#skF_6','#skE_8')
| $less('#skE_7','#skF_5') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_17434]) ).
tff(c_17450,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_16178,c_16258,c_17436]) ).
tff(c_17454,plain,
( minsol_model_ub('#skE_7','#skF_5','#skF_6')
| model_ub('#skE_7','#skF_5','#skE_9') ),
inference(splitRight,[status(thm)],[c_17353]) ).
tff(c_17463,plain,
model_ub('#skE_7','#skF_5','#skE_9'),
inference(splitLeft,[status(thm)],[c_17454]) ).
tff(c_17481,plain,
~ $less('#skE_9',summation('#skF_1'('#skE_7','#skF_5','#skE_9'))),
inference(resolution,[status(thm)],[c_17463,c_80]) ).
tff(c_17504,plain,
'#skF_1'('#skE_7','#skF_5','#skE_9') = '#skE_10',
inference(define,[status(thm),theory(equality)],[c_17481]) ).
tff(c_17503,plain,
~ $less('#skE_9',summation('#skF_1'('#skE_7','#skF_5','#skE_9'))),
inference(resolution,[status(thm)],[c_17463,c_80]) ).
tff(c_17514,plain,
~ $less('#skE_9',summation('#skE_10')),
inference(demodulation,[status(thm),theory(equality)],[c_17504,c_17503]) ).
tff(c_17527,plain,
summation('#skE_10') = '#skE_11',
inference(define,[status(thm),theory(equality)],[c_17514]) ).
tff(c_16261,plain,
summation('#skE_7') = '#skE_8',
inference(define,[status(thm),theory(equality)],[c_14135]) ).
tff(c_16298,plain,
! [Y_2a: $int] :
( ~ $less(summation(Y_2a),'#skE_8')
| $less(Y_2a,'#skE_7') ),
inference(superposition,[status(thm),theory(equality)],[c_16261,c_90]) ).
tff(c_17645,plain,
( ~ $less('#skE_11','#skE_8')
| $less('#skE_10','#skE_7') ),
inference(superposition,[status(thm),theory(equality)],[c_17527,c_16298]) ).
tff(c_18169,plain,
~ $less('#skE_11','#skE_8'),
inference(splitLeft,[status(thm)],[c_17645]) ).
tff(c_17517,plain,
summation('#skE_10') = '#skE_11',
inference(define,[status(thm),theory(equality)],[c_17514]) ).
tff(c_17516,plain,
~ $less('#skE_9',summation('#skE_10')),
inference(demodulation,[status(thm),theory(equality)],[c_17504,c_17503]) ).
tff(c_17524,plain,
~ $less('#skE_9','#skE_11'),
inference(demodulation,[status(thm),theory(equality)],[c_17517,c_17516]) ).
tff(c_17319,plain,
'#skF_3'('#skE_7','#skF_5','#skF_6') = '#skE_9',
inference(define,[status(thm),theory(equality)],[c_16949]) ).
tff(c_17318,plain,
! [Z_5859a: $int] :
( $less('#skF_3'('#skE_7','#skF_5','#skF_6'),'#skF_6')
| $less('#skF_6',summation(Z_5859a))
| $less(Z_5859a,'#skE_7')
| $less(Z_5859a,'#skF_5') ),
inference(resolution,[status(thm)],[c_16924,c_16176]) ).
tff(c_17329,plain,
! [Z_5859a: $int] :
( $less('#skE_9','#skF_6')
| $less('#skF_6',summation(Z_5859a))
| $less(Z_5859a,'#skE_7')
| $less(Z_5859a,'#skF_5') ),
inference(demodulation,[status(thm),theory(equality)],[c_17319,c_17318]) ).
tff(c_17360,plain,
$less('#skE_9','#skF_6'),
inference(splitLeft,[status(thm)],[c_17329]) ).
tff(c_16260,plain,
summation('#skE_7') = '#skE_8',
inference(define,[status(thm),theory(equality)],[c_14135]) ).
tff(c_16213,plain,
max('#skE_7','#skF_5') = '#skE_7',
inference(demodulation,[status(thm),theory(equality)],[c_16140,c_14132]) ).
tff(c_16172,plain,
minsol_model_max('#skE_7','#skF_5','#skF_6'),
inference(demodulation,[status(thm),theory(equality)],[c_16140,c_14063]) ).
tff(c_16376,plain,
! [X_5730a: $int,Y_5731a: $int,N_5732a: $int,N_5733a: $int] :
( ~ minsol_model_max(X_5730a,Y_5731a,N_5732a)
| ~ $less(N_5733a,N_5732a)
| $less(N_5733a,summation(max(X_5730a,Y_5731a))) ),
inference(resolution,[status(thm)],[c_82,c_11424]) ).
tff(c_16379,plain,
! [N_5733a: $int] :
( ~ $less(N_5733a,'#skF_6')
| $less(N_5733a,summation(max('#skE_7','#skF_5'))) ),
inference(resolution,[status(thm)],[c_16172,c_16376]) ).
tff(c_16382,plain,
! [N_5733a: $int] :
( ~ $less(N_5733a,'#skF_6')
| $less(N_5733a,'#skE_8') ),
inference(demodulation,[status(thm),theory(equality)],[c_16260,c_16213,c_16379]) ).
tff(c_16384,plain,
$lesseq('#skF_6','#skE_8'),
inference(quantifierElimination,[status(thm),theory('LIA')],[c_16382]) ).
tff(c_16386,plain,
~ $less('#skE_8','#skF_6'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_16384]) ).
tff(c_18172,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_18169,c_17524,c_17360,c_16386]) ).
tff(c_18175,plain,
$less('#skE_10','#skE_7'),
inference(splitRight,[status(thm)],[c_17645]) ).
tff(c_17462,plain,
model_ub('#skE_7','#skF_5','#skE_9'),
inference(splitLeft,[status(thm)],[c_17454]) ).
tff(c_18029,plain,
'#skF_1'('#skE_7','#skF_5','#skE_9') = '#skE_10',
inference(define,[status(thm),theory(equality)],[c_17481]) ).
tff(c_18047,plain,
( ub('#skE_7','#skF_5','#skE_10')
| ~ model_ub('#skE_7','#skF_5','#skE_9') ),
inference(superposition,[status(thm),theory(equality)],[c_18029,c_79]) ).
tff(c_18305,plain,
ub('#skE_7','#skF_5','#skE_10'),
inference(demodulation,[status(thm),theory(equality)],[c_17462,c_18047]) ).
tff(c_18314,plain,
~ $less('#skE_10','#skE_7'),
inference(resolution,[status(thm)],[c_18305,c_85]) ).
tff(c_18326,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_18175,c_18314]) ).
tff(c_18332,plain,
minsol_model_ub('#skE_7','#skF_5','#skF_6'),
inference(splitRight,[status(thm)],[c_17454]) ).
tff(c_18335,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_18332,c_16176]) ).
tff(c_18344,plain,
! [Z_6229a: $int] :
( $less('#skF_6',summation(Z_6229a))
| $less(Z_6229a,'#skE_7')
| $less(Z_6229a,'#skF_5') ),
inference(splitRight,[status(thm)],[c_17329]) ).
tff(c_18364,plain,
( $less('#skF_6','#skE_8')
| $less('#skE_7','#skE_7')
| $less('#skE_7','#skF_5') ),
inference(superposition,[status(thm),theory(equality)],[c_16257,c_18344]) ).
tff(c_18366,plain,
( $less('#skF_6','#skE_8')
| $less('#skE_7','#skF_5') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_18364]) ).
tff(c_18367,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_16178,c_16258,c_18366]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM860_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
% 0.19/0.35 % Computer : n016.cluster.edu
% 0.19/0.35 % Model : x86_64 x86_64
% 0.19/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.35 % Memory : 8042.1875MB
% 0.19/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.19/0.35 % CPULimit : 300
% 0.19/0.35 % WCLimit : 300
% 0.19/0.35 % DateTime : Thu Aug 3 15:03:07 EDT 2023
% 0.19/0.36 % CPUTime :
% 14.79/4.63 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 15.67/4.84
% 15.67/4.84 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 16.08/4.93
% 16.08/4.93 Inference rules
% 16.08/4.93 ----------------------
% 16.08/4.93 #Ref : 0
% 16.08/4.93 #Sup : 2052
% 16.08/4.93 #Fact : 26
% 16.08/4.93 #Define : 60
% 16.08/4.93 #Split : 228
% 16.08/4.93 #Chain : 0
% 16.08/4.93 #Close : 67
% 16.08/4.93
% 16.08/4.93 Ordering : LPO
% 16.08/4.93
% 16.08/4.93 Simplification rules
% 16.08/4.93 ----------------------
% 16.08/4.93 #Subsume : 487
% 16.08/4.93 #Demod : 1316
% 16.08/4.93 #Tautology : 848
% 16.08/4.93 #SimpNegUnit : 223
% 16.08/4.93 #BackRed : 224
% 16.08/4.93
% 16.08/4.93 #Partial instantiations: 0
% 16.08/4.93 #Strategies tried : 1
% 16.08/4.93
% 16.08/4.93 Timing (in seconds)
% 16.08/4.93 ----------------------
% 16.08/4.94 Preprocessing : 0.58
% 16.08/4.94 Parsing : 0.30
% 16.08/4.94 CNF conversion : 0.04
% 16.08/4.94 Main loop : 3.00
% 16.08/4.94 Inferencing : 0.73
% 16.08/4.94 Reduction : 0.65
% 16.08/4.94 Demodulation : 0.44
% 16.08/4.94 BG Simplification : 0.17
% 16.08/4.94 Subsumption : 0.51
% 16.08/4.94 Abstraction : 0.10
% 16.08/4.94 MUC search : 0.38
% 16.08/4.94 Cooper : 0.62
% 16.08/4.94 Total : 3.91
% 16.08/4.94 Index Insertion : 0.00
% 16.08/4.94 Index Deletion : 0.00
% 16.08/4.94 Index Matching : 0.00
% 16.08/4.94 BG Taut test : 0.00
%------------------------------------------------------------------------------