TSTP Solution File: NUM859_1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : NUM859_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 : n006.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 11.28s 3.77s
% Output : CNFRefutation 12.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 33
% Syntax : Number of formulae : 653 ( 393 unt; 25 typ; 0 def)
% Number of atoms : 1023 ( 115 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 706 ( 311 ~; 383 |; 4 &)
% ( 6 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number arithmetic : 982 ( 551 atm; 48 fun; 48 num; 335 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 : 22 ( 20 usr; 16 con; 0-3 aty)
% Number of variables : 335 (; 334 !; 1 ?; 335 :)
% 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('#skF_6',type,
'#skF_6': $int ).
tff('#skE_2',type,
'#skE_2': $int ).
tff('#skE_1',type,
'#skE_1': $int ).
tff('#skE_6',type,
'#skE_6': $int ).
tff('#skE_5',type,
'#skE_5': $int ).
tff('#skE_8',type,
'#skE_8': $int ).
tff('#skF_8',type,
'#skF_8': $int ).
tff('#skE_4',type,
'#skE_4': $int ).
tff('#skF_5',type,
'#skF_5': $int ).
tff('#skF_4',type,
'#skF_4': $int ).
tff('#skE_3',type,
'#skE_3': $int ).
tff('#skF_7',type,
'#skF_7': $int ).
tff('#skE_9',type,
'#skE_9': $int ).
tff('#skF_9',type,
'#skF_9': $int ).
%Foreground operators:
tff(minsol_model_ub,type,
minsol_model_ub: ( $int * $int * $int ) > $o ).
tff('#skF_3',type,
'#skF_3': ( $int * $int * $int ) > $int ).
tff(model_max,type,
model_max: ( $int * $int * $int ) > $o ).
tff(minsol_model_max,type,
minsol_model_max: ( $int * $int * $int ) > $o ).
tff(summation,type,
summation: $int > $int ).
tff(max,type,
max: ( $int * $int ) > $int ).
tff('#skF_1',type,
'#skF_1': ( $int * $int * $int ) > $int ).
tff(model_ub,type,
model_ub: ( $int * $int * $int ) > $o ).
tff(ub,type,
ub: ( $int * $int * $int ) > $o ).
tff('#skF_2',type,
'#skF_2': ( $int * $int * $int ) > $int ).
tff(f_56,axiom,
! [Xa: $int,Ya: $int,Za: $int] :
( ub(Xa,Ya,Za)
<=> ( $lesseq(Xa,Za)
& $lesseq(Ya,Za) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ub) ).
tff(f_69,axiom,
! [Xa: $int,Ya: $int,Na: $int] :
( model_ub(Xa,Ya,Na)
<=> ? [Za: $int] :
( ub(Xa,Ya,Za)
& $lesseq(Za,Na) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',model_ub_2) ).
tff(f_89,axiom,
! [Xa: $int,Ya: $int,Na: $int] :
( minsol_model_ub(Xa,Ya,Na)
<=> ( model_ub(Xa,Ya,Na)
& ! [Za: $int] :
( model_ub(Xa,Ya,Za)
=> $lesseq(Na,Za) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',minsol_model_ub) ).
tff(f_49,axiom,
! [Xa: $int,Ya: $int] :
( ( max(Xa,Ya) = Ya )
| ~ $lesseq(Xa,Ya) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',max_2) ).
tff(f_61,axiom,
! [Xa: $int,Ya: $int,Na: $int] :
( model_max(Xa,Ya,Na)
<=> $lesseq(max(Xa,Ya),Na) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',model_max_2) ).
tff(f_79,axiom,
! [Xa: $int,Ya: $int,Na: $int] :
( minsol_model_max(Xa,Ya,Na)
<=> ( model_max(Xa,Ya,Na)
& ! [Za: $int] :
( model_max(Xa,Ya,Za)
=> $lesseq(Na,Za) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',minsol_model_max) ).
tff(f_95,negated_conjecture,
~ ! [Xa: $int,Ya: $int,Za: $int] :
( minsol_model_ub(Xa,Ya,Za)
<=> minsol_model_max(Xa,Ya,Za) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',max_is_ub_1) ).
tff(f_44,axiom,
! [Xa: $int,Ya: $int] :
( ( max(Xa,Ya) = Xa )
| ~ $lesseq(Ya,Xa) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',max_1) ).
tff(c_13,plain,
! [X_7a: $int,Y_8a: $int,Z_9a: $int] :
( ub(X_7a,Y_8a,Z_9a)
| ~ $lesseq(X_7a,Z_9a)
| ~ $lesseq(Y_8a,Z_9a) ),
inference(cnfTransformation,[status(thm)],[f_56]) ).
tff(c_83,plain,
! [X_7a: $int,Y_8a: $int,Z_9a: $int] :
( ub(X_7a,Y_8a,Z_9a)
| $less(Z_9a,X_7a)
| $less(Z_9a,Y_8a) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_13]) ).
tff(c_21,plain,
! [X_13a: $int,Y_14a: $int,N_15a: $int,Z_18a: $int] :
( model_ub(X_13a,Y_14a,N_15a)
| ~ ub(X_13a,Y_14a,Z_18a)
| ~ $lesseq(Z_18a,N_15a) ),
inference(cnfTransformation,[status(thm)],[f_69]) ).
tff(c_8522,plain,
! [X_3915a: $int,Y_3916a: $int,N_3917a: $int,Z_3918a: $int] :
( model_ub(X_3915a,Y_3916a,N_3917a)
| ~ ub(X_3915a,Y_3916a,Z_3918a)
| $less(N_3917a,Z_3918a) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_21]) ).
tff(c_8527,plain,
! [X_7a: $int,Y_8a: $int,N_3917a: $int,Z_9a: $int] :
( model_ub(X_7a,Y_8a,N_3917a)
| $less(N_3917a,Z_9a)
| $less(Z_9a,X_7a)
| $less(Z_9a,Y_8a) ),
inference(resolution,[status(thm)],[c_83,c_8522]) ).
tff(c_9530,plain,
! [X_4319a: $int,Y_4320a: $int,N_4321a: $int,Z_4322a: $int] :
( model_ub(X_4319a,Y_4320a,N_4321a)
| $less(N_4321a,Z_4322a)
| $less(Z_4322a,X_4319a)
| $less(Z_4322a,Y_4320a) ),
inference(resolution,[status(thm)],[c_83,c_8522]) ).
tff(c_42,plain,
! [N_27a: $int,X_25a: $int,Y_26a: $int] :
( ~ $lesseq(N_27a,'#skF_3'(X_25a,Y_26a,N_27a))
| minsol_model_ub(X_25a,Y_26a,N_27a)
| ~ model_ub(X_25a,Y_26a,N_27a) ),
inference(cnfTransformation,[status(thm)],[f_89]) ).
tff(c_71,plain,
! [X_25a: $int,Y_26a: $int,N_27a: $int] :
( $less('#skF_3'(X_25a,Y_26a,N_27a),N_27a)
| minsol_model_ub(X_25a,Y_26a,N_27a)
| ~ model_ub(X_25a,Y_26a,N_27a) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_42]) ).
tff(c_9771,plain,
! [X_4414a: $int,Y_4415a: $int,N_4416a: $int,Z_4417a: $int] :
( $less('#skF_3'(X_4414a,Y_4415a,N_4416a),N_4416a)
| minsol_model_ub(X_4414a,Y_4415a,N_4416a)
| $less(N_4416a,Z_4417a)
| $less(Z_4417a,X_4414a)
| $less(Z_4417a,Y_4415a) ),
inference(resolution,[status(thm)],[c_9530,c_71]) ).
tff(c_8783,plain,
! [X_4013a: $int,Y_4014a: $int,N_4015a: $int,Z_4016a: $int] :
( model_ub(X_4013a,Y_4014a,N_4015a)
| $less(N_4015a,Z_4016a)
| $less(Z_4016a,X_4013a)
| $less(Z_4016a,Y_4014a) ),
inference(resolution,[status(thm)],[c_83,c_8522]) ).
tff(c_8973,plain,
! [X_4094a: $int,Y_4095a: $int,N_4096a: $int,Z_4097a: $int] :
( $less('#skF_3'(X_4094a,Y_4095a,N_4096a),N_4096a)
| minsol_model_ub(X_4094a,Y_4095a,N_4096a)
| $less(N_4096a,Z_4097a)
| $less(Z_4097a,X_4094a)
| $less(Z_4097a,Y_4095a) ),
inference(resolution,[status(thm)],[c_8783,c_71]) ).
tff(c_7,plain,
! [X_5a: $int,Y_6a: $int] :
( ( max(X_5a,Y_6a) = Y_6a )
| ~ $lesseq(X_5a,Y_6a) ),
inference(cnfTransformation,[status(thm)],[f_49]) ).
tff(c_86,plain,
! [X_5a: $int,Y_6a: $int] :
( ( max(X_5a,Y_6a) = Y_6a )
| $less(Y_6a,X_5a) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_7]) ).
tff(c_19,plain,
! [X_10a: $int,Y_11a: $int,N_12a: $int] :
( model_max(X_10a,Y_11a,N_12a)
| ~ $lesseq(max(X_10a,Y_11a),N_12a) ),
inference(cnfTransformation,[status(thm)],[f_61]) ).
tff(c_81,plain,
! [X_10a: $int,Y_11a: $int,N_12a: $int] :
( model_max(X_10a,Y_11a,N_12a)
| $less(N_12a,max(X_10a,Y_11a)) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_19]) ).
tff(c_33,plain,
! [N_21a: $int,X_19a: $int,Y_20a: $int] :
( ~ $lesseq(N_21a,'#skF_2'(X_19a,Y_20a,N_21a))
| minsol_model_max(X_19a,Y_20a,N_21a)
| ~ model_max(X_19a,Y_20a,N_21a) ),
inference(cnfTransformation,[status(thm)],[f_79]) ).
tff(c_227,plain,
! [X_157a: $int,Y_158a: $int,N_159a: $int] :
( $less('#skF_2'(X_157a,Y_158a,N_159a),N_159a)
| minsol_model_max(X_157a,Y_158a,N_159a)
| ~ model_max(X_157a,Y_158a,N_159a) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_33]) ).
tff(c_3513,plain,
! [X_1621a: $int,Y_1622a: $int,N_1623a: $int] :
( $less('#skF_2'(X_1621a,Y_1622a,N_1623a),N_1623a)
| minsol_model_max(X_1621a,Y_1622a,N_1623a)
| $less(N_1623a,max(X_1621a,Y_1622a)) ),
inference(resolution,[status(thm)],[c_81,c_227]) ).
tff(c_65,plain,
( minsol_model_max('#skF_4','#skF_5','#skF_6')
| ~ minsol_model_max('#skF_7','#skF_8','#skF_9') ),
inference(cnfTransformation,[status(thm)],[f_95]) ).
tff(c_143,plain,
~ minsol_model_max('#skF_7','#skF_8','#skF_9'),
inference(splitLeft,[status(thm)],[c_65]) ).
tff(c_3531,plain,
( $less('#skF_2'('#skF_7','#skF_8','#skF_9'),'#skF_9')
| $less('#skF_9',max('#skF_7','#skF_8')) ),
inference(resolution,[status(thm)],[c_3513,c_143]) ).
tff(c_3896,plain,
max('#skF_7','#skF_8') = '#skE_4',
inference(define,[status(thm),theory(equality)],[c_3531]) ).
tff(c_3928,plain,
( ( '#skF_8' = '#skE_4' )
| $less('#skF_8','#skF_7') ),
inference(superposition,[status(thm),theory(equality)],[c_86,c_3896]) ).
tff(c_3932,plain,
$less('#skF_8','#skF_7'),
inference(splitLeft,[status(thm)],[c_3928]) ).
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_87,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_3919,plain,
( ( '#skF_7' = '#skE_4' )
| $less('#skF_7','#skF_8') ),
inference(superposition,[status(thm),theory(equality)],[c_3896,c_87]) ).
tff(c_3930,plain,
$less('#skF_7','#skF_8'),
inference(splitLeft,[status(thm)],[c_3919]) ).
tff(c_3953,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_3932,c_3930]) ).
tff(c_3956,plain,
'#skF_8' = '#skE_4',
inference(splitRight,[status(thm)],[c_3928]) ).
tff(c_3597,plain,
max('#skF_7','#skF_8') = '#skE_4',
inference(define,[status(thm),theory(equality)],[c_3531]) ).
tff(c_4045,plain,
max('#skF_7','#skE_4') = '#skE_4',
inference(demodulation,[status(thm),theory(equality)],[c_3956,c_3597]) ).
tff(c_3603,plain,
max('#skF_7','#skF_8') = '#skE_4',
inference(define,[status(thm),theory(equality)],[c_3531]) ).
tff(c_3628,plain,
( ( '#skF_8' = '#skE_4' )
| $less('#skF_8','#skF_7') ),
inference(superposition,[status(thm),theory(equality)],[c_3603,c_86]) ).
tff(c_3661,plain,
$less('#skF_8','#skF_7'),
inference(splitLeft,[status(thm)],[c_3628]) ).
tff(c_3626,plain,
( ( '#skF_7' = '#skE_4' )
| $less('#skF_7','#skF_8') ),
inference(superposition,[status(thm),theory(equality)],[c_3603,c_87]) ).
tff(c_3637,plain,
$less('#skF_7','#skF_8'),
inference(splitLeft,[status(thm)],[c_3626]) ).
tff(c_3662,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_3661,c_3637]) ).
tff(c_3665,plain,
'#skF_8' = '#skE_4',
inference(splitRight,[status(thm)],[c_3628]) ).
tff(c_189,plain,
! [X_127a: $int,Y_128a: $int,N_129a: $int,Z_130a: $int] :
( model_ub(X_127a,Y_128a,N_129a)
| ~ ub(X_127a,Y_128a,Z_130a)
| $less(N_129a,Z_130a) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_21]) ).
tff(c_194,plain,
! [X_7a: $int,Y_8a: $int,N_129a: $int,Z_9a: $int] :
( model_ub(X_7a,Y_8a,N_129a)
| $less(N_129a,Z_9a)
| $less(Z_9a,X_7a)
| $less(Z_9a,Y_8a) ),
inference(resolution,[status(thm)],[c_83,c_189]) ).
tff(c_211,plain,
! [X_153a: $int,Y_154a: $int,N_155a: $int,Z_156a: $int] :
( model_ub(X_153a,Y_154a,N_155a)
| $less(N_155a,Z_156a)
| $less(Z_156a,X_153a)
| $less(Z_156a,Y_154a) ),
inference(resolution,[status(thm)],[c_83,c_189]) ).
tff(c_3136,plain,
! [X_1442a: $int,Y_1443a: $int,N_1444a: $int,Z_1445a: $int] :
( $less('#skF_3'(X_1442a,Y_1443a,N_1444a),N_1444a)
| minsol_model_ub(X_1442a,Y_1443a,N_1444a)
| $less(N_1444a,Z_1445a)
| $less(Z_1445a,X_1442a)
| $less(Z_1445a,Y_1443a) ),
inference(resolution,[status(thm)],[c_211,c_71]) ).
tff(c_2218,plain,
! [X_1080a: $int,Y_1081a: $int,N_1082a: $int,Z_1083a: $int] :
( $less('#skF_3'(X_1080a,Y_1081a,N_1082a),N_1082a)
| minsol_model_ub(X_1080a,Y_1081a,N_1082a)
| $less(N_1082a,Z_1083a)
| $less(Z_1083a,X_1080a)
| $less(Z_1083a,Y_1081a) ),
inference(resolution,[status(thm)],[c_211,c_71]) ).
tff(c_247,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,max(X_172a,Y_173a)) ),
inference(resolution,[status(thm)],[c_81,c_227]) ).
tff(c_265,plain,
( $less('#skF_2'('#skF_7','#skF_8','#skF_9'),'#skF_9')
| $less('#skF_9',max('#skF_7','#skF_8')) ),
inference(resolution,[status(thm)],[c_247,c_143]) ).
tff(c_949,plain,
max('#skF_7','#skF_8') = '#skE_4',
inference(define,[status(thm),theory(equality)],[c_265]) ).
tff(c_1010,plain,
( ( '#skF_8' = '#skE_4' )
| $less('#skF_8','#skF_7') ),
inference(superposition,[status(thm),theory(equality)],[c_949,c_86]) ).
tff(c_1021,plain,
$less('#skF_8','#skF_7'),
inference(splitLeft,[status(thm)],[c_1010]) ).
tff(c_1008,plain,
( ( '#skF_7' = '#skE_4' )
| $less('#skF_7','#skF_8') ),
inference(superposition,[status(thm),theory(equality)],[c_949,c_87]) ).
tff(c_1019,plain,
$less('#skF_7','#skF_8'),
inference(splitLeft,[status(thm)],[c_1008]) ).
tff(c_1022,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_1021,c_1019]) ).
tff(c_1025,plain,
'#skF_8' = '#skE_4',
inference(splitRight,[status(thm)],[c_1010]) ).
tff(c_608,plain,
max('#skF_7','#skF_8') = '#skE_4',
inference(define,[status(thm),theory(equality)],[c_265]) ).
tff(c_1167,plain,
max('#skF_7','#skE_4') = '#skE_4',
inference(demodulation,[status(thm),theory(equality)],[c_1025,c_608]) ).
tff(c_614,plain,
max('#skF_7','#skF_8') = '#skE_4',
inference(define,[status(thm),theory(equality)],[c_265]) ).
tff(c_675,plain,
( ( '#skF_8' = '#skE_4' )
| $less('#skF_8','#skF_7') ),
inference(superposition,[status(thm),theory(equality)],[c_614,c_86]) ).
tff(c_708,plain,
$less('#skF_8','#skF_7'),
inference(splitLeft,[status(thm)],[c_675]) ).
tff(c_673,plain,
( ( '#skF_7' = '#skE_4' )
| $less('#skF_7','#skF_8') ),
inference(superposition,[status(thm),theory(equality)],[c_614,c_87]) ).
tff(c_684,plain,
$less('#skF_7','#skF_8'),
inference(splitLeft,[status(thm)],[c_673]) ).
tff(c_709,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_708,c_684]) ).
tff(c_712,plain,
'#skF_8' = '#skE_4',
inference(splitRight,[status(thm)],[c_675]) ).
tff(c_57,plain,
( minsol_model_max('#skF_4','#skF_5','#skF_6')
| minsol_model_ub('#skF_7','#skF_8','#skF_9') ),
inference(cnfTransformation,[status(thm)],[f_95]) ).
tff(c_274,plain,
minsol_model_ub('#skF_7','#skF_8','#skF_9'),
inference(splitLeft,[status(thm)],[c_57]) ).
tff(c_72,plain,
! [X_25a: $int,Y_26a: $int,N_27a: $int] :
( model_ub(X_25a,Y_26a,N_27a)
| ~ minsol_model_ub(X_25a,Y_26a,N_27a) ),
inference(cnfTransformation,[status(thm)],[f_89]) ).
tff(c_275,plain,
minsol_model_ub('#skF_7','#skF_8','#skF_9'),
inference(splitLeft,[status(thm)],[c_57]) ).
tff(c_24,plain,
! [X_13a: $int,Y_14a: $int,N_15a: $int] :
( $lesseq('#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_168,plain,
! [N_114a: $int,X_115a: $int,Y_116a: $int] :
( ~ $less(N_114a,'#skF_1'(X_115a,Y_116a,N_114a))
| ~ model_ub(X_115a,Y_116a,N_114a) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_24]) ).
tff(c_173,plain,
! [N_27a: $int,X_25a: $int,Y_26a: $int] :
( ~ $less(N_27a,'#skF_1'(X_25a,Y_26a,N_27a))
| ~ minsol_model_ub(X_25a,Y_26a,N_27a) ),
inference(resolution,[status(thm)],[c_72,c_168]) ).
tff(c_291,plain,
~ $less('#skF_9','#skF_1'('#skF_7','#skF_8','#skF_9')),
inference(resolution,[status(thm)],[c_275,c_173]) ).
tff(c_315,plain,
'#skF_1'('#skF_7','#skF_8','#skF_9') = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_291]) ).
tff(c_78,plain,
! [X_13a: $int,Y_14a: $int,N_15a: $int] :
( ub(X_13a,Y_14a,'#skF_1'(X_13a,Y_14a,N_15a))
| ~ model_ub(X_13a,Y_14a,N_15a) ),
inference(cnfTransformation,[status(thm)],[f_69]) ).
tff(c_336,plain,
( ub('#skF_7','#skF_8','#skE_1')
| ~ model_ub('#skF_7','#skF_8','#skF_9') ),
inference(superposition,[status(thm),theory(equality)],[c_315,c_78]) ).
tff(c_354,plain,
~ model_ub('#skF_7','#skF_8','#skF_9'),
inference(splitLeft,[status(thm)],[c_336]) ).
tff(c_360,plain,
~ minsol_model_ub('#skF_7','#skF_8','#skF_9'),
inference(resolution,[status(thm)],[c_72,c_354]) ).
tff(c_366,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_274,c_360]) ).
tff(c_373,plain,
ub('#skF_7','#skF_8','#skE_1'),
inference(splitRight,[status(thm)],[c_336]) ).
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_85,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_387,plain,
~ $less('#skE_1','#skF_8'),
inference(resolution,[status(thm)],[c_373,c_85]) ).
tff(c_787,plain,
~ $less('#skE_1','#skE_4'),
inference(demodulation,[status(thm),theory(equality)],[c_712,c_387]) ).
tff(c_598,plain,
max('#skF_7','#skF_8') = '#skE_4',
inference(define,[status(thm),theory(equality)],[c_265]) ).
tff(c_597,plain,
'#skF_2'('#skF_7','#skF_8','#skF_9') = '#skE_3',
inference(define,[status(thm),theory(equality)],[c_265]) ).
tff(c_596,plain,
( $less('#skF_2'('#skF_7','#skF_8','#skF_9'),'#skF_9')
| $less('#skF_9',max('#skF_7','#skF_8')) ),
inference(resolution,[status(thm)],[c_247,c_143]) ).
tff(c_609,plain,
( $less('#skE_3','#skF_9')
| $less('#skF_9','#skE_4') ),
inference(demodulation,[status(thm),theory(equality)],[c_598,c_597,c_596]) ).
tff(c_611,plain,
$less('#skF_9','#skE_4'),
inference(splitLeft,[status(thm)],[c_609]) ).
tff(c_305,plain,
'#skF_1'('#skF_7','#skF_8','#skF_9') = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_291]) ).
tff(c_304,plain,
~ $less('#skF_9','#skF_1'('#skF_7','#skF_8','#skF_9')),
inference(resolution,[status(thm)],[c_275,c_173]) ).
tff(c_312,plain,
~ $less('#skF_9','#skE_1'),
inference(demodulation,[status(thm),theory(equality)],[c_305,c_304]) ).
tff(c_829,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_787,c_611,c_312]) ).
tff(c_832,plain,
'#skF_7' = '#skE_4',
inference(splitRight,[status(thm)],[c_673]) ).
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_84,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_389,plain,
~ $less('#skE_1','#skF_7'),
inference(resolution,[status(thm)],[c_373,c_84]) ).
tff(c_897,plain,
~ $less('#skE_1','#skE_4'),
inference(demodulation,[status(thm),theory(equality)],[c_832,c_389]) ).
tff(c_944,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_897,c_611,c_312]) ).
tff(c_948,plain,
~ $less('#skF_9','#skE_4'),
inference(splitRight,[status(thm)],[c_609]) ).
tff(c_1027,plain,
'#skF_2'('#skF_7','#skF_8','#skF_9') = '#skE_3',
inference(define,[status(thm),theory(equality)],[c_265]) ).
tff(c_74,plain,
! [X_19a: $int,Y_20a: $int,N_21a: $int] :
( model_max(X_19a,Y_20a,'#skF_2'(X_19a,Y_20a,N_21a))
| minsol_model_max(X_19a,Y_20a,N_21a)
| ~ model_max(X_19a,Y_20a,N_21a) ),
inference(cnfTransformation,[status(thm)],[f_79]) ).
tff(c_1043,plain,
( model_max('#skF_7','#skF_8','#skE_3')
| minsol_model_max('#skF_7','#skF_8','#skF_9')
| ~ model_max('#skF_7','#skF_8','#skF_9') ),
inference(superposition,[status(thm),theory(equality)],[c_1027,c_74]) ).
tff(c_1373,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(demodulation,[status(thm),theory(equality)],[c_1025,c_1025,c_1025,c_1043]) ).
tff(c_1381,plain,
~ model_max('#skF_7','#skE_4','#skF_9'),
inference(splitLeft,[status(thm)],[c_1373]) ).
tff(c_1384,plain,
$less('#skF_9',max('#skF_7','#skE_4')),
inference(resolution,[status(thm)],[c_81,c_1381]) ).
tff(c_1389,plain,
$less('#skF_9','#skE_4'),
inference(demodulation,[status(thm),theory(equality)],[c_1167,c_1384]) ).
tff(c_1391,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_948,c_1389]) ).
tff(c_1395,plain,
( minsol_model_max('#skF_7','#skE_4','#skF_9')
| model_max('#skF_7','#skE_4','#skE_3') ),
inference(splitRight,[status(thm)],[c_1373]) ).
tff(c_1422,plain,
model_max('#skF_7','#skE_4','#skE_3'),
inference(splitLeft,[status(thm)],[c_1395]) ).
tff(c_16,plain,
! [X_10a: $int,Y_11a: $int,N_12a: $int] :
( $lesseq(max(X_10a,Y_11a),N_12a)
| ~ model_max(X_10a,Y_11a,N_12a) ),
inference(cnfTransformation,[status(thm)],[f_61]) ).
tff(c_82,plain,
! [N_12a: $int,X_10a: $int,Y_11a: $int] :
( ~ $less(N_12a,max(X_10a,Y_11a))
| ~ model_max(X_10a,Y_11a,N_12a) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_16]) ).
tff(c_1431,plain,
~ $less('#skE_3',max('#skF_7','#skE_4')),
inference(resolution,[status(thm)],[c_1422,c_82]) ).
tff(c_1440,plain,
~ $less('#skE_3','#skE_4'),
inference(demodulation,[status(thm),theory(equality)],[c_1167,c_1431]) ).
tff(c_272,plain,
minsol_model_ub('#skF_7','#skF_8','#skF_9'),
inference(splitLeft,[status(thm)],[c_57]) ).
tff(c_37,plain,
! [X_25a: $int,Y_26a: $int,Z_30a: $int,N_27a: $int] :
( ~ model_ub(X_25a,Y_26a,Z_30a)
| ~ minsol_model_ub(X_25a,Y_26a,N_27a)
| $lesseq(N_27a,Z_30a) ),
inference(cnfTransformation,[status(thm)],[f_89]) ).
tff(c_73,plain,
! [X_25a: $int,Y_26a: $int,Z_30a: $int,N_27a: $int] :
( ~ model_ub(X_25a,Y_26a,Z_30a)
| ~ minsol_model_ub(X_25a,Y_26a,N_27a)
| ~ $less(Z_30a,N_27a) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_37]) ).
tff(c_340,plain,
! [Z_217a: $int,N_220a: $int,Y_219a: $int,N_218a: $int,X_221a: $int] :
( ~ minsol_model_ub(X_221a,Y_219a,N_220a)
| ~ $less(N_218a,N_220a)
| $less(N_218a,Z_217a)
| $less(Z_217a,X_221a)
| $less(Z_217a,Y_219a) ),
inference(resolution,[status(thm)],[c_211,c_73]) ).
tff(c_345,plain,
! [N_218a: $int,Z_217a: $int] :
( ~ $less(N_218a,'#skF_9')
| $less(N_218a,Z_217a)
| $less(Z_217a,'#skF_7')
| $less(Z_217a,'#skF_8') ),
inference(resolution,[status(thm)],[c_272,c_340]) ).
tff(c_1119,plain,
! [N_218a: $int,Z_217a: $int] :
( ~ $less(N_218a,'#skF_9')
| $less(N_218a,Z_217a)
| $less(Z_217a,'#skF_7')
| $less(Z_217a,'#skE_4') ),
inference(demodulation,[status(thm),theory(equality)],[c_1025,c_345]) ).
tff(c_1397,plain,
( $lesseq('#skF_9','#skF_7')
| $lesseq('#skF_9','#skE_4') ),
inference(quantifierElimination,[status(thm),theory('LIA')],[c_1119]) ).
tff(c_1399,plain,
( ~ $less('#skF_7','#skF_9')
| ~ $less('#skE_4','#skF_9') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_1397]) ).
tff(c_1026,plain,
~ $less('#skF_8','#skF_7'),
inference(splitRight,[status(thm)],[c_1010]) ).
tff(c_1137,plain,
~ $less('#skE_4','#skF_7'),
inference(demodulation,[status(thm),theory(equality)],[c_1025,c_1026]) ).
tff(c_947,plain,
$less('#skE_3','#skF_9'),
inference(splitRight,[status(thm)],[c_609]) ).
tff(c_1441,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_1440,c_1399,c_1137,c_947]) ).
tff(c_1447,plain,
minsol_model_max('#skF_7','#skE_4','#skF_9'),
inference(splitRight,[status(thm)],[c_1395]) ).
tff(c_1135,plain,
~ minsol_model_max('#skF_7','#skE_4','#skF_9'),
inference(demodulation,[status(thm),theory(equality)],[c_1025,c_143]) ).
tff(c_1450,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_1447,c_1135]) ).
tff(c_1453,plain,
'#skF_7' = '#skE_4',
inference(splitRight,[status(thm)],[c_1008]) ).
tff(c_1575,plain,
max('#skE_4','#skF_8') = '#skE_4',
inference(demodulation,[status(thm),theory(equality)],[c_1453,c_608]) ).
tff(c_1455,plain,
'#skF_2'('#skF_7','#skF_8','#skF_9') = '#skE_3',
inference(define,[status(thm),theory(equality)],[c_265]) ).
tff(c_1471,plain,
( model_max('#skF_7','#skF_8','#skE_3')
| minsol_model_max('#skF_7','#skF_8','#skF_9')
| ~ model_max('#skF_7','#skF_8','#skF_9') ),
inference(superposition,[status(thm),theory(equality)],[c_1455,c_74]) ).
tff(c_1811,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(demodulation,[status(thm),theory(equality)],[c_1453,c_1453,c_1453,c_1471]) ).
tff(c_1819,plain,
~ model_max('#skE_4','#skF_8','#skF_9'),
inference(splitLeft,[status(thm)],[c_1811]) ).
tff(c_1822,plain,
$less('#skF_9',max('#skE_4','#skF_8')),
inference(resolution,[status(thm)],[c_81,c_1819]) ).
tff(c_1827,plain,
$less('#skF_9','#skE_4'),
inference(demodulation,[status(thm),theory(equality)],[c_1575,c_1822]) ).
tff(c_1829,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_948,c_1827]) ).
tff(c_1833,plain,
( minsol_model_max('#skE_4','#skF_8','#skF_9')
| model_max('#skE_4','#skF_8','#skE_3') ),
inference(splitRight,[status(thm)],[c_1811]) ).
tff(c_1889,plain,
model_max('#skE_4','#skF_8','#skE_3'),
inference(splitLeft,[status(thm)],[c_1833]) ).
tff(c_1898,plain,
~ $less('#skE_3',max('#skE_4','#skF_8')),
inference(resolution,[status(thm)],[c_1889,c_82]) ).
tff(c_1907,plain,
~ $less('#skE_3','#skE_4'),
inference(demodulation,[status(thm),theory(equality)],[c_1575,c_1898]) ).
tff(c_1547,plain,
! [N_218a: $int,Z_217a: $int] :
( ~ $less(N_218a,'#skF_9')
| $less(N_218a,Z_217a)
| $less(Z_217a,'#skE_4')
| $less(Z_217a,'#skF_8') ),
inference(demodulation,[status(thm),theory(equality)],[c_1453,c_345]) ).
tff(c_1803,plain,
( $lesseq('#skF_9','#skE_4')
| $lesseq('#skF_9','#skF_8') ),
inference(quantifierElimination,[status(thm),theory('LIA')],[c_1547]) ).
tff(c_1805,plain,
( ~ $less('#skE_4','#skF_9')
| ~ $less('#skF_8','#skF_9') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_1803]) ).
tff(c_1454,plain,
~ $less('#skF_7','#skF_8'),
inference(splitRight,[status(thm)],[c_1008]) ).
tff(c_1565,plain,
~ $less('#skE_4','#skF_8'),
inference(demodulation,[status(thm),theory(equality)],[c_1453,c_1454]) ).
tff(c_1908,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_1907,c_1805,c_1565,c_947]) ).
tff(c_1914,plain,
minsol_model_max('#skE_4','#skF_8','#skF_9'),
inference(splitRight,[status(thm)],[c_1833]) ).
tff(c_1563,plain,
~ minsol_model_max('#skE_4','#skF_8','#skF_9'),
inference(demodulation,[status(thm),theory(equality)],[c_1453,c_143]) ).
tff(c_1917,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_1914,c_1563]) ).
tff(c_1924,plain,
minsol_model_max('#skF_4','#skF_5','#skF_6'),
inference(splitRight,[status(thm)],[c_57]) ).
tff(c_76,plain,
! [X_19a: $int,Y_20a: $int,N_21a: $int] :
( model_max(X_19a,Y_20a,N_21a)
| ~ minsol_model_max(X_19a,Y_20a,N_21a) ),
inference(cnfTransformation,[status(thm)],[f_79]) ).
tff(c_144,plain,
! [N_102a: $int,X_103a: $int,Y_104a: $int] :
( ~ $less(N_102a,max(X_103a,Y_104a))
| ~ model_max(X_103a,Y_104a,N_102a) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_16]) ).
tff(c_149,plain,
! [N_21a: $int,X_19a: $int,Y_20a: $int] :
( ~ $less(N_21a,max(X_19a,Y_20a))
| ~ minsol_model_max(X_19a,Y_20a,N_21a) ),
inference(resolution,[status(thm)],[c_76,c_144]) ).
tff(c_1946,plain,
~ $less('#skF_6',max('#skF_4','#skF_5')),
inference(resolution,[status(thm)],[c_1924,c_149]) ).
tff(c_1976,plain,
max('#skF_4','#skF_5') = '#skE_5',
inference(define,[status(thm),theory(equality)],[c_1946]) ).
tff(c_2001,plain,
( ( '#skF_5' = '#skE_5' )
| $less('#skF_5','#skF_4') ),
inference(superposition,[status(thm),theory(equality)],[c_1976,c_86]) ).
tff(c_2020,plain,
$less('#skF_5','#skF_4'),
inference(splitLeft,[status(thm)],[c_2001]) ).
tff(c_1999,plain,
( ( '#skF_4' = '#skE_5' )
| $less('#skF_4','#skF_5') ),
inference(superposition,[status(thm),theory(equality)],[c_1976,c_87]) ).
tff(c_2010,plain,
$less('#skF_4','#skF_5'),
inference(splitLeft,[status(thm)],[c_1999]) ).
tff(c_2021,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_2020,c_2010]) ).
tff(c_2024,plain,
'#skF_5' = '#skE_5',
inference(splitRight,[status(thm)],[c_2001]) ).
tff(c_61,plain,
( ~ minsol_model_ub('#skF_4','#skF_5','#skF_6')
| minsol_model_ub('#skF_7','#skF_8','#skF_9') ),
inference(cnfTransformation,[status(thm)],[f_95]) ).
tff(c_241,plain,
~ minsol_model_ub('#skF_4','#skF_5','#skF_6'),
inference(splitLeft,[status(thm)],[c_61]) ).
tff(c_2060,plain,
~ minsol_model_ub('#skF_4','#skE_5','#skF_6'),
inference(demodulation,[status(thm),theory(equality)],[c_2024,c_241]) ).
tff(c_2234,plain,
! [Z_1083a: $int] :
( $less('#skF_3'('#skF_4','#skE_5','#skF_6'),'#skF_6')
| $less('#skF_6',Z_1083a)
| $less(Z_1083a,'#skF_4')
| $less(Z_1083a,'#skE_5') ),
inference(resolution,[status(thm)],[c_2218,c_2060]) ).
tff(c_2569,plain,
'#skF_3'('#skF_4','#skE_5','#skF_6') = '#skE_6',
inference(define,[status(thm),theory(equality)],[c_2234]) ).
tff(c_70,plain,
! [X_25a: $int,Y_26a: $int,N_27a: $int] :
( model_ub(X_25a,Y_26a,'#skF_3'(X_25a,Y_26a,N_27a))
| minsol_model_ub(X_25a,Y_26a,N_27a)
| ~ model_ub(X_25a,Y_26a,N_27a) ),
inference(cnfTransformation,[status(thm)],[f_89]) ).
tff(c_2585,plain,
( model_ub('#skF_4','#skE_5','#skE_6')
| minsol_model_ub('#skF_4','#skE_5','#skF_6')
| ~ model_ub('#skF_4','#skE_5','#skF_6') ),
inference(superposition,[status(thm),theory(equality)],[c_2569,c_70]) ).
tff(c_2621,plain,
~ model_ub('#skF_4','#skE_5','#skF_6'),
inference(splitLeft,[status(thm)],[c_2585]) ).
tff(c_2629,plain,
! [Z_9a: $int] :
( $less('#skF_6',Z_9a)
| $less(Z_9a,'#skF_4')
| $less(Z_9a,'#skE_5') ),
inference(resolution,[status(thm)],[c_194,c_2621]) ).
tff(c_2631,plain,
( $lesseq($sum(1,'#skF_6'),'#skF_4')
| $lesseq($sum(1,'#skF_6'),'#skE_5') ),
inference(quantifierElimination,[status(thm),theory('LIA')],[c_2629]) ).
tff(c_2633,plain,
( ~ $less('#skF_4',$sum(1,'#skF_6'))
| ~ $less('#skE_5',$sum(1,'#skF_6')) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_2631]) ).
tff(c_2025,plain,
~ $less('#skF_5','#skF_4'),
inference(splitRight,[status(thm)],[c_2001]) ).
tff(c_2062,plain,
~ $less('#skE_5','#skF_4'),
inference(demodulation,[status(thm),theory(equality)],[c_2024,c_2025]) ).
tff(c_1966,plain,
max('#skF_4','#skF_5') = '#skE_5',
inference(define,[status(thm),theory(equality)],[c_1946]) ).
tff(c_1965,plain,
~ $less('#skF_6',max('#skF_4','#skF_5')),
inference(resolution,[status(thm)],[c_1924,c_149]) ).
tff(c_1973,plain,
~ $less('#skF_6','#skE_5'),
inference(demodulation,[status(thm),theory(equality)],[c_1966,c_1965]) ).
tff(c_2634,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_2633,c_2062,c_1973]) ).
tff(c_2638,plain,
( minsol_model_ub('#skF_4','#skE_5','#skF_6')
| model_ub('#skF_4','#skE_5','#skE_6') ),
inference(splitRight,[status(thm)],[c_2585]) ).
tff(c_2649,plain,
model_ub('#skF_4','#skE_5','#skE_6'),
inference(splitLeft,[status(thm)],[c_2638]) ).
tff(c_2650,plain,
model_ub('#skF_4','#skE_5','#skE_6'),
inference(splitLeft,[status(thm)],[c_2638]) ).
tff(c_79,plain,
! [N_15a: $int,X_13a: $int,Y_14a: $int] :
( ~ $less(N_15a,'#skF_1'(X_13a,Y_14a,N_15a))
| ~ model_ub(X_13a,Y_14a,N_15a) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_24]) ).
tff(c_2668,plain,
~ $less('#skE_6','#skF_1'('#skF_4','#skE_5','#skE_6')),
inference(resolution,[status(thm)],[c_2650,c_79]) ).
tff(c_2690,plain,
'#skF_1'('#skF_4','#skE_5','#skE_6') = '#skE_7',
inference(define,[status(thm),theory(equality)],[c_2668]) ).
tff(c_2700,plain,
( ub('#skF_4','#skE_5','#skE_7')
| ~ model_ub('#skF_4','#skE_5','#skE_6') ),
inference(superposition,[status(thm),theory(equality)],[c_2690,c_78]) ).
tff(c_2721,plain,
ub('#skF_4','#skE_5','#skE_7'),
inference(demodulation,[status(thm),theory(equality)],[c_2649,c_2700]) ).
tff(c_2735,plain,
~ $less('#skE_7','#skE_5'),
inference(resolution,[status(thm)],[c_2721,c_85]) ).
tff(c_2680,plain,
'#skF_1'('#skF_4','#skE_5','#skE_6') = '#skE_7',
inference(define,[status(thm),theory(equality)],[c_2668]) ).
tff(c_2679,plain,
~ $less('#skE_6','#skF_1'('#skF_4','#skE_5','#skE_6')),
inference(resolution,[status(thm)],[c_2650,c_79]) ).
tff(c_2687,plain,
~ $less('#skE_6','#skE_7'),
inference(demodulation,[status(thm),theory(equality)],[c_2680,c_2679]) ).
tff(c_2559,plain,
'#skF_3'('#skF_4','#skE_5','#skF_6') = '#skE_6',
inference(define,[status(thm),theory(equality)],[c_2234]) ).
tff(c_2558,plain,
! [Z_1083a: $int] :
( $less('#skF_3'('#skF_4','#skE_5','#skF_6'),'#skF_6')
| $less('#skF_6',Z_1083a)
| $less(Z_1083a,'#skF_4')
| $less(Z_1083a,'#skE_5') ),
inference(resolution,[status(thm)],[c_2218,c_2060]) ).
tff(c_2566,plain,
! [Z_1083a: $int] :
( $less('#skE_6','#skF_6')
| $less('#skF_6',Z_1083a)
| $less(Z_1083a,'#skF_4')
| $less(Z_1083a,'#skE_5') ),
inference(demodulation,[status(thm),theory(equality)],[c_2559,c_2558]) ).
tff(c_2590,plain,
$less('#skE_6','#skF_6'),
inference(splitLeft,[status(thm)],[c_2566]) ).
tff(c_1975,plain,
max('#skF_4','#skF_5') = '#skE_5',
inference(define,[status(thm),theory(equality)],[c_1946]) ).
tff(c_28,plain,
! [X_19a: $int,Y_20a: $int,Z_24a: $int,N_21a: $int] :
( ~ model_max(X_19a,Y_20a,Z_24a)
| ~ minsol_model_max(X_19a,Y_20a,N_21a)
| $lesseq(N_21a,Z_24a) ),
inference(cnfTransformation,[status(thm)],[f_79]) ).
tff(c_178,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_28]) ).
tff(c_186,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,max(X_10a,Y_11a)) ),
inference(resolution,[status(thm)],[c_81,c_178]) ).
tff(c_1938,plain,
! [N_12a: $int] :
( ~ $less(N_12a,'#skF_6')
| $less(N_12a,max('#skF_4','#skF_5')) ),
inference(resolution,[status(thm)],[c_1924,c_186]) ).
tff(c_2015,plain,
! [N_12a: $int] :
( ~ $less(N_12a,'#skF_6')
| $less(N_12a,'#skE_5') ),
inference(demodulation,[status(thm),theory(equality)],[c_1975,c_1938]) ).
tff(c_2016,plain,
$lesseq('#skF_6','#skE_5'),
inference(quantifierElimination,[status(thm),theory('LIA')],[c_2015]) ).
tff(c_2018,plain,
~ $less('#skE_5','#skF_6'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_2016]) ).
tff(c_2738,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_2735,c_2687,c_2590,c_2018]) ).
tff(c_2744,plain,
minsol_model_ub('#skF_4','#skE_5','#skF_6'),
inference(splitRight,[status(thm)],[c_2638]) ).
tff(c_2747,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_2744,c_2060]) ).
tff(c_2750,plain,
! [Z_1083a: $int] :
( $less('#skF_6',Z_1083a)
| $less(Z_1083a,'#skF_4')
| $less(Z_1083a,'#skE_5') ),
inference(splitRight,[status(thm)],[c_2566]) ).
tff(c_2754,plain,
( $lesseq($sum(1,'#skF_6'),'#skF_4')
| $lesseq($sum(1,'#skF_6'),'#skE_5') ),
inference(quantifierElimination,[status(thm),theory('LIA')],[c_2750]) ).
tff(c_2756,plain,
( ~ $less('#skF_4',$sum(1,'#skF_6'))
| ~ $less('#skE_5',$sum(1,'#skF_6')) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_2754]) ).
tff(c_2757,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_2756,c_2062,c_1973]) ).
tff(c_2760,plain,
'#skF_4' = '#skE_5',
inference(splitRight,[status(thm)],[c_1999]) ).
tff(c_2796,plain,
~ minsol_model_ub('#skE_5','#skF_5','#skF_6'),
inference(demodulation,[status(thm),theory(equality)],[c_2760,c_241]) ).
tff(c_3152,plain,
! [Z_1445a: $int] :
( $less('#skF_3'('#skE_5','#skF_5','#skF_6'),'#skF_6')
| $less('#skF_6',Z_1445a)
| $less(Z_1445a,'#skE_5')
| $less(Z_1445a,'#skF_5') ),
inference(resolution,[status(thm)],[c_3136,c_2796]) ).
tff(c_3272,plain,
'#skF_3'('#skE_5','#skF_5','#skF_6') = '#skE_8',
inference(define,[status(thm),theory(equality)],[c_3152]) ).
tff(c_3288,plain,
( model_ub('#skE_5','#skF_5','#skE_8')
| minsol_model_ub('#skE_5','#skF_5','#skF_6')
| ~ model_ub('#skE_5','#skF_5','#skF_6') ),
inference(superposition,[status(thm),theory(equality)],[c_3272,c_70]) ).
tff(c_3311,plain,
~ model_ub('#skE_5','#skF_5','#skF_6'),
inference(splitLeft,[status(thm)],[c_3288]) ).
tff(c_3319,plain,
! [Z_9a: $int] :
( $less('#skF_6',Z_9a)
| $less(Z_9a,'#skE_5')
| $less(Z_9a,'#skF_5') ),
inference(resolution,[status(thm)],[c_194,c_3311]) ).
tff(c_3321,plain,
( $lesseq($sum(1,'#skF_6'),'#skE_5')
| $lesseq($sum(1,'#skF_6'),'#skF_5') ),
inference(quantifierElimination,[status(thm),theory('LIA')],[c_3319]) ).
tff(c_3323,plain,
( ~ $less('#skE_5',$sum(1,'#skF_6'))
| ~ $less('#skF_5',$sum(1,'#skF_6')) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_3321]) ).
tff(c_2761,plain,
~ $less('#skF_4','#skF_5'),
inference(splitRight,[status(thm)],[c_1999]) ).
tff(c_2798,plain,
~ $less('#skE_5','#skF_5'),
inference(demodulation,[status(thm),theory(equality)],[c_2760,c_2761]) ).
tff(c_3324,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_3323,c_2798,c_1973]) ).
tff(c_3328,plain,
( minsol_model_ub('#skE_5','#skF_5','#skF_6')
| model_ub('#skE_5','#skF_5','#skE_8') ),
inference(splitRight,[status(thm)],[c_3288]) ).
tff(c_3340,plain,
model_ub('#skE_5','#skF_5','#skE_8'),
inference(splitLeft,[status(thm)],[c_3328]) ).
tff(c_3341,plain,
model_ub('#skE_5','#skF_5','#skE_8'),
inference(splitLeft,[status(thm)],[c_3328]) ).
tff(c_3359,plain,
~ $less('#skE_8','#skF_1'('#skE_5','#skF_5','#skE_8')),
inference(resolution,[status(thm)],[c_3341,c_79]) ).
tff(c_3381,plain,
'#skF_1'('#skE_5','#skF_5','#skE_8') = '#skE_9',
inference(define,[status(thm),theory(equality)],[c_3359]) ).
tff(c_3391,plain,
( ub('#skE_5','#skF_5','#skE_9')
| ~ model_ub('#skE_5','#skF_5','#skE_8') ),
inference(superposition,[status(thm),theory(equality)],[c_3381,c_78]) ).
tff(c_3412,plain,
ub('#skE_5','#skF_5','#skE_9'),
inference(demodulation,[status(thm),theory(equality)],[c_3340,c_3391]) ).
tff(c_3428,plain,
~ $less('#skE_9','#skE_5'),
inference(resolution,[status(thm)],[c_3412,c_84]) ).
tff(c_3371,plain,
'#skF_1'('#skE_5','#skF_5','#skE_8') = '#skE_9',
inference(define,[status(thm),theory(equality)],[c_3359]) ).
tff(c_3370,plain,
~ $less('#skE_8','#skF_1'('#skE_5','#skF_5','#skE_8')),
inference(resolution,[status(thm)],[c_3341,c_79]) ).
tff(c_3378,plain,
~ $less('#skE_8','#skE_9'),
inference(demodulation,[status(thm),theory(equality)],[c_3371,c_3370]) ).
tff(c_3262,plain,
'#skF_3'('#skE_5','#skF_5','#skF_6') = '#skE_8',
inference(define,[status(thm),theory(equality)],[c_3152]) ).
tff(c_3261,plain,
! [Z_1445a: $int] :
( $less('#skF_3'('#skE_5','#skF_5','#skF_6'),'#skF_6')
| $less('#skF_6',Z_1445a)
| $less(Z_1445a,'#skE_5')
| $less(Z_1445a,'#skF_5') ),
inference(resolution,[status(thm)],[c_3136,c_2796]) ).
tff(c_3269,plain,
! [Z_1445a: $int] :
( $less('#skE_8','#skF_6')
| $less('#skF_6',Z_1445a)
| $less(Z_1445a,'#skE_5')
| $less(Z_1445a,'#skF_5') ),
inference(demodulation,[status(thm),theory(equality)],[c_3262,c_3261]) ).
tff(c_3293,plain,
$less('#skE_8','#skF_6'),
inference(splitLeft,[status(thm)],[c_3269]) ).
tff(c_1972,plain,
max('#skF_4','#skF_5') = '#skE_5',
inference(define,[status(thm),theory(equality)],[c_1946]) ).
tff(c_2808,plain,
max('#skE_5','#skF_5') = '#skE_5',
inference(demodulation,[status(thm),theory(equality)],[c_2760,c_1972]) ).
tff(c_1921,plain,
minsol_model_max('#skF_4','#skF_5','#skF_6'),
inference(splitRight,[status(thm)],[c_57]) ).
tff(c_2851,plain,
minsol_model_max('#skE_5','#skF_5','#skF_6'),
inference(demodulation,[status(thm),theory(equality)],[c_2760,c_1921]) ).
tff(c_2854,plain,
! [N_12a: $int] :
( ~ $less(N_12a,'#skF_6')
| $less(N_12a,max('#skE_5','#skF_5')) ),
inference(resolution,[status(thm)],[c_2851,c_186]) ).
tff(c_2865,plain,
! [N_12a: $int] :
( ~ $less(N_12a,'#skF_6')
| $less(N_12a,'#skE_5') ),
inference(demodulation,[status(thm),theory(equality)],[c_2808,c_2854]) ).
tff(c_2873,plain,
$lesseq('#skF_6','#skE_5'),
inference(quantifierElimination,[status(thm),theory('LIA')],[c_2865]) ).
tff(c_2875,plain,
~ $less('#skE_5','#skF_6'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_2873]) ).
tff(c_3430,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_3428,c_3378,c_3293,c_2875]) ).
tff(c_3436,plain,
minsol_model_ub('#skE_5','#skF_5','#skF_6'),
inference(splitRight,[status(thm)],[c_3328]) ).
tff(c_3439,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_3436,c_2796]) ).
tff(c_3442,plain,
! [Z_1445a: $int] :
( $less('#skF_6',Z_1445a)
| $less(Z_1445a,'#skE_5')
| $less(Z_1445a,'#skF_5') ),
inference(splitRight,[status(thm)],[c_3269]) ).
tff(c_3444,plain,
( $lesseq($sum(1,'#skF_6'),'#skE_5')
| $lesseq($sum(1,'#skF_6'),'#skF_5') ),
inference(quantifierElimination,[status(thm),theory('LIA')],[c_3442]) ).
tff(c_3446,plain,
( ~ $less('#skE_5',$sum(1,'#skF_6'))
| ~ $less('#skF_5',$sum(1,'#skF_6')) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_3444]) ).
tff(c_3447,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_3446,c_2798,c_1973]) ).
tff(c_3453,plain,
minsol_model_ub('#skF_7','#skF_8','#skF_9'),
inference(splitRight,[status(thm)],[c_61]) ).
tff(c_3454,plain,
minsol_model_ub('#skF_7','#skF_8','#skF_9'),
inference(splitRight,[status(thm)],[c_61]) ).
tff(c_3465,plain,
~ $less('#skF_9','#skF_1'('#skF_7','#skF_8','#skF_9')),
inference(resolution,[status(thm)],[c_3454,c_173]) ).
tff(c_3492,plain,
'#skF_1'('#skF_7','#skF_8','#skF_9') = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_3465]) ).
tff(c_3508,plain,
( ub('#skF_7','#skF_8','#skE_1')
| ~ model_ub('#skF_7','#skF_8','#skF_9') ),
inference(superposition,[status(thm),theory(equality)],[c_3492,c_78]) ).
tff(c_3548,plain,
~ model_ub('#skF_7','#skF_8','#skF_9'),
inference(splitLeft,[status(thm)],[c_3508]) ).
tff(c_3554,plain,
~ minsol_model_ub('#skF_7','#skF_8','#skF_9'),
inference(resolution,[status(thm)],[c_72,c_3548]) ).
tff(c_3560,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_3453,c_3554]) ).
tff(c_3567,plain,
ub('#skF_7','#skF_8','#skE_1'),
inference(splitRight,[status(thm)],[c_3508]) ).
tff(c_3581,plain,
~ $less('#skE_1','#skF_8'),
inference(resolution,[status(thm)],[c_3567,c_85]) ).
tff(c_3785,plain,
~ $less('#skE_1','#skE_4'),
inference(demodulation,[status(thm),theory(equality)],[c_3665,c_3581]) ).
tff(c_3587,plain,
max('#skF_7','#skF_8') = '#skE_4',
inference(define,[status(thm),theory(equality)],[c_3531]) ).
tff(c_3586,plain,
'#skF_2'('#skF_7','#skF_8','#skF_9') = '#skE_3',
inference(define,[status(thm),theory(equality)],[c_3531]) ).
tff(c_3585,plain,
( $less('#skF_2'('#skF_7','#skF_8','#skF_9'),'#skF_9')
| $less('#skF_9',max('#skF_7','#skF_8')) ),
inference(resolution,[status(thm)],[c_3513,c_143]) ).
tff(c_3598,plain,
( $less('#skE_3','#skF_9')
| $less('#skF_9','#skE_4') ),
inference(demodulation,[status(thm),theory(equality)],[c_3587,c_3586,c_3585]) ).
tff(c_3600,plain,
$less('#skF_9','#skE_4'),
inference(splitLeft,[status(thm)],[c_3598]) ).
tff(c_3478,plain,
'#skF_1'('#skF_7','#skF_8','#skF_9') = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_3465]) ).
tff(c_3477,plain,
~ $less('#skF_9','#skF_1'('#skF_7','#skF_8','#skF_9')),
inference(resolution,[status(thm)],[c_3454,c_173]) ).
tff(c_3485,plain,
~ $less('#skF_9','#skE_1'),
inference(demodulation,[status(thm),theory(equality)],[c_3478,c_3477]) ).
tff(c_3805,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_3785,c_3600,c_3485]) ).
tff(c_3808,plain,
'#skF_7' = '#skE_4',
inference(splitRight,[status(thm)],[c_3626]) ).
tff(c_3583,plain,
~ $less('#skE_1','#skF_7'),
inference(resolution,[status(thm)],[c_3567,c_84]) ).
tff(c_3873,plain,
~ $less('#skE_1','#skE_4'),
inference(demodulation,[status(thm),theory(equality)],[c_3808,c_3583]) ).
tff(c_3891,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_3873,c_3600,c_3485]) ).
tff(c_3895,plain,
~ $less('#skF_9','#skE_4'),
inference(splitRight,[status(thm)],[c_3598]) ).
tff(c_3594,plain,
'#skF_2'('#skF_7','#skF_8','#skF_9') = '#skE_3',
inference(define,[status(thm),theory(equality)],[c_3531]) ).
tff(c_4020,plain,
'#skF_2'('#skF_7','#skE_4','#skF_9') = '#skE_3',
inference(demodulation,[status(thm),theory(equality)],[c_3956,c_3594]) ).
tff(c_4036,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_4020,c_74]) ).
tff(c_4378,plain,
~ model_max('#skF_7','#skE_4','#skF_9'),
inference(splitLeft,[status(thm)],[c_4036]) ).
tff(c_4381,plain,
$less('#skF_9',max('#skF_7','#skE_4')),
inference(resolution,[status(thm)],[c_81,c_4378]) ).
tff(c_4386,plain,
$less('#skF_9','#skE_4'),
inference(demodulation,[status(thm),theory(equality)],[c_4045,c_4381]) ).
tff(c_4388,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_3895,c_4386]) ).
tff(c_4392,plain,
( minsol_model_max('#skF_7','#skE_4','#skF_9')
| model_max('#skF_7','#skE_4','#skE_3') ),
inference(splitRight,[status(thm)],[c_4036]) ).
tff(c_4401,plain,
model_max('#skF_7','#skE_4','#skE_3'),
inference(splitLeft,[status(thm)],[c_4392]) ).
tff(c_4410,plain,
~ $less('#skE_3',max('#skF_7','#skE_4')),
inference(resolution,[status(thm)],[c_4401,c_82]) ).
tff(c_4419,plain,
~ $less('#skE_3','#skE_4'),
inference(demodulation,[status(thm),theory(equality)],[c_4045,c_4410]) ).
tff(c_3451,plain,
minsol_model_ub('#skF_7','#skF_8','#skF_9'),
inference(splitRight,[status(thm)],[c_61]) ).
tff(c_4008,plain,
minsol_model_ub('#skF_7','#skE_4','#skF_9'),
inference(demodulation,[status(thm),theory(equality)],[c_3956,c_3451]) ).
tff(c_4216,plain,
! [Z_1991a: $int,N_1994a: $int,N_1992a: $int,Y_1993a: $int,X_1995a: $int] :
( ~ minsol_model_ub(X_1995a,Y_1993a,N_1994a)
| ~ $less(N_1992a,N_1994a)
| $less(N_1992a,Z_1991a)
| $less(Z_1991a,X_1995a)
| $less(Z_1991a,Y_1993a) ),
inference(resolution,[status(thm)],[c_211,c_73]) ).
tff(c_4221,plain,
! [N_1992a: $int,Z_1991a: $int] :
( ~ $less(N_1992a,'#skF_9')
| $less(N_1992a,Z_1991a)
| $less(Z_1991a,'#skF_7')
| $less(Z_1991a,'#skE_4') ),
inference(resolution,[status(thm)],[c_4008,c_4216]) ).
tff(c_4228,plain,
( $lesseq('#skF_9','#skF_7')
| $lesseq('#skF_9','#skE_4') ),
inference(quantifierElimination,[status(thm),theory('LIA')],[c_4221]) ).
tff(c_4230,plain,
( ~ $less('#skF_7','#skF_9')
| ~ $less('#skE_4','#skF_9') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_4228]) ).
tff(c_3957,plain,
~ $less('#skF_8','#skF_7'),
inference(splitRight,[status(thm)],[c_3928]) ).
tff(c_4013,plain,
~ $less('#skE_4','#skF_7'),
inference(demodulation,[status(thm),theory(equality)],[c_3956,c_3957]) ).
tff(c_3894,plain,
$less('#skE_3','#skF_9'),
inference(splitRight,[status(thm)],[c_3598]) ).
tff(c_4422,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_4419,c_4230,c_4013,c_3894]) ).
tff(c_4428,plain,
minsol_model_max('#skF_7','#skE_4','#skF_9'),
inference(splitRight,[status(thm)],[c_4392]) ).
tff(c_4011,plain,
~ minsol_model_max('#skF_7','#skE_4','#skF_9'),
inference(demodulation,[status(thm),theory(equality)],[c_3956,c_143]) ).
tff(c_4431,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_4428,c_4011]) ).
tff(c_4434,plain,
'#skF_7' = '#skE_4',
inference(splitRight,[status(thm)],[c_3919]) ).
tff(c_4536,plain,
max('#skE_4','#skF_8') = '#skE_4',
inference(demodulation,[status(thm),theory(equality)],[c_4434,c_3597]) ).
tff(c_4495,plain,
'#skF_2'('#skE_4','#skF_8','#skF_9') = '#skE_3',
inference(demodulation,[status(thm),theory(equality)],[c_4434,c_3594]) ).
tff(c_4511,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_4495,c_74]) ).
tff(c_4719,plain,
~ model_max('#skE_4','#skF_8','#skF_9'),
inference(splitLeft,[status(thm)],[c_4511]) ).
tff(c_4722,plain,
$less('#skF_9',max('#skE_4','#skF_8')),
inference(resolution,[status(thm)],[c_81,c_4719]) ).
tff(c_4727,plain,
$less('#skF_9','#skE_4'),
inference(demodulation,[status(thm),theory(equality)],[c_4536,c_4722]) ).
tff(c_4729,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_3895,c_4727]) ).
tff(c_4733,plain,
( minsol_model_max('#skE_4','#skF_8','#skF_9')
| model_max('#skE_4','#skF_8','#skE_3') ),
inference(splitRight,[status(thm)],[c_4511]) ).
tff(c_4833,plain,
model_max('#skE_4','#skF_8','#skE_3'),
inference(splitLeft,[status(thm)],[c_4733]) ).
tff(c_4842,plain,
~ $less('#skE_3',max('#skE_4','#skF_8')),
inference(resolution,[status(thm)],[c_4833,c_82]) ).
tff(c_4851,plain,
~ $less('#skE_3','#skE_4'),
inference(demodulation,[status(thm),theory(equality)],[c_4536,c_4842]) ).
tff(c_4483,plain,
minsol_model_ub('#skE_4','#skF_8','#skF_9'),
inference(demodulation,[status(thm),theory(equality)],[c_4434,c_3451]) ).
tff(c_4693,plain,
! [N_2196a: $int,Z_2193a: $int,X_2197a: $int,N_2194a: $int,Y_2195a: $int] :
( ~ minsol_model_ub(X_2197a,Y_2195a,N_2196a)
| ~ $less(N_2194a,N_2196a)
| $less(N_2194a,Z_2193a)
| $less(Z_2193a,X_2197a)
| $less(Z_2193a,Y_2195a) ),
inference(resolution,[status(thm)],[c_211,c_73]) ).
tff(c_4698,plain,
! [N_2194a: $int,Z_2193a: $int] :
( ~ $less(N_2194a,'#skF_9')
| $less(N_2194a,Z_2193a)
| $less(Z_2193a,'#skE_4')
| $less(Z_2193a,'#skF_8') ),
inference(resolution,[status(thm)],[c_4483,c_4693]) ).
tff(c_4702,plain,
( $lesseq('#skF_9','#skE_4')
| $lesseq('#skF_9','#skF_8') ),
inference(quantifierElimination,[status(thm),theory('LIA')],[c_4698]) ).
tff(c_4704,plain,
( ~ $less('#skE_4','#skF_9')
| ~ $less('#skF_8','#skF_9') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_4702]) ).
tff(c_4435,plain,
~ $less('#skF_7','#skF_8'),
inference(splitRight,[status(thm)],[c_3919]) ).
tff(c_4488,plain,
~ $less('#skE_4','#skF_8'),
inference(demodulation,[status(thm),theory(equality)],[c_4434,c_4435]) ).
tff(c_4852,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_4851,c_4704,c_4488,c_3894]) ).
tff(c_4858,plain,
minsol_model_max('#skE_4','#skF_8','#skF_9'),
inference(splitRight,[status(thm)],[c_4733]) ).
tff(c_4486,plain,
~ minsol_model_max('#skE_4','#skF_8','#skF_9'),
inference(demodulation,[status(thm),theory(equality)],[c_4434,c_143]) ).
tff(c_4861,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_4858,c_4486]) ).
tff(c_8462,plain,
minsol_model_max('#skF_4','#skF_5','#skF_6'),
inference(splitRight,[status(thm)],[c_65]) ).
tff(c_8446,plain,
! [N_3870a: $int,X_3871a: $int,Y_3872a: $int] :
( ~ $less(N_3870a,max(X_3871a,Y_3872a))
| ~ model_max(X_3871a,Y_3872a,N_3870a) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_16]) ).
tff(c_8451,plain,
! [N_21a: $int,X_19a: $int,Y_20a: $int] :
( ~ $less(N_21a,max(X_19a,Y_20a))
| ~ minsol_model_max(X_19a,Y_20a,N_21a) ),
inference(resolution,[status(thm)],[c_76,c_8446]) ).
tff(c_8468,plain,
~ $less('#skF_6',max('#skF_4','#skF_5')),
inference(resolution,[status(thm)],[c_8462,c_8451]) ).
tff(c_8553,plain,
max('#skF_4','#skF_5') = '#skE_5',
inference(define,[status(thm),theory(equality)],[c_8468]) ).
tff(c_8585,plain,
( ( '#skF_5' = '#skE_5' )
| $less('#skF_5','#skF_4') ),
inference(superposition,[status(thm),theory(equality)],[c_86,c_8553]) ).
tff(c_8589,plain,
$less('#skF_5','#skF_4'),
inference(splitLeft,[status(thm)],[c_8585]) ).
tff(c_8576,plain,
( ( '#skF_4' = '#skE_5' )
| $less('#skF_4','#skF_5') ),
inference(superposition,[status(thm),theory(equality)],[c_8553,c_87]) ).
tff(c_8587,plain,
$less('#skF_4','#skF_5'),
inference(splitLeft,[status(thm)],[c_8576]) ).
tff(c_8601,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_8589,c_8587]) ).
tff(c_8604,plain,
'#skF_5' = '#skE_5',
inference(splitRight,[status(thm)],[c_8585]) ).
tff(c_6725,plain,
! [X_3032a: $int,Y_3033a: $int,N_3034a: $int] :
( $less('#skF_2'(X_3032a,Y_3033a,N_3034a),N_3034a)
| minsol_model_max(X_3032a,Y_3033a,N_3034a)
| ~ model_max(X_3032a,Y_3033a,N_3034a) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_33]) ).
tff(c_6983,plain,
! [X_3125a: $int,Y_3126a: $int,N_3127a: $int] :
( $less('#skF_2'(X_3125a,Y_3126a,N_3127a),N_3127a)
| minsol_model_max(X_3125a,Y_3126a,N_3127a)
| $less(N_3127a,max(X_3125a,Y_3126a)) ),
inference(resolution,[status(thm)],[c_81,c_6725]) ).
tff(c_69,plain,
( ~ minsol_model_ub('#skF_4','#skF_5','#skF_6')
| ~ minsol_model_max('#skF_7','#skF_8','#skF_9') ),
inference(cnfTransformation,[status(thm)],[f_95]) ).
tff(c_4869,plain,
~ minsol_model_max('#skF_7','#skF_8','#skF_9'),
inference(splitLeft,[status(thm)],[c_69]) ).
tff(c_7007,plain,
( $less('#skF_2'('#skF_7','#skF_8','#skF_9'),'#skF_9')
| $less('#skF_9',max('#skF_7','#skF_8')) ),
inference(resolution,[status(thm)],[c_6983,c_4869]) ).
tff(c_7495,plain,
max('#skF_7','#skF_8') = '#skE_4',
inference(define,[status(thm),theory(equality)],[c_7007]) ).
tff(c_7546,plain,
( ( '#skF_8' = '#skE_4' )
| $less('#skF_8','#skF_7') ),
inference(superposition,[status(thm),theory(equality)],[c_7495,c_86]) ).
tff(c_7559,plain,
$less('#skF_8','#skF_7'),
inference(splitLeft,[status(thm)],[c_7546]) ).
tff(c_7544,plain,
( ( '#skF_7' = '#skE_4' )
| $less('#skF_7','#skF_8') ),
inference(superposition,[status(thm),theory(equality)],[c_7495,c_87]) ).
tff(c_7557,plain,
$less('#skF_7','#skF_8'),
inference(splitLeft,[status(thm)],[c_7544]) ).
tff(c_7560,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_7559,c_7557]) ).
tff(c_7563,plain,
'#skF_8' = '#skE_4',
inference(splitRight,[status(thm)],[c_7546]) ).
tff(c_7141,plain,
max('#skF_7','#skF_8') = '#skE_4',
inference(define,[status(thm),theory(equality)],[c_7007]) ).
tff(c_7715,plain,
max('#skF_7','#skE_4') = '#skE_4',
inference(demodulation,[status(thm),theory(equality)],[c_7563,c_7141]) ).
tff(c_7147,plain,
max('#skF_7','#skF_8') = '#skE_4',
inference(define,[status(thm),theory(equality)],[c_7007]) ).
tff(c_7198,plain,
( ( '#skF_8' = '#skE_4' )
| $less('#skF_8','#skF_7') ),
inference(superposition,[status(thm),theory(equality)],[c_7147,c_86]) ).
tff(c_7238,plain,
$less('#skF_8','#skF_7'),
inference(splitLeft,[status(thm)],[c_7198]) ).
tff(c_7196,plain,
( ( '#skF_7' = '#skE_4' )
| $less('#skF_7','#skF_8') ),
inference(superposition,[status(thm),theory(equality)],[c_7147,c_87]) ).
tff(c_7209,plain,
$less('#skF_7','#skF_8'),
inference(splitLeft,[status(thm)],[c_7196]) ).
tff(c_7239,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_7238,c_7209]) ).
tff(c_7242,plain,
'#skF_8' = '#skE_4',
inference(splitRight,[status(thm)],[c_7198]) ).
tff(c_4935,plain,
! [X_2296a: $int,Y_2297a: $int,N_2298a: $int,Z_2299a: $int] :
( model_ub(X_2296a,Y_2297a,N_2298a)
| ~ ub(X_2296a,Y_2297a,Z_2299a)
| $less(N_2298a,Z_2299a) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_21]) ).
tff(c_4940,plain,
! [X_7a: $int,Y_8a: $int,N_2298a: $int,Z_9a: $int] :
( model_ub(X_7a,Y_8a,N_2298a)
| $less(N_2298a,Z_9a)
| $less(Z_9a,X_7a)
| $less(Z_9a,Y_8a) ),
inference(resolution,[status(thm)],[c_83,c_4935]) ).
tff(c_6001,plain,
! [X_2735a: $int,Y_2736a: $int,N_2737a: $int] :
( $less('#skF_3'(X_2735a,Y_2736a,N_2737a),N_2737a)
| minsol_model_ub(X_2735a,Y_2736a,N_2737a)
| ~ model_ub(X_2735a,Y_2736a,N_2737a) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_42]) ).
tff(c_6114,plain,
! [X_2788a: $int,Y_2789a: $int,N_2790a: $int,Z_2791a: $int] :
( $less('#skF_3'(X_2788a,Y_2789a,N_2790a),N_2790a)
| minsol_model_ub(X_2788a,Y_2789a,N_2790a)
| $less(N_2790a,Z_2791a)
| $less(Z_2791a,X_2788a)
| $less(Z_2791a,Y_2789a) ),
inference(resolution,[status(thm)],[c_4940,c_6001]) ).
tff(c_5144,plain,
! [X_2380a: $int,Y_2381a: $int,N_2382a: $int,Z_2383a: $int] :
( model_ub(X_2380a,Y_2381a,N_2382a)
| $less(N_2382a,Z_2383a)
| $less(Z_2383a,X_2380a)
| $less(Z_2383a,Y_2381a) ),
inference(resolution,[status(thm)],[c_83,c_4935]) ).
tff(c_5572,plain,
! [X_2567a: $int,Y_2568a: $int,N_2569a: $int,Z_2570a: $int] :
( $less('#skF_3'(X_2567a,Y_2568a,N_2569a),N_2569a)
| minsol_model_ub(X_2567a,Y_2568a,N_2569a)
| $less(N_2569a,Z_2570a)
| $less(Z_2570a,X_2567a)
| $less(Z_2570a,Y_2568a) ),
inference(resolution,[status(thm)],[c_5144,c_71]) ).
tff(c_4902,plain,
minsol_model_max('#skF_4','#skF_5','#skF_6'),
inference(splitRight,[status(thm)],[c_65]) ).
tff(c_4870,plain,
! [N_2262a: $int,X_2263a: $int,Y_2264a: $int] :
( ~ $less(N_2262a,max(X_2263a,Y_2264a))
| ~ model_max(X_2263a,Y_2264a,N_2262a) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_16]) ).
tff(c_4875,plain,
! [N_21a: $int,X_19a: $int,Y_20a: $int] :
( ~ $less(N_21a,max(X_19a,Y_20a))
| ~ minsol_model_max(X_19a,Y_20a,N_21a) ),
inference(resolution,[status(thm)],[c_76,c_4870]) ).
tff(c_4908,plain,
~ $less('#skF_6',max('#skF_4','#skF_5')),
inference(resolution,[status(thm)],[c_4902,c_4875]) ).
tff(c_4971,plain,
max('#skF_4','#skF_5') = '#skE_5',
inference(define,[status(thm),theory(equality)],[c_4908]) ).
tff(c_4996,plain,
( ( '#skF_5' = '#skE_5' )
| $less('#skF_5','#skF_4') ),
inference(superposition,[status(thm),theory(equality)],[c_4971,c_86]) ).
tff(c_5012,plain,
$less('#skF_5','#skF_4'),
inference(splitLeft,[status(thm)],[c_4996]) ).
tff(c_4994,plain,
( ( '#skF_4' = '#skE_5' )
| $less('#skF_4','#skF_5') ),
inference(superposition,[status(thm),theory(equality)],[c_4971,c_87]) ).
tff(c_5005,plain,
$less('#skF_4','#skF_5'),
inference(splitLeft,[status(thm)],[c_4994]) ).
tff(c_5013,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_5012,c_5005]) ).
tff(c_5016,plain,
'#skF_5' = '#skE_5',
inference(splitRight,[status(thm)],[c_4996]) ).
tff(c_4968,plain,
~ minsol_model_ub('#skF_4','#skF_5','#skF_6'),
inference(splitLeft,[status(thm)],[c_61]) ).
tff(c_5037,plain,
~ minsol_model_ub('#skF_4','#skE_5','#skF_6'),
inference(demodulation,[status(thm),theory(equality)],[c_5016,c_4968]) ).
tff(c_5588,plain,
! [Z_2570a: $int] :
( $less('#skF_3'('#skF_4','#skE_5','#skF_6'),'#skF_6')
| $less('#skF_6',Z_2570a)
| $less(Z_2570a,'#skF_4')
| $less(Z_2570a,'#skE_5') ),
inference(resolution,[status(thm)],[c_5572,c_5037]) ).
tff(c_5646,plain,
'#skF_3'('#skF_4','#skE_5','#skF_6') = '#skE_6',
inference(define,[status(thm),theory(equality)],[c_5588]) ).
tff(c_5662,plain,
( model_ub('#skF_4','#skE_5','#skE_6')
| minsol_model_ub('#skF_4','#skE_5','#skF_6')
| ~ model_ub('#skF_4','#skE_5','#skF_6') ),
inference(superposition,[status(thm),theory(equality)],[c_5646,c_70]) ).
tff(c_5722,plain,
~ model_ub('#skF_4','#skE_5','#skF_6'),
inference(splitLeft,[status(thm)],[c_5662]) ).
tff(c_5730,plain,
! [Z_9a: $int] :
( $less('#skF_6',Z_9a)
| $less(Z_9a,'#skF_4')
| $less(Z_9a,'#skE_5') ),
inference(resolution,[status(thm)],[c_4940,c_5722]) ).
tff(c_5732,plain,
( $lesseq($sum(1,'#skF_6'),'#skF_4')
| $lesseq($sum(1,'#skF_6'),'#skE_5') ),
inference(quantifierElimination,[status(thm),theory('LIA')],[c_5730]) ).
tff(c_5734,plain,
( ~ $less('#skF_4',$sum(1,'#skF_6'))
| ~ $less('#skE_5',$sum(1,'#skF_6')) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_5732]) ).
tff(c_5017,plain,
~ $less('#skF_5','#skF_4'),
inference(splitRight,[status(thm)],[c_4996]) ).
tff(c_5065,plain,
~ $less('#skE_5','#skF_4'),
inference(demodulation,[status(thm),theory(equality)],[c_5016,c_5017]) ).
tff(c_4957,plain,
max('#skF_4','#skF_5') = '#skE_5',
inference(define,[status(thm),theory(equality)],[c_4908]) ).
tff(c_4956,plain,
~ $less('#skF_6',max('#skF_4','#skF_5')),
inference(resolution,[status(thm)],[c_4902,c_4875]) ).
tff(c_4964,plain,
~ $less('#skF_6','#skE_5'),
inference(demodulation,[status(thm),theory(equality)],[c_4957,c_4956]) ).
tff(c_5735,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_5734,c_5065,c_4964]) ).
tff(c_5739,plain,
( minsol_model_ub('#skF_4','#skE_5','#skF_6')
| model_ub('#skF_4','#skE_5','#skE_6') ),
inference(splitRight,[status(thm)],[c_5662]) ).
tff(c_5749,plain,
model_ub('#skF_4','#skE_5','#skE_6'),
inference(splitLeft,[status(thm)],[c_5739]) ).
tff(c_5750,plain,
model_ub('#skF_4','#skE_5','#skE_6'),
inference(splitLeft,[status(thm)],[c_5739]) ).
tff(c_5768,plain,
~ $less('#skE_6','#skF_1'('#skF_4','#skE_5','#skE_6')),
inference(resolution,[status(thm)],[c_5750,c_79]) ).
tff(c_5790,plain,
'#skF_1'('#skF_4','#skE_5','#skE_6') = '#skE_7',
inference(define,[status(thm),theory(equality)],[c_5768]) ).
tff(c_5800,plain,
( ub('#skF_4','#skE_5','#skE_7')
| ~ model_ub('#skF_4','#skE_5','#skE_6') ),
inference(superposition,[status(thm),theory(equality)],[c_5790,c_78]) ).
tff(c_5821,plain,
ub('#skF_4','#skE_5','#skE_7'),
inference(demodulation,[status(thm),theory(equality)],[c_5749,c_5800]) ).
tff(c_5835,plain,
~ $less('#skE_7','#skE_5'),
inference(resolution,[status(thm)],[c_5821,c_85]) ).
tff(c_5780,plain,
'#skF_1'('#skF_4','#skE_5','#skE_6') = '#skE_7',
inference(define,[status(thm),theory(equality)],[c_5768]) ).
tff(c_5779,plain,
~ $less('#skE_6','#skF_1'('#skF_4','#skE_5','#skE_6')),
inference(resolution,[status(thm)],[c_5750,c_79]) ).
tff(c_5787,plain,
~ $less('#skE_6','#skE_7'),
inference(demodulation,[status(thm),theory(equality)],[c_5780,c_5779]) ).
tff(c_5636,plain,
'#skF_3'('#skF_4','#skE_5','#skF_6') = '#skE_6',
inference(define,[status(thm),theory(equality)],[c_5588]) ).
tff(c_5635,plain,
! [Z_2570a: $int] :
( $less('#skF_3'('#skF_4','#skE_5','#skF_6'),'#skF_6')
| $less('#skF_6',Z_2570a)
| $less(Z_2570a,'#skF_4')
| $less(Z_2570a,'#skE_5') ),
inference(resolution,[status(thm)],[c_5572,c_5037]) ).
tff(c_5643,plain,
! [Z_2570a: $int] :
( $less('#skE_6','#skF_6')
| $less('#skF_6',Z_2570a)
| $less(Z_2570a,'#skF_4')
| $less(Z_2570a,'#skE_5') ),
inference(demodulation,[status(thm),theory(equality)],[c_5636,c_5635]) ).
tff(c_5667,plain,
$less('#skE_6','#skF_6'),
inference(splitLeft,[status(thm)],[c_5643]) ).
tff(c_4963,plain,
max('#skF_4','#skF_5') = '#skE_5',
inference(define,[status(thm),theory(equality)],[c_4908]) ).
tff(c_5069,plain,
max('#skF_4','#skE_5') = '#skE_5',
inference(demodulation,[status(thm),theory(equality)],[c_5016,c_4963]) ).
tff(c_4865,plain,
minsol_model_max('#skF_4','#skF_5','#skF_6'),
inference(splitRight,[status(thm)],[c_65]) ).
tff(c_5044,plain,
minsol_model_max('#skF_4','#skE_5','#skF_6'),
inference(demodulation,[status(thm),theory(equality)],[c_5016,c_4865]) ).
tff(c_4924,plain,
! [X_2292a: $int,Y_2293a: $int,Z_2294a: $int,N_2295a: $int] :
( ~ model_max(X_2292a,Y_2293a,Z_2294a)
| ~ minsol_model_max(X_2292a,Y_2293a,N_2295a)
| ~ $less(Z_2294a,N_2295a) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_28]) ).
tff(c_5134,plain,
! [X_2376a: $int,Y_2377a: $int,N_2378a: $int,N_2379a: $int] :
( ~ minsol_model_max(X_2376a,Y_2377a,N_2378a)
| ~ $less(N_2379a,N_2378a)
| $less(N_2379a,max(X_2376a,Y_2377a)) ),
inference(resolution,[status(thm)],[c_81,c_4924]) ).
tff(c_5137,plain,
! [N_2379a: $int] :
( ~ $less(N_2379a,'#skF_6')
| $less(N_2379a,max('#skF_4','#skE_5')) ),
inference(resolution,[status(thm)],[c_5044,c_5134]) ).
tff(c_5140,plain,
! [N_2379a: $int] :
( ~ $less(N_2379a,'#skF_6')
| $less(N_2379a,'#skE_5') ),
inference(demodulation,[status(thm),theory(equality)],[c_5069,c_5137]) ).
tff(c_5141,plain,
$lesseq('#skF_6','#skE_5'),
inference(quantifierElimination,[status(thm),theory('LIA')],[c_5140]) ).
tff(c_5143,plain,
~ $less('#skE_5','#skF_6'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_5141]) ).
tff(c_5838,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_5835,c_5787,c_5667,c_5143]) ).
tff(c_5844,plain,
minsol_model_ub('#skF_4','#skE_5','#skF_6'),
inference(splitRight,[status(thm)],[c_5739]) ).
tff(c_5847,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_5844,c_5037]) ).
tff(c_5850,plain,
! [Z_2570a: $int] :
( $less('#skF_6',Z_2570a)
| $less(Z_2570a,'#skF_4')
| $less(Z_2570a,'#skE_5') ),
inference(splitRight,[status(thm)],[c_5643]) ).
tff(c_5852,plain,
( $lesseq($sum(1,'#skF_6'),'#skF_4')
| $lesseq($sum(1,'#skF_6'),'#skE_5') ),
inference(quantifierElimination,[status(thm),theory('LIA')],[c_5850]) ).
tff(c_5854,plain,
( ~ $less('#skF_4',$sum(1,'#skF_6'))
| ~ $less('#skE_5',$sum(1,'#skF_6')) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_5852]) ).
tff(c_5855,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_5854,c_5065,c_4964]) ).
tff(c_5858,plain,
'#skF_4' = '#skE_5',
inference(splitRight,[status(thm)],[c_4994]) ).
tff(c_5891,plain,
~ minsol_model_ub('#skE_5','#skF_5','#skF_6'),
inference(demodulation,[status(thm),theory(equality)],[c_5858,c_4968]) ).
tff(c_6130,plain,
! [Z_2791a: $int] :
( $less('#skF_3'('#skE_5','#skF_5','#skF_6'),'#skF_6')
| $less('#skF_6',Z_2791a)
| $less(Z_2791a,'#skE_5')
| $less(Z_2791a,'#skF_5') ),
inference(resolution,[status(thm)],[c_6114,c_5891]) ).
tff(c_6305,plain,
'#skF_3'('#skE_5','#skF_5','#skF_6') = '#skE_8',
inference(define,[status(thm),theory(equality)],[c_6130]) ).
tff(c_6321,plain,
( model_ub('#skE_5','#skF_5','#skE_8')
| minsol_model_ub('#skE_5','#skF_5','#skF_6')
| ~ model_ub('#skE_5','#skF_5','#skF_6') ),
inference(superposition,[status(thm),theory(equality)],[c_6305,c_70]) ).
tff(c_6497,plain,
~ model_ub('#skE_5','#skF_5','#skF_6'),
inference(splitLeft,[status(thm)],[c_6321]) ).
tff(c_6505,plain,
! [Z_9a: $int] :
( $less('#skF_6',Z_9a)
| $less(Z_9a,'#skE_5')
| $less(Z_9a,'#skF_5') ),
inference(resolution,[status(thm)],[c_4940,c_6497]) ).
tff(c_6507,plain,
( $lesseq($sum(1,'#skF_6'),'#skE_5')
| $lesseq($sum(1,'#skF_6'),'#skF_5') ),
inference(quantifierElimination,[status(thm),theory('LIA')],[c_6505]) ).
tff(c_6509,plain,
( ~ $less('#skE_5',$sum(1,'#skF_6'))
| ~ $less('#skF_5',$sum(1,'#skF_6')) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_6507]) ).
tff(c_5859,plain,
~ $less('#skF_4','#skF_5'),
inference(splitRight,[status(thm)],[c_4994]) ).
tff(c_5880,plain,
~ $less('#skE_5','#skF_5'),
inference(demodulation,[status(thm),theory(equality)],[c_5858,c_5859]) ).
tff(c_6510,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_6509,c_5880,c_4964]) ).
tff(c_6514,plain,
( minsol_model_ub('#skE_5','#skF_5','#skF_6')
| model_ub('#skE_5','#skF_5','#skE_8') ),
inference(splitRight,[status(thm)],[c_6321]) ).
tff(c_6523,plain,
model_ub('#skE_5','#skF_5','#skE_8'),
inference(splitLeft,[status(thm)],[c_6514]) ).
tff(c_6524,plain,
model_ub('#skE_5','#skF_5','#skE_8'),
inference(splitLeft,[status(thm)],[c_6514]) ).
tff(c_6542,plain,
~ $less('#skE_8','#skF_1'('#skE_5','#skF_5','#skE_8')),
inference(resolution,[status(thm)],[c_6524,c_79]) ).
tff(c_6564,plain,
'#skF_1'('#skE_5','#skF_5','#skE_8') = '#skE_9',
inference(define,[status(thm),theory(equality)],[c_6542]) ).
tff(c_6574,plain,
( ub('#skE_5','#skF_5','#skE_9')
| ~ model_ub('#skE_5','#skF_5','#skE_8') ),
inference(superposition,[status(thm),theory(equality)],[c_6564,c_78]) ).
tff(c_6595,plain,
ub('#skE_5','#skF_5','#skE_9'),
inference(demodulation,[status(thm),theory(equality)],[c_6523,c_6574]) ).
tff(c_6611,plain,
~ $less('#skE_9','#skE_5'),
inference(resolution,[status(thm)],[c_6595,c_84]) ).
tff(c_6554,plain,
'#skF_1'('#skE_5','#skF_5','#skE_8') = '#skE_9',
inference(define,[status(thm),theory(equality)],[c_6542]) ).
tff(c_6553,plain,
~ $less('#skE_8','#skF_1'('#skE_5','#skF_5','#skE_8')),
inference(resolution,[status(thm)],[c_6524,c_79]) ).
tff(c_6561,plain,
~ $less('#skE_8','#skE_9'),
inference(demodulation,[status(thm),theory(equality)],[c_6554,c_6553]) ).
tff(c_6263,plain,
'#skF_3'('#skE_5','#skF_5','#skF_6') = '#skE_8',
inference(define,[status(thm),theory(equality)],[c_6130]) ).
tff(c_6262,plain,
! [Z_2791a: $int] :
( $less('#skF_3'('#skE_5','#skF_5','#skF_6'),'#skF_6')
| $less('#skF_6',Z_2791a)
| $less(Z_2791a,'#skE_5')
| $less(Z_2791a,'#skF_5') ),
inference(resolution,[status(thm)],[c_6114,c_5891]) ).
tff(c_6270,plain,
! [Z_2791a: $int] :
( $less('#skE_8','#skF_6')
| $less('#skF_6',Z_2791a)
| $less(Z_2791a,'#skE_5')
| $less(Z_2791a,'#skF_5') ),
inference(demodulation,[status(thm),theory(equality)],[c_6263,c_6262]) ).
tff(c_6442,plain,
$less('#skE_8','#skF_6'),
inference(splitLeft,[status(thm)],[c_6270]) ).
tff(c_5898,plain,
max('#skE_5','#skF_5') = '#skE_5',
inference(demodulation,[status(thm),theory(equality)],[c_5858,c_4963]) ).
tff(c_5878,plain,
minsol_model_max('#skE_5','#skF_5','#skF_6'),
inference(demodulation,[status(thm),theory(equality)],[c_5858,c_4865]) ).
tff(c_5969,plain,
! [X_2724a: $int,Y_2725a: $int,N_2726a: $int,N_2727a: $int] :
( ~ minsol_model_max(X_2724a,Y_2725a,N_2726a)
| ~ $less(N_2727a,N_2726a)
| $less(N_2727a,max(X_2724a,Y_2725a)) ),
inference(resolution,[status(thm)],[c_81,c_4924]) ).
tff(c_5972,plain,
! [N_2727a: $int] :
( ~ $less(N_2727a,'#skF_6')
| $less(N_2727a,max('#skE_5','#skF_5')) ),
inference(resolution,[status(thm)],[c_5878,c_5969]) ).
tff(c_5975,plain,
! [N_2727a: $int] :
( ~ $less(N_2727a,'#skF_6')
| $less(N_2727a,'#skE_5') ),
inference(demodulation,[status(thm),theory(equality)],[c_5898,c_5972]) ).
tff(c_5976,plain,
$lesseq('#skF_6','#skE_5'),
inference(quantifierElimination,[status(thm),theory('LIA')],[c_5975]) ).
tff(c_5978,plain,
~ $less('#skE_5','#skF_6'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_5976]) ).
tff(c_6612,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_6611,c_6561,c_6442,c_5978]) ).
tff(c_6618,plain,
minsol_model_ub('#skE_5','#skF_5','#skF_6'),
inference(splitRight,[status(thm)],[c_6514]) ).
tff(c_6621,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_6618,c_5891]) ).
tff(c_6624,plain,
! [Z_2791a: $int] :
( $less('#skF_6',Z_2791a)
| $less(Z_2791a,'#skE_5')
| $less(Z_2791a,'#skF_5') ),
inference(splitRight,[status(thm)],[c_6270]) ).
tff(c_6627,plain,
( $lesseq($sum(1,'#skF_6'),'#skE_5')
| $lesseq($sum(1,'#skF_6'),'#skF_5') ),
inference(quantifierElimination,[status(thm),theory('LIA')],[c_6624]) ).
tff(c_6629,plain,
( ~ $less('#skE_5',$sum(1,'#skF_6'))
| ~ $less('#skF_5',$sum(1,'#skF_6')) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_6627]) ).
tff(c_6630,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_6629,c_5880,c_4964]) ).
tff(c_6671,plain,
minsol_model_ub('#skF_7','#skF_8','#skF_9'),
inference(splitRight,[status(thm)],[c_61]) ).
tff(c_6672,plain,
minsol_model_ub('#skF_7','#skF_8','#skF_9'),
inference(splitRight,[status(thm)],[c_61]) ).
tff(c_4883,plain,
! [N_2271a: $int,X_2272a: $int,Y_2273a: $int] :
( ~ $less(N_2271a,'#skF_1'(X_2272a,Y_2273a,N_2271a))
| ~ model_ub(X_2272a,Y_2273a,N_2271a) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_24]) ).
tff(c_4888,plain,
! [N_27a: $int,X_25a: $int,Y_26a: $int] :
( ~ $less(N_27a,'#skF_1'(X_25a,Y_26a,N_27a))
| ~ minsol_model_ub(X_25a,Y_26a,N_27a) ),
inference(resolution,[status(thm)],[c_72,c_4883]) ).
tff(c_6683,plain,
~ $less('#skF_9','#skF_1'('#skF_7','#skF_8','#skF_9')),
inference(resolution,[status(thm)],[c_6672,c_4888]) ).
tff(c_6853,plain,
'#skF_1'('#skF_7','#skF_8','#skF_9') = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_6683]) ).
tff(c_6869,plain,
( ub('#skF_7','#skF_8','#skE_1')
| ~ model_ub('#skF_7','#skF_8','#skF_9') ),
inference(superposition,[status(thm),theory(equality)],[c_6853,c_78]) ).
tff(c_6881,plain,
~ model_ub('#skF_7','#skF_8','#skF_9'),
inference(splitLeft,[status(thm)],[c_6869]) ).
tff(c_6887,plain,
~ minsol_model_ub('#skF_7','#skF_8','#skF_9'),
inference(resolution,[status(thm)],[c_72,c_6881]) ).
tff(c_6893,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_6671,c_6887]) ).
tff(c_6900,plain,
ub('#skF_7','#skF_8','#skE_1'),
inference(splitRight,[status(thm)],[c_6869]) ).
tff(c_6914,plain,
~ $less('#skE_1','#skF_8'),
inference(resolution,[status(thm)],[c_6900,c_85]) ).
tff(c_7325,plain,
~ $less('#skE_1','#skE_4'),
inference(demodulation,[status(thm),theory(equality)],[c_7242,c_6914]) ).
tff(c_7131,plain,
max('#skF_7','#skF_8') = '#skE_4',
inference(define,[status(thm),theory(equality)],[c_7007]) ).
tff(c_7130,plain,
'#skF_2'('#skF_7','#skF_8','#skF_9') = '#skE_3',
inference(define,[status(thm),theory(equality)],[c_7007]) ).
tff(c_7129,plain,
( $less('#skF_2'('#skF_7','#skF_8','#skF_9'),'#skF_9')
| $less('#skF_9',max('#skF_7','#skF_8')) ),
inference(resolution,[status(thm)],[c_6983,c_4869]) ).
tff(c_7142,plain,
( $less('#skE_3','#skF_9')
| $less('#skF_9','#skE_4') ),
inference(demodulation,[status(thm),theory(equality)],[c_7131,c_7130,c_7129]) ).
tff(c_7144,plain,
$less('#skF_9','#skE_4'),
inference(splitLeft,[status(thm)],[c_7142]) ).
tff(c_6843,plain,
'#skF_1'('#skF_7','#skF_8','#skF_9') = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_6683]) ).
tff(c_6842,plain,
~ $less('#skF_9','#skF_1'('#skF_7','#skF_8','#skF_9')),
inference(resolution,[status(thm)],[c_6672,c_4888]) ).
tff(c_6850,plain,
~ $less('#skF_9','#skE_1'),
inference(demodulation,[status(thm),theory(equality)],[c_6843,c_6842]) ).
tff(c_7362,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_7325,c_7144,c_6850]) ).
tff(c_7365,plain,
'#skF_7' = '#skE_4',
inference(splitRight,[status(thm)],[c_7196]) ).
tff(c_6916,plain,
~ $less('#skE_1','#skF_7'),
inference(resolution,[status(thm)],[c_6900,c_84]) ).
tff(c_7439,plain,
~ $less('#skE_1','#skE_4'),
inference(demodulation,[status(thm),theory(equality)],[c_7365,c_6916]) ).
tff(c_7490,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_7439,c_7144,c_6850]) ).
tff(c_7494,plain,
~ $less('#skF_9','#skE_4'),
inference(splitRight,[status(thm)],[c_7142]) ).
tff(c_7565,plain,
'#skF_2'('#skF_7','#skF_8','#skF_9') = '#skE_3',
inference(define,[status(thm),theory(equality)],[c_7007]) ).
tff(c_7586,plain,
( model_max('#skF_7','#skF_8','#skE_3')
| minsol_model_max('#skF_7','#skF_8','#skF_9')
| ~ model_max('#skF_7','#skF_8','#skF_9') ),
inference(superposition,[status(thm),theory(equality)],[c_7565,c_74]) ).
tff(c_7915,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(demodulation,[status(thm),theory(equality)],[c_7563,c_7563,c_7563,c_7586]) ).
tff(c_7923,plain,
~ model_max('#skF_7','#skE_4','#skF_9'),
inference(splitLeft,[status(thm)],[c_7915]) ).
tff(c_7926,plain,
$less('#skF_9',max('#skF_7','#skE_4')),
inference(resolution,[status(thm)],[c_81,c_7923]) ).
tff(c_7931,plain,
$less('#skF_9','#skE_4'),
inference(demodulation,[status(thm),theory(equality)],[c_7715,c_7926]) ).
tff(c_7933,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_7494,c_7931]) ).
tff(c_7937,plain,
( minsol_model_max('#skF_7','#skE_4','#skF_9')
| model_max('#skF_7','#skE_4','#skE_3') ),
inference(splitRight,[status(thm)],[c_7915]) ).
tff(c_7963,plain,
model_max('#skF_7','#skE_4','#skE_3'),
inference(splitLeft,[status(thm)],[c_7937]) ).
tff(c_7972,plain,
~ $less('#skE_3',max('#skF_7','#skE_4')),
inference(resolution,[status(thm)],[c_7963,c_82]) ).
tff(c_7981,plain,
~ $less('#skE_3','#skE_4'),
inference(demodulation,[status(thm),theory(equality)],[c_7715,c_7972]) ).
tff(c_6634,plain,
minsol_model_ub('#skF_7','#skF_8','#skF_9'),
inference(splitRight,[status(thm)],[c_61]) ).
tff(c_6818,plain,
! [X_3053a: $int,Y_3054a: $int,N_3055a: $int,Z_3056a: $int] :
( model_ub(X_3053a,Y_3054a,N_3055a)
| $less(N_3055a,Z_3056a)
| $less(Z_3056a,X_3053a)
| $less(Z_3056a,Y_3054a) ),
inference(resolution,[status(thm)],[c_83,c_4935]) ).
tff(c_7016,plain,
! [Y_3144a: $int,N_3141a: $int,N_3142a: $int,Z_3145a: $int,X_3143a: $int] :
( ~ minsol_model_ub(X_3143a,Y_3144a,N_3142a)
| ~ $less(N_3141a,N_3142a)
| $less(N_3141a,Z_3145a)
| $less(Z_3145a,X_3143a)
| $less(Z_3145a,Y_3144a) ),
inference(resolution,[status(thm)],[c_6818,c_73]) ).
tff(c_7027,plain,
! [N_3141a: $int,Z_3145a: $int] :
( ~ $less(N_3141a,'#skF_9')
| $less(N_3141a,Z_3145a)
| $less(Z_3145a,'#skF_7')
| $less(Z_3145a,'#skF_8') ),
inference(resolution,[status(thm)],[c_6634,c_7016]) ).
tff(c_7658,plain,
! [N_3141a: $int,Z_3145a: $int] :
( ~ $less(N_3141a,'#skF_9')
| $less(N_3141a,Z_3145a)
| $less(Z_3145a,'#skF_7')
| $less(Z_3145a,'#skE_4') ),
inference(demodulation,[status(thm),theory(equality)],[c_7563,c_7027]) ).
tff(c_7940,plain,
( $lesseq('#skF_9','#skF_7')
| $lesseq('#skF_9','#skE_4') ),
inference(quantifierElimination,[status(thm),theory('LIA')],[c_7658]) ).
tff(c_7942,plain,
( ~ $less('#skF_7','#skF_9')
| ~ $less('#skE_4','#skF_9') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_7940]) ).
tff(c_7564,plain,
~ $less('#skF_8','#skF_7'),
inference(splitRight,[status(thm)],[c_7546]) ).
tff(c_7688,plain,
~ $less('#skE_4','#skF_7'),
inference(demodulation,[status(thm),theory(equality)],[c_7563,c_7564]) ).
tff(c_7493,plain,
$less('#skE_3','#skF_9'),
inference(splitRight,[status(thm)],[c_7142]) ).
tff(c_7982,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_7981,c_7942,c_7688,c_7493]) ).
tff(c_7988,plain,
minsol_model_max('#skF_7','#skE_4','#skF_9'),
inference(splitRight,[status(thm)],[c_7937]) ).
tff(c_7686,plain,
~ minsol_model_max('#skF_7','#skE_4','#skF_9'),
inference(demodulation,[status(thm),theory(equality)],[c_7563,c_4869]) ).
tff(c_7991,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_7988,c_7686]) ).
tff(c_7994,plain,
'#skF_7' = '#skE_4',
inference(splitRight,[status(thm)],[c_7544]) ).
tff(c_8145,plain,
max('#skE_4','#skF_8') = '#skE_4',
inference(demodulation,[status(thm),theory(equality)],[c_7994,c_7141]) ).
tff(c_7996,plain,
'#skF_2'('#skF_7','#skF_8','#skF_9') = '#skE_3',
inference(define,[status(thm),theory(equality)],[c_7007]) ).
tff(c_8017,plain,
( model_max('#skF_7','#skF_8','#skE_3')
| minsol_model_max('#skF_7','#skF_8','#skF_9')
| ~ model_max('#skF_7','#skF_8','#skF_9') ),
inference(superposition,[status(thm),theory(equality)],[c_7996,c_74]) ).
tff(c_8348,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(demodulation,[status(thm),theory(equality)],[c_7994,c_7994,c_7994,c_8017]) ).
tff(c_8356,plain,
~ model_max('#skE_4','#skF_8','#skF_9'),
inference(splitLeft,[status(thm)],[c_8348]) ).
tff(c_8359,plain,
$less('#skF_9',max('#skE_4','#skF_8')),
inference(resolution,[status(thm)],[c_81,c_8356]) ).
tff(c_8364,plain,
$less('#skF_9','#skE_4'),
inference(demodulation,[status(thm),theory(equality)],[c_8145,c_8359]) ).
tff(c_8366,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_7494,c_8364]) ).
tff(c_8370,plain,
( minsol_model_max('#skE_4','#skF_8','#skF_9')
| model_max('#skE_4','#skF_8','#skE_3') ),
inference(splitRight,[status(thm)],[c_8348]) ).
tff(c_8409,plain,
model_max('#skE_4','#skF_8','#skE_3'),
inference(splitLeft,[status(thm)],[c_8370]) ).
tff(c_8418,plain,
~ $less('#skE_3',max('#skE_4','#skF_8')),
inference(resolution,[status(thm)],[c_8409,c_82]) ).
tff(c_8427,plain,
~ $less('#skE_3','#skE_4'),
inference(demodulation,[status(thm),theory(equality)],[c_8145,c_8418]) ).
tff(c_8088,plain,
! [N_3141a: $int,Z_3145a: $int] :
( ~ $less(N_3141a,'#skF_9')
| $less(N_3141a,Z_3145a)
| $less(Z_3145a,'#skE_4')
| $less(Z_3145a,'#skF_8') ),
inference(demodulation,[status(thm),theory(equality)],[c_7994,c_7027]) ).
tff(c_8371,plain,
( $lesseq('#skF_9','#skE_4')
| $lesseq('#skF_9','#skF_8') ),
inference(quantifierElimination,[status(thm),theory('LIA')],[c_8088]) ).
tff(c_8373,plain,
( ~ $less('#skE_4','#skF_9')
| ~ $less('#skF_8','#skF_9') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_8371]) ).
tff(c_7995,plain,
~ $less('#skF_7','#skF_8'),
inference(splitRight,[status(thm)],[c_7544]) ).
tff(c_8119,plain,
~ $less('#skE_4','#skF_8'),
inference(demodulation,[status(thm),theory(equality)],[c_7994,c_7995]) ).
tff(c_8428,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_8427,c_8373,c_8119,c_7493]) ).
tff(c_8434,plain,
minsol_model_max('#skE_4','#skF_8','#skF_9'),
inference(splitRight,[status(thm)],[c_8370]) ).
tff(c_8117,plain,
~ minsol_model_max('#skE_4','#skF_8','#skF_9'),
inference(demodulation,[status(thm),theory(equality)],[c_7994,c_4869]) ).
tff(c_8437,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_8434,c_8117]) ).
tff(c_8441,plain,
~ minsol_model_ub('#skF_4','#skF_5','#skF_6'),
inference(splitRight,[status(thm)],[c_69]) ).
tff(c_8632,plain,
~ minsol_model_ub('#skF_4','#skE_5','#skF_6'),
inference(demodulation,[status(thm),theory(equality)],[c_8604,c_8441]) ).
tff(c_9001,plain,
! [Z_4097a: $int] :
( $less('#skF_3'('#skF_4','#skE_5','#skF_6'),'#skF_6')
| $less('#skF_6',Z_4097a)
| $less(Z_4097a,'#skF_4')
| $less(Z_4097a,'#skE_5') ),
inference(resolution,[status(thm)],[c_8973,c_8632]) ).
tff(c_9175,plain,
'#skF_3'('#skF_4','#skE_5','#skF_6') = '#skE_6',
inference(define,[status(thm),theory(equality)],[c_9001]) ).
tff(c_9201,plain,
( model_ub('#skF_4','#skE_5','#skE_6')
| minsol_model_ub('#skF_4','#skE_5','#skF_6')
| ~ model_ub('#skF_4','#skE_5','#skF_6') ),
inference(superposition,[status(thm),theory(equality)],[c_9175,c_70]) ).
tff(c_9217,plain,
~ model_ub('#skF_4','#skE_5','#skF_6'),
inference(splitLeft,[status(thm)],[c_9201]) ).
tff(c_9230,plain,
! [Z_9a: $int] :
( $less('#skF_6',Z_9a)
| $less(Z_9a,'#skF_4')
| $less(Z_9a,'#skE_5') ),
inference(resolution,[status(thm)],[c_8527,c_9217]) ).
tff(c_9232,plain,
( $lesseq($sum(1,'#skF_6'),'#skF_4')
| $lesseq($sum(1,'#skF_6'),'#skE_5') ),
inference(quantifierElimination,[status(thm),theory('LIA')],[c_9230]) ).
tff(c_9234,plain,
( ~ $less('#skF_4',$sum(1,'#skF_6'))
| ~ $less('#skE_5',$sum(1,'#skF_6')) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_9232]) ).
tff(c_8605,plain,
~ $less('#skF_5','#skF_4'),
inference(splitRight,[status(thm)],[c_8585]) ).
tff(c_8634,plain,
~ $less('#skE_5','#skF_4'),
inference(demodulation,[status(thm),theory(equality)],[c_8604,c_8605]) ).
tff(c_8543,plain,
max('#skF_4','#skF_5') = '#skE_5',
inference(define,[status(thm),theory(equality)],[c_8468]) ).
tff(c_8542,plain,
~ $less('#skF_6',max('#skF_4','#skF_5')),
inference(resolution,[status(thm)],[c_8462,c_8451]) ).
tff(c_8550,plain,
~ $less('#skF_6','#skE_5'),
inference(demodulation,[status(thm),theory(equality)],[c_8543,c_8542]) ).
tff(c_9235,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_9234,c_8634,c_8550]) ).
tff(c_9239,plain,
( minsol_model_ub('#skF_4','#skE_5','#skF_6')
| model_ub('#skF_4','#skE_5','#skE_6') ),
inference(splitRight,[status(thm)],[c_9201]) ).
tff(c_9247,plain,
model_ub('#skF_4','#skE_5','#skE_6'),
inference(splitLeft,[status(thm)],[c_9239]) ).
tff(c_9248,plain,
model_ub('#skF_4','#skE_5','#skE_6'),
inference(splitLeft,[status(thm)],[c_9239]) ).
tff(c_9266,plain,
~ $less('#skE_6','#skF_1'('#skF_4','#skE_5','#skE_6')),
inference(resolution,[status(thm)],[c_9248,c_79]) ).
tff(c_9299,plain,
'#skF_1'('#skF_4','#skE_5','#skE_6') = '#skE_7',
inference(define,[status(thm),theory(equality)],[c_9266]) ).
tff(c_9315,plain,
( ub('#skF_4','#skE_5','#skE_7')
| ~ model_ub('#skF_4','#skE_5','#skE_6') ),
inference(superposition,[status(thm),theory(equality)],[c_9299,c_78]) ).
tff(c_9345,plain,
ub('#skF_4','#skE_5','#skE_7'),
inference(demodulation,[status(thm),theory(equality)],[c_9247,c_9315]) ).
tff(c_9359,plain,
~ $less('#skE_7','#skE_5'),
inference(resolution,[status(thm)],[c_9345,c_85]) ).
tff(c_9289,plain,
'#skF_1'('#skF_4','#skE_5','#skE_6') = '#skE_7',
inference(define,[status(thm),theory(equality)],[c_9266]) ).
tff(c_9288,plain,
~ $less('#skE_6','#skF_1'('#skF_4','#skE_5','#skE_6')),
inference(resolution,[status(thm)],[c_9248,c_79]) ).
tff(c_9296,plain,
~ $less('#skE_6','#skE_7'),
inference(demodulation,[status(thm),theory(equality)],[c_9289,c_9288]) ).
tff(c_9165,plain,
'#skF_3'('#skF_4','#skE_5','#skF_6') = '#skE_6',
inference(define,[status(thm),theory(equality)],[c_9001]) ).
tff(c_9164,plain,
! [Z_4097a: $int] :
( $less('#skF_3'('#skF_4','#skE_5','#skF_6'),'#skF_6')
| $less('#skF_6',Z_4097a)
| $less(Z_4097a,'#skF_4')
| $less(Z_4097a,'#skE_5') ),
inference(resolution,[status(thm)],[c_8973,c_8632]) ).
tff(c_9172,plain,
! [Z_4097a: $int] :
( $less('#skE_6','#skF_6')
| $less('#skF_6',Z_4097a)
| $less(Z_4097a,'#skF_4')
| $less(Z_4097a,'#skE_5') ),
inference(demodulation,[status(thm),theory(equality)],[c_9165,c_9164]) ).
tff(c_9206,plain,
$less('#skE_6','#skF_6'),
inference(splitLeft,[status(thm)],[c_9172]) ).
tff(c_8549,plain,
max('#skF_4','#skF_5') = '#skE_5',
inference(define,[status(thm),theory(equality)],[c_8468]) ).
tff(c_8648,plain,
max('#skF_4','#skE_5') = '#skE_5',
inference(demodulation,[status(thm),theory(equality)],[c_8604,c_8549]) ).
tff(c_8629,plain,
minsol_model_max('#skF_4','#skE_5','#skF_6'),
inference(demodulation,[status(thm),theory(equality)],[c_8604,c_4865]) ).
tff(c_8505,plain,
! [X_3907a: $int,Y_3908a: $int,Z_3909a: $int,N_3910a: $int] :
( ~ model_max(X_3907a,Y_3908a,Z_3909a)
| ~ minsol_model_max(X_3907a,Y_3908a,N_3910a)
| ~ $less(Z_3909a,N_3910a) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_28]) ).
tff(c_8767,plain,
! [X_4006a: $int,Y_4007a: $int,N_4008a: $int,N_4009a: $int] :
( ~ minsol_model_max(X_4006a,Y_4007a,N_4008a)
| ~ $less(N_4009a,N_4008a)
| $less(N_4009a,max(X_4006a,Y_4007a)) ),
inference(resolution,[status(thm)],[c_81,c_8505]) ).
tff(c_8770,plain,
! [N_4009a: $int] :
( ~ $less(N_4009a,'#skF_6')
| $less(N_4009a,max('#skF_4','#skE_5')) ),
inference(resolution,[status(thm)],[c_8629,c_8767]) ).
tff(c_8773,plain,
! [N_4009a: $int] :
( ~ $less(N_4009a,'#skF_6')
| $less(N_4009a,'#skE_5') ),
inference(demodulation,[status(thm),theory(equality)],[c_8648,c_8770]) ).
tff(c_8774,plain,
$lesseq('#skF_6','#skE_5'),
inference(quantifierElimination,[status(thm),theory('LIA')],[c_8773]) ).
tff(c_8776,plain,
~ $less('#skE_5','#skF_6'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_8774]) ).
tff(c_9362,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_9359,c_9296,c_9206,c_8776]) ).
tff(c_9368,plain,
minsol_model_ub('#skF_4','#skE_5','#skF_6'),
inference(splitRight,[status(thm)],[c_9239]) ).
tff(c_9371,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_9368,c_8632]) ).
tff(c_9374,plain,
! [Z_4097a: $int] :
( $less('#skF_6',Z_4097a)
| $less(Z_4097a,'#skF_4')
| $less(Z_4097a,'#skE_5') ),
inference(splitRight,[status(thm)],[c_9172]) ).
tff(c_9376,plain,
( $lesseq($sum(1,'#skF_6'),'#skF_4')
| $lesseq($sum(1,'#skF_6'),'#skE_5') ),
inference(quantifierElimination,[status(thm),theory('LIA')],[c_9374]) ).
tff(c_9378,plain,
( ~ $less('#skF_4',$sum(1,'#skF_6'))
| ~ $less('#skE_5',$sum(1,'#skF_6')) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_9376]) ).
tff(c_9379,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_9378,c_8634,c_8550]) ).
tff(c_9382,plain,
'#skF_4' = '#skE_5',
inference(splitRight,[status(thm)],[c_8576]) ).
tff(c_9410,plain,
~ minsol_model_ub('#skE_5','#skF_5','#skF_6'),
inference(demodulation,[status(thm),theory(equality)],[c_9382,c_8441]) ).
tff(c_9799,plain,
! [Z_4417a: $int] :
( $less('#skF_3'('#skE_5','#skF_5','#skF_6'),'#skF_6')
| $less('#skF_6',Z_4417a)
| $less(Z_4417a,'#skE_5')
| $less(Z_4417a,'#skF_5') ),
inference(resolution,[status(thm)],[c_9771,c_9410]) ).
tff(c_9947,plain,
'#skF_3'('#skE_5','#skF_5','#skF_6') = '#skE_8',
inference(define,[status(thm),theory(equality)],[c_9799]) ).
tff(c_9973,plain,
( model_ub('#skE_5','#skF_5','#skE_8')
| minsol_model_ub('#skE_5','#skF_5','#skF_6')
| ~ model_ub('#skE_5','#skF_5','#skF_6') ),
inference(superposition,[status(thm),theory(equality)],[c_9947,c_70]) ).
tff(c_10014,plain,
~ model_ub('#skE_5','#skF_5','#skF_6'),
inference(splitLeft,[status(thm)],[c_9973]) ).
tff(c_10027,plain,
! [Z_9a: $int] :
( $less('#skF_6',Z_9a)
| $less(Z_9a,'#skE_5')
| $less(Z_9a,'#skF_5') ),
inference(resolution,[status(thm)],[c_8527,c_10014]) ).
tff(c_10029,plain,
( $lesseq($sum(1,'#skF_6'),'#skE_5')
| $lesseq($sum(1,'#skF_6'),'#skF_5') ),
inference(quantifierElimination,[status(thm),theory('LIA')],[c_10027]) ).
tff(c_10031,plain,
( ~ $less('#skE_5',$sum(1,'#skF_6'))
| ~ $less('#skF_5',$sum(1,'#skF_6')) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_10029]) ).
tff(c_9383,plain,
~ $less('#skF_4','#skF_5'),
inference(splitRight,[status(thm)],[c_8576]) ).
tff(c_9418,plain,
~ $less('#skE_5','#skF_5'),
inference(demodulation,[status(thm),theory(equality)],[c_9382,c_9383]) ).
tff(c_10032,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_10031,c_9418,c_8550]) ).
tff(c_10036,plain,
( minsol_model_ub('#skE_5','#skF_5','#skF_6')
| model_ub('#skE_5','#skF_5','#skE_8') ),
inference(splitRight,[status(thm)],[c_9973]) ).
tff(c_10052,plain,
model_ub('#skE_5','#skF_5','#skE_8'),
inference(splitLeft,[status(thm)],[c_10036]) ).
tff(c_10053,plain,
model_ub('#skE_5','#skF_5','#skE_8'),
inference(splitLeft,[status(thm)],[c_10036]) ).
tff(c_10071,plain,
~ $less('#skE_8','#skF_1'('#skE_5','#skF_5','#skE_8')),
inference(resolution,[status(thm)],[c_10053,c_79]) ).
tff(c_10104,plain,
'#skF_1'('#skE_5','#skF_5','#skE_8') = '#skE_9',
inference(define,[status(thm),theory(equality)],[c_10071]) ).
tff(c_10120,plain,
( ub('#skE_5','#skF_5','#skE_9')
| ~ model_ub('#skE_5','#skF_5','#skE_8') ),
inference(superposition,[status(thm),theory(equality)],[c_10104,c_78]) ).
tff(c_10150,plain,
ub('#skE_5','#skF_5','#skE_9'),
inference(demodulation,[status(thm),theory(equality)],[c_10052,c_10120]) ).
tff(c_10166,plain,
~ $less('#skE_9','#skE_5'),
inference(resolution,[status(thm)],[c_10150,c_84]) ).
tff(c_10094,plain,
'#skF_1'('#skE_5','#skF_5','#skE_8') = '#skE_9',
inference(define,[status(thm),theory(equality)],[c_10071]) ).
tff(c_10093,plain,
~ $less('#skE_8','#skF_1'('#skE_5','#skF_5','#skE_8')),
inference(resolution,[status(thm)],[c_10053,c_79]) ).
tff(c_10101,plain,
~ $less('#skE_8','#skE_9'),
inference(demodulation,[status(thm),theory(equality)],[c_10094,c_10093]) ).
tff(c_9937,plain,
'#skF_3'('#skE_5','#skF_5','#skF_6') = '#skE_8',
inference(define,[status(thm),theory(equality)],[c_9799]) ).
tff(c_9936,plain,
! [Z_4417a: $int] :
( $less('#skF_3'('#skE_5','#skF_5','#skF_6'),'#skF_6')
| $less('#skF_6',Z_4417a)
| $less(Z_4417a,'#skE_5')
| $less(Z_4417a,'#skF_5') ),
inference(resolution,[status(thm)],[c_9771,c_9410]) ).
tff(c_9944,plain,
! [Z_4417a: $int] :
( $less('#skE_8','#skF_6')
| $less('#skF_6',Z_4417a)
| $less(Z_4417a,'#skE_5')
| $less(Z_4417a,'#skF_5') ),
inference(demodulation,[status(thm),theory(equality)],[c_9937,c_9936]) ).
tff(c_9978,plain,
$less('#skE_8','#skF_6'),
inference(splitLeft,[status(thm)],[c_9944]) ).
tff(c_9436,plain,
max('#skE_5','#skF_5') = '#skE_5',
inference(demodulation,[status(thm),theory(equality)],[c_9382,c_8549]) ).
tff(c_9407,plain,
minsol_model_max('#skE_5','#skF_5','#skF_6'),
inference(demodulation,[status(thm),theory(equality)],[c_9382,c_4865]) ).
tff(c_9520,plain,
! [X_4315a: $int,Y_4316a: $int,N_4317a: $int,N_4318a: $int] :
( ~ minsol_model_max(X_4315a,Y_4316a,N_4317a)
| ~ $less(N_4318a,N_4317a)
| $less(N_4318a,max(X_4315a,Y_4316a)) ),
inference(resolution,[status(thm)],[c_81,c_8505]) ).
tff(c_9523,plain,
! [N_4318a: $int] :
( ~ $less(N_4318a,'#skF_6')
| $less(N_4318a,max('#skE_5','#skF_5')) ),
inference(resolution,[status(thm)],[c_9407,c_9520]) ).
tff(c_9526,plain,
! [N_4318a: $int] :
( ~ $less(N_4318a,'#skF_6')
| $less(N_4318a,'#skE_5') ),
inference(demodulation,[status(thm),theory(equality)],[c_9436,c_9523]) ).
tff(c_9527,plain,
$lesseq('#skF_6','#skE_5'),
inference(quantifierElimination,[status(thm),theory('LIA')],[c_9526]) ).
tff(c_9529,plain,
~ $less('#skE_5','#skF_6'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_9527]) ).
tff(c_10167,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_10166,c_10101,c_9978,c_9529]) ).
tff(c_10173,plain,
minsol_model_ub('#skE_5','#skF_5','#skF_6'),
inference(splitRight,[status(thm)],[c_10036]) ).
tff(c_10176,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_10173,c_9410]) ).
tff(c_10179,plain,
! [Z_4417a: $int] :
( $less('#skF_6',Z_4417a)
| $less(Z_4417a,'#skE_5')
| $less(Z_4417a,'#skF_5') ),
inference(splitRight,[status(thm)],[c_9944]) ).
tff(c_10185,plain,
( $lesseq($sum(1,'#skF_6'),'#skE_5')
| $lesseq($sum(1,'#skF_6'),'#skF_5') ),
inference(quantifierElimination,[status(thm),theory('LIA')],[c_10179]) ).
tff(c_10187,plain,
( ~ $less('#skE_5',$sum(1,'#skF_6'))
| ~ $less('#skF_5',$sum(1,'#skF_6')) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_10185]) ).
tff(c_10188,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_10187,c_9418,c_8550]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM859_1 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.14 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.14/0.35 % Computer : n006.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu Aug 3 14:38:28 EDT 2023
% 0.14/0.35 % CPUTime :
% 11.28/3.77 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 11.74/3.88
% 11.74/3.88 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 12.12/3.96
% 12.12/3.96 Inference rules
% 12.12/3.96 ----------------------
% 12.12/3.96 #Ref : 0
% 12.12/3.96 #Sup : 1075
% 12.12/3.96 #Fact : 20
% 12.12/3.96 #Define : 35
% 12.12/3.96 #Split : 95
% 12.12/3.96 #Chain : 0
% 12.12/3.96 #Close : 44
% 12.12/3.96
% 12.12/3.96 Ordering : LPO
% 12.12/3.96
% 12.12/3.96 Simplification rules
% 12.12/3.96 ----------------------
% 12.12/3.96 #Subsume : 219
% 12.12/3.96 #Demod : 619
% 12.12/3.96 #Tautology : 391
% 12.12/3.96 #SimpNegUnit : 37
% 12.12/3.96 #BackRed : 207
% 12.12/3.96
% 12.12/3.96 #Partial instantiations: 0
% 12.12/3.97 #Strategies tried : 1
% 12.12/3.97
% 12.12/3.97 Timing (in seconds)
% 12.12/3.97 ----------------------
% 12.12/3.97 Preprocessing : 0.60
% 12.12/3.97 Parsing : 0.31
% 12.12/3.97 CNF conversion : 0.04
% 12.12/3.97 Main loop : 2.12
% 12.12/3.97 Inferencing : 0.55
% 12.12/3.97 Reduction : 0.44
% 12.12/3.97 Demodulation : 0.31
% 12.12/3.97 BG Simplification : 0.14
% 12.12/3.97 Subsumption : 0.34
% 12.12/3.97 Abstraction : 0.08
% 12.12/3.97 MUC search : 0.22
% 12.12/3.97 Cooper : 0.42
% 12.12/3.97 Total : 2.93
% 12.12/3.97 Index Insertion : 0.00
% 12.12/3.97 Index Deletion : 0.00
% 12.12/3.97 Index Matching : 0.00
% 12.12/3.97 BG Taut test : 0.00
%------------------------------------------------------------------------------